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3 years ago

Graph 4x^2+4y^2=64. what is the domain and range?

Mathematics

1 answer:

marin [14]3 years ago

8 0

Answer:

domain: [-4,4]

range: [-4,4]

Step-by-step explanation:

4x^2+4y^2=64 reduces to:

x^2 + y^2 = 16 This is a circle with center at (0,0) and radius 4.

x and y are both restricted by the radius, which is 4.

domain: [-4,4]

range: [-4,4]

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Identify the vertex , focus, and directrix x=-1/28y^2

liraira [26]

Directrix: x=7
Focus:(-7,0)
Vertex:(0,0)

5 0

3 years ago

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

Andru [333]

Answer:

There is no sufficient evidence to support the claim that wedding cost is less than $30000.

Step-by-step explanation:

Values (x) ∑(Xi-X)^2

----------------------------------

29.1 0.1702

28.5 1.0252

28.8 0.5077

29.4 0.0127

29.8 0.0827

30.1 0.3452

30.6 1.1827

----------------------------------------

236.1 3.4088

Mean = 236.1 / 8 = 29.51

$S_{x}=\sqrt{3.4088/(8-1)}=0.6978$

Statement of the null hypothesis:

H0: u ≥ 30 the mean wedding cost is not less than $30,000

H1: u < 30 the mean wedding cost is less than $30,000

Test Statistic:

$t=\frac{X-u}{S/\sqrt{n}}=\frac{29.51-30}{0.6978/\sqrt{8}}= \frac{-0.49}{0.2467}=-1.9861$

Test criteria:

SIgnificance level = 0.05

Degrees of freedom = df = n - 1 = 8 - 1 = 7

Reject null hypothesis (H0) if

$t$

Finding in the t distribution table α=0.05 with df=7, we have

$t_{0.05,7}=2.365$

$t>-t_{0.05,7}$ = -1.9861 > -2.365

Result: Fail to reject null hypothesis

Conclusion: Do no reject the null hypothesis

u ≥ 30 the mean wedding cost is not less than $30,000

There is no sufficient evidence to support the claim that wedding cost is less than $30000.

Hope this helps!

5 0

3 years ago

The perimeter of a quadrilateral (four-sides polygon) is 50 inches. The longest side is three times as long as the shortest side

kkurt [141]

The side lengths of quadrilateral are 21 inches; 11 inches; 11 inches; 7 inches.

<u>SOLUTION:</u>

Given, the perimeter of a quadrilateral (four-side polygon) is 50 inches.

Let the length of shortest side be n inches. The longest side is three times as long as the shortest side.

That is, length of largest side = 3n inches

The other two sides are equally long and are 4 inches longer than the shortest side.

Then, length of remaining two sides = 4 + n inches

We have to find the length of all four sides.

Now, we know that, perimeter = 50 inches

$\begin{array}{l}{\rightarrow \text { Sum of all sides }=50} \\\\ {\rightarrow n+3 n+n+4+n+4=50} \\\\ {\rightarrow n+3 n+n+n=50-4-4} \\\\ {\rightarrow 6 n=42} \\\\ {\rightarrow n=7}\end{array}$

So, length of sides will be,

$7 \text { inches; } 3\times7=21 \text { inches; } 7+4=11 \text { inches; } 7+4=11 \text { inches. }$

6 0

3 years ago

Which expression represents"divide the sum of x and 2 by 4"?

labwork [276]

Answer:

Step-by-step explanation:

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3 0

3 years ago

For how many (not necessarily positive) integer values of n is the value 4000x(0.4)^n an integer?

Delicious77 [7]

The number of integer values of n for which the value 4000 × (0.4)ⁿ is an integer is; 9

<h3>How to find the integer values in algebra?</h3>

We are given the expression;

4000 × (0.4)ⁿ

This can also be expressed as;

4000 × (²/₅)ⁿ which can further be expressed in exponent form as;

(2⁵ × 5³) × (²/₅)ⁿ = 2⁽⁵ ⁺ ⁿ⁾ × 5⁽³ ⁻ ⁿ⁾

Since this expression is an integer, we need:

1) 5 + n ≥ 0 for which n ≥ -5

2) 3 - n ≥ 0 for which n ≤ 3

Taking the intersection gives;

-5 ≤ n ≤ 3

Thus;

Number of Integer Values = 3 - (-5) + 1 = 9

Read more about Integer Values at; brainly.com/question/17695139

#SPJ1

3 0

2 years ago