Answer:
yes it is little different from the confidence interval (30.4 ≤μ≤ 32.8) changes statistics
90% confidence interval estimate of the mean is
(30.1048 , 33.0952)
Step-by-step explanation:
Step(I):-
Given sample size 'n' = 153
Given mean of the sample x⁻ = 31.5
Sample standard deviation 'S' = 7.1 h g
90% confidence interval estimate of the mean is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 153-1 =152
t₀.₀₅ =1.9757
Step(ii)
90% confidence interval estimate of the mean is
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
[tex](31.5 - 1.9757 } \frac{7.1}{\sqrt{153} } , 31.5 + 1.9757 \frac{7.1}{\sqrt{153} } )[/tex]
( 31.5 - 1.1340 , 31.5 + 1.1340)
(30.366 , 32.634)
90% confidence interval estimate of the mean is
(30.4 , 32.6)
b)
Given sample size 'n' = 15
Given mean of the sample x⁻ = 31.6
Sample standard deviation 'S' = 2.7 h g
90% confidence interval estimate of the mean is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 15-1 =14
t₀.₀₅ =2.1448
90% confidence interval estimate of the mean is
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
[tex](31.6 - 2.1448 } \frac{2.7}{\sqrt{15} } , 31.6 + 2.1448 \frac{2.7}{\sqrt{15} } )[/tex]
( 31.6 - 1.4952 , 31.6 + 1.4952)
(30.1048 , 33.0952)
Conclusion:-
yes it is little different from the confidence interval (30.4 ≤μ≤32.8)
The sum of two odd integers is an even integer.
1. True
2. False
Answer:
True.
Step-by-step explanation:
Try out some numbers:
3 + 3 = 6
5 + 5 = 10
11 + 11 = 22
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM. W(5,1), X(1,7), Y(9,9), and Z(11,7) O(10,1), P(6,7), Q(14,9), and R(16,7) S(4, 16), T(10, 20), U(12, 12), and V(10, 10) A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10) E(5,6), F(1,12), G(9,14), and H(11,12) a translation 2 units right and 3 units down arrowRight a translation 3 units left and 2 units up arrowRight a translation 3 units down and 3 units left arrowRight a sequence of reflections across the x- and y-axes, in any order arrowRight
Answer:
See Explanation
Step-by-step explanation:
Given:
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10).
(a)If we translate quadrilateral JKLM 3 units down and 3 units left:
(x-3,y-3), we obtain: W(5,1), X(1,7), Y(9,9), and Z(11,7)
Therefore, we match it with: A translation 3 units down and 3 units left
(b)If we translate quadrilateral JKLM 2 units right and 3 units down:
(x+2,y-3), we obtain: O(10,1), P(6,7), Q(14,9), and R(16,7)
Therefore, we match it with:A translation 2 units right and 3 units down
S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
(c) If we transform quadrilateral JKLM by a sequence of reflections across the x- and y-axes, in any order, we obtain:
A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10)
(d)If we translate quadrilateral JKLM 3 units left and 2 units up:
(x-3,y+2), we obtain:E(5,6), F(1,12), G(9,14), and H(11,12)
Therefore, we match it with: A translation 3 units left and 2 units up
(e)S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
No suitable transformation is found from JKLM to STUV.
Answer:
a translation 3 units down and 3 units left
W(5,1), X(1,7), Y(9,9), and Z(11,7)
a translation 2 units right and 3 units down
O(10,1), P(6,7), Q(14,9), and R(16,7)
a sequence of reflections across the
x- and y-axes, in any order
S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
a translation 3 units left and 2 units up
E(5,6), F(1,12), G(9,14), and H(11,12)
Given h(x)=5x-5, find h(2)
Answer:
5
Step-by-step explanation:
h(2)=5(2)-5
5 x 2 = 10
10 - 5 = 5
The value of the function h(x) = 5x - 5 at x = 2 will be 5.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The function is given below.
h(x) = 5x - 5
Then the value of the function at x = 2 will be
h(2) = 5 (2) - 5
h(2) = 10 - 5
h(2) = 5
The value of the function h(x) = 5x - 5 at x = 2 will be 5.
More about the value of expression link is given below.
