Can anyone help me pls

Answer:

attached below is the solution

Step-by-step explanation:

|x| < 7

= -7 < x < 7

| y | < 3

= -3< y < 3

attached below is the shaded region in the xy-plane

Answer:

The answer is below

Step-by-step explanation:

Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16

Solution:

Given that the ellipse has the equation: 4x² + 16y² = 16

let us make x the subject of the formula, hence:

4x² + 16y² = 16

4x² = 16 - 16y²

Dividing through by 4:

x² = (16 - 16y²)/4

x² = 4 - 4y²

Taking square root of both sides:

[tex]x=\sqrt{4-4y^2 }\\[/tex]

The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4xy

[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]

Therefore the length = 2x = 2√2, the width = 2y = 2/√2

Answer:

$12.49

Step-by-step explanation:

cost of two purses = $57.97 - cost of dress = $57.97 - $32.99 = $24.98

cost of one purse = $24.98 ÷ 2 = $12.49

Answer:

probability that a rivet is defective is 0.00868

Step-by-step explanation:

given data

rivets = 20

all seam need reworking P = 16% = 0.16

solution

we consider here probability of a defective rivet = p

and 0.16 = P [Seam needs reworking) = P (at least one rivet in the seam is defective)

so that for non-defective = 1 - P [all the rivets are non-defective]

and that will be here as = 1 - P [rivet 1 is non-defective, rivet 2 is non-defective, rivet 3 is non-defective,...............,rivet 20 is non-defective]

= [tex]1 - (p})^{20}[/tex]     ....................1

so

1-0.16 = [tex]1 - (p})^{20}[/tex]

0.84 = [tex]1 - (p})^{20}[/tex]

[tex]0.84^{\frac{1}{20}}[/tex] = 1 - p

solve it we get

p = 0.00868

so, probability that a rivet is defective is 0.00868

Answer:

24

Step-by-step explanation:

because  its 24 gkrjkkmn lol

Question:

[tex]5x-3y=14[/tex]

[tex]3x-5y=2[/tex]

Find x and y

Answer:

[tex]x = 4[/tex]

[tex]y =2[/tex]

Step-by-step explanation:

Given

[tex]5x-3y=14[/tex]  -- (1)

[tex]3x-5y=2[/tex] -- (2)

Required

Find x and y

We'll solve this using elimination method.

Multiply (1) by 3 and (2) by 5 to eliminate x

([tex]5x-3y=14[/tex]) * 3

([tex]3x-5y=2[/tex]) * 5

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

[tex]15x - 9y = 42[/tex]

[tex]15x - 25y =10[/tex]

Subtract

[tex]15x - 9y = 42[/tex]

- ([tex]15x - 25y =10[/tex])

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

[tex]15x - 15x - 9y + 25y = 42 - 10[/tex]

[tex]- 9y + 25y = 42 - 10[/tex]

[tex]16y = 32[/tex]

Make y the subject

[tex]y = \frac{32}{16}[/tex]

[tex]y =2[/tex]

Substitute 2 for y in [tex]5x-3y=14[/tex]

[tex]5x - 3 * 2 = 14[/tex]

[tex]5x - 6 = 14[/tex]

Collect Like Terms

[tex]5x = 14+6[/tex]

[tex]5x = 20[/tex]

Make x the subject

[tex]x = \frac{20}{5}[/tex]

[tex]x = 4[/tex]

Answer:

B

Step-by-step explanation:

(x+4)(3x^2-7)

multiply and get 3x^3 +12x^2 -7x -28 which is anwser choice b

Step-by-step explanation:

let the angles be ' 7x, 8x and 5x'

as we know, the sum of all the angles of a triangle is 180 degree, so,

7x + 8x + 5x = 180

20 = 180

x = 180/2

x = 90 degrees

7x = 7 × 90 = 630 degree

8x = 8 × 90 = 720 degrees

5x = 5 × 90 = 540 degrees

therefore, 5x is the smallest degrees

Answer:

The value of the test statistic is t = 2.19.

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Sample of 1300 voters:

This means that [tex]n = 1300[/tex]

Found that 45% of the residents favored construction.

This means that [tex]X = 0.45[/tex]

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.

This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:

[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]

So, the test statistic is:

[tex]t = \frac{X - \mu}{s}[/tex]

[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]

[tex]t = 2.19[/tex]

The value of the test statistic is t = 2.19.

Answer:

9

Step-by-step explanation:

Move the variable to the other side of the equation

144 ÷ 16 = a

9 = a

Check:

144 ÷ a = 16 (Correct)

9514 1404 393

Answer:

  1)  c, f

  2) a, e

  3) b, d

Step-by-step explanation:

If you think about the units associated with a coordinate (feet, for example), then you may recognize the following

a) each difference is of "feet", so each difference will have units of "feet". The ratio of "feet" to "feet" cancels the units, leaving a pure number. In this case, it is called "steepness" in selection e. Steepness is given by the slope formula (2).

__

b) The difference in parentheses has units of "feet" (as in (a)), so the square will be "square feet". The sum of two of those will still be "square feet" and the square root of that will be "feet". The units of the formula are those of distance, or length, matching selection d. Distance is given by the distance formula (3).

__

c) The form shown is an ordered pair. That is the same as the representation of a coordinate point, selection f. Coordinates of a point are given by the midpoint formula (1).

Answer:

Its oka linden

Step-by-step explanation:

Just cause

Answer:

Step-by-step explanation:

Given the expression

[tex]\lim_{x \to \ 0} \frac{sin^2x}{x}[/tex]

Substitute the value of x in the function

[tex]= \frac{sin ^2(0)}{0}\\= 0/0 (indeterminate) \\[/tex]

Apply l'hospital rule

[tex]\lim_{x \to \ 0} \frac{d/dx(sin^2x)}{d/dx(x)} \\= \lim_{x \to \ 0} \frac{(2sinxcosx)}{1} \\[/tex]

Substitute the value of x

= 2 sin(0)cos(0)

= 2 * 0 * 1

= 0

Hence the limit of the function is 0

Answer: the initial number of water lily’s

Step-by-step explanation:

the value 1.106 represents the population increase rate

edge 2021

The value 3.915 represents the initial population of water lilies

The standard exponential equation is given as y = ab^x

where;

Given the exponential equation y = 3.915(1.106^x

On comparison, we can see that;

a  = 3. 915

This shows that the value 3.915 represents the initial population of water lilies

Learn more on exponential equation here: https://brainly.com/question/2456547

Answer:

It will read the same at F = -40.

Step-by-step explanation:

The relation between fahrenheit and celsius is given by the following equation:

[tex]C = \frac{5(F-32)}{9}[/tex]

At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer?

This is F for C = F. So

[tex]C = \frac{5(F-32)}{9}[/tex]

[tex]F = \frac{5(F-32)}{9}[/tex]

[tex]9F = 5F - 160[/tex]

[tex]4F = -160[/tex]

[tex]F = -\frac{160}{4}[/tex]

[tex]F = -40[/tex]

It will read the same at F = -40.

Explanation

-1.25+2.5=1.25

Answer:

1.25 is the answer .......

Step-by-step explanation:

hello will u be friend with me

Answer:

3

Step-by-step explanation:

_+(-4) = -1

_-4 = -1

_ = 3

Answer:

x=9

Step-by-step explanation:

13+14=3x

27=3x

27/3=x

9=x

Answer: 24

Step-by-step explanation:

3x + 9 = 5x - 3

9 = 2x - 3

12 = 2x

x = 6

6 * 4  =24

4x = 24

Answer:

it's 78<C. < means less than

Answer:

4.5 (j + m) + 27

Step-by-step explanation:

Answer:

apples cost a total of 2.16

cherrys cost a total of 9.05

Step-by-step explanation:

1.35*1.6=2.16

3.62*2.5=9.05

Answer:

0.45 and 0.5

Step-by-step explanation:

plato/edmentum

The 90% confidence interval for the true proportion of club members who use compost is given as (0.4, 0.507)

This refers to the probability of a parameter falling across a set of values around the mean.

To find the 90% confidence interval,

Probability=  45%= 0.45

Level of significance= 90%

1-0.90

= 0.10

[tex]z\alpha /2 = z(0.1/2) = 0.05[/tex]

The value of 0.05

P0.05= 1.645

P ± 1.645 x [tex]\sqrt{P0-p/n}[/tex]

0.45 ± 1.645 * [tex]\sqrt{0.48 (1-0.45)/200}[/tex]

0.45 ± 1.645 * 0.035178

0.45 ± 0.0578

0.45 - 0.0578, 0.45 + 0.0578

(0.4, 0.507)

Read more about confidence intervals here:

https://brainly.com/question/15712887

#SPJ5

Answer:

Hey

Step-by-step explanation:

Where is the question

Answer:

3[tex]\sqrt{5}[/tex]

Answer:

The equation of a line passing through points [tex](x_1,y_1)[/tex]and [tex](y_1,y_2)[/tex] is given by:

[tex]y-y_1 = \frac{(y_2-y_1)}{x_2-x_1}(x-x_1)[/tex]

According to question, the passing points of the line are (1,1) and (3,-3). So, its equation is given by:

[tex]y-1 = \frac{-3-1}{3-1} (x-1) \\or, y-1 = \frac{-4}{2}(x-1)\\or, 2y-2 = -4x+4\\or, 4x + 2y = 2+4\\or, 4x+2y = 6\\or, 2x+y = 3 is the required equation.[/tex]

Answer:

Step-by-step explanation:

b = 10

Substitute b in every equation below and compare the results

A. 2(b + 4) = 16

B.  2(b + 2) = 40

C. 3(b - 2) = 24

D. 2(8 + b) = 42

E. 3(b - 4) = 20

Answer:

C. 3(b - 2) = 24..