Answer:
The estimate is [tex]P__{hat}} \pm E = 0.37 \pm 0.0348[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 522
The sample proportion of students would like to talk about school is [tex]\r p__{hat}} = 0.37[/tex]
Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645[/tex]
Generally the margin of error can be mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }[/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }[/tex]
=> [tex]E = 0.0348[/tex]
Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is
[tex]P__{hat}} \pm E[/tex]
substituting values
[tex]0.37 \pm 0.0348[/tex]
Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined:
%u2022 The amount earned in commissions last month (Y).
%u2022 The number of miles driven last month (X2)
%u2022 The number of sales calls made last month (X1)
($000) Calls Driven Commissions
($000) Calls Driven
22 139 2,371 38 146 3,290
13 132 2,226 44 144 3,103
33 144 2,731 29 147 2,122
38 142 3,351 38 144 2,791
23 142 2,289 37 149 3,209
47 142 3,449 14 131 2,287
29 138 3,114 34 144 2,848
38 139 3,342 25 132 2,690
41 144 2,842 27 132 2,933
32 134 2,625 25 127 2,671
20 135 2,121 43 154 2,988
13 137 2,219 34 147 2,829
47 146 3,463
Click here for the Excel Data File
Develop a regression equation including an interaction term. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Commissions = + Calls + Miles - X1X2
Complete the following table. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Predictor Coef SE Coef T P
Constant
Calls
Miles
X1X2
Compute the value of the test statistic corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
Value of the test statistic
Is there a significant interaction between the number of sales calls and the miles driven?
Answer:
There is no significant interaction between the number of sales calls and the miles driven.
Step-by-step explanation:
The variables are defined as follows:
Dependent (Y) = amount earned in commissions last month
Independent (X₁) = number of miles driven last month
Independent (X₂) = number of sales calls made last month
In this case we need to test whether there is a significant interaction between the number of sales calls and the miles driven.
The hypothesis can be defined as follows:
H₀: There is no significant interaction.
Hₐ: There is a significant interaction.
Assume that the significance level of the test is, α = 0.05.
Use the Data Analysis tool in Excel to form the regression equation.
For the regression equation, we need to compute the values of (X₁ × X₂).
Steps:
Go to Data - Data Analysis - Regression. A dialog box will open.Select the Y values in the "Input Y range" and values of X₁, X₂ and X₁ × X₂ in the "Input X range".Click OK.The output of the regression analysis is attached below.
The regression equation is:
[tex]Y=-455.07+3.128\cdot X_{1}+0.143\cdot X_{2}-0.001\cdot X_{1}X_{2}[/tex]
Consider the third table in the regression output.
The test statistic corresponding to the interaction term is:
t = -1.85
The p-value for the test of the interaction term is:
p-value = 0.078.
The p-value of the test is more than the significance value.
The null hypothesis will not be rejected.
Thus, concluding that there is no significant interaction between the number of sales calls and the miles driven.
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction? Select three options. m = StartFraction 10 over 4 EndFraction m = negative StartFraction 10 over 4 EndFraction m = negative five-halves StartFraction 11 over 4 EndFraction + m = negative one-fourth Negative five-fourths + m = negative StartFraction 15 over 4 EndFraction
Answer:
1) m = negative StartFraction 10 over 4 EndFraction
2) m = negative five-halves
3) m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]
Step-by-step explanation:
The given equation is:
=> [tex]\frac{3}{4} +m = -\frac{7}{4}[/tex]
Subtracting 3/4 to both sides
=> m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]
=> m = [tex]\frac{-10}{4}[/tex]
=> m = [tex]-\frac{5}{2}[/tex]
Answer:
-5/2 ye
cause ya do the math
Step-by-step explanation:
Find the hcf of 15a²b² and -24ab | plzzz solve
Answer:
[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, let's find the factors of these two numbers and I will put in boxes the common factors.
[tex]15a^2b^2=\boxed{3}\cdot 5\cdot \boxed{a} \cdot a \cdot \boxed{b} \cdot b \\ \\ \\-24ab=(-1)\cdot 2 \cdot \boxed{3} \cdot 4 \cdot \boxed{a} \cdot \boxed{b}[/tex]
The Highest Common Factor (HCF) is found by finding all common factors and selecting the largest one. So, in this case, it gives
[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the equation of the following graph in vertex form? Courtesy of Texas Instruments A. y = (x − 4)2 − 4 B. y = (x + 4)2 − 4 C. y = (x + 2)2 + 6 D. y = (x + 2)2 + 12
Answer:
A: y = (x − 4)^2 − 4
Step-by-step explanation:
vertex=(4.-4)
A: y = (x − 4)^2 − 4
y=x^2-8x+16-4
y=x^2-8x+12 (a=1,b=-8,c=12)
the y intercept is (0,12)
vertex ( h, k)
h=-b/2a ⇒ h=-(-8)/2=4
plug the value of h in the equation y=x^2-8x+12
k=4²-8(4)+12
k=16-32+12
k=-4
v(4,-4)
The required equation of the given graph in vertex form is y = (x − 4)² − 4. which is the correct answer would be option (A).
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) are the x and y-coordinates of the vertex.
The vertex = (4, -4) is given in the shown graph.
As per option (A),
y = (x − 4)² − 4
y = x²-8x+16-4
y = x²-8x+12 (a=1,b=-8,c=12)
the y-intercept is (0,12)
vertex ( h, k)
h = -b/2a ⇒ h=-(-8)/2=4
Substitute the value of h in the equation y = x²-8x+12
k = 4²- 8(4) + 12
k =16 - 32 + 12
k = -4
Thus, the vertex is (4,-4)
Hence, the correct answer would be option (A).
Learn more about the parabola here:
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Evaluate the following geometric sum.
1/2 + 1/10 + ( 1/50) + (1/250 ) + midline ellipsis + (1/31,250)
Answer:
39062/62,500Step-by-step explanation:
Given the following geometric progression; 1/2 + 1/10 + ( 1/50) + (1/250 ) + ... + (1/31,250),the sum of the arithmetic geometric progression is expressed using the formula below;
Sn = a(1-rⁿ)/1-r for r less than 1
r is the common ratio
n is the number of terms
a is the first term of the series
In between the mid-line ellipsis there are 2 more terms, making the total number of terms n to be 7]
common ratio = (1/10)/(1/2) = (1/50)/(1/10) = (1/250)/(1/50) = 1/5
a = 1/2
Substituting the given values into the equation above
S7 = 1/2{1 - (1/5)⁷}/1 - 1/5
S7 = 1/2(1- 1/78125)/(4/5)
S7 = 1/2 (78124/78125)/(4/5)
S7 = 78124/156,250 * 5/4
S7 = 390,620/625000
S7 = 39062/62,500
Hence the geometric sum is 39062/62,500
my number is the first multiple of 3,6, and 9 what is my number
Answer:
18 is the first multiple of 3,6, and 9.
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.
3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.
Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.
the mean cost of domestic airfares is RS 385 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of RS 110. What is the probability that a domestic airfare is RS 550 or more?
Answer: 0.0668
Step-by-step explanation:
Given the following :
Mean (m) Cost = RS385
Standard deviation (s) = RS110
Assume a normal distribution, Probability that domestic airfare is RS550 or more?
