A model of a soccer ball is made up of regular pentagons and hexagons. The side length of one of the pentagons measures 2 inches and the apothem measures about 1. 38 inches. What is the area of one of the pentagons? state your answer to the nearest tenth. Square inches the side length of one of the hexagons measures 2 inches and the apothem measures about 1. 73 inches. What is the area of one of the hexagons? state your answer to the nearest tenth. Square inches.

The interest rate is 5.597% per year.

Given,

principle amount,P =$3000

time period,t =13 years

Total amount including interest,A=$6200

To find interest rate when the the principle amount is compounded monthly use formula,

\(r=n[(\frac{A}{P})^{\frac{1}{nt}}-1]*100\)

where, n=number of compounding periods=12 months

\(r=12[(\frac{6200}{3000})^{\frac{1}{12*13}}-1]*100\\\\r=0.05597*100\\\\r=5.597\)

Hence, the interest rate is 5.597% per year.

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Answer:

Use the equation 500x0.04x20 and then 500x20 and add the sums up and get 10,400 i believe is im wrong sorry :/

$900 is the total amount of money she has after 20 years.

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

From the formula of simple interest A = P(1 + rt)

Where A = amount earned

P = principal amount

r = rate of interest

t = time

In our case

P = 500

r = 4%

t = 20

Thus,

Amount earned after 20 years = 500(1 + 4*20/100)

Amount earned after 20 years = 500(1 + 4/5)

Amount earned after 20 years = 900

therefore, the total amount of money she has after 20 years is $900.

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Answer:

Ok

Step-by-step explanation:

The probability of randomly picking 3 red marbles in a row is:

P = 0.0315

If all the marbles have the same probability of being randomly selected, then the probability of selecting at random a red marble is equal to the quotient between the number of red marbles and the total number of marbles in the bag.

There are 6red ones and (6 + 8 + 5 = 19) 19 marbles in total, then the probability is:

P = 6/19

And we want to do this thing 3 time (when we get the red marble we return it to the bag).

Then we will have the probabilities:

q = 6/19

k = 6/19

The joint probability of these 3 events is the product between the individual probabilities, we will get:

P = (6/19)*(6/19)*(6/19) = 0.0315

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To sketch the graph of the function `f(x) = - 5 sin 6 5 4 3 2 -&t -7n -65-4n -3n-2n - j -2 -3 -4 -5 -6 + - (a) 27 3 4 5 \ / 67 8`, we first need to identify its key features, which are:Amplitude = 5

Period = 2π/6

= π/3

Phase Shift = 2

The graph of the function `f(x) = - 5 sin 6x + 2` can be obtained by starting with the standard sine graph and making the following transformations:Reflecting it about the x-axis by multiplying the entire function by -1.

Multiplying the entire function by 5 to increase the amplitude.

Shifting the graph to the right by 2 units.For the specific domain provided in the question, we have:27 < 6x + 2 < 67 or 25/6 < x < 65/6.

This gives us a range of approximately 4.17 ≤ x ≤ 10.83.

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We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.

The result of a multiplication operation is a product.

There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.

So, we have:
5/8 and 4

5/8 is in the form p/q which represents the fraction that must be multiplied by 4.

Now, calculate the product as follows:

5/8 * 4

5/2

Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

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Answer:

number is 66

Step-by-step explanation:

let the number be n , then

78 - \(\frac{1}{2}\) n = 45 ( subtract 78 from both sides )

- \(\frac{1}{2}\) n = - 33 ( multiply both sides by - 2 to clear the fraction )

n = 66

The required number is 66

Answer:

y=400x+0

or simply

y=400x

Step-by-step explanation:

Ok slope= Rise over run

Y-intercept= point where x is 0

y-intercept= (0,0)

slope= 400/1=400

m=slope

b=y-intercept

y=mx+b

y=400x+0

Answer:

The tax itself would be $1.44 and the total would be $25.44

Step-by-step explanation:

You multiply 24 by 6% (0.06) and get 1.44 then you add that to the original cost (24) and get $25.44.

Total cost will be $25.44.

What is Percentage?

A relative value indicating hundredth part of any quantity is called percentage.

Given that;

Cost of shirt = $24

Tax = 6%

Now,

The value of tax = 24 × 6%

                         = 24 × 6/100

                         = 1.44

So, Total cost =  $24 + $1.44

                     = $25.44

Thus, Total cost will be $25.44.

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The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

6 < 2x + 4

-4          -4      subtract 4 to each side, 4's will cancel out on the right side.

________

\(\frac{2}{2}\) < \(\frac{2x}{2}\)      divide 2 on each side, 2's will cancel out on the right side.

1 < x, final answer.

Please reach out to me if you have any further questions :)

The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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Market Size: Qualitative data, Nominal scale. Promotion: Qualitative data, Nominal scale. Week: Qualitative data, Ordinal scale.

a) The categorical qualitative variables from the ones listed above are as follows  :Market Size.

This variable represents the size of the customer base (small, medium, or large market).Promotion: Type represents which promotion the store ran (Promotion 1, 2, or 3. They ran three different promotions for a new product to see which one is more effective.).

b) The numerical (quantitative) variables from the ones listed above are as follows: Sales: (In Thousands) represents the number sales (in $1000) made in the specified week of December (Week).Age: Store represents the age of the store in years. Week: Number represents the week in which the promotion ran (Week 1, 2, 3, 4 - captured sales of new product over four weeks) c) Level of measurement for each variable is given as follows :Sales: Quantitative data, Ratio scale.Age: Quantitative data, Ratio scale.

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x 2, and the second side is expressed by  2x-25 , The value of x is 5.

What is isosceles triangles ?

An isosceles triangle is a triangle with two sides of equal length. These two sides are called the legs and they are congruent. The third side is called the base and it is not necessarily congruent to the legs. The angle opposite to the base is called the vertex angle.

To solve for x, we can start by isolating x on one side of the equation.

We can do this by subtracting x^2 from both sides ,

x^2 - x^2 = 2x-25 - x^2

we get 0 = 2x - 25 - x^2

Now we can add x^2 to both sides ,

x^2 = 2x - 25

Now we can move the -25 to the other side of the equation ,

x^2 - 2x + 25 = 0

Now we can factor the left side of the equation ,

(x-5)(x-5) = 0

Now we can solve for x by setting each factor equal to zero ,

x-5 = 0 , x = 5

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

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A class hierarchy is a diagram that shows the inheritance relationship between classes.

It is similar to a family tree in that it shows the parent-child relationships between classes. In a class hierarchy, the parent class is called the superclass and the child class is called the subclass. The subclass inherits the properties and behaviors of the superclass, and can also add new properties and behaviors of its own.

The class hierarchy is an important concept in object-oriented programming, as it allows for code reuse and the creation of complex systems with modular, reusable components.

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The missing values in the diagram given that figure ABCD is a dilation of figure KLMN, are:

AB = 4

LM = 20

∠B = 98.87°

∠N = 141.87°

Dilation is a form of transformation whereby a new figure is formed by enlarging or reducing an original figure by a scale factor. After dilation, the corresponding sides of both figures are proportional, while the corresponding angles of both figures are congruent to each other.

Find AB:

AB/KL = DC/NM

Plug in the values

AB/10 = 4/10

AB(10) = 4(10)

AB = 40/10

AB = 4

Find LM:

BC/LM = DC/NM

Plug in the values

8/LM = 4/10

8(10) = 4(LM)

LM = 80/4

LM = 20

∠B = ∠L = 98.87°

∠N = ∠D = 141.87°

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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Answer are:
1. The sequence converges.
2. The limit is 0.
3. N/A, since the sequence converges.
4. N/A, since the limit is not 0.
5. N/A, since the limit is not 2

To determine if the sequence {an} converges, we need to find its limit. Let's first look at the expression for an:

an = (3n^5 – 5n^3 + 2) / (2n^4 + 4n^2 + 1)

We can simplify this expression by dividing each term by n^4:

an = (3/n^1 – 5/n^3 + 2/n^5) / (2 + 4/n^2 + 1/n^4)

As n approaches infinity, all the terms with powers of n in the denominator approach 0, so we can simplify the expression further:

an ≈ 3/(2n^4) = 3/2n^4

This means that the sequence {an} converges to 0, since the terms get smaller and smaller as n gets larger.

So the answers are:

1. The sequence converges.
2. The limit is 0.
3. N/A, since the sequence converges.
4. N/A, since the limit is not 0.
5. N/A, since the limit is not 2.

