To compare the number of artists with hit songs to the total number of artists signed, write a ratio using the two numbers. The ratio of artists with hit songs (10) to total artists signed (12) simplifies to 5:6 after dividing by the greatest common factor.
Explanation:The student has asked to write a ratio comparing the number of artists with hit songs to the total number of artists signed by a music company in 2002. To do this, we take the number of artists with hit songs and place it in the numerator (top part) of the ratio and the total number of artists in the denominator (bottom part).
To write the ratio in its simplest form, we divide the numerator and the denominator by their greatest common factor if necessary. In this case, the ratio is already in the simplest form.
Step-by-Step Solution:
Number of artists with hit songs: 10
Total number of artists signed: 12
Write the ratio as 10:12
Simplify the ratio by dividing both numbers by 2, the greatest common factor, to get 5:6
So, the simplified ratio of the number of artists with hit songs to the total number of artists signed is 5:6.
(0,8) is the ONLY solution to the system of equations:
3y - 6x = 24
8 + 2x = y
True or False
Answer:
False, there are infinite solutions
Step-by-step explanation:
Try solving this
3y - 6x = 24
8 + 2x = y
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 = 24 true
11. Find mZGJK.
Ġ
(5x + 8) H
(7x-16)
Answer:
x = 2Step-by-step explanation:
To find [tex]x[/tex], we need to solve the equation
[tex]G=H[/tex]
Where [tex]G=5x+8[/tex] and [tex]H=7x-16[/tex].
Replacing expressions, we have
[tex]5x+8=7x-16\\16+8=7x+5x\\24=12x\\x=\frac{24}{12}\\ x=2[/tex]
Now, we can find the value of each expression.
[tex]G=5x+8=5(2)+8=10+8=18\\H=7x-16=7(2)-16=14-16=-2[/tex]
A circle is centered on point B. Points A, C and D lie on its circumference.
If angle ADC measures 35, what does angle ABC measure?
Answer:
70 on khan academy
Step-by-step explanation:
Applying the inscribed angle theorem, the measure of angle ABC in the circle is: 70°.
What is the Inscribed Angle Theorem?Based on the inscribed angle theorem, in a circle, measure of central angle = twice the inscribed angle.
Angle ADC is the inscribed angle = 35°
Angle ABC is the central angle = 2(measure of inscribed angle)
Angle ABC = 2(35)
Angle ABC = 70°
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4y + 1.8 = 14.7 y=
Answer:
y=1.7
Step-by-step explanation:
4y+18=14.7y
18=14.7y-4y
18=10.7y
18/10.7=10.7y/10.7
1.7=y
Need help with number 2. If you don’t know it just leave it like it is (someone literally wrote “the umm” as an answer on my previous post, just don’t)
Answer: I think it is the number of cubes you add with each layer
Step-by-step explanation:
like you add 12 cubes with each layer- so the height is multiplied by 12 btw :)
Good luck with your homework
Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded.Find the number of elements in the sample space whose outcomes are all possible sequences of three rolls of the die.(a)Find the probability of the event that exactly one of the colors that appears face up is red.Incorrect: Your answer is incorrect.(b)Find the probability of the event that at least one of the colors that appears face up is red
Answer:
Prob (Exactly one die has red) = 2/9
Prob (No die has red) = 5/9
Step-by-step explanation:
Prob (Red on a die) = 2/6 = 1/3
Prob (Blue on a die) = 2/6 = 1/3
Prob (Yellow on a die) = 2/6 = 1/3
Two die rolled :-
Prob (one die has red) =
Prob (one die has read & other die has non red, blue or yellow )
= (1/3) x (2/3) = 2/9
Prob atleast one die has red = 1 - Prob (No die has red)
= 1 - Prob (both die have non red, yellow or blue)
= 1 - [ (2/3) (2/3) ]
= 1 - 4/9 = 5/9
What size cop would someone with a head circumference of 570 mm need
La empresa de telefonía le cobra los primeros 20 minutos a $30 cada uno y los que consuma después de estos los cobra a $20 cada uno. Los cobros se hacen en cada línea independiente.
