Find the value of each variable to the nearest 10th. Be sure to write an equation and circle the answer.

The mean caloric intake of an adult male is 2800 with a standard deviation of 115. To verify this information, a sample of 25 me

erma4kov [3.2K]

Answer:

Step-by-step explanation:

We would use the t- distribution.

From the information given,

Mean, μ = 2950

Standard deviation, σ = 115

number of sample, n = 25

Degree of freedom, (df) = 25 - 1 = 24

Alpha level,α = (1 - confidence level)/2

α = (1 - 0.98)/2 = 0.01

We will look at the t distribution table for values corresponding to (df) = 24 and α = 0.01

The corresponding z score is 2.492

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

2950 ± 2.492 × 115/√25

= 2950 ± 2.492 × 23

= 2950 ± 57.316

The lower end of the confidence interval is 2950 - 57.316 =2892.68

The upper end of the confidence interval is 2950 + 57.316 = 3007.32

The solution is correct.

8 0

3 years ago

Using the distance formula , find the distance from the center of your habitat to the point (x, y). Write this equation. Your an

alexdok [17]

Answer:

See explanation

Step-by-step explanation:

The distance formula is given by:

$d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} }$

We want to find the distance between (a,b) and (x,y).

The center of the habitat is missing in the question.

Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:

$d = \sqrt{(x - a)^{2} + {(y - b)}^{2} }$

For instance if the center of your habitat us (2,-1), then

$d = \sqrt{(x - 2)^{2} + {(y + 1)}^{2} }$

6 0

3 years ago

Bob wants to buy a TV that cost $500 plus 8% tax. He is getting a bonus of $45 and a birthday gift of $85 which he plans to use

Genrish500 [490]

Answer:

He needs to work for 40 whole hours

Step-by-step explanation:

In this question, we are tasked with calculating the amount a Tv will cost Bob in terms of the number of hours he needs to work.

Let’s look at the total cost he has to pay.

a. $500

b. 8% tax = 8/100 * 500 = $40

c. He is paying 2 bills of $35 each making a total of 2 * $35 = $70

The total amount he is to pay is thus; 500 + 40 + 70 = $610

Let’s look at his income ;

a. Bonus $45

b. Birthday gift $85

The total amount of money he has asides his salary to offset the bill is 45 + 85 = $130

The balance to pay from his salary would be $610 - $130 = $480

The number of hours he has to work since he earns $12 per hour would be 480/12 = 40 hours of work

5 0

3 years ago

Read 2 more answers

Which of the following values are in the range of the function shown below?

Andrews [41]

I think the answers are 2,1,0

6 0

2 years ago

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago