Which statements are true about dilations? Select all that apply.

Based on the relationship between the length and width of the rectangle, the length of the rectangle for the various values of the width is given below:

The relationship between the length and the width of the rectangle is a linear relationship given by the linear equation below:

l = w/3

where;

l is the length of the rectangle

w is the width of the rectangle

When w = 1

l = 1/3

When w = 3

l = 3/3

l = 1

when w = 7

l = 7/3

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Answer:

there are 24 different choices available to guests when booking their stay at the bed and breakfast.

Step-by-step explanation:

To find the total number of choices available to guests at the bed and breakfast, you can use the multiplication principle of counting.

According to the multiplication principle, if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

Using this principle, we can calculate the total number of choices available to guests by multiplying the number of choices for each option:

Choice of 3 themes for their room: 3 options

Choice of 2 sizes of rooms: 2 options

Choice of 4 breakfast options: 4 options

Total number of choices = 3 x 2 x 4 = 24

Therefore, there are 24 different choices available to guests when booking their stay at the bed and breakfast.

There is no such point that requires exactly three numbers to specify its location.

A mathematical notion known as the Euclidean plane symbolizes a two-dimensional environment in which points, lines, and forms may be specified and altered. The Greek mathematician Euclid, who originally described the geometry of the plane in his book Elements, is honoured by the name of the object. The Pythagorean theorem is used to calculate distance in the Euclidean plane, while degrees or radians are used to calculate angles.

The plane doesn't have any points that can be precisely located by three integers. Each point in the Euclidean plane may be found using only two integers, namely its x- and y-coordinates.

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The interest to be paid by the student is $126.875 and the amount is $7126.875

The simple interest is the interest amount for a particular principal amount of money at some rate of interest.

Given that, a student takes a loan on SI on $7000 for 3 months and the rate of interest is 7.25%

SI = PRT / 100

Putting the values,

SI = 7000 x 3 x 7.25 / 1200

= 126.875

Amount = Principal + Interest

Amount = 7000 + 126.875

= 7126.875

Hence, the interest to be paid by the student is $126.875 and the amount is $7126.875

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The measure of side Q'N' after a dilation of quadrilateral NOPQ by a scale factor of 2/3 is 12 units

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Scale factor is the ratio of new side to original side. It is given as:

Scale factor = new side / original side

Given that the scale factor is 2/3 and the side QN is 18, hence:

QN * scale factor = Q'N'

Substituting:

18 * 2/3 = Q'N'

Q'N' = 12

The measure of side Q'N' is 12 units

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Let d be the distance in miles from the airport that a plane should begin descending. According to the problem statement, we can write the equation:

d/3 = 10

To solve for d, we can isolate it by multiplying both sides of the equation by 3:

d = 3 * 10

Therefore, the pilot should begin descending when the plane is 30 miles from the airport.

Answer: b = 8

Step-by-step explanation:

From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.

Let's factor the equation and set each factor equal to zero:

x²(x+3)(x - b) = 0

x = 0 or x + 3 = 0 or x - b = 0

Solving for x in each case, we get:

x = 0 or x = -3 or x = b

Since the sum of the solutions is 5, we can write:

0 + (-3) + b = 5

Simplifying, we get:

b - 3 = 5

Adding 3 to both sides, we get:

b = 8

Therefore, the value of b is 8.

The perimeter of the wall in a classroom is 26 meters.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, a wall in a classroom measures, the length is 10 m and the height is 3 m.

So, the perimeter of wall is 2(Length+Height)

= 2(10+3)

= 2×13

= 26 meters

A computer desk has a length of 70 cm and a breadth of 40 cm.

Now, the perimeter of a computer desk is 2(Length+Breadth)

= 2(70+40)

= 220 cm

220 cm can be written as 220/100 = 2.2 meters

Number of computers v=can be placed along wall =15/2.2

= 6.8

≈ 7

Therefore, approximately 7 computers desks place along the wall.

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The answer is (iv) 150. This result can be obtained by applying the alternate segment theorem.

A circle is a shape with all points at an equal distance from the center. It has no sides or angles and is the only two-dimensional shape with this property. It is also the most basic of all shapes, and is found in nature in many forms, such as raindrops, the sun, and even the human pupil. Circles are often used in art, design, and architecture, and are sometimes even used to represent infinity.

This theorem states that if two chords of a circle intersect at right angles, then the angles in the alternate segments of the circle are equal. In this case, the alternate segments are APQ and CQP. Hence, ∠APQ + ∠CQP = 150°.

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Using percentage, the true proportion of registered voters who are Democrats is = 64.

What do you mean by percentage?

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.

It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.

In the question,

Sample size, n = 140.

Now 46% of the registered voters are Democrats.

Now the no. of registered voters =

46% of 140

= 46/100 × 140

= 6440/100

= 64.4

≈ 64

Therefore, 64 is the true proportion of registered voters who are Democrats.

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Answer:

Step-by-step explanation:

Equate whats inside (arguments) \sin with base period of sine function 2\pi and solve for x to get period,

\pi x=2\pi\implies x=2

So the period of the graph of the given function is precisely 2.

Hope this helps :)

The scale of the map is 1/10,000.

The formula used to find the formula to find the scale is

scale = length on the map / actual length

Given,

Actual length of the golf park = 2.5 km

length on map = 250 mm

Here, we need to convert both lengths into the same units

2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm

we know that,

scale = length on the map / actual length

= 250 mm / 2,500,000 mm

= 1/10,000.

Therefore, the scale of the map is 1/10,000.

i.e, one unit on the map is equal to 10,000 units of length in reality.

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Answer: 545,884,646.36 ft3.

Step-by-step explanation:

The volume of the cylinder is calculated using the formula V=πr2h, where r is the radius of the cylinder and h is the height. The radius of the cylinder can be calculated by dividing the diameter (125 times the height) by 2.

Therefore, the radius = (125 * 1934) / 2 = 118,550 / 2 = 59,275 ft

Plugging in the values of radius and height into the formula, the volume of the cylinder is V = 3.14 * (59,275)2 * 1934 = 545,884,646.36 ft3

Rounding to the nearest hundredth, the volume of the cylinder is 545,884,646.36 ft3.

Answer:

$53.25

Step-by-step explanation:

$[tex]\frac{355}{100}= 1[/tex]%

$[tex]15\frac{355}{100} = 15[/tex]%[tex]= 53.25[/tex]$

Answer:

53.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's first find the number of 12-year-olds and 13-year-olds in the band:

Let x be the number of 12-year-olds.

Then the number of 13-year-olds is 1.25x (125% of x).

The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).

Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.

The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:

The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.

10% of 100 is 10, so there are 10 14-year-olds.

Now we can find the portion of the band for each age group:

12-year olds: fraction = 40/100 = 2/5, percent = 40%

13-year olds: fraction = 50/100 = 1/2, percent = 50%

14-year olds: fraction = 10/100 = 1/10, percent = 10%

The volume of the solid right pyramid is, x²y cm³.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.

The number of sides on its base is equal to the number of lateral faces.

The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

We know, Area of a square is a product of it's any two sides.

Now, If we want to determine the volume we have to multiply the height also(another dimension).

Therefore, From the given information and options, A pyramid with square bases(x) and a height of 'y' will have a volume,

= x×x×y cm³.

= x²y cm³.

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Answer:

Step-by-step explanation:

number of minuties for whole cycle

green time+yellow time+ orange time

2+2+2=6

min to seconds==> 1min=60 seconds

so 6*60=360 seconds

Enjoy:)

Therefore , the solution of the given problem of rational numbers comes out to be  that 9/18 is a rational number

Rational numbers are those that can be written as the ratio (not the fraction) of two integers. A fraction with a nonzero denominator is considered sensible. Examples of rational numbers include 1/2, 1/5, but it also 3/4. Additionally, "0" can be written in many different ways as a real purpose, such as 0/1, 0/2, as well as 0/3. But 1/0, 2/0, 3/0, and so forth. The number of seven is reasonable. Two parameters can be divided to produce a rational figure.

Here,

Because 9/18 can be written as a ratio of two numbers, it is a rational number. By dividing the numerator and denominator by their largest common factor, which is 9 in this instance, we can simplify the expression 9/18:

=> 9/18

=> (9 ÷ 9) / (18 ÷ 9) = 1/2

We can see that 9/18 is a rational number because 1/2 is also a ratio of two numbers.

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A statement is not true about the dot plot to the right include the following: A. the French Club has a greater mean than the Spanish Club.

In Mathematics, a dot plot is a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

Mean of French Club = 1/12(18 + (19 × 4) + (20 × 4) + (21 × 2) + 22)

Mean of French Club = 1/12(238)

Mean of French Club = 119/6 = 19.83.

Mean of Spanish Club = 1/12(18 + (19 × 2) + (20 × 3) + (21 × 3) + (22 × 3))

Mean of Spanish Club = 1/12(246)

Mean of Spanish Club = 123/6 = 20.5.

Therefore, 19.83 is less than 20.5.

Median of French Club = 20

Median of Spanish Club = (20 + 21)/2 = 20.5.

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Answer:

48%      hope this helps!

Step-by-step explanation:

188-127= 61 <--(increase)

divide increase by original( 61/127= 0.480)

Multiply by 100 to get percent (0.480x100= 48%)

The given investment realized a loss of $3.75 with 31.25% decrease.

The amount made by selling a product, which should be greater than the product's cost price, is generally referred to as the profit. It is the profit generated by all business activities. In other words, a product is deemed to have made a profit if its selling price (SP) exceeds its cost price (CP). It explains the financial gain realised when the revenue from a company activity outpaces the costs, like as taxes and expenses, involved in maintaining a business activity.

Given : Purchase Price: $12.00

            Selling Price: $8.25

Since the purchase price is more than the selling prize, So the investment has been sold at a loss.

The loss on investment = Purchasing price - Selling price

                                       = $ 12 - 8.25

                                       = $3.75.

% of decrease = (loss/ purchasing price) × 100

                        = 3.75/12 × 100

                        = 31.25 %

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For the specified functions, there is no answer. By graphing the functions, the answer has been discovered.

The method of graphing a function begins with creating the graph of a pertinent function. The function equation will be satisfied at a point on a curve if it reflects the function at that location.

We are given two functions as f(x) = -x² + 8x - 13 and g(x) = x + 3

The graph of the given functions has been plotted and attached below.

In the graph, the red function represents the f(x) function and the blue line represents the g(x) function.

From the graph, we can see that the two does not meet.

Hence, there is no solution for the given functions.

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Step-by-step explanation:

We have the formula for the surface area of a rectangular box given by:

S = 4LW + 2WH

Substituting the given values, we get:

138 = 4(9)(3) + 2(3)H

Simplifying, we get:

138 = 108 + 6H

6H = 138 - 108

6H = 30

H = 30/6

H = 5

Therefore, the value of the unknown variable H is 5.

Answer: The numerator is the percentage change in quantity demanded, which is (Q2 - Q1)/[(Q2 + Q1)/2] = (4500 - 5000)/[(4500 + 5000)/2] = -0.1818

The denominator is the percentage change in price, which is (P2 - P1)/[(P2 + P1)/2] = (3500 - 3000)/[(3500 + 3000)/2] = 0.1429

The numerator divided by the denominator is -0.1818/0.1429 = -1.2727

The price elasticity of demand is greater than 1 in absolute value, which means the demand is elastic.

Using the midpoint formula, we can calculate the price elasticity of demand as:

[(Q2 - Q1)/((Q1 + Q2)/2)] / [(P2 - P1)/((P1 + P2)/2)]

Substituting the given values, we get:

[(-500)/((5000 + 4500)/2)] / [(3500 - 3000)/((3500 + 3000)/2)]

Simplifying, we get:

-0.1818 / 0.1429 = -1.2727

Since the price elasticity of demand is greater than 1 in absolute value, the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price, and the university can expect a relatively large decrease in enrollment due to the tuition increase.

Step-by-step explanation:

Check the picture below.

[tex]\sin(24^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{17}}\implies 17\sin(24^o )=y \\\\[-0.35em] ~\dotfill\\\\ \sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{y}}\implies \theta =\sin^{-1}\left( \cfrac{4}{y} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{4}{17\sin(24^o )} \right)\implies \theta \approx 35.3^o[/tex]

Make sure your calculator is in Degree mode.

Therefore , the solution of the given problem of unitary method  comes out to be each Disc cost $10.80 before taxes.

The measurements taken from this nanosecond subset must be multiplied by two in order to complete the task using the unitary technique. In essence, the characterised by a group and the colour sections are both removed from the unit method when a desired object is present. For example, 40 pens with a variable price would pay Inr ($1.01).

Here,

Let's name the CDs' pre-tax cost "x" for simplicity. The overall cost of the CDs before tax is two times because Lena purchased two of them for the same price. The cost of the Discs, with the addition of the $1.80 sales tax, is:

=> 2x + $1.80

Given that we know the final price, including tax, was $23.40, we can create the following equation:

=> 2x + $1.80 = $23.40

By deducting $1.80 from each half, we arrive at:

=> 2x = $21.60

When you divide both parts by 2, you get:

=> x = $10.80

As a result, each Disc cost $10.80 before taxes.

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XPO's minimum tax credit carryover to 2019 is $20,500.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.

Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.

To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:

Minimum tax credit carryover = $51,000 - $30,500 = $20,500

Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.

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(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.

The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.

(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:

N(t) = No e^(-0.088t)

where No is the initial amount of the substance present at t=0.

(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:

N(t) = 400 e^(-0.088t)

To find how much will remain after 3 days, we need to evaluate N(3):

N(3) = 400 e^(-0.088*3) ≈ 323.3 g

Therefore, approximately 323.3 g of the substance will remain after 3 days.

(iii) The rate of change of the amount of the substance after t days is given by:

dN/dt = -0.088N

To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:

dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day

Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.

(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:

N(t) = 200

Substituting No = 400 into the exponential function, we get:

400 e^(-0.088t) = 200

Dividing both sides by 400, we get:

e^(-0.088t) = 0.5

Taking the natural logarithm of both sides, we get:

ln(e^(-0.088t)) = ln(0.5)

Simplifying, we get:

-0.088t = ln(0.5)

Solving for t, we get:

t ≈ 7.88 days

Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.

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