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Anestetic [448]
2 years ago
6

Solve the equation by completing the square

%208" id="TexFormula1" title=" {k}^{2} - 8k + 20 = 8" alt=" {k}^{2} - 8k + 20 = 8" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
love history [14]2 years ago
5 0
This is ageyes ! algebra one or two
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The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis
andreyandreev [35.5K]

Answer:

a. Let the variable be x for the fundraising activities and M as the revenue for foundation.

b. M =0.60x

c. $43.2

d. $1416.67

Step-by-step explanation:

Given that:

The World Issues club donates 60% of the total of their fundraising activities.

Answer a.

Let us choose the variable x to represent the money earned during fundraising activities and M for the revenue generated for foundation.

Answer b.

Foundation will receive 60% of the total of the fundraising activities.

Equation to determine the money that will be received by foundation:

M = 60\%\ of\ x\\OR\\M = 0.6x

Answer c.

Given that x = $72, M = ?

Putting the value of x in the equation above:

M = 0.6 \times 72\\\Rightarrow \$43.2

Answer d.

Given that M = $850, x = ?

Putting the value of M in the equation above to find x:

850= 0.6 \times x\\\Rightarrow x = \dfrac{850}{0.6}\\\Rightarrow x = \$ 1416.67

So, the answers are:

a. Let the variable be x for the fundraising activities and M as the revenue for foundation.

b. M =0.60x

c. $43.2

d. $1416.67

5 0
3 years ago
- 5/6e (the fraction) - 2/3e (the fraction)=-24
Wewaii [24]

Answer:

I believe this is the correct answer. e = 16

3 0
3 years ago
If t follows a t7 distribution, find t0 such that (a) p(|t | < t0) = .9 and (b) p(t > t0) = .05.
Thepotemich [5.8K]

Answer:

a) P(-t_o < t_7

Using the symmetrical property we can write this like this:

1-2P(t_7

We can solve for the probability like this:

2P(t_7

P(t_7

And we can find the value using the following excel code: "=T.INV(0.05,7)"

So on this case the answer would be t_o =\pm 1.895

b) For this case we can use the complement rule and we got:

1-P(t_7

We can solve for the probability and we got:

P(t_7

And we can use the following excel code to find the value"=T.INV(0.95;7)"

And the answer would be t_o = 1.895

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.  

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For this case we know that t \sim t(df=7)

And we want to find:

Part a

P(|t|

We can rewrite the expression using properties for the absolute value like this:

P(-t_o < t_7

Using the symmetrical property we can write this like this:

1-2P(t_7

We can solve for the probability like this:

2P(t_7

P(t_7

And we can find the value using the following excel code: "=T.INV(0.05,7)"

So on this case the answer would be t_o =\pm 1.895

Part b

P(t>t_o) =0.05

For this case we can use the complement rule and we got:

1-P(t_7

We can solve for the probability and we got:

P(t_7

And we can use the following excel code to find the value"=T.INV(0.95;7)"

And the answer would be t_o = 1.895

5 0
3 years ago
A company sells dog treats. The company's fixed and variable costs are modeled by the function C(x)=1.4x+2000. Their revenue is
Naya [18.7K]

<u>Answer:</u>

<u>20,000 packages.</u>

<u>Step-by-step explanation:</u>

The rest of the question is as following:

If x represents the number of packages of dog treats, how many packages do they have to sell to break even? Round your answer to the nearest whole number, and do not include units.

=========================================

The function of fixed and variable costs ⇒ C(x) = 1.4x + 2000

The function of revenue ⇒ R(x) = 1.5x

The even situation will happen when costs = revenue

∴ C(x) = R(x)

∴ 1.4 x + 2000 = 1.5x

Solve for x:

∴ 1.5x - 1.4x = 2000

∴ 0.1 x = 2000

∴ x = 2000/0.1 = 20,000

The even will happen when they sell <u>20,000</u> packages

So, To break even, they have to sell more than 20,000 packages .

3 0
3 years ago
What is the product of 1 2/3 and −3 1/2 ?
Zinaida [17]

1/2*-3 1/2 = -21/4  = -5 1/4= <em>-5.25</em>

I hope this helps!!


8 0
2 years ago
Read 2 more answers
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