Answer:
Step-by-step explanation:
How to solve a quadratic equation using the Quadratic Formula.
Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, c.
Write the Quadratic Formula. Then substitute in the values of a, b, c.
Simplify.
Check the solutions.
The four methods for solving a quadratic issue are the quadratic formula, using square roots, factoring, and completing the square.
What is meant by quadratic equations?A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a ≠ 0.
Problems involving squares and quadrangles and quadratic equations are closely related. In actuality, the word quadratic comes from the Latin word quadratus, which means square.
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem. An overview of all the many approaches to solving a quadratic equation is what I'd want to discuss right now.
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Find the mean of tese numbers 2,9,10,6,8
Answer:324234
Step-by-step explanation:
Answer:
The mean of the data set is 7.
2 + 9 + 10 + 6 + 8
= 35
35 ÷ 5
= 7
Step-by-step explanation:
You're welcome
suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. what is the probability that the number will be more than 7 or odd? (enter your probability as a fraction.)
The probability that the number will be more than 7 or odd is 7/10.
The number more than 7 or odd is 1, 3, 5, 7, 8, 9, 10
So probability of 7 number is,
P(A) = number of favorable outcomes of an event / total number of events occurring in a sample
P(A) = 7/10
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
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the marked price of an article is 2080. After allowing d% discount and levying (d-2)% VAT, the cost of the article becomes Rs. 1997.84. Find the discount amount and VAT amount
The vat rate is 13%
What is vat rate?
Vat rate is a consumption tax assessed on the value added in each production stage of a good or service.
Given:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)Add VAT:
2080*(1 - 0.01d) + (d - 2)%2080*(1 - 0.01d) * (1 + (d -2)/100)2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84(1 - 0.01d)(0.98 + 0.01d) = 1997.84/20800.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605- 0.0001d² + 0.0002d + 0.98- 0.9605 = 00.0001d²- 0.0002d - 0.0195 = 0d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Then
VAT rate = 15 - 2 = 13%
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For circular motion on a circle of radius r, linear speed equals angular speed divided by r. (T/F)
For circular motion on a circle of radius r, linear speed equals angular speed divided by r. This statement is false.
What is angular speed?
The definition of angular speed is the rate at which angular displacement changes, and it is written as follows -
ω = θ/t
where θ is the angular displacement, t is the time and ω is the angular speed.
The statement says that for circular motion on a circle of radius r, linear speed equals angular speed divided by r.
Consider that an object moves around a circle of radius r at a constant speed v.
If s is the distance travelled in time t around the circle then linear speed v is defined as v = s/t.
Also if θ is the angle swept out by this object in time t then the angular speed is defined as ω = θ/t.
Thus, there is some relationship between linear speed and angular speed -
Linear speed = v = s/t
= rθ/t = r(θ/t) = rω
where is ω measured in radians per unit time and for a circle of radius r, a central angle of radians subtends an arc whose length s is s = rθ.
Hence, notice that linear speed is equal angular speed multiplied, not divided, by r.
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Unit 6 Final Test
Would appreciate some help as soon as its available (Has 3 parts) (ASAP)
1. The population of a town was 88 in 2016. The population quadruples every year. (a) Use the exponential growth model to write an equation that estimates the population t years after 2016. (b) Estimate the population of the town in 2023. Show your work. Answer:
2. Convert the following into a single log statement from the many log statements to 1. 7 Log x + 2log y – log 23 – 3 log z NOTE: You must show this in at least two steps. 1st line should be to convert the 2 the 3 and the 7 only. 2nd line can be the final answer. Answer:
3. A savings account is started with an initial deposit of $500. The account earns 7% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach 1 million. Show your work. Note: 1 million is a 1 with 6 zeros. Note2: you must use log functions to solve. Answer:
1. (a) An equation that estimates the population t years after 2016 is
P = [tex]88({4t)[/tex].
b. The population of the town in 2023 is 2564.
2. log x + 2log y - log 23 - 3 log z is equal to log (x + y²)/log (23 + z³).
3. (a) An equation to represent the amount of money in the account as a function of time in years is A = 500(1 + 7/100)ⁿ.
(b) The amount of time it takes for the account balance to reach 1 million
is 112.5 years approximately.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]
1. Given, The population of a town was 88 in 2016. The population quadruples every year.
Therefore, The exponential model of this situation is P = [tex]88({4t)[/tex].
Now, From 2016 to 2023 it is 7 years.
Therefore, P = [tex]88({4\times7})[/tex].
P = 2564.
2. Given, log x + 2log y - log 23 - 3 log z.
= log x + log y² - log 23 - log z³.
= log x + log y² - (log 23 + log z³).
= log (x + y²) - log (23 + z³).
= log (x + y²)/log (23 + z³).
3. Given, A savings account is started with an initial deposit of $500. The account earns 7% interest compounded annually.
We know the formula for compound interest is, A = P(1 + r/100)ⁿ.
a. A = 500(1 + 7/100)ⁿ.
b. 1000000 = 500(1 + 7/100)ⁿ.
2000 = (1 + 7/100)ⁿ.
2000 = 1.07ⁿ.
log_1.07 2000 = n.
n = 112.5 years approximately.
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. using social media in a job search. according to inc, 79% of job seekers used social media in their job search in 2018. many believe this number is inflated by the proportion of 22- to 30-year-old job seekers who use social media in their job search. a survey of 22- to 30-year-old job seekers showed that 310 of the 370 respondents use social media in their job search. in addition, 275 of the 370 respondents indicated they have electronically submitted a resume to an employer. a. conduct a hypothesis test to determine if the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that use social media in their job search. use a 5 .05. b. conduct a hypothesis test to determine if the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer. using a 5 .05, what is your conclusion?
In case of (a) Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
a. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who use social media in their job search, we need to set up the null and alternative hypotheses:
H0: p = 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is equal to the proportion of the population that use social media in their job search)
Ha: p > 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is greater than the proportion of the population that use social media in their job search)
Where p is the true proportion of 22- to 30-year-old job seekers who use social media.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as: z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 310/370 = 0.838 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.838 - 0.79) / sqrt(0.79 * (1 - 0.79) / 370) = 3.41
Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search.
b. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume, we need to set up the null and alternative hypotheses:
H0: p = 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is equal to 70%)
Ha: p > 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is greater than 70%)
Where p is the true proportion of 22- to 30-year-old job seekers who have electronically submitted a resume.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as:
z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 275/370 = 0.743 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.743 - 0.70) / sqrt(0.70 * (1 - 0.70) / 370) = 2.01
Since 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
Therefore, In case of (a) Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
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In case of (a) Since 3.41 > 1.64485, job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
a. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who use social media in their job search, we need to set up the null and alternative hypotheses:
H0: p = 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is equal to the proportion of the population that use social media in their job search)
Ha: p > 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is greater than the proportion of the population that use social media in their job search)
Where p is the true proportion of 22- to 30-year-old job seekers who use social media.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as: z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 310/370 = 0.838 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.838 - 0.79) / sqrt(0.79 * (1 - 0.79) / 370) = 3.41
Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search.
b. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume, we need to set up the null and alternative hypotheses:
H0: p = 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is equal to 70%)
Ha: p > 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is greater than 70%)
Where p is the true proportion of 22- to 30-year-old job seekers who have electronically submitted a resume.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as:
z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 275/370 = 0.743 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.743 - 0.70) / sqrt(0.70 * (1 - 0.70) / 370) = 2.01
Since 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
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illustrate the net force f1 f2 as the geometric addition of the two force vectors. (b) compute the net force, the vector sum of the force vectors.
The magnitude of the net force is 149.33 N.
a) To illustrate the net force F1 + F2 as a geometric addition of the two force vectors, we can use the tail-to-tip method to add the vectors head-to-tail and then connect the tail of the first vector to the tip of the second vector to form the net force vector.
b) To compute the net force as the vector sum of the two force vectors, we can use the components of the two vectors to find the components of the net force. Using the trigonometric relationship between the angle and the components of a force vector, the x and y components of the force vectors can be calculated as follows:
F1x = F1 * cos(30) = 86.6025 N
F1y = F1 * sin(30) = 50 N
F2x = F2 * cos(45) = 35.3553 N
F2y = F2 * sin(45) = 35.3553 N
The x and y components of the net force are found by adding the corresponding components of the individual force vectors:
Fnetx = F1x + F2x = 86.6025 N + 35.3553 N = 122 N
Fnety = F1y + F2y = 50 N + 35.3553 N = 85.3553 N
c) To compute the magnitude of the net force, we use the Pythagorean theorem to find the magnitude from the components:
Fnet = √(Fnetx² + Fnety²) = √(122² + 85.3553²) = 149.33 N
So, the magnitude of the net force is 149.33 N.
Complete Question
Two forces are applied to an object, with magnitudes and directions shown in the image below:
(a) Illustrate the net form F1 + F2 as the geometric addition of the two force vectors.
(b) Compute the net force, the vector sum of the force vectors.
(c) Compute the magnitude of the net force. Include N (newton) for units of force.
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flight 202's arrival time is normally distributed with a mean arrival time of 4:30 p.m. and a standard deviation of 15 minutes. find the probability that a randomly chosen arrival time is within the given time period
The required probability is 0.953.
We know that the mean μ is:
μ = 4:30 p.m.
The standard deviation is:
σ = 0:15 minutes
The Z-score is: Z = (x-μ)/σ
We seek to find probability P(4:00 p.m. < x < 5:00 p.m.)
The Z-score is:
Z = (x-μ)/σ = 4:00 - 4:30/0:15 = -2
The score of Z =-2 means that 4:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35% and
Z = (x-μ)/σ = 5:00 - 4:30/0:15 = 2
The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%.
∴ P(4:00 p.m. < x < 5:00 p.m.) = 100% - 2.35% - 2.35%
= 95.3% = 0.953
Thus, the required probability is 0.953.
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The required probability is 0.953.
We know that the mean μ is:
μ = 4:30 p.m.
The standard deviation is:
σ = 0:15 minutes
The Z-score is: Z = (x-μ)/σ
We seek to find probability P(4:00 p.m. < x < 5:00 p.m.)
The Z-score is:
Z = (x-μ)/σ = 4:00 - 4:30/0:15 = -2
The score of Z =-2 means that 4:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35% and
Z = (x-μ)/σ = 5:00 - 4:30/0:15 = 2
The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%.
∴ P(4:00 p.m. < x < 5:00 p.m.) = 100% - 2.35% - 2.35%
= 95.3% = 0.953
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A restaurant charges `\$10` for each burrito and a `\$5` delivery fee. What is the total cost to have `4` burritos deliver
Answer:60
Step-by-step explanation:
10+5=15
15x4=60
What i the area of ΔABC given a = 12 in, b = 24 in, and m∠C = 26°? Round the anwer to three decimal place. 63. 125 in2
93. 156 in2
109. 808 in2
129. 426 in2
Answer: 63.125
Step-by-step explanation: I got it correct ;)
Rylan earns $200 for working 16 hours this week.
How much does he earn per hour?
Answer:
Rylan earns $12.50 per hour
Step-by-step explanation:
1. First start by writing the given its always easier when you're able to see the problem.
$200 = 16 hrs
$ x = 1 hr
2. Next divide
[tex]\frac{200}{16}[/tex] = 12.50
find the solution of the initial value problem y'' 2y' 5y = 12e^-t cos(2t), y(0) = 10, y'(0) = 0
The solution to the initial value problem is:y(t) = (10 - (12/7))e^(t) cos(2t) + (12/7)e^(-t) cos(2t).
The characteristic equation of this linear second order ordinary differential equation is:
m^2 - 2m + 5 = 0
The roots of this characteristic equation are m = 1 ± 2i, which means the general solution to the homogeneous equation is:
y(t) = c1e^(t) cos(2t) + c2e^(t) sin(2t)
To find the particular solution, we can use the method of undetermined coefficients and guess that yp(t) = Ae^(-t) cos(2t) + Be^(-t) sin(2t).
Substituting this into the differential equation, we get:
2Ae^(-t) cos(2t) - 2Ae^(-t) sin(2t) + 5Ae^(-t) cos(2t) - 5Be^(-t) sin(2t) = 12e^(-t) cos(2t)
Comparing coefficients, we have:
2A - 2A + 5A = 12
7A = 12
A = 12/7
-5B = 0
B = 0
So the particular solution is:
yp(t) = (12/7)e^(-t) cos(2t)
The general solution to the non-homogeneous equation is then:
y(t) = c1e^(t) cos(2t) + c2e^(t) sin(2t) + (12/7)e^(-t) cos(2t)
Using the initial conditions, we can find the values of c1 and c2:
y(0) = 10 = c1 + (12/7)
c1 = 10 - (12/7)
y'(0) = 0 = c2e^(0) sin(0)
c2 = 0
Therefore, the solution to the initial value problem is: y(t) = (10 - (12/7))e^(t) cos(2t) + (12/7)e^(-t) cos(2t)
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The temperature was -3, 0, 2, -1, and -3 on five consecutive days. What was the average temperature for those five days?
Answer:
-1 degrees
Step-by-step explanation:
The average = sum of all values/# of values = sum of all temperatures/# of days=
(-3+0+2-1-3)/5= -1
Someone answer this
Answer:
I believe the answer is b??
Remove the outlier from Gretchen’s data set, and recalculate the mean, median, standard deviation, and interquartile range. Use the graphing tool to visualize the data.
Question
Which statements are true about Gretchen’s adjusted data set?
The data set is approximately symmetric.
The center moved closer to the center of Manuel’s data set.
The data set is skewed left.
The spread values are closer to the spread values of Manuel’s data set.
The center moved farther from the center of Manuel’s data set.
The spread values are farther from the spread values of Manuel’s data set.
The true statements bout Gretchen's adjusted data set are (1), (4), and (5).
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
It is given that:
Which statements are true about Gretchen's adjusted data set:
The options are:
The data set is approximately symmetric.
The center moved farther from the center of Manuel's data set.
The center moved closer to the center of Manuel's data set.
The spread values are closer to the spread values of Manuel's data set.
The data set is skewed left.
The spread values are farther from the spread values of Manuel's data set.
As we know,
The spread values are more similar to Manuel's data set's spread values, and the data set is roughly symmetric and tilted to the left.
The true statements are:
The data set is approximately symmetric.
The spread values are closer to the spread values of Manuel's data set.
The data set is skewed left.
Thus, the true statements bout Gretchen's adjusted data set are (1), (4), and (5).
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WILL GIVE BRAINLIEST AND 50 POINTS PLS DO MY HW BY FEBRUARY 2ND
Answer: dunno, maybe try using your brain?
Step-by-step explanation:
POINTS AND BRAINLIEST
Answer:
On Monday, the baker makes 36 blueberry muffins, so the total number of muffins she makes that day is 36/0.4 = 90.
On Tuesday, the baker makes a total of 60 muffins, so the number of blueberry muffins she makes that day is 60*0.4 = 24.
Let vector a = a1i + a2j + a3k vector b = b1i + b2j + b3k and vector c = c1i + c2j + c3k be three non-zero vectors such that vector c is a unit vector perpendicular to both the vectors a and vector b. If the angle between vector a and vector b is π/6 then |a1 a2 a3 b1 b2 b3 c1 c2 c3|2 is equal toa 0b 1
The correct option is C) [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
Vectors, in Math's, are objects which have both, magnitude and direction. Magnitude defines the size of the vector.