2- Si Andrea quiere saber cuánto paga el lunes puede
A. Sumar los minutos de ambas líneas y multiplicar por $30
B. Multiplicar 10 por $30, 25 por $20 y sumar los resultados.
C. Multiplicar 10 por $30, 20 por $30 y 5 por $20 y sumar los resultados
D. Sumar los minutos de ambas líneas y multiplicar por $20
La mejor forma para calcular el costo que Andrea pagará por los minutos de teléfono el lunes depende del número total de minutos hablados. Primero, multiplicar los primeros 20 minutos al precio de $30 cada uno. Después, si hubiera minutos adicionales, multiplicarlos al precio de $20 cada uno y sumar ambos montos.
Explanation:Para calcular cuánto paga Andrea por los minutos de teléfono el lunes, debemos tener en cuenta la tarifa descrita: los primeros 20 minutos se cobran a $30 cada uno, y cualquier minuto adicional es a $20. No tenemos la información sobre cuántos minutos usó en total Andrea, pero podemos evaluar las opciones dadas.
La opción B parece la más adecuada si consideramos que Andrea usó 10 minutos en una línea y 25 minutos en la otra, donde los primeros 20 minutos de ambas líneas suman 30 minutos, multiplicados por $30, y los 5 minutos restantes se multiplicarían por $20. Sin embargo, si esta fue la distribución real de los minutos debería sumarse los primeros 20 minutos de cada línea a $30 cada uno, lo que indica que tal vez la opción C seria la correcta. La opción A y D son incorrectas porque no toman en cuenta la tarifa diferenciada.
An oblique hexagonal prism has a base area of 42
square cm. The prism is 4 cm tall and has an edge
length of 5 cm.
What is the volume of the prism?
cubic centimeters
5 cm
4 cm i
Answer:
168 cm³
Step-by-step explanation:
The base area of the oblique hexagonal prism = 42 cm²
the height of the prism = 4 cm
Volume of the prism = Base area × height = 42 cm² × 4 cm = 168 cm³
The volume of the oblique hexagonal prism is 260.00 cubic centimeters. This is calculated by multiplying the base area (65.00 square cm) by the height (4 cm) using the formula Volume = Base Area × Height.
To find the volume of an oblique hexagonal prism, you can use the formula:
Volume = Base Area × Height
You're given that the base area is 42 square cm and the height is 4 cm. Now, let's determine the base shape of the hexagonal prism.
A hexagon has six sides, and each side is an equilateral triangle with an edge length of 5 cm. To find the area of one of these equilateral triangles, you can use the formula:
Area of Equilateral Triangle = (side length^2 * √3) / 4
Area of Equilateral Triangle = (5 cm^2 * √3) / 4 ≈ 10.83 square cm
Since there are six identical triangles in the hexagonal base, the total base area is:
Base Area = 6 * Area of Equilateral Triangle ≈ 6 * 10.83 square cm ≈ 65.00 square cm
Now, you can calculate the volume:
Volume = Base Area × Height
Volume = 65.00 square cm × 4 cm = 260.00 cubic cm
So, the volume of the oblique hexagonal prism is 260.00 cubic centimeters.
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What is the solution set of |–x| = 3.5?
Answer:
x = -3.5, 3.5
Step-by-step explanation:
| -x| = 3.5
x = -3.5, 3.5
Tell me if I am wrong.
Can I get brainliest
Final answer:
The solution set of the equation |–x| = 3.5 is found to be {3.5, -3.5}, considering both positive and negative values of x.
Explanation:
The solution set of |–x| = 3.5 involves considering two cases based on the absolute value:
When x is negative, the equation becomes -(-x) = 3.5, which simplifies to x = 3.5.
When x is positive, the equation remains -x = 3.5, resulting in x = -3.5.
Therefore, the solution set is {3.5, -3.5}.
Solve each triangle. Round to the nearest tenth
Answer:
5) 54.
6) 20.
Step-by-step explanation:
Does that help
Answer:
78 6 9
Step-by-step explanation:
The area of each triangular base is:
A = 1/2(b)(h)
A = 1/2(3)(4)
A = ft2
There are two bases, so total base area is ft2.
The lateral area is:
A = (12)(3) + 12(5) + 12(4)
A = ft2
The total surface area is ft2.
HURRY QUICKEST ANSWER THAT IS CORRECT GET BRAINLESET
Answer:
6 ft² — each base12 ft² — total base area144 ft² — lateral area156 ft² — total surface areaStep-by-step explanation:
You are given the formulas for computing the area of a triangular prism, along with dimension values filled in. You need only to perform the arithmetic.
Base areaThea area of each base is ...
A = 1/2(b)(h) = 1/2(3)(4) = 6 . . . . ft²
There are 2 bases, so the total base area is ...
A = 2(6 ft²) = 12 ft²
Lateral areaThe lateral area is the sum of the areas of each of the rectangular faces. For triangle sides of a, b, c, and prism height h, the lateral area is ...
A = (h)(a) +(h)(b) +(h)(c) = (12)(3) +(12)(5) +(12)(4) = 144 . . . ft²
Total areaThe total area is the sum of the base area and the lateral area:
total area = (12 ft²) +(144 ft²) = 156 ft²
Answer:
6
12
144
156
Step-by-step explanation:
A population of values has a normal distribution with μ=204.9μ=204.9 and σ=81.9σ=81.9. You intend to draw a random sample of size n=222n=222. What is the mean of the distribution of sample means? μ¯x=μx¯= (Enter your answer as a number accurate to 4 decimal places.) What is the standard deviation of the distribution of sample means? (Report answer accurate to 4 decimal places.) σ¯x=σx¯=
8)Let XX represent the full height of a certain species of tree. Assume that XX has a normal probability distribution with μ=75.9μ=75.9 ft and σ=9.6σ=9.6 ft. You intend to measure a random sample of n=181n=181 trees. What is the mean of the distribution of sample means? μ¯x=μx¯= What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 4 decimal places.) σ¯x=σx¯=
9) A population of values has a normal distribution with μ=135.7μ=135.7 and σ=88σ=88. You intend to draw a random sample of size n=59n=59. Find the probability that a single randomly selected value is greater than 117.4. P(X > 117.4) = Find the probability that a sample of size n=59n=59 is randomly selected with a mean greater than 117.4. P(¯xx¯ > 117.4) = Enter your answers as numbers accurate to 4 decimal places.
Answer:
7. μ=204.9 and σ=5.4968
8. μ=75.9 and σ=0.7136
9. p=0.9452
Step-by-step explanation:
7. - Given that the population mean =204.9 and the standard deviation is 81.90 and the sample size n=222.
-The sample mean,[tex]\mu_x[/tex]is calculated as:
[tex]\mu_x=\mu=204.9, \mu_x=sample \ mean[/tex]
-The standard deviation,[tex]\sigma_x[/tex] is calculated as:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{81.9}{\sqrt{222}}\\\\=5.4968[/tex]
8. For a random variable X.
-Given a X's population mean is 75.9, standard deviation is 9.6 and a sample size of 181
-#The sample mean,[tex]\mu_x[/tex] is calculated as:
[tex]\mu_x=\mu\\\\=75.9[/tex]
#The sample standard deviation is calculated as follows:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{9.6}{\sqrt{181}}\\\\=0.7136[/tex]
9. Given the population mean, μ=135.7 and σ=88 and n=59
#We calculate the sample mean;
[tex]\mu_x=\mu=135.7[/tex]
#Sample standard deviation:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{88}{\sqrt{59}}\\\\=11.4566[/tex]
#The sample size, n=59 is at least 30, so we apply Central Limit Theorem:
[tex]P(\bar X>117.4)=P(Z>\frac{117.4-\mu_{\bar x}}{\sigma_x})\\\\=P(Z>\frac{117.4-135.7}{11.4566})\\\\=P(Z>-1.5973)\\\\=1-0.05480 \\\\=0.9452[/tex]
Hence, the probability of a random sample's mean being greater than 117.4 is 0.9452
A mass that weighs 8 lb stretches a spring 6 in. The system isacted on by an external force of 8 sin 8t lb. If the mass is pulleddown 3 in and then released, determine the position of the mass atany time. Determine the first four times at which the velocity ofthe mass is zero.
Answer:
t= 1/8, pi/8, 2pi/8,3pi/8
Step-by-step explanation:
Given
m=(8/32) lb s^2/ft
K=8/(6/12)=16 lb/ft
Use the following equation and plug in values
mu''+ku=f(t)
1/4u''+16u=8sin8t
u''+64u=32sin8t
This equation corresponds to the following homogeneous equation
u''+64u=0
r=+/-8i
uc(t)=c1cos8t+c2sin8t
Now find the particular solution
u(t)=Atcos8t+Btsin8t
u'(t)=-8Atsin8t+Acos8t+B8tcos8t+Bsin8t
u''(t)=-8tAsin8t-64Atcos8t-8Asin8t+B8cos8t-64Btsin8t+8Bcos8t
Substitute these values into the original equation and solve for Aand B
A=-2 B=0
the particular solution is u(t)=-2tcos8t
the general solution is u=u1(t)+u(t)
u=c1cos8t+c2sin8t-2tcos8t
Use the initial conditions to solve for c1 andc2
c1+0=(1/4) 8c2-2=0
c1=(-1/4) c2=(1/4)
u=(1/4)[cos8t+sin8t-8tcos8t]
To solve the next step differentiate u
u'=-2sin8t+2cos8t-2cos8t+16tsin8t
= -2sin8t+16sin8t
= 2sin8t(8t-1)
Velocity=2sin8t(8t-1)
Set this equation equal to zero to solve for zero velocity
8t-1=0 t=1/8
t= 1/8, pi/8, 2pi/8,3pi/8
Data were collected on annual personal time (in hours) taken by a random sample of 16 women (group 1) and 7 men (group 2) employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family. The results of the test are tequals2.02 with an associated p-value of 0.0352. The correct conclusion at alphaequals0.05 is to _______.
Answer:
We reject the null hypothesis
Step-by-step explanation:
In statistical hypothesis testing, the p-value or probability value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct
Since the p value is less than a, you would reject the null hypothesis and conclude that women take more personal time than men.
Each week, copies of a national magazine are delivered to three different stores that have ordered 25 copies, 75 copies, and 120 copies, respectively. How many copies should be packaged together so that no packages need to be opened during delivery? The number of copies per package should be as large as possible
Final answer:
To find the optimal number of copies per package for delivery to three stores, we calculate the greatest common divisor of 25, 75, and 120, which is 5. Thus, copies should be packaged in groups of 5.
Explanation:
The subject of this question is Mathematics, and it seems best suited for a Middle School grade level. The problem presented is to find the largest number of copies that can be packaged together without needing to open any packages during delivery to three different stores which have ordered 25, 75, and 120 copies respectively.
The solution involves finding the greatest common divisor (GCD) of the three numbers. The GCD of 25, 75, and 120 is the largest number that divides all three without leaving a remainder. By using the Euclidean algorithm or prime factorization, we can determine that the GCD of 25, 75, and 120 is 5. Therefore, the magazine copies should be packaged in groups of 5 to ensure that no packages need to be opened during delivery and the number of copies per package is maximized.
Mr. Anderson has 4 recipes for granola. Recipe 1 A 2-column table with 3 rows is titled Recipe 1. Column 1 is labeled Honey (tablespoons) with entries 5, 10, 15. Column 2 is labeled Oats (cups) with entries 2, 4, 6. Recipe 2 A 2-column table with 3 rows is titled Recipe 2. Column 1 is labeled Honey (tablespoons) with entries 6, 10, 14. Column 2 is labeled Oats (cups) with entries 3, 5, 7. Recipe 3 A 2-column table with 3 rows is titled Recipe 3. Column 1 is labeled Honey (tablespoons) with entries 3, 6, 9. Column 2 is labeled Oats (cups) with entries 1, 2, 3. Recipe 4 A 2-column table with 3 rows is titled Recipe 1. Column 1 is labeled Honey (tablespoons) with entries 8, 10, 12. Column 2 is labeled Oats (cups) with entries 4, 5, 6. Which recipe has the greatest ratio of honey to oats?
Answer:
Recipe 3
Step-by-step explanation:
Honey to Oats ratios for the four recipes are ...
1: 5/2 = 2.5
2: 6/3 = 2.0
3: 3/1 = 3.0
4: 8/4 = 2.0
The greatest ratio of Honey to Oats is found in Recipe 3, where it is 3:1.
