Answer:
a) -0.94
b) 0.3472
c) -2.327, 2.327
Step-by-step explanation:
A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5.
At the null hypothesis, we test if the proportion is of 0.5, that is:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, we test if the proportion is different from 0.5, that is:
[tex]H_1: p \neq 0.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.5 is tested at the null hypothesis:
This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5[/tex]
A random sample of 551 children aged 6-10 showed that 48% of them play a sport.
This means that [tex]n = 551, X = 0.48[/tex]
(a) Calculate the value of the test statistic used in this test.
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{551}}}[/tex]
[tex]z = -0.94[/tex]
So the answer is -0.94.
(b) Use your calculator to find the P-value of this test.
The p-value of the test is the probability that the sample proportion differs from 0.5 by at least 0.02, which is P(|z| > 0.94), which is 2 multiplied by the p-value of Z = -0.94.
Looking at the z-table, z = -0.94 has a p-value of 0.1736.
2*0.1736 = 0.3472, so 0.3472 is the answer to option b.
(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level.
Two-tailed test(test if the mean differs from a value), Z with a p-value of 0.02/2 = 0.01 or 1 - 0.01 = 0.99.
Looking at the z-table, this is z = -2.327 or z = 2.327.
A function does not have any x-intercepts. What
might be true about its domain and range?
The domain exists on all real numbers i.e {x∈R}∈
The range exists all on real numbers except at y = 0
Domains are all input values of a function for which the function exists while ranges are all the output values for which the function exists.
Since the x-intercept of a function exists at where y = 0, this means that the point where a function does not have any x-intercepts are all other points on the graph except at y = 0.
The following statements are therefore true;
The domain exists on all real numbers i.e {x∈R}The range exists all on real numbers except at y = 0Learn more here: https://brainly.com/question/12648810
The vertex form of the equation of a vertical parabola is given by , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra. Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part F
What is the value of p for your parabola?
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Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
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Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
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Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
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Part J
To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:
focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.
Answer:
Step-by-step explanation:
Focus: (6,4)
Directrix lies 6 units below the focus, so the parabola opens upwards and focal length p = 6/2 = 3.
The equation of the directrix is y = -2.
The vertex is halfway between focus and directrix, at (6,1).
Equation of the parabola:
y = (1/(4p))(x-6)²+1 = (1/12)(x-6)²+1
The equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
What are parabolas?Parabolas are used to represent a quadratic equation in the vertex form
The given parameters are:
Focus = (6,4)
Directrix (x) = 6 units below the focus,
Start by calculating the focal length (p)
[tex]p = \frac x2[/tex]
This gives
[tex]p = \frac 62[/tex]
[tex]p = 3[/tex]
Next, calculate the vertex as follows:
[tex](h,k) = (6,2/2)[/tex]
Simplify
[tex](h,k) = (6,1)[/tex]
The equation of the parabola is then calculated a:
[tex]y = \frac{1}{4p}(x - h)^2 + k[/tex]
So, we have:
[tex]y = \frac{1}{4*3}(x - 6)^2 + 1[/tex]
Simplify
[tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Hence, the equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Read more about parabola at:
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Find the area AND perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
a=40+8pi, p=4pi+4(sqrt of 29)
Step-by-step explanation:
rsm geometry class 122?
The tires Mary wants to buy for her car cost $100 per tire. A store is offering the following deal. Buy a tire and get the 4th tire for 75% off! Mary will buy 4 tires using the deal. A sales tax of 8% will be charged after applying the discount. How much money will Mary saveby using the deal instead of paying the full price for all 4 tires?
she saved $162
hope it helps
Is x - 0.30x equivalent to 0.70x?
hi
it's equal to as X = 1X
so 1X-0.3X = 0.7X
Answer:
yes
Step-by-step explanation:
as
x - 0.3x = 1×x - 0.3x = (1-0.3)x = 0.7x
What is the constant of proportionality between y and x in the graph?
Answer:
4
Step-by-step explanation:
Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4
How many prime numbers are there between 1 to 100? a) 17 b) 25 c) 32 d) None of these
Answer:
b)25
Step-by-step explanation:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
The least-squares regression equation
y = 3 + 1.16x can be used to predict the height of a plant (in centimeters) after x weeks. Suppose the height of a plant was 9.2 centimeters after 5 weeks.
Calculate and interpret the residual for this plant after 5 weeks.
The residual is
✔ 0.4
, which means that the predicted height of the plant is
✔ 0.4 centimeters less
than the actual height of the plant of
✔ 9.2
centimeters.
Answer:
✔ 0.4
✔ 0.4 centimeters less
✔ 9.2
1.16(5) + 3 = 8.8
9.2 - 8.8 = .4
ED2021
The residual is 0.4
What is regression?
'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'
According to the given problem,
y = 3 + 1.16x
After 5 weeks, x = 5,
⇒ y = 3 + 1.16(5)
⇒ y = 3 + 5.8
⇒ y = 8.8
Now subtracting y from actual height of plant,
⇒ 9.2 - 8.8
= 0.4
Hence, we can conclude the residual to be 0.4.
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Find the greatest common factor of these two expressions.
14w5y8x2 and 7w6x2
Answer:
[tex]7w^{5}x^{2}[/tex]
Step-by-step explanation:
We can start by looking at each variable and and constant separately. In the first one, the constant part is 14 and in the second its 7. We can notice that the GCF of these two is 7. Next we have the part with w. The first one is w^5 while the second is w^6. We can notice that we can factor w^5 out of both, so it is the GCF. We can notice that only the first one has a y, so we can ignore it since it is not in common with both expressions. Lastly, we have x: the first has x^2 and the second has x^2 as well. They are the same, so the GCF would just be x^2.
Now, we can multiply the results together to get the GCF of the whole expressions:
7 * w^5 * x^2 = [tex]7w^{5}x^{2}[/tex]
a can do a piece of work in 10 days and B can do in 15 days in how many days would they finish the work if they do it
A can do a piece of work in 10 days and B can do it 15 days. If both of them are working together, half of the work can be finished in?
Here we find,LCM of 10 and 15 is 30.
A can do ( 1 /10 th ) of the work in one day Or, ( 3/30th ).B can do ( 1/15th ) of the work in one day ( or 2/30th ).Working together, A and B can do
= (3/30) + (2/30) = 5/30= 1/6 th of the work in one day.So, they would require 30/5 or 6 days to complete the task.
!!I NEED THE ANSWER PLS!!
Which of the following represents the divisor and the dividend for the
synthetic division problem below?
- 3/ 2 4 -4 6
A. -3 and -2x2 - 4x2 + 4x-6
B. x+3 and -2x2 - 4x +47-6
C. X+3 and 2x + 4x2 - 4x+6
D. *-3 and 2x2 + 4x2 - 4x+6
Answer:
B
Step-by-step explanation:
B . x+3 and -2x2 - 4x +47-6
B . x+3 and -2x2 - 4x +47-6
The divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
What is synthetic division?"It is a way of dividing one polynomial by another polynomial of first degree."
What is dividend?"The value that is divided by another value to get the result. "
What is divisor?"The value that divides another number either completely or with a remainder."
For given question,
We have been given a synthetic division problem.
- 3/ 2 4 -4 6
We need to represent the divisor and the dividend for the given synthetic division problem.
We know that, to perform synthetic division, here are the steps:
- The leading coefficient of the divisor should also be 1.
- Express the dividend in standard form.
- Write the leading coefficient in the dividend.
- Place the product of the number you brought down and the number in the division box in the preceding column.
- Write the result at the bottom of the row.
So, the divisor of the given synthetic division form would be,
x - (-3) = x + 3
And the dividend of the given synthetic division form would be,
There are four leading coefficient.
This means the dividend polynomial must be of degree 3.
From the leading coefficients 2 4 -4 6
[tex]2x^3+4x^2-4x+6[/tex]
Therefore, the divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
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Please find the volume
Answer:
27/4 units^3
Step-by-step explanation:
V= area of the base × length
V= 3 3/8 × 2
= 27/4 units^3
Answer:
6 1/4 units ^3
Step-by-step explanation:
The volume is given by
V = Bh where B is the area of the base and h is the height
V = 3 3/8 *2
Changing to improper fractions
V = (8*3+3)/8 *2
= 27/8 *2
= 27 * 2/8
=27/4
Changing back to a mixed number
= 6 1/4
correct answer gets brainliest!
find two expressions whose difference is 3x + 4
Answer:
(7x+4) and (4x)
Step-by-step explanation:
The two expressions are (7x+4) and (4x)
Solve this inequality: 4x-8>-40
Answer:
x > - 8
Step-by-step explanation:
4x - 8 > - 40
4x > - 40 + 8
4x > - 32
Divide 4 on both sides,
4x / 4 > - 32 / 4
x > - 8
All quesions please. As fast as possible would be nice
Answer:
Vhjaakkjvvkllmn aar
Step-by-step explanation:
Vbkisavn
Vhikjsqiol
NG Jill quolk
Hill s njknbn
Look at the image for the question?
Answer:
Surface area = the sum of the area of all six sides:
(11 · 10) + (11 · 10) + (11 · 8) + (11 · 8) + (8 · 10) + (8 · 10)
= 110 + 110 + 88 + 88 + 80 + 80
= 220 + 176 + 160
= 556 ft²
Answer:
556 ft^2
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(lw+wh+lh) where h is the height l is the length and w is the width
SA = 2( 11*10+10*8+11*8)
= 2(110+80+88)
=2(278)
=556 ft^2
Find the value of x.
x
9
9
7
x = [?]
Answer:
14
Step-by-step explanation:
Find the output, hhh, when the input, ttt, is 353535.
h = 50 - \dfrac{t}{5}h=50−
5
t
h, equals, 50, minus, start fraction, t, divided by, 5, end fraction
h=
9514 1404 393
Answer:
43
Step-by-step explanation:
Put the value where t is and do the arithmetic.
h = 50 -t/5
h = 50 -35/5 = 50 -7 = 43
The output, h, is 43 when the input is 35.
Answer:
43
Step-by-step explanation:
The answer is 43 on Khan :)
Sarah has two similar rectangular boxes. The dimensions of Box 1 are four times those of Box 2.
How many times greater is the surface area of Box 1 than the surface area of Box 2?
8
64
4
16
Answer:
16
Step-by-step explanation:
an area is always calculated by multiplying 2 dimensions.
when changing the dimensions, then the change factors for EACH dimension go into the calculation too.
therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.
this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.
just think
16×a + 16×b + 16×c ... = 16×(a+b+c+...)
and you understand why.
graph the inaquality 16>_w
Answer:
A graph is below.
Step-by-step explanation:
Which sequence is arithmetic?
O 2, 6, 18, 54, ...
O 3, 6, 12, 24, ...
O 11, 14, 17, 20, ...
O 7, 11, 13, 18, ...
Answer:
11, 14, 17, 20, ...
Step-by-step explanation:
An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.
(g o f)(6)
A. Find f(6)
B. Substitute the value you found in part A into g(x) to find g(f(6))
Step-by-step explanation:
A. gof=g(f(x))
= g(f(6))
=6×6
36
please help me with this
Given:
d = 2
f = 4
To find:
Value of [tex]\frac{14(7)-d}{2f}[/tex]
Steps:
we need to substitute and then find the value,
[tex]= \frac{14(7)-2}{2(4)}\\ \\=\frac{98-2}{8} \\\\=\frac{96}{8}\\\\=12[/tex]
Therefore, the answer is option C) 12
Happy to help :)
If you need help, feel free to ask
Describe how to find the domain of a square root function just by looking at the function.
Answer:
Step 1: Set the expression inside the square root greater than or equal to zero. Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol. Step 3: Write the answer using interval notation.
help me by using formula how did came by reason
Answer:
angleABC=isosceles triangle
angleB=(180-50)÷2=65
angle B=angleX(alternative angle)
angleB=65degree
Does anyone know this?
Answer:
the first term is -4
the difference is 3.
*notice how each term increases by 3:
-4 + 3 = -1
-1 + 3 = 2
2 + 3 = 5
Step-by-step explanation:
With a two dimensional surface, if we take (2, 1) as the center point and consider
a transformation with a rotation angle of 45◦, then point (3, 3) is transformed
into point (----)?
Answer:
Step-by-step explanation:
Distance between (2,1) and (3,3) = √5
parametric equations for circle of radius √5, centered at (2,1):
x = √5cosθ+2
y = √5sinθ+1
At (3,3), θ = arccos(1/√5) ≅ 63.4°
After 45° transformation:
θ' = 63.4° + 45° = 108.4°
x' = √5cos(108.4°)+2 = 1.29
y' = √sin(108.4°)+1 = 3.12
(3,3) transformed to (1.29,3.12)
Write an algebraic expression for each person’s share, if P people share 16 slices of pizza equally.
Answer:
P /16
Step-by-step explanation:
Take the total amount, P and divide by the number of people sharing, 16
P /16
Phân loại theo kiểu bố trí (cấu trúc) của mẫu sổ kế toán không gồm sổ nào trong các sổ dưới đây
Answer:
I I want everything in English
Step-by-step explanation:
it is difficult to read other languages write it in English please
The point p=(2/5,y) lies on the unit circle below what is the value of y in simplest form
Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
