Write an equation of the line with the given slope and y-intercept.


slope: −3

y-intercept: 5

y=

Answer:

done same as before put value and do process like simplify

Answer:

Amount invested at 8% rate of interest = $11000

Amount invested at 9% rate of interest = $9000

Step-by-step explanation:

Let Amy invested amount in a account with 8% simple interest = $a

Then the interest gained after one year = \(\frac{\text{Principal amount}\times \text{Rate of interest}\times \text{Time}}{100}\)

                                                                  = \(\frac{a\times 8\times 1}{100}\)

                                                                  = 0.08a

Remaining amount for the investment = $(20000 - a)

Interest earned after one year with rate of interest 9%

= \(\frac{(20000-a)\times 9\times 1}{100}\)

= $(1800 - 0.09a)

Total interest earned after 1 year = $1690

0.08a + (1800 - 0.09a) = 1690

1800 - 0.01a = 1690

0.01a = 110

a = $11000

Amount invested at 8% rate of interest = $11000

Amount invested at 9% rate of interest = $(20000 - 11000) = $9000

Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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a. The two equations for the cost of buying groceries and meals are 13f + 4k = 487 and 65+2k = 232

b. The average costs of one fast food meal and of one trip to kroger is $77.33

To calculate the average cost, we divide the total cost by the number of meals or trips. For example, in the first month, the total cost of fast food meals and grocery trips was $487, and there were 13 fast food meals and 4 grocery trips. Therefore, the average cost of a fast food meal can be calculated by dividing the total cost of fast food meals ($487) by the number of fast food meals (13):

Average cost of a fast food meal = $487 / 13 = $37.46

Similarly, we can calculate the average cost of a grocery trip in the first month by dividing the total cost of grocery trips ($487 - total cost of fast food meals) by the number of grocery trips (4):

Average cost of a grocery trip = ($487 - $37.46 x 13) / 4 = $89.38

Using the same method, we can calculate the average cost of a fast food meal and a grocery trip in the second month. In the second month, the total cost of fast food meals and grocery trips was $232, and there were 6 fast food meals and 2 grocery trips. Therefore, the average cost of a fast food meal is:

Average cost of a fast food meal = $232 / 6 = $38.67

And the average cost of a grocery trip is:

Average cost of a grocery trip = ($232 - $38.67 x 6) / 2 = $77.33

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Answer:

Step-by-step explanation:

Isolate the term of e from one side of the equation.

First, you subtract by 3 from both sides.

⇒ 2e+3-3=5-3

Solve.

Subtract the numbers from left to right.

⇒ 5-3=2

Rewrite the problem down.

⇒ 2e=2

Divide by 2 from both sides.

⇒ 2e/2=2/2

Solve.

Divide the numbers from left to right.

⇒ 2/2=1

⇒ e=1

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

e = 1

Step-by-step explanation:

Subtract 3 both sides:

⇒ 2e + 3 = 5

⇒ 2e + 3 - 3 = 5 - 3

⇒ 2e = 2

Divide both sides by 2:

⇒ 2e = 2

⇒ 2e/2 = 2/2

⇒ e = 1

for an approximate result, divide the time value by 3.154e+7

so the answer is 31.71 calendar years

There are approximately 31.71 years in 1 billion seconds. The solution has been obtained by using the unit conversion.

What is unit conversion?

A unit conversion is used to express the same attribute in a different unit of measurement. Instead of using hours to represent time, you could use minutes, and instead of using miles to express distance, you could use feet. Measurements are frequently requested in one set of units, such as chains, but are given in another set, such as feet.

We are given 1 billion seconds which are to be converted into years.

We know that 1 second = 3.171e-8 years

So,

⇒1,000,000,000 seconds = 1,000,000,000 * 3.171e-8

⇒1,000,000,000 seconds = 31.71 years

Hence, there are approximately 31.71 years in 1 billion seconds.

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Answer:

The formula for the perimeter of a rectangle is often written as P = 2l + 2w, where l is the length of the rectangle and w is the width of the rectangle.

Step-by-step explanation:

Answer:

Reflect shape A on the line y=-1

Step-by-step explanation:

None needed you get full marks from the sentence above :)

Answer:

This is duplicate question

Step-by-step explanation:

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link is here for answer

The equation is x+15=3(x-5)

He is 15.

Answer:

108°

Step-by-step explanation:

The sum of angles on a straight line is 180°

Therefore:

x + 72° = 180°

x = 180° - 72°

x = 108°

Therefore, the value of x is 108°

The domain is  {x| x ∈ R, x≠ ±1} and the range is {y| y ∈ R}.

The vertical asymptotes are at x = 1 and x = -1

The horizontal asymptote is at y = 3.

To find the domain we need to look at the horizontal axis, here we can see that the function extends to the left and to the right, then we will have the set of all real numbers, except for the two values of x where we have asymptotes, these are x = -1 and x = 1

Then the domain is:

D = {x| x ∈ R, x≠ ±1}

And the range is the set of all real numbers:

R = {y| y ∈ R}

And the vertical asymptotes as we already said are at x = ± 1, while the horizontal ones are at y = 3.

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(i) When testing whether girls who attended girls-only high schools do better in math, it is important to control for various factors that could potentially influence math scores.

Some factors to consider are:

(ii) The equation relating the math score (score) to girlhs (dummy variable indicating girls-only high school attendance) and other factors can be written as:

score = β0 + β1 * girlhs + β2 * socioeconomic status + β3 * prior academic performance + β4 * school quality + β5 * peer effects + β6 * teacher quality + β7 * access to resources + ε

This equation represents the structural relationship between the math score and the factors being controlled for. The coefficients β1, β2, β3, β4, β5, β6, and β7 represent the respective effects of girlhs and the other factors on the math score.

(iii) Parental support and motivation, which are unmeasured factors, may be correlated with girlhs. This is because parents who choose to send their daughters to girls-only high schools might have certain preferences or beliefs regarding education, which could include providing higher levels of support and motivation. However, without directly measuring parental support and motivation, it is difficult to establish a definitive correlation.

(iv) To ensure that numghs (the number of girls-only high schools within a 20-mile radius of a girl's home) is a valid instrumental variable (IV) for girlhs, certain assumptions are needed:

(v) If the coefficient estimate on the chosen IV numghs is negative and statistically significant in the reduced form estimation, it suggests a strong relationship between the instrumental variable and the attendance at girls-only high schools. This provides some confidence in the validity of the IV. However, the decision to proceed with IV estimation should also consider other factors such as the strength of the instruments, the overall model fit, and the robustness of the results to alternative specifications.

It is important to carefully evaluate the assumptions and limitations of the IV estimation approach before drawing conclusions in math.

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The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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Answer:

\( = \frac{ - xy + {y}^{4} + {y}^{3} + {x}^{3}y + {x}^{3} - {x}^{2} }{x {y}^{3} + {xy}^{2} - {y}^{3} - {y}^{2} } \)

Step-by-step explanation:

\(( \frac{x}{y} + \frac{y}{x - 1} ) + ( \frac{ {x}^{2} }{ {y}^{2} } - \frac{x}{y + 1} )\)

\( \frac{xy \times (x - 1) \times (y + 1) + {y}^{3} \times (y + 1) + {x}^{2} \times (x - 1) \times (y + 1) - {xy}^{2} \times (x - 1)}{ {y}^{2} \times (x - 1) \times (y + 1)} \)

\(\frac{( {x}^{2} y - xy) \times (y + 1) + {y}^{4} + {y}^{3} + ( {x}^{3} - {x}^{2} ) \times (y + 1) - {x}^{2} {y}^{2} + {xy}^{2} }{( {xy}^{2} - {y}^{2} ) \times (y + 1)}\)

\( \frac{ {x}^{2} {y}^{2} + {x}^{2} y - {xy}^{2} - xy + {y}^{4} + {y}^{3} + {x}^{3} y + {x}^{3} - {x}^{2}y - {x}^{2} - {x}^{2} {y}^{2} + {xy}^{2} }{( {xy}^{3} + {xy}^{2} - {y}^{3} - {y}^{2} ) } \)

\( = \frac{ - xy + {y}^{4} + {y}^{3} + {x}^{3}y + {x}^{3} - {x}^{2} }{x {y}^{3} + {xy}^{2} - {y}^{3} - {y}^{2} } \)

Answer:

2

Step-by-step explanation:

Answer:

scalene because all the angles are different in an isosceles triangle 2 angles are the same

Answer:

Scalene triangle

Step-by-step explanation:

the answer is the scalene triangle

Answer:

29=6+k

Step-by-step explanation:

The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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Answer:

The answer is -4/21

Step-by-step explanation:

The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²

Missing data from the problem:

radius of the barrel = 0.4 meters

height of the barrel = 1.2 meters

The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:

A = 2. πr² + 2. πr.h

Where:

r = radius

h = height

Plug the parameters into the formula:

A = 2. π(0.4)² + 2. π(0.4).(1.2)

A = 13 m²

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There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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Answer:

92.4

Step-by-step explanation:

50$ + 120% = 110

110 - 20% = 88

88 + 5% = 92.4

The total price of a bench with the 20% discount plus a 5% sales tax is $92.4.

Markup percentage is defined as the total profit of the commodity in terms of percentage. It is calculated by dividing the difference of the selling price and the cost with the cost and then multiply to 100.

Markup Percentage = [(sales price - cost) / cost] × 100

Cost of a bench = $50

There is 120% markup in the bench

Selling price = $50 + ($50 × 120%)

                     = $50 + ($50 × 1.2)

                     = $50 + $60

                     = $110

At the end of the season, owner gives 20% discount.

Price of the bench after 20% discount = $110 - (20% × 110)

                                                                = $110 - (0.2 × 110)

                                                                = $110 - $22

                                                                = $88

There is a sales tax of 5%.

Last selling price of the bench = $88 + (5% × $88)

                                                   = $88 + (0.05 × $88)

                                                   = $88 + $4.4

                                                   = $92.4

Hence, the owner sells the bench at the season at $92.4.

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Using DeMorgan's Law, an expression for the complement of F if F(x,y,z) = (x′ + y)(x + z)(y′ + z)′ is F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz.

To find the complement of F, we first need to apply DeMorgan's Law, which states that the complement of a product is the sum of the complements of the terms. So, we can rewrite F(x,y,z) as:
F(x,y,z) = (x' + y)(x + z)(y' + z)'
Using DeMorgan's Law, we can take the complement of each term inside the parentheses, and then switch the operation from multiplication to addition:
F'(x,y,z) = (x' * y')(x' * z') + (x * y')(x' * z') + (x' * y)(y' * z') + (x * y)(y' * z') + (x * z)(y' * z')
Simplifying this expression, we get:
F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz
Therefore, the complement of F(x,y,z) is F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz.

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The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Answer:

A. \(\triangle\)DEF where \(\angle D = 75^{\circ}\) and \(\angle E = 20^{\circ}\).

Step-by-step explanation:

At first we must keep in mind that two triangles are similar when they have same angle configuration, that is, each pair of angles is congruent. If \(\triangle\)ABC and \(\triangle\)DEF, then \(\angle A \equiv \angle D\) and \(\angle B \equiv \angle E\). Hence, \(\angle D = 75^{\circ}\) and \(\angle E = 20^{\circ}\).

In a nutshell, correct answer is A.

This investigation's goal is to demonstrate how quickly and easily we can determine the diameter of the sun using basic geometry.

The cards must remain parallel and separated by a predetermined amount. Then, a tiny hole must be cut on one card so that sunlight can pass through and create the sun's picture on the other card. We base the formula described above on the diameter of this photograph of the sun. The diameter of the sun's picture on the card is now measured because we can choose the distance between the cards, and we already know that the sun is nearly 150 million kilometers away from the earth. i.. e. Since three of the values are known, we can use the technique above to determine the fourth unknown quantity and measure the diameter.

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The equation of a parabola is a quadratic equation.

The equation of the parabola is: \(\mathbf{y = 4x^2 + 32x -32}\)

The points are given as:

\(\mathbf{(x,y) = (-5,-224),(-3,-92),(1,4)}\)

Substitute these values in:

\(\mathbf{y = ax^2 + bx +c}\)

So, we have:

\(\mathbf{-224 = a(-5)^2 + b(-5) +c}\)

\(\mathbf{-224 = 25a - 5b +c}\) ------ (1)

\(\mathbf{-92 = a(-3)^2 + b(-3) +c}\)

\(\mathbf{-92 = 9a -3b +c}\) ---- (2)

\(\mathbf{4 = a(1)^2 +b(1) +c}\)

\(\mathbf{4 = a +b +c}\) ---- (3)

Subtract (3) from (2)

\(\mathbf{9a - a - 3b - b + c - c =-92 - 4}\)

\(\mathbf{8a - 4b =-96}\)

Multiply by 3

\(\mathbf{24a - 12b = -288}\)

Subtract (3) from (1)

\(\mathbf{25a -a - 5b -b +c - c = -224 - 4}\)

\(\mathbf{24a - 6b = -228}\)

Subtract \(\mathbf{24a - 6b = -228}\) from \(\mathbf{24a - 12a = -288}\)

\(\mathbf{24a- 24a - 12ba +6b = -288 + 96}\)

\(\mathbf{- 6b = -192}\)

Divide through by -6

\(\mathbf{b = 32}\)

Substitute \(\mathbf{b = 32}\) in \(\mathbf{8a - 4b =-96}\)

\(\mathbf{8a - 4 \times 32 = -96}\)

\(\mathbf{8a - 128 = -96}\)

Collect like terms

\(\mathbf{8a = 128 -96}\)

\(\mathbf{8a = 32}\)

Divide both sides by 8

\(\mathbf{a = 4}\)

Substitute \(\mathbf{a = 4}\) and \(\mathbf{b = 32}\) in \(\mathbf{4 = a +b +c}\)

\(\mathbf{4 + 32 + c = 4}\)

\(\mathbf{36 + c = 4}\)

Subtract 36 from both sides

\(\mathbf{c = -32}\)

Substitute values of a, b and c in: \(\mathbf{y = ax^2 + bx +c}\)

\(\mathbf{y = 4x^2 + 32x -32}\)

Hence, the equation of the parabola is: \(\mathbf{y = 4x^2 + 32x -32}\)

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The independent variable in this study is the place of residence, specifically whether the participants live in Florida or Pennsylvania.

The researcher is interested in examining the relationship between the location of residence and the amount of money spent on clothes. By selecting participants from both Florida and Pennsylvania, the researcher can compare the spending habits of individuals from these two locations and determine if there is a significant difference. Thus, the independent variable is the categorical variable that defines the groups being compared, which in this case is the place of residence.

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