4x - 2y = 7
x + 2y = 3
5x = 10
x=2 and y=0
Answer:
{x,y} = {2,1/2}
Step-by-step explanation:
Solve by Substitution :
1. Solve equation [2] for the variable x
[2] x = -2y + 3
2. Plug this in for variable x in equation [1]
[1] 4•(-2y+3) - 2y = 7
[1] - 10y = -5
3.Solve equation [1] for the variable y
[1] 10y = 5
[1] y = 1/2
By now we know this much :
x = -2y+3
y = 1/2
4.Use the y value to solve for x
x = -2(1/2)+3 = 2
Solution :
{x,y} = {2,1/2}
Martha’s annual salary last year was $72,000. What was her gross pay each month?
Answer:
$6000
Step-by-step explanation:
so she made 72000 in a year, a year as 12 months so to find the monthly rate we just need to divide 72000 by 12 which gives 6000
Answer:
The Correct answer is 6000
Step-by-step explanation:
All you do is divide all the months in a year by how much she got paid to find salary.
The radius of the earth is 3959 miles. A meteor with a diameter of 750 miles strikes the earth in unpopulated area. What percentage of the earths surface is affected by the meteor strike
Answer:
0.9%
Step-by-step explanation:
To determine the percentage of Earth's surface affected by a meteor strike, we calculate the surface area of Earth and the area of impact, then divide the area of impact by Earth's total surface area and multiply by 100 to get a percentage. Using the given Earth's radius of 3959 miles and the meteor's diameter of 750 miles, the affected area is approximately 0.224% of Earth's surface.
Explanation:To calculate the percentage of the Earth's surface affected by a meteor strike, we can use the formula for the surface area of a sphere and the formula for the surface area of a circle, which represents the affected area.
The total surface area of the Earth (AEarth) is given by 4πr2, where r is the radius of the Earth. The radius of the Earth is 3959 miles.
The surface area affected by the meteor (AMeteor) can be approximated by the surface area of a circle, πd2/4, where d is the diameter of the meteor. The diameter of the meteor is 750 miles. Therefore, the affected area is approximately π * (7502)/4.
Now we can calculate both the total surface area of the Earth and the affected area:
AEarth = 4π * (39592) = about 197 million square milesAMeteor = π * (7502)/4 = about 441,963 square milesTo find the percentage of the surface affected, we divide the affected area by the total surface area and then multiply by 100:
Percentage = (AMeteor / AEarth) * 100
Percentage = (441,963 / 197,000,000) * 100 = 0.224% of the Earth's surface is affected by the meteor strike.
Based on this data, what is a reasonable estimate of the probability that Todd runs more than 15 km tomorrow?
Answer: 5/13
Step-by-step explanation:
I got it correct
> (889 x 27) + 50 is __
than 889 x 27
+27 more
+
50 less
• 27 less
27 less
50 more
Answer:
50 is more than 27
Step-by-step explanation:
27 comes before 50
(1) True/False: (a) To reduce the margin of error in a stratified sample, we should design strata so that the units within each stratum are as similar as possible. (b) To reduce the margin of error in a cluster sample, we should design clusters so that the units within each cluster are as similar as possible.
Answer:
(1) True / False: (a) To reduce the margin of error in a stratified sample, we must design strata so that the units within each stratum are as similar as possible.
R = True, since to have a more exact margin you have to eliminate the errors, and as we do it by running error by error, in order to obtain a point on the graph where the products are within the positive margin and you can obtain a graph less error than the beginning.
(b) To reduce the margin of error in a group sample, we must design groups so that the units within each group are as similar as possible.
R = if this type of procedure is reliable because it helps you to correct the errors of the procedure, but to be able to do it you have to have very well accounted for, each piece of information, whether negative or positive, of the study being carried out and from there to create data that help reduce the margin of error.
Sergio weighed 2.9 kg at birth. Convert this to grams.
Answer:
2900g
Step-by-step explanation:
1kg=1000g
2.9(1000)
=2900g
If you deposit $5,000 into an account that pays 4% simple interest, what will the balance be in 6 years?
