The required area of the given triangle is given as 15 cm².
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
To calculate the area of a triangle with its vertices A(2, 5), B(3, -1), and C(-2, -1),
Evaluate the absolute value of the expression 1/2
= 1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|
Substitute the value in the above expression
= 1/2|2(-1 + 1) + 3(-1 - 5) -2(5 + 1)|
= 1/2[30]
= 15 cm²
Thus, the required area of the given triangle is given as 15 cm².
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The table shows the amount of money, A, in a savings account after m months.
The equations that represent the balance A after m months are given as follows:
A - 700 = 100m.A = 700 + 100m.A = 1200 + 100(m - 5).What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the initial amount.For this problem, we have that each month, the balance increases by 100, hence the slope m is given as follows:
m = 100.
Hence:
y = 100x + b.
When x = 5, y = 1200, hence the intercept b is given as follows:
1200 = 500 + b
b = 700.
Hence these following two equations are correct:
A - 700 = 100m.A = 700 + 100m.Taking the fifth month as the initial month, we consider an intercept of 1200, hence the final equation is given as follows:
A = 1200 + 100(m - 5).
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Complete the process of solving the equation.
Fill in the missing term and select the missing description. Simplify any
fractions.
11(u-4)=-11
U-4 =-1
U=
Add 4 to both sides
Find the value of x. Give reasons to justify your solution.
How the ffffffffffffffffffffffffffffffffffffffffff
POPULATION A city's population is 358,000 and is decreasing at an annual rate of 0.25%.
Which function represents the estimated population after "t" years?
Answer:
pop'n = 358000*(1-0.25%)^t
Step-by-step explanation:
pop'n = 358000
decreasing rate = 0.25%
after t years
pop'n = 358000*(1-0.25%)^t
Which expression represents the correct form for the quotient and remainder, written as partial fractions, of
8x3-2x2-67x-24
The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
Which expression represents the correct form for the quotient and remainder?
(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)
This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.
The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.
The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.
To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.
The result is 4x².
Then, subtract 4x² from 8x²³ to get the remainder of 4x³.
Next, divide 4x² into 21².
The result is 33x.
Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.
Finally, divide 4x²-33x into 67x.
The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.
This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.
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determine if the statements are true or false. an even degree polynomial must be an even function. true false every polynomial of odd degree has at least one zero. true false every rational function that is not a polynomial has a vertical asymptote. a. true b. false
A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.
An even degree must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.
Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.
Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.
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Presidential Poll. A research group suspects that less than 48% of Americans support the Republican presidential candidate. To test this claim, they randomly call Americans until they get 1000 responses. Of the 1000 people who responded, 477 of them say they support the Republican presidential candidate. Test the research group's suspicion at a 5% level of significance.
(b) Find the p-value (round to four decimal places).
The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.
what is null hypothesis ?A type of data hypothesis known as both a null hypothesis claims that a certain collection of data has no statistically significant results. The viability of hypotheses be evaluated using sample. Sometimes refers to as "zero," and symbolized as H0. The premise made by the researchers is that there is a correlation between the variables. The h0, on the other hand, says that such an association doesn't quite exist. Despite its inability to seem significant, the null hypothesis is a crucial component of a study.
given
Calculating the p-value requires knowledge of the distribution of your test statistic under the assumption that the null hypothesis is true.
Cdf as the p-value for the left-tailed test (x).
Right-tail test: p-value = 1 - cdf (x).
The two-tailed test's p-value is 2 mincdf(x), 1 - cdf (x).
The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.
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Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. a. List the sample points.b. Assign probabilities to the sample points.c. Determine the probability of observing each of the following events:A: { Two blue marbles are drawn. }B:{ A red and a blue marble are drawn. }C:{ Two red marbles are drawn. }
The probabilities of all the events related to drawing two marbles without replacement are discussed below.
What is meant by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
Number of blue marbles B = 2
Number of red marbles R = 3
Number of marbles drawn = 2
a) Sample points are different possible combinations.
{ R,R} , {R,B}, {B, R}, {B,B}
b) Probablitiy of { R,R} = 3/5 * 2/4 = 6/20 = 3/10 = 0.3
Probablitiy of {R,B} = 3/5 * 2/4 = 0.3
Probablitiy of {B,R} = 2/5* 3/4 = 0.3
Probablitiy of {B,B} = 2/5 * 1/4 = 0.1
c) A: { Two blue marbles are drawn. }
Probability = 2/5 * 1/4 = 0.1
B:{ A red and a blue marble are drawn. }
Probability = 0.3 ( from above)
C:{ Two red marbles are drawn. }
Probability = 0.3 (from above)
Therefore the different sample points are found and probabilities of different events are also found.
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 6.7 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth.
Answer:
7.4
Step-by-step explanation:
Use Pythagorean Theorem: [tex]a^2+b^2+c^2[/tex]
In this case we have a and c. So let's plug those into the equation:
[tex](6.7)^2+b^2=10^2[/tex]
[tex]44.9+b^2=100[/tex]
[tex]b=\sqrt{55.1}[/tex]
[tex]b=7.4[/tex]
angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence.
Angelique needs 3 8/15 hours to completely build the fence.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Angelique builds a fence and she can build 5/8 of the fence in 2 5/6 = 17/6 hours.
We know a number multiplied to its reciprocal is 1.
Therefore, The amount of time Angelique needs to complete the fence is,
(5/8)×(8/5) the complete fence in (17/6)×(8/5) hours.
= 136/30 hours.
= 3 16/30 hours.
= 3 8/15 hours.
Q. Angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence, how much time she needs to complete the fence?
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The sum of the angles of a triangle is 180". One angle of a triangle 100% and the magnitude of the other two is in the ratio 2:3. Determine the magnitudes of the other two angles.
Answer:
The two angles are 32 degrees and 48 degrees.
Step-by-step explanation:
If one angle of a triangle is 100 degrees, then the sum of the other two angles is 80 degrees (180 - 100). If the magnitude of the other two angles is in the ratio 2:3, then we can call the first angle 2x and the second angle 3x. The sum of these two angles is 5x, so 5x = 80, and x = 16. So, the two angles are 2x = 32 degrees and 3x = 48 degrees.
Jewel completed 12 out of 20 of her homework questions last night. What percent did she complete?
Answer:
60%
Step-by-step explanation:
12/20 = 3/5 = 0.6 = 60%
Hey there! To find out how much of her homework Jewel completed, all we need to do is a little math. First, let's divide the number of questions she did by the total number of questions. That's 12 divided by 20 which equals 0.6.
Now, we just need to turn that decimal into a percentage. To do that, we simply multiply 0.6 by 100, which gives us 60. And voila! Jewel completed 60% of her homework.
I’m confused please help
Answer:
First option: 4.9 in
Step-by-step explanation:
The area of a circle, given radius = r is computed using the formula
A = πr²
Here we are given the area and asked to find the radius r
A = 75.43 in² = πr²
So
πr² = 75.43
r² = 75.43/π
= 24.01
= 24 rounded to nearest integer
r = √24
= 4.9
please help me with this question thank you
The average rate of change for the given function is -72.
What Is the Average Rate of Change?
To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change. To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.
The rate of the change for the interval [a,b] is given by
[tex]\frac{f(b)-f(a)}{b-a} \\[/tex]
For the given interval [3,11],
[tex]= \frac{f(11)-f(3)}{11-3} \\\\= \frac{-623+47}{8} \\\\= -72[/tex]
So, the required average rate of change is -72.
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A runner wants to be able to run 600 meters in 60 seconds. What miles per hour speed must the runner attain to accomplish this goal? The runner knows that there are 1690 meters in a mile. Round to the nearest whole number
Answer:
21 miles per hour
Step-by-step explanation:
Express the gross salary g of a person who earns per hour as a function of the number x of hours worked.
