the equations 6x + 5y = 28 and 10x + 14y = 58 represent the cost for lunch and dinner for a family eating out on vacation. if x is the number of adults and y is the number of children, how many adults are in the family?

The sample proportion would be 0.5.we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.

To determine what sample proportion would yield a p-value of 0.05, we must first understand the formula for calculating a p-value. The formula for a p-value is p-value = 1 - [tex](1 - proportion)^n[/tex], where n is the sample size. By manipulating this equation, we can solve for the proportion when the p-value is equal to 0.05. We can isolate the proportion by taking the inverse of both sides of the equation, which yields: proportion = 1 - [tex](1 - 0.05)^(1/n)[/tex]. Since the sample size is 90, we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.

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The equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be [tex]y = ax^2 + bx + c[/tex].

Using the point (0, -8), we get:

[tex]-8 = a(0)^2 + b(0) + c[/tex]

c = -8

Using the point (-1, 1), we get:

[tex]1 = a(-1)^2 + b(-1) - 8[/tex]

a - b = 9

Using the point (-3, 1), we get:

[tex]1 = a(-3)^2 + b(-3) - 8[/tex]

9a - 3b = 27

Using the point (-4, -8), we get:

[tex]-8 = a(-4)^2 + b(-4) - 8[/tex]

16a - 4b = 0

Using the point (-2, 4), we get:

[tex]4 = a(-2)^2 + b(-2) - 8[/tex]

4a - 2b = 12

Solving this system of equations, we get:

a = -3

b = -12

c = -8

Therefore, the equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

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Therefore, the mean salary paid to the office assistants in this company is $24,000.Answer: B. $24,000

A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. The mean salary paid to the office assistants in this company can be calculated by taking the weighted average of the mean salaries of the two offices.
Here's the formula to calculate the weighted average:
Weighted average = (weight1 × value1 + weight2 × value2) / (weight1 + weight2)
Where weight represents the number of data points, and value represents the mean salary of office assistants.
In this question, the weight of the New Jersey office is 128, and the weight of the Utah office is 32. The value of the New Jersey office is $28,500, and the value of the Utah office is $22,500.
Now let's plug in the values:
Weighted average = (128 × 28,500 + 32 × 22,500) / (128 + 32)
= (3,648,000 + 720,000) / 160
= 24,000

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Answer: D

Step-by-step explanation:

Its the fairest way to pick a random person

Answer:

1 ft per 4 seconds

120 seconds

72 seconds

Step-by-step explanation:

Answer:[tex]3\sqrt{2}[/tex]

Step-by-step explanation:

in order to make a right triangle point should be either (1,4) or (4,1)

each way hypotenuse of this triangle is

[tex]known coordinates are (4,4)-- > (x1,y1)\\ and (1,1)-- > (x2,y2) \\\sqrt{(x1-x2)^{2}+(y1-y2)^{2}} =\sqrt{(4-1)^{2}+(4-1)^{2}}=\sqrt{9+9}=\sqrt{3^{2}*2}=3\sqrt{2}[/tex]

According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.

The angles add up to 180 degrees.

Then we receive,

[tex]a + 86 =180[/tex]

Or, a = 180 -86

Or, a = 94°.

As a result, an is 94°.

The angle an is 94 degrees.

Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.

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Opioids are a class of drugs that include both prescription painkillers, such as oxycodone, hydrocodone, and fentanyl, and illegal drugs, such as heroin.

Opioids are highly addictive and can lead to physical dependence and addiction with prolonged use. They can also cause a range of negative side effects, including drowsiness, confusion, constipation, nausea, and respiratory depression, which can be life-threatening in high doses.

Opioid addiction has become a major public health crisis in many countries, including the United States, where it has been linked to a dramatic increase in overdose deaths.

The numbers that match the phrases are;

1 - j

2 - c

3 - b

4 - a

5 - i

6 - d

7 - e

8 - f

9 - j

10 - h

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Step-by-step explanation:

If your age is ' a ' then your max heart rate = 220 - a

The exact dimensions (in inches) of the cylindrical mailing tube that may be mailed using the postal service is 7 inches radius and a length of 14 inches.

To find the maximum volume of the mailing tube, maximize the function:

V = πr²L

subject to the constraint:

C = 2πr + L = 84

where C is the girth.

