Exponential Functions

Determine which of the following exponential formula(s) represents exponential function II in the graph above.
(a) 10(1.2)t (β) 10(1.5)t
(x) 20(1.2)t (8) 30(0.85)t
(8) 30(0.95)t (∅) 30(1.05)t

a. x c. 8
b. a d. ∅

Please select the best answer from the choices provided

Answer:

+ 8

Step-by-step explanation:

This is an arithmetic progression (AP) as there is a common difference between successive terms.

For example, looking at the first two terms,

Difference = 2nd term - 1st term

                  = -11 -(-19)

                  = -11 + 19

                  = +8

To check,

Looking at the second and third terms,

Difference = 3rd term - 2nd term

                  = -3 -(-11)

                  = -3 + 11

                  = +8

Hence, there is a common difference of +8 between consecutive terms, making it an AP.

Answer:

1.69

approximately 2 wax cubes

Step-by-step explanation:

number of wax cubes needed = volume of square pyramid / volume of cube

Volume of a pyramid = 1/3 x ( base area x height)

base area = length²

6² = 36

volume = 1/3 x (36 x 9) = 108

volume of a cube = length³

4³ = 64cm³

108/64 = 1.69

Answer:

254.57 in^3

Step-by-step explanation:

A cylinder has a height of 9 inches. The radius of the cylinder is 1 / 3 the height of the cylinder. What is the approximate volume of the cylinder?

volume of a cylinder = nr^2h

n = 22/7

r = radius

radius = 9 x 1/3 = 3 inches

(22/7) x (3^2) x 9 = 254.57 in^3

Answer:

c

Step-by-step explanation:

The mean price of a gallon of gas at the five stations is $3.81. Therefore, option A is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

Given that, Yesterday, the price of a gallon of gas at five gas stations was $3.56, $3.71, $3.62, $3.93, and $3.83, respectively.

Today each gas station raised its price by $0.08

Now, mean =(3.56+3.71+3.62+3.93+3.83+5×0.08)/5

= (18.65+0.4)/5

= 19.05/5

= $3.81

Therefore, option A is the correct answer.

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Answer: mean = 6

median = 7

mode = 8

Step-by-step explanation:

Answer:

14 cases

Step-by-step explanation:

Let x be the number of personal injury cases this year by Gypsum Goode

x* 9/7 = 18

Multiply each side by 7/9

x * 9/7 *7/9 = 18 * 7/9

x = 14

Answer:

the triangle is translated 2 units up, and is reflected across the x axis

Step-by-step explanation:

Answer:

6 1/5

Step-by-step explanation:

Answer:

31/5 into a mixed number would be 6 1/5 .

Answer:

150 kg

Step-by-step explanation:

30% of 500 kg

[tex]=0.30*500[/tex]

[tex]=150[/tex]

150 kg

Answer:

2

Step-by-step explanation:

2 + 2 - 4 + 2 = 2

Answer:

2

Step-by-step explanation:

2 + 2 = 4

4 - 4 = 0

0 + 2 = 2

The number of students that were in Mr Marco's class will be 9 students

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Here, the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint

The number of students that were in Mr Marco's class will be:

= 6 ÷ 2/3

= 6 × 3/2

= 9 students

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Answer:

91 ways. So the answer to the problem's question is THIS : in 15*91 = 1365 ways.

Step-by-step explanation:

Answer: y= -4 divided by 3 • x (-1)

Step-by-step explanation:

✨photo math✨

Answer:

I. Radius, r = 5.82 in

II. S.A of a sphere = 19.61 meters

Step-by-step explanation:

Given the following data;

I. Volume of cylinder = 542π in³

Height = 16 in

To find the radius of the cylinder;

Volume of cylinder = πr²h

542π = πr²*16

Dividing both sides by π, we have;

542 = 16r²

r² = 542/16

r² = 33.875

Radius, r = 5.82 in

II. Volume of sphere = 5.055π m³

To find the surface area of the sphere;

First of all, we would find the radius of the sphere.

[tex] Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} [/tex]

Substituting into the formula, we have;

[tex] 5.055 \pi = \frac {4}{3} \pi r^{3} [/tex]

Cross-multiplying, we have;

[tex] 5.055 \pi * 3 = 4 \pi r^{3} [/tex]

[tex] 15.165 \pi = 4 \pi r^{3} [/tex]

Dividing both sides by 4π, we have;

[tex] 3.79 = r^{3} [/tex]

Taking the cube root of both sides, we have;

r = 1.56 m

Next, we find the surface area (S.A) of the sphere;

S.A of a sphere = 4πr

S.A of a sphere = 4*3.142*1.56

S.A of a sphere = 19.61 meters

Answer:

I think it's TWO

Step-by-step explanation:

The piecewise function f(x) = 1/2 |x| is equivalent to -

1/2 |x| = {- x/2}   {x < 0}

1/2 |x| = {x/2}   {x ≥ 0}

Given is the absolute value function -

f(x) = 1/2 |x|

We can write it as a piecewise function as follows. The given function is as follows :

f(x) = 1/2 |x|

The absolute value function is given as -

|x| = - x   {x < 0}

|x| = x     {x ≥ 0}

So, we can write the piecewise function as -

1/2 |x| = {- x/2}   {x < 0}

1/2 |x| = {x/2}   {x ≥ 0}

Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -

1/2 |x| = {- x/2}   {x < 0}

1/2 |x| = {x/2}   {x ≥ 0}

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Answer: A. The first one

Step-by-step explanation:

The first data can be represented in the box plot if the restaurant records the number of tables served each night, and option (A) is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have data:

Minimum = 3

Lower = quartile = 14

Median = 23

Upper quartile = 29

Maximum = 40

From the above data, we can plot the data in the box plot.

Thus, the first data can be represented in the box plot if the restaurant records the number of tables served each night, and option (A) is correct.

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Using a calculator we can approximate this to be A ≈ 568.89 cm^2.

A regular decagon is a two-dimensional geometric shape with ten sides of equal length and ten interior angles of equal measure. It is a polygon, which is a two-dimensional shape made up of line segments (straight sides).

The approximate area of a regular decagon can be calculated using the formula A = (5/2) * a^2 * tan(π/5), where a is the length of each side. Since the radius of the decagon is 8 cm, the length of each side can be calculated using the formula a = 2r * sin(π/10) where r is the radius.

Plugging these values into the formula we get A = (5/2) * (2 * 8 * sin(π/10))^2 * tan(π/5) which simplifies to A = 320 * sin^2(π/10) * tan(π/5).
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.

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Answer: 8(r-t)

Step-by-step explanation:

[tex](12r+2t)-(4r+10t)=12r+2t-4r-10t=8r-8t=8(r-t)[/tex]

Answer:

d 10

Step-by-step explanation:

Answer:

Answer is D I’ve done it and got it right before

Step-by-step explanation:

Answer:

5.

Step-by-step explanation:

Given that Nicholas performs an experiment in which he pulls a marble from a bag, and in his experiment, he finds that he is twice as likely to pull a red marble as a blue marble, to determine, if Nicholas pulls 10 red marbles, how many blue marbles does he pull, the following calculation must be performed:

10/2 = X

5 = X

Therefore, Nicholas pulls 5 blue marbles from the bag.

Answer:

arcPSU = 224degrees

Step-by-step explanation:

From the given diagram;

arcPSU = arcPQ + arcQR + arcRS + arcST + arcTU

Given

arcPQ = arcTU

arcQR = arcRS = 37

arcAST = 90

Since 136 + arcPQ + 37+37+90+arcTU = 360

136+2arcPQ+ 37+37+90= 360

2arcPQ+300 = 360

2arcPQ = 360 - 300

2arcPQ = 60

arcPQ = 60/2

arcPQ = 30degrees

Substitute into the above expression

arcPSU = arcPQ + arcQR + arcRS + arcST + arcTU

arcPSU = 360 - arcPU

arcPSU = 360 - 136

arcPSU = 224degrees

By solving system of linear equation we get Cost for 1 cheeseburger $5 and 1 cups of lemonade $2

A system of linear equations is a collection of two or more linear equations that have the same variables. A linear equation is an equation in which the highest power of the variable is 1. In other words, the equation is a straight line when graphed.

Here is an example of a system of linear equations:

3x + 2y = 19

2x + 4y = 18

This is a system of equations problem, where we can use the information provided to set up two equations and then solve for the unknown variables. Let x be the cost of one cheeseburger and y be the cost of one cup of lemonade.

From the information provided, we know that:

3x + 2y = 19 (the cost of 3 cheeseburgers and 2 cups of lemonade is $19)

2x + 4y = 18 (the cost of 2 cheeseburgers and 4 cups of lemonade is $18)

To find the cost of one cheeseburger and one cup of lemonade, we can solve this system of equations. One way to do this is by substitution.

3x + 2y = 19

we get

[tex]x=\frac{19-2y}{3}[/tex]

substituting x in equation 2x+4y=18

we get

 [tex]2(\frac{19-2y}{3})+4y=18[/tex]

[tex]38 - 4y + 12y = 54\\8y = 16\\y = 2[/tex]

substituting y in equation 3x+2y=19

[tex]3x+2(2)=19\\3x=19-4\\3x=15\\x=5[/tex]

The cost of one cup of lemonade is $2

The cost of one cheeseburger is $5

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Answer:

−12r+32−2r 2

Step-by-step explanation:

(−8−r)(2r−4)

Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.

−16r+32−2r

2

+4r

Combine −16r and 4r to get −12r.

Answer:

R-12

Step-by-step explanation:

Open the parenthesis, then solve

-8-r + 2r-4

-r+2r-8-4

r-12

Your answer will be R-12

Answer: Expected Value = -0.31

We expect to lose about 31 cents each time we play the game.

============================================================

Explanation:

A = event of selecting a king

B = event of not selecting a king

P(A) = 4/52 since there are 4 kings out of 52 total. This fraction reduces to 1/13.

P(B) = 48/52 = 12/13

Note: P(A) + P(B) = 1.

V(A) = net value of selecting a king

V(A) = 100-8 = 92, so you net $92 if event A occurs.

V(B) = -8, meaning you lose 8 dollars if you select anything but a king

We multiply the probability values with their corresponding net values

P(A)*V(A) = (1/13)*(92) = 7.07692 approximately

P(B)*V(B) = (12/13)*(-8) = -7.38462 approximately

Add up the results:

7.07692 + (-7.38462) = -0.3077

The expected value is approximately -0.3077 which rounds to -0.31

We expect to lose on average 31 cents each time we play the game. The nonzero expected value means this is not a mathematically fair game.

The missing side length is 5.7.

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The matching of the items as follows ,a - 4 , b - 5, c - 1 , d - 6 ,  e - 2 , f - 3

What is a number ?

number is used to represent the quantity of number  and it is even used for calculations.  

a) Multiplicative inverse

if the product the given number and reciprocal of the given number is 1.

so,

5 * 1/5  = 1

as LHS = 5 * 1/5  = 1

RHS = 1

Hence , a - 4

b )  Additive inverse

if the summation of the given number and opposite sign of given number results 0 .

7 + (-7) = 0

LHS = 7+ (-7) = 0

RHS = 0

hence , b - 5

c ) Commutative Property of Multiplication

if a.b = b.a hence it is in Commutative Property of Multiplication .

so,  5.6 = 6.5

hence , c - 1

d) Distributive property

if a ( b + c ) = a*b + a*c than it is in distributive property .

hence , d - 6

e) Additive Identity Property

if a+ 0 = a hence it is Additive Identity Property

so , b - 2

f ) Associative Property of Addition

if (a+b) + c = a + (b+c ) hence it is in Associative Property of Addition

so , f - 3.

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