Complete question is;
A square pyramid has side lengths each measuring 8 centimeters. The height of the pyramid is 3 centimeters. What is the lateral area of the pyramid?
Answer:
Lateral area = 80 cm²
Step-by-step explanation:
We are given;
Side length; a = 8 cm
Height of pyramid; h = 3 cm
Now, formula for Lateral area of pyramid = ½ × p × L
Where p is perimeter of base and L is slant length.
Since we know the side length and height of pyramid, we can find the slant height using Pythagoreas theorem.
L² = (½×side length)² + h²
L² = (½×8)² + 3²
L² = 16 + 9
L = √25
L = 5 cm
Now perimeter of square base = 4a = 4 x 8 = 32cm
So,
Lateral area = ½ × p × L = ½ × 32 × 5
Lateral area = 80 cm²
Answer:
80 square centimeters
Step-by-step explanation:
we need to find the hypotenuse or the slant height of the triangle so 3^2+4^2 = the square root of 25 = 5
We got 4 because half of 8 is 4 and we are basically cutting the triangle in half because the height (3) is perpendicular to the side length.
8(5)/2 = 20
20(4) = 80
Which is greater 16/12 or 9/3
Answer:
[tex] \frac{16}{12} \: \: < \frac{9}{3} [/tex]
9/3 is greater
Step-by-step explanation:
[tex] \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{9}{3} \\ \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{9 \times 4}{3 \times 4} \\ \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{36}{12} \\ \frac{16}{12} \: < \: \frac{36}{12} \\ \\ so \\ \frac{16}{12} < \frac{9}{3} [/tex]
Answer:
the answer is attached to the picture
what is 4 3/8 - 5 1/2 ?
Answer:-1.125
Step-by-step explanation:
What two things should be done before one performs a regression analysis?
Answer:
Plot the given data or information graphicallyObtain the line of best fit.Step-by-step explanation:
what is regression analysis ?Regression analysis is a statistical method that is used to examine the relationship between two or more variables.
There are many types of regression analysis which can be used to examine the influence of one or more independent variables on a dependent variable.
to carry out regression analysis the analyst must carry out the following
Plot the given data or information graphicallyObtain the line of best fit.Some of the various types of regression models are
Linear Regression. Polynomial Regression. Logistic Regression. Quantile Regression. Ridge Regression. Lasso Regression etc.The things that should be done before performing a regression analysis include:
Plot the given data or information graphicallyObtain the line of best fit.It should be noted that a regression analysis simply refers to a statistical method which examines the relationship between two or more variables.
To do a regression analysis, plot the given data or information graphically and then obtain the line of best fit.
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Your friend deposits $6000 in an investment account that earns 7.3% annual interest. Find the balance after 18 years when the interest is compounded quarterly.
Answer: $22,063.2
Step-by-step explanation:
quarterly means that 4 times per year this interest, the balance can be find by the equation:
A = P*(1 + r/4)^(4*t)
Where P is the initial value, r is the rate of increase (7.3% in this case, but remember that you must use the decimal form; 0.073) and t is the number of years:
so we have:
B = $6,000*( (1 + 0.073/4)^(4*18) = $22,063.2
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
In the attached file
Answer:
The explanation below should guide you to solve it's
Step-by-step explanation:
x2 + y2 - 14x -18y +105 =0
Now the standard form a the equation of a circle is
(X-Xo)2 + (y-yo)2 = r2
The above expressions becomes
x2- 14x + (-14/2)2 - (- 14/2)2 + y2 -18y + (-18/2)2 - (-18/2)2 + 105 =0
The above manipulation does not alter the equation and it's a way of forming squares of a quadratic equation.
(x - 7)2 + (y - 9)2 -49 - 81 + 105 = 0
(x - 7)2 + (y - 9)2 -130 + 105 = 0
(x - 7)2 + (y - 9)2 -25 = 0
(x - 7)2 + (y - 9)2= 25
From the analysis above you can determine the centres of the circle denoted by Xo and Yo as well as the radius which is the square root of the expression at the right
Write the slope-intercept form of the equation for the line
Answer:
y=3x-1
Step-by-step explanation:
start at (-1,-4) and go up 6 and over 2, thats your slope or m.
the y intercept is -1
Answer: y=3x-1
Step-by-step explanation:
(1,2) and (-1,-4) are on the so we could use then to find the slope.
2-(-4)=6
1-(-1)= 2
6/2=3
We know the y-intercept is -1 because the line passes through (0,-1) which is on the y axis. And the y-intercept is when x is 0.
so the equation will be y = 3x -1
Please answer this correctly I want helping hand people to answer this
Answer:
10
Step-by-step explanation:
Take 4 times 2.5 since 25 / 10 = 2.5
4 x 2.5 = 10
Madison drew Triangle D E F. In her triangle, Measure of angle D is represented as x degrees. The measure of Angle E is half the measure of Angle D. The measure of Angle F is 2 degrees less than twice Measure of angle D. What is Measure of angle F?
