Suppose that a company's sales were $1,000,000 6 years ago and are $9,000,000 at the end of the 6 years. Find the geometric mean growth rate of sales. (Round your answer to 4 decimal places.)
Answers
Answer:
The geometric mean growth rate of sales is 1.4422.
Step-by-step explanation:
We have two sales values, one from 6 years ago and the other from now.
We have to calculate the geometric growth rate of sales.
We have:
[tex]y(-6)=1,000,000\\\\y(0)=9,000,000[/tex]
We can write the relation between these two values as:
[tex]y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422[/tex]
The geometric mean growth rate of sales is 1.4422.
Related Questions
A random sample of 150 mortgages in the state of Florida was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is ________.
Answers
Answer:
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
What are two possible measures of the angle below?
Answers
The smaller angle, inside the bold lines, is -90 degrees.
The larger angle, outside the bold lines, is 270 degrees.
Angles can be measured in increments between -90° and 630°.
What angles are created when two lines cross one other?Two straight lines are considered to be intersecting if they come together at the same point. The intersection of two lines is known as the junction point. When two lines intersect, four angles are produced. The sum of the four angles is always 360 degrees.
Two straight lines that cross one other and produce right angles are called perpendicular lines. There are four right angles created when two perpendicular lines cross.
There are two types of angle connections produced when lines intersect:
Congruent opposite angles
Nearby angles are helpful
The information is
Let O (0, 0) be the origin, where the y and x axes must connect.
Thus, the angles on the four quadrants of the axis are produced.
The fourth quadrant's crossing lines create an angle that is given by For, the anticlockwise measure, A = -90°.
B = 360n - 180° for the clockwise measure, and n = 3 in this case.
Hence, when we simplify, we obtain
The second angle has a length of = 630°.
As a result, the angles are 90° and 630°.
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A certain manufactured product is supposed to contain 23% potassium by weight. A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2. If the mean percentage is found to differ from 23, the manufacturing process will be recalibrated.
a. State the appropriate null and alternate hypotheses.
b. Should the process be recalibrated? Explain.
c. Compute the P-value.
Answers
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%
(b) We conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) P-value is 0.6%.
Step-by-step explanation:
We are given that a certain manufactured product is supposed to contain 23% potassium by weight.
A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.
Let [tex]\mu[/tex] = mean percentage of potassium by weight.
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23% {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23% {means that the mean percentage is different from 23 and the manufacturing process will be re-calibrated}
The test statistics that would be used here One-sample t-test statistics as we don't know about 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 percentage = 23.2
s = sample standard deviation = 0.2
n = sample of specimens = 10
So, the test statistics = [tex]\frac{23.2-23}{\frac{0.2}{\sqrt{10} } }[/tex] ~ [tex]t_9[/tex]
= 3.162
The value of t test statistic is 3.162.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.
(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) The P-value of the test statistics is given by;
P-value = P( [tex]t_9[/tex] > 3.162) = 0.006 or 0.6%
(a) Null Hypothesis, [tex]H_o:\mu[/tex]: = 23%
Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%
(b) We conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) P-value is 0.6%.
What is a null hypothesis?The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
We are given that a certain manufactured product is supposed to contain 23% potassium by weight.
A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.
Let = mean percentage of potassium by weight.
(a) Null Hypothesis, [tex]H_o:\mu[/tex]: = 23% {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}
Alternate Hypothesis, [tex]H_A:\mu\neq[/tex]: 23% {means that the mean percentage is different from 23 and the manufacturing process will be re-calibrated}
The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;
[tex]TS=\dfrac{X-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_{n-1}[/tex]
where, = sample mean percentage = 23.2
s = sample standard deviation = 0.2
n = sample of specimens = 10
So, the test statistics = [tex]\dfrac{23.2-23}{\frac{0.2}{\sqrt{10}}}[/tex] ~ [tex]t_g[/tex]
= 3.162
The value of t test statistic is 3.162.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.
(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) The P-value of the test statistics is given by;
P-value = P( [tex]t_g[/tex] > 3.162) = 0.006 or 0.6%
Hence ,
(a) Null Hypothesis, [tex]H_o:\mu[/tex]: = 23%
Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%
(b) We conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) P-value is 0.6%.
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Given ∠E≅∠P, K is the midpoint of EP Prove EG≅MP
Answers
Answer:
∠E≅∠P || Given
∠EKG≅∠PKM || Vertical angles
EK≅KP || Midpoint Theorem
EKG≅PKM || AAS(Angle Angle Side)
EG≅MP || CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Step-by-step explanation:
What is the approximate length of minor arc LM? Round to
the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters
Answers
Answer:its 15.7
Step-by-step explanation:
Answer:
15.7
Step-by-step explanation:
Write the coordinates of the vertices of a triangle A'B'C' that results from a translation of triangle ABC two units to the right and four units down .
Answers
Answer:
A'(4,-6) , B'(0,1), C'(-2,-2)
Step-by-step explanation:
From the given graph the coordinates of ΔABC area A (2,-2), B(-2,5) and C(-4,2)
If a translation is applied on ΔABC two units to the right and four units down to create ΔA'B'C'.
Then to find the coordinates of ΔA'B'C' will be we need to apply the translation rule
[tex](x,y)\rightarrow(x+2,y-4)[/tex]
Now, [tex]A(2,-2)\rightarrow A'(2+2,-2-4)=A'(4,-6)[/tex]
[tex]B(-2,5)\rightarrow B'(-2+2,5-4)=B'(0,1)[/tex]
and [tex]C(-4,2)\rightarrow C'(-4+2,2-4)=C'(-2,-2)[/tex]
Find tan x if sec x = sort 37/6 and sin x <0
Answers
Answer:
tan(x) = -1/6
Step-by-step explanation:
We can use the relation between tan and sec:
[tex]\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}[/tex]
The tangent of x is -1/6.
What is the solution? X/12+3< or = 7
Answers
Answer:
x <= 48
Step-by-step explanation:
Subtract 3 from both sides
x/12 <= 4
Multiply by 12
x <= 48
Solve 23 - Q >-3(2-6)
Answers
Answer:
q < 11
Step-by-step explanation:
Distribute the -3
23 - q > 12
Add q and subtract 12
q < 11
Step-by-step explanation:
the answer is
q<11
23-q>12
Which of the following sequences is arithmetic? A 3, 9, 15, 21, 27, . . . B 3, 9, 17, 27, 39, . . . C 3, 9, 27, 81, 243, . . .
Answers
Answer:
A) 3, 9, 15, 21, 27, . . .
Step-by-step explanation:
EDGE 2020
Answer:
The second answer is 6.
Step-by-step explanation:
D=6
simplify 2x+x+x+2y times 3y times y
Answers
Answer:
12 x y² + 6 y³
Step-by-step explanation:
Step(i):-
Given ( 2 x + x + x + 2 y ) times 3 y times y
( 2 x + x + x + 2 y ) × 3 y × y = ( 4 x + 2 y) × 3 y × y = ( 4 x + 2 y) 3 y²
By applying Distributive property
( a + b ) c = a . c + b . c
= 4 x . 3 y² + 2 y . 3 y²
= 12 x y² + 6 y³
Final answer:-
( 2 x + x + x + 2 y ) times 3 y times y = 12 x y² + 6 y³
Concur Technologies Inc is a large expense-management company located in Redmond Washington. The wall street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city with an avg daily hotel room rate of $198 and an avg amount speny on entertainment, including group meals and tickets for shows sports and other events of $172 in comparison the U.S averages for these two categories were $89 for the room rate and $99 for entertainment the following table shows the average daily hotel room rate and the amount spent on the entertainment for a sample of 9 of the 25 most visited U.S cities Room Rate EntertainmentCity ($) ($)Boston 148 161Denver 96 105Nashville 91 101New orleans 110 142Phoenix 90 100San Diego 102 120San Francisco 136 167San Jose 90 140Tampa 82 98 develop a scatter diagram for these data with the room rate as the independent variablewhat does the scatter diagram developed in part (a.) indicate about the relationship between the two variablesdevelop the least squares estimated regression equationprovide an interpretation for the slope of the estimated regression equationthe avg room rate in Chicago is $128 considerably higher than the U.S avg predict the entertainment expense per day in Chicago
Answers
Answer:
Step-by-step explanation:
Hello!
Given the variables
X: daily hotel room rate
Y: amount spent on the entertainment
See second attachment for scatter plot.
The population regression equation is E(Yi)= α + βXi
To estimate the y-intercept and the slope of the regression equation you have to apply the following formulas:
[tex]b= \frac{sum XY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
a= Y[bar]-bX[bar]
n= 9; ∑X= 945; ∑X²= 103325; ∑Y= 1134 ∑Y²= 148804; ∑XY= 123307
X[bar]= ∑X/n= 945/9= 105
Y[bar]= ∑Y/n= 1134/9= 126
[tex]b= \frac{123307-\frac{945*1134}{9} }{103325-\frac{(945)^2}{9} }= 1.03[/tex]
a= 126 - 1.03*105= 17.49
^Y= 17.49 + 1.03Xi
Slope interpretation: The estimated average amount spent on entertainment increases 1.03 every time the daily hotel room rate increases one unit.
If the room rate for Chicago is $128 (X), to predict the mount spent in entertainment (Y) you have replace it in the estimated regression line:
^Y= 17.49 + 1.03Xi= 17.49 + 1.03*128= 149.33
The expected amount spent on entertainment for Chicago is $149.33
I hope this helps!
What is the circumference of the circle? Use 3.14 for Pi. A circle with diameter 33 centimeters.
Answers
Answer:
207.24cm
Step-by-step explanation:
Circumference=2pi*r
=2 (3.14)(33)
=207.24cm
The circumference of the circle is 103.62 cm².
Given that, a circle with diameter of 33 cm.
Radius=d/2=16.5 cm.
What is the formula to find the circumference of the circle?The formula to find the circumference of the circle is 2πr.
Now, 2×3.14×16.5=103.62 cm².
Therefore, the circumference of the circle is 103.62 cm².
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Lesson 10 congruent triangles unit test
Answers
Answer:
Step-by-step explanation:
Wheres the question??
Please help me HURRY!!!!!!
Answers
A supervisor records the repair cost for 14 randomly selected refrigerators. A sample mean of $79.20 and standard deviation of $10.41 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $79.20
Standard deviation r = $10.41
Number of samples n = 14
Confidence interval = 90%
Using the z table;
The critical value that should be used in constructing the confidence interval.
z(α=0.05) = 1.645
Critical value at 90% confidence z = 1.645
Substituting the values we have;
$79.20+/-1.645($10.42/√14)
$79.20+/-1.645($2.782189528308)
$79.20+/-$4.576701774067
$79.20+/-$4.577
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result
Answers
Answer:
4.76% probability that a randomly selected person from the population has a positive test result
Step-by-step explanation:
We have these following probabilities:
4% probability of having the disease.
If a person has a disease, 95% probability of a positive test.
100-4 = 96% probability a person does not have the disease.
If a person does not have the disease, 1% probability of a positive test.
What is the probability that a randomly selected person from the population has a positive test result
95% of 4% and 1% of 96%. So
p = 0.95*0.04 + 0.01*0.96 = 0.0476
4.76% probability that a randomly selected person from the population has a positive test result
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a left-tailed test is z = -1.63.
a. 0.1032; fail to reject the null hypothesis
b. 0.0516; reject the null hypothesis
c. 0.9484; fail to reject the null hypothesis
d. 0.0516; fail to reject the null hypothesis
Answers
Answer:
Option d
Step-by-step explanation:
The p-value is 0.0516 which is not statistically significant to reject the null hypothesis. Thus we will fail to reject the null hypothesis.
g(x)4x^2-16x+7 completing the square
Answers
Decimal form:
X= 5.32 X= -1.32
If that’s not what your looking for then the answer is: y= 4(x-2)^2 -9
By completing the square the function will be, g(x)=4(x-2)²-9
What is standard form of the equation?The standard form of the quadratic equation will be ax²+bx+c=0.
Equate the given equation with standard form of equation and determine the values of a, b, and c.
a=4
b=-16
c=7
For completing the square, add and subtract [tex]\frac{b^2}{4a}=\frac{(-16)^2}{4\times4}=16[/tex] in the given equation.
g(x)=4x²-16x+16-16+7
g(x)=(4x²-16x+16)-9
g(x)=4(x²-4x+4)-9
The term x²-4x+4 is equivalent to (x-2)².
g(x)=4(x-2)²-9
So, the given function is same as g(x)=4(x-2)²-9.
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In order to solve for the variable in the equation 2 (x + 3) + 5 x = 3 (2 x minus 1), Jaleesa begins by applying the distributive property, then combines like terms. Which equation is the result of these steps?
Answers
Answer:
7x+6 = 6x-3
Step-by-step explanation:
2 (x + 3) + 5 x = 3 (2 x - 1)
Distribute
2x+6+5x = 6x-3
Combine like terms
7x+6 = 6x-3
Answer:
7x + 6 = 6x - 3 Option A
Step-by-step explanation:
Now Jalesa wants to simplify this equation.
Firstly applying the distributive property
Distribute the 2 over the parenthesis and distribute the over the parenthesis
that is,
2*x + 2*3 + 5x = 3*2x - 3*1
2x + 6 + 5x = 6x - 3
After that combine like terms
2x + 5x + 6 = 6x - 3
7x + 6 = 6x - 3
Result is:
7x + 6 = 6x - 3
That's the final answer.
In football seasons, a team gets 3 points for a win, 1 point for a draw and 0 points for a
loss. In a particular season, a team played 34 games and lost 6 games. If the team had a
total of 70 points at the end of the season, what is the difference between games won and lost
Answers
Answer:
The difference between the games won and lost = 21 - 6 =15
Step-by-step explanation:
According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.
A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.
The team played a total of 34 games.
Total games played = 34
Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,
34 - 6 = 28 games was won or draw
Let
the number of games won = x
the number of game drew = y
3x + y = 70.............(i)
x + y = 28................(ii)
x = 28 - y
insert the value of x in equation(i)
3(28 - y) + y = 70
84 - 3y + y = 70
84 - 70 = 3y -y
14 = 2y
divide both sides by 2
y = 14/2
y = 7
insert the value of y in equation(ii)
x + y = 28
x = 28 - 7
x = 21
The team won 21 games , drew 7 games and lost 6 games.
The difference between the games won and lost = 21 - 6 =15
42,000 as a multipul of a power of 10
Answers
Answer:
[tex] 4.2 \times {10}^{4} [/tex]
Step-by-step explanation:
[tex]42000 = 4.2000 \times \times {10}^{4} \\ = 4.2 \times {10}^{4} [/tex]
PLEASE HURRY! Circle B is shown. Line segments A B and C B are radii. The length of A B is 6. Sector A B C is shaded. The measure of central angle ABC is StartFraction pi Over 2 EndFraction radians. What is the area of the shaded sector? 6Pi units squared 9Pi units squared 18Pi units squared 36Pi units squared
Answers
Answer:
(B)[tex]9 \pi $ units squared[/tex]
Step-by-step explanation:
In circle B, AB is one of the radii; and
AB=6
Central Angle of ABC [tex]=\dfrac{\pi}{2}$ radians[/tex]
Now, Area of a Sector
[tex]\text{Area of a Sector}=\dfrac{\theta}{2\pi} \times \pi r^2 \\=\dfrac{\frac{\pi}{2}}{2\pi} \times \pi \times 6^2\\=\dfrac{\pi}{4\pi} \times \pi \times 6^2\\=\dfrac{36}{4} \times \pi \\= 9 \pi $ units squared[/tex]
Answer:
b
Step-by-step explanation:
Given the function f(x) = 2|x + 6|- 4, for what values of x is f(x) = 6?
x=-1, x = 11
x=-1, x=-11
x = 14, x=-26
x = 26. x=-14
Answers
Answer:
solution is [tex]\boxed{x=-1,x=-11}[/tex]
Step-by-step explanation:
f(x)=2|x+6|-4
either x+6 is positive and then |x+6|=x+6
or it is negative and |x+6| = -(x+6)=-x-6
case 1: x>=-6
f(x)= 2x+12-4=2x+8
f(x)=6 <=> 2x+8=6 <=> 2x = 6-8=-2 <=> x = -1
case 2: x<=-6
f(x)=-2x-12-4=-2x-16
f(x)=6 <=> -2x-16=6 <=> 2x=-16-6 = -22 <=> x = -11
so to recap, the solutions are x=-1 and x=-11
The value of x from the modulus value function is x = -1 and x = -11
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 2 | x + 6 | - 4 be equation (1)
On simplifying , we get
when the value of f ( x ) = 6
Substituting the value of f ( x ) = 6 , we get
6 = 2 | x + 6 | - 4
Adding 4 on both sides , we get
2 | x + 6 | = 10
Divide by 2 on both sides , we get
| x + 6 | = 5
And , If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
So , the two values of x are given by
when x + 6 = -5 and x + 6 = 5
x = -1 and x = -11
Hence , the values of x of modulus function is x = -1 and x = -11
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Four men are to divide K500 equally among them. When the money was given, 20% was taken away.
How much each did the four men receive?
Answers
Answer: 20% of 500= 100
So 500-100 = 400
4x100= 400
Step-by-step explanation:
Gary buys a 3 1/2 pound bag of dog food every 3 weeks. Gary feeds his dog the same amount of food each day. Which expression can Gary use to determine the number of pounds of dog food his dog eats each year?
Answers
Answer:
7/2 x 52/3
Step-by-step explanation:
Steps:
Since 1 year = 52 weeks
52*7/2*3= 7/2*52/3
Since 1 year equal 52 weeks meaning we have to times 52 by 7/2 then times by 3 the weeks. The answer is below.
Answer: 7/2 x 52/3
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Hope this helps.
The table represents a linear equation.
Which equation correctly uses point (-2, -6) to write the
equation of this line in point-slope form?
х
-4
-2
6
10
y
-11
-6
14
24
y-6 = {(x - 2)
• y-6 = (x - 2)
y +6 = } (x + 2)
y+6= {(x + 2)
Answers
Answer:
see below
Step-by-step explanation:
Considering the last two table entries, we can find the slope of the line to be ...
Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
For (h, k) = (-2, -6) and m = 5/2, this is ...
y -(-6) = 5/2(x -(-2))
y +6 = 5/2(x +2) . . . . . matches the last choice
Answer:
d is the right choice
Step-by-step explanation:
A random sample of math majors taking an introductory statistics course were surveyed after completing the final exam. They were asked, "How many times did you review your final exam before handing it in to the professor?" The results are displayed in a probability density function for the random variable X, the number of times students reviewed their exam before handing it in. Find the standard deviation of X. Round the final answer to two decimal places. x P(X = x) 1 1/5 2 2/5 7 2/5
Answers
Answer:
[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]
The variance would be given by:
[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]
And the deviation would be:
[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]
Step-by-step explanation:
For this case we have the following distribution given:
X 1 2 7
P(X) 1/5 2/5 2/5
We need to begin finding the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]
The variance would be given by:
[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]
And the deviation would be:
[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]
Could someone help me with this trigonometry question where you have find the x which is the adjacent. the reference angle is 39 degree and the opposide side is 30 cm.
Answers
Answer:
37.047
Step-by-step explanation:
Sin(39) = 30/hyp
Cos(39) = x/hyp
hyp = 30/Sin(39)
and hyp = x/Cos(39)
hyp = hyp
30/Sin(39) = x/Cos(39)
x = 30(Cos(39))/Sin(39)
x is approximately equal to 37.047
What is the difference?
х
4
x2-2x-15 x² + 2x-35
x2 + 3x+12
(x-3)(x-5)(x+7)
x(x+3-12)
(x+3)(x-5)(x+7)
x2 + 3x+12
(x+3)(x-5)(x+7)
x2 + 3x-12
(x+3)(x-5)(x+7)
Answers
The difference of the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first equation be P = x / ( x² - 2x - 15 )
Let the second equation be Q = 4 / x² + 2x - 35 )
Now , A = P - Q
On simplifying , we get
A = x / ( x² - 2x - 15 ) - 4 / x² + 2x - 35 )
Taking the LCM , we get
A = x ( x + 7 ) - 4 ( x + 3 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = x² + 7x - 4x + 12 / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Therefore , the value of A is ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Hence , the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
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