Answer:
$6,200 i hope this helps! :)
Step-by-step explanation:
the 4% interest of the $5000 4% of 5000 = 200
multiply by 6 for the 6 years 200 * 6 = 1200
add the 1200 to the 5000 5000 + 1200 = 6,200
Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 29 6 39 35 3 46 35 7 35 29 4 38 31 The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.
To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.
Explanation:To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.
The null hypothesis (H0) is that the mean difference is equal to $10, while the alternative hypothesis (Ha) is that the mean difference is not equal to $10.We calculate the sample mean difference and the standard deviation of the differences.We calculate the t-statistic using the formula: t = (sample mean difference - hypothesized mean difference) / (standard deviation of the differences / sqrt(n)), where n is the number of pairs of observations.We compare the t-statistic to the critical value from the t-distribution with n-1 degrees of freedom at a significance level of 0.05.If the absolute value of the t-statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean difference is not equal to $10. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean difference is not equal to $10.A report on the U.S. economy indicates that 28% of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities judged to be especially economically depressed and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities? What are the correct null and alternative hypotheses for testing such a claim?
Answer:
For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:
NUll hypothesis: [tex]p \leq 0.28[/tex]
Alternative hypotheis: [tex] p >0.28[/tex]
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Solution to the problem
For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:
NUll hypothesis: [tex]p \leq 0.28[/tex]
Alternative hypotheis: [tex] p >0.28[/tex]
In a certain power plant it was found necessary to store some water in a vertical tank 5 inches in diameter and 10 ft. long at a temperature of 200 degrees F. When the water temperature dropped to 125 degrees F it was necessary to replenish the tank with hot water. Observations showed that it cooled 10 degrees F in 1 hour 15 minutes at an outside temperature of 75 degrees F. How long will it take to cool to 125 degrees F when the 100 drop in 1.25 hours occurs with the initial water temperature of 2000 F.
Answer:
It takes approximately 13.737 hours for the 200 degree water to cool down to 125 degrees.
Step-by-step explanation:
Recall Newton's Law of heating and cooling for an object of initial temperature [tex]T_0[/tex], in an ambient temperature [tex]T_a[/tex]:
[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}[/tex]
where t is the time elapsed.
We know the ambient temperature and the initial temperature of the object, but we don't know the value of the constant "k" that describes the cooling process. We can obtain such value (k) by using the information that the 200 degrees water cooled 10 degrees in 1.25 hours.
In such case we have:
[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}\\200-10=75+(200-75)\,e^{-k(1.25)}\\190=75+125\,e^{-k(1.25)}\\190-75=125\,e^{-k(1.25)}\\115=125\,e^{-k(1.25)}\\\frac{115}{125}= e^{-k(1.25)}\\0.92=e^{-k(1.25)}\\ln(0.92)=-k\,(1.25)\\k=\frac{ln(0.92)}{-1.25} \\k=0.0667[/tex]
Therefore, we have now the complete expression for the cooling process:
[tex]T(t)=75+125\,e^{-0.0667\,t}[/tex]
To find the time it takes to cool the 200 degree water down to 125 degrees, we use:
[tex]125=75+125\,e^{-0.0667\,t}\\125-75=125\,e^{-0.0667\,t}\\50=125\,e^{-0.0667\,t}\\\frac{50}{125} =e^{-0.0667\,t}\\0.4=e^{-0.0667\,t}\\ln(0.4)=-0.0667\,\,t\\t=\frac{ln(0.4)}{-0.0667} \\t=13.737\,\,hours[/tex]
-2/7х=-1/3, срочно(если что это дроби)
To solve the equation -2/7x=-1/3 for x, you would divide both sides by -2/7. This translates to multiplication of -1/3 by the reciprocal of -2/7 which is -7/2. By performing this multiplication, x equals to 7/6.
Explanation:The equation at question here is -2/7x=-1/3. To solve for x, we need to isolate x on one side of the equation. To do this, we can divide both sides of the equation by -2/7, which is the coefficient of x in the equation. Performing this operation (also known as the division property of equality), we get:
x = (-1/3) ÷ (-2/7)
When we divide by a fraction, it's the same as multiplying by its reciprocal, so:
x = (-1/3) * (-7/2)
Performing this multiplication gives x = 7/6.
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What is the factored expression of 6k+21?
A. 3(2k+6)
B. 3(k+6)
C. 3(2k+7)
Answer:
the answer is C. 3(2k + 7) i hope this helps! :)
Step-by-step explanation:
trying to find 6k + 21
given 3(2k + 6)
distribute the 3 to both inside the parenthesis 6k + 18
given 3(k + 6)
distribute the 3 to both inside the parenthesis 3k + 18
given 3(2k + 7)
distribute the 3 again to both inside of the parenthesis 6k + 21
Answer:
C. 3(2k+7)
Step-by-step explanation:
you should mark me brainliest lol
Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at (6,3). Which point
on the y-axis could be on the edge of the circle if the distance from the center of the circle to the edge is 10 units?
Answer:
(0, –5)
Step-by-step explanation:
If you don't see this option there is another option, (0 , 11) is also correct.
You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of x, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y)= ( , )
Answer:
The solutions listed from the smallest to the greatest are:
x: [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: -1 1 -1 1
Step-by-step explanation:
The slope of the tangent line at a point of the curve is:
[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
[tex]m = -\frac{\cos 2\theta}{\sin \theta}[/tex]
The tangent line is horizontal when [tex]m = 0[/tex]. Then:
[tex]\cos 2\theta = 0[/tex]
[tex]2\theta = \cos^{-1}0[/tex]
[tex]\theta = \frac{1}{2}\cdot \cos^{-1} 0[/tex]
[tex]\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]
[tex]\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]
The first four solutions are:
x: [tex]\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: 1 -1 1 -1
The solutions listed from the smallest to the greatest are:
x: [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: -1 1 -1 1
Using derivatives of the parametric curves and the solving a trigonometric equation, it is found that the points (x,y) are:
[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
Given two parametric curves x(t) and y(t), the slope of the tangent line is given by:
[tex]m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
The tangent line is horizontal for:
[tex]\frac{dy}{dt} = 0, \frac{dx}{dt} \neq 0[/tex]
In this problem, since we are working with trigonometric functions sine and cosine, they will never be simultaneously 0, hence, the equation of interest is:
[tex]\frac{dy}{dt} = 0[/tex]
Then:
[tex]y(t) = \sin{2\theta}[/tex]
[tex]\frac{dy}{d\theta} = 2cos{2\theta}[/tex]
Hence:
[tex]2\cos{2\theta} = 0[/tex]
[tex]\cos{2\theta} = 0[/tex]
[tex]\cos{2\theta} = \cos{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]2\theta = \frac{k\pi}{2}[/tex]
[tex]\theta = \frac{k\pi}{4}, k = 1, 3, 5, \cdots[/tex]
Hence, the points (x,y) are:
[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
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Based on the graph of an exponential function f(x)=b^x, for b >0, describe how you can verify that the output of the function can NEVER be equal to zero.
Answer:
see the explanation
Step-by-step explanation:
we know that
The equation of a exponential growth function is given by
[tex]f(x)=a(b^x)[/tex]
where
a is the initial value or y-intercept
b is the factor growth (b>0)
In this problem
a=1
so
[tex]f(x)=b^x[/tex]
we know that
The graph of the function has no x-intercept
Remember that the x-intercept of a function is the value of x when the value of the function is equal to zero
That means ----> The output of the function can NEVER be equal to zero
Verify
For f(x)=0
[tex]0=b^x[/tex]
Apply log both sides
[tex]log(0)=xlog(b)[/tex]
Remember that
log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.
Final answer:
Exponential functions with a positive base can never output zero due to their growth pattern.
Explanation:
Exponential functions of the form f(x) = b^x, where b is greater than 0, never output zero.
To verify this, consider that any positive number raised to any power will never result in zero, as it will approach zero but never reach it. For example, 2^x will grow rapidly but never touch zero. This property holds true for all exponential functions with a positive base.
An ant arrives at the snail’s starting position at time t=12 minutes and follows the snail’s path. During the interval 12≤t≤15 minutes, the ant travels in the same direction as the snail with a constant acceleration of 2 inches per minute per minute. The ant catches up to the snail at time t=15 minutes. The ant’s velocity at time t=12 is B inches per minute. Find the value of B.
Answer:
B=22.348 Inches per minutes
Step-by-step explanation:
A snail is traveling along a straight path. The snail’s velocity can be modeled by [tex]v(t)=1.4ln(1+t^2)[/tex] inches per minute for 0 ≤ t ≤ 15 minutes.
If the snail's velocity is [tex]v(t)=1.4ln(1+t^2)[/tex] per minute, its displacement for 0 ≤ t ≤ 15 minutes is given by the integral:
[tex]\int_{0}^{15}1.4ln(1+t^2)dt=76.04307[/tex]
The ant travels with a constant acceleration of 2 Inches per minute.
Therefore, the velocity of the ant will be:
[tex] \int 2 dt=2t+c,[/tex] inches per minutes, for some constant c.
For the interval, 12≤t≤15, the displacement of the ant is:
[tex] \int_{12}^{15}(2t+c)dt=t^2+ct|_{12}^{15}=81+3c[/tex]
Since the snails displacement and that of the ant are equal in 12≤t≤15.
81+3c=76.04307
3c=76.04307-81
3c=-4.95693
c=-1.65231
The velocity of the ant at t=12 is therefore:
2t+c=2(12)-1.65231=22.348 Inches per minutes
B=22.348 Inches per minutes
The value of B to the nearest whole number, given all of the factors enumerated above, is 22.4 inches/Min. (For the full answer, please see the attached.)
What is velocity?This simply refers to the pace or rate at which an object or a person changes their position in relation to a frame of reference. It is also a function of time.
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256 divided by 11 equals what
23.27
Use a calculator
For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. A biomarker for bone formation measured was osteocalcin (OC), measured in the blood. The units are nanograms per milliliter (ng/ml). For the 31 subjects in the study the mean was 33.4 ng/ml. Assume that the standard deviation is known to be 19.6 ng/ml. Report the 95% confidence interval:
Answer:
The 95% confidence interval is between 26.5 ng/ml and 40.3 ng/ml
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{19.6}{\sqrt{31}} = 6.9[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 33.4 - 6.9 = 26.5 ng/ml
The upper end of the interval is the sample mean added to M. So it is 6.4 + 33.4 + 6.9 = 40.3 ng/ml
The 95% confidence interval is between 26.5 ng/ml and 40.3 ng/ml
The 95% confidence interval for the mean measurement of the biomarker osteocalcin (OC) is approximately 26.64 ng/ml to 40.16 ng/ml.
Explanation:To calculate the 95% confidence interval for the mean measurement of the biomarker osteocalcin (OC), we can use the formula:
CI = Mean ± Z * (SD / sqrt(n))
Where CI is the confidence interval, Mean is the sample mean, SD is the known standard deviation, Z is the Z-score corresponding to the desired confidence level, and n is the sample size.
In this case, the sample mean is 33.4 ng/ml, the known standard deviation is 19.6 ng/ml, and the sample size is 31. The Z-score for a 95% confidence level is approximately 1.96. Plugging these values into the formula:
CI = 33.4 ± 1.96 * (19.6 / sqrt(31))
Simplifying the formula:
CI = 33.4 ± 6.76
Therefore, the 95% confidence interval for the mean measurement of osteocalcin is approximately 26.64 ng/ml to 40.16 ng/ml.
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1x2x2x2..........50=50!
Consider testing Upper H 0 : mu equals 20H0: μ=20 against Upper H Subscript a Baseline : mu less than 20Ha: μ<20 where muμ is the mean number of latex gloves used per week by all hospitalemployees, based on the summary statistics nequals=444, x overbarxequals=19.3 and sequals=11.1 Complete parts a and b.
Answer:
Test: [tex]\mu[/tex] < 20 with normal distⁿ
Hypothesis test:
H0: [tex]\mu \ge[/tex] 20 (Null Hypothesis, H₀ : [tex]\mu[/tex] = 20 is also correct)
H1: [tex]\mu[/tex] < 20 (Alternative Hypothesis, also called H₁)
This is lower tailed test.
Since sample is large, sample standard deviation can be taken as an approximation of population standard deviation.
x = 19.3
[tex]\sigma[/tex] = 11.1
n = 444
significance level, [tex]\alpha[/tex] = 0.05 (If no value is given, we take level of 0.05)
Test statistic [tex]z* = \frac{x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]= \frac{19.3-20}{11.1/\sqrt{444}}[/tex]
= - 1.33
The attached files contains additional information
what is the equation of the line that passes through the point (-2,-2)and has a slope of 2
Answer:
y+2 = 2(x+2)
Step-by-step explanation:
given point (a,b) and slope m, point slope form of a line is:
y-b = m(x-a)
A clothing store is having a sale on shirts and jeans.Five shirts and 3 pairs jeans cost $220. Six shirts and 2 pairs of jeans cost $200. How much is the cost of one shirt? How much is the cost of pair of jeans?
Answer:
Shirt: $20
Trouser: $40
Step-by-step explanation:
5x + 3y = 220
6x + 2y = 200
3x + y = 100
y = 100 - 3x
5x + 3(100 - 3x) = 220
5x + 300 - 9x = 220
4x = 80
x = 20
y = 100 - 3(20)
y = 40
The cost of a shirt is $20 and the cost of pair of a jeans is $40.
Given that, five shirts and 3 pairs of jeans cost $220. Six shirts and 2 pairs of jeans cost $200.
We need to find the cost of one shirt and the cost of pair of jeans.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1.
A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, and C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations.
Let the cost of a shirt be x and the cost of pair of jeans be y.
Now, five shirts and 3 pairs of jeans cost $220.
That is, 5x+3y=220------(1)
Six shirts and 2 pairs of jeans cost $200.
6x+2y=200------(2)
Multiplying the equation (1) with 2, we get 10x+6y=440------(3)
Multiplying the equation (2) with 3, we get 18x+6y=600------(4)
Now, equation (4)-(3) is 8x=160
⇒x=$20
Substitute x=20 in equation (1), we get 5(20)+3y=220
⇒y=$40
Therefore, the cost of a shirt is $20 and the cost of pair of a jeans is $40.
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Use a series to estimate the following integral's value with an error of magnitude less than 10 Superscript negative 5. Integral from 0 to 0.5 sine x squared dx Integral from 0 to 0.5 sine x squared dxalmost equals nothing (Do not round until the final answer. Then round to five decimal places as needed.)
Answer:
Hey Tamia,
the answer is 0.4969564
Please rate me as brainiest as the answer explanation is in attached picture, which will clear every step.
Thanks
Step-by-step explanation:
To estimate the integral within an error rate, use the power series expansion of sin(x) to construct an equivalent series for sin(x²). Add terms until the error is less than [tex]10^{-5}[/tex]. Integrate each term from 0 to 0.5.
Explanation:To estimate the value of the integral ∫ from 0 to 0.5 sin(x²) dx with an error of magnitude less than 10^-5, we can use a power series expansion of sin(x). The power series expansion is given as sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + .... Now since we are interested in sin(x²), we just replace x in the above series with x²: sin(x²) = x² - (x²)³/3! + (x²)⁵/5! - (x²)⁷/7! + .... This series can be truncated at any term, and the remaining terms would represent the error in your approximation. We keep adding terms until we reach an error less than [tex]10^{-5}[/tex]. Finally, integrate term by term from 0 to 0.5 to get the approximate value of the original integral.
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Round your answer to the nearest hundredth.
Step-by-step explanation:
cosB=4/5
B=36.86°
Hope it helps u
Over which interval on the x-axis is there a negative rate of change in the function?
–2 to –1
–1.5 to 0.5
0 to 1
0.5 to 1.5
Answer:
A -2 to -1
Step-by-step explanation:
What is the slope of the line shown on the graph?
a 5/4
b 4/5
c -5/4
d -4/5
Answer:
B
Step-by-step explanation:
Take 2 points and use the slope formula
The 2 points: (0,0) and (5,4)
The slope formula is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{2} }[/tex]
We can say (0,0) is our first point, and (5,4) is our second, and substitute them in. y2 is 4, y1 is 0, x2 is 5, and x2 is 0.
[tex]m=\frac{4-0}{5-0}[/tex]
[tex]m=\frac{4}{5}[/tex]
So, the slope if 4/5, or choice B
With gasoline prices increasing, drivers are more concerned with their cars’ gasoline consump- tion. For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2. Now that his car is 5 years old, he would like to know whether the variability of gas mileage has changed. He recorded the gas mileage from his last eight fill-ups; these are listed here. Conduct a test at a 10% significance level to infer whether the variability has changed.
28 25 29 25 32 36 27 24
Answer:
The calculated chi -square value =5.7356 Is less than12.01 at 0.1level of significance .
The null hypothesis is accepted.
The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.
Step-by-step explanation:
Step:-(1)
Given data 28 25 29 25 32 36 27 24
Sample size 'n' = 8
mean of the sample (x⁻) = ∑x /n = [tex]\frac{28+ 25+ 29 +25 +32 +36 + 27 + 24}{8}[/tex]
mean of the sample (x⁻) = 28.25
x x- x⁻ (x-x⁻ )²
28 28 - 28.25 = -0.25 0.0625
25 25 -28.25 = -3.25 10.56
29 29-28.25 = 0.75 0.5625
25 25-28.25 = -3.25 10.56
32 32-28.25 = 3.75 14.06
36 36-28.25 = 7.75 60.06
27 27-28.25 = -1.25 1.5625
24 24-28.25 = -4.25 18.06
∑(x-x⁻)² = 115.4875
Step:-(2)
The sample standard deviation
S² = ∑(x-x⁻)²/n-1 = [tex]\frac{115.4875 }{7}[/tex] = 16.49
By using χ² distribution
χ² = [tex]\frac{ns^2 }{variance}[/tex]
By above test can be applied only if the population from which sample is drawn normal.
Given data For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.
Population variance σ² = 23
Step:-(3)
Null hypothesis :H₀:σ² = 23
Alternative hypothesis :H₁:≠23
[tex]X^{2} = \frac{8 (16.49)}{23}=5.7356[/tex]
The calculated chi -square value =5.7356
The degrees of freedom γ=n-1 =8-1=7
The tabulated value of chi -square = 12.01 at 0.1level of significance (check table)
The calculated chi -square value =5.7356 Is less than12.01 at 0.1level of significance .
The null hypothesis is accepted.
Conclusion:-
The null hypothesis is accepted.
The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.
Alicia earned the following amounts pet sitting: $28, $36, $15, $43, $28. Explain how you would describe the data. Use at least 4 words from the Word List in your explanation.
Answer: Step-by-step explanation:
Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.
smaller and larger solution
(x+6)(-x+1)=0
Answer:
x = -6,1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A teaching assistant collected data from students in one of her classes to investigate whether study time per week (average number of hours) differed between students in the class who planned to go to graduate school and those who did not. Complete parts (a) through (C). Data Full data set Graduate school: 13, 7, 15, 10, 5, 5, 2, 3, 12, 16, 15, 39, 8 14, 10, 17, 3, 27, 15, 5, 5 No graduate school: 6, 8, 14, 6, 5, 13, 10, 10, 13, 5 Find a 95% confidence interval comparing the population means. Interpret. Find a 95% confidence interval comparing the population means. The 95% confidence interval for (mu _1 - mu _2) is (1.6, 7.0) (Round to the nearest tenth as needed.)
The given 95% confidence interval of (1.6, 7.0) for the difference between the average weekly study times (mu_1 - mu_2) means we are 95% confident that students planning to attend graduate school study between 1.6 to 7 hours more per week on average than those who do not.
Explanation:The teaching assistant is comparing the average weekly study times between students intending to go to graduate school and those who are not with the use of data. The relevant statistical concept in this context is the confidence interval for the difference in population means.
The given 95% confidence interval for the difference between the average weekly study times (mu_1 - mu_2) is (1.6, 7.0). This interval was calculated from the provided data, and it provides a statistical estimation that, in this context, means we are 95% sure that students who plan to attend graduate school study between 1.6 to 7 hours more per week on average compared to those who do not plan to go to graduate school.
To interpret this, you can say that we are 95% confident that the true difference in average weekly study times between the two groups falls within this interval. As the entire interval is positive, we may infer that those planning for graduate school likely study more on average than their peers not planning for graduate school.
Learn more about confidence interval here:https://brainly.com/question/34700241
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