P(x > 550)
Find the z - score
Z - score = (x - m) / s
Where x = 550
Z = (550 - 385) / 110
Z = 165 / 110 = 1.5
P(Z > 1.5) = 1 - P(Z ≤1.5)
Using the z table : 1.5 = 0.9332
Therefore,
1 - P(Z ≤1.5) = 1 - 0.9332 = 0.0668
P(x > 550) = 0.0668
Amy have 398.5 L of apple juice . Avery have 40098 ml of apple juice how many do they have all together
Answer: 438.5L = 438000ml
Step-by-step explanation:
5x - y = -7
4x + 2y = – 14
Answer:
[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that you want to solve this system of two equations
(1) 5x - y = -7
(2) 4x + 2y = -14
We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y
2*(1)+(2) gives
10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28
<=>
14x = - 28 we can divide by 14 both parts
x = -28/14 = -2
and then we replace x in (1)
5*(-2)-y=-7
-10-y=-7 add 7
-10-y+7=0
-3-y=0 add y
-3 = y
which is equivalent to y = -3
do not hesitate if you have any question
Answer:
x = -2, y = -3
Step-by-step explanation:
5x - y = -7
4x + 2y = – 14
Multiply the first equation by 2
2(5x - y) = 2*-7
10x -2y = -14
Add this to the second equation to eliminate y
10x -2y = -14
4x + 2y = – 14
---------------------------
14x = -28
Divide by 14
14x/14 = -28/14
x = -2
Now find y
4x+2y = -14
4*-2 +2y = -14
-8+2y = -14
Add 8 to each side
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
Help someone!! Thank you
I suppose this is saying that 20%, 25% and 55% are each a whole number of science students. The GCD is 5%, 1/20th, so minimum 20 people total. 55% are studying biology, that's 11.
Answer: C. 11
Select the correct option.
In a game, bonus points are awarded based on the number of the level that is cleared. The bonus points are calculated by a function
that is 15 times the cube root of the level cleared and rounded to the closest integer value.
Which of the following options represents the bonus points scored as the levels advance?
Answer:
Graph A.
Step-by-step explanation:
Write an equation of the line that passes through the point (–1, 4) with slope 2. A. y+1=−2(x−4) B. y+1=2(x−4) C. y−4=2(x+1) D. y−4=−2(x+1) CHOSE ONE!
Answer:
[tex]y-4=2\,(x+1)[/tex]
which agrees with answer C in your list of possible answers.
Step-by-step explanation:
We can use the general point-slope form of a line of slope m and going through the point [tex](x_0, y_0)[/tex]:
[tex]y-y_0=m(x-x_0)[/tex]
which in our case, given the info on the slope (2) and the point (-1, 4) becomes:
[tex]y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)[/tex]
Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 52 37 44 42 38 41 48 43 39 36 55 42 35 15 52 39 50 29 30
Answer:
(a) [tex]Q_1=36.5,M=Q_2=41,Q_3=46[/tex]
(b) [tex]IQR=9.5[/tex]
(c) 15
Step-by-step explanation:
The given data set is
41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30
Arrange the data in ascending order.
15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55
Divide the data in four equal parts.
(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)
Now,
[tex]Q_1=\dfrac{36+37}{2}=36.5[/tex]
[tex]M=Q_2=\dfrac{41+41}{2}=41[/tex]
[tex]Q_3=\dfrac{44+48}{2}=46[/tex]
[tex]IQR=Q_3-Q_1=46-36.5=9.5[/tex]
Range for outlier is
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)][/tex]
[tex]=[22.25,60.25][/tex]
Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.
Kite LMNO is shown below.
What is the measure of angle M
Answer:
<M = 78°
Step-by-step explanation:
The sum of angles in a kite is 360°.
One of the properties of a kite is that one pair of opposite angles are equal.
Since it is not <L and <N, it must be <O and <M
Therefore:
<O = <M = x
=> x + x + 130 + 74 = 360
2x + 204 = 360
2x = 360 - 204
2x = 156
x = 156/2 = 78°
This means that <M = 78°
Rachel Plant has $28,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $80 a share. If stock B doubles in value and stock A goes up 50%, her stock will be worth $54,000. How many shares of each stock does she own?
Answer:
A= 66.6667
B = 333.3333
Step-by-step explanation:
Initial value of A = $20
Initial value of B = $80
Initial total=$ 28000
A moves up 50%= 20+(0.5*20)
A moves up 50% = 20+10
A moves up 50% =$ 30
B double it values = $80*2
B double it values = $160
Now total value is = $54000
A20+B80= 28000... equation 1
A30+B160= 54000.... equation 2
Multiplying equation 1 * 2
Multiplying equation 2 * 1
A40 +B160 = 56000
A30+B160= 54000
A30 = 2000
A= 2000/30
A= 200/3
A= 66.6667
A20+B80= 28000
Substituting A
200/3 (20) +B80= 28000
B80= 28000-4000/3
B80= 80000/3
B= 80000/240
B = 333.3333
Proving the sum of the Interior Angle Measures of a Triangle is 180
Answer:
theres the screenshot of it
The solution to prove the sum of the interior angles of a triangle is 180° is
∠1 + ∠2 + ∠3 = 180° ( angles in a straight line )
∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the angles inside the triangle are ∠2 , ∠5 and ∠6
Now , the lines l₁ and l₂ are two parallel lines
From the figure ,
The measure of ∠1 = The measure of ∠5 ( alternate interior angles )
The measure of ∠3 = The measure of ∠6 ( alternate interior angles )
Now , for a straight line , the measure of angle = 180°
So , ∠1 + ∠2 + ∠3 = 180° ( angles in a straight line ) ( angle addition )
And , the sum interior angles of a triangle is 180°
So , ∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle ) ( substitution )
Hence , the sum of the angles inside a triangle is 180°
To learn more about triangles click :
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Someone help me with this, please!
Answer:
B = 26.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin B = 4/9
Take the inverse sin of each side
sin ^-1 sin ( B) = sin ^-1 ( 4/9)
B = 26.38779996
B = 26.4
Answer:
[tex]26.4\º[/tex]
Step-by-step explanation:
[tex]\theta=?[/tex]
[tex]$\sin(\theta)=\frac{opp}{hyp} = \frac{4}{9} $[/tex]
[tex]$\theta=\sin^{-1}\frac{4}{9} =\arcsin\frac{4}{9} \approx 26.4\º$[/tex]
Imagine a man in the Chicago suburbs went outside to shovel his driveway after the Feb 10, 2018 snowstorm and had a heart attack while shoveling. When the police discovered the body later that day at 4PM, his body temperature had dropped from 98.6°F to 42°F. The environmental air temperature was 10°F. What time did he die from the heart attack?
Answer:
I did my best with the information! The Man died at around 11:20 am.
Step-by-step explanation:
So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.
helpppppppp i give you stars bralienst,and also thanks
Answer:
50% of 100<75% of 104
50% of 100>75% of 60
Step-by-step explanation:
For the inequality to support the statement, we can use 50% of 100 which is 50
Now we need to find "any other number" that is greater. I'll use 104 since it divides evenly. 75% of 104 is 78, 50<78
Now for the second one, we can use 50% of 100 again which is 50.
This time we need to find another number that is less than. I'll use 60. 75% of 60 is 45. 50>45
I NEED HELP!
Rectangle ABCD is drawn with diagonal AC, which has a measure of 20cm. Angle BACmeasures 30°. What is the
perimeter and area of the rectangle?
Answer:
Perimeter = 54.6 cm
Area = 173 cm²
Step-by-step explanation:
sin 30 = x/20
x = 10
cos 30 = y /20
y = 17.3
perimeter = 10 + 17.3 + 10 + 17.3 = 54.6 cm
area = 10 * 17.3 = 173 cm²
what percentage of 40 is 8?
(A) 5%
(B) 20%
(C) 32%
(D) 150%
Answer:
20%
Step-by-step explanation:
When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.
Hence,
8 is 20% of 40.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
The answer is option B.
Step-by-step explanation:
Let the percentage be x
We have
[tex] \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20[/tex]
Hope this helps you
Write the following numbers in decreasing order: −4; 1 2 3 ; 0.5; −1 3 4 ; 0.03; −1; 1; 0; −10; 54
Answer:
123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134
Step-by-step explanation:
123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
120
Step-by-step explanation:
Answer: 120
Hope that helped!(:
A market trader has 100 oranges for sale, 4 of them are unripe, what is the
probability that an orange chosen at random is ripe?
4/100?
90/100?
2/5?
24/25?
[tex]\bold{Answer}:\quad \dfrac{24}{25}[/tex]
Step-by-step explanation:
There are 100 oranges. 4 of them are unripe which means 96 are ripe.
[tex]\dfrac{ripe}{total}=\dfrac{96}{100}\quad \div \dfrac{4}{4}=\large\boxed{\dfrac{24}{25}}[/tex]
Hypothesis Testing
Problem 1. Adults saving for retirement
In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does
the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why.
8. What do you conclude?
Problem 2: Google Stock
Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has
decreased substantially. In 2010, the mean daily volume in Google stock was 5.44 million shares, according to Yahoo!Enance. A random sample of 35 trading days in 2014 resulted in a
sample mean of 3.28 million shares with a standard deviation of 1.68 million shares. Does the evidence suggest that the volume of Google stock has changed since 2007? Use a 0.05 level of
significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why
8. What do you conclude?
Answer:
Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2: We conclude that the volume of Google stock has changed.
Step-by-step explanation:
Problem 1:
We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.
Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50% {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}
Alternate Hypothesis, [tex]H_A[/tex] : p > 50% {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}
This is a right-tailed test.
The test statistics that would be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53
n = sample of adult Americans = 295
So, the test statistics = [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]
= 1.03
The value of z-test statistics is 1.03.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)
= 1 - 0.8485 = 0.1515
Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2:
We are given that a random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.
Let [tex]\mu[/tex] = mean daily volume in Google stock
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares {means that the volume of Google stock has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares {means that the volume of Google stock has changed}
This is a two-tailed test.
The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares
s = sample standard deviation = 1.68 million shares
n = sample of trading days = 35
So, the test statistics = [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= -7.606
The value of t-test statistics is -7.606.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%
Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the volume of Google stock has changed.
A 6 foot person casts a 26 foot shadow. What is the angle of elevation of the sun? (nearest whole degree)
Answer:
13°
Step-by-step explanation:
The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.
The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft
Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:
[tex] tan x = \frac{opposite}{adjacent} [/tex]
[tex] tan x = \frac{6}{26} [/tex]
[tex] tan x = 0.2308 [/tex]
x = tan-¹(0.2308)
x = 12.996
x ≈ 13° (to the nearest whole degree)
The angle of elevation of the sun = 13°
6th grade math help me, please :)))
85% x 1600/100 = 1360 number of seats sold
Probability can never be equal to 154Probability can never be equal to 154
Answer: True
Step-by-step explanation:
The probability of an event occurring lies between zero and one. A probability of 0 means that the event has no chance of happening for example, rolling a die once and getting a number greater than 6 while a probability of 1 means the event will definitely happen for example, getting a number less than 7 when you roll a die once.
Every other probability falls in-between this range so probability can never be 154.
-5/2x-3 is less than or equal to 2 what is the solution.
Answer: 1/4≤x
Step-by-step explanation:
-5/(2x-3)≤2
Multiply by (2x-3)
-5≤4x-6
Add 6
1≤4x
1/4≤x
Hope it helps <3
Answer:
[tex]x \geq 1/4[/tex]
Step-by-step explanation:
=> [tex]\frac{-5}{2x-3} \leq 2[/tex]
Multiplying both sides by (2x-3)
=> [tex]-5 \leq 2(2x-3)[/tex]
=> [tex]-5 \leq 4x-6[/tex]
Adding 6 to both sides
=> [tex]-5+6 \leq 4x[/tex]
=> [tex]4x\geq 1[/tex]
Dividing both sides by 4
=> [tex]x \geq 1/4[/tex]
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.