The composition of functions, j, k, m, and n, when completed is shown below.
How to complete the composition of functions ?To complete the composition of functions j, k, m, and n, we can write the composite functions in the following form:
(j∘k)(x) = j(k(x))
(j∘m)(x) = j(m(x))
(j∘n)(x) = j(n(x))
(k∘m)(x) = k(m(x))
(k∘n)(x) = k(n(x))
(m∘n)(x) = m(n(x))
Each of the composite functions would be:
(j∘k)(x) = j(k(x)) = j(x + 2) = (x + 2)² = x² + 4x + 4
(j∘m)(x) = j(m(x)) = j(x - 6) = (x - 6)² = x² - 12x + 36
(j∘n)(x) = j(n(x)) = j(3x) = (3x)² = 9x²
(k∘m)(x) = k(m(x)) = k(x - 6) = (x - 6) + 2 = x - 4
(k∘n)(x) = k(n(x)) = k(3x) = (3x) + 2 = 3x + 2
(m∘n)(x) = m(n(x)) = m(3x) = (3x) - 6 = 3x - 6
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You solved this problem in another question: A video rental store keeps a list of their top 15 movie rentals each week. This week the is includes 5 action,
4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to
show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie? EXPLAIN how the probability would
change if two more comedy movies were added to the list in place of the 2 mystery movies.
The probability of the store manager selecting 2 comedies and 1 action movie out of the list of 15 movies is 0.066
The probability of the store manager selecting 2 comedies and 1 action movie out of the new list of 15 movies is 0.165
Using this formula, we can find the total number of ways in which the manager can select any 3 movies from the list of 15, which is:
¹⁵C₃ = 455
Next, we need to determine the number of ways in which the manager can select 2 comedies and 1 action movie out of the list of 15 movies. To do this, we first need to determine the total number of comedies and action movies in the list, which is 4 and 5, respectively.
⁴C₂ x ⁵C₁ = 30
Therefore, the probability of the store manager selecting 2 comedies and 1 action movie out of the list of 15 movies is:
30/455 = 0.066
Now, if two more comedy movies were added to the list in place of the 2 mystery movies, the total number of comedies in the list would increase from 4 to 6, while the total number of action movies would remain the same at 5.
Using the same formula as before, the new total number of ways in which the manager can select any 3 movies from the list of 15 movies would still be 455.
The number of ways in which the manager can select 2 comedies and 1 action movie from the new list of movies can be found using the same product rule of probability as before. We can select 2 comedies from 6 in 6C2 ways, and 1 action movie from 5 in 5C1 ways. The new total number of ways in which 2 comedies and 1 action movie can be selected is:
⁶C₂ x ⁵C₁ = 75
Therefore, the probability of the store manager selecting 2 comedies and 1 action movie out of the new list of 15 movies is:
75/455 = 0.165
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at a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). the remaining students do not win a prize. if 150 students play the game at the booth, how much money should the carnival committee expect to pay for prizes for that booth?: *
For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.
We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%
The percentage of students win a jump rope = 16%
The percentage of students win a t-shirt
= 6%
The winning amount for stuffed toy game = $ 3.60
The winning amount for jump rope game = $1.20
The winning amount for t-shirt game
= $7.90
The remaining students do not win a prize. Now, total number of students play the game at the booth = 150
So, number of students who win stuffed toy = 22% of 150 = 33
Number of students who win jump rope = 16% of 150 = 24
Number of students who win stuffed toy
= 6% of 150 = 9
For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6
= 218.7
Hence required value is $218.70.
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please help, due today
The table represents a linear relationship.
x −1 0 1
y −3 1 5
Which equation represents the table?
A. y equals one fourth times x minus 2
B. y equals negative one fourth times x plus 1
C. y = −4x − 2
D. y = 4x + 1
The equation that represents the linear relationship in the table is D. y = 4x + 1.
Which equation represents the table of values?To find the equation that represents the linear relationship in the table, we need to determine the slope and y-intercept of the line that passes through the given points.
We can use the formula for the slope of a line, which is:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the first two points from the table, we get:
m = (1 - (-3))/(0 - (-1)) = 4/1 = 4
So, the slope of the line is 4.
To find the y-intercept, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
Using the point (0, 1) and the slope m = 4, we get:
y - 1 = 4(x - 0)
y = 4x + 1
So, the equation is D. y = 4x + 1.
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a local politician is concerned that a program for the homeless in the city is discriminating against blacks and other minorities. the following data were taken from a random sample of black and white homeless people. race black white received services yes 6 7 13 no 4 9 13 10 16 26 a. is there a statistically significant relationship between race and whether the person received services from the program? b. compute column and row percentages for the table to determine the pattern of the relationship. which group was more likely to receive services in the sample? interpret both the column and row percentages that you have obtained.
(a) There is no statistically significant relationship between race and receiving services from the program.
(b) Black homeless people were more likely to receive services (60%) than white homeless people (43.75%).
How to find the relationship between race and receiving services?a. To test whether there is a statistically significant relationship between race and whether the person received services from the program, we can use a chi-squared test of independence.
The null hypothesis is that there is no relationship between race and receiving services, and the alternative hypothesis is that there is a relationship.
Using a chi-squared calculator, we obtain a chi-squared statistic of 0.267 and a p-value of 0.605. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is no statistically significant relationship between race and receiving services from the program.
How to find more likely to receive services?b. To compute column and row percentages, we can first calculate the total number of black and white homeless people who received services and who did not receive services:
Black homeless people who received services: 6/10 = 60%Black homeless people who did not receive services: 4/10 = 40%White homeless people who received services: 7/16 = 43.75%White homeless people who did not receive services: 9/16 = 56.25%We can also calculate the percentage of all homeless people who received services or did not receive services, by adding up the numbers in each column:
Percentage of homeless people who received services: 13/26 = 50%Percentage of homeless people who did not receive services: 13/26 = 50%In the sample, black homeless people were more likely to receive services (60%) than white homeless people (43.75%).
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Consider the two triangles shown below. Two triangles. The first triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. The second triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. Two triangles. The first triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. The second triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. Note: The triangles are not drawn to scale. Are the two triangles congruent
In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.
Congruent?Congruent is a mathematical term used to describe two figures or shapes that have the same size and shape. In other words, two figures are congruent if they have exactly the same dimensions and the same angles. When two figures are congruent, they can be superimposed on each other without any overlap or gap between them. Congruent figures are often denoted by the symbol ≅. For example, if two triangles have the same size and shape, we can write them as ∆ABC ≅ ∆DEF, which means that triangle ABC is congruent to triangle DEF. Congruent figures play an important role in geometry and other branches of mathematics.
Yes, the two triangles are congruent.
In Euclidean geometry, if two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles are congruent. This is known as the angle-side-angle (ASA) congruence criterion.
In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.
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Two bank accounts open with deposits of $1,810 and annual interest rates of 2.5%. Bank A uses simple interest and Bank B uses interest compounded monthly How much more in interest does the account at Bank B earn in 5 years?
[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank A} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1810)(0.025)(5) \implies I = 226.25 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank B} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]
[tex]A = 1810\left(1+\frac{0.025}{12}\right)^{12\cdot 5} \implies A \approx 2050.73~\hfill \underset{ interest }{\stackrel{2050.73~~ - ~~1810 }{\approx 240.73}} \\\\[-0.35em] ~\dotfill\\\\ 240.73~~ - ~~226.25 ~~ \approx ~~ \text{\LARGE 14.48}[/tex]
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 98° is added to the data, how does the mean change?
The mean increases by 8.2°.
The mean decreases by 8.2°.
The mean increases by 1.4°.
The mean decreases by 1.4°.
"The mean increases by 8.2°."
What is mean?The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in the set and dividing by the total number of values.
To find the mean of a set of data, you add up all the values in the set and divide the sum by the number of values in the set.
Let's first find the original mean of the data:
mean =[tex](58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12[/tex]
mean = [tex]825 / 12[/tex]
mean =[tex]68.75[/tex]
Now, if we add 98 to each value in the set, the new set becomes:
[tex](156, 159, 169, 175, 189, 198, 203, 200, 193, 180, 164, 155)[/tex]
To find the new mean, we add up all the values in the new set and divide the sum by the number of values in the set:
new mean =[tex](156 + 159 + 169 + 175 + 189 + 198 + 203 + 200 + 193 + 180 + 164 + 155) / 12[/tex]
new mean = [tex]2021 / 12[/tex]
new mean = [tex]168.42[/tex]
Therefore, the mean increases by 8.67 degrees (rounded to two decimal places). None of the given answer options are an exact match to this value, but the closest option is "The mean increases by 8.2°."
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"The mean increases by 8.2°."
What is mean?
The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in the set and dividing by the total number of values.
To find the mean of a set of data, you add up all the values in the set and divide the sum by the number of values in the set.
Let's first find the original mean of the data:
mean =(58+61+ 71+ 77+ 91+100+105+102+95+82+66+57)/12
mean = 825/12
mean = 68.75
Now, if we add 98 to each value in the set, the new set becomes:
156,159,169,175,189,198,203,200,193,180,164,155.
To find the new mean, we add up all the values in the new set and divide the sum by the number of values in the set:
new mean = (156+159+169+175+189+198+203+200+193+180+164+155)/12
new mean = 2021/12
new mean = 168.42
Therefore, the mean increases by 8.67 degrees (rounded to two decimal places). None of the given answer options are an exact match to this value, but the closest option is "The mean increases by 8.2°."
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Special Right Triangles (Radical Answers)
The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.
The triangle is given as equilateral and the length of the perpendicular of the given equilateral triangle is 13.85.
What is Pythagorean theorem?It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, the longest side of the triangle. This theorem can be used to determine the length of the sides of a right triangle if two sides are known.
The triangle is given as equilateral. As we know he perpendicular in a equilateral triangle divides a line into to equal parts, so
Base= 8+8
= 16
As it is a equilateral triangle, all the sides will be equal.
Now, we can use the Pythagorean theorem to find the length of the perpendicular, which can be found by using the formula:
16²= 8² + x²
x² = 16²- 8²
x = √192
x = 13.85
Thus, the length of the perpendicular of the given equilateral triangle is 13.85.
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A traffic expert wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. She assumes that each car is 20 feet long, travels at speed N, and follows the car in front of it at a safe distance for that speed. She finds that the number
of cars that can pass a given spot per minute is modeled by the function
N = 81s/20+20(s/24)^2
Answer: The given function is:
N = 81s / (20 + 20(s/24)^2)
where:
N = number of cars that can pass a given spot per minute
s = speed of the cars in miles per hour (mph)
To find the maximum number of cars that can safely travel on the road at a given speed, we need to find the value of s that maximizes the function N.
Taking the derivative of N with respect to s:
dN/ds = (81 / (20 + 20(s/24)^2)) * (20/24 - (2s/24^2) * (s/24))
Setting dN/ds to zero to find the critical point:
0 = (81 / (20 + 20(s/24)^2)) * (20/24 - (2s/24^2) * (s/24))
Simplifying and solving for s:
20/24 = (2s/24^2) * (s/24)
20 * 24 = 2s * s
s^2 = (20 * 24) / 2
s^2 = 240
s = sqrt(240)
s ≈ 15.4919 mph
Therefore, the maximum number of cars that can safely travel on the road at a speed of 15.4919 mph is:
N = 81s / (20 + 20(s/24)^2) = 81(15.4919) / (20 + 20((15.4919)/24)^2) ≈ 180.19 cars per minute.
Step-by-step explanation:
since we are comparing the start and end weights of the ferrets, this would be [ select ] data. b. what parameter are we trying to estimate?
This data would be considered "paired" data.
The population of ferrets from which our sample was drawn, represented as μd, where μd = μend - μstart, and μ represents the population mean.
What type of data would comparing ?We are dealing with "paired" data since we are comparing the weights of the same ferrets at two different points in time.
how is this parameter represented symbolically?The parameter we are trying to estimate is the mean difference in weight between the start and end of the study for the population of ferrets from which our sample was drawn.
This mean difference in weight can be represented as μd, where μd = μend - μstart, and μ represents the population mean. To estimate this parameter, we would need to calculate the difference in weight for each ferret and then take the average of these differences. This estimate would then provide us with an understanding of how much, on average, the ferrets in the population have gained or lost weight over the course of the study.
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#SPJ11a work system has five continuous stations that have process times of 5, 8, 4, 7, and 8 min/unit respectively. what is the process time of the system?
The process time of the system is 32 min/unit.
A rectangle with dimensions 6 cm and w cm is partitioned into two smaller rectangles.
Explain why each of these expressions represents the area, in cm2, of the shaded region.
The Area of shaded region is 6 (w- 4).
We have,
length= w unit
shorter length = 4 unit
width = 6 unit
So, Area of larger rectangle
= l w
= 6 x w
and, Area of smaller rectangle
= l w
= 6 x 4
= 24 cm²
So, the Area of shaded region
= 6w - 24
= 6 (w- 4)
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A rectangular prism is shown in the image.
A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.
What is the volume of the prism?
Therefore, the volume of the rectangular prism is 87.5 cubic yards.
What is prism?A prism is a transparent object, usually made of glass or plastic, that refracts or bends light as it passes through it. It has at least two flat surfaces, called faces, that are usually parallel and rectangular in shape, and two non-parallel faces, called bases, which are usually triangular in shape. When light enters a prism, it is refracted, or bent, as it passes through the prism and is separated into its component colors, creating a rainbow effect. Prisms are often used in optics and science experiments to study the properties of light, such as its wavelength and polarization. They are also commonly used in optical instruments such as binoculars, telescopes, and cameras to help focus and direct light.
The volume V of a rectangular prism is given by the formula:
V = length x width x height
In this case, the length is 5 yards, the width is also 5 yards, and the height is 3- and one-half yard.
To calculate the volume, we can plug this value into the formula:
V = 5 yards x 5 yards x 3.5 yards
Simplifying this expression, we get:
V = 87.5 cubic yards
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Answer:
The volume of a rectangular prism is the product of its length, width, and height. In this case, the length is 5 yards, the width is 5 yards, and the height is 3.5 yards. Therefore, the volume of the prism is 5 * 5 * 3.5 = 87.5 cubic yards.
Here is the calculation:
Volume = length * width * height
= 5 yards * 5 yards * 3.5 yards
= 87.5 cubic yards
Step-by-step explanation:
explain whether the two vector-valued functions you found in parts a and c should parameterize the same tangent line
No, the two vector-valued functions found in parts a and c should not parameterize the same tangent line. The vector-valued function found in part a is a linear function, while the vector-valued function found in part c is a quadratic function. Therefore, the two functions will not parameterize the same tangent line.
Helppp
Please
I need help
According to the information, the surface area of the first prism is 795 cm², sencond prism is 843 in², and the cylinder is 3775.87 mm²
How to find the surface area of two triangular prims?To find the surface area of two triangular prisms, we need to add the surface area of each prism. We can use the formula we found in the previous question to calculate the surface area of each triangular prism:
Surface area of first triangular prism = 2(0.5 x base x height) + perimeter x height
where base is the width of the triangular face, height is the height of the triangular face, and perimeter is the sum of the lengths of the three sides of the triangular face.
In this case, the first triangular face has a base of 9 cm, a height of 16 cm, and a perimeter of (9+15+12)=36 cm. Therefore, the area of each triangular face is:
0.5 x 9 cm x 16 cm = 72 cm²
The rectangular faces have dimensions of 9 cm x 15 cm, 15 cm x 16 cm, and 9 cm x 16 cm. Therefore, the area of each rectangular face is:
9 cm x 15 cm = 135 cm²
15 cm x 16 cm = 240 cm²
9 cm x 16 cm = 144 cm²
The total surface area of the first triangular prism is:
2(72 cm²) + (135 cm² + 240 cm² + 144 cm²) = 795 cm²
Similarly, for the second triangular prism, we have:
Surface area of second triangular prism = 2(0.5 x base x height) + perimeter x height
where base is the width of the triangular face, height is the height of the triangular face, and perimeter is the sum of the lengths of the three sides of the triangular face.
In this case, the second triangular face has a base of 8 in, a height of 15 in, and a perimeter of (8+15+20)=43 in. Therefore, the area of each triangular face is:
0.5 x 8 in x 15 in = 60 in²
The rectangular faces have dimensions of 8 in x 21 in, 15 in x 21 in, and 8 in x 15 in. Therefore, the area of each rectangular face is:
8 in x 21 in = 168 in²
15 in x 21 in = 315 in²
8 in x 15 in = 120 in²
The total surface area of the second triangular prism is:
2(60 in²) + (168 in² + 315 in² + 120 in²) = 843 in²
Therefore, the surface area of two triangular prisms is:
795 cm² + 843 in² = 795 cm² + (843 in² x 6.452 cm²/in²) ≈ 5508 cm²
For the cylinder, we can use the formula we found in the previous question to calculate the surface area:
Surface area of cylinder = 2πr² + 2πrh
where r is the radius of the circular face, h is the height of the cylinder.
In this case, the radius is 14 mm and the height is 29 mm. Therefore, the surface area of the cylinder is:
2π(14 mm)² + 2π(14 mm)(29 mm) = 2π(14 mm)(43 mm) ≈ 3775.87 mm²
Therefore, the surface area of two triangular prisms and a cylinder is approximately:
5508 cm² + 3775.87 mm² = 5508 cm² + (3775.87 mm² x 0.01 m²/mm²) ≈ 5885.47 cm²
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The following numbers appear in a table of random digits:38683 50279 38224 09844 13578 28251 12708 24684A scientist will be measuring the total amount of leaf litter in a random sample (n =5) of forest sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02, . . . ,45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct?A) Her sample is 38, 25, 02, 38, 22B) Her sample is 38, 68, 35, 02, 22C) Her sample is 38, 35, 27, 28, 08D) Her sample is 38, 65, 35, 02, 79E) Her sample is 38, 35, 02, 22, 40
The correct answer is B) Her sample is 38, 68, 35, 02, 22. This is because the scientist is selecting a random sample of 5 forest sites from a population of 45 without replacement. She is using consecutive pairs of digits from the table of random digits to select her sample.
Starting at the beginning of the line of random digits, the first pair is 38, which corresponds to forest site 38. The second pair is 68, which corresponds to forest site 68. The third pair is 35, which corresponds to forest site 35. The fourth pair is 02, which corresponds to forest site 02. And the fifth pair is 22, which corresponds to forest site 22.
Now, let's select a random sample of 5 forest sites without replacement:
1) 38
2) 35
3) 02
4) 22
5) 24
Thus, the correct answer is not listed in the given options. However, based on the consecutive pairs of digits and following the process mentioned, the sample should be 38, 35, 02, 22, and 24.
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7(x + 2) = 7x + 14 how many solutions are there
what is the general formula for the bayesian credible interval? what distribution is the critical value taken from?
Answer: p(θ|x) dθ = 1 − α.
Step-by-step explanation: the critical value is computed based on the given significance level α and the type of probability distribution of the idealized model
bianca runs a fruit store.she startied thursday with 14 pear brainlys in stock.duriiiing th eday,she sold 11 pears and goat a shipment contained 4 times as many pears as she started the day with
Answer: Bianca runs a fruit store. She started Thursday with 14 pears in stock. During the day, she sold 11 pears and got a shipment containing 4 times as many pears as she started the day with. This means that Bianca received a shipment of 14 * 4 = 56 pears. By the end of the day, Bianca had 14 - 11 + 56 = 59 pears in stock
Rick is building a sandbox for his cousins in the shape of a parallelogram. When drawn on a coordinate plane, the sandbox has vertices at (-4,0), (-2,6), (4,0), and (2,-6). If every unit represents a foot, what area does the sandbox cover?
~a.) 24ft²
~b.) 36ft²
~c.) 48ft²
~d.) 64ft²
The area of the sandbox of parallelogram shape is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are equal in length and parallel to each other. Additionally, opposite angles of a parallelogram are congruent (i.e., have the same measure).
According to the given informationWe can choose any side of the parallelogram as the base, and the distance from that side to the opposite side as the height. Let's choose the side between (-4,0) and (-2,6) as the base. The length of this side is the distance between these two points:
√[(-2-(-4))² + (6-0)²] = √40 = 2√10
The height of the parallelogram is the distance between the line containing (-2,6) and (4,0) and the point (2,-6). We can find the equation of the line containing (-2,6) and (4,0) by finding the slope and y-intercept:
Slope: (0-6)/(4-(-2)) = -6/6 = -1
Y-intercept: y = mx + b -> 0 = (-1)(4) + b -> b = 4
Therefore, the equation of the line is y = -x + 4. We can find the distance between this line and the point (2,-6) by substituting x = 2 into the equation and finding the corresponding y-value:
y = -x + 4 = -2
The distance between the line and the point (2,-6) is the absolute value of the difference between the y-coordinate of the point and the y-coordinate of the line:
|(-6) - (-2)| = 4
Therefore, the height of the parallelogram is 4 feet.
The area of the parallelogram is then:
A = base x height = (2√10) x 4 = 8√10
Rationalizing the denominator, we get:
A = 8√10 x √10/√10 = 80/√10 = 80√10/10 = 8√10
Therefore, the area of the sandbox is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².
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A recipe calls for 3 teaspoons of orange juice. A can of orange juice is 11 FL oz. How many teaspoons of juice are in the can?
So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.
what is unitary method ?A mathematical method called the unitary method is used to address proportionality-related issues. It is a technique that entails determining the value of a single unit prior to applying that value to determine the value of any quantity of units. Problems involving ratios et proportions are frequently solved using the unitary technique. The unitary approach can be used to determine the price of any quantity of apples, for instance, if 5 vegetables cost $2. We can build up a proportion to determine how much 10 apples would cost: 5 apples x $2 Equals 10 apples x. where 10 apples cost x dollars.
given
We can start by applying the conversion rule that states that 6 teaspoons (tsp) of liquid equal 1 fluid ounce (FL oz). The following is how we can convert 11 FL oz to teaspoons:
6 teaspoons per FL oz times 11 FL oz equals 66 teaspoons.
Thus, an 11 FL oz can of orange juice has 66 teaspoons of orange juice.
We can also figure out how many cans of orange juice are required for the recipe as it calls for 3 tablespoons of orange juice.
[tex]0.5 FL oz = 3 tsp * 6 tsp/FL oz[/tex]
So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.
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Can someone help me?
answer
a 17× + 5× + 16 + 7
b 22× + 23
Step-by-step explanation:
the perimeter of a shape is calculated by adding up all the the sides.
part a asks you to use all four lengths so just place them side by side with the addition sign.
in part b you are asked to simplify it so you have to add the like terms. 17× and 15x add up to 22 and 16 and 7 add up to 23.this is the simplest we can go since 22x and 23 are not like terms.
hope this helps :)
for a certain type of hay fever, medicine h has a 30% probability of working. in which distributions does the variable x have a binomial distribution? select each correct answer.
The distribution in which variable x has binomial distribution are as follow,
Option A) When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.
Option D) When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.
When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.
This variable X follows a binomial distribution .
Because there are two independent trials two patients.
With a constant probability of success 30%.
And the outcome of one trial doesn't affect the outcome of the other.
When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.
This variable X does not follow a binomial distribution.
Because the probability of success is not constant it's the complement of 30%, which is 70%.
Also, the outcome of one trial affects the outcome of the other trials.
As there are only six patients .
Number of patients for whom medicine does not work depends on number of patients for whom it worked.
When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.
This variable X follows a binomial distribution.
Because there are six independent trials six patients with a constant probability of success (30%) .
The outcome of one trial doesn't affect the outcome of the other.
When the medicine is tried with two patients, X is the number of doses each patient needs to take.
This variable X does not follow a binomial distribution.
Because it's not a count of successes out of a fixed number of independent trials.
But rather a continuous variable that can take any non-negative value.
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The above question is incomplete, the complete question is:
For a certain type of hay fever, Medicine H has a 30% probability of working.
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.
B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.
C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.
D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.
Find the base area (B), lateral area (L) and surface area (S) of the solid. Round to the
nearest tenth, if necessary.
10.4 cm
B = 96
L =
12 cm
S=
12 cm
12 cm
8 cm
cm²
cm²
cm²
The base, lateral area and surface area is B = 96 cm², L = 499.2 cm²,S = 691.2 cm²
What is Lateral Area ?The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.
To find the lateral area (L) of this solid, we need to calculate the area of the four rectangles that make up the sides of the solid. Since each rectangle has a height of 10.4 cm and a width of 12 cm, the area of one rectangle is:
A = 10.4 cm * 12 cm = 124.8 cm²
Since there are four rectangles, the total lateral area is:
L = 4 * A = 4 * 124.8 cm² = 499.2 cm²
To find the surface area (S) of the solid, we need to add the lateral area to the area of the two circular bases. The base area is given as 96 cm², so the area of both bases is:
A = 2 * 96 cm² = 192 cm²
Therefore, the total surface area is:
S = L + A = 499.2 cm² + 192 cm² = 691.2 cm²
Rounding to the nearest tenth, we have:
B = 96 cm²
L = 499.2 cm²
S = 691.2 cm²
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Help please? I just need an answer. A clear explanation earns brainliest. this is a repost since i posted the wrong photo last time.
Answer: x^2+2x-7/x-1
a random sample of 380 found that 67% of the readers owned a personal computer. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is 6.51.
The test statistic for this problem can be calculated using the formula:
z = (p - P) / √(P * (1 - P) / n)
Where p is the sample proportion (0.67 in this case), P is the hypothesized population proportion (we don't know this value, so we assume it to be 0.5 for a two-tailed test), n is the sample size (380), and z is the standard normal distribution value corresponding to the level of significance.