Recipe 3 is the answer.
just took the test.
Use the distributive property to write the following expression WITH parentheses:
6x+18
Answer:
6(x+3)
Step-by-step explanation:
6x+18
6*x + 3*6
Factor out a 6
6(x+3)
Solve the equation 1/2y - 21/4 = 35/4 for y. Identify the sequence of operations used to solve the equation.
Answer:
y = 1/28
Step-by-step explanation:
Given the expression:
½y - 21/4 = 35/4
We'll have to Multiply through with the LCM which is (2y * 4 = 8y)
(8y) ½y - (8y) 21/4 = (8y) 35/4
4 - 2y * 21 = 2y * 35
4 - 42y = 70y
4 = 70y + 42y
4 = 112y
Divide through by 112 to make y the subject.
y = 4 / 112
y = 1 / 28
Answer: y = 28
Step-by-step explanation:
Add both sides by 21/4 to cancel out the 21/4 on the left side. 1/2y = 56/4
You can rewrite the fraction 56/4 as 28/2 by dividing the numerator and denominator by 2. 1/2y = 28/2
Multiply both sides by 2 and you get y = 28
Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on.
Answer:
The sixth term;
= 16 + (6-1)4 = 16 +20 = 36
Sixth term = 36
Pattern; a = 16, d = 4
16,20,24,28,32,36...
Completed question;
Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on. describe the pattern of the sequence. How many chairs are in the 6th row?
Step-by-step explanation:
This scenario can be represented by an arithmetic progression sequence.
nth term of an AP = a + (n-1)d
Where;
a = first term
d = common difference
n = term number
Given;
First term a = 16
Second term = a + d = 20
since a = 16
a+d = 16+d = 20
d = 20-16 = 4
The sixth term;
= 16 + (6-1)4 = 16 +20 = 36
Sixth term = 36
Pattern; a = 16, d = 4
16,20,24,28,32,36...
The circumference of the inner circle is 22 ft. The distance between the inner circle
and the outer circle is 3 ft. By how many feet is the circumference of outer circle
22
greater than the circumference of the inner circle? Use 7 for it.
ft greater than the circumference of the inner circle.
The circumference of outer circle is about
(Round to the nearest tenth as needed.)
hol hornemar
Answer:
Radius of outer circle = 6.5 ft
Circumference outer circle = 40.9 ft
Step-by-step explanation:
We can find the radius of the inner circle
C = 2 * pi r
22 = 2 * pi *r
22 /2pi = 2pi r/2pi
11/pi = r
11/(22/7) =r
3.5 =r
Add 3 to get the radius of the outer circle
The radius of the outer circle is 3+3.5 = 6.5 ft
We can find the circumference of the outer circle by
C = 2*pi*r
C = 2 * 22/7 *6.5
C=40.85714286
Rounding to the nearest tenth
C = 40.9 ft
Answer:
18.9 ft
40.9 ft
Step-by-step explanation:
Circumference of the inner circle:
22 = 2 pi × r
22 = 2 × 22/7 × r
r = 7/2 = 3.5
Distance between the circles is the difference between the radii
Outer circle radius: 3.5 + 3 = 6.5
Circumference of the outer circle is:
2 × 22/7 × 6.5
40.85614286
To the nearest tenth: 40.9
Difference between the circumferences:
40.9 - 22
18.9 ft
How many solutions does this linear system have?
y=2x-5
-8x - 4y=-20
one solution: (-2.5, 0)
one solution: (25,0)
no solution
infinite number of solutions
Answer:
The solution is (0.4;-4.2). I'm not sure since my solution is none of your alternatives, but I don't think I have made any mistakes.
Step-by-step explanation:
Replace the y at the second eq.
-8x-4(2x-5)=-20
-16x+20=-20
-16x=-40
x=0.4
Therefore y equals:
2×0.4-5=-4.2
Answer:
one solution: (2.5,0)
Step-by-step explanation:
Ezra enjoys gardening.
Let SSS represent the number of sunflower plants and LLL represent the number of lily plants Ezra's water supply can water.
