Answer: x= 7
Step-by-step explanation:
-2x= -14 Divide both sides by -2
x= 7
check
-2(7) = -14
-14 = -14
Answer:
x = 7
Step-by-step explanation:
-2x = -14
Divide each side by -2
-2x/-2 = -14/-2
x = 7
A tool rental store charges a flat fee of $10.00 to rent a chain saw, and $4.25 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.
Answer:
y= 4.25x + $10
Step-by-step explanation:
A tool rental shop charges a flat fee of $10.00 to rent out their chain saw
An amount of $4.25 is charged for each of the days
Let x represent the amount that is charged for each day
Let y represent the total cost of the chain saw
Since the rental fee for each day is given as $4.25 and the flat fee is given as $10 then, the equation can be expressed as
y= $4.25x + $10
Hence the equation that expresses the cost y of renting this saw if it is rented for x days is y= $4.25x + $10
Given: AB = CD 1 = 4 Prove: AD = CB Which of the following triangle congruence theorems would be used in this proof? SSS SAS ASA
Answer:
SAS
Step-by-step explanation:
.. cuz, it just is c:
By ''SAS congruency'' theorem we can prove AD = CB.
We have to given that,
In a figure,
AB = CD
∠1 = ∠4
Now, In triangle ADC and triangle ABC,
AC = AC (Common side)
∠1 = ∠4 (Given)
AB = CD (Given)
Hence, By SAS Congruency theorem,
Δ ADC ≅ Δ ABC
So, We get;
AD = CB
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ2
You are considering a stock investment in one of two firms (Lotsof Debt, Inc. and LotsofEquity, Inc.), both of which operate in the same
industry. LotsofDebt, Inc. finances its $32.00 million in assets with $30.00 million in debt and $2.00 milion in equity. LotsofEquity, Inc.
finances its $32.00 million in assets with $2.00 million in debt and $30.00 million in equity.
Calculate the debt ratio. (Round your answers to 2 decimal places.)
Debt ratio
LotsofDebt, Inc.
LotsofEquity, Inc.
%
Calculate the equity multiplier. (Round your answers to 2 decimal places.)
LotsofDebt, Inc.
LotsofEquity, Inc.
Equity multiplier
times
times
Calculate the debt-to-equity. (Round your answers to 2 decimal places.)
Debt-to-equity
LotsofDebt, Inc.
LotsofEquity, Inc.
times
times
Answer:
LotsofDebt, Inc Debt Ratio is 93.75%
LotsofEquity, Inc Debt Ratio is 6.25%
equity multiplier LotsofDebt, Inc is 16
equity multiplier LotsofEquity, Inc is 1.0666666667
debt-to-equity LotsofDebt, Inc is $15 million
debt-to-equity LotsofEquity, Inc. is $0.0666666667 million
Step-by-step explanation:
In order to calculate the debt ratio of LotsofDebt, Inc and LotsofEquity, Inc. we would have to make the following calculations:
Debt Ratio = Debt/Assets
According to the given data we have the following:
LotsofDebt, Inc Debt=$30 million
LotsofDebt, Inc Asset=Debt + Equity = $30 million + $2 million = $32 million
Therefore, LotsofDebt, Inc Debt Ratio =$30 million/$ 32 million
LotsofDebt, Inc Debt Ratio= 93.75%
LotsofEquity, Inc. Debt=$2 million
LotsofEquity, Inc Asset= Debt + Equity = $2 million + $30 million
LotsofEquity, Inc Debt Ratio = $2 million/$32 million
LotsofEquity, Inc Debt Ratio = 6.25%
In order to calculate the equity multiplier of LotsofDebt, Inc and LotsofEquity, Inc. we would have to make the following calculations:
equity multiplier =Assets/Equity
equity multiplier LotsofDebt, Inc.=$32 million/$2 million
equity multiplier LotsofDebt, Inc= 16
equity multiplier LotsofEquity, Inc=$32 million/$30 million
equity multiplier LotsofEquity, Inc = 1.0666666667
In order to calculate the debt-to-equity of LotsofDebt, Inc and LotsofEquity, Inc. we would have to make the following calculations:
debt-to-equity LotsofDebt, Inc=Debt/Equity
debt-to-equity LotsofDebt, Inc=$30 million/$2 million
debt-to-equity LotsofDebt, Inc= $15 million
debt-to-equity LotsofEquity, Inc.= $2 million/$30 million = 0.0666666667
debt-to-equity LotsofEquity, Inc.= $0.0666666667 million
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode?
Answer:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
z -value = 0.33022
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
Step-by-step explanation:
From the summary of the given statistical data sets.
Let consider to [tex]p_1[/tex] represent percentage of the first group ; &
[tex]p_2[/tex] represent percentage of the second group
The null and the alternative hypothesis can be stated s follows:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
At the level of significance ∝ = 0.1; the two tailed critical value from the z-table
[tex]z_{\alpha/2} = 1.65[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
However; from the question:
There are 55 people in the first group and this group will be administered the new drug.
There are 45 people in the second group and this group will be administered a placebo.
After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.
The test statistic for the for the first group who suffered from the second episode can be denoted as :
[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]
The test statistic for the for the second group who suffered from the second episode can be denoted as :
[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]
where;
[tex]n_1[/tex] = sample size of group 1 = 55
[tex]n_2[/tex] = sample size of group 2 = 45
The total probability of both group is :
[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]
[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]
[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]
[tex]\hat p = \dfrac{10.1}{100}[/tex]
[tex]\hat p = 0.101[/tex]
The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]
Now; The test statistics is determined to be :
[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]
[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]
z = 0.33022
Hence; the value for the test statistics = 0.33022
the value for the test statistics = 0.33
From the z value; The P-value for the test statistics can be computed as:
P-value = 2P(Z ≥ |z|)
P-value = 2P(Z ≥ 0.33022)
P-value = 2 × P (Z ≤ - 0.33022)
From the z table Z ≤ - 0.33022 = 0.3707
P-value = 2 × 0.3707
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
find the inverse of the one-to-one function f(x)=-8x+8
Answer:
[tex]\huge\boxed{f^{-1}(x)=-\dfrac{1}{8}x+1}[/tex]
Step-by-step explanation:
[tex]f(x)=-8x+8\to y=-8x+8[/tex]
change x with y
[tex]x=-8y+8[/tex]
solve for y
[tex]-8y+8=x[/tex] subtract 8 from both sides
[tex]-8y+8-8=x-8[/tex]
[tex]-8y=x-8[\tex] divide both sides by (-8)
[tex]\dfrac{-8y}{-8}=\dfrac{x}{-8}-\dfrac{8}{-8}\\\\y=-\dfrac{1}{8}x+1[/tex]
In a random sample of 500 handwritten zip code digits, 464 were read correctly by an optical character recognition (OCR) system operated by the U.S. Postal Service (USPS). USPS would like to know whether the rate is at least 90% correct.
Required:
Do the data provide evidence that the rate is at least 90% at a 0.05?
Answer:
z= 2.38
P = 0.008656
Step-by-step explanation:
Here n= 500 and p~= 464/500= 0.928 and q`= 1- 0.928 = 0.072
We formulate our null and alternate hypothesis as
H0 = 0.9 ; H0 > 0.9
The degree of confidence = 90%
z₀.₀₅ = 1.645 for α= 0.05
We use the test statistic
z= x- np/√npq
z= 466-500 *0.9/ √500 * 0.9(1-0.9)
z= 466- 450/ √45
z= 16/6.7082
z= 2.38
As the calculated value of z= 2.38 is greater than α =1.645 so we reject H0.
If H0 is true the P value is calculated as
P = 1- Ф( 2.38)
P = 1-0.991344=0.008656
A company manufacturing oil seals wants to establish X and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows:
sigma^25_i = 1 X_t = 1, 253.75, sigma^25_i = 1 R_i = 14.08
(a) Find the control limits that should be used on the X and R control charts. For n = 5, A2 = 0.577, D4 = 2.114, D3 = 0
(b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.
Answer:
A ) i) X control chart : upper limit = 50.475, lower limit = 49.825
ii) R control chart : upper limit = 1.191, lower limit = 0
Step-by-step explanation:
A) Finding the control limits
grand sample mean = 1253.75 / 25 = 50.15
mean range = 14.08 / 25 = 0.5632
Based on X control CHART
The upper control limit ( UCL ) =
grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475
The lower control limit (LCL)=
grand sample mean - A2 * mean range = 50.15 - 0.577(0.5632) = 49.825
Based on R control charts
The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191
The lower control limit = D3 * mean range = 0 * 0.5632 = 0
B) estimate the process mean and standard deviation
estimated process mean = 50.15 = grand sample mean
standard deviation = mean range / d2 = 0.5632 / 2.326 = 0.2421
note d2 is obtained from control table
8,5,15,18,3,what's next
13 since i think it's when a single didget number has a 1 at the beginning. i might be wrong thoough
If you continue adding fractions according to this pattern when will you reach a sum of 2?
