The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72

The perimeter of the rectangle is  20 + 20√3 inches.

The perimeter of a rectangle is sum of the whole side of the rectangle. The side bounded by the rectangle is the perimeter of the rectangle.

Therefore,  the diagonal of the rectangle is given as 20 inches.

Using trigonometric ratios, let's find the sides of the rectangle.

sin 30 = opposite / hypotenuse

sin 30 = x / 20

x = 20 sin 30

x = 20 × 0.5

x = 10 inches

Therefore, using Pythagoras theorem,

20² - 10² = b²

b² = 400 - 100

b = √300

b = √100 × 3

b = 10√3

Hence,

perimeter of the rectangle = 2(l + w)

perimeter of the rectangle = 2(10 + 10√3)

perimeter of the rectangle = 20 + 20√3

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Answer: 8

Step-by-step explanation:

7.69 to the nearest whole number is 8

A total of 30 golf balls are there in the bag that weighs 1110 grams.

A total of 69 golf balls weights 2553 grams in a bag.

It is asked that how much golf balls does make 1110 grams of weight.

Let us say that the weight of one ball is X.

So, Using unitary method,

We can write,

69 times mass of one golf ball = 2553 grams.

69X = 2553

X = 2553/69

X = 37 grams.

Hence, the weight of one ball is 37 grams.

Now, let us say that Y balls weights 1110 grams,

So, we can write,

Y time weight of one ball = 1110

37Y = 1110

Y = 1110/37

Y = 30.

Hence, 30 golf balls will weight 1110 grams.

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Answer:

30

Step-by-step explanation:

The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.

A function f is has an inverse if it is both one-to-one and onto.

Given the function f(x) = 1/3x-2

we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;

y = 1/3x - 2

by cross multiplication

3x - 2 = 1/y

add 2 to both sides of the equation

3x = 1/y + 2

3x = (1 + 2y)/y

divide both sides of the equation by 3

x = (1 + 2y)/y ÷ 3

x = (1 + 2y)/3y

So, f^-1(x) = (1 + 2x)/3x

Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.

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The explicit formula is a_n = 3+4n

From the question, we have

a1 = 7

We know that,

a_n = a_1 +(n-1)d

a_n = 7 +(n-1)4

a_n = 7+4n-4

a_n = 3+4n

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer:

the options are wrong

Step-by-step explanation:

Answer:

C. 8

Step-by-step explanation:

2 x 8 = 16

16 - 16 = 0

2 x 0 = 0

Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.

Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10

Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.

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The correct option c) 120; for the assignment of 7 students to 10 seats in a row.

The formula for finding the combination is-

ⁿCₓ = n!/ x!(n - x)!

Where,

For the given question.

Total students to be assigned a seat = 7.

Total seats in a classroom = 10.

Thus, Applying combination;

¹⁰C₇ = 10!/7!(10 - 7)!

¹⁰C₇ = 120

Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.

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Answer:

                                 x1  y1    x2  y2

1. 0 - explanation - (4, -2)   (9, -2)     -2 - -2

                                                              4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0

2. it would be defined or 0

Answer:

1.5

Step-by-step explanation:

we calculate the circumference of this circle.

circumference of a circle=2πr

data:

r=8 mm

circumference=2(8 mm)π=16π mm

2)we calculate the measure, in radians of the angle.

We know that:

circumference of a circle=2π radians

therefore:

16π mm=2π radians.

16 π mm--------------------------2π radians

12 mm-----------------------------  x

x=(12 mm  *  2π radians) / 16π mm=1.5 radians.

The other sides of the new triangle are  13, 26 and 26 inches as calculated by the properties of similarity.

We know that when two triangles are similar then the ratio of the sides are also equal.

Let the original triangle be ΔABC and the new triangle be ΔXYZ

So from the property of similarity.

AB/XY = BC /YZ = CA/ ZX

Now it is given AB = 3 inches

XY = 13 inches

Hence AB/XY = 13/3

Hence YZ = 13 / 3 × 6 =26 inches

Again ZX = 26 inches

Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another.

Triangles can have different diameters despite having comparable exteriors. Triangles that are congruent and similar to each other usually don't match up.

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Answer:2.86

Step-by-step explanation:

3.5(x +2) = 17

3.5x + 7 = 17

3.5x =17 - 7

3.5x =10

x = 10/3.5

x = 2.86

The bar for 11th graders show 30% for preferring Salad.

Given, that the lunch orders from an upperclassman picnic.

                         11th Grade                      12th Grade                     Total

Salad                      12%                                  6%                              18%

Sandwich               20%                                24%                             44%

Soup                       8%                                  30%                             38%

Total                       40%                                 60%                            100%

To find the relative frequency we divide the frequency by the total.

hence, to find the relative frequency for 11th graders preferring Salad

12/40 = 0.3 = 30%

Hence, the bar for 11th graders show 30% for preferring Salad.

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The needed sample size is 1419. Sample Size is defined as the number of observations in the study.

In the question we have ,

estimate value of all voters who believe global warming ( p) = 82% = 0.82

margin of error (M.E) = 2% = 0.02

confidence of interval is calculated by estimate point value and add or subtract margin of error .

here,we have the value of confidence of interval is 95% = 0.95

Margin of error formula is

M.E = Z × √(p(1-p)/n)

where, p --> is estimated value

n---> sample size , which we required

Z ----> is z-value for observation

for the confidence of interval level 95% , the Z-value is 1.96 exist.

put all value in above formula we get,

0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)

=> 0.02 = 1.96× √(0.82×0.18/n)

= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n

=> n = 1419

So, sample size is large and it is 1419.

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Answer:

Step-by-step explanation:

yes, it is a function

Answer: no

Step-by-step explanation: you have -2,-5 and -2,0 you cant have 2 or more x values that are the same.

Nick got a total of $33.25 for his part of work.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.

Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -

y₁/x₁ = y₂/x₂

We can write -

x/3.5 = (52.25 - x)/2

2x = 3.5(52.25 - x)

2x = 182.875 - 3.5x

x = 33.25

Therefore, Nick got a total of $33.25 for his part of work.

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The probability of pulling a spade or a four of hearts is 0.264 .

we have , from a deck of cards

probability of pulling a spade = 1/4 = 13/52

probability of not pulling a spade 3/4 = 39/52

probability of pulling a 4 of hearts = 1/52

probability of not pulling a spade = 51/52

we have to find the probability of pulling a spade or a four of hearts from a random shuffled deck

So we can get three cases :

case  A :

getting a spade and not getting four of hearts

∴ P (A) = [tex](\frac{13}{52} ) (\frac{51}{52} )[/tex] = 663/2704

case  B :

not getting a spade and getting four of hearts

P(B) = [tex](\frac{39}{52}) (\frac{1}{52} )[/tex]  =  39/2704

case  C :

getting a spade and getting four of hearts

P(C) = [tex](\frac{13}{52})(\frac{1}{52} )[/tex] = 13/2704

therefore , the required probability will become

P = P(A) +P(B) + P(C)

P = 715/ 2704

P = 0.264

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Step-by-step explanation:

750 people go on a coach trip each coach can hold 55 people How many coaches are needed?

750/55 = 13.636 coaches are needed.

Because you cannot have a partial coach, you round up to needing 14 coaches.

Answer:

one is 203

two is 87

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9

Answer:

3/2

Step-by-step explanation:

To multiply fraction×fraction, you multiply top×top and bottom×bottom.

2/3 × 3/2

= 6/6

= 1

The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.

The inequality that represents the bid for the artwork is A. b ≥ 25,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.

Let the minimum bid be b. This will be b ≥ 25,000.

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The rate of change in height when height is 6 inches is 2.37 inches per second approximately.

We know that the volume of cube with length L, width W and height H is given by,

V = L*B*H

So given that the length is 15 inches

the width is 16 inches

Let the height be h inches.

So now the volume is given by,

V = 15*16*h

Differentiating the volume with respect to time 't' we get,

dV/dt = 15*16 dh/dt

Now given that the rate of change in volume per second is 569 cubic inches.

So, dV/dt = 569

So, 15*16 dh/dt = 569

dh/dt = 569/(15*16) = 569/240 = 2.37 (approx)

So the rate of change in height is 2.37 inches approximately.

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Answer:

Each pineapple costs £0.70.

Step-by-step explanation:

Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.

Helen's total cost would be:  P*C = total cost.

The total cost is the difference between £5 and £3.60, which is  £1.40.

We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:

P*C = total cost

2*C = £1.40

C = £0.70

Answer:

it's a answer done bro

The percent decrease in the travel time after getting a new job is 36%.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.

decrease in time = 48 - 30.72

decrease in time = 17.28

Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.

percent decrease = (17.28 / 48) x 100

percent decrease = 36%

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Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1

In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.

The square root of the variance yields the standard deviation, i.e.

Standard deviation = [tex]\sqrt{variance[/tex]

Given that sample, the variance is 49.7 and we have to calculate the standard deviation.

Standard deviation (σ) = [tex]\sqrt{variance[/tex]

= [tex]\sqrt{49.7}[/tex]

= 7.0498

=7.1

Hence, the standard deviation for the population for the given variance is 7.1

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Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.

As given in the question,

Inequality which have like variables term on each side of the given inequality symbol is :

a. 15c + 25 ≤ 115

In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.

Not correct option.

b. 0.75r - 6.25 > 10

In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.

Not correct option.

c. 16 - 2x > x + 16

In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.

Correct option.

d. 12.25h -175 < 5,000

In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.

Not correct option.

Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.

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