What is the domain of the function y = l n (StartFraction negative x + 3 Over 2 EndFraction)
x less-than 2
x greater-than 2
x less-than 3
x greater-than 3

Answer:

Fraction =  13/20

Decimal =  0.65

Percent = 65%

Step-by-step explanation:

Given:

13 out of 20 emails in mail inbox are junk emails

Solve for:

The experimental probability that next email is junk

Solution:

Step 1: Define the formula for calculating the probability

P = number of elements/total number of elements

Step 2: Perform the calculation

The number of elements (junk emails) = 13

The total number of elements (all emails) = 20

=> P(obtain odd number in experiment) in fraction form = 13/20

=> P(obtain odd number in experiment) in decimal from = 0.65

=> P(obtain odd number in experiment) in percent form = 0.65 x 100 = 65%

Hope this helps!

:)

Answer:

Gabrielle drove to the soccer game at the speed of 18 miles/hour

Step-by-step explanation:

Given: Distance covered = 72 miles

On the way back, she had to drive 18 miles per hour slower due to road construction which made the trip take 9 hours longer.

To find: speed

Solution:

Let speed be x miles/hour

Time taken = distance covered/time taken = [tex]\frac{72}{x}[/tex]  hours

On the way back, she had to drive 18 miles per hour slower due to road construction

So, new speed = ( x - 18 ) miles/hour

Time taken as per new speed = [tex]\frac{72}{x-18}[/tex]  hours

According to question,

[tex]\frac{72}{x-18}-\frac{72}{x}=9\\\frac{1}{x-18}-\frac{1}{x}=\frac{9}{72}\\\frac{x-x+18}{x(x-18)}=\frac{1}{8}\\x^2-18x-144=0\\x^2-24x+6x-144=0\\x(x-18)+6(x-18)=0\\(x-18)(x+6)=0\\x=18\,,\,-6[/tex]

Being a speed, x can not be negative. So, [tex]x=-6[/tex] is rejected

So,

Gabrielle drove to the soccer game at the speed of 18 miles/hour

Answer;

Option B is correct.

The function increases at a constant multiplicative rate.

Step-by-step Explanation:

Complete Question

A table representing the function f(x) = 2(3/2)ˣ is shown below. What is true of the given function?

x | f(x)

0 | 2

1 | 3

2 | 4.5

3 | 6.75

a) The function increases at a constant additive rate.

b) The function increases at a constant multiplicative rate.

c) The function has an initial value of 0.

d) As each x value increases by 1, the y values increase by 1.

Solution

The function provided is

f(x) = 2(3/2)ˣ

We will take as h of the options one at a time to investigate which one is true.

a) The function increases at a constant additive rate.

A function that increases at an additive rate is one whose value as x increases, also changes with a constant difference between consecutive terms. That is, the consecutive terms of the functions for consecutive whole number values of x, will be like an Arithmetic progression with a constant common difference. If this function increased at an additive rate,

f(1) - f(0) = f(2) - f(1) = f(3) - f(2)

Inserting the values

3 - 2 = 4 5 - 3 = 6.75 - 4.5

1 ≠ 1.5 ≠ 2.25

Hence, this statement isn't true.

b) The function increases at a constant multiplicative rate.

For the function to increase at a multiplicative rate, the consecutive terms of the functions for consecutive whole number values of x will behave like a geometric progression with a common ratio. That is, the division of the (n+1)th term and the nth term of the function will always be a constant. That is,

f(1) ÷ f(0) = f(2) ÷ f(1) = f(3) ÷ f(2)

Inserting the values

(3/2) = (4.5/3) = (6 75/4.5)

1.5 = 1.5 = 1.5

The ratio is truly constant, hence, we can conclude that this statement is true and the function increases at a constant multiplicative rate.

c) The function has an initial value of 0.

For this to be true, f(0) = 0.

But from the table, it is evident that f(0) = 2, hence, the initial value of the function isn't 0 and this statement is false.

d) As each x value increases by 1, the y values increase by 1.

We've already checked the difference between consecutive terms of the functions for consecutive whole number values of x, the difference includes, 1, 1.5 and 2.25. Hence, as each x value increases by 1, the y values do NOT always increase by 1 and this statement is false.

Hope this Helps!!!

Answer:

B

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

Yes . This would be an isosceles triangle (2 angles being 9 units long.

Answer:

∛2 can be written as [tex]2^\frac{1}{3}[/tex]. The way i like to remember how to write fractional exponents is that the index of the radical (3 in this case) is the denominator of the fractional exponent and the power of the number inside the radical (1 in this case) is the numerator.

Answer:

2 1/3 is the answer

Step-by-step explanation:

Answer:

x <19.5

Step-by-step explanation:

X-3.3< 16.2

Add 3.3 to each side

X-3.3+3.3< 16.2+3.3

x <19.5

Answer:The second term is -23

Step-by-step explanation:

Step 1- multiply

4x-5=-20

Step 2- subtract

-20 - 3=-23

Answer:

A.

Step-by-step explanation:

The sum of a number, x, and 4 just means x + 4.

If we take twice this sum, it implies that we take the resulting number and multiply it by 2.

Our resulting number is x + 4, so we are left with 2(x + 4).

I hope this helps!

The correct answer is twice the sum of a number and four.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, 2(x+4)

The sum of a number, x, and 4 just means x + 4.

Taking twice of the sum, it implies that we take the resulting number and multiply it by 2.

The resulting number is x + 4, so it is 2(x + 4).

Hence, The correct answer is twice the sum of a number and four.

For more references on expression, click;

https://brainly.com/question/14083225

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Answer:

g(x) = [tex]8(\frac{1}{2})^x[/tex]

Step-by-step explanation:

Let the equation of the graphed exponential function is,

g(x) = [tex]a(b)^x[/tex]

Two points (0, 8) and (1, 2) lie on this graph.

For (0, 8),

g(0) = [tex]a(b)^0[/tex]

8 = a(1)

a = 8

For other point (1, 2),

g(1) = [tex]a(b)^1[/tex]

2 = ab

2 = 8b

b = [tex]\frac{2}{8}[/tex]

b = [tex]\frac{1}{4}[/tex]

Therefore, given exponential function wiil be,

g(x) = [tex]8(\frac{1}{2})^x[/tex]

Answer:

8⋅(1/4)^x

Step-by-step explanation:

trust me thats the answer

Answer:

B, The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

1. Rearrange the first equation to isolate either x or y.

x = -y + 24

2. Plug this new equation into the second equation to find the value of y.

3(-y + 24) + 5y = 100

-3y + 72 + 5y = 100

2y + 72 = 100

2y = 28

y = 14

3. Plug the value of y back into the other equation to find the value of x.

x = -14 + 24

x = 10

There are fourteen 5-point questions and ten 3-point questions.

Answer:

b)  The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

edgen2020

Answer:

t= -2

Step-by-step explanation:

9+4t=7t+15

Subtract 4t from both sides

9=3t+15

Subtract 15 from both sides

-6=3t

3t= -6

Divide both sides by 3

t= -2

In the Pythagorean theorem, a squared minim b squared equals c squared. If you apply that formule to question 2.

17^2-8^2 = 289 - 64 = 225 = 15^2.

Therefore, the answer to first question is yes

Then, for question 2, you do the same thing.

41^2 - 40^2 = 51

Here, 51 is not a square number. Most importantly it is not the square of9,

So this triangle is not right angled

Answer:

C. Hollow cone frustum

Step-by-step explanation:

Revolved it in my head, because the line isn't touching the triangle it will be hollow, because the triangle has a slope the shape will taper.

Answer:

option 3

Step-by-step explanation:

[tex](\sqrt[3]{8})^{\frac{1}{4}x}=(8^{\frac{1}{3}})^{\frac{1}{4}x}\\\\=8^{\frac{1}{3}*\frac{1}{4}x}\\\\=8^{\frac{1}{12}x}\\\\=\sqrt[12]{8}^{x}[/tex]

Answer:

4 units

Step-by-step explanation:

Length would be 6 units and width would be 4 units

6*4 = 24 proving my claim to be true

Answer:

Width = 4 units

Step-by-step explanation:

Let us pose the width as w, and the length as l. If the length is 2 units greater than the width, consider the following;

[tex]l = 2 + w,\\\\w = width,\\l = length[/tex]

The area of this rectangle can be determined through length * width / l * w, and is given to be 24 square units. We can say l = 2 + w instead, solving for the width ( w );

[tex]( 2 + w ) * w = 24,\\2w+w^2=24,\\\left(w-4\right)\left(w+6\right)=0,\\w = 4, w = - 6\\\\Solution - width = 4 units[/tex]

As the width couldn't be a negative value, we had to take the positive of 4 and - 6, which was 4 units.

Answer:

x = 24

Step-by-step explanation:

y=  -16

-16 x 6 = -96

y= -96

x= 4

4 x 6 = 24

x=24

Answer:

n = 20

Step-by-step explanation:

cross multiply and divide

18n = 360

n = 20

Answer:

$70.20

Step-by-step explanation:

We need to first find the cost per gallon of the gas.

The person in front bought 15 gals at $40.50. The price of each gallon will therefore be:

40.50 / 15 = $2.70

You need to buy 26 gallons. The cost will be:

26 * 2.70 = $70.20

You will spend $70.20.

Answer:

-29m+62n

Step-by-step explanation:

5 (3m+6n)-4 (11m-8m)

15m+30n-44m+30n

15m-44m +32n+30n

-29m +62n

Answer:

Option (D).

Step-by-step explanation:

Initial population of the deer [tex]P_{0}[/tex] = 4800

Decrease in the population of the deer after every 8 years = [tex]\frac{1}{2}\times (\text{Initial population})[/tex]

Decrease in population is an exponential process, so the expression representing population will be,

[tex]P_{t}=P_{0}(1-r)^x[/tex]

Where [tex]P_{t}[/tex] is the population after 'x' slots of 8 years.

r = fraction of decrease in the population

x = [tex]\frac{\text{Number of years}}{8}[/tex]

By substituting the values of r and x in the expression,

[tex]P_{t}=P_{0}(1-\frac{1}{2})^{\frac{t}{8}}[/tex]

[tex]P_{t}=4800(\frac{1}{2})^{\frac{t}{8}}[/tex]

Therefore, Sylvia should do few corrections in her expression.

(8) should be replaced by ([tex]\frac{1}{2}[/tex]) and [tex]\frac{t}{2}[/tex] should be replaced by [tex]\frac{t}{8}[/tex].

Option D. will be the answer.

Answer:

the answer is A. y=-2x+3

i hope this helps

Answer:

false

Step-by-step explanation:

Answer:

10 5/8

Step-by-step explanation:

Answer:

10/9

Step-by-step explanation:

average rate of change in 0≤x≤9

=(3-(-7))/(9-0)=10/9

Answer:

The solution is 10/9

Step-by-step explanation:

Step 1: identify the right approach:

Given a function g(x) over a period of time, to find the average rate of change of g(x) over this period of time, we divide the change in g(x) by the change in x.

Step 2: Perform the calculation:

As shown in picture,

x = 0 => g(x) = -7

x = 9 => g(x) = 3

=> The change of x over interval [0, 9] is:

x_change = 9 - 0 = 9

=> The change of g(x) over interval [0, 9] is:

g(x)_change = 3 - (-7) = 10

=> The average rate (r) of change of g(x) over interval [0, 9] is:

r = g(x)_change/x_change = 10/9

Hop this helps!

:)

Answer:

c)

Step-by-step explanation:

The equation of the circle that has a center (-1, 2) and radius of 8 will be (x + 1)² + (y – 2)² = 64. Then the correct option is D.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x – h)² + (y – k)² = r²

A circle with center (-1, 2) and radius of 8.

Then the equation of the circle will be

(x – h)² + (y – k)² = r²

(x + 1)² + (y – 2)² = 8²

(x + 1)² + (y – 2)² = 64

Thus, the equation of the circle that has a center (-1, 2) and radius of 8 will be (x + 1)² + (y – 2)² = 64.

Then the correct option is D.

Learn more about the equation of a circle here:

https://brainly.com/question/10165274

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Answer:

x = 1.32, -5.32

Step-by-step explanation:

x^2 + 4x - 7

Set equal to zero

x^2 + 4x - 7 =0

Add 7 to each side

x^2 + 4x =7

Take the coefficient of x and divide by 2

4/2

Square it

2^2 =4

Add to each side

x^2+4x+4 = 7+4

(x+2)^2 = 11

Take the square root of each side

x+2 = ±sqrt(11)

Subtract 2 from each side

x = -2 ±sqrt(11)

x=1.31662

x=-5.31662

To 2 decimal places

x = 1.32, -5.32

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 1.50

Answer:

$1000.45 is the new price.

Step-by-step explanation:

The fastest way in which to answer this question is to multiply $935.00 by 1.07.  That ".07" comes from "7%."

1.07($935.00) = $1000.45 is the new price.