MATHEMATICS COLLEGE

Which of the following scatterplots would have a trend line with a positive slope?

Answers

Answer 1

Answer: the first one will be positive!

Answer 2

Answer:

Answer:

It's the first answer.

Step-by-step explanation:

As demonstrated through the image, the slope increases. Thus making it a positive slope.

Related Questions

Two cars are traveling at 40 and 50 miles per hour, respectively. If the second cars out 5 miles behind the first car. How long will it take the second car to overtake the first car.
What’s the square root of 9/100
A)0.5B)2.5C)-0.5D)-2.5
A sixth-grade class is painting a mural. To make a darker shade of orange, they use a ratio of 5 ounces of red paint to3 ounces of yellow paint. Use this ratio to consider the amount of yellow paint needed for each amount of red paintlisted in the table.PointRed Paint, x (ounces)Yellow Paint, y ounces)A5tsB15C20
A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, which statement must be true? The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 3 to 2. The ratio of paperback books to hardback books is 3 to 2. There are exactly 2 paperback books in the library. There are exactly 2 paperback books in the library. There are exactly 8 hardback books in the library. There are exactly 8 hardback books in the library.

A vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m. What is the vehicle's acceleration if its value may b assumed to be constant? A.2.0m/s
B.5.0m/s
C.10m/s
D.15m/s

Answers

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

Given that, a vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m.

What is an acceleration?

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction-or change both.

Here, Δx = 45 m, v₀ = 0 m/s and v = 30 m/s

Using the formula v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2b (45 m)

b = 10 m/s

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

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Answer:

C. 10 m/s²

Step-by-step explanation:

Given:

Δx = 45 m

v₀ = 0 m/s

v = 30 m/s

Find: a

v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2a (45 m)

a = 10 m/s²

If f (x)=x/2+8 what is f (x) when x=10

Answers

Answer: 13

Step-by-step explanation: Plug 10 in for x; 10/2=5; 5+8=13

Which of terms could be added to √5?

Answers

10 is the correct answer

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Answers

Answer:

Iteration 1: $x_(2)=1.446$

Iteration 2: $x_(3)=1.337$

Step-by-step explanation:

Formula for Newton's method is,

$x_(n+1)=x_n-(f\left(x_n\right))/(f'\left(x_n\right))$

Given the initial guess as $x_(1)=1.6$ , therefore value of n = 1.

Also, $f\left(x\right)=x^(9)-9$ .

Differentiating with respect to x,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9-9\right)$

Applying difference rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9\right)-(d)/(dx)\left(9\right)$

Applying power rule and constant rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=\left(9x^(9-1)\right)-0$

$(d)/(dx)\left(f\left(x\right)\right)=9x^(8)$

Substituting the value,

$x_(1+1)=x_1-(f\left(x_1\right))/(f'\left(x_1\right))$

$x_(2)=1.6-(f\left(1.6\right))/(f'\left(1.6\right))$

Calculating the value of $f\left(1.6\right)$ and $f'\left(1.6\right)$

Calculating $f\left(1.6\right)$

$f\left(1.6\right)=\left(1.6\right)^(9)-9$

$f\left(1.6\right)=59.71947674$

Calculating $f'\left(1.6\right)$ ,

$f'\left(1.6\right)=9\left(1.6\right)^(8)$

$f'\left(1.6\right)=386.5470566$

Substituting the value,

$x_(2)=1.6-(59.71947674)/(386.5470566)$

$x_(2)=1.446$

Therefore value after second iteration is $x_(2)=1.446$

Now use $x_(2)=1.446$ as the next value to calculate second iteration. Here n = 2

Therefore,

$x_(2+1)=x_2-(f\left(x_2\right))/(f'\left(x_2\right))$

$x_(3)=1.446-(f\left(1.446\right))/(f'\left(1.446\right))$

Calculating the value of $f\left(1.446\right)$ and $f'\left(1.446\right)$

Calculating $f\left(1.446\right)$

$f\left(1.446\right)=\left(1.446\right)^(9)-9$

$f\left(1.446\right)=18.63851065$

Calculating $f'\left(1.446\right)$ ,

$f\left(1.446\right)=9\left(1.446\right)^(8)$

$f\left(1.446\right)=172.0239252$

Substituting the value,

$x_(3)=1.446-(18.63851065)/(172.0239252)$

$x_(3)=1.337$

Therefore value after second iteration is $x_(3)=1.337$

Final answer:

To calculate two iterations of Newton's Method, use the formula xn+1 = xn - f(xn)/f'(xn). Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, calculate f(xn) and f'(xn) at x1 and then use the formula to find x2 and x3.

Explanation:

To calculate two iterations of Newton's Method, we need to use the formula:

xn+1 = xn - f(xn)/f'(xn)

Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, we can proceed as follows:

Calculate f(xn) at x1: f(1.6) = (1.6)9 - 9 = 38.5432
Calculate f'(xn) at x1: f'(1.6) = 9(1.6)8 = 368.64
Calculate x2: x2 = 1.6 - f(1.6)/f'(1.6) = 1.6 - 38.5432/368.64 = 1.494
Repeat the process to find x3 using the updated x2 as the initial guess.

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In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. In another city known for biotech firms, 334 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. Perform a two-proportion hypothesis test to determine whether there is a difference in the proportions of college graduates with outstanding student loans who currently owe more than $50,000 in these two cities. Use α=0.05. Assume that the samples are random and independent. Let the first city correspond to sample 1 and the second city correspond to sample 2. For this test: H0:p1=p2; Ha:p1≠p2, which is a two-tailed test. The test results are: z≈−1.17 , p-value is approximately 0.242

Answers

Answer:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

$p_v =2*P(Z<-1.182)=0.2372$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_(1)=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_(2)=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_(1)=800$ sample 1

$n_(2)=800$ sample 2

$p_(1)=(311)/(800)=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_(2)=(334)/(800)=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_(1)-p_(2)}{\sqrt{\hat p (1-\hat p)((1)/(n_(1))+(1)/(n_(2)))}}$ (1)

Where $\hat p=(X_(1)+X_(2))/(n_(1)+n_(2))=(311+334)/(800+800)=0.403$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

4) Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z<-1.182)=0.2372$

Emily and Miranda are standing outside. Emily is 5 feet tall and casts a shadow of 28 inches. Miranda's shadow is 29.4 inches long. Approximately how tall is Miranda?

Answers

Answer:

5.25ft

Step-by-step explanation:

i got the question right so thats it

Answer:

5 1/4

Step-by-step explanation:

5 1/4 to decimal form is 5.25

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