A) 36 degrees
B)56 degrees
C)102 degrees
D)147 degrees
Answer:
102 degrees.
Step-By-Step Explanation:
We know that D is x and E is 1/2x and Angle F is 2 less than angle D.
So if we use the sum of 180 and solve for x, we will find angle D.
This is the equation: x+.5x+2x-2=180
solve: 3.5x -2 = 180
+2 +2
3.5x=182
/3.5x /3.5x
X = 52
2(52)-2 = 102 degrees
Thus the answer is 102 degrees
hope this helped:)
Answer:
102º
Step-by-step explanation:
Is the point (7,0) located on the x axis
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Yes. As the y value is 0, this point would be on the x axis
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Which expression represents the quotient of 5 and y, decreased by the product of 3 and z?
Answer:
5/y-3z
Step-by-step explanation:
Quotient is division
Product is multiplication
please mark brainliest
The equivalent value of the expression is A = 5/y - 3z
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.
Given data ,
Let the expression be represented as A
Now , the value of A is
A = quotient of 5 and y, decreased by the product of 3 and z
Now , quotient of 5 and y = 5/y
And , product of 3 and z = 3z
So , On simplifying the expression , we get
A = 5/y - 3z
Hence , the equation is A = 5/y - 3z
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There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
(A) Approximately normal with mean $206,274 and standard deviation $3,788
(B) Approximately normal with mean $206,274 and standard deviation $37,881
(C) Approximately normal with mean $206,274 and standard deviation $520
(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788
(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881
Answer:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Right skewed
Mean $206,274
Standard deviation $37,881.
Sample:
By the Central Limit Theorem, approximately normal.
Mean $206,274
Standard deviation [tex]s = \frac{37881}{\sqrt{100}} = 3788.1[/tex]
So the correct answer is:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem.
Given :
There were 5,317 previously owned homes sold in a western city in the year 2000.The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. Simple random samples of size 100.According to the central limit theorem the approximately normal mean is $206274.
Now, to determine the approximately normal standard deviation, use the below formula:
[tex]s =\dfrac{\sigma }{\sqrt{n} }[/tex] ---- (1)
where 's' is the approximately normal standard deviation, 'n' is the sample size, and [tex]\sigma[/tex] is the standard deviation.
Now, put the known values in the equation (1).
[tex]s = \dfrac{37881}{\sqrt{100} }[/tex]
s = 3788.1
[tex]\rm s \approx 3788[/tex]
So, the correct option is A).
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Simplify the expression by combining like terms.
Write the terms in alphabetical order of the
variables.
6x - 6y + 6z + 18x - 11y + 2z
Answer:
24x - 17y + 8z
Step-by-step explanation:
A copy machine makes 24 copies per minute. How many copies does it make in 3 minutes and 45 seconds?
copies
Х
?
Answer:
90 copies
Step-by-step explanation:
24*3= 72
1/2*24= 12 for 30 seconds
1/2*6= 6 for 15 seconds
45/15=3
72+18= 90
What would you do to find the area of 5/8 of a circle?
Answer:
5/8 * pi r^2
Step-by-step explanation:
First , you find the full area of the circle
A = pi r^2
Then multiply by the fraction that you want to find
5/8 * pi r^2
A sprinkler swings back and fourth between A and B in such a way that <1 is congruent to <2. <1 and <3 are complementary, and <2 and <4 are complementary. If m<1=47.5 degrees, find m<2, m<3, and m<4
Answer:
Congruent
Step-by-step explanation:
Answer:
I think is congruent, but I m not sure
What is the sum of this infinite geometric series? 1/4, 1/5, 4/25, 16/125
Answer:
5/4Step-by-step explanation:
Given infinite geometric series
1/4, 1/5, 4/25, 16/125, ...We see that
a = 1/4r = 4/5Sum of the series
S = a*1/(1 -r)S = 1/4*1/(1 - 4/5) = 1/4*1/(1/5) = 1/4*5 = 5/4Answer:5/4
Step-by-step explanation:
Write the slope-Intercept form of the equation for the line
Answer:
Equation : y = -0.9x − 1.5
Step-by-step explanation:
Slope is rise over run, 7 over 8
-7/8 = -0.875, round to nearest tenth
-0.875 = -0.9
y- intercept is the point that crosses the y-axis,
the line crosses the y-axis at -1.5
The new Elk Grove radio station KFIN, features the top 60 songs for that week. The #1 song is played 60 times, the #2 song is played 59 times, the #3 song is played 58 times, and so on until the #60 song is played once. Each song takes 3 minutes to play.
The station also has 24 ten-minute news breaks each day, and the rest of the time is sold for advertising. If the station charges $100 for every 30 seconds of advertising, how much money do they take in each week?
Answer:
Step-by-step explanation:
The number of times that each song is played is reducing in arithmetic progression. We would determine the total number of time for plating all the songs in a week by applying the formula for determining the sum of the n terms in an arithmetic sequence. It is expressed as
Sn = n/2(2a + (n - 1)d
Where
d represents the common difference
n represents the number of terms
a represents the first term of the sequence
Sn represents the sum of n terms if the sequence.
From the information given,
a = 60
n = 60
d = - 1
Sn = 60/2(2 × 60 + (60 - 1)-1)
Sn = 30(120 - 59)
Sn = 1830 times
The 60 songs are played for 1830 times in a week. If each song takes 3 minutes to play, then the total time taken to play the songs for 1830 times in a week is
3 × 1830 = 5490 minutes
7 days = 1 week
24 hours = 1 day
60 minutes = 1 hour
The number of minutes in a week is
7 × 24 × 60 = 10080 minutes
The station also has 24 ten-minute news breaks each day. The number of minutes of break for each day is
24 × 10 = 240 minutes
The amount of break time in a week is
240 × 7 = 1680 minutes
If the remaining minutes is meant for advertising, then the number if minutes available for advertising is
10080 - (5490 + 1680) = 2910 minutes
1 minute = 60 seconds
2910 minutes = 2910 × 60 = 174600 seconds
If the station charges $100 for every 30 seconds of advertising, then the amount that they take in each week(for 174600 seconds) is
(174600 × 100)/30 = $5820000
Suppose we want to choose 6 objects, without replacement, from 11 distinct objects.
(a) How many ways can this be done, if the order of the choices matters?
0
(b) How many ways can this be done, if the order of the choices does not matter?
Answer:
a) 332640 ways
b) 462 ways
Step-by-step explanation:
Order:
If the order of the choices matters, we use the permutations formula. If they do not matter, we use the combinations formula.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 objects, from a set of 11.
a) Order matters, so permutation.
[tex]P_{(11,6)} = \frac{11!}{(11-6)!} = 332640[/tex]
b) Order does not matter, so combinations.
[tex]C_{11,6} = \frac{11!}{6!(11-6)!} = 462[/tex]
What is the cost of 12 cupcake at meg’s cupcakes ?
Answer:
36
Step-by-step explanation:
15 divided by 5 would = 3
3 is the cost of 1 cupcake
3 x 12 is 36
Answer:
36
Step-by-step explanation:
The pattern is times 3 so 12 times 3 is 36
1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several times, and the values are: 0.082601, 0.082621, 0.082589, 0.082617, 0.082598. Please use student’s t to find the confidence interval at the 95% confidence level. 2) If one wants the confidence interval to be two thirds of the previous one, how many times should a student repeat? (Assuming the standard deviation is the same as the previous one)?
Answer:
1) [tex]0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588[/tex]
[tex]0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219[/tex]
b) [tex] ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653[/tex]
And we want 2/3 of the margin of error so then would be: [tex] 2/3 ME = 0.00001111[/tex]
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (2)
Replacing we got:
[tex]n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12[/tex]
So the answer for this case would be n=12 rounded up to the nearest integer
Step-by-step explanation:
Information given
0.082601, 0.082621, 0.082589, 0.082617, 0.082598
We can calculate the sample mean and deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=0.0826052[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=0.000013424 represent the sample standard deviation
n=5 represent the sample size
Part 1
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=5-1=4[/tex]
The Confidence level is 0.95 or 95%, and the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value would be using the t distribution with 4 degrees of freedom: [tex]t_{\alpha/2}=2.776[/tex]
Now we have everything in order to replace into formula (1):
[tex]0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588[/tex]
[tex]0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219[/tex]
Part 2
The original margin of error is given by:
[tex] ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653[/tex]
And we want 2/3 of the margin of error so then would be: [tex] 2/3 ME = 0.00001111[/tex]
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (2)
Replacing we got:
[tex]n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12[/tex]
So the answer for this case would be n=12 rounded up to the nearest integer
The figure shows a square plot of land in tiny town. The diagonal line represents a new road that was recently built. How long is the new road? Round the nearest tenth if necessary.
A. 9 miles
B. 18 miles
C. 10.7 miles
D. 12.7 miles
Answer:
A. 9 miles
Step-by-step explanation:
if you flip one of the sides to be to be diagonal then it is the same length as the road.
11(11d+3z+8)for d = 10 and z = 12
Answer: 1,694
Step-by-step explanation: 11(11d + 3z + 8) d = 10 and z = 12
121d + 33z + 88
121(10) + 33(12) + 88
1210 + 396 + 88
1,694
Which point shows the location of 5 – 2i on the complex plane below? On a coordinate plane, points A, B, C, and D are shown. Point A is 2 units to the left of the origin and 5 points up from the origin. Point B is 2 points to the right of the origin and 5 points down from the origin. Point C is 5 points to the right of the origin and 2 points down from the origin. Point D is 5 points to the left of the origin and 2 points down from the origin. point A point B point C point D
Answer:
The Point C shows the location of 5-2i in the complex plane: 5 points to the right of the origin and 2 points down from the origin.
Step-by-step explanation:
We have the complex number 5-2i and we have to show the location of the point that represents that number in the complex plane
In the complex plane the real numbers are located in the horizontal axis, increasing to the right. The positives real numbers are at the right of the origin and the negatives to the left.
The complex numbers are located in the vertical axis, with the positives over the origin and the negatives below the origin.
This complex number 5-2i is the sum of a real part (5) and a imaginary part (-2i), so the point will be 5 units rigth on the horizontal axis (for the real part) and 2 units down in the vertical axis (for the imaginary part).
Answer:
c. point c
Step-by-step explanation:
Which describes the cross section of the rectangular prism that passes through vertices A, B, C, and D?
Answer:
C
Step-by-step explanation:
Suppose that Matthew can choose to get home from work by car or bus.
When he chooses to get home by car, he arrives home after 7 p.m. 6 percent of the time.
When he chooses to get home by bus, he arrives home after 7 p.m. 25 percent of the time.
Because the bus is cheaper, he uses the bus 70 percent of the time.
What is the approximate probability that Matthew chose to get home from work by bus, given that he arrived home after 7 p.m.?
A-70%
B-91%
C-18%
D-20%
Answer:
B-91%
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: arriving home after 7 p.m.
Event B: getting home by bus.
When he chooses to get home by bus, he arrives home after 7 p.m. 25 percent of the time.
This means that [tex]P(A|B) = 0.25[/tex]
Because the bus is cheaper, he uses the bus 70 percent of the time.
This means that [tex]P(B) = 0.7[/tex]
Probability of getting home after 7 p.m.
70% of the time he uses bus, and by bus, he arrives arrives home after 7 p.m. 25 percent of the time.
100 - 70 = 30% of the time he uses the car, and by car, he arrives home after 7 p.m. 6 percent of the time.
So
[tex]P(A) = 0.7*0.25 + 0.3*0.06 = 0.193[/tex]
What is the approximate probability that Matthew chose to get home from work by bus, given that he arrived home after 7 p.m.?
[tex]P(B|A) = \frac{0.7*0.25}{0.193} = 0.9067[/tex]
Rouding up, 91%.
So the correct answer is:
B-91%
y = 6x - 4
y = -x + 3
Answer:
(1, 2)
Step-by-step explanation:
Subtract the second equation from the first:
(y) -(y) = (6x -4) -(-x +3)
0 = 7x -7 . . . . . simplify
0 = x - 1 . . . . . . divide by 7
1 = x . . . . . . . . . add 1
y = -1 +3 = 2 . . . substitute into the second equation
The solution is (x, y) = (1, 2).
Which number line shows the solution if 4x - 36 < -12?
One solution was found :
x = 9
Events A and B are independent. The probability of A occuring is 2/3. The probability of B occuring is 1/4 what is p(A and B)
Answer: A 1/10
Step-by-step explanation: edge 2021
You work for a candy company and the manufacturing manager claims that the production line produces bags of candy with an average of exactly 50 candies per bag. You are skeptical about this and you decide to test the claim by counting the candies in a sample of 25 bags. You discover in your sample that x = 48 and s = 5. Determine whether have enough statistical evidence to reject the level of 0.05. Show your work and give all the necessary numbers required to reach your conclusion. Be sure to indicate all the necessary steps for a hypothesis test. Repeat the p-value.
Answer:
Step-by-step explanation:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H₀: u = 50
H₁: u ≠ 50
Null hypothesis: The production line produce bags of candy has an average of exactly 50 candies per bag.
Alternative hypothesis: The production line produce bags of candy does not have an average of exactly 50 candies per bag.
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1.0
Test Statistic
t = (x - u) / SE
t = - 2.0
DF = n - 1
D.F = 24
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the t statistic having 24 degrees of freedom is less than -2.0 or greater than 2.0.
Thus, the P-value = 0.057
Statistic result
Interpret results. Since the P-value (0.057) is greater than the significance level (0.05), we failed to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the production line produce bags of candy with an average of exactly 50 candies per bag.