Which linear inequality is represented by the graph?

y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2

Answer:  A, B, and D

Step-by-step explanation:

Input the coordinates into the inequality to see which makes a true statement:

                             5x - 2y < 8

A) x = -1, y = 1       5(-1) - 2(1) < 8

                              -5  -  2   < 8

                                    -7     < 8       TRUE!

B) x = -3, y = 4       5(-3) - 2(4) < 8

                              -15  -  8   < 8

                                    -23    < 8     TRUE!

C) x = 4, y = 0       5(4) - 2(0) < 8

                              20  -  0   < 8

                                    20     < 8    False

D) x = -2, y = 3       5(-2) - 2(3) < 8

                              -10  -  6   < 8

                                    -16     < 8   TRUE!

Answer:

[tex]\boxed{x = 9}[/tex]

Step-by-step explanation:

m = -1/3

b = 7

And y = 4 (Given)

Putting all of the givens in [tex]y = mx+b[/tex] to solve for x

=> 4 = (-1/3) x + 7

Subtracting 7 to both sides

=> 4-7 = (-1/3) x

=> -3 = (-1/3) x

Multiplying both sides by -3

=> -3 * -3 = x

=> 9 = x

OR

=> x = 9

Answer:

x = 9

Step-by-step explanation:

m = -1/3

b = 7

Using slope-intercept form:

y = mx + b

m is slope, b is y-intercept.

y = -1/3x + 7

Solve for x:

Plug y as 4

4 = 1/3x + 7

Subtract 7 on both sides.

-3 = -1/3x

Multiply both sides by -3.

9 = x

The area of the surface above the region R is 4096π square units.

Given that:

The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]

The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].

To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.

The integral for the area is given by:

[tex]Area = \int\int_R f(x, y) dA[/tex]

To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.

Using polar coordinates, we can parameterize the region R as follows:

x = rcos(θ)

y = rsin(θ)

where r goes from 0 to 8, and θ goes from 0 to 2π.

Now, rewrite the integral in polar coordinates:

[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]

Now, we can integrate with respect to r first and then with respect to θ:

[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]

Integrate with respect to r:

[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]

Now, we can integrate with respect to θ:

[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]

Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))

Area = 4096π + 128(0) - 0

Area = 4096π square units

So, the area of the surface above the region R is 4096π square units.

Learn more about Integration here:

https://brainly.com/question/31744185

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Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}[/tex]

[tex]P(First\ White) = \dfrac{3}{10}[/tex]

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

[tex]P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }[/tex]

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]

Answer:

  73/55

Step-by-step explanation:

The cosecant (csc) is one of the reciprocal functions:

  csc(θ) = 1/sin(θ)

  sec(θ) = 1/cos(θ)

  cot(θ) = 1/tan(θ)

So, if we can find the sine, we can find the cosecant.

__

The mnemonic SOH CAH TOA reminds you that the sine is ...

  Sin = Opposite/Hypotenuse

The above tells you that ...

  Csc = 1/Sin = Hypotenuse/Opposite

The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...

  csc(θ) = 73/55

Answer:

[tex]csc (\theta)=\frac{33}{55}[/tex]

Step-by-step explanation:

Hello!

1) The cosecant function is the inverse the sine function. So we can write:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:

[tex]sin(\theta)=\frac{55}{33}[/tex]

3) So, remembering operations with fractions then the cosecant is:

[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]

[tex]csc (\theta)=\frac{33}{55}[/tex]

Answer:

115 miles

Step-by-step explanation:

First find the distance at 50 mph

d = 50 mph * .5 hours

   = 25 miles

Then find the distance at 60 mph

d = 60 mph * 1.5 hours

   = 90 miles

Add the distances together

25+90

115 miles

Answer:

he drives a 115 miles

Step-by-step explanation:

if he drives 50 mph for half an hour he drove 25 miles then if he drives 60 mph for 1 hour and 30 minutes he would of drove 90 miles. 60 + 30=90

90+25=115 so he drove 115 miles.

Answer:

D. is used to reveal an underlying pattern in the data.

Step-by-step explanation:

Smoothing a time series is achieved when a computer uses some pre-programmed calculation methods to remove noise from large volumes of data. Smoothing helps a user detect patterns in a set of data, thus making it possible to make future predictions. For example, smoothing can be used in the prediction of the rise and fall of stock prices. This helps the traders to have an idea of what to expect in the cost of trading.

Although smoothing reveals the patterns in a set of data, it provides no explanation as to why it is so. It is left to the researcher to draw conclusions as to the reasons for the patterns.

Answer:

The spread of the data in Set B is greater than the spread of the data in Set A.

Step-by-step explanation:

Just took the test :3

Answer:

Nicholas

Step-by-step explanation:

If you want an explanation I can add one

Answer:

6x + y = -18

Step-by-step explanation:

The given equation is,

y - 6 = -6(x + 4)

We have to rewrite this equation in the form of Ax + By = C

Where A, B and C are the integers.

By solving the given equation,

y - 6 = -6x - 24 [Distributive property]

y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]

y = -6x - 18

y + 6x = -6x + 6x - 18

6x + y = -18

Here A = 6, B = 1 and C = -18.

Therefore, 6x + y = -18 will be the equation.

Answer:

since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,

sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft

Answer:

increase of 30

Step-by-step explanation:

1255- 1075 = 180

This is an increase of 180

Divide by the number of numbers which is 6

180 /6 = 30

The mean will increase by 30

Answer:

+30

Step-by-step explanation:

1255- 1075 = 180

180 /6 = 30

Answer:

y = -3.5x² + 2.7x -8.2

Step-by-step explanation:

the quadratic equation is set up as a² + bx + c, so just plug in the values

Answer:

[tex]-3.5x^2 + 2.7x -8.2[/tex]

Step-by-step explanation:

Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].

So, we can use your values of a, b, and c, and plug them into the equation.

A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].

B is 2.7, so the second term is [tex]2.7x[/tex]

And -8.2 is the C, so the third term is [tex]-8.2[/tex]

So we have [tex]-3.5x^2+2.7x-8.2[/tex]

Hope this helped!

Answer: length = 1, width = 1, height = 3, volume = 5

Step-by-step explanation:

Degree is the biggest exponent for the variables in the expression

Length = 4x - 1. The exponent for x is 1 --> degree = 1

Width = x          The exponent for x is 1  --> degree = 1

Height = x³       The exponent for x³ is 3  --> degree = 3

Volume = 4x⁵ - x⁴.  The biggest exponent for x is 5  --> degree = 5

Answer:

- First answer: 1

- Second answer: 1

- Third answer: 3

- Last answer: 5

Step-by-step explanation:

Correct on E2020

Answer:

The correct answer is the first one.

Step-by-step explanation:

Let's analyse the effect of each modification in the function.

The value 6 multiplying the cot function means a vertical stretch.

The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.

The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.

The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6

And the value of 4 summing the whole equation is a vertical shift of 4 units up.

So the correct answer is the first one.

Answer:

option 1

Step-by-step explanation:

Answer:

a) $3700

b) $555

Step-by-step explanation:

The length of the loan is 3 years.

The interest after 3 years is $444.

The rate of the Simple Interest is 4%.

Simple Interest is given as:

I = (P * R * T) / 100

where P = principal (amount borrowed)

R = rate

T = length of years

Therefore:

[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]

P = $3700

She borrowed $3700

b) If the simple interest was 5%, then:

I = (3700 * 5 * 3) / 100 = $555

The interest would be $555.

Answer:

j < 2

Step-by-step explanation:

Simplify both sides of the inequality and isolating the variable would get you the answer

Answer:

Range { 2,6,8}

Step-by-step explanation:

The domain is the input and the range is the output

Range { 2,6,8}

Answer:

2, 6, 8

Step-by-step explanation:

The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.

Answer:

answer is

B) 36,72,80

Step-by-step explanation:

because is the right angle it is exactly 90°

Answer:

77

Step-by-step explanation:

At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.

Answer:

e

Step-by-step explanation:

e

Answer:

Hey there!

The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.

Let me know if this helps :)

Answer: Rectangle

Step-by-step explanation:

In a rectangular prism, every cross-section parallel to a side is a rectangle.

Hope it helps <3

Answer: 168

Step-by-step explanation:

First, let's count the types of selection:

We can select:

Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)

Pack: standard, custom, or sport styling, (3 options)

type of transmission: Manual or automatic (2 options)

Color: (7 options)

The total number of combinations is equal to the product of the number of options in each selection:

C = 4*3*2*7 = 168

Answer:

Option A is the correct option

Step-by-step explanation:

Since, we know that angle at center is double that of the circumference.

JL = 2 × 84°

calculate the product

= 168°

Hope this helps..

Best regards!!

Answer:

Option A is the correct answer.

Step-by-step explanation:

By the incribed angle theorem, we have

1/2of angle JKL.

so, JL = 84°×2

Therefore, the answer is 168°.

Hope it helps..

Answer:

a[tex]\geq[/tex]-3

Step-by-step explanation:

Answer:

-3  ≤  a

Step-by-step explanation:

6≥ -6(a+2)

Divide each side by -6, remembering to flip the inequality

6/-6 ≤ -6/-6(a+2)

-1 ≤ (a+2)

Subtract 2 from each side

-1 -2  ≤  a+2-2

-3  ≤  a

I hope this will help uh.....

The correct graph will be the first one (A)

Answer:

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Step-by-step explanation:

From the summary of the given statistical dataset

The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:

[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5

[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]

[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]

[tex]\sigma_{\overline x }[/tex] = 0.5

Thus X [tex]\sim[/tex] N (64.5,0.5)

Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:

[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>3 })[/tex]

[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]

[tex]P(\overline X > 66) = 1- 0.9987[/tex]

[tex]P(\overline X > 66) =0.0013[/tex]

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Answer:

f(x) = (x + 6)² - 29

Step-by-step explanation:

Given

f(x) = x² + 12x + 7

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

x² + 2(6)x + 36 - 36 + 7

= (x + 6)² - 29, thus

f(x) = (x + 6)² - 29

answers are 6, and -29

Answer:

Step-by-step explanation:

Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.

  Linda has $15

  Reuben has $25 . . . . . . $10 more than Linda

  Manuel has $30 . . . . . . twice what Linda has

Answer:

The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .

Step-by-step explanation:

We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

So, the area of an equilateral triangle =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

where, s = side of an equilateral triangle

A  =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

Cross multiplying the fractions we get;

[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]

[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]

Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;

[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]

Taking square root both sides we get;

[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).