0.7S+0.5L \leq 110.7S+0.5L≤110, point, 7, S, plus, 0, point, 5, L, is less than or equal to, 11
Ezra waters 101010 lily plants. How many sunflower plants can he water at most with the remaining amount of water?
Answer:
8
Step-by-step explanation:
You want to know the number of sunflower plants (S) that can be watered along with 10 lily plants (L) if the water supply is described by ...
0.7S +0.5L ≤ 11
SolutionSubstituting 10 for L, we have ...
0.7S +0.5(10) ≤ 11
0.7S +5 ≤ 11
0.7S ≤ 6
S ≤ 6/0.7 ≈ 8.57
We want to count only plants that can be watered completely, so we need to round this number to the next lower integer.
Ezra can water 8 sunflower plants with the remaining water.
Answer the question bellow
Answer:
B?
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
D is not a function because for every X value, there may be more than 1 corresponding Y value past 0. For instance, if you input x=1 into this function, you get both 2 and -2, which does not make this a proper function.
45 POINTS PLZ ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x = 3/4 x 21
Step-by-step explanation:
Answer:
I believe it is #2:
x = 3/4 × 21.
What is the surface area of this rectangular pyramid?
4 mm
5 mm
5 mm
square millimeters
To calculate the surface area of a rectangular pyramid, you need to find the base area and the areas of the triangular faces, then sum them up. In this case, the surface area of the given rectangular pyramid is 65 square millimeters.
The surface area of a rectangular pyramid is calculated by adding the base area to the sum of the areas of the four triangular faces.
Find the base area: Base area = length x width = 5 mm x 5 mm = 25 mm².Find the area of each triangular face: Use the formula A = 0.5 x base x height. Given dimensions, calculate the area of one triangle: A = 0.5 x 4 mm x 5 mm = 10 mm².Calculate the total surface area by summing base area and 4 times the area of one triangle: Total surface area = 25 mm² + 4(10 mm²) = 65 mm². Therefore, the surface area of the rectangular pyramid is 65 square millimeters.The cross section of a water bin is shaped like a trapezoid. The bases of the trapezoid are 21 feet and 5 feet long. It has an area of 26 square feet. What is the height of the cross section?
Answer:
2 feet
Step-by-step explanation:
We are given that
[tex]b_1=21 feet[/tex]
[tex]b_2=5feet[/tex]
Area of trapezoid=26 square ft
We have to find the height of the cross section.
We know that
Area of trapezoid=[tex]\frac{1}{2}(b_1+b_2)h[/tex]
Using the formula
[tex]26=\frac{1}{2}(21+5)[/tex]
[tex]26=\frac{1}{2}(26)h[/tex]
[tex]h=\frac{26\times 2}{26}=2 feet[/tex]
Hence, the height of cross section =2 feet
A cut piece of ribbon is 21 inches long. The piece of ribbon is 15% of the original length of the ribbon.
How long was the original length of ribbon?
Answer:
The original length of the rope is 140
Step-by-step explanation:
21x (100/15)
Answer:
140
Step-by-step explanation:
.
A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.
The test statistic for comparing men and women's attitudes towards sexual discrimination is calculated using the formula for the Z test for two proportions. You use the proportion of men and women who believe it's a problem and the totals for each group to calculate the test statistic.
Explanation:The question deals with the comparison of attitudes towards sexual discrimination between men and women, using hypothesis testing for two proportions. In this scenario, the null hypothesis (H0) would state that the proportion of men (p1) who believe sexual discrimination is a problem is equal to the proportion of women (p2) who believe the same. The alternative hypothesis (H1) suggests that the proportions differ (p1 != p2).
The test statistic for two proportions is calculated as follows:
Z = (p1 - p2) / sqrt(P(1-P)(1/n1 + 1/n2))
where p1 = 11/50, p2 = 19/40, P = (11+19)/(50+40), n1 = 50, n2 = 40.
First, calculate the sample proportions:
p1 = 11/50 = 0.22p2 = 19/40 = 0.475Next, calculate the combined proportion:
P = (11+19)/(50+40) = 30/90 = 1/3Now calculate the standard error:
SE = sqrt((1/3)*(2/3)*(1/50 + 1/40))Finally, calculate the Z value:
Z = (0.22 - 0.475) / SEAfter performing the calculations, you would obtain the value of the test statistic, which is needed to determine if the belief in sexual discrimination as a problem significantly differs between men and women.