It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
According to the given conditions,
[tex]c1^{2}+c2^{2} +c3^{2} = 1, a.c =0, b.c=0[/tex]
and [tex]cos\frac{π}{6} = \frac{\sqrt{3} }{2} =\frac{a1b1+a2b2+a3c3}{\sqrt{a1^{2} +a2^{2} +a3^{2} } \sqrt{x=b1^{2} +b2^{2} +b3^{2} } }[/tex]
thus, a1c1+a2c2+a3c3=0 , b1c1+b2c2=b3c3=0
and [tex]\frac{\sqrt{3} (a1^{2}+a2^{2} +a3^{2} )^{1/2} (b1^{2}+b2^{2} +b3^{2} )^{1/2} }{2}[/tex] = a1b1+a2b2+a3b3
Now,
[tex]\left[\begin{array}{ccc}a1&b1&c1\\a2&b2&c2\\a3&b3&c3\end{array}\right]^{2}[/tex]
= [tex]\left[\begin{array}{ccc}a1&a2&a3\\b1&b2&b3\\c1&c2&c3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a1&b1&c1\\a2&b2&c2\\a3&b3&c3\end{array}\right][/tex]
= [tex](a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} ) - (a1b1+a2b2+a3b3)^{2}[/tex]
= [tex](a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} ) -\frac{3}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
= [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
Therefore, The correct option is C) [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
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parallel, perpendicular,
or neither.
2. AB formed by (3, 7) and (-6, 1)
CD formed by (-6, -5) and (0, -1)
Answer: ez, the answer is Parallel
Step-by-step explanation:
because ab and cd are parallel lines
AB is formed by (3,7) and (-6, 1)
CD is formed by (-6,-5) and (0,-1)
testing the two lines are parallel or perpendicular or neither, is done by determining their gradients
Triangle AB = Gradient of AB = Triangle Y over triangle X = 1-7 over -6-3 = -6 over -9 = 2/3
Triangle CD = Gradient of Triangle CD = Triangle Y over Triangle X = -1 - -5 over 0 - -6 = 1 + 5 over 0 + 6 = 4 over 6 = 2/3
So the two lines AB and CD have the same gradient and thus the two lines are PARALLEL to each other.
function statements are contained within the function ____.
A function statement is contained within the function block. A function block is a set of instructions within a program that defines what the function should do when it is called.
It is generally surrounded by curly braces and contains one or more lines of code.
A function statement usually contains a formula and calculation. The formula is an expression that specifies the calculation that should be performed when the function is called. The calculation is the result of the formula, which is the value that will be returned when the function is called.
For example, if we have a function that calculates the area of a circle, the formula might be A = πr^2 and the calculation would be A = 3.14 * r^2. The formula describes how the area of a circle is calculated and the calculation is the result of that formula. When the function is called, the calculation will be performed and the result will be returned.
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Two sides of the triangle abc has side ab = 22 cm and side ac = 8 cm. Compute the probable perimeter of the triangle.
The perimeter of the triangle is (30+x) cm
What is perimeter of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Perimeter is the distance around the edge of a shape.
To find the perimeter of a triangle , we add all the sides together.
Two sides are 22 cm and 8cm
Represent the other sides of the triangle by x
therefore the perimeter will be calculated as:
22+8+x
P = (30+x)cm
therefore the perimeter of the triangle is( 30+x)cm for any value of x
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when you are looking at a figure, when can you say on average? why?
When talking about a figure, you can say "on average" when you are discussing a measure of central tendencies, such as the mean, median, or mode.
This is because these measures represent the "average" point in the data set. For example, if you are looking at a figure that consists of the average monthly temperatures for a given region, the mean would be the average temperature (on average) for that region.
Similarly, if you are looking at a figure that consists of the average daily prices of a certain stock, the mean would be the average daily price (on average) for that stock. In either case, the mean is the "average" point in the data set.
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who did more one girls did 42 push ups in 6 mins a other 24 in 3 mins
Answer:
The girl who completed 42 push-ups in 6 minutes did more push-ups than the girl who completed 24 push-ups in 3 minutes.
Step-by-step explanation:
Write the equation of the line in slope-intercept form (y=mx+b):
a = ( 0 , - 4 )
b = ( - 2 , - 2 )
[tex]m = - \frac{y(a) - y(b)}{x(a) - x(b)} \\ [/tex]
[tex]m \: = \frac{ - 4 - ( - 2)}{0 - ( - 2)} \\ [/tex]
[tex]m = \frac{ - 4 + 2}{2} \\ [/tex]
[tex]m = \frac{ - 2}{2} \\ [/tex]
[tex]m = - 1[/tex]
1. What is the minimum number of divisions made by Euclid's algorithm among all inputs 1 Sab S 10? Give your answer as a number. 2. What is the maximum number of divisions made by Euclia's algorithm among all inputs 1 € ab 10? (to answer this question, check the algorithm's performance on all pairs 1 Sa, bs 10). Give your answer as a number.
The minimum amount of number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 0, as the greatest common divisor of any two numbers between 1 and 10 must be 1. The maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19, as the greatest common divisor of 8 and 10 requires 19 divisions.
Euclid's algorithm is an efficient method for finding the greatest common divisor (GCD) of two integers. It works by repeatedly dividing larger numbers by smaller numbers until the remainder is 0. The GCD of two integers is then equal to the smaller number. The minimum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 0, as the GCD of any two numbers between 1 and 10 must be 1. This is because any two numbers between 1 and 10 have only 1 as their common divisor. On the other hand, the maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19, as the GCD of 8 and 10 requires 19 divisions. This is due to the fact that 8 and 10 have no common divisors except for 1, so the algorithm must divide 8 by 10 repeatedly until the remainder is 0. Thus, the maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19.
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A watch which was bought for R250, was sold for R375. What profit made on the sale? atima has 56 roses, 48 irises and 16 freesias. She wants to cre ouquets using all the flowers. Calculate the highest number ouquets she can make without having any flowers left over Fatima paid R240 for her flowers and sold the bouquets for
Solving the provided question, we can say that the highest number bouquets she can make without having any flowers left is calculated by Highest Common Factor so, HCF of 56, 48 and 16 is 8
What is Highest Common Factor?In mathematics, the highest positive integer that divides the corresponding integers is known as the greatest common divisor of two or more non-zero integers. The greatest common factor (HCF) of two or more numbers is the sum of those two or more numbers. As a result, it is frequently referred to as the largest common divisor (GCF). Take the prime factors of the two (or more) integers and determine the shared prime factors to determine the greatest common divisor. Following that, the sum of common prime factors is the greatest common divisor. A specified number divided by the biggest integer results in the greatest common divisor.
the highest number bouquets she can make without having any flowers left is calculated by Highest Common Factor so, HCF of 56, 48 and 16 is 8
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suppose that f(x) has a domain of [6,17] and a range of [6,13] . what are the domain and range of:
A) f(x) +5
Domain: x ∈ (5, 15)
Range: f(x) ∈ (12, 22)
B) f(x + 5)
Domain: x ∈ (0, 10)
Range: f(x) ∈ (7, 17)
C) f(5x)
Domain: x ∈ (1, 3)
Range: f(x) ∈ (7, 17)
D) 5f(x)
Domain: x ∈ (5, 15)
Range: f(x) ∈ (35, 85)
Now, According to the question:
Domain:
Consider a function y = t(x), where y is the dependent variable and x is the independent variable. Domain value represents the value(s) of the independent variable at which the given function is defined. On the other hand, the corresponding values of y represents the range of that function.
f(x) has a domain of (5, 15) and a range of (7, 17)
A) f(x) + 5
The domain will be the same as the domain of f(x) but the range will be (7 + 5 , 17 + 5) i.e., (12, 22)
Domain: x ∈ (5, 15)
Range: f(x) ∈ (12, 22)
B) f(x + 5)
The domain will be (5 -5, 15-5) i.e., (0, 10) but the range will be the same.
Domain: x ∈ (0, 10)
Range: f(x) ∈ (7, 17)
C) f(5x)
The domain will be [tex](\frac{5}{5},\frac{15}{5} )[/tex] i.e., (1, 3) but the range will be the same.
Domain: x ∈ (1, 3)
Range: f(x) ∈ (7, 17)
D) The domain will be the same as the domain of f(x) but the same will be (5× 7, 17× 5) i.e., (35, 85)
Domain: x ∈ (5, 15)
Range: f(x) ∈ (35, 85)
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The given question is incomplete,
So, This question like that the given question:
Suppose that f(x) has a domain of (5, 15) and a range of (7,17).
What are the domains and the ranges of the following?
A) f(x) +5
B) f(x + 5)
C) f(5x)
D) 5f(x)
You own Company X. When you started the company, you Initially Invested $12,000. You also borrowed $12,000 through a five-year (long-term) loan, of which you have paid back $2,018. You have retained $1,291 In earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term Investment. The company owns land and a building worth $8,878 and equipment worth $4,230. As of today, the company has $8,250 in cash, $1,225 In Inventory, and is due to receive accounts worth $675. However, the company owes its suppliers $485 and has a $500 loan to pay off in the next six months
The preparation of Company X's balance sheet as the current date is as follows:
Company X
Balance SheetAs of current date
Current Assets:Cash $8,250
Inventory 1,225
Accounts Receivable 675 $10,150
Long-term Assets:Long-term investment $1,000
Land and building 8,878
Equipment 4,230 $14,108
Total Assets $24,258
Current Liabilities:Accounts Payable $485
Short-term loan 500 $985
Long-term Liabilities:Long-term loan $9,982
Total liabilities $10,967
Equity:Initial capital $12,000
Retained earnings 1,291 $13,291
Total liabilities and equity $24,258
What is the balance sheet?The balance sheet is a financial statement that shows the assets, liabilities, and equity balances of an entity at a point in time.
Assets describe the things owned by the entity while liabilities refer to its debts. The difference between assets and liabilities is the equity (or the portion of assets belonging to the owners).
Analysis:Initial investment = $12,000
Retained Earnings = $1,291
Long-term loan = $9,982 ($12,000 - $2,018)
Land and building = $8,878
Equipment = $4,230
Cash $8,250
Inventory = $1,225
Accounts Receivable = $675
Accounts Payable = $485
Short-term loan = $500
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Question Completion:Prepare Company X's balance sheet.
For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R
a) basis is [ p , q , r . r ]
b) the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R is 3 for subspace
since the two given equation are in three variable and constants
2q -r= p -----(1)
r= q -s -----(2)
p= q +2r -----(3)
From (2):
r +s= q (+s on both sides)
s= q -r -----(4) (-r on both sides)
Substitute. (3) into (1):
2q -r= q +2r
2q -q= 2r +r
q= 3r -----(5)
Substitute (5) into (4):
s= 3r -r
s= 2r (proved)
hence subspace is [ p , q , r . r ]
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How do you find a formula for the general term an of the sequence?
A sequence is characterised as one that adheres to a predetermined pattern. The following term is created by increasing or decreasing the previous word by a certain amount.
On occasion, an expression is followed by every term in the series. The general formula for an AP is T n = a + (n - 1) d.
What does the sequence's general word mean?Understanding the underlying pattern or rule that creates the sequence is necessary for formulating the general term an of the sequence. Finding a formula for the overall term of a series can be done in a number of ways, including:
1) Finding a pattern: In some cases, a pattern can be found by examining the terms of the sequence and looking for a common ratio or difference. For instance, the formula for the general term can be written as a = a1 + (n - 1)d, where a1 is the first term and d is the common difference, assuming the terms of a sequence are rising by a constant amount.
2) Recurrence relations are used to characterise some sequences. These relations define the nth term in terms of the phrases that came before it. If the recurrence relation, for instance, is a = an-1 + an-2, then the general term's formula can be discovered by resolving the recurrence relation.
3) Making use of generating functions: Sequences can be represented mathematically using generating functions. A formula for the general term of a sequence can be discovered by fiddling with the generating function.
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