-1.9+4+(-1.6) simplify the expression

Answer:

Stephanie runs the fastest per second: 14 feet per second

Step-by-step explanation:

To find the fastest speed, you need to see which person runs the most per second:

Stephanie runs 14 feet per second

Brooke runs 589 feet in 44 seconds.

Find the amount of feet per second by dividing:

[tex]\frac{589}{44} =13.4[/tex]

Brooke runs about 13.4 feet per second

Will runs 1 mile in 454 seconds.

Convert the miles to feet:

There are 5,280 feet in a mile. If Will runs 5,280 feet in 454 seconds, divide to find how much he runs per second:

[tex]\frac{5280}{454}= 11.6[/tex]

Will runs about 11.6 feet per second.

Rob runs 548 feet in a minute.

Convert the minute into seconds. There are 60 seconds in a minute. Divide the feet by the seconds to find how fast he runs per second:

[tex]\frac{548}{60}= 9.1[/tex]

Rob runs about 9.1 feet per second.

Stephanie runs 14 feet per second, the fastest time:

| 14 |, 13.4, 11.6, 9.1

Finito.

Answer:

Step-by-step explanation:

Hello!

The researcher's objective is to test if the variance of the annual repair costs increases with the age of the automobile, i.e. the older the car, the more the repairs costs. The parameters of the study are the population variances of the annual repair costs of 4 years old cars and 2 years old cars.

X₁: Costs of annual repair of a 4 years old car.

Assuming X₁~N(μ₁;δ₁²)

A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170

n₁= 26 and S₁= $170

X₂: Costs of annual repair of a 2 years old car.

Assuming X₂~N(μ₂;σ₂²)

A sample of 25 automobiles 2 years old showed a sample standard deviation for the annual repair cost of $100.

n₂= 25 and S₂= $100

a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for older automobiles.

H₀: δ₁² ≤ σ₂²

H₁: δ₁² > σ₂²

b. At a .01 level of significance, what is your conclusion? What is the p-value? Discuss the reasonableness of your findings.

This is a variance ratio test and you have to use a Snedecor's F-statistic:

[tex]F= \frac{S^2_1}{S_2^2} * \frac{Sigma_1^2}{Sigma_2^2}~~F_{n_1-1;n_2-1}[/tex]

[tex]F_{H_0}= \frac{28900}{10000}*1= 2.89[/tex]

This test is one-tailed to the right and so is the p-value, you have to calculate it under a F₂₅;₂₄

P(F₂₅;₂₄≥2.89)= 1 - P(F₂₅;₂₄<2.89)= 1 - 0.994= 0.006

Using the p-value approach the decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

α: 0.01

The p-value is less than the level of significance, the decision is to reject the null hypothesis.

Then using a 1% level, you can conclude that the population variance of the cost of annual repairs for 4 years old cars is greater than the population variance of the cost of annual repairs for 2 years old cars.

I hope this helps!

Answer:

Step-by-step explanation:

As each exterior angle is 45o , number of angles or sides of the polygon is 360o45o=8 . Further as each exterior angle is 45o , each interior angle is 180o−45o=135o .

The sum of the interior angles of a 45-gon is 7740 degrees.

To calculate the sum of interior angles of a 45-gon, or any polygon, we can use the formula (n - 2) *180 degrees, where n is the number of sides in the polygon. For a 45-gon, we substitute n with 45:

(45 - 2) * 180 = 43 * 180 = 7740

Therefore, the sum of the interior angles of a 45-gon is 7740 degrees.

3/6 or 1/2

could please check out my questions? thx!

Answer: The ice image, bottom left.

Step-by-step explanation:

The albedo values give information about the proportion of radiation that a given object surfaces, for example, if an object has an albedo value of 0.2, this means that the object reflects 0.2*100% = 20% of the radiation.

You usually can see that darker objects have a smaller albedo value, while clearer objects have a bigger albedo value, meaning that as clearer is the color, usually it reflects a bigger proportion of the radiation.

Here we have that the bigger albedo value is in the ice ( 0.55), so the correct image is the ice image, at the bottom left.

Answer:

P(x=2) = 0.2368

Step-by-step explanation:

given data

stocks of local interest N = 20

stocks increased K = 10

stocks decreased =  5

remained unchanged = 5

solution

we take here no of stock that are increased randomly n = 2

so here Hypergeometric random variable can take integer value

{max(0, n+k - N ), min(n,K) } = {0,2}

so here

P(x=2)

so

P(x=k)  = [tex]\frac{(^K_k)\times (^{N-K}_{n-k}) }{(^N_n)}[/tex]      .......................1

P(x=2 ) = [tex]\frac{(^{10}_2)\times (^{20-10}_{2-2}) }{(^{20}_2)}[/tex]    

solve it we get

P(x=2 ) = 0.236842

now we use excel function as

HYPGEOM.DIST (k,n,N.cumulative)   .....................2

so it will be

HYPGEOM.DIST (2,2,10,,false)

we get

HYPGEOM.DIST (2,2,10,,false)  = 0.236842

so

P(x=2) = 0.2368

Answer:

Estimate = $34.50

Actual charge $33.47

Step-by-step explanation:

To estimate, we round the numbers

9.7 gallons rounds to 10 gallons

10 gallons * 3.45 per gallon =34.50

This is an overestimation

The actual charge

9.7* 3.45 =33.465

We round to the nearest cent

33.47

Answer:

Estimate: $34.5

Actual: $33.465

Step-by-step explanation:

9.7 is approximately 10

Estimate

10 × 3.45 = 34.5

Actual:

9.7 × 3.45 = 33.465

Answer:

From hypothesis, there is sufficient evidence to conclude that there is significant difference in two proportions.

Step-by-step explanation:

sample proportion for 1=12/20=0.6

sample proportion for 2=13/40=0.325

pooled proportion=25/60=0.4167

Test statistic:

z=(0.6-0.325)/sqrt(0.4167*(1-0.4167)*((1/20)+(1/40)))

z=2.037

p-value=2*P(z>2.037)=0.0417

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that there is significant difference in two proportions.

Answer:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

Answer:

30

Step-by-step explanation:

0.5 *  unknown number = 15

but  

we see unknown number = 15 / 0.5 = 30

The ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.

To find the ratio of 3 circles to 4 triangles, we compare the number of circles to the number of triangles.

Given:

Circles = 3

Triangles = 4

The ratio of circles to triangles is expressed as 3:4. This means for every 3 circles, there are 4 triangles.

If we want to express it as a fraction, we can write it as 3/4. This implies that for every set of 3 circles, there are 4 triangles.

To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case. Therefore, the simplified ratio is still 3:4.

In conclusion, the ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.

The complete question is here:

What is the ratio of 3 circles to 4 triangles?

Answer:

no optimal solution as feasible region is empty

Step-by-step explanation:

The complete question is:

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 6x − 6y subject to 5x ≤ y y ≤ 2x 7 x + y ≥ 9 x + 2y ≤ 22 x ≥ 0, y ≥ 0.

See the attachment to understand the following explanation.

The shaded regions shown in attachment obeys all constraints except for 5x ≤ y and y ≤ 2x. The shaded region 1 obeys all constraints except y ≤ 2x and shaded region 2 obeys all constraints except 5x ≤ y. So there is no feasbile region. Hence no optimal solution exists

To solve the linear programming problem, the constraints must be graphed to identify the bounded feasible region, if any exists. The objective function is then minimized by evaluating it at each vertex of this region. The solution is either one of these vertices or the problem may indicate no solution if the region is empty or the function is unbounded.

The given linear programming (LP) problem requires us to minimize the objective function c = 6x - 6y subject to a set of given constraints. To solve this problem, we graph the constraints and identify the feasible region. The constraints are:

Given that the inequalities form a bounded region, we then inspect the vertices of this feasible region to find the point that minimizes the objective function. The solution is either one of these vertices or it is non-existent if the feasible region is empty or the objective function is unbounded. In this problem, given the constraints and the positive coefficients of the objective function, the feasible region is bounded, and thus we should be able to find a minimum point by evaluating the objective function at each vertex of the feasible region.

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Answer:

The correct answer to the question is C.

Step-by-step explanation:

The length of the red line is |x – h|. The length of the blue line is |y – k|. The equation of the circle will be (x-h)²+(y-k)²=r².

