Graph the equation using the slope and the​ y-intercept.

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

We have,

The actual dimensions of the island are 3 1/2 feet by 1 3/4 feet.

We need to find the dimensions of the island on the blueprint, given that the scale of the blueprint is 1 inch = 2 feet.

To convert the actual dimensions to the dimensions on the blueprint, we need to use the scale factor of 1 inch = 2 feet.

We can set up a proportion to relate the actual dimensions to the dimensions on the blueprint:

Actual dimension/blueprint dimension = scale factor

Let x be the length of the island on the blueprint.

Then we can set up the following proportion:

3.5 feet / (1.75 feet)

= x inches / 7 inches

Simplifying,

2 = x / 7

Multiplying both sides by 7, we get:

x = 14 inches

The length of the island on the blueprint is 14 inches.

Similarly, we can find the width of the island on the blueprint:

1.75 feet / 3.5 feet

= y inches / 7 inches

Simplifying, we have:

0.5 = y / 7

Multiplying both sides by 7, we get:

y = 3.5 inches

The width of the island on the blueprint is 3.5 inches.

Thus,

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

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It will take approximately 8 days for the virus to grow from 180 to 260.

We can set up a proportion to solve this problem. Let "x" represent the number of days it will take for the virus to grow from 180 to 260.

The proportion can be set up as follows;

(Change in value) / (Time taken) = (Change in value) / (Time taken)

Using the given information, we have;

(260 - 180) / x = (230 - 180) / 5

Simplifying the fractions on both sides of the equation, we get:

80 / x = 50 / 5

Cross-multiplying, we have;

80 × 5 = 50 × x

400 = 50x

Dividing both sides of the equation by 50, we get;

x = 400 / 50

x = 8

Therefore, it will take 8 days.

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Answer:

7 should go in the green blank.

10/x = x/7

No, It is not possible for 75% of the people surveyed at the park to purchase any two combination of the treats unless 14 people from the 'No preference group" decide to pick a treat. The two best frozen treat to pick will be Ice-cream sandwich and frozen fruit bar. With these two, 174 people are guaranteed to purchase the product.

To find the 75% chance of people surveyed buying any two combination we say

58 + 95 + 79 + 17 = 250

75% of 250 = 187.5 which is 188

We need to see if 188 of people will pick up a treat based on the survey

58 + 95 = 153 < 188

95 + 79 = 174 < 188  however, if  14 people from no preference group purchase, then, this is the best combination.

58 + 79 =  137 < 188

The answer provided is based on the question below as seen in the picture;

Is it possible to select a combination of two frozen treats so that 75% of the people surveyed would be able to purchase their favorite? If so, which two types of frozen treats should you select? Use words and numbers to justify your answer

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Answer:

The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.

Step-by-step explanation:

Answer: 12 people

Step-by-step explanation:

0.30 x 40 = 12

Answer:

(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:

FV = P * ((1 + r)^n - 1) / r) * (1 + r)

where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.

In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:

FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)

FV ≈ €743,704.96

Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.

(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:

PV = P * ((1 - (1 + r)^(-n)) / r)

where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.

In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:

PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)

P ≈ €22,630.53

Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.

(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).

Total deposits = €22,630.53 * 30 = €678,915.90

Total withdrawals = €25,000 * 20 = €500,000

Initial balance = €743,704.96

Total interest earned = Total withdrawals - Total deposits - Initial balance

Total interest earned = €500,000 - €678,915.90 - €743,704.96

Total interest earned ≈ -€922,620.86

Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.

Step-by-step explanation:

These fractions are equivalent fractions by algebraic property:

Case 1: YES

Case 2: NO

Case 3: YES

Case 4: NO

Case 5: YES

Case 6: YES

Case 7: NO

Case 8: YES

Case 9: YES

Case 10: YES

Case 11: NO

Case 12: YES

Case 13: NO

Case 14: YES

Case 15: YES

Case 16: YES

Case 17: NO

Case 18: YES

In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:

a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.

Now we proceed to determine if each pair is equivalent:

Case 1

2 / 3 = (2 · 2) / (3 · 2)

2 / 3 = 4 / 6 (YES)

Case 2

2 / 6 = (2 · 3) / (6 · 3)

2 / 6 = 6 / 18 (NO)

Case 3

9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)

Case 4

3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)

Case 5

7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)

Case 6

4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)

Case 7

5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)

Case 8

2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)

Case 9

6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)

Case 10

4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)

Case 11

9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)

Case 12

1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)

Case 13

12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)

Case 14

8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)

Case 15

5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)

Case 16

6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)

Case 17

3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)

Case 18

10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)

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Answer:

Well, if Alice buys 12 shirts which each cost $18.99 the equation would be 18.99 * 12 which = 227.88

Alice spent $227.88 on 12 shirts

Step-by-step explanation:

Answer:

Well, if Alice buys 12 shirts which each cost $18.99 the equation would be 18.99 * 12 which = 227.88

Step-by-step explanation:

Answer:

The problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.

X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.

We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.

To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.

We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.

Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.

Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.

Answer:

4x² - 11xy - 3y²

Step-by-step explanation:

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

Multiply each term of the first binomial by each term of the second binomial.

= 4x² - 12xy + xy - 3y²

Now combine like terms.

= 4x² - 11xy - 3y²

Answer:

The formula looks like this:

where SA = surface area, l = length, w = width, and h = height. In the rectangular prism net above, l = 8 inches, w = 5 inches, and h = 3 inches. Simply put these numbers into the formula and solve for surface area.

Answer:

-13

Step-by-step explanation:

To add fractions, find the lowest common denominator and then combine

Answer:

first option

Step-by-step explanation:

differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

then

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{dt}[/tex] × [tex]\frac{dt}{dx}[/tex] = [tex]\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

y = t² + 4t

[tex]\frac{dy}{dt}[/tex] = 2t + 4

x = t - 3

[tex]\frac{dx}{dt}[/tex] = 1

then

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{2t+4}{1}[/tex] = 2t + 4

Answer:

2t + 4

Step-by-step explanation:

A parametric equation is one where x and y are defined separately in terms of a third variable (often the parameter t).

To find dy/dx from parametric equations, differentiate each equation with respect to the parameter t, then use the chain rule:

[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}}[/tex]

Differentiate the two parametric equations with respect to t:

[tex]x=t-3 \implies \dfrac{\text{d}x}{\text{d}t}=1[/tex]

[tex]y=t^2+4t \implies \dfrac{\text{d}y}{\text{d}t}=2t+4[/tex]

Use the chain rule to combine them:

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}\\\\&=(2t+4) \times \dfrac{1}{1}\\\\&=2t+4\end{aligned}[/tex]

Therefore:

[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=2t+4}[/tex]

The volume of a sphere of radius 9.5 cm is approximately 3589.5 cm³

From the question, we are to calculate the volume of a sphere

The volume of a sphere is given by the formula

V = 4/3 πr³

Where V is the volume of the sphere

and r is the radius of the sphere

From the given information,

r = 9.5 cm

Thus,

Volume of the sphere = 4/3 × π × 9.5³

Put π = 3.14

Volume of the sphere = 4/3 × 3.14 × 9.5³

Volume of the sphere = 3589.54333 cm³

Volume of the sphere ≈ 3589.5 cm³

Hence,

The volume of the sphere is 3589.5 cm³

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The inequality that represents the sentence "The stadium held less than 25,000 people" is given as follows:

c < 25,000.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The amount is less than in this problem, hence the symbol is given as follows:

<.

As the amount is less than 25000, the inequality is given as follows:

c < 25,000.

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The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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The value of f(1) is 3.

An estimate of the value of f(-1) is -0.2.

The values of x for which f(x) = 1 are: x = (0, 3).

The value of x such that f(x) = 0 is x = -0.5.

The domain of f is {-2, 4}.

The range of f is {-1, 3}.

The interval over which f is increasing is {-2, 1}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of the function shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-2, 4}.

Range = {-1, 3}.

In conclusion, we can logically deduce that this function is increasing over the [-2, 1] and decreasing over the interval [1, 4].

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4 is the value of the variable x.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

We can simplify the left side of the equation by using the properties of exponents:

[tex](7q^{3x})^3 = 7^3 * (q^{3x})^3 = 343q^{9x}\\\\343q^{9x} = 343q^{36}\\\\q^{9x} = q^{36[/tex]

Now we can use the property that if [tex]a^b = a^c[/tex], then b = c. Therefore:

9x = 36

Dividing both sides by 9, we get:

x = 4

Therefore, the value of x that satisfies the equation is 4.

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Answer: z = 8

Step-by-step explanation:

The diagram shows us that 8z + 3z + 2 = 90

so we can say that: 11z = 88

therefore z = 8.

Note: diagrams can be misleading! this diagram technically shows us that 64 < 26!

Answer:

13: (2,3) 14: A. Yes, 90, 180, 270 B. No C. No

Step-by-step explanation:

13. Right: -2+4, Down: 5-2

14. If it can be rotated and be similar, it has rotational.

The aspects of the scenario that bring the validity of the conclusion made by the representatives of the government would be:

The sample size used by the representatives in the survey was only 50 individuals, which might not be sufficient to represent the views of the entire town's population accurately. A more extensive sample size would provide a more precise approximation of the public opinion.

Moreover, the conductance of the survey on the existing boardwalk presents the possibility of sampling bias since those who visit the boardwalk could hold different opinions towards the new construction than those that do not visit.

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a) The polar coordinates of point A are (√(18), π/4).

b) The curve is a circle centered at the origin with radius 6.

c) The directed distance is the value of r, which is 6 √(3).

To find the polar coordinates of point A on the curve, we need to convert the point from Cartesian to polar coordinates. The conversion formula is:

r = √(x² + y²)

θ = arctan(y/x)

Using the values of point A, we have:

r = √((-3)² + (-3)²) = √(18)

θ = arctan((-3)/(-3)) = arctan(1) = π/4

To find the polar form of the equation x² + y² + 6y = 0, we need to convert it from Cartesian to polar coordinates. The conversion formulae are:

x = r cos(θ)

y = r sin(θ)

Using these formulae, we can rewrite the equation as:

r² cos²(θ) + r² sin²(θ) + 6r sin(θ) = 0

Simplifying this equation, we get:

r = -6 sin(θ) / (1 - cos²(θ))

To find the directed distance when θ equals 4 π over 3, we need to substitute this value of θ into the polar equation we found in Part B. Doing so, we get:

r = -6 sin(4 π/3) / (1 - cos²(4 π/3))

r = -6(-√(3)/2) / (1 - (-1/2)²)

r = 6 √(3)

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The area of the parallelogram is 8.5 square miles. This is found by multiplying the length of one of the parallel sides, 2 miles, by the height, which is given as 4 1/4 miles.

To find the area of a parallelogram, we can multiply the length of one of its parallel sides by the length of its perpendicular height. Therefore, to find the area of this parallelogram, we need to determine its height.

We are given that one of the parallel sides has a length of 4 1/4 mi and the other has a length of 2 mi. We are also given that the length of the perpendicular on one of the parallel sides is 4 1/4 mi, which means that this is the height of the parallelogram.

So, the area of the parallelogram is

Area = base x height

Area = 2 mi x 4 1/4 mi

Area = 8 1/2 mi²

Therefore, the area of the parallelogram is 8 1/2 square miles or 8.5 square miles.

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The solution is , price of jeans = RD$ 1140 and, price of  handbag =

RD$ 2110.

Here, we have,

given that,

Margarita went to the store and bought a bag and some jeans for a total of RD$3,250.

Knowing that the handbag exceeds the jeans by RD$970,

now, we have to find that, how many do she pay for each article.

let, price of jeans = RD$ x

so, price of  handbag = RD$ (x +970)

ATQ, we get,

RD$ x + RD$ (x +970) = RD$3,250

or, RD$ 2x + 970 = RD$3,250

or, RD$ 2x = RD$ 2280

or, x = RD$ 1140

Hence, price of jeans = RD$ 1140 and, price of  handbag = RD$ 2110.

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There 1365 ways to choose four people from the group of fifteen.

b. There are 70 ways to choose  four Republicans from the group of eight Republicans.

C. The probability is about  0.0513, or  5.13%.

a.  To know the ways that four people can be selected from this group of fifteen is by:

nCr = n! / (r! x (n-r)!),

Where:

n  = total number of items

r = is the number of items to be selected,

!  = the factorial of a number.

Putting in the values into the the formula:

15C4 = 15! / (4! x (15-4)!)

(15-4)! = 11!

15C4 = 1365

B.  Since:

n = 8

r = 4

Putting in the values into the the formula:

8C4 = 8! / (4!  x (8-4)!)

(8-4)! = 4!

8C4 = 70

c. The  Probability = Number of ways to choose four Republicans / Number of ways to choose four people

Hence  Probability = 70 / 1365

                             =  0.0513

Therefore, the probability that the selected group will consist of all Republicans is about  0.0513, or  5.13%.

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The bearing of C to A is 239⁰.

The bearing of C to A is calculated by finding the value of angle C using cosine rule since we know the value of all the sides of the triangle.

AB² = AC² + CB² - 2(AC)(CB) cosC

12.5² = 16.25² + 8.5² - 2(16.25 x 8.5) x cos C

156.25 = 336.3125 - 276.25cosC

276.25cosC = 180.06

cosC = 180.06/276.25

cos (C) = 0.6518

C = cos⁻(0.6518)

C = 49.3⁰

The value of angle A is calculated as follows;

Sin A/CB = Sin C/AB

sin A/8.5 = sin 49.3/12.5

sin A = 8.5 [sin 49.3/12.5]

sin A = 0.5157

A = sin⁻¹ (0.5157)

A = 31⁰

The bearing of C to A is calculated as;

= 270⁰ - 31⁰

= 239⁰

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If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

Option A is the correct answer.

We have,

A horizontal translation moves every point of a figure the same distance in the same direction.

In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.

A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.

A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.

A 90° clockwise rotation would rotate the figure 90 degrees to the right.

Thus,

If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

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Answer:

[tex]\sqrt[]{72}[/tex]

6.3141414141414...

[tex]\sqrt[4]{64}[/tex]

8.121 121 112 111...

Step-by-step explanation:

irrational numbers are real numbers that cannot be expressed as a ratio of integers.

example of irrational number [tex]\sqrt[]{2}[/tex]

example of rational number 2, 3, -4, etc.