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a punter kicks a football. Its height, h(t), in metres, t seconds after the kick is given by the equationh (t)=−4.9t2+18.24t+0.8. The height of an approaching blocker’s hands is modelled by the equationg (t)=−1.43t+4.26, using the same t. Can the blocker knock down the punt.
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Answer:
Yes
Step-by-step explanation:
−4.9t² + 18.24t + 0.8 = −1.43t + 4.26
-4.9t² + 19.67t - 3.46 = 0
4.9t² - 19.67t + 3.46 = 0
Using quadratic formula:
t = [19.67 +/- sqrt(319.0929l)]/9.8
t = (19.67 +/- 17.8631716109)/9.8
t = 3.8299154705, 0.1843702438
Since the two can be at the same height at the same time, the blocker can knock down the punt
Yes, the blocker can block down the punt.
To determine whether the blocker can knock down the punt, compare the heights of the football and the blocker’s hands at the same time t. The equations for the height of the football h(t) and the height of the blocker’s hands g(t) are given as follows:
[tex]h(t)=-4.9t^2+18.24t+0.8[/tex]
[tex]g(t)=-1.43t+4.26[/tex]
For the blocker to knock down the punt, the heights must be equal at some time t. Therefore, solve for t when h(t) = g(t):
[tex]-4.9t^2+18.24t+0.8=-1.43t+4.26[/tex]
First, move all terms to one side of the equation to set it to zero:
[tex]-4.9t^2+18.24t+0.8+1.43t-4.26=0[/tex]
Combine like terms:
[tex]-4.9t^2+19.67t-3.46=0[/tex]
This is a quadratic equation of the form [tex]ax^2+bx+c[/tex], where:
a=−4.9, b=19.67, c=−3.46
We can solve this quadratic equation using the quadratic formula:
[tex]t=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values of a, b, and c:
[tex]t = \frac{-19.67\pm\sqrt{(19.67)^2-4(-4.9)(-3.46)} }{2(-4.9)}=\frac{-19.67 \pm \sqrt{386.909 - 67.816} }{-9.8}=\frac{-19.67\pm\sqrt{319.903} }{-9.8}[/tex]
[tex]t = \frac{-19.67\pm 17.89 }{-9.8}[/tex]
Now solve for both possible values of t:
[tex]t_1 = \frac{-19.67+17.89}{-9.8} = \frac{-1.78}{-9.8} \approx 0.18\ seconds[/tex]
[tex]t_2 = \frac{-19.67-17.89}{-9.8} = \frac{-37.56}{-9.8} \approx 3.83\ seconds[/tex]
Next, check if these times are within the reasonable range for a football to stay in the air. Since 0.186 seconds and 3.83 seconds are within a typical range for a football's hang time, let's proceed to compare the heights at these times.
For t = 0.186 seconds:
[tex]h(0.186)=-4.9(0.18)^2+18.24(0.18)+0.8[/tex]
[tex]h(0.18) = -4.9(0.0324)+3.2832+0.8[/tex]
[tex]h(0.18)= -0.15876+3.2832+0.8 = 3.92444\ meters[/tex]
[tex]g(0.18)=-1.43(0.18)+4.26[/tex]
[tex]g(0.18) = -0.2574+4.26 = 4.0026[/tex]
For t = 3.83 seconds:
[tex]h(3.83)=-4.9(3.83)^2+18.24(3.83)+0.8[/tex]
[tex]h(3.83)=-4.9(14.6689)+69.8592+0.8[/tex]
[tex]h(3.83)=-71.8781+69.8592+0.8 = -2.0189+0.8=-1.2189\ meters[/tex]
[tex]g(3.83)=-1.43(3.83)+4.26[/tex]
[tex]g(3.83)=-5.4769+4.26[/tex]
[tex]g(3.83)=-1.2169\ meters[/tex]
Since at t = 0.186 seconds, the heights h(0.186) and g(0.186) are nearly equal and are positive, the blocker can knock down the punt at t around 0.186 seconds.