Write an equation to solve each problem and then solve it. There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?

Answer:

10 pints

Step-by-step explanation:

There are 8 pints in a gallon, so ...

(1.25 gal) × (8 pt/gal) = 10 pt

The first meeting point of the ferries represents half of the total roundtrip, while the second meeting point represents a quarter of it. Knowing this proportion and the distances at which the meetings happen, we conclude that the distance between shores A and B is 200 meters.

This problem can be solved using rates and proportions. Consider the total round trip of each ferry. The first meeting is at 100 meters from shore B and the second meeting is  50 meters from shore A.

Imagine a full roundtrip travel, from A to B and back to A. When the ferries meet for the first time, they have collectively completed one full round trip (distance A to B and B back to A). At their second meeting, they have collectively made two full round trips.

This means that the first meeting happened at 1/2 of the round trip distance and the second meeting happened at 1/4 of the round trip distance, meaning that the second meeting point was half the distance of the first meeting point. Based on where the second meeting point is (50 meters from shore A), we know that the first meeting point (100 meters from shore B) is twice the distance of the second meeting point from shore A.

Now, we understand the distances as follow: the total distance from shore A to shore B is the sum of the distance from the first meeting point to shore B (100 meters) and twice the distance from the second meeting point to shore A (2*50 meters), which sums up to 200 meters. Therefore, the distance between shores A and B is 200 meters.

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Answer:

Answer is 6 ways

Step-by-step explanation:

Given that a family wants to visit three different places as Philadelphia, Baltimore, and Washington.

We have to find the number of ways these three can be visited.

Here this is a question of permutation since order matters.

There are 3 cities and these can be visited in 3P3 ways =3!

=3x2x1 =6 ways

There are in total 6 different ways that the family can visit three different places as Philadelphia, Baltimore, and Washington.

Answer:

[tex]x=9[/tex] and [tex]y=13[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to solve our given system algebraically.

[tex]5x-3y=6...(1)[/tex]

[tex]6x-4y=2...(2)[/tex]

From equation (1), we will get:

[tex]x=\frac{6+3y}{5}[/tex]

Upon substituting this value in equation (2), we will get:

[tex]6(\frac{6+3y}{5})-4y=2[/tex]

[tex]\frac{36+18y}{5}-4y=2[/tex]

[tex]\frac{36+18y}{5}-\frac{5*4y}{5}=2[/tex]

[tex]\frac{36+18y-20y}{5}=2[/tex]

[tex]\frac{36-2y}{5}=2[/tex]

[tex]\frac{36-2y}{5}*5=2*5[/tex]

[tex]36-2y=10[/tex]

[tex]36-36-2y=10-36[/tex]

[tex]-2y=-26[/tex]

[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]

[tex]y=13[/tex]

Upon substituting [tex]y=13[/tex] in equation (1), we will get:

[tex]5x-3(13)=6[/tex]

[tex]5x-39=6[/tex]

[tex]5x-39+39=6+39[/tex]

[tex]5x=45[/tex]

[tex]\frac{5x}{5}=\frac{45}{5}[/tex]

[tex]x=9[/tex]

Answer:

Option A.

Step-by-step explanation:

To determine an appropriate model of the data each data should satisfy the expression.

For function 1. f(x) = -x² + 4x

Now for each point

f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0

therefore the given points lie on the function.

For option 2

f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0

Therefore points do not lie on the function.

For Option 3.

f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1

Therefore the points do not satisfy the expression.

For option 4.

f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1

Therefore, the points do not satisfy the expression.

Option A. is the correct option.

Final answer:

The slope of the line that passes through the points (4,1) and (2,8) is calculated using the slope formula and results in a slope of -3.5.

Explanation:

To find the slope of a line passing through the ordered pairs (4,1) and (2,8), you can use the slope formula:

Plugging in the values, we get:

Therefore, the slope of the line that passes through the points (4,1) and (2,8) is -3.5.

The slope of the line passing through the given points is -3.5.

Let’s find the slope of the line passing through the points (4, 1) and (2, 8).

The slope of a line can be calculated using the following formula:

[tex]\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

where:

• [tex](x_1) and (y_1)[/tex] are the coordinates of the first point (in this case, (4, 1)).

• [tex](x_2) and (y_2)[/tex] are the coordinates of the second point (in this case, (2, 8)).

Let’s compute the slope:

1. Difference in (x)-coordinates: [tex](x_2 - x_1 = 2 - 4 = -2)[/tex]

2. Difference in (y)-coordinates:[tex](y_2 - y_1 = 8 - 1 = 7)[/tex]

Now, calculate the slope:

[tex]\text{slope} = \frac{7}{-2} = -3.5[/tex]

Therefore, the slope of the line passing through the given points is -3.5.

The sum of the first 10 terms for the sequence given is 620,004.

A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,

Sum of n terms of GP = aₙ = arⁿ-1 / r-1,

a₁ = 21

r = 3

So,

a₁₀ = 21 × 3¹⁰-1 / 3-1

a₁₀ = 21 × 29,524

a₁₀ = 620,004

Hence the sum is 620,004.

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Answer: B. 29° & 61°

Step-by-step explanation:

The correct answer is:  B) 10

Step 1:

To calculate the number of two-topping sandwiches you can make from the given toppings, you can use the combination formula:

[tex]\[C(n, k) = \frac{n!}{k!(n-k)!}\][/tex]

Where:

- [tex]\(n\)[/tex] is the total number of toppings available (5 in this case).

- [tex]\(k\)[/tex] is the number of toppings you want to choose (2 in this case).

- [tex]\(C(n, k)\)[/tex] represents the number of combinations.

Step 2:

Substituting the values:

[tex]\[C(5, 2) = \frac{5!}{2!(5-2)!}\][/tex]

[tex]\[C(5, 2) = \frac{5!}{2!3!}\][/tex]

[tex]\[C(5, 2) = \frac{5 × 4}{2 × 1}\][/tex]

[tex]\[C(5, 2) = \frac{20}{2}\][/tex]

[tex]\[C(5, 2) = 10\][/tex]

So, you can make [tex]\(10\)[/tex] two-topping sandwiches from the given toppings.

Answer:

50

Step-by-step explanation:

Let

The relationship between x and y can be represented through a linear equation.

y = a . x + b

where,

a is the slope

b is the y-intercept

The slope represents the cost per each person employed, that is, a = $28,826.00/person.

Then,

y = ($28,826.00/person) . x + b

Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).

$41,949.00 = ($28,826.00/person) . 0 + b

b = $41,949.00

The final equation is

y = ($28,826.00/person) . x + $41,949.00

If the company will spend $1,483,249.00 (y = $1,483,249.00.),

$1,483,249.00 = ($28,826.00/person) . x + $41,949.00

1,441,300 = ($28,826.00/person) . x

x = 50 person (50 people)

The company intends to employ 50 people next year.