Using Lagrange multipliers, we need to solve the system of equations:

∇V = λ∇C

2πrL = λ(2π)

πr² = λ

2πr + L = 84

Taking the ratio of the first two equations:

L = 2r

Substituting this into the third equation:

4πr + 2r = 84

Simplifying:

r = 7

Substituting this into the equation L = 2r:

L = 14

Therefore, the cylindrical mailing tube of greatest volume that may be mailed using the postal service has a radius of 7 inches and a length of 14 inches.

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Image transcribed:

A package to be mailed using a certain postal service may not measure more than 84 inches in length plus girth. (Length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.)

length

girth

Use Lagrange multipliers to find the exact dimensions (in inches) of the cylindrical mailing tube of greatest volume that may be mailed using the postal service.

radius ______ in

length ______ in

The value of ∠K is 78°

The tangent of a circle is a straight line that touches the circle at exactly one point, and it is perpendicular to the radius of the circle at that point.

Given that, a tangent JK is lying on the circle H whose radius are HJ and HM,

So, ∠HMJ = ∠HJM = 84°

and JK ⊥ HJ   (JK is a tangent on radius HJ)

So, ∠HJK = 90°

∠HJM + ∠MJK = ∠HJK

84° + ∠MJK = 90°

∠MJK = 6°

Using exterior angle property;

∠MKJ + ∠MJK = ∠HJM

∠MKJ + 6° = 84°

∠MKJ = 84° - 6° = 78°         (∠MKJ means ∠K)

Therefore, ∠K = 78°

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To answer this problem, we must utilize the information provided to calculate the number of round trips Spencer takes every week. Spencer commutes a total of 16 miles each week,

which translates to 8 miles to work and 8 miles home. We also know that he lives around a quarter mile from his employment.  the number of round trips Spencer takes every week. Spencer commutes a total of 16 miles each week, Thus we can create an equation to calculate the number of round trips he takes 8 = (4/5) * n where n is the number of trips Spencer takes. To find n, we can cross-multiply: 8 * 5 = 4 * n n = 20/4 n = 5 As a result,Spencer lives 4/5 mile. In one week, he commutes a total of 16 miles to and from work.  Spencer makes five round journeys to and from work each week.

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The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.

It has one or more variables, and based on the values of the variables, it can either be true or false. Equations are frequently employed in a wide range of mathematical applications, from straightforward algebraic equations to more intricate differential equations used in calculus and physics. Equations are used to depict relationships between various mathematical objects or values. An essential part of addressing algebraic problems is to solve equations to determine the values of the variables that make the equation true.

given

We can solve one equation for one variable and then insert the expression into the second equation to apply the substitution method. For instance, we can resolve the first equation for y as follows:

y = 2x + 6

After that, we may enter the following expression in place of y in the second equation:

2x + 6 = -9x - 1

Then, we may find x:

11x = -7

x = -7/11

We may use one of the original equations to obtain the value of y once we have determined the value of x:

y = 2(-7/11) + 6 = 23/11

The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.

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The equation of the circle is 16 x^2 + 16x +16 y^2- 4y -45 =0  

Here the center of circle is at (1/2, 1/4 ) and radius is √ 3

The equation of a circle with center (h , k) and radius r is given by

(x - h)^2 + ( y - k)^2 = r^2

Here it is given that the center of circle  (-1/2 , 1/4) = (h, k) and radius r= √ 3

Therefore the equation of required circle is

(x - (-1/2) )^2 + (y-1/4)^2= √ 3^2

=> x^2  + 1/4 + x + y^2 +1/16 - 4y= 3

=> 16x^2 + 4 +16x+ 16 y^2 -4y +1= 48

=>16 x^2 + 16x +16 y^2- 4y -45 =0

therefore the required equation of circle is

16 x^2 + 16x +16 y^2- 4y -45 =0

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Answer:

a. To find the volume when the width is 5 inches, we plug in w=5 into the equation:

V = 2w³ - 7w² + 3w

V = 2(5)³ - 7(5)² + 3(5)

V = 250 - 175 + 15

V = 90

Therefore, the volume is 90 cubic inches.

b. To factor the polynomial, we can first factor out a w:

V = w(2w² - 7w + 3)

Then we can factor the quadratic expression in parentheses:

V = w(2w - 1)(w - 3)

Each factor represents a dimension of the rectangular prism:

w is the width

2w - 1 is the length

w - 3 is the height

c. If the width is 5 inches, we can use the factorization from part b to find the other dimensions:

length = 2w - 1 = 2(5) - 1 = 9 inches

height = w - 3 = 5 - 3 = 2 inches

This means that the rectangular prism has dimensions 5 inches by 9 inches by 2 inches. We can also use the dimensions to calculate the volume:

V = 5 × 9 × 2 = 90 cubic inches

This is the same as the answer from part a.

d. The graph of the polynomial is:

Graph of the polynomial

The x-intercepts are approximately 0.5 and 3. These correspond to the widths at which the volume is 0, which means the rectangular prism has zero volume. In other words, the x-intercepts represent the points where the rectangular prism collapses into a flat shape.

e. The domain of the function is all real numbers, since we can plug in any width w and get a corresponding volume. The range of the function is also all real numbers, since the volume can be any positive or negative value depending on the width. Specifically, the range is (-∞, ∞).

Answer:

The answer is

-7/8 + 3/10

Step-by-step explanation:

See the picture

Hope you understand :)

The population of the city will be approximately 597,543 people after 11 years.

We can solve this problem using the formula for exponential growth:

[tex]N = P(1 + r)^t[/tex]

where:

N = final population

P = initial population

r = annual growth rate (as a decimal)

t = number of years

In this case, we have:

P = 370,000

r = 0.0475 (since the annual growth rate is 4.75%)

t = 11

Substituting these values into the formula, we get:

[tex]N = 370,000(1 + 0.0475)^{11}[/tex]

Using a calculator, we can simplify this expression to:

N = 597,542.64

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The surface area of the cylinder is approximately 127.17 cm².

Surface area of cylinder is the total space covered by the flat surfaces of the bases of the cylinder and its curved surface. The formula for the surface area of a cylinder is: 2πr² + 2πrh.

To solve this problem, we first need to find the radius of the cylinder. The diameter of the cylinder is 3 cm, so the radius is half of that:

r = 3/2

= 1.5 cm

We need to substitute the values we know into the formula for surface area:

= 2π(1.5)² + 2π(1.5)(12)

= 2π(2.25) + 2π(18)

= 4.5π + 36π

= 40.5π

We will now approximate the value of π to get the numerical answer, so, our Surface Area will be:

= 40.5π

= 40.5 * π

= 40.5 * 3.14

≈ 127.17 cm²

Answered question "A cylinder is 12 cm tall and has a diameter of 3 cm. What is the surface area?"

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When the equilibrium point is above the potential GDP line, the economy is experiencing inflationary pressure.

In the AD/AS model, whether the economy is in a recession is illustrated by how close the equilibrium is to the potential GDP line. The potential GDP line represents the maximum level of output that an economy can produce with its existing resources and technology.What is the AD/AS model?The AD/AS model is a graphical representation of the macroeconomic relationship between aggregate demand (AD) and aggregate supply (AS). This model is used to explain the behavior of the economy by demonstrating how changes in the level of aggregate demand and aggregate supply can impact the economy's level of output and prices.

The model's AD curve represents the total demand for all goods and services in an economy at different price levels. The AS curve represents the total supply of all goods and services in the economy at different price levels.

The intersection of the AD and AS curves represents the equilibrium point where the economy's output level and price level are determined. The economy is in a recession when the equilibrium point is below the potential GDP line.

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The population of bacteria after 15 days is 384,000.

An equation is a mathematical statement that expresses the equality of two expressions, typically separated by an equal sign (=). It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. Equations are used to solve problems in various fields of study, such as physics, engineering, economics, and mathematics. They are also used in everyday life, such as calculating the cost of groceries or determining the time it takes to complete a task. Solving an equation involves finding the values of the variables that make the equation true.

The exponential growth model for this scenario can be written as:

y = a * (2ˣ)

Where:

y = population of bacteria after x days

a = initial population of bacteria = 12,000

x = number of days

Substituting the given values into the equation, we get:

y = 12,000 * (2ˣ)

To determine the population of bacteria after 15 days, we simply substitute x = 15 into the equation:

y = 12,000 * (2¹⁵)

y = 12,000 * 32

y = 384,000

Therefore, the population of bacteria after 15 days is 384,000.

