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The measurement pairs that could be the dimensions of rectangle B include:

A. 6cm by 1.5cm

D. 18cm by 4.5vm

F. 80cm by 20cm

From the information, Rectangle A measures 12 cm by 3cm. Therefore, it should be noted that the scale factor is:

= 12/3

= 4/1

Therefore, the options should also have that same constant of 4:1

In this case, 6cm by 1.5cm, 18cm by 4.5cm, and 80cm by 20cm all possess this. This illustrates the concept of equivalent dimensions since they all have a ratio of 4:1.

The complete question is written below.

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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

A. 6 cm by 1.5 cm

B.10 cm by 2 cm

C. 13 cm by 4 cm

D.18 cm by 4.5 cm

E.80 cm by 20 cm

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, or, in standard algebraic notation, a² + b² = c².

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b² = c².

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

First use the Pythagorean theorem. a² + b² = c²

then take the first derivative of it to get

2a(a') + 2b(b') = 2c(c')

Now figure out how far the train is after 4 seconds

6(4)=24

70² + 24² = c²

c = 74

Now plug in the variables you know

2(70)0 + 2(24)6 = 2(74)c' and solve for c' or the rate of change of c.

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All right angles are congruent which is determined by the definitions of a right angle and congruent angles.

Congruent angles are two or more angles that are identical to each other. As a result, the measurements of these angles are equivalent.

Given that ∠1 and ∠2 are right angles.

By the definition of right angles i.e. right angle is one that is exactly 90 degrees. It is precisely one-quarter of a circle. When a pie is divided into four equal pieces, the tip of each slice forms a straight angle.

⇒ m ∠1 =90° ; m ∠2 = 90°

By the substitution to get

⇒ m ∠1 = m ∠2

Therefore, ∠1 ≅ ∠2

Hence, all right angles are congruent which is determined by the definitions of a right angle and congruent angles.

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The equation which describes Riya's graph is:

a). C(t) = -3t + 24.

We can easily find out the equation by concentrating on the axes.

For example,

Just look from the graph the value of C when t = 0.

We can conclude that C should be equal to 24 when t is equal to 0.

Now, let us put this value of t ( which is 0) in the equations one by one:

a). C(t) = -3t + 24

=> C(0) = -3 (0) + 24

=> C(0) = 24.

So, equation a). satisfies the given criteria.

Similarly, b) also qualifies but c) and d) are not equal to 24 when t = 0.

So, remove them.

Now, let's look at the value of t when C=0.

We can see that t should be equal to 8.

Let's put this value in equations,

a). 0 = -3t + 24

=> 3t = 24

=> t = 8.

Now, we can see that equation a). satisfies all the given conditions for the graph.

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So, as shown at the function

f(x) is constant at the middle interval (10 , 15)

at which f(x) = 2 and the digit 2 is constant

so, the answer is (10 , 15)

Data

Length = 15 ft

Width = 8 ft

Area

Answer:96

Step-by-step explanation: Answer is 96 because you can do 16 times 3 which is 48 so for the fifth seat to the end will be 96 ways.

Hope this helps! :)

Answer:

x = 7.2

Step-by-step explanation:

[tex]5(x - 3) = 21[/tex]

[tex]x - 3 = 4.2[/tex]

[tex]x = 7.2[/tex]

The expression for the sequence of operations is 2(t x 5).

Expression:

Expression consists of minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Here we have the phrase "multiply t by 5, then double the result"

Now we have to written the algebraic expression for it.

For the given phrase, we have to divide it into two part,

The first part is "multiply t by 5",

So, it can be written as

=> 5 x t

Now, we have to move on to the next part that is,

"double the result".

For that, we have to multiply the first part by 2,

It can be written as,

=> 2 x ( 5 x t)

Therefore, the resulting expression is 2(5t).

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A) distribution of x and its parameter(s) is (λ^x e^-λ ) / x!  

B) standard deviation of x is 1

C) probability that x is (inclusively) within one standard deviation of the mean of x is 0.7358

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A) The poisson distribution with mean is followed by X = λ = 1

Therefore, ≈ (λ = 1)

Distribution of X is:

(λ^x e^-λ ) / x!   ,    x = 0, 1, 2, 3 ......

B) Standard Deviation of X is :

σx = √x = 1

C) Probability of X = P (-1 ≤ x ≤ 1)

P(x = 0) + P(x = 1)

= (1⁰ e⁻¹) / 0! + 1¹ e-¹ / 1!

= 2e⁻¹

= 0.7358

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1. The fraction of the fish has he already consumed is 17/30.

2. The fraction of the garden is left for her to completely cover is 2/15.

3. The oil and gas that affected the ozone layer in the projection is 1 1/5.

4. The fraction of his total salary is allotted to House Rental is 3/10.

1. Mr. Beeg ate 1/6 of the fish for breakfast and 2/5 of the fish over lunch. The fraction already consumed will be:

= 1/6 + 2/5

= 5/30 + 12/30

= 17/30

2. Tita Flan covered 2/3 of the garden on the 1st day, 1/5 of the garden on the 2nd day. the fraction of the garden is left for her to completely cover the mini park with trees will be:

= 1 - (1/5 + 2/3)

= 1 - 13/15

= 2/15

3. It estimated to 2/5 of depletion of the ozone layer and projections revealed that by the year 2050, its effect will have increased three times. This will be:

= 2/5 × 3

= 6/5

= 1 1/5

4. The fraction of his total salary is allotted to House Rental will be:

= House rental / 2

= 3/5 / 2

= 3/10

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The resulting value for the quotient of 21 and a equals 30 is 7/10.

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three.

Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b

Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;

21/a = 30

Cross multiply

30a = 21

Divide both sides by 30

30a/30 = 21/30

a = 21/30

a = 7/10

Hence the value of a from the equivalent expression is 7/10.

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Given:

Total number of people surveyed = 205

a) Percentage of the survey respondents that do not like both hamburgers and burritos.

Number of people that do not like both = 54

To find the percentage of the respondents that do not like both, we have:

Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%

b) Marginal relative frequency of all customers that like hambugers.

Given:

Number of customers that like hamburgers = 110

To find the marginal relative frequency, we have:

The marginal relative frequency of all customers that like hambugers is 54%

c) Conditional relative frequencies:

i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:

ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:

Answer:

16.  36.67

17.  40

Step-by-step explanation:

See attached worksheet

The sampling method used here is systematic sampling.

What is systematic sampling?

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The slope of the line will be positive 9. Then the correct option is C.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope is given as,

Slope = m = (y₂ - y₁) / (x₂ - x₁)

Determine whether a line's slope, which represents the linear connection, is positive, negative, zero, or undefined without using a graph. Next, locate the slope. A babysitter may make $9 per hour and $36 per 4 hours.

Slope = (36 - 9) / (4 - 1)

Slope = 27 / 3

Slope = 9

The slope of the line will be positive 9. Then the correct option is C.

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The equation that relates M to R is M = 13 - R

From the question, we have the following parameters:

The total number of new magazines is the sum of the number of magazines read and the number of magazines left

This is represented as

Total number of new magazines = Number of magazines read + Number of magazines left

Substitute the known values in the above equation

13 = R +M

Make M the subject

M = 13 - R

Hence, the equation is M = 13 - R

See attachment for the graph

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The equation of the line that passes through point (-5,3) and perpendicular to y=5x-3 is y = -(1/5)x + 2.

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Given the data in the question;

First, determine the slope of the initial line using the slope intercept-form. y = mx + b

y = 5x - 3 compared with the slope intercept form,

Slope m = 5

Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/5

Next, find the equation of the perpendicular line, by using the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( -1/5 ) and point (-5,3).

y - y₁ = m( x - x₁ )

y - 3 = -1/5( x - (-5) )

y - 3 = -1/5( x + 5 )

y - 3 = -1/5(x) -5/5

y - 3 = -1/5(x) - 1

y = -1/5(x) - 1 + 3

y = -(1/5)x + 2

Therefore, the equation of the perpendicular line is y = -(1/5)x + 2.

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The table that represents a linear function is Table 1. Thus, the correct option is A.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

We know that, slope m= (y2-y1)/(x2-x1)

Table 1:

Put (x1, y1)=(1, 5) and (x2, y2)=(2, 9) in slope formula

That is, (9-5)/(2-1)

= 4

Similarly, the slope between last two points is (9-5)/(4-1)

=4

Table 2:

Put (x1, y1)=(1, -5) and (x2, y2)=(2, 10) in slope formula

That is, (10+5)/(2-1)

= 15

Similarly, slope between last two points (20+15)/(4-3)

=35

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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265 students at this college have taken a course in either calculus or discrete mathematics.

Let X = number of students who have taken a course in calculus

Y = number of students who have taken a course in discrete mathematics

To determine the number of students who have taken a course in calculus only, subtract 135 from 324.

Only X = X - X∩Y

Only X = 324 - 135

Only X = 189

To determine the number of students who have taken a course in discrete mathematics only, subtract 135 from 211.

Only Y = Y - X∩Y

Only Y = 211 - 135

Only Y = 76

To determine the number of students who have taken a course in either calculus or discrete mathematics, add 189 and 76.

either X or Y = only X + only Y

either X or Y = 189 + 76

either X or Y = 265

To better illustrate the X and Y, see the attached photo of the Venn Diagram.

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Answer: (2, 5/2)

Step-by-step explanation:

CD=(2, 4),(2, 1)

((2+2)/2, (4+1)/2)=

(4/2, 5/2)=(2, 5/2)

The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.

A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.

The linear equations are given below.

y = -3x + 9        ...1

3y = -9x + 9     ...2

Divide the equation 2 by 3, then the equation will become.

y = -3x + 3

The slope of the lines is the same but the lines are separated by a distance.

The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

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Answer:

C

Step-by-step explanation:

8.5 - 5.6666= 2.83

Answer:

C. 2 5/6

Step-by-step explanation:

8 1/2 - 5 2/3    1. convert mixed numbers into an improper fraction

17/2 - 17/3       2. convert fractions into 2 numbers that can be subtracted

51/6 - 34/6      3. subtract

17/6                 4. convert to mixed number

2 5/6

The weight of Brad is 70 lb and the weight of Sean is 150 lb now.

According to the question,

We have the following information:

Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb.

Now, let's take Brad's weight to be x lb.

So, we have:

Sean's weight = (10+2x) lb

Now, when Brad gains 10 lb, we have the following expression:

(x+10)+(10+2x) = 230

3x+20 = 230

3x = 230-20

3x = 210

x= 210/3

x = 70 lb

Now, Sean's weight = (10+2x) lb

Putting the value of x:

Sean's weight = 10+2*70

Sean's weight = 10+140

Sean's weight = 150 lb

Hence, the weight of Brad is 70 lb and the weight of Sean is 150 lb now.

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ANSWER:

78.5 ft

STEP-BY-STEP EXPLANATION:

One trip equals the circumference of the circle.

The circumference of a circle is calculated by means of the following formula:

Therefore, we substitute and calculate the distance the pony would walk for a trip:

That is, the number of feet the pony walks is 78.5

A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

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Answer:

4(4x + 7)

Step-by-step explanation:

To answer this question you need to understand what GCF is

GCF is Greatest Common Factor

GCF is the highest number that divides exactly into two or more numbers.

The expression is 16x + 28

The highest number that can divide 16 and 28 is 4

Dividing 16x + 28 gives => 16x/4 + 28/4 => 4x + 7

So the factored expression is

4(4x + 7)

Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1