Question 1 of 13
Chloe and Julia are running partners. In a series of practice runs, they run
longer and longer distances without changing pace. They each set up a table
to show the ratios of distance to time for their runs.
Chloe
Julia
Distance (m) Time () Distance (m) Time (s)
25
4.
30
5
50
00
60
10
75
12.
90
15
100
16
150
25
150
24
300
50
300
48
Which statement is true about the ratios shown?

Answer:

333

Step-by-step explanation:

Answer:

Conclusion

   There is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean

Step-by-step explanation:

From the question we are told that

   The population mean for EBR is  \(\mu_ 1 = \$239,000\)

    The sample mean for Ascension parish  is \(\= x_2 = \$246,000\)

   The  p-value  is  \(p-value = 0.045\)

     The level of significance is  \(\alpha = 0.01\)

The null hypothesis is  \(H_o : \mu_2 = \mu_1\)

The  alternative hypothesis is  \(H_a : \mu_2 > \mu_1\)

Here \(\mu_2\) is the population mean for Ascension parish

   From the data given values we see that  

          \(p-value > \alpha\)

So we fail to reject the null hypothesis

So we conclude that there is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Answer: 35 , 14

Step-by-step explanation:

[3(-2)^2-4 ]+[8 (3)-3]                     [8(3)-3] -[ 3(-1)^2-4]

35                                                      14

Answer:

0

Step-by-step explanation:

Discounts are used to reduce the price of items

The percentage discount during the sale is 22.41%

The given parameters are:

Worth = Rs 58000

Selling price = Rs 45000

Start by calculating the discount amount

Discount = Worth - Selling Price

So, we have:

Discount = Rs 58000 - Rs 45000

Discount = Rs 13000

The percentage discount is then calculated as:

\(\% Discount = \frac{Discount}{Worth}\)

This gives

\(\% Discount = \frac{13000}{58000}\)

Simplify

\(\% Discount = 22.41\%\)

Hence, the percentage discount during the sale is 22.41%

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Answer:

x = 15

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

\(\frac{x}{21-x}\) = \(\frac{25}{10}\) ( cross- multiply )

10x = 25(21 - x)

10x = 525 - 25x ( add 25x to both sides )

35x = 525 ( divide both sides by 35 )

x = 15

Answer:

9-4x is simplified

Step-by-step explanation:

hope this helps

Answer: 13.3333333333333333333333334

Step-by-step explanation:

8/300 x 500

Answer:

First, we find how many red beads there are:

2 + 1 + 3 = 6

12 - 6 = 6

Red beads = 6

Now we add the red beads and the purple beads:

Purple beads = 3

Red beads = 6

3 + 6 = 9

9/12 = 3/4

Hope this helps!

You don't shade a region when graphing just a line, but you do when graphing an inequality.

It should be noted that a graph is a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

It should be noted that an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.

This is used most often to compare the two numbers on the number line by their size.

On the other hand, the graphing inequalities shows what part of the number line contains values that will be able to satisfy the given inequality.

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The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Carlene's employer's contribution to the 401(k) was of $3,200., using proportions.

A proportion is a fraction of a total amount, and this fraction is combined with basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

The proportion of her salary that she contributed to the 401(k) plan is of:

4000/40000 = 0.1.

The first 6% of her salary is:

0.06 x 40000 = $2,400.

Hence her employee contributed $2,400 relative to the first 6% of her salary.

For the 4% between 6% and 10%, the employee contributed 50% of her contributions, hence:

0.5 x (4000 - 2400) = 0.5 x 1600 = $800.

Hence the total contribution by the employee is of:

2400 + 800 = $3,200.

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Answer:

Part A: 146°

Part B: 70°

Part C: 104°

Step-by-step explanation:

Part A:

m<SHI = 34° (given)

m<SHI + m<MIH = 180° (same side interior angles of a transversal are supplementary)

34° + m<MIH = 180° (Substitution)

Subtract 34° from each side

m<MIH = 180° - 34°

m<MIH = 146°

Part B:

m<HAL = 110° (given)

m<HAV + m<HAL = 180° (linear pair)

m<HAV + 110° = 180° (substitution)

Subtract 110° from each side

m<HAV = 180° - 110°

m<HAV = 70°

m<AVM = m<HAV (alternate interior angles are congruent)

m<AVM = 70°

Part C:

The obtuse angle formed = m<HAV + SHI (exterior angle of a triangle = the sum of two opposite interior angles of a ∆)

The obtuse angle formed = 70° + 34° = 104°

Answer: 1085

Step-by-step explanation:

Answer:

The second step because she distributed within the parentheses without adding the negative sign to 13

Answer:

AB/2 = 6 and 12 = AB

Step-by-step explanation:

Answer:

\(Width = 59\)

Step-by-step explanation:

Given

The above data

Required

The class width

To do this, we simply calculate the difference between the class limits of any one of the classes.

Taking 1187–1246 as a point of reference, the class width is:

\(Width = 1246 - 1187\)

\(Width = 59\)

Reasonably simple series with a tail that is thicker than the tail of the given Σ 1n × >> Σ (1/2), Σ (1/3)^n has a thicker tail than Σ (1/2)^n.

One possible series with a thicker tail than Σ (1/2)^n is the series Σ (1/3)^n, which can be written as:

1 + 1/3 + 1/9 + 1/27 + 1/81 + ...

To see that this series has a thicker tail than Σ (1/2)^n, we can compare the nth terms of the two series:

(1/2)^n = 1/2 × 1/2 × ... × 1/2 (n factors)

(1/3)^n = 1/3 × 1/3 × ... × 1/3 (n factors)

Since 1/2 > 1/3, the nth term of Σ (1/2)^n is greater than the nth term of Σ (1/3)^n for all n. However, the sum of the first k terms of Σ (1/3)^n is:

1 + 1/3 + 1/9 + ... + (1/3)^k

= (1 - (1/3)^k) / (1 - 1/3)

= (3/2) (1 - (1/3)^k)

which approaches 3/2 as k approaches infinity. In contrast, the sum of the first k terms of Σ (1/2)^n is:

1 + 1/2 + 1/4 + ... + (1/2)^k

= (1 - (1/2)^(k+1)) / (1 - 1/2)

= 2 (1 - (1/2)^(k+1))

which approaches 2 as k approaches infinity. Therefore, the series Σ (1/3)^n has a thicker tail than Σ (1/2)^n.

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Answer:

A = 5

Step-by-step explanation:

The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

The solution for the given system of equations is

x = 3

y = -12

What are linear equations in two variables?

Therefore, a linear equation in two variables is any equation that can be written in the form ax + by + c = 0, where a, b, and c are real values, and a and b are not equal to zero.

Given two linear equations of two variables.

y = -4x .....eq 1

6x - y = 30 .....eq 2

We have to solve them using substitution.

Now,

by substituting eq 1 in eq 2,

6x -(-4x) = 30

6x + 4x = 30

10x = 30

x = 3

from eq 1,

y = -4x = -4*3 = -12

Therefore, x = 3 and y = -12

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Answer: 59 cars per month

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are 4 possibilities:

First ball Second ball

1. Black Pink

2. Black Black

3. Pink Pink

4. Pink Black

The first and the forth options are the the probabilities that there is picked one ball for each color. (2 possibilities )

The second and the third options are the probabilities that there ate picked 2 balls of same colour.

(2 possibilities)

There are 4 possibilities in total. So the probability is 2/4=1/2

Answer:

C) 19, remainder 2

Step-by-step explanation:

Divide 78 by 4

78/4 = 19.5, or 19R2

The result of 78 divided by 4 is 19 with a remainder of 2, option C is correct.

When you divide 78 by 4, divide the leftmost digit (7) by 4.

4 can go into 7 one time, so the first digit of the quotient is 1.

Then, you multiply the quotient digit (1) by the divisor (4) and subtract the result from the original number.

7 - (1 × 4)

= 7 - 4

= 3

You then bring down the next digit from the original number, which is 8, and divide it by the divisor (4) again.

Now, you divide 38 by 4. 4 can go into 38 nine times, so the second digit of the quotient is 9.

Multiply the quotient digit (9) by the divisor (4) and subtract the result from the remaining part of the original number.

38 - (9×4)

= 38 - 36

= 2

There are no more digits left in the original number to bring down.

The remainder is 2 because there is still some value left that cannot be divided evenly by 4.

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The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Mixed fraction:

3 2/5 = 17/5

4 4/5 = 24/5

Miles she ran:

17/5 + 24/5

= 41/5 miles or 8.2 miles