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this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.

a) The equation that represents this situation is:

2x + 2y = 175

where x is the length of the short sides (in feet) and y is the length of the long sides (in feet).

b) The equation in terms of y is:

2(6) + 2y = 175

which simplifies to:

12 + 2y = 175

2y = 163

y = 81.5

However, this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.

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Answer:

Step-by-step explanation:

EZ

its 21

Answer:

C

Step-by-step explanation:

The red graph is obtained by shifting the graph of f(x) = 4 - x² upwards by some amount. We can see that the highest point on the red graph occurs at x = 0, where the value is 4.

To shift the graph of f(x) upwards by 3 units, we can add 3 to the entire function:

f(x) + 3 = 4 - x² + 3

= 7 - x²

So the equation of the red graph is:

g(x) = 7 - x²

Therefore, the correct answer is option C: g(x) = 7 - x².

Xavier rode 7.5 miles and Aiguo rode twice as much, or 15 miles.

Let x be the number of miles Xavier rode. Since Aiguo rode twice as many miles as Xavier, let 2x be the number of miles Aiguo rode.

Together, they rode a total of 22.5 miles, so we have the equation:

x + 2x = 22.5

Simplifying, we will get:

3x = 22.5

x = 22.5/3

x = 7.5

We can check our answer by verifying that the sum of their distances is indeed 22.5 miles:

= 7.5 + 15

= 22.5

Therefore, the solution is x = 7.5 and y = 15.

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The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.

Explain function?

A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.

The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]

To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]

So, the corrected version of the solution is:

Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.

Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]

Step 3: The decay factor is [tex]0.3.[/tex]

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The area of the bedroom in the terms of p and q is (6p7q)² square units.

What is the area of square?

The amount of square units required to fill a square is referred to as the area of a square. In general, the region contained within a flat object's or 2D figure's boundary is referred to as the area. The unit of measurement is square, with square metres serving as the default.

We are given that a bedroom is in the shape of a square with the length as 6p7q.

We know that area of a square is the square of the side.

So, from this we get

⇒ Area = (6p7q)² square units

Hence, the area of the bedroom in the terms of p and q is (6p7q)² square units.

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when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.

Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and  36 cm.Now the volume of the container is:

V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now  we convert the above result  into millimeters by  multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm

Now to find the volume of the syrup that was poured into the container,  we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:

1/3(V) + x = 1/2(V), where v is the  volume of the container in millimeters, so we substitute the calculated value of the volume we get :

=>1/3(V) + x = 1/2(V)

=>x = 1/2(V) - 1/3(V)

=> x = 1/6(V) = 1/6(3,456,000)  = 576,000 cubic mm

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Therefore , the solution of the given problem of equation comes out to be the equation has a slope of 1/2 and a y-intercept of -1, and is written as y = 1/2x - 1.

In intricate algorithms, variable words are frequently used to demonstrate consistency between two incompatible assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization results in c + 7 rather than a singular formula that divides 12 into two components and can be applied to data obtained from y + 9.

Here,

We must isolate y on the left side of the equation in order to convert the provided equations to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

=> y = -x - 4:

=> x + y = -4

=> y = -x - 4

As a result, the equation has a slope of -1 and a y-intercept of -4, and is written as y = -x - 4.

=> y = 1/2x - 1:

=> y - 1/2x = -1

=> y - 1/2x + 1 = 0

The words with y and the constant term must be combined in order to represent this equation in slope-intercept form:

=> y + 1 = 1/2x

By taking away 1 from both edges, we obtain:

=> y = 1/2x - 1

As a result, the equation has a slope of 1/2 and a y-intercept of -1, and is written as y = 1/2x - 1.

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The prime factors or the prime numbers whose product is 51 are 3 and 17.

What is the operation of prime numbers?

The operation of prime numbers refers to the various mathematical operations that can be performed using prime numbers. Prime numbers are positive integers that have exactly two divisors, 1 and the number itself. Some of the important operations involving prime numbers include:

Now,

If you meant to ask for the prime factors of 51, then they are 3 and 17.

because 51 is divisible by 3 because 5+1=6

and after dividing 51/3=17 which is also a prime number.

Hence,

            the prime factors of 51 are 3 and 17.

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