The equation of a circle is given by the general equation,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) are the coordinates of the centre of the circle, and r is the radius of the circle.

As it is given that the blue line and the red line are the radii of the circle, therefore, they will be joining any point on the circle to the centre of the circle.

Given that the blue line is represented by |y+k| while the red line is represented by |x+h|, therefore, the coordinate of the centre of the circle will be (h,k). And the radius of the circle will be r. Thus, the equation of the circle will be (x-h)²+(y-k)²=r².

Learn more about Equation of a circle:

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Answer:

h= 7.5

Step-by-step explanation:

8h=60

One solution was found :

                  h = 15/2 = 7.500

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    8*h-(60)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  8h - 60  =   4 • (2h - 15)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    2h-15 = 0

Add  15  to both sides of the equation :

                     2h = 15

Divide both sides of the equation by 2:

                    h = 15/2 = 7.500

One solution was found :

                  h = 15/2 = 7.500

Processing ends successfully

Answer: h = 7.5

Step-by-step explanation: To solve for h in this equation, we want to to get h by itself on the left side of the equation.

Since h is being multiplied by 8, to get h by itself, we need to divide by 8 on the left side of the equation.

If we divide by 8 on the left side,

we must also divide by 8 on the right side.

On the left, the 8's cancel out so we are simply left with h.

On the right we have 60/8 which is 7.5.

So we have h = 7.5.

Answer: a) The explanatory variable is hours of study per week and the response variable is GPA.

b) The relantioship between the variables seems to be positive.

c) B. Observational Study.

d) A. NO. We cannot conclude that studying loger hours leads to higher GPA since this study is observational.

Step-by-step explanation: a) Explanatory Variable is a type of independent variable, which means it is a variable that doesn't depend on the other variables. However, in explanatory variable, there is a subtle relation between variables. For that reason, Hours of Study per week is an explanatory variable. Response Variable is the dependent variable, it is the result when you change the other variable. For that reason, GPA is the response variable.

b) Observing the graphic, which is in the attachment, it can be observed that students who study more hours per week, tend to have higher GPA. For example, people who studied 60 hours per week have a GPA closer to 4.

c) Observational Studies are those experiment where the researches only observe their object of interest without changing or interfering in the outcome. Experimental Studies are the ones where the researchers introduce an interference and study their effect on the randomized groups.

Since this experiment is based on observation only, the study is an Observational Study.

d) Because it's an observational study, we can't correlate or associate the variables, since the researchers only obtain their results through observation of the behaviour of the students, without changing it.

We need to calculate a z-score to determine the probability of getting a month with a temperature of 34 degrees or higher, and then subtract that probability from 1 to get the final result.

To solve this problem, we're dealing with a normal distribution. The average maximum monthly temperature in Campinas, Brazil is given as the mean (29.9 degrees). The standard deviation has been given as 2.31 degrees.

We're asked to find the percentage of months that would have a maximum temperature of 34 degrees or higher. This can be interpreted as finding the probability of a temperature being more than 34 degrees. We first need to find the number of standard deviations away from the mean 34 degrees is, which is known as Z-score.

The formula for Z-score is (X - mean) / standard deviation. So, our calculation would be (34 - 29.9) / 2.31. The resultant Z-score would have to be looked up in a standard normal distribution table, which will give us the probability up to that point. As we want the probability of the temperature being higher, we'll subtract the value we get from 1 (as total probability is 1), which would give us the percentage of months with a maximum temperature of 34 degrees or higher.

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Answer: 27?

Step-by-step explanation:

Answer

The best estimate for 48 and 21 is 50 and 20.  50-20= 30 so 30 is ur answer

Step-by-step explanation:

Answer:

9 feet = Perimeter of the triangle.

Step-by-step explanation:

Here, this question is incomplete and lacks essential data. So, still we will try to figure it out. What we can learn from this question.

So, first of all it talks about perimeter. So, let's understand first, what is perimeter and how it can be calculated for a triangle.

What is Perimeter?

So, Perimeter is actually the distance or path covered by a particular 2 dimensional shape. For example, square, triangle, rectangle.

Furthermore,

In this question, we have been given s = 3 feet. We can say that it is a length of one side of a triangle and triangle must be equilateral triangle having all sides equal to one another.

Equilateral Triangle have all sides equal to one another.

Here, we s1 = 3 so, other sides would be s2 = 3 and s3 = 3

Finally, here is the formula for the calculation of Perimeter of a triangle.

P = a + b + c

where, a, b, c represents sides of the triangle.

P = 3 + 3 + 3

P = 9

Hence, the perimeter of the triangle in this question is 9 feet.

The credit card balance at 5 months, 1 year, and 2 years to see the progression of debt repayment is $695, $669.67 and $669.70 respectively.

Calculate B(5) by substituting t = 5 into the formula B(t) = 700(.9894t), giving B(5) = 700(.9894*5) = $695.58.

Find B(12) by substituting t = 12 into the formula, giving B(12) = 700(.9894*12) = $669.67.

To check if the balance is paid off after 2 years, find B(24) = 700(.9894*24) = $632.70.

which indicates the balance is not paid off in 2 years.

Using the t-distribution, we have that:

a)

i) The test statistic is t = 0.746.

ii) The p-value is of 0.2299.

b) The 90​% confidence interval is from -1.25 to 3.25.

Item a:

For a right-tailed test, we test if [tex]x_1[/tex] is greater than [tex]x_2[/tex], hence:

The standard errors are:

[tex]S_{e1} = \frac{5}{\sqrt{25}} = 1[/tex]

[tex]S_{e2} = \frac{4}{\sqrt{20}} = 0.8944[/tex]

The distribution of the difference has mean and standard error given by:

[tex]\overline{x} = x_1 - x_2 = 11 - 10 = 1[/tex]

[tex]s = \sqrt{S_{e1}^2 + S_{e2}^2} = \sqrt{1^2 + 0.8944^2} = 1.34[/tex]

We have the standard deviation for the samples, hence, the t-distribution is used.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{1 - 0}{1.34}[/tex]

[tex]t = 0.746[/tex]

The test statistic is t = 0.746.

The p-value is found using a t-distribution calculator, with t = 0.746, 25 + 20 - 2 = 43 df and 0.05 significance level.

Item b:

The critical value for a 90% confidence interval with 43 df is [tex]t = 1.6811[/tex].

The interval is:

[tex]\overline{x} \pm ts[/tex]

Hence:

[tex]\overline{x} - ts = 1 - 1.6811(1.34) = -1.25[/tex]

[tex]\overline{x} + ts = 1 + 1.6811(1.34) = 3.25[/tex]

The 90​% confidence interval is from -1.25 to 3.25.

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Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because i said so

Answerhshxbx

Ste-by-step explanation:

Hwsjbb

Answer:  x=9,y=-1/3

Step-by-step explanation: This is for Q. 16

Rearrange terms to line up properly.

x-3y=10

x+3y=8

eliminate y terms

x=10

x=8   now add all like terms, remember it's a given that there's a one in

         front of a variable.

2x=18 solve for x

x=9 now plug in the nine into one of the original eq.s and solve for y

9+3y=8

3y=-1

y=-1/3  always check solutions in both eq.s to vertify. they both work    

Answer:

Q6: x= 10, y = -11

Q8: x= -3; y= 8

Q10: k= 7; j= -1

Step-by-step explanation:

Question6.

2x + y = 9..............1

-2x - 3y = 13...............2

Let's eliminate x by adding equation 1 and 2.

-2y = 22

y = 22/-2

y = -11

Substitute y = -11 in equation 1.

2x + y = 9

2x + (-11) = 9

2x - 11 = 9

2x = 9 + 11

2x = 20

x = 20/2

x = 10

x =10; y= -11

Question 8.

x + 2y = 13.............(I)

x + 6y = 45......…....(2)

By elimination method, let's take off x by subtracting equation 1 from 2.

6y - 2y = 45 - 13

4y = 32

y = 8.

Substitute y = 8 in equation 1.

x + 2y = 13

x + 2(8) = 13

x + 16 = 13

x = 13 - 16

x = -3

y= 8; x = -3

Question 10:

2j + 3k = 19 ..............1

2j + 7k = 47...............2

Let's eliminate j by subtracting equation 1 from equation 2.

4k = 28

k = 28/4

k= 7

Substitute k = 7 in equation 1.

2j + 3k = 19

2j + 3(7) = 19

2j + 21 = 19

2j = 19 - 21

2j = -2

j= -1

k= 7; j = -1

Answer:

The standard error of the estimate is 413.4498

Step-by-step explanation:

According to the given data of ,in order to calculate the standard error of the estimate we would have to use the following formula:

Standard Error =sqrt(SSE/(n-p-1))

Standard Error =sqrt(4102577/(27-2-1))

Standard Error = 413.4498

The standard error of the estimate is 413.4498

Answer:

Answer A.

Step-by-step explanation:

Recall that [tex]f(x) = \frac{x^2-4}{x-2}[/tex]

we will calculate the lateral limits of f when x approches x=2. Note that

[tex] \lim_{x\to 2^{+}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{+}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]

[tex] \lim_{x\to 2^{-}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{-}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]

We can clasify the discontinuity as follows:

- Removable discontinuity if both lateral limits are equal and finite.

- Jump discontinuity if both lateral limits are finite but different.

- Essential discontinuity if one of the limits is not finite and the other one is finite.

Based on this classification, since both lateral limits are equal, the discontinuity is a removable discontinuity

The solution of the differential equation is:

[tex]y = \frac{1}{-0.1 + 0.02*t}[/tex]

Here we need to solve:

[tex]\frac{dy}{dt} = -0.02*y^2[/tex]

This is a separable differential equation, we can rewrite this as:

[tex]\frac{dy}{y^2} = -0.02dt[/tex]

Now we integrate in both sides to get:

[tex]\int\limits\frac{dy}{y^2} = \int\limits-0.02dt\\\\-\frac{1}{y} = -0.02*t + C[/tex]

Where C is a constant of integration.

Solving for y, we get:

[tex]y = \frac{1}{-C + 0.02*t}[/tex]

And we know that for t = 0, there are 10 grams of substance, then:

[tex]10 = \frac{1}{-C + 0.02*0} = -\frac{1}{C} \\\\C = -1/10 = -0.1[/tex]

So the equation is:

[tex]y = \frac{1}{-0.1 + 0.02*t}[/tex]

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Final answer:

To find the total cost of the watch and the clock, set up equations based on the given relationships, solve for the individual costs, and then add them together. The total cost amounts to $176.

Explanation:

The student is asking to find the total cost of two items - a watch and a clock. The clock costs 4/7 of what the watch costs, and the watch costs $48 more than the clock. Let's denote the cost of the clock as c and the cost of the watch as w. The problem gives us two equations: w = c + $48 and c = (4/7)w. Now, we can solve these equations to find the individual costs of the clock and the watch, then sum them to find the total cost.

Step-by-step Solution

Substitute the value of c from the second equation into the first equation: w = (4/7)w + $48.

Multiply both sides of the equation by 7 to eliminate the fraction: 7w = 4w + $336.

Subtract 4w from both sides: 3w = $336.

Divide both sides by 3 to find the cost of the watch: w = $112.

Now that we have the cost of the watch, we can substitute it back into the equation c = (4/7)w to find the cost of the clock: c = (4/7) x $112 = $64.

The total cost of both items is the sum of the cost of the clock and the cost of the watch: w + c = $112 + $64 = $176.

Therefore, the total cost of the watch and the clock together is $176.

Answer:

3.75

Step-by-step explanation:

Hope this helps

Answer:

$420

Step-by-step explanation:

To work this out you would need to find the 25% decrease of 560. To do this you would first divide 25 by 100, which gives you 0.25. Then you would minus 0.25 from 1, which gives you 0.75. This is because when finding percentage decreases you would first have to convert it into a decimal. Then you would have to minus it from 1 , to make sure that it will be a 25% decrease not a 75% decrease. Then you would multiply 560 by 0.75, which gives you 420.

1) Divide 25 by 100.

[tex]25/100=0.25[/tex]

2) Minus 0.25 from 1.

[tex]1-0.25=0.75[/tex]

3) Multiply 560 by 0.75.

[tex]560*0.75=$420[/tex]