Answer:
You will never be able to reach the sum of 2
Step-by-step explanation:
What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then it’s measure is 90
Answer:
"If an angle has measure 90°, then it is a right angle" , True
Step-by-step explanation:
We have the following:
"If an angle is a right angle, then it’s measure is 90"
The idea is to write the opposite of the previous conditional statement.
We know that if the statement is "If p, then q", then its inverse will be "If q, then p".
So the opposite of our given statement will be :
"If an angle has measure 90°, then it is a right angle"
And this statement is true since every angle that measures 90 ° is considered a right angle.
given that (-9,-3) is on a graph of f(x), find the corresponding point for the function f(x+1)
Answer:
(-10, -3)
Step-by-step explanation:
Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).
State the slope of the line.
1
0
Undefined
-4
Answer:
Hey there!
The slope of a vertical line is undefined! The run is zero, and as we know, dividing by zero is undefined!
Hope this helps :)
Answer:
Undefined
Step-by-step explanation:
A vertical line has an undefined slope or there is no slope of the line.
Questions:
1. What do you notice about how the angles fit together around a point?
2. What is the measure of a straight angle?
3. Describe the relationship amoung the measure of the angles of ∆ABC
4. The triangle sum theorem states that forma ∆ ABC, m<A + m<A = 180°. Is this true? Explain
1. The angles form a straight angle
2. A straight angle is defined to be 180 degrees
3. The three angles of any triangle always add to 180, as the diagram shows.
4. This is false. We need to add the three different angles A,B,C to get 180. Adding angle A to itself may not lead to 180. A+A = 180 only happens when angle A is a right angle (90 degree angle).
The valve was tested on 240240 engines and the mean pressure was 7.57.5 pounds/square inch (psi). Assume the population standard deviation is 1.01.0. The engineer designed the valve such that it would produce a mean pressure of 7.67.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.10.1 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.
Answer:
z = 1.55
Step-by-step explanation:
The answer is attached.
A rectangular waterbed is 8 ft long, 5 fr, wide and 1 ft tall.
How many gallons of water are needed to fill the waterbed?
Assume 1 gallon is 0.13 ft.³ round to the nearest whole gallon
Answer: 308 gallons of water.
Step-by-step explanation:
First find the volume of the water been.
The volume of a rectangular prism uses the formula
V= L * W *H
V = 8 * 5 * 1
V = 40 ft^3
Now we will convert 40ft into gallons using what they gave us that 1 gallon is 0.13 ft^3
[tex]\frac{1}{x} = \frac{0.13}{40}[/tex] which means if 1 gallon is 0.13 cubic feet how much will 40 cubic feet be when converted to gallons.
Solve by cross product.
0.13x = 40 divide both sides by 0.13
x= 308
Solve the equation below for x.
-1
2(3x - 4) = 11
An open box with no lid has a square base and four sides of equal height. The height is 4 inches
greater than the length and width (which are the same). What are the dimensions of the box if the
volume is 63 cubic inches and the surface area is 93 square inches?
PLEASE SHOW YOUR WORK:) THANK YOU SO MUCH
Answer:
width = length = 3 inches
height = 7 inches
Step-by-step explanation:
If x is the width and length of the base, and y is the height, then:
y = x + 4
The volume of the box is:
63 = x²y
The surface area of the box is:
93 = x² + 4xy
Substitute the first equation into the third.
93 = x² + 4x (x + 4)
93 = x² + 4x² + 16x
0 = 5x² + 16x − 93
0 = (x − 3) (5x + 31)
x = 3
y = 7
Use the second equation to check your answer.
63 = (3)²(7)
63 = 63
Answer:
Length=Width=3
Height=7.
Step-by-step explanation:
First, let's write some equations. So, we have an open box (with no lid) that has a square base. It has a height 4 units more of its width/length.
