3. A local charity sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.

Answers

Answer 1

Answer:

On creating and solving the linear inequality based on the given conditions, the charity needs at least 1000 race entries to raise at least $55,000.

What is linear inequality?

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

Let the number of race entries be x.

5000 + 55x + 10000 - 15x >= 55000

40x >= 40000

x >= 1000

The charity needs at least 1000 race entries to raise at least $55,000.

Learn more about linear inequality here

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Answer 2

Answer: 55-15= 40

55,000-10,000=45,000

45000/55=819

i think it is 819?

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Answers

t² -7 + 12t⁻² = 0

Multiply each side by t² :

t⁴ -7t² + 12 = 0

This is a quadratic equation in the variable ' t² '.
For just a moment, to avoid confusion, let U = t².
Then the equation is

U² - 7U + 12 = 0
whence
(U - 4) (U - 3) = 0
and
U = 4 and U = 3 .

Now we can go back to ' t² ' in place of U :

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$t^2-7+12t^(-2)=0\n t^4-7t^2+12=0\n t^4-3t^2-4t^2+12=0\n t^2(t^2-3)-4(t^2-3)=0\n (t^2-4)(t^2-3)=0\n (t-2)(t+2)(t^2-3)=0\n t=2 \vee t=-2 \vee t=-√(3)\vee t=\sqrt3$

Shiloh has to earn at least $200 to meet her fundraising goal. She has only 100 cakes that she plans to sell at 5 dollars each. Which inequality shows the number of cakes, x, Shiloh can sell to meet her goal?

Answers

Answer:

$40 \leq x \leq 100$

Step-by-step explanation:

Cost of 1 cake = $5

Let x be the no. of cakes

So, Cost of x cakes = 5x

Since we are given that Shiloh has to earn at least $200

So, $5x\geq 200$

$x\geq 40$

So, the no. of the cakes should be sold more than or equal to 40

We are also given that She has only 100 cakes

So, the maximum number of cakes she can sold is 100 i.e. $x\leq 100$

So, Inequality becomes : $40 \leq x \leq 100$

Hence inequality shows the number of cakes, x, Shiloh can sell to meet her goal is $40 \leq x \leq 100$

she will only have to sell 40 cakes to earn $200

0.1m+8-12 when m=30 and n=1/4

Answers

Answer: Look at this

Substitute the given numbers and do the arithmetic.

... 0.1·30 + 8 - 12·(1/4) = 3 + 8 - 3 = 8

Step-by-step explanation:

One recipe calls for 3/4 cup of milk. A different recipe calls for 1/2 as much milk as the first recipe. How much milk does the second recipe call for?

Answers

For this problem you need to divide 3/4 by 2. For division of fractions, invert and multiply.

2/1 = 1/2

3/4 • 1/2

3 • 1 = 3
4 • 2 = 8

1/2 of 3/4 cup of milk = 3/8 of a cup of milk.

Answer:

3/8

Step-by-step explanation:

Elsa knows that for every bushel of apples she sells she earns $9 and for every basket of pears she earns $11. She uses the expression 9a + 11p to keep track of her earnings. Part A: Identify the coefficients and variables in the expression. (3 points)

Part B: How many terms are in the expression, what are they, and how do you know? (4 points)

Part C: Which term in the expression shows the total earned from selling baskets of pears? (3 points)

Answers

A. Variables are A and P and the coefficiants are 9 and 11

B. 2 terms , 9a and 11p , there are 2 "groups" that are separated by the addition sign

C. 11p shows the total earned you would just have to plug in the amound of baskets of pears on for p and multiply 11 and p to find out the amount earnes

The coefficients are 9 and 11 since they are multiplied by a variable; the variables are a and p since a and p are unknown.
There are two terms in the expression. The terms are 9a and 11p. They can be a separate part of an equation, a series, or another expression.
11p is the term that shows the total earned from selling baskets of pears since $11 is how much Elsa gets for every basket of pears.

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