Plugging in the values, we get:
z = (0.67 - 0.5) / √(0.5 * (1 - 0.5) / 380) = 6.51
So the value of the test statistic is 6.51.
The test statistic is a measure of how far the sample proportion deviates from the hypothesized population proportion under the null hypothesis. In this case, we assume that the population proportion is 0.5 (since we have no reason to believe otherwise), and we calculate the probability of observing a sample proportion of 0.67 or greater assuming this null hypothesis is true.
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Find if the table is linear or quadratic or neither
For table 14, the table is neither.
Option C is correct.
For table 15, the table is neither.
Option C is correct.
How do we calculate?Table 14:
The difference between 22 and 48 is -26
The difference between 39 and 22 is 17
The difference between 40 and 39 is 1
The difference between 42 and 40 is 2
The difference between 42 and 42 is 0
Because the differences are not constant, the table is neither linear nor quadratic.
For table 15, we check if the difference in y-values is constant:
The difference between 4 and 1 is 3
The difference between 1 and 1 is 0
The difference between 0 and 1 is -1
The difference between 1 and 4 is 3
The difference between 4 and 9 is 5
The difference between 9 and 16 is 7
Because the differences between y-values are not constant, the table is neither linear nor quadratic.
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2 pints
4 quarts
gallon
gallon
1
16
8 cups
19 quart
1 gallon
B
1 quart
2
(FO
>
1 cup
(0
(W)
None
D
ee
The answer to the given question is You have a total of 40 cups.
How to solve
Convert each measurement to cups:
2 pints = 4 cups (1 pint = 2 cups)
4 quarts = 16 cups (1 quart = 4 cups)
1 gallon = 16 cups (1 gallon = 4 quarts = 16 cups)
1 quart = 4 cups
Add up the total cups:
4 cups (from 2 pints) + 16 cups (from 4 quarts) + 16 cups (from 1 gallon) + 4 cups (from 1 quart) = 40 cups
Answer: You have a total of 40 cups.
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If you have 2 pints, 4 quarts, 1 gallon, and 1 quart, how many total cups do you have?
Five balls, A, B, C, D, and E, weigh 30g, 50g, 50g, 50g, and 80g each. Which ball weighs 30g?
Answer:
Step-by-step explanation:
C
Answer:
A
Step-by-step explanation:
You want to know which ball weighs 30 g if balls A, B, C, D, E weigh 30, 50, 50, 50, 80 grams.
CorrespondenceThe given information does not say what the correspondence is between weights and ball designators. If we assume the given order is the same for designators as for weights, then the first letter corresponds to the first weight, and ...
Ball A weighs 30 g.
__
Additional comment
If there's more to the question, you'd have to use that additional information to decide.
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according to the centers for disease control and prevention, 60% of all american adults ages 18 to 24 currently drink alcohol. is the proportion of california college students who currently drink alcohol different from the proportion nationwide? a survey of 450 california college students indicates that 66% curre quizlert
the proportion of California college students who currently drink alcohol different from the proportion nationwide p0 = 0.60 (nationwide proportion from CDC)
Information provided; we can determine if the proportion of California college students who currently drink alcohol is different from the proportion nationwide by conducting a hypothesis test. Here are the steps:
The null hypothesis (H0) and alternative hypothesis (H1):
H0: The proportion of California college students who drink alcohol is the same as the nationwide proportion.
(p = 0.60).
H1: The proportion of California college students who drink alcohol is different from the nationwide proportion.
(p ≠ 0.60).
The sample proportion (p-hat), sample size (n), and the population proportion (p0):
p-hat = 0.66 (66% of the 450 California college students surveyed)
n = 450 (sample size)
p0 = 0.60 (nationwide proportion from CDC)
The test statistic (z) using the following formula:
[tex]z = (p-hat - p0) / \sqrt((p0 \times (1 - p0)) / n)[/tex]
A standard normal distribution table or calculator to find the p-value associated with the test statistic.
Compare the p-value to a predetermined significance level (α), usually set at 0.05.
- If the p-value is less than α, reject the null hypothesis (H0), suggesting that the proportion of California college students who drink alcohol is different from the nationwide proportion.
- If the p-value is greater than α, fail to reject the null hypothesis (H0), indicating that there is not enough evidence to suggest a difference between the two proportions.
Determine if the proportion of California college students who drink alcohol is significantly different from the nationwide proportion.
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