First, let's write the equation for the volume. The volume of a rectangular prism is:
[tex]V=lwh[/tex]
Recall that we have a square base. In other words, the length and width are exactly the same. Therefore, we can do the following substitution:
[tex]V=(w)wh=w^2(h)[/tex]
Now, recall that the height is four units more than the width/length. Therefore, we can make the following substitution:
[tex]V=w^2(w+4)\\63=w^2(w+4)[/tex]
We can't really do anything with this. Let's next find the equation for the surface area.
So, we have 5 sides (not 6 because we have no lid). The bottom side is a square, so it's area is w^2. Since we have a square base, the remaining four sides will have an area w(w+4). In other words:
[tex]93=w^2+4(w(w+4))[/tex]
The left term represents the area of the square base. The right term represents the area of one of the rectangular sides, times sides meaning four sides. Simplify:
[tex]93=w^2+4w^2+16w\\5w^2+16w-93=0[/tex]
This seems solvable. Let's try it. Trying factoring by guessing and checking.
We can see that it is indeed factor-able. -15 and 31 are the numbers:
[tex]5w^2-15w+31w-93=0\\5w(w-3)+31(w-3)=0\\(5w+3)(w-3)=0\\w=3\\h=w+4=7[/tex]
We ignore the other one because width cannot be negative.
So, the width/length is 3 and the height is 7. We can check this by plugging this into the volume formula:
[tex]63\stackrel{?}{=}(3)^2(7)\\63\stackrel{\checkmark}{=}63[/tex]
What is the inverse of the function below?
f(x) = x-5
A. f^-1(x) = x + 5
B. f^-1(X) = x-5
C. f^-1(x) = -x + 5
D. f^-1(x) = -x-5
Answer:
f^-1(x) = x + 5
Step-by-step explanation:
f(x) = x-5
y = x-5
Exchange x and y
x = y-5
Solve for y
x+5 = y-5+5
x+5 =y
The inverse is x+5
use the associative property to rewrite (26+92)+17
Answer:
(26+92)+17 = 26 + ( 92+17)
Step-by-step explanation:
The associative property of addition is
a + (b + c) = (a + b) + c
We want to move the parentheses
(26+92)+17 = 26 + ( 92+17)
A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled?
a. n=36, p=0.97, x=1
b. n=12, p=0.36, x=97
c. n=12, p=0.97, x=0
d. n=36, p=0.97, x=36
Answer:
Option d: n = 36, p = 0.97, x = 36.
Step-by-step explanation:
We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.
We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.
Let X = Number of cans that are properly filled
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]
where, n = number of trials (samples) taken = 36 cans
x = number of success = all cans are properly filled = 36
p = probabilitiy of success which in our question is probability that
can have the correct amount, i.e. p = 97%
So, X ~ Binom (n = 36, p = 0.97)
Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.
The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% confidence interval to 4%, about how many Americans would we need to survey
Answer:
The sample size is [tex]n = 600[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.48[/tex]
The margin of error is [tex]MOE = 0.04[/tex]
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
Generally the margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }[/tex]
substituting values
[tex]0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }[/tex]
[tex]0.02041 = \sqrt{ \frac{0.48(52 )}{n} }[/tex]
[tex]0.02041 = \sqrt{ \frac{ 0.2496}{n} }[/tex]
[tex]0.02041^2 = \frac{ 0.2496}{n}[/tex]
[tex]0.0004166 = \frac{ 0.2496}{n}[/tex]
=> [tex]n = 600[/tex]
Find magnetic azimuth from stream 89 degrees magnetic azimuth from pond 14degrees
Answer:
The Azimuths are 81 degrees, 6 degrees for Grid Azimuths and 269 degrees, 194 degrees for back Azimuths
Step-by-step explanation:
Stream = 89 degrees and Pond = 14 degrees
To Convert to grid Azimuth
G-M Azimuth of 89-8=81 degrees
G-M Azimuth of 14-8=6 degrees
To obtain the back Azimuth for the stream
89+180=269 degrees
To obtain the back Azimuth for the pond
14+180=194 degrees
janie and her friends played a question and answer game. their scores at the end of thegame were 14, 15, 8, 15, 3, 0, and 12. find the median score of the game
Answer:
12
Step-by-step explanation:
Well first step to finding median is order the scores from least to greatest,
0, 3, 8, 12, 14, 15, 15
Now we can start crossing the numbers off.
After we've crossed 3 numbers off from each side,
we get 12.
Thus,
12 is the median of the number set,
Hope this helps :)
Answer:
12
Step-by-step explanation:
First we need to put the numbers in order from smallest to largest
14, 15, 8, 15, 3, 0, and 12
becomes
0 , 3 , 8 , 12 , 14, 15, 15
Then the median is the middle number
There are 7 numbers
7/2 = 3.5
The middle is the 4th number ( 3 on the left and 3 on the right)
0 , 3 , 8 , 12 , 14, 15, 15
The median is 12
ABC has been translated 5 units to the right, as shown in the diagram. What is the length of ?
A.
15
B.
6
C.
31
D.
10
Answer:
(A) 15 centimeters
Step-by-step explanation:
A midsegment of a triangle is always 2 things:
Half the size of the bottom of the triangle (in this case AC)
Parallel to the bottom of the triangle.
Since ABC is an equilateral triangle, we know that EVERY side is 30cm, including AC.
So the midsegment of ABC, LM, must be 15 cm.
Hope this helped!
Please help. I’ll mark you as brainliest if correct!
Answer:
(x, 2 -2x)
Step-by-step explanation:
Written in standard form, both equations are ...
2x +y = 2
Since they are both the same, there are an infinite number of solutions. We can write those solutions in terms of x as ...
y = 2 -2x
The solutions are ...
(x, 2 -2x)
Multiply (x2 + 3x + 4)(3x2 - 2x + 1).
Answer:
The answer is
3x⁴ + 7x³ + 7x² - 5x + 4Step-by-step explanation:
(x² + 3x + 4)(3x² - 2x + 1)
Expand the terms
We have
3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4
Group like terms
That's
3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4
Simplify
We have the final answer as
3x⁴ + 7x³ + 7x² - 5x + 4Hope this helps you
Salaries of 43 college graduates who took a statistics course in college have a mean,66,000 , of . Assuming a standard deviation, 18908 , of $, construct a %99 confidence interval for estimating the population mean .
Answer:
$[58543.42; 73456.58]
Step-by-step explanation:
Hello!
For the variable
X: salary of a college graduate that took a statistics course
Out of n= 43 students, the calculated mean is [tex]\frac{}{X}[/tex]= $66000
The population standard deviation is δ= $18908
There is no information about the variable distribution, but since the sample size is big enough (n≥30), you can apply the CLT and approximate the distribution of the sample mean to normal [tex]\frac{}{X}[/tex]≈N(μ;σ²/n)
Then you can apply the approximation of the standard normal distribution to calculate the 99% CI
[tex]\frac{}{X}[/tex] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Singma}{\sqrt{n} }[/tex]
[tex]Z_{1-\alpha /2}= Z_{0.995}= 2.586[/tex]
[tex]\frac{Singma}{\sqrt{n} }= \frac{18908}{\sqrt{43} }= 2883.44[/tex]
[66000±2.586*2883.44]
$[58543.42; 73456.58]
With a 99% confidence level you'd expect that the interval $[58543.42; 73456.58] will include the average salary of college graduates that took a course of statistics.
I hope this helps!
Find the next two !!!
It's adding 3 and subtracting 2 every time.
This means the next two terms would be +3 and -2 since the last one was -2.
The next term = 4+3=7
The next next term = 7-2=5
Answer:
Answer : 7 , 5Please see the attached picture.
Hope it helps...
Best regards!!
In a class full of men and women, 5 9 of the class are women. What is the ratio of men to women in its simplest form?
Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
∫x2/x1−20x2−125dx
Answer:
125/6(In(x-25)) - 5/6(In(x+5))+C
Step-by-step explanation:
∫x2/x1−20x2−125dx
Should be
∫x²/(x²−20x−125)dx
First of all let's factorize the denominator.
x²−20x−125= x²+5x-25x-125
x²−20x−125= x(x+5) -25(x+5)
x²−20x−125= (x-25)(x+5)
∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx
x²/(x²−20x−125) =x²/((x-25)(x+5))
x²/((x-25)(x+5))= a/(x-25) +b/(x+5)
x²/= a(x+5) + b(x-25)
Let x=25
625 = a30
a= 625/30
a= 125/6
Let x= -5
25 = -30b
b= 25/-30
b= -5/6
x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)
∫x²/(x²−20x−125)dx
=∫125/6(x-25) -∫5/6(x+5) Dx
= 125/6(In(x-25)) - 5/6(In(x+5))+C