Answer:
Gross salary =G
Number of worked hours =x
Dollar per hour =$12
substitute the given data into the gross salary formula and simplify.
Gross salary = (number of worked hours)
G =(x) (12)
G =12x
Therefore, G(x) =12x
Hence the function is G(x) = 12x
Elizabeth has 10 mangoes
eats 5 and gives
2 to Mary and throws 1 away how many mangoes are left
Answer:
2
Step-by-step explanation:
10-5=5.....the ones she ate
5-2=3 .... the 2 she gave to Mary
3-1 =2.....the one she threw away
2 mangoes!
10 - 5 = 5
5 - 2 = 3
3 - 1 = 2
June 1
June 12
• June 23
Jun 30
Inventory 150 unit cost 6$ total cost900$
purchase450 unit cost7$ total 3150$
Purchase400 unit cost 8$ total 3200$
Inventory 80
Assume a Sale of 500 units occured on June 15
for a Selling price of $9 and a sale of 420 units on
June 27 for $9
? The cost of goods available for Sale?
?calculate Moving-Average unit cost of for
June 1.
June12.
June 15.
June23.
June27.
?Calculate the cost of ending inventoryfor each cost flow assumption, using a
perpetual inventory System. Round average cost per Unit
3 decimal places.
on Round answer to 3 decimal
Answer:
Step-by-step explanation:
Cost of goods available for sale:
Starting inventory: 150 units * $6/unit = $900
Purchase on June 1: 450 units * $7/unit = $3150
Purchase on June 23: 400 units * $8/unit = $3200
Total cost: $900 + $3150 + $3200 = $7450
Moving Average Unit Cost:
June 1: $7450 / (150 + 450) = $7/unit (rounded to 3 decimal places)
June 12: $7450 / (150 + 450 + 400) = $7.36/unit (rounded to 3 decimal places)
June 15: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)
June 23: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)
June 27: $7450 / (150 + 450 + 400 + 500 + 420) = $7.43/unit (rounded to 3 decimal places)
Cost of ending inventory using perpetual inventory system:
FIFO: $7.51/unit * 80 units = $604 (rounded to 3 decimal places)
LIFO: $7/unit * 80 units = $560 (rounded to 3 decimal places)
Average Cost: $7.43/unit * 80 units = $594.4 (rounded to 3 decimal places)
If you want to estimate the mean height of all the .students at a university, which one of the following sampling strategies would be best? Why? Note that none of the methods are true simple random samplesi. Measure the heights of 50 students found in the gym during basketball intramurals ii. Measure the heights of all engineering majors. iii. Measure the heights of the students selected by choosing the first name on each page of the cam pus phone book.
The optimum sampling strategy is (iii), which is listed below.
By selecting a student's initial name from each page of the cam pus phone book, you may measure the heights of the chosen pupils.
What is Sampling?Sampling is a technique for selecting a small group of people or a subset of the population in order to make generalizations and estimate the features of the population. In order to acquire relevant information without studying the entire society, researchers commonly use a variety of sampling approaches in market research.
To ascertain the average height of all students at a certain institution and guarantee that the result is statistically reliable, the sampling process must be applied.
a. Measure the heights of 50 students found in the gym during basketball intramurals.
This approach is not ideal since you would only sample basketball players while leaving all other university students out; hence, your sample would not be representative of all students, simply those who play basketball.
b. Measure the heights of all engineering majors.
This approach is flawed since the sample exclusively includes engineering majors, leaving out students studying other courses.
c. Measure the heights of the students selected by choosing the first name on each page of the campus phone book.
This strategy, which is the finest of the three, allows you to select students independent of the sport or subject they are pursuing. It is more representative of the university student population.
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Find the value of X and Y.
The value of the side lengths x and y are 29.4 units and 17 units
How to determine the values of the sidesFrom the information given, we have that;
The hypotenuse side = 34The opposite side = yThe adjacent side = xUsing the cosine identity'
sin 30 = y/34
find the value
0. 5000 (34) = y
Multiply
y = 17 units
Using the cosine identity
cos 30 = x/34
multiply
x = 34(0.8660)
x = 29. 4 units
Hence, the values are 17 units and 29. 4 units
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there are 21 sedans and 12 sports utility rehicles on the lot of a used car dealership. If he ratio of sedans to SUV's stays the same, now man sedans will be in the lot of 99 vehicles?
Answer: 63 sedans
Step-by-step explanation:
21 * 3
Alvin's age is two times Elga's age. The sum of their ages is 27. What is Elga's age?
Answer:
52
Step-by-step explanation:
my boy its 52 she said times it means multiply
What is the value of x?
Answer:
im pretty sure ia 31,61
Step-by-step explanation:
√ always together equals about 15 but as of your value of eggs that could not be possible so establishing the 6 x -5 doesn't make any difference apart from the question being so brought a part the answer would be above 30 it could be 30 to 65 anything but if you equal those balls at the bottom you get to .5 as again does 2.5 x 8 has something that equals a bunch of those 2.5 x 8 is 24.5 making 24.5 but the top one makes it al be 31.5Answer: 10⁰
Step-by-step explanation:
We know that,
the summation of 3 angles of a triangle is 180⁰.
now, (6x-5)⁰+(5x-5)⁰+8x⁰=180
or, 19x-10=180⁰
or, 19x=190⁰
or, x= (190/19)⁰
or, x= 10⁰
What is the sum of this expression?
Answer:
B. 9[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Rewriting the two fractions in the expression:
=[tex]\frac{[(8)(2)]+1}{8} + \frac{[(8)(7)]+3}{8}[/tex]
=[tex]\frac{17}{8} + \frac{59}{8}[/tex]
Since the denominators of both the fractions is the same, then the denominator of the resulting simplified fraction will also be the same. In addition, everything written in the numerator level will be copied down as it is:
=[tex]\frac{17 + 59}{8}[/tex]
=[tex]\frac{76}{8}[/tex]
Divide the numerator and denominator by the Highest Common Factor '4':
= [tex]\frac{19}{2}[/tex]
Apply Long Division since:
The numerator is greater than the denominator and The numerator and the denominator cannot be further reduced or simplifiedChoose the highest quotient to be multiplied by 2 to give a number closest to 19 but still less than 19. The quotient turns out to be 9. The remainder is 1
∴ Sum of the expression = 9[tex]\frac{1}{2}[/tex]
What is the simplified form of 4 log3x + 6 log3y - 7 log3z?
The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
The simplification of the provided logarithmic expression can be done as follows:-
6 log₃x - 7 log₃y + 4 log₃z,
= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}
= log₃x⁶ + log₃z⁴ - log₃y⁷
= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}
= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.
Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
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Simplify
4x^3 - 12x^2
4x^2 + 7x - 2
2x^2 -6x
5x^2 + 11x + 2
2x(5x + 1) / (4x - 1) is the final expression.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(4x³ - 12x²) / (4x² + 7x - 2) / (2x² - 6x) / (5x² + 11x + 2)
= (4x³ - 12x²) x (5x² + 11x + 2) / (4x² + 7x - 2) x (2x² - 6x)
Now,
(4x³ - 12x²) = 4x² (x - 3) _____(1)
And,
(5x² + 11x + 2)
Middle term factorizing
= 5x² + (10 + 1)x + 2
= 5x² + 10x + x + 2
= 5x (x + 2) + 1(x + 2)
= (x + 2) (5x + 1) ______(2)
And,
(4x² + 7x - 2)
Middle term factorizing
= 4x² + (8 - 1)x - 2
= 4x² + 8x - x - 2
= 4x(x + 2) - 1(x + 2)
= (4x - 1) (x + 2) ______(3)
And,
(2x² - 6x) = 2x (x - 3) ______(4)
From (1), (2), (3), and (4) we get,
(4x³ - 12x²) x (5x² + 11x + 2) / (4x² + 7x - 2) x (2x² - 6x)
= [ 4x² (x - 3) x (x + 2) (5x + 1) ] / [ (4x - 1) (x + 2) x 2x(x - 3) ]
(x + 2) and (x - 3) gets canceled.
= [4x² (5x + 1)] / [(4x - 1) 2x]
= 2x(5x + 1) / (4x - 1)
Thus,
2x(5x + 1) / (4x - 1)
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Use StatKey or other technology to find the regression line to predict Y from X using the following data.
X 10 20 30 40 50 60
Y 111 109 110 94 92 93
Click here to access StatKey.
Round your answer for the intercept to one decimal place and the answer for the slope to two decimal places.
The regression equation is Enter your answer; The regression equation, intercept
+ Enter your answer; The regression equation, slope
X.
The regression equation is Y = 95.0 + 0.84X.The regression line is a mathematical model that is used to predict the value of a dependent variable (Y) based on the value of an independent variable (X).
In this case, the regression line is used to predict Y from X using the following data: X = 10, 20, 30, 40, 50, 60 and Y = 111, 109, 110, 94, 92, 93. By using a regression analysis tool such as StatKey, we can calculate the regression equation that best fits this data. The regression equation is Y = 95.0 + 0.84X, where 95.0 is the intercept and 0.84 is the slope. This equation can be used to make predictions about the value of Y for a given value of X. The rounded answer for the intercept is 95.0 and the rounded answer for the slope is 0.84.
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Find the point-slope equation of the plane passing through the point (2, -12, 4) and having x-slope 15 and y-slope -19.Z = ___
The Point-Slope equation is Z = 15X - 19Y + 204.
What is the slope-point form?
The slope-point form of a line in 3-dimensional space is a equation of the form:
Z = m_x (X - X_0) + m_y (Y - Y_0) + Z_0
where (X_0, Y_0, Z_0) is a point on the line, m_x is the x-slope, and m_y is the y-slope.
Given:
point (2, -12, 4) and x-slope 15 and y-slope -19, we can use the point-slope form to find the equation of the plane:
Z = 15 (X - 2) - 19 (Y + 12) + 4
Hence, the point-slope equation of the plane passing through the point (2, -12, 4) and having x-slope 15 and y-slope -19 is:
Z = 15X - 30 - 19Y + 228 + 4
Z = 15X - 19Y + 204
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is the following statement true or false? all other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median.
All other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median. The given statement is true.
What is the mean and median?
Outliers are values that are significantly different from the other values in a data set, and their presence can greatly affect the value of measures of central tendency, such as the mean and the median.
The mean is a measure of central tendency that is calculated as the sum of all the values in a data set divided by the number of values. The presence of outliers can greatly affect the mean because outliers can have a large impact on the sum of the values in the data set. For example, if a data set has a few very large outliers, the mean will be pulled up to be much higher than the median, which represents the midpoint of the data set.
On the other hand, the median is a measure of central tendency that is calculated as the middle value of a data set when the values are arranged in order. The median is not as sensitive to outliers as the mean because outliers do not affect the median unless the number of outliers is so large that it changes the value of the middle value.
Hence, all other things being equal, outliers tend to have a greater effect on the value of the mean than on the value of the median.
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Please Help I need this ASAP will award Brainliest if correct
The center of dilation is (1, -4).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the given graph,
Vertices of RSTV are R(1, -4), S(2, 0), T(1, 2) and V(-2, 1).
Vertices of R'S'T'V' are R'(1, -4), S'(4.5, 2), T'(2, 5) and V'(-2.5, 3.5).
Here, the center of dilation is (1, -4).
The transformation is enlargement by scale factor 1.5
Therefore, the center of dilation is (1, -4).
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