If an object goes from 60 mph to 30 mph in 5 seconds, what is its acceleration?

1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

Learn more about perimeter of triangle here: https://brainly.com/question/24382052

#SPJ1

A 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

We know that, the confidence interval is:

\(\bar{x}\pm z\frac{\sigma}{n}\)

where,

\(\bar{x}\) is the sample mean.

z is the critical value.

n is the sample size.

σ (OR s) is the standard deviation for the population.

In this question, we need to calculate the 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was 101.82, with a population standard deviation of 1.2

The critical value is z = 1.96

We have been given x¯ = 25.6, σ = 0.6 and n = 150

\(\Rightarrow \bar{x}+ z\frac{\sigma}{\sqrt{n} } \\\\= 25.6+ 1.96\frac{0.6}{\sqrt{150} } \\\\=25.67\)

And

\(\Rightarrow \bar{x}- z\frac{\sigma}{\sqrt{n} } \\\\= 25.6- 1.96\frac{0.6}{\sqrt{150} } \\\\=25.504\)

Required interval is (25.504, 25.67)

Thus, the mean weight level( 25.6 grams) is accurate.

Therefore, a 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

Learn more about the confidence interval here:

brainly.com/question/28064687

#SPJ4

Answer: $8.50

Step-by-step explanation:

The expected gain (loss) is a weighted average of the probability of the different gains (losses) and the gains or losses.

Expected gain or loss for stock JKL:

= (Probability of losing $25 * -25) + ( Probability of gaining $5 * 5) + ( Probability of gaining $45 * 45)

= (15% * -25) + (65% * 5) + (20% * 45)

= -3.75 + 3.25 + 9

= $8.50

Answer:8.50$

Step-by-step explanation:

Answer:

Shift f(x) = 3x one unit to the left and four units up

Step-by-step explanation:

We need to translate :

Here we need to use a bit of logic.

Answer:

Shift f(x) = 3x one unit to the left and four units up

Step-by-step explanation:

put it on test

Dilating polygon WXYZ will change the side lengths of the polygon

The true statement is (b) the slope of WX is 3/4, and the length of W'X' is 15

The coordinates are given as:

\(\mathbf{W = (3,2)}\)

\(\mathbf{X = (7,5)}\)

The slope of WX is:

\(\mathbf{m =\frac{y_2 - y_1}{x_2 -x_1}}\)

So, we have:

\(\mathbf{m =\frac{5-2}{7-3}}\)

\(\mathbf{m =\frac{3}{4}}\)

The length of WX is calculated using:

\(\mathbf{WX = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\)

So, we have:

\(\mathbf{WX = \sqrt{(7- 3)^2 + (5- 2)^2}}\)

\(\mathbf{WX = \sqrt{25}}\)

\(\mathbf{WX = 5}\)

The scale factor is 3.

So, the distance W'X' is:

\(\mathbf{W'X' = 3 \times WX}\)

This gives

\(\mathbf{W'X' = 3 \times 5}\)

\(\mathbf{W'X' = 15}\)

Hence, the true statement is (b)

Read more about dilations at:

https://brainly.com/question/13176891

Answer:

(b) the slope of WX is 3/4, and the length of W'X' is 15

Step-by-step explanation:

got it right on plato/edmentum

Answer: Their total budget last year was $44,000.

Step-by-step explanation:

Given: Smiths spend 6% of their budget on entertainment.

Total budget this year = $ 2000 more than last year.

Let x = Budget for this year.

Money on entertainment = 0.06x = 2760

\(\Rightarrow\ x=\dfrac{2760}{0.06}= \$46,000\)

⇒ Budget for this year = $ 46,000

Budget for last year = $ 46,000 - $2,000 = $44,000

Hence, their total budget last year was $44,000.

Answer:

98 m long

Step-by-step explanation:

588/6 = 98 m long

Answer:

x=12

Step-by-step explanation:

ab=dc so 15=x+3 you subtract 3 from both sides... x=12

Answer:

720\(\sqrt{5x}\)

Step-by-step explanation:

First you want to simplify both of them. To do this on 4\(\sqrt{30^{2} }\) you can just cancel out the square and the square root to get 4 x 30 which is 120. Now you simplify 3\(\sqrt{20x}\) you do this by splitting the radical into 2 radicals. So you want to take out a perfect square which in this case is \(\sqrt{4}\) and you have \(\sqrt{5x}\) left over. This brings us to 120 x 3 x 2 (2 is the square root of 4) \(\sqrt{5x}\). Now multiply 120 x 3 x 2 and get 720\(\sqrt{5x}\).

Answer:

1. $19.91

Step-by-step explanation:

Therefore, the present value of the perpetuity that pays $1,800 per year forever, assuming a 5% interest rate, is $36,000. To find the present value of a perpetuity that pays $1,800 per year forever, we can use the formula:
Present Value = Cash Flow / Interest Rate

In this case, the cash flow is $1,800 and the interest rate is 5%. Plugging these values into the formula, we get:
Present Value = $1,800 / 0.05. Simplifying this equation, we find that:
Present Value = $36,000

To know more about perpetuity visit:

https://brainly.com/question/28205403

#SPJ11

Answer: I don’t see your question about your problem in mathematics.

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:

2(0) - x = -6

0 - x = -6

-x = -6

x = 6

Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.

Answer:

4.21*10 to the 9th power

Step-by-step explanation:

4 is the first whole number; Place an decimal point just after and include the whole numbers afterward as the decimal; 4.21. Then count everything beyond the first whole number and you get 9 (including zeros) .

Therefore, 4.21 * 10 to the 9th power

Answer:

Easy

Step-by-step explanation:

-19-9=-28

-28/-4=7

thus x=7

In general, two congruent segments have the same measure. Since no more information about the figure is given, we would need to estimate the measurement of each of its segments.

A) Notice that

B)

C)

D)

E)

Answer:

Step-by-step explanation:

C

Answer:i

Step-by-step explanation:

On any triangle, the sum of the measures of the internal angles is 180°. Then:

Substitute the expressions for each angle, solve for x and find the measure of each angle:

To find the measure of each angle, substitute x=24 into the expressions:

Therefore, the measures of the three angles are:

The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.

The probability of getting 2 socks of the same color is given by P(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks).Given, There are 8 blue socks. There are 8 white socks. There are 2 gray socks. Now, we will find the probability of getting 2 blue socks: Probability of selecting one blue sock from 8 blue socks is 8/18.

Probability of selecting another blue sock from 7 blue socks is 7/17.Probability of getting 2 blue socks is P(2 blue socks) = 8/18 * 7/17 = 28/153. Now, we will find the probability of getting 2 white socks: Probability of selecting one white sock from 8 white socks is 8/18.Probability of selecting another white sock from 7 white socks is 7/17.Probability of getting 2 white socks is P(2 white socks) = 8/18 * 7/17 = 28/153.

Now, we will find the probability of getting 2 gray socks: Probability of selecting one gray sock from 2 gray socks is 2/18.Probability of selecting another gray sock from 1 gray sock is 1/17.Probability of getting 2 gray socks is P(2 gray socks) = 2/18 * 1/17 = 1/153.

Therefore,The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.

Learn more about Probability

brainly.com/question/30034780

#SPJ11

Answer: 4x^6

Step-by-step explanation:

Para responder esta pregunta debemos conocer que es un monomio, su grado y el coeficiente.

Un monomio es un polinomio que posee 1 solo termino, el grado se refiera a la potencia a la que esta elevada la variable (en este caso usaremos la letra x)

El coeficiente es el número que está a la izquierda de una variable:

Entonces:

Monomio de grado 6 y coeficiente 4

4x^6

Answer:

The slope is -4/5. Hope this helps!

Step-by-step explanation

To find the slope- Look at both points, Count how many units it is from the other point. Count how many units down and how many units right. Then its rise over run. So how many units down would go ontop of how many units right. This means the answer should be -4/5

Answer:

5/4

Step-by-step explanation:

Total length = Sum of the length of the two pieces of wood :

\( \frac{1}{2} + \frac{3}{4} \\ lcm = 4 \\ \)

Adjust values according to the lcm

\(4 \div 2 \times 1 = 2 \\ 4 \div 4 \times 3 = 3 \\ = \frac{3 + 2}{4} \\ = \frac{5}{4} \)

Answer:

(I think it MIGHT be) 5/4

Step-by-step explanation:

The girl that answered me up above is right

only Outcome D is a Pareto efficient outcome. In this given scenario, "A and D" are Pareto efficient outcomes.What is Pareto efficiency? Pareto efficiency is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.

What are the given allocations and benefits of individuals? The net benefit for each individual in each allocation is given below: (The two numbers in each of the following brackets indicate the net benefits for individual 1 and individual 2, respectively.) Outcome A: (10, 25) Outcome B: (20, 10) Outcome C: (14, 20)Outcome D: (15, 15) Which of the outcomes are Pareto efficient?

Now, let's see which of the given outcomes are Pareto efficient: Outcome A: If we take Outcome A, then individual 1 gets 10 and individual 2 gets 25 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome B, then individual 1 gets 20 which is greater than 10 as his net benefit, and the net benefit for individual 2 would become 10 which is still greater than 25. Therefore, Outcome A isn't Pareto efficient. Outcome B: If we take Outcome B, then individual 1 gets 20 and individual 2 gets 10 as their net benefits.

But the allocation isn't Pareto efficient because if we take Outcome C, then individual 1 gets 14 which is less than 20 as his net benefit, and the net benefit for individual 2 would become 20 which is greater than 10. Therefore, Outcome B isn't Pareto efficient.Outcome C: If we take Outcome C, then individual 1 gets 14 and individual 2 gets 20 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome A, then individual 1 gets 10 which is less than 14 as his net benefit, and the net benefit for individual 2 would become 25 which is greater than 20. Therefore, Outcome C isn't Pareto efficient.

Outcome D: If we take Outcome D, then individual 1 gets 15 and individual 2 gets 15 as their net benefits. The allocation is Pareto efficient because there is no other allocation where one individual will be better off without harming the other individual.Therefore, only Outcome D is a Pareto efficient outcome.

To Know more about  Pareto efficiency  Visit:

https://brainly.com/question/30140525

#SPJ11

The required percentage yield for the reaction when theoretical yield and actual yield are given is calculated to be 85.5 %.  

The maximum mass that can be generated when a particular reaction occurs is referred to as theoretical yield.

Theoretical yield is given as mt = 9.23 g

The actual amount of product recovered is given as ma = 7.89 g

We must comprehend that in order to calculate the reaction's percent yield, we must divide the total amount of product recovered by the utmost amount that can be recovered. If we multiply by 100%, we can represent this fraction as a percentage.

Percentage yield = ma/mt × 100 = 7.89/9.23 × 100 = 85.5 %

To know more about reactions:

https://brainly.com/question/29191570

#SPJ4

The monic cubic polynomial with integer coefficients is x³ - 3x² + 3x + 2 with the leading coefficient as 1.

In order to find a monic cubic polynomial with integer coefficients, we can use the following method:

Let us assume that the cubic polynomial is of the form:x³ + bx² + cx + d

We need to find the values of b, c, and d such that the polynomial is monic and has integer coefficients.

Since the polynomial is monic, the coefficient of x³ is 1.

Therefore, we can write the polynomial as:x³ + bx² + cx + d = (x - r)(x² + px + q)

Where r is the root of the cubic polynomial, and p and q are constants to be determined.

We know that the sum of the roots of a cubic polynomial is equal to -b/1 = -b.

Therefore, the sum of the roots of our cubic polynomial is equal to:r - p/1 = -bOr,r + p = -b ...(1)

Also, we know that the product of the roots of a cubic polynomial is equal to -d/1 = -d.

Therefore, the product of the roots of our cubic polynomial is equal to r(q - r).

Thus,r(q - r) = -d ...(2)

Solving equations (1) and (2) for r and q, we get:

r = -b/3q = b²/3 - d

Hence, we can write the cubic polynomial as:

x³ + bx² + cx + d = (x + b/3)(x² + (b²/3 - d)x + r(b²/3 - d))

Let us choose d = 2 and r = 1, then we have:b = -3

Substituting these values, we get:x³ - 3x² + 3x + 2 = (x - 1)(x² - 2x - 2)

Therefore, the monic cubic polynomial with integer coefficients is x³ - 3x² + 3x + 2.

Let us know more about monic cubic polynomial : https://brainly.com/question/32564110.

#SPJ11

The statement which accurately describes the helicopter's force is: C. the toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.

Newton's Third Law of Motion states that for every action there is an equal but opposite reaction. This ultimately implies that, in every interaction, there is a pair of forces acting on the two interacting objects.

Next, we would determine the resultant forces in the two scenarios as follows:

Resultant force A = Forward force - Wind force

Resultant force A = 15 N - 10 N

Resultant force A = 5 Newton.

Resultant force B = Upward force - Force of gravity

Resultant force B = 10 N - 5 N

Resultant force B = 5 Newton.

In this context, we can reasonably infer and logically deduce that the toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.

Read more on Newton's Third Law of Motion here: https://brainly.com/question/25998091

#SPJ1

Step-by-step explanation:

so, we need to find the x values (A) that create the defined result values (f(x)) of B.

so, when taking the lower interval limit of B as the first f(x), we get

-1 = (x-2)/3

-3 = x - 2

-1 = x

so, the lower interval limit for A is also -1.

-1 as input value for the function delivers also -1 as functional result.

now for the upper limit :

2 = (x-2)/3

6 = x - 2

8 = x

so, the upper interval limit for A is 8.

and since the limit is excluded for B, it is also excluded for A.

so, C) is the correct answer.