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One number is 5 more than another. The difference between their squares is 105. What are the numbers?
Answer: 8 & 13
Step-by-step explanation:
13 squared is 169 and 8 squared is 64, and the difference of those two squares would be 169 - 64 = 105. Hope this helps!
No clue how to graph this any help would be greatly appreciated
Answer:
First, you can graph the y-intercept. The y-intercept would be (0,3) or in your equation, the number 3. Next, you could create a table by substituting values for x such as 1, 2, 3, or 4. This will give you easy numbers to graph. Instead of creating a table, perhaps you want to graph this by plotting the slope. Since the slope is 3/2, is means that it is going up, because the number is positive. An easy way to start would be starting at your y-intercept, (0,3), you could go two to the right and three up. That is a point. Then you could go the way down; two to the left and three down. Finally, you can draw a line connecting the points together.
I hope this helped you! Have a great rest of your day!
Calculate the slope of a line passing through point A at (2, 1) and point B at (4, 2). Calculate to one decimal place.
Answer: 0.5
Step-by-step explanation:
To find the slope of a line with two given points, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
[tex]m=\frac{2-1}{4-2}=\frac{1}{2}=0.5[/tex]
The slope is 0.5.
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective components is at most .10. The distributor decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2. Let X denote the number of defective components in the sample. What is the distribution of X? Justify your answer.
Required:
What is the probability that the batch will be accepted when the actual proportion of defectives (p) is:_______
a, 0.01
b. 0.05
c. 0.10
d. 0.20
e. 0.25
Answer:
c. 0.10
Step-by-step explanation:
Hello!
To accept a batch of components, the proportion of defective components is at most 0.10.
X: Number of defective components in a sample of 10.
This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)
The distributor will accept the batch if at most two components are defective, symbolically:
P(X≤2)
Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2
P(X≤2)= 0.9298
I hope this helps!
which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answer:
Measuring it with a ruler and jotting down the length.
Step-by-step explanation:
If you are copying a line segment, the best way to copy it perfectly is to take the measure of the original line segment and copy down the measurement and then construct the other line segment to the exact measure.
Answer:
Brianlliest!
Step-by-step explanation:
you must measure the current line segment and copy it with the same length and make a new one
The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498.a. To perform this study, we should form a null hypothesis stating that the average is ______________ 100,000. (Please fill in only one of the following: "less than", "less than or equal to", "equal to", "greater than", "greater than or equal to". Please do not use symbols.)b. At the 10% significant level, the p-value/statistics is _____________________ (Please keep three decimal points) so we should __________________ the null hypothesis (Please only fill in "reject" or "not reject".).c. Hence, we may conclude that the average _________________ increased (Please only fill in "has" or "has not") and the probability that our conclusion is correct is at least _________________ percent.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ equal to 100000
For the alternative hypothesis,
H1: µ greater than 100000
This is a right tailed test
Since the population standard deviation is nit given, the distribution is a student's t.
Since n = 200
Degrees of freedom, df = n - 1 = 200 - 1 = 199
t = (x - µ)/(s/√n)
Where
x = sample mean = 103157
µ = population mean = 100000
s = samples standard deviation = 27498
t = (103157 - 100000)/(27498/√200) = 1.62
We would determine the p value using the t test calculator.
p = 0.053
Alpha = 10% = 0.1
Since alpha, 0.1 > than the p value, 0.053, then
b) At the 10% significant level, the p-value/statistics is 0.053, so we should not reject the null hypothesis.
c) Hence, we may conclude that the average has not increased and the probability that our conclusion is correct is at least 90 percent.
Solve each equation.
13x+9] = 30
12x+ 1 = -13
|X+2+4= 11
x = 5
x = 7
O x = 1, -19
no solution
0 x = -7
no solution
o
no solution
O x=-14, 12
Ox=5,-9
OX= 7, -11
O x = 7, -13
O x= -7,6
DONE
DONE
DONEM
Answer:
13x+9=30
13x=30+9
13x=39
divide both sides by 13
x=3
12x+1=-13
12x=-13-1
12x=-14
divide both sides by 12
x=7/6
x+2+4=11
x+6=11
x=11_6
x=5
The solution {x} for each function is -
{x} = 21/13{x} = -7/6{x} = 5What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to solve each of the functions given.
.
{ 1 } -
13x + 9 = 30
13x = 21
{x} = 21/13
{ 2 } -
12x + 1 = - 13
12x = - 14
x = -14/12
{x} = -7/6
{ 3 } -
x + 2 + 4= 11
x = 11 - 2 - 4
{x} = 5
Therefore, the solution {x} for each function is -
{x} = 21/13{x} = -7/6{x} = 5To solve more questions on functions, visit the link below-
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For the rational function f(x)=x-2/3x^2+x-2, solve f(x)=2
Answer:
When f(x) = 2, x = 1/2, -2/3
Step-by-step explanation:
Step 1: Set equation equal to 2
[tex]2 = \frac{x-2}{3x^2 +x -2}[/tex]
Step 2: Multiply both sides by denominator
2(3x² + x - 2) = x - 2
Step 3: Distribute
6x² + 2x - 4 = x - 2
Step 4: Isolate everything to one side
6x² + x - 2 = 0
Step 5: Factor
(2x - 1)(3x + 2) = 0
Step 6: Find roots
x = 1/2, -2/3
Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of $176.47 on groceries, $78.66 for phone, and $62.37 on gas. Estimate his monthly total for groceries, phone, and gas by first rounding to the nearest $10.
Answer:
Yearly budget= $3840
Monthly budget= $320
Step-by-step explanation:
His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.
For groceries= $176.47
Round off=$ 180.00
For phone =$ 78.66
Round off = $80.00
For gas = $62.37
Round off= $60.00
His total round off = $180+$80+$60
His total round off = $320
Before the round off, his total spending was $176.47+$78.66+$62.37
= $317.5
So his monthly budget should be $320
And yearly budget =$ 320*12
Yearly budget= $3840
The profit, in thousands of dollars, from the sale of x thousand candles can be estimated by P(x) = 5 x - 0.7 x ln x.
1) Find the marginal profit, P'(x).
2) Find P'(10), and explain what this number represents. What does P'(10) represent?
A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
B. The additional profit, in thousands of dollars, when 10,000 candles are sold.
C. The additional cost, in thousands of dollars, to produce a thousand candles once 10,000 candles have already been sold.
D The additional cost, in thousands of dollars, to produce 10,000 candles.
C. How many thousands of candles should be sold to maximize profit?
1) The marginal profit is [tex]4.3 - 0.7 ln(x)[/tex].
2) The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
Thus, option (A) is correct.
C) To maximize profit 462,481 thousands of candles should be sold.
Given: [tex]P(x) = 5 x - 0.7 x[/tex] [tex]{\text}ln x.[/tex]
1) Take the derivative of the profit function P(x) with respect to x.
P(x) = 5x - 0.7x ln(x)
To find P'(x), differentiate each term separately using the power rule and the derivative of ln(x):
[tex]P'(x) = 5 - 0.7(1 + ln(x))[/tex]
= [tex]5 - 0.7 - 0.7 ln(x)[/tex]
= [tex]4.3 - 0.7 ln(x)[/tex]
2) Substitute x = 10 into the derivative:
P'(10) = 4.3 - 0.7 ln(10)
= 4.3 - 0.7(2.30259)
= 4.3 - 1.61181
= 2.68819
Therefore, the additional profit for selling a thousand candles once 10,000 candles have already been sold.
Thus, option (A) is correct.
C) Set P'(x) = 0 and solve for x:
[tex]4.3 - 0.7 ln(x) = 0[/tex]
[tex]0.7 ln(x) = 4.3[/tex]
[tex]{\text} ln(x) = 4.3 / 0.7[/tex]
[tex]{\text} ln(x) = 6.14286[/tex]
[tex]x = e^{6.14286[/tex]
[tex]x = 462.481[/tex]
Therefore, 462,481 thousands of candles should be sold.
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1) The marginal profit, P'(x), is -0.7ln(x) + 4.3.
2) The number of thousands of candles that should be sold to maximize profit is approximately 466.9.
1) To find the marginal profit, P'(x), we need to take the derivative of the profit function, P(x), with respect to x. Using the power rule and the chain rule, we can differentiate the function:
P(x) = 5x - 0.7x ln(x)
Taking the derivative with respect to x:
P'(x) = 5 - 0.7(ln(x) + 1)
Simplifying:
P'(x) = 5 - 0.7ln(x) - 0.7
P'(x) = -0.7ln(x) + 4.3
2) To find P'(10), we substitute x = 10 into the marginal profit function:
P'(10) = -0.7ln(10) + 4.3
Using a calculator, we can evaluate this expression:
P'(10) ≈ -0.7(2.3026) + 4.3 ≈ -1.6118 + 4.3 ≈ 2.6882
The value of P'(10) is approximately 2.6882.
Now, let's interpret what P'(10) represents:
The correct interpretation is A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
P'(10) represents the rate at which the profit is changing with respect to the number of candles sold when 10,000 candles have already been sold. In other words, it measures the additional profit (in thousands of dollars) for each additional thousand candles sold once 10,000 candles have already been sold.
Lastly, to determine the number of thousands of candles that should be sold to maximize profit, we need to find the critical points of the profit function P(x). This can be done by setting the derivative P'(x) equal to zero and solving for x.
-0.7ln(x) + 4.3 = 0
-0.7ln(x) = -4.3
ln(x) = 4.3 / 0.7
Using properties of logarithms:
x = e^(4.3 / 0.7)
Using a calculator, we can evaluate this expression:
x ≈ e^(6.1429) ≈ 466.9
for such more question on marginal profit
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Choose the name of the highlighted part of the figure.
O A.
side
OB.
Vertex
O c. angle
In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz at all, and decides to randomly guess the answers. Find the probabilities of each of the following events:
a. The first question she gets right is the 3rd question?
b. She gets exactly 3 or exactly 4 questions right?
c. She gets the majority of the questions right?
Answer:
a [tex]\mathbf{P(X=3)=0.1406}[/tex]
b [tex]\mathbf{\[P\left( {X = 3 \ or \ 4 } \right) = 0.1025}[/tex]
c [tex]\mathbf{\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.1035}[/tex]
Step-by-step explanation:
Given that:
In a multiple choice quiz:
there are 5 questions
and 4 choices for each question (a, b, c, d)
let X be the correctly answered question = 1 answer only
and Y be the choices for each question = 4 choices
The probability that Robin guessed the correct answer is:
Probability = n(X)/n(Y)
Probability = 1//4
Probability = 0.25
The probability mass function is :
[tex]P(X=x)=0.25 (1-0.25)^{x-1}[/tex]
We are to find the required probability that the first question she gets right is the 3rd question.
i.e when x = 3
[tex]P(X=3)=0.25 (1-0.25)^{3-1}[/tex]
[tex]P(X=3)=0.25 (0.75)^{2}[/tex]
[tex]\mathbf{P(X=3)=0.1406}[/tex]
b) Find the probability that She gets exactly 3 or exactly 4 questions right
we know that :
n = 5 questions
Probability P =0.25
Let represent X to be the number of questions guessed correctly i,e 3 or 4
Then; the probability mass function can be written as:
[tex]\[P\left( {X = x} \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\x\\\end{array}} \right){\left( {0.25} \right)^x}{\left( {1 - 0.25} \right)^{5 - x}}\][/tex]
[tex]P(X = 3 \ or \ 4)= P(X =3) +P(X =4)[/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\3\\\end{array}} \right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \left( {\begin{array}{*{20}{c}}\\5\\\\4\\\end{array}} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \dfrac{5!}{3!(2)!}\right){\left( {0.25} \right)^3}{\left( {0.75} \right)^{2}}\] + \dfrac{5!}{4!(1)!} \right){\left( {0.25} \right)^4}{\left( {0.75} \right)^{1}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = 0.0879+0.0146[/tex]
[tex]\mathbf{\[P\left( {X = 3 \ or \ 4 } \right) = 0.1025}[/tex]
c) Find the probability if She gets the majority of the questions right.
We know that the probability mass function is :
[tex]\[P\left( {X = x} \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\x\\\end{array}} \right){\left( {0.25} \right)^x}{\left( {1 - 0.25} \right)^{5 - x}}\][/tex]
So; of She gets majority of her answers right ; we have:
The required probability is,
[tex]P(X>2) = P(X=3) +P(X=4) + P(X=5)[/tex]
∴
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\3\\\end{array}} \right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \left( {\begin{array}{*{20}{c}}\\5\\\\4\\\end{array}} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\]+ \left( {\begin{array}{*{20}{c}}\\5\\\\5\\\end{array}} \right){\left( {0.25} \right)^5}{\left( {1 - 0.25} \right)^{5 - 5}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\] + \dfrac{5!}{5!(5-5)!} \right){\left( {0.25} \right)^5}{\left( {1 - 0.25} \right)^{5 - 5}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.75} \right)^{2}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {0.75} \right)^{1}}\] + \dfrac{5!}{5!(5-5)!} \right){\left( {0.25} \right)^5}{\left( {0.75} \right)^{0}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.0879 + 0.0146 + 0.001[/tex]
[tex]\mathbf{\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.1035}[/tex]
can someone help me plzz!
Answer:
126.6Option A is the right option.
Step-by-step explanation:
Sum of angles in triangle= 180°
[tex]85 + 53 + m < a = 180 \\ or \: 138 + m < a = 180 \\ or \:m < a = 180 - 138 \\ m < a = 42[/tex]
Applying sine rule:
[tex] \frac{sin \: a \: }{a} = \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: (85)}{b} = \frac{sin(42)}{85} \\ 85 \: sin \: (85) = \: b \: sin \: (42) \\ b = \frac{85 \: sin \: (85)}{sin \: 42} \\ ac = 126.6[/tex]
Hope this helps....
Good luck on your assignment...
est the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Upper H 0 : p equals 0.89 versus Upper H 1 : p not equals 0.89 n equals 500 comma x equals 430 comma alpha equals 0.01 Is np 0 (1 minus p 0 )greater than or equals 10? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. No, because np 0 (1 minus p 0 )equals nothing. B. Yes, because np 0 (1 minus p 0 )equals 48.95. Your answer is not correct. Now find ModifyingAbove p with caret.
Answer:
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population proportion significantly differs from 0.89.
The requirements for the test are satisfief.
n(1-p)=70>10
Step-by-step explanation:
This is a hypothesis test for a proportion.
There are 3 requirements to have a valid test of proportion: random sample, independence and normal.
For the first two (random and independent sample) we don't have details, but we assume the sampling has been random.
The latter can be verified by calculating np and n(1-p):
[tex]np=430>10\\\\n(1-p)=70>10[/tex]
Both are bigger than 10, so the normal approximation can be considered appropiate.
The claim is that the population proportion significantly differs from 0.89.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.89\\\\H_a:\pi\neq 0.89[/tex]
The significance level is 0.01.
The sample has a size n=500.
The sample proportion is p=0.86.
[tex]p=X/n=430/500=0.86[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.89*0.11}{500}}\\\\\\ \sigma_p=\sqrt{0.000196}=0.014[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.86-0.89+0.5/500}{0.014}=\dfrac{-0.029}{0.014}=-2.072[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z<-2.072)=0.038[/tex]
As the P-value (0.038) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population proportion significantly differs from 0.89.
If the density of an object is 8 g/cm³, and the mass is 200M m g. What is the volume of the object?
Answer:
Step-by-step explanation:
the mass is 2000 mg, or 2 g.
the density is 8 g/cm^3
divide 2 by 8
0.25 cm^3
if this helped, mark as brainliest :)
The quantities x and y are proportional.
x y
11 1 2/9
21 2 1/3
45 5
find the constant of proportionality (r) in the equation y=rx
Answer: r = 1/9
Step-by-step explanation:
y = rx --> [tex]r=\dfrac{y}{x}[/tex]
[tex]1)\ y=1\dfrac{2}{9}\rightarrow\dfrac{11}{9}\\\\.\quad x=11\\\\r=\dfrac{11}{9}\div11\\\\\\r=\dfrac{11}{9}\times \dfrac{1}{11}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]
[tex]2)\ y=2\dfrac{1}{3}\rightarrow\dfrac{7}{3}\\\\.\quad x=21\\\\r=\dfrac{7}{3}\div21\\\\\\r=\dfrac{7}{3}\times \dfrac{1}{21}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]
[tex]3)\ y=5\\\\.\quad x=45\\\\r=5\div45\\\\\\r=\dfrac{5}{45}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]
Suppose f(x)=x^2 and g(x) =7x^2 which statement best compares the graph of g(x) with the graph f(x)
Answer:
The graph g(x) is the graph f(x) vertically stretched by a factor of 7.
Step-by-step explanation:
Quadratic Equation: f(x) = a(bx - h)² + k
Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.
Answer:
The graph g(x) is the graph f(x) vertically stretched by a factor of 7.
Step-by-step explanation:
Quadratic Equation: f(x) = a(bx - h)² + k
Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.
2{ 5[7 + 4(17 - 9) - 22]}
Answer:
170
one-hundred seventy
Step-by-step explanation:
[tex]2(5(7+4(17 - 9)-22))=\\2(5(7+4(8)-22))=\\2(5(7+32-22))=\\2(5(39-22))=\\2(5(17))=\\2(85)=\\170[/tex]
Answer:
170.
Step-by-step explanation:
2{ 5[7 + 4(17 - 9) - 22]}
2{5[7+32 -22]}
2{5[17]}
2[85] = 170
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is: Compute E(Y) Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is:
y | P(Y)
0 | 0.50
1 | 0.20
2 | 0.25
3 | 0.05
Compute E(Y)
Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
Answer:
The expected value E(Y) is
[tex]E(Y) = 0.85[/tex]
The expected amount of the surcharge is
[tex]E(100Y^2) = 165[/tex]
Step-by-step explanation:
Let Y be the number of moving violations for which the individual was cited during the last 3 years.
The given probability mass function (pmf) of Y is
y | P(Y)
0 | 0.50
1 | 0.20
2 | 0.25
3 | 0.05
Compute E(Y)
The expected value E(Y) is given by
[tex]E(Y) = \sum Y \cdot P(Y) \\\\E(Y) = 0 \cdot 0.50 + 1 \cdot 0.20 + 2 \cdot 0.25 + 3 \cdot 0.05 \\\\E(Y) = 0.85[/tex]
Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
The expected amount of the surcharge is given by
[tex]E(100Y^2) = 100E(Y^2)[/tex]
Where
[tex]E(Y^2) = \sum Y^2 \cdot P(Y) \\\\E(Y^2) = 0^2 \cdot 0.50 + 1^2 \cdot 0.20 + 2^2 \cdot 0.25 + 3^2 \cdot 0.05\\\\E(Y^2) = 1.65[/tex]
So, the expected amount of the surcharge is
[tex]E(100Y^2) = 100E(Y^2) \\\\E(100Y^2) = 100 \cdot 1.65 \\\\E(100Y^2) = 165[/tex]
Help please! Simplify 7/ √x
Answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Step-by-step explanation:
To simplify 7/√x, we need to rationalize:
[tex]\frac{7}{\sqrt{x} } (\frac{\sqrt{x} }{\sqrt{x} } )[/tex]
When we multiply the 2, we should get our answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Step-by-step explanation:
[tex]\frac{7}{\sqrt{x} } \\\\\frac{7}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } \\\\\frac{7\sqrt{x} }{\sqrt{x\sqrt{x} } } \\[/tex]
[tex]\frac{7\sqrt{x} }{x}[/tex]
Hope this helps! :)
The product of two whole numbers is 1000. If neither of the numbers is a multiple of 10, what is their sum?
Answer:
133
Step-by-step explanation:
1000 = 2 * 2 * 2 * 5 * 5 * 5
To not have a multiple of 10, you cannot have 2 and 5 as factors of the same number.
One number is 2^3 = 8.
The other number is 5^3 = 125.
8 * 125 = 1000, so the two do multiply to 1000.
Neither 8 nor 125 is a multiple of 10.
8 + 125 = 133
Answer:
133
Step-by-step explanation:
We are given that the product of two numbers is 1000. Let's first list out the factors of 1000 (factors are numbers that evenly divide into 1000):
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
We see that the pairs are:
(1, 1000)
(2, 500)
(4, 250)
(5, 200)
(8, 125)
(10, 100)
(20, 50)
(25, 40)
An easy way to see if a number is divisible by 1000 is to check is it has a zero at the end. Notice that all of the pairs have at least one number that ends with at least 1 zero except (8, 125), so this is the pair of numbers we're looking for.
The sum is thus 8 + 125 = 133.
~ an aesthetics lover
there is 54 g of fruits in a smoothie. If the ratio of strawberry and blueberry in the smoothie is 5:4, how much of each fruit is there in the smoothie?
Answer:
strawberry: 30 gblueberry: 24 gStep-by-step explanation:
The total number of ratio units is 5+4 = 9, so each of them represents ...
(54 g)/9 = 6 g
of fruit. Multiplying the ratio by this value shows you the amount of each kind of fruit:
strawberry : blueberry = 5 : 4 = 5(6 g) : 4(6 g)
strawberry : blueberry = 30 g : 24 g
There are 30 g of strawberry and 24 g of blueberry in the smoothie.
I need help I don’t understand
Answer:
6
Step-by-step explanation:
you have to distributw the 4 to the 1/4 so essentially youre multiplying the exponents. think of it as 4*1/4 and youll have 4/4 which equals to 1. 6^1 is just 6 so thats the answer
well first you have to multiply 6 by 1/4 and then you have to do this: 1.5*1.5*1.5*1.5 to get your answer i think....
Hunter is 9 years older than 3 times the age of his nephew. Hunter is 33 years old. How old is his nephew?
Answer:
8 years old.
(3x+9)
(3(8)+9)=33
(7k-4)(7k^2+4k-1) mulityply the polynomials
Answer:
49k^3 -23k -4
Step-by-step explanation:
The distributive property is your friend.
[tex](7k-4)(7k^2+4k-1)=7k(7k^2+4k-1)-4(7k^2+4k-1)\\\\=49k^3+28k^2-7k-28k^2-16k+4\\\\=49k^3+k^2(28-28)+k(-7-16)-4\\\\=\boxed{49k^3-23k-4}[/tex]
What is the simplified value of this expression pls help
Answer:
7
Step-by-step explanation:
Remove parentheses.
[tex]\frac{-8+4(4.5)}{6.25-8.25} \\[/tex]
Add −8 and 4.5.
[tex]\frac{4(-3.5)}{6.25 - 8.25} \\\\[/tex]
Subtract 8.25 from 6.25.
[tex]\frac{4*-3.5}{-2}[/tex]
Multiply 4 by −3.5.
[tex]\frac{-14}{-2}[/tex]
Divide −14 by −2.
= 7
Three polynomials are factored below but some coefficients and constants are missing. all of the missing values of a, b, c and d are integers. 1. x^2 +2x-8=(ax+b)(cx+d) 2. 2x^3+2x^2-24x=2x(ax+b)(cx+d) 3. 6x^2-15x-9=(ax+b)(cx+d) Fill in the table with the missing values of a,b,c and d.
Answer:
1) d = 42) b = -3. c = 1 3) a = 3 and d = 1Step-by-step explanation:
To get the missing values in the table, we will factorize the given expression and compare the factored expression with the expression containing the missing constants.
1) For the expression x²+2x-8, on factorizing we have;
x²+2x-8
= (x²+4x)-(2x-8)
Factoring out the common terms from both parenthesis;
= x(x+4)-2(x+4)
= (1x+4)(1x-2)
= (1x-2)(1x+4)
Comparing the resulting expression with (ax+b)(cx+d)
a = 1, b = -2, c = 1 and d = 4
2) For the expression 2x³+2x²-24x
Factoring out the common term we will have;
= 2x(x²+x-12)
= 2x(x²-3x+4x-12)
= 2x{x(x-3)+4(x-3)}
= 2x{(x+4)(x-3)}
= 2x(1x-3)(1x+4)
Comparing the resulting expression with 2x(ax+b)(cx+d)
a = 1, b = -3. c = 1 and d = 4
3) For the expression 6x²-15x-9 we will have;
On simplifying,
= 6x²+3x-18x-9
= 3x(2x+1)-9(2x+1)
= (3x-9)(2x+1)
Comparing the resulting expression with (ax+b)(cx+d)
a = 3, b = -9, c = 2 and d = 1
Answer:
see picture attachment
Step-by-step explanation: