y ≥ 2x+4
y≤ - x² +6

Need to list all points of intersection from system of inequalities

System of linear equations for the graph below are y = -1/3(x) + 6 and

y = 4/3(x) + 1.

From the graph:

points for the line (0,1) and (3,5) .

points for the line (0,6) and (3,5)

slope m = y2 - y1 / x2 -x1

= 5 - 1 / 3 - 0

= 4/3

substitute (0,1) and m value in y = mx + c

1 = 4/3*0 + c

1 = 0 + c

c = 1

c and m value substitute

y = mx +c

y = 4/3(x) + 1

slope of (0,6) and (3,5) m = 5 - 6 / 3 - 0

= -1/3

substitute (0,6) and m value in y = mx + c

6 = -1/3*0 + c

6 = 0 + c

c = 6

c and m value substitute

y = mx + c

y = -1/3(x) + 6

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Answer:

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

Slope-intercept form:

Find the value of b:

The line is:

Answer:

y = (-5/4)x + 13

Step-by-step explanation:

Formula we use,

→ y = mx + b

Now the value of b will be,

→ 3 = (-5/4)8 + b

→ 3 = -40/4 + b

→ 3 = -10 + b

→ 3 + 10 = b

→ [ b = 13 ]

Then the equation will be,

→ y = mx + b

→ 3 = (-5/4)8 + 13

→ y = (-5/4)x + 13

Thus, answer is y = (-5/4)x + 13.

Answer:

Parent function:

f(x) = √x

Add a number to the value of the function, such as k:

f(x) = (√x) + k

If k is positive, the function moves up. If k is negative, the function moves down.

The value of the scale on the map is 18 cm 1 mi

Knowing the distance between two places on the map and measuring that distance on the map will yield the scale. Additionally, if a map has division lines, they are normally spaced apart by a mile. Example 4: On the map, the separation between points A and B is 6 inches

The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale."

People can accurately visualise how the distances mentioned on the map are plotted by using map scales. This is helpful in figuring out how to get from one place to another, especially if one travels or works in a profession that requires similar knowledge.

Given,

Model cm/actual miles

12/2/3

= 12/1,3/2

=18/1

=18:1

Therefore the value of the scale on the map is 18 cm 1 mi

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Using probability of a randomly chosen person, 270 people should have age less than or equal to 25.

From the given question,

Mean = 48.69

Standard Deviation = 17.993

We have to find the distribution of age is normal calculate the number of people who should be 25 years of age or less.

If 'X' is the age of a randomly selected individual in the sample, and that individual has a mean and a standard deviation that are normally distributed, then that individual's age has a standard normal score of -

Z = X- Mean/standard deviation

Z = X-48.69/17.993

Thus, Z-score for 25 year old is -

Z = 25 -48.69/17.993

Z = -23.69/17.993

Z = -1.317

Z= -1.317(approx)

The probability of a randomly chosen person to be 25 years of age or less in the sample is -

P(X < 25) = P(Z < -1.317)

P(X < 25) = 0.0939

As there are N = 2867 people in the data, so number of people expected to have age less than 25 is -

n = N x P(X < 25)

n = 2867 x 0.0939

n = 269.21

n = 270(approx)

Thus, 270 people should have age less than or equal to 25.

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Right question

"If the mean is 48.69 and the standard deviation 17.993. Assuming the distribution of age is normal calculate the number of people who should be 25 years of age or less.

Statistic

Number valid = 2867

The function has a maximum value of 30 at x = 3

From the question, we have the following equation that can be used in our computation:

F(x) = -3x²+18x+3

This can be expressed properly as

F(x) = -3x² + 18x + 3

A quadratic function is represented as

F(x) = ax² + bx + 3

By comparison, we have

a = -3

For a quadratic function to have a maximum value, the value of a must be less than 0

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

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Rotation is represented by a table fan, Dilation enlargement by flowers, reflection by ducks building a heart, and translation by a window picture.

Compared to translation, reflection, and rotation, what is a dilation?

Dilation:

Translation:

Reflection:

Rotation:

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Answer:

78 children

266 Adults

Step-by-step explanation:

Find the picture attached.

The angles will be x = 8° and y = 21°

given information:

∠AOB = 180°

∠EOG = 90°

∠EOF and ∠FOG are complementary angles. Complementary angles are those whose sum is equal to 90° and it is given to us in the question.

∠EOG = ∠EOF + ∠FOG

90° = 27° + 3y

90 - 27 = 3y

63 / 3 = y

y = 21°

Similarly  ∠AOE , ∠AOG and ∠GOB are supplementary to each other. Supplementary angles are those whose sum is equal to 180°

∠AOB = ∠AOE + ∠AOG + ∠GOB

180° = x + 90° + 8x + 18°

180 - 90 - 18 = 9x

9x = 72

x = 72 / 9

x = 8°

Hence we can clearly say that x = 8° and y = 21°

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62 hours is 86% percent of 3 days

What is percentage and how to calculate it?

Percentage is the ratio in which the denominator is 100. To calculate the percentage we multiply the obtained value by 100.

We are given 62 hours and 3 days

Now 1 day has 24 hours

Hence 3 days will have 3*24 = 72 hours

Now To find the percentage we first have to find the ratio of 62 and 72

And to do that we divide 62 by 72

we get 62/72 = 0.86

To get the percentage we multiply this value by 100

0.86 * 100= 86%

Hence, 62 is 86% of 3 days

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This is the way to find the endpoint if a confidence interval in the TI calculator:

An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.

A confidence interval is used to calculate an estimate for an unknown population parameter. Specifically, to provide an interval so that any value of the parameter falling inside the range is a credible value, and values falling outside the interval are implausible

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Answer: B

Step-by-step explanation:

B

Reason: supplimentry angles as the line is transervsal of line m and n .

Which means that 132°=2x

and using algebra you know that x=66°

Answer:it will be D

Step-by-step explanation: because $100 + 4%=$100.4

The annual percentage yield (APY) of Russ is 4.39 %

What is Annual Percentage Yield?

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.

Given data ,

Deposit amount of Russ = $ 4500

Interest rate R = 4.3 %

And it is given that the interest rate is compounded daily , so

Interest rate R = 4.3 % / 365

                        = 0.043 / 365

                        = 0.0001178

Now , The annual percentage yield (APY) is calculated as

The interest amount = 4500 x ( 1 + 0.0001178 )³⁶⁵

                                  = 4500 x ( 1.0001178 )³⁶⁵

                                  = 4500 x 1.04393211

                                  = 4697.694

                                  ≈ 4697.69

Therefore , the interest will be

= 4697.69 - 4500

= $ 197.69

Now , the annual percentage yield (APY) is given by

= Interest / Deposit

= 197.69 / 4500

= 0.0439

≈ 4.39 %

Hence , annual percentage yield (APY) of Russ is 4.39 %

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The amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.

Given,

A patient is administered 310cm^3 of a saline and water solution that is labeled as 9% saline.

What is saline solution?

Salt and water are combined to make saline. Because of its salt content (0.9% saline), which is comparable to that of tears, blood, and other bodily fluids, a normal saline solution is known as normal. Isotonic solution is another name for it.

Here,

Amount of saline = 0.09 × 310 = 27.9

Amount of water = 310 - 27.9 = 282.1

Thus, the amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.

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The total cost for Bolt Electric Company and Zap Electric Company are y = 0.12r + 2.83 and y = 0.06r + 6.55 respectively

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.

The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:

y = 0.12r + 2.83

The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:

y = 0.06r + 6.55

The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83

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The expectation, E(3y +2) and variance, Var(3y+2) of the random variable are 13.4 and 19.44 respectively

The expectations or expected value E(y) of a random variable can be thought of as the “average” value of the random variable. It is also called its mean

By definition:

if y = ax + b

then E(y) = aE(x) + b

where a,b = constant

The variance V(y) of  a random variable is the measure of spread for the distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value

By definition

if y = ax + b

V(b) = 0

V(y) = V(ax) + V(b)

      = a²V(x) + 0

where a,b = constant

Given: E(y)= 3.8 and Var(y)= 2.16

Calculate E( 3y +2) and Var( 3y+ 2)

E(3y +2) = 3E(y) + 2            since E(y) = 3.8

           = 3×3.8 + 2

          = 11.4+2

          = 13.4

Var(3y+2) =  3²Var(y) + 0

               = 9×2.16

               = 19.44

Therefore, E(3y +2) is 13.4 and Var(3y+2) is 19.44

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The solution of the polynomial equation x(x - 2) = 48 by factoring is x = 8 or x = -6

Given the polynomial equation x(x−2) = 48

x(x−2) = 48

x² - 2x = 48

x² - 2x - 48 = 0

x² -8x+6x - 48 = 0

By factoring the equation, we have:

x(x-8) + 6(x-8) = 0

(x-8) (x+6) = 0

x-8 = 0 or x+6 = 0

x = 8 or x = -6

Therefore, the solution of the polynomial equation is x = 8 or x = -6. Type x = 8 or x = -6 in the answer box

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The coordinates of the image are -2P

From the question, we have the following parameters that can be used in our computation:

Ry = -2(P)

To calculate the coordinate of the image, we simply open the bracket

So, we have

Ry = -2(P)

Solving further, the equation can be represented as

Ry = -2 * P

Evaluate the product

So, we have the following representation

Ry = -2P

Hence, the image has an coordinate or ordered pair of -2P

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The area of the sector is 8800cm²

What is an area of the sector?

The area of the sector refers to the area encircled by a circle's sector. A sector always originates from the center of the circle.

What is curved surface area?

The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Total Surface Area: This is the combined area of the bases and the curved surface.

Here, we have

Radius = 28cm,  Height = 96cm

L² = 96² + 28²

= 9216 + 784

= 10000

L = √10000

= 100cm

curved surface area = πrl

= 22/7×28×100

= 8800cm²

area of cone = area of sector

area of sector = 8800cm2

Hence, the area of the sector is 8800cm²

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As per the given demand function and equilibrium point, the consumers' surplus is 852.072.

What is consumer surplus?

Consumer advantages from market competition are measured economically as consumer surplus. When customers pay less for a good or service than they are willing to, this is known as a consumer surplus.

Given demand function,

[tex]D(q) = \frac{3000}{(3q+1)^2}[/tex]

at q = 4

putting value of q in function,

[tex]q' = \frac{3000}{(3(4)+1)^2}[/tex]

[tex]q' = \frac{3000}{169}[/tex]

Finding Consumer Surplus

[tex]CS = \int\limits^q_0 {D(q) - q'} \, dq[/tex]

[tex]CS = \int\limits^4_0 {\frac{3000}{(3q+1)^2} - \frac{3000}{169} } \, dq[/tex]

[tex]CS = [-\frac{1000}{3q+1} - \frac{3000q}{169}]^4_0[/tex]

CS = [-(76.923)-(71.005)] - [-1000]

CS = -147.928+1000

CS = 852.072

Therefore, consumers' surplus is 852.072.

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Complete Question

Find the consumers surplus if the demand function for a particular beverage is given by D(q)=(3000)/((3q+1)^(2)) and if the supply and demand are in equilibrium at q=4

We conclude that 80% of patients stop smoking when given sustained care.

Given,

The number of patients given sustained care = 175

Patients who were no longer smoking after one month = 82.3%

Significance level = 0.05

We have to claim that 80% of patients stop smoking when given sustained care.

Let p = percentage of patients stop smoking when given sustained care.

So, Null Hypothesis, H₀ : p = 80%     {means that 80% of patients stop smoking when given sustained care}

Alternate Hypothesis, Hₐ : p  80%     {means that different from 80% of patients stop smoking when given sustained care}

The test statistics that would be used here One-sample z test for proportions;  

                      T.S. =  [tex]\frac{p_{0} -p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where,  p₀ = sample proportion of patients who stop smoking when given sustained care = 82.3%

n = sample of patients = 175

So, the test statistics  =  [tex]\frac{0.823-0.80}{\sqrt{\frac{0.823(1-0.823)}{175} } }[/tex]

                                    =  0.80

The value of z test statistics is 0.80

Also, P-value of the test statistics is given by the following formula;

 P-value = P(Z > 0.80) = 1 - P(Z  > 0.80)

  = 1 - 0.21185 = 0.78815

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that 80% of patients stop smoking when given sustained care.

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The parabola's graph leads us to deduce that the quadratic equation is

x² + 5x + 1.

An algebraic expression with variables and constants is known as a quadratic equation.

Since the degree of a quadratic equation is two, it has two roots.

We are aware that the roots of a quadratic equation can be found at the vertex of a parabola, which is the graph of a quadratic function.

Given, The roots of the equation are x = - 4 and x = - 1, and the quadratic expression is, as the vertex of the parabola is at (-4, -1),

(x + 4)(x + 1).

= x² + x + 4x + 1.

= x² + 5x + 1.

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The sixth term of an arithmetic sequence is 3/2 and the twelfth term is 5/2. The common difference is 1/6.

A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d". So, subtract the first term from the second term, the second term from the third term, etc. to find the common difference of an arithmetic sequence. The common difference is the difference that exists between every pair of phrases that follow one another in a series. For instance, the number 3 is a common difference in the series 4, 7, 10, 13, etc. An arithmetic progression is a series of differences.

Given,

a₆ = 3/2

a₁₂ = 5/2

Arithmetic sequence:

a₇ = a₆ + d

a₈ = a₇ + d

a₈ = a₆ + 2d

a₉ = a₈ + d

a₉ = a₆ + 3d

...

a₁₂ = a₁₁ + d

a₁₂ = a₆ + 6d

As given,

a₆ = 3/2

a₁₂ = 5/2

Equating,

5/2 = 3/2 + 6d

6d = 1

d = 1/6

The sixth term of an arithmetic sequence is 3/2 and the twelfth term is 5/2. The common difference is 1/6.

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Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Given terms:

  [tex]a_6=\dfrac{3}{2}[/tex]

  [tex]a_{12}=\dfrac{5}{2}[/tex]

Substitute the given terms into the formula to create two equations for a:

Equation 1

[tex]\begin{aligned}a_6=a+(6-1)d&=\dfrac{3}{2}\\\\a+5d&=\dfrac{3}{2}\\\\a&=\dfrac{3}{2}-5d\end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}a_{12}=a+(12-1)d&=\dfrac{5}{2}\\\\a+11d&=\dfrac{5}{2}\\\\a&=\dfrac{5}{2}-11d\end{aligned}[/tex]

Substitute the second equation into the first equation and solve for d:

[tex]\begin{aligned}\implies \dfrac{5}{2}-11d&=\dfrac{3}{2}-5d\\\\\dfrac{5}{2}-11d-\dfrac{3}{2}&=\dfrac{3}{2}-5d-\dfrac{3}{2}\\\\\dfrac{2}{2}-11d&=-5d\\\\1-11d&=-5d\\\\1-11d+11d&=-5d+11d\\\\1&=6d\\\\\dfrac{1}{6}&=\dfrac{6d}{6}\\\\\dfrac{1}{6}&=d\end{aligned}[/tex]

Therefore, the common difference of the arithmetic sequence is ¹/₆.

The distance between the points in radical form is [tex]\sqrt{52}[/tex]

What is distance formula ?

Formula for distances between pairs of points, an algebraic expression that expresses distances as a function of the coordinates of the points The Pythagorean theorem is the foundation for distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space.

To calculate the distance we use distance formula

[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]

where [tex](x_{1},y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] are the 2 coordinates

[tex](x_{1},y_{1} )[/tex] = (-2,-4)

[tex](x_{2} , y_{2} )[/tex] = (4,0)

d = √(4 - (-2))² + (0 - (-4))²

d = √6² + 4²

d = √36 + 16

d = √52

√52 → radical form

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Remember rules with angles when parallels are present (alternate interior/exterior angles, corresponding angles, same side interior/exterior angles, etc.)

Statements                         Reasons

∠3 = ∠5                            m || n, alternate interior angles

∠5 = ∠13                          a || b, corresponding angles

∠3 = ∠13                          substitution property: ∠3 =∠5 and ∠5 =∠13

Answer:

[tex]y=-\frac{2}{3}x+1.[/tex]

Step-by-step explanation:

1. common form of slope-interception form is:

y=(slope)*x-interception;

Then

[tex]2. \ y=-\frac{2}{3} x+interception;[/tex]

3. in order to calculate the 'interception' is it needed to substitute the given coordinates into this non-completed equation:

[tex]5=-\frac{2}{3} *(-6)+interception; \\interception=1;[/tex]

4. finally, the required equation is:

[tex]y=-\frac{2}{3} x+1.[/tex]

The amount of money to represent Arthur's Schedule C (Form 1040) deduction for refreshments is: C. $480.

In Economics, there are different types of tax which are levied on individuals (employees) or business firms by the government, and these include the following:

A Form 1040 was formally referred to as U.S. Individual Income Tax Return or Schedule C and it can be defined as an internal revenue service (IRS) tax form which is used by taxpayers in the United States of America, to file their annual income tax return.

In this scenario, Arthur's deduction for refreshments should be recorded as $480 in the Schedule C (Form 1040).

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Complete Question:

Arthur is a ride-hailing driver. He spent $500 on bottled water during the year. He personally consumed $20 of the water he purchased, but the remaining $480 was consumed by riders. How much is Arthur's Schedule C (Form 1040) deduction for refreshments?

$0

$240

$480

$500