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Answer:

yes

Step-by-step explanation:

hopes this helped;0

Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

Answer:

They get 4 good points!

Step-by-step explanation:

21-17= 4:)

Answer:

x=0

x=7

Step-by-step explanation:

x²-x-1=6x-1

x²-x-1-6x+1=0

x²-7x=0

x(x-7)=0

x=0

x-7=0

x=7

Total distance represented by the simplified expression for which the car was tested equals option c. x² + 2x - 4 .

Total distance drive on flat road = x miles

Total distance drive on downhill =  (x²+ 3) miles

Total distance drive on uphill =  ( x - 7 ) miles

Simplified expression which is equivalent to total distance drive by a car

= Distance drive on ( flat road + downhill + uphill )

= ( x +  x²+ 3 + x - 7 ) miles

= ( x² + 2x - 4 ) miles

Therefore, the simplified expression equivalent to the total distance drive by a tested car is equal to option c.  ( x² + 2x - 4 ) miles.

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The above question is incomplete , the complete question is:

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road,    (x²+ 3) miles downhill, and (x - 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?

a.3x² _ 4

b. 3x² + 10

c. x² + 2x - 4

d. x² + 2x + 10

Answer:

1) Slope= 2, y-intercept=4, equation: y=2x+4

2.Slope= -10 , y-intercept= 60 , equation: y=-10x+60

Step-by-step explanation:

Slope formula: \(\frac{y_{2}-y_1 }{x_2-x_1}\)

1. Plug in two sets of cordinates into the equation

(0,2) (2,8)

2. Solve, slope =2

3. Plug in one pair into the point slope formula

Point slope formula: \(y-y_1=slope(x-x_1)\)

4. y-8=2(x-2)

5.y-8=2x-4

6. y=2x+4

Do the same for the other equation

Answer:

1: slope

2: y-intercept

1a: slope= 3

1b: 2

y=3x+2

2a: slope= -10

2b: 60

y= -10x+60

Step-by-step explanation:

x = -2/3 or -4

see the attachment for solution

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The type of conic section that is represented in the provided equation form is ellipse.

To identify the type of conic section from an equation whether it is circle or ellipse.

Let us  suppose the equation as,

\(Ax^{2} +By^{2}+Cx+Dy+E=0\)

In this equation,

We have to identify the type of conic section that has the equation,

\(4x^{2} +25y^{2}=100\)

By comparing this equation with the above equation, we get,

\(A=4\\B=25\)

Here neither \(A\) or \(B\) is equal to \(0\) and the sign of both are

similar(positive), so the equation form is ellipse.

Therefore, the type of conic section which is represented in the provided equation form is ellipse.

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The constant of proportionality is 2.02.

According to the concept of proportion, two ratios are in proportion when they are equal.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised. A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Four dozen gourmet donuts cost a total of $96.96.

So, if y be the total cost of the donuts and x be the number of donuts.

then the proportionality is

y= kx

k= y/x

k = 96.96 / (4 x 12)

k= 96.96/ 48

k= 2.02

Hence, the constant of proportionality is 2.02.

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The large-sample z statistic is 1.923. Based on this result, we reject the null hypothesis and conclude that there is evidence to suggest that a majority of people prefer the taste of fresh-brewed coffee over instant coffee.

To test the claim that a majority of people prefer fresh-brewed coffee, we need to set up the null and alternative hypotheses:

Null hypothesis: p ≤ 0.5 (i.e., the proportion of people who prefer fresh-brewed coffee is less than or equal to 0.5)

Alternative hypothesis: p > 0.5 (i.e., the proportion of people who prefer fresh-brewed coffee is greater than 0.5)

We will use a one-tailed test with a significance level of α = 0.05.

To calculate the large-sample z statistic, we first need to calculate the sample proportion of people who prefer fresh-brewed coffee

P = (60 - 21) / 60 = 0.65

where 60 is the total number of subjects and 21 is the number who prefer instant coffee.

Next, we need to calculate the standard error of the sample proportion:

SE = sqrt(P(1-P)/n) = sqrt(0.65(1-0.65)/60) = 0.078

where n is the sample size.

Finally, we can calculate the z statistic:

z = (P - p) / SE = (0.65 - 0.5) / 0.078 = 1.923

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The given question is incomplete, the complete question is:

A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic