What is the average rate of change? Problem in the picture

Answer:

Step-by-step explanation:

All you have to do is put the values of x in the inequality.

The first, x=-45:

put that into x/-5 = -45/-5 =9 and so on.

Hope this helps :)

Answer: 4

Step-by-step explanation: 15-11=4

The statement that is true is: B. A piece of copy paper is approximately four times thicker than a human hair.

Scientific notation is a system of expressing extremely large figures in a standard form.

Considering the figures given in the question,

Thickness of copy paper = 4 × 10^-3 in

Thickness of human hair = 1 × 10^-3 in

So that;

Thickness of copy paper/ Thickness of human hair = 4 × 10^-3/ 1 × 10^-3

                                                    = 4 × 10^-3 * 10^3

                                                    = 4

Thus it can be concluded that the copy paper is approximately four times thicker than a human hair. Thus option B.

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The measure of angle TSK is given as follows:

m < TSK = 35º.

On a triangle, the sum of the measures of the internal angles is of 180º.

For triangle TSK, the internal angle measures are given as follows:

Then the measure of angle TSK is obtained as follows:

m < TSK + 22 + 123 = 180

m < TSK = 180 - 145

m < TSK = 35º.

Meaning that the last option is correct.

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Answer:

So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.

Step-by-step explanation:

Given,

The equation is  

5x-2w+t

and also given the

x=3

w=1/2

and t=8

Now ,

if we substitute the value of x,w and t,

We get,

5 × 3 - 2 × (1/2) + 8

= 15 - 1 + 8

= 22

So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.

The coordinates of the image of triangle ABC are A''(x, y) = (- 4, 2), B''(x, y) = (0, 0) and C''(x, y) = (2, 4).

Triangles are generated by the location of three distinct points on Cartesian plane. In this problem we find the representation of a triangle, whose vertices are listed below:

A(x, y) = (1, 0), B(x, y) = (3, - 1), C(x, y) = (4, 1)

We need to apply the following rigid transformations:

Translation

(x, y) → (x - 3, y + 1)

Dilation centered at the origin with scale factor 2

(x, y) → (2 · x, 2 · y)

Now we proceed to determine the coordinates of the image:

Translation

A'(x, y) = (- 2, 1), B'(x, y) = (0, 0), C'(x, y) = (1, 2)

Dilation

A''(x, y) = (- 4, 2), B''(x, y) = (0, 0), C''(x, y) = (2, 4)

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113.097 is the area (i used 3.14) pls comment for explanation :)

The required solution of the given expression δ = 0.0002. as of the given conditions

Functions is 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 |x - 3| < δ, we want to find a value of delta such that |5x - 15| < 0.001.

Starting with the inequality |x - 3| < δ, we can substitute x = 3 + delta or x = 3 - δ. Let's consider the case x = 3 + δ,

|5x - 15| = |5(3 + δ) - 15|
            = |15 + 5δ- 15|
                = |5δ|

Now, we want |5δ| to be less than 0.001. So, we can divide both sides of the inequality by 5,

|5δ|/5 < 0.001/5

|δ| < 0.001/5

Therefore, if the delta is less than 0.001/5, we have |5x - 15| < 0.001.

Similarly, if x = 3 - delta, we have:

|5x - 15| = |5(3 - δ) - 15| = |15 - 5δ - 15| = |-5δ|

|-5δ|/5 < 0.001/5

|δ| < 0.001/5

So, if δis less than 0.001/5, then |5x - 15| < 0.001 for both x = 3 + delta and x = 3 - δ.

Therefore, if |x - 3| < 0.001/5, then |5x - 15| < 0.001.

So, δ= 0.001/5 = 0.0002.

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a) The rate in this problem is 23 miles.

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel 276 miles.

Unit rate is the ratio of two different units, with denominator as 1.

Given:

A certain car gets 23 miles to the galloon open highway.

a) The rate in this problem is 23 miles

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel

23/ 1 = x/ 12

x= 23 . 12

x= 276 miles

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Answer:

C

Step-by-step explanation:

The area formula of a circle is A=[tex]\pi r^{2}[/tex], where r (or radius) is equal 1/2 times diameter (or d/2). So pi times (10/2)^2= 78.54 and  pi times (16/2)^2=201.06.   201.06-78.54 = about 122.52, which is closest to 122.46, or C.

The ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

Given that the ant can travel at a constant speed of 980 inches every 5 minutes.

Thus,

5 minutes = 980 inches

1 minute = x inches

Using cross multiplication method or Butterfly method of multiplication we have:

x = 980/5

x = 196 inches.

In 7 minutes the ant can travel:

(7)(196) = 1372 inches.

Hence, the ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.

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To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.

(a) The yearly percent rate of growth of the world population is 1.0103%.

(b) The world population in 2020 was 7.68 billion people. The model predicts that the world population in 2026 will be 8.336 billion people.

(c) The projected average rate of change of the world population between 2020 and 2026 is 0.556 million people per year.

(a) The yearly percent rate of growth of the world population can be found by taking the exponential rate of change of the equation. The rate of change is 1.0103%.

(b) To find the world population in 2020, we can plug in t=0 into the equation. This gives us P=7.68 billion people. To find the world population in 2026, we can plug in t=6 into the equation. This gives us P=8.336 billion people.

(c) To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.

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The value of CD is 9.92 cm

Given:

Find: CD

Triangle ABC is an isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,

m<A = <mB = 72°

The sum of the measures of all interior angles is 180°, thus

m<C =  180° -72° - 72° = 36°

The area of the triangle ABC is

AABC= 1/2AC.BC.sin<C

If we expand,

AC = 10.43cm

Consider right triangle ACD. In this triangle,

sin <A = CD/AC

sin 72° = CD/10.43

therefore,

CD = 9.92 cm.

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Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°

Find: CD

Add  up all the sides:

-x^2+2x+3x-4+2x^2+5

x^2+5x+1

The value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

A relation is a function if it has only One y-value for each x-value.

The given function is f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 such that x=5

We need to find the value of f(5)

Plug x=5 in the above function

f(x) = x⁴ - 7x³ + 2x² + 40x

f(5) = 5⁴ - 7(5)³ + 2(5)² + 40(5)

=625-875+50+200

=0

Hence, the value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

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Complete question is below

f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 find value of f(5)

The composite function is given below with examples.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Consider two functions f(x) and g(x).

Now,

f o g = f(g(x)) is called a composite function.

f(x) = 2x + 1

g(x) = x + 2

So,

(f o g)(x)

= f(g(x))

= f(x + 1)

= 2 (x + 1) + 1

= 2x + 2 + 1

= 2x + 3

Thus,

The composite function is given above with examples.

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The volume of the triangular prism is 30. 04 cubic yards

The volume of the cylinder is  380.38 cubic km

The formula for calculating the volume of a triangular prism is expressed as;

Volume = 1/2 bhl

Now, substitute the values

Volume = 1/2 × 3.08 × 5.84 × 3. 34

Multiply the values

Volume = 30. 04 cubic yards

The formula for the volume of a cylinder is expressed as;

Volume = πr²h

Radius = 3km

Substitute the values

Volume = 3. 14 × 9 × 13.46

Multiply

Volume = 380.38 cubic km

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The values 6, 4 and 12 are the measures of PR, PQ and RI respectively.

The given diagram is a triangle and the expression to be used based on the theorem is expressed as:

TP/TQ = PR+3/15

3/5 =  PR+3/15

5(PR +3)= 3(15)
5(PR + 3) = 45

PR + 3 = 9

PR = 9 - 3

PR = 6

For the measure of PQ

PQ^2 = 5^2 - 3^2

PQ^2 = 25 - 9

PQ = 4

Determine the measure of RI

3/PQ = TR/RI
3/4 = 9/RI

1/4 = 3/RI
RI = 12

Hence the measure of PR, PQ and RI are 6, 4, and 12 respectively

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Answer: god

Step-by-step explanation: god god god god god god god god

The mean and the standard deviation are  144 and 4.3200

from the question, we have the following parameters that can be used in our computation:

Proportion, p = 64%

Sample size, n = 225

The mean is calculated as

Mean = np

Substitute the known values in the above equation, so, we have the following representation

Mean = 64% * 225

Mean = 144

The standard deviation is calculated as

SD = √Mean * (1 - p)

substitute the known values in the above equation, so, we have the following representation

SD = √144 * (1 - 64%)

Evaluate

SD = 4.3200

Hence, the mean is 144

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Complete question

Coffee: The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample of 225 U.S. adults is selected. Round your answers to at least four decimal places as needed.

(a) Find the mean

(b) Find the standard deviation

Answer:

[tex]a \sqrt[5]{b} [/tex]

Step-by-step explanation:

solution Given:

[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]

since i indices rule if the power is same it can be multiplied or divided.

[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]

since power is added of like terms in multiplication

[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]

again simplifying

[tex] \sqrt[5]{ {a}^{5} b} [/tex]

by using indices formula

[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]

we get

[tex]a \sqrt[5]{b} [/tex]

Answer:

[tex]a \sqrt[5]{b}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]

As the exponents are the same,

[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]

Collect like terms:

[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]

Simplify the exponents:

[tex](a^5b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]

[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]

Simplify:

[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]

[tex]a \cdot b^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]a \sqrt[5]{b}[/tex]

The solution is, he is now 21 yrs old.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

William is 6 years older than Camila.

Nine years ago he was twice Camila’s age.

let, he is now = x yrs

Camila’s age = y yrs.

so, we get,

x-y = 6 .....(1)

and, x-9 = 2(y-9) ....(2)

solving we get,

x-9 = 2(x-6-9)

or, x = 21

Hence, The solution is, he is now 21 yrs old.

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Using a system of equations, the number of points given for an arrow in target B is 7.

A system of equations means two or more equations solved at the same time or concurrently.

A system of equations is also described as simultaneous equations since they are solved simultaneously.

                              Target A    Target B   Total Score

Rence shots                3                1                  19

Sunil shots                  2                2                22

Let the points for an arrow into target A = x

Let the points for an arrow into target B = y

3x + y = 19 ... Equation 1

2x + 2y = 22 ... Equation 2

Multiply Equation 1 by 2:

6x + 2y = 38 ... Equation 3

Subtract Equation 2 from Equation 3:

6x + 2y = 38

-

2x + 2y = 22

4x = 16

x = 4

From Equation 1, substitute x = 4:

3x + y = 19

3(4) + y = 19

12 + y = 19

y = 19 -12

y = 7

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Answer:

$ 546.00

Step-by-step explanation:

Simple Interest = P x r x  t

where t = number of years

r = interest rate per year as a decimal

P = amount invested(deposit)

We are given that r = 7.8% per year = 7,8/100 = 0.078

However, since this is the yearly interest, the monthly interest = 0.078/12

The time period is 42 months

Initial deposit = $2,000

Therefore interest
I = 2000x (0.078/12) x 42 =  $ 546.00

The value of the variables in the parallelogram are such that:

This is a parallelogram which means that angles on the same line will add up to 180 degrees.

The value of x is therefore:

( x - 5 ) + ( 2x + 11 ) = 180

3x + 6 = 180

x = ( 180 - 6 ) / 3

x = 58

The value of y is:

2 y + ( 58 - 5 ) = 180

2 y = 180 - 53

y = 127 / 2

y = 63.5

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The required, Ask each regular customer which flavor they would like to see in his shop, would be the best method. Option C is correct.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Asking each regular customer which flavor they would like to see in the shop would be the best method because the customers are the ones who will be buying and consuming the ice cream, so their preferences are the most important. By directly asking the customers for their opinions, the owner can get a better understanding of what flavors people are interested in, and it can also help to build a relationship with the customers by showing that their input is valued.

Option A, determining the current best-selling flavor, would only provide information about the current sales and not necessarily reflect customers' interests in new flavors. Option B, visiting other ice cream shops, could provide some ideas, but it would not necessarily reflect the local market and the preferences of the shop's specific customer base. Option D, randomly generating customers to survey, may not be representative of the actual customer base and may not provide a reliable indication of which new flavor to sell.

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Answer:

C = 235

Step-by-step explanation:

given the graph passes through (10, 1 ) then the coordinates of the point make the equation true.

substitute x = 10, y = 1 into the equation and solve for C

10² + 1² + 12(10) + 14(1) - C = 0

100 + 1 + 120 + 14 - C = 0

235 - C = 0 ( subtract 235 from both sides )

- C = - 235 ( multiply both sides by - 1 )

C = 235

Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.

The vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:

A = (90°, 1 + 2) = (90°, 3)

Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).

b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:

A = (90°, -1)

Therefore, the coordinates of the vertex A of the curve y = -sin x are

(90°, -1).

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The value of 4(3/2) times 1 is 6.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

Given:

4(3/2) times 1

Simplifying 4 (3/2) we get

= 4(3/2)

= 12/2

= 6

Now, we have to find 6 times of 1.

= 6 x 1

= 6

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