Use the graph of the function y = 4x to answer the following questions.

The domain of the function is
to
because an exponent can be any real number.

The true statement is an exponential function will MULTIPLY the same number each time.

A linear function is represented as:

y = mx + b

An exponential function is represented as:

[tex]y = ab^x[/tex]

The factor [tex]b^x[/tex] means that the number b is multiplied by itself x times

Hence, the word that completes the blank is (a) exponential

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Exponential functions multiply a constant number each time to show growth or decay.

Exponential functions will multiply the same number each time. They model exponential growth or decay where the value increases or decreases at a constant rate over time.

For example, if you multiply 2 by itself multiple times: 2^1, 2^2, 2^3, the result will keep growing exponentially.

In math, exponential functions are denoted as f(x) = a*b^x, where 'b' is the constant multiplied each time for growth or decay.

Answer:

B)

Step-by-step explanation:

If you try to divide 135 with each number,every number is divisible by 135 XD

Answer:

Sarah spent $15.75 at the movies on a ticket and snacks.

She earned $40 babysitting.

She bought a book for $9.50.

She has $34.75 left.

=> The amount of money she started with:

A = 34.75 + 9.5 - 40 + 15.75 = 20$

Hope this helps!

:)

Answer:

I think the answer is 9 3/4, 9.5, 9 3/8, 9.125

Answer:

a3 = 45

Step-by-step explanation:

a1 = 20

an = a(n-1) *3/2  where n is the term number

a2 = a(2-1) *3/2

     a1 *3/2

We know a1 = 20

a2 = 20*3/2 = 30

a3 = a(3-1) *3/2

    = a2 *3/2

We know a2 = 30

    = 30*3/2 = 45

Answer:

The test statistic is [tex]t = -62.5[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 0.2*500 = 100[/tex]

The alternate hypotesis is:

[tex]H_{1} < 0.2*500 < 100[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

In this problem:

[tex]X = 75, \mu = 100, \sigma = \sqrt{500*0.8*0.2} = 8.94, n = 500[/tex]

So

[tex]t = \frac{75 - 100}{\frac{8.94}{\sqrt{500}}}[/tex]

[tex]t = -62.5[/tex]

The test statistic is [tex]t = -62.5[/tex]

Answer:

[tex]z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{500}}}=-2.795[/tex]  

Step-by-step explanation:

Data given by the problem

n=500 represent the random sample taken

X=75 represent the students in favor to reducing the deficit using only spending cuts

[tex]\hat p=\frac{75}{500}=0.15[/tex] estimated proportion of favor to reducing the deficit using only spending cuts

[tex]p_o=0.2[/tex] is the value that we want to check

z would represent the statistic

System of hypothesis

We want to cehck if the true proportion of students in favor to reducing the deficit using only spending cuts is less than 0.2.:  

Null hypothesis:[tex]p\geq 0.2[/tex]  

Alternative hypothesis:[tex]p < 0.2[/tex]  

The statistic for this case is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info provided we got:

[tex]z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{500}}}=-2.795[/tex]  

Answer:

9.433 miles

Step-by-step explanation:

c^2 = a^2 + b^2

The distance between the planes ABC is the square root of 89 miles, which is approximately 9.43 miles.

The distance between the planes ABC can be found using the Pythagorean theorem since the relationship between the sides AB, BC, and AC forms a right triangle. Given that AB is 5 miles, BC is 8 miles, and AC is the hypotenuse, the distance between the planes ABC can be calculated as follows:

[tex]$$ AC^2 = AB^2 + BC^2 $$[/tex]

Substitute the given values:

[tex]$$ AC^2 = 5^2 + 8^2 $$[/tex]

[tex]$$ AC^2 = 25 + 64 $$[/tex]

[tex]$$ AC^2 = 89 $$[/tex]

Therefore, the distance between the planes ABC is the square root of 89 miles, which is approximately 9.43 miles.

The future value of Michael's investment after 5 years is $44,038.01.

The future value of an annuity can be determined using the following formula:

[tex]FV=PV(1+r/n)^{n}[/tex]

FV = future value

PV = present value

r = annual interest rate

n = number of periods interest held

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 20 quarters (5 years x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $2,440.38

Total Interest = $440.38

Thus, the value of Michael's investment after 5 years is $2,440.38.

Answer:

18 inches

OQ2 + PQ2 = OP2

PQ2 = OP2 - OQ2

= (OR + PR) SQUARE - OQ2

= (24/2 + 10 ) SQUARE - 24/12Square

= 22square - 12square

PQ = Root 340

= 18 inches...

The answer is 18 inches.

OQ2 + PQ2 = OP2

PQ2 = OP2 - OQ2

= (OR + PR) SQUARE - OQ2

= (24/2 + 10 ) SQUARE - 24/12Square

= 22² - 12²

PQ = √ 340

= 18 inches.

Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.

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Answer:

Step-by-step explanation:

The measure of center of a group of data is a single central value such as the mean and the median.

The mean is the arithmetical average of the sum of the data and the median is the middle value of the data when placed in ascending sequence.

The measure of variability  gives an indication of the spread of the data about the mean. Examples are  the Standard Deviation and the Interquartile Range.

Explaining the difference between a measure of center and a measure of variability.

The measure is an estimate or assesses the extent, quality, value, or effect of (something).

The measure of the center of a group of data is a single central value such as the mean and the median.

The mean is the arithmetical average of the sum of the data and the median is the middle value of the data when placed in ascending sequence.

The measure of variability gives an indication of the spread of the data about the mean. Examples are the Standard Deviation and the Interquartile Range.

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Answer:D

Step-by-step explanation:

Answer:1

Step-by-step explanation:

(x+2)(x+3)

x^2+3x+2x+6

x^2+5x+6

Therefore the coefficient of x^2 is 1

Answer:

1

Step-by-step explanation:

(x+2) (x+3)

FOIL

x^2 + 3x+2x+6

x^2 +5x+6

The coefficient of x^2 is 1

Answer:

7 students

Step-by-step explanation:

Answer:

the answer is 7 people

Step-by-step explanation:

have a great day!

Answer:

x= -7    x=3

Step-by-step explanation:

(x-2)(x+5)=18

FOIL

x^2 +5x -2x-10 = 18

Subtract 18 from each side

x^2 +5x -2x-10-18 = 18-18

x^2 +3x -28 =0

Factor

What 2 numbers multiply to -28 and add to 3

7*-4 = -28

7-4 =3

(x+7) (x-3) =0

Using the zero product property

x+7 =0    x-3 =0

x= -7    x=3

Answer:

− 2( 5 y + 3 ) ( y − 6 )

Step-by-step explanation:

hope it helps

Answer:

800

Step-by-step explanation:

1.35x = 1080 -->

x = 1080/1.35 -->

800

Answer:Ella's Procedure And Conclusion are incorrect

Step-by-step explanation:

Answer:

Ellas procedure and conclusion are incorrect

Step-by-step explanation:

Answer: add 4 on both sides

Step-by-step explanation:

Answer:

Isolate the constant

Step-by-step explanation:

i just took it on edge A

Ahmed's first error was in step 3 where he failed to express 54 in terms of π.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

We have,

Diameter = 6 cm

1. Radius = diameter/2

= 6/2

= 3cm

2. Area of base = π × 3²

                          = 9π cm²

3. Multiply the area of the base by the height

= 9π x 6

= 54π cm³

4. Divide 54π by 3 to find the volume of the cone

= 54π/3

= 18π cm³

So, the volume of the cone is 18π cm³.

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Answer:

8

Step-by-step explanation:

0.2:2.5*100 =

( 0.2*100):2.5 =

20:2.5 = 8

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 4.9

For the alternative hypothesis,

µ < 4.9

This is a left tailed test.

If the population variance is 0.36, the population standard deviation would be √0.36 = 0.6 psi

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 4.9

x = 4.8

σ = 0.6

n = 210

z = (4.8 - 4.9)/(0.6/√210) = - 2.42

Looking at the normal distribution table, the probability corresponding to the z score is 0.0078

Since alpha, 0.1 > than the p value, 0.0078, then we would reject the null hypothesis. Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications.

Answer:

  5.7 meters

Step-by-step explanation:

The Pythagorean theorem can be used to find the second leg (b) of a triangle with diagonal (c) 6 meters and first leg (a) 2 meters.

  c^2 = a^2 + b^2

  6^2 = 2^2 +b^2

  b^2 = 36 -4 = 32

  b = √32 ≈ 5.7 . . . . meters

The kitchen is about 5.7 meters long.

The length of the kitchen, where a mouse has made holes in opposite corners with a diagonal distance of 6 meters across a width of 2 meters, is approximately 5.7 meters.

To find the length of the kitchen where a mouse has made holes in opposite corners, forming a diagonal of 6 meters across a width of 2 meters, we can use the Pythagorean theorem.

1. Understanding the problem:

  - The width of the kitchen (distance between the holes along one side) is w = 2 meters.

  - The diagonal distance (distance between the holes) is d = 6 meters.

2. Applying the Pythagorean theorem:

  - In a rectangle, the diagonal d , the width w, and the length l form a right triangle.

  - The Pythagorean theorem states [tex]\( d^2 = w^2 + l^2 \)[/tex].

3. Substitute the given values:

  [tex]\[ 6^2 = 2^2 + l^2 \][/tex]

  [tex]\[ 36 = 4 + l^2 \][/tex]

4. Solve for [tex]\( l^2 \)[/tex] :

  [tex]\[ l^2 = 36 - 4 \][/tex]

  [tex]\[ l^2 = 32 \][/tex]

5. Find l (length of the kitchen):

  [tex]\[ l = \sqrt{32} \][/tex]

  [tex]\[ l \approx 5.7 \text{ meters (rounded to the nearest tenth)} \][/tex]

Therefore, the length of the kitchen is approximately [tex]\( \boxed{5.7} \)[/tex]meters.

The length of the kitchen, rounded to the nearest tenth, where a mouse has made holes in opposite corners with a diagonal distance of 6 meters across a width of 2 meters, is [tex]\( \boxed{5.7} \)[/tex] meters. This solution utilizes the Pythagorean theorem to determine the missing dimension of the rectangle based on given measurements.

Answer:

The total number of ways of assignment is 314,790,828,599,338,321,972,833,000.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]

In this case we need to determine the number of ways in which the drugs are assigned to each mouse.

It is provided that new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes.

Drug A is to be given to 22 mice.

Compute the number of ways to assign drug A to 22 mice as follows:

[tex]{60\choose 22}=\frac{60!}{22!(60-22)!}\\\\=\frac{60!}{22!\times 38!}\\\\=14154280149473100[/tex]

Now the remaining number if mice are: 60 - 22 = 38.

Compute the number of ways to assign drug B to 22 mice as follows:

[tex]{38\choose 22}=\frac{38!}{38!(38-22)!}\\\\=\frac{38!}{22!\times 16!}\\\\=22239974430[/tex]

Now the remaining number if mice are: 38 - 22 = 16.

Compute the number of ways to assign no drug to 16 mice as follows:

[tex]{16\choose 16}=\frac{16!}{16!(16-16)!}\\\\=1[/tex]

The total number of ways of assignment is:

[tex]N = {60\choose 22}\times {38\choose 22}\times {16\choose 16}\\\\=14154280149473100\times 22239974430\times 1\\\\=314,790,828,599,338,321,972,833,000[/tex]

Thus, the total number of ways of assignment is 314,790,828,599,338,321,972,833,000.

Final answer:

The number of ways to assign treatments to the mice can be found using combinations. The calculation involves selecting a certain number of mice from the total pool and dividing it by the number of ways to arrange those mice within the group. The total number of ways to assign treatments to the mice is approximately 10,682,514,784,300.

Explanation:

When assigning treatments to the mice, we have 22 mice for drug A, 22 mice for drug B, and 16 mice for the control group. The assignment of treatments can be thought of as distributing the mice among these three groups.

To find the number of ways this can be done, we can use the concept of combinations. We can think of selecting 22 mice for drug A from the total pool of 60 mice, and then selecting 22 mice for drug B from the remaining pool. The remaining 16 mice automatically go to the control group.

The number of ways to select 22 mice out of 60 is denoted as C(60,22) and is calculated using the formula C(n, r) = n! / (r!(n-r)!). Therefore, the number of ways to assign treatments to the mice is C(60,22) multiplied by the number of ways to assign the remaining 22 mice to drug B, which is C(38,22).

Using a calculator or software, we can calculate C(60,22) as approximately 95,023,780 and C(38,22) as approximately 112,385.

Therefore, the total number of ways to assign treatments to the mice is approximately 95,023,780 * 112,385 = 10,682,514,784,300.

Answer: Each gallon costs $3.85

Step-by-step explanation:

We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:

$46.20 ÷ 12 = $3.85

Each gallon costs $3.85

I hope this helps!

Answer:

Each gallon costs $3.85

Step-by-step explanation: We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:$46.20 ÷ 12 = $3.85Each gallon costs $3.85I hope this helps!

Answer:it’s ACD=ECB

Step-by-step explanation:

The correct option is Segment Addition Postulate.

Similarity of triangles. The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Here, we have,

The segment addition postulate states that where there are two points on a line A and C and a third point B can only be located on the line segment AB if and only if the the distances between point A and point B as well as the distance between point B and point C satisfy the equation AB + BC = AC

Therefore, given that in the figure,  the point B is in between point A and point C on segment AC then AB + BC

Similarly, AD = AE + ED.

The correct option is Segment Addition Postulate.

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complete question:

BE || CD 1. Given 2. ∠A ≅ ∠A 2. Reflexive Property 3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅. 4. ∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅. 5. ΔABE ∼ ΔACD 5. AA Similarity Postulate 6. AC AB = AD AE 6. Definition of Similar Triangles 7. AC = AB + BC, AD = AE + ED 7. ??? 8. AB + BC AB = AE + ED AE 8. Substitution 9. AB AB + BC AB = AE AE + ED AE 9. Addition 10. BC AB = ED AE 10. Subtraction Fill in the missing reason for the proof. A) Transitive Property B) Subtraction Property C) SSS Similarity Theorem D) Segment Addition Postulate

Answer:

Callie's comparison of two options for college education

The true statement is:

She would save $11,300 by choosing option A.

Step-by-step explanation:

Cost Analyses:

Option A:            Community College  + University               Total Expenses

Tuition & Fees    $5,800 ($2,900 x 2) + $19,000 ($9,500 x 2)    = $24,800

Scholarships       ($1,600) ($800 x 2)   + ($20,000) ($10,000 x 2)=($21,600)

Room & Board    $2,500 ($1,250 x 2)  + $23,000 ($11,500 x 2) =   $25,500

Work-Study                                            + ($4,000)  ($2,000 x 2)  = ($4,000)

Total Cost           $6,700                       + $18,000      =                    $24,700

Option B:            4 years' University

Tuition & Fees    $38,000 ($9,500 x 4)

Scholarships       ($40,000) ($10,000 x 4)

Room & Board    $46,000 ($11,500 x 4)

Work-Study         ($8,000)  ($2,000 x 4)

Total Cost          $36,000

Difference between the two options = $11,300 ($36,000 - $24,700

Answer: She would save $11,300 by choosing option A

Step-by-step explanation:

Community College Financial Analysis:

Tuition and fees = 2900

Scholarship and grant = 800

Rooms and board = 1250

University Financial Analysis:

Tuition and fees = 9500

Scholarship and grant = 10000

Rooms and board = 11500

Work study - 2000

Option A :

First two years at college :2 × (2900 + 1250 - 800)

2 × (3350) = $6700

2 years at university : 2 × (9500 +11500 - 2000 - 10000)

2 × 9000 = 18000

Option A total = $(18,000 + 6700) = $24,700

Option B :

4 years at university : 4 × (9500 +11500 - 2000 - 10000)

4 × 9000 = $ 36000

She would be saving $(36,000 - 24,700) = $11,300 by choosing option A

Answer:

1728 cubic in

Step-by-step explanation:

24 in x 8 in x 9 in = 1728 cubic in

Final answer:

The volume of water in Sam's aquarium is 1,728 cubic inches, calculated by multiplying the length (24 inches), width (8 inches), and height (9 inches) of the aquarium.

Explanation:

The volume of Sam's aquarium can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. The dimensions given are 24 inches long, 8 inches wide, and 9 inches tall.

To find out how many cubic inches of water the aquarium can hold, we multiply these dimensions:

× 24 inches (length)
× 8 inches (width)
× 9 inches (height)

Thus, the volume of the aquarium is:

24 inches × 8 inches × 9 inches = 1,728 cubic inches

Answer:

B graph 2

Step-by-step explanation: