find constant rate of change​

Answer:

f(x)=3x+4 and g(x)=2x3

find.

a:fg(x)

b:gf(x)

Answer: $0.08

Step-by-step explanation:

First, let's find last week's price

Take 35.40 divided by 12 = $2.95 per gallon

Next, find this week's price

Take 25.83 divided by 9 = $2.87 per gallon

Then take 2.95 - 2.87 = $0.08

The tree will be 75 feet tall when it will be fully grown.

The total tree height is the distance between the tree's base and its highest point on the ground. A yardstick provides a quick and relatively accurate way to gauge the height of a tree.

If the tree is currently 60 feet tall and is approximately 80% of its full height, we can assume that the tree will be 100% of its full height when it is fully grown. To determine the full height of the tree, we can use the proportion:

60 feet / 80% = X feet / 100%

We can then cross-multiply to solve for X:

X = (60 feet * 100%) / 80%

= 75 feet

So, when the tree is fully grown, it will be approximately 75 feet tall.

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In the first circle, the measure of angle ABC is 24°

In the second circle, the measure of angle ABC is 20°

From the question, we are to determine the measure of angle ABC

In the first diagram,

The measure of the arc is 48°

From one of the circle theorems, we have that

The angle subtended by an arc in a circle is twice the angle subtended at the circumference.

Then, we can write that

2 × ∠ ABC = 48°

∠ ABC = 48°/2

∠ ABC = 24°

Question 5

Using the same theorem,

The angle subtended by an arc at the center of the circle is twice the angle subtended at the circle

∠ ABC = 1/2 × 40°

∠ ABC = 20°
Hence, the measure of the angle is 20°

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Answer:

Step-by-step explanation:

[tex]log_{10}(2000xy)-(log_{10}x})(log_{10}y)=4\\\\log_{10}(2000(xy))-log_{10}(xy)=4\\\\log_{10}(2000)+log_{10}(xy)-log_{10}(xy)=4\\\\log_{10}(2(1000)=4\\\\log_{10}2+log_{10}(1000)=4\\\\log_{10}2+log_{10}(10^3)=4\\\\log_{10}2+3log_{10}(10)=4\\\\log_{10}2\approx0.3\\\\Hence,\\\\log_{10}2+3\neq 4[/tex]

[tex]log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\\\\log_{10}(2(yz))-log_{10}(yz)=1\\\\log_{10}2+log_{10}(yz)-log_{10}(yz)=1\\\\log_{10}2\neq 1[/tex]

[tex]log_{10}(zx)-(log_{10}z)(log_{10}x)=0\\\\log_{10}(zx)-log_{10}(zx)=0\\\\0\equiv0[/tex]

If you assume that there is a 0.990.99 percent chance that you will find a prize in the cereal box, the odds are 99:1.

A probability is a measure of how likely or likely it is that a certain event will occur. Probabilities can be represented as percentages between 0% and 100% as well as proportions between 0 and 1.

How likely an event is to occur is determined by the concept of probability. For instance, meteorologists can predict the possibility of rain by looking at weather patterns. In epidemiology, probability theory is used to understand the relationship between exposures as well as the risk of health effects.

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The sum of two number is 92. Their difference i 20Let x and y represent the 2 number. Let x=the lager value and smaller valuex = 92 + 20 = 11,y = 92 - 20 = 72

Let x = the larger value and y = the smaller value.

We know that the sum of x and y is 92, so

x + y = 92

We also know that the difference between x and y is 20, so

x - y = 20

Add the two equations to get

2x = 112

Divide by 2 to get

x = 112

Substitute x = 112 into the first equation to get

112 + y = 92

Subtract 112 from both sides to get

y = 72

Therefore, the two numbers are x = 112 and y = 72.

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Answer:

it would be quadrant |||

so answer choice C

Step-by-step explanation:

Let's say Chloe spent X

Then Amy spent 60% more so Amy spent

X+60% of X =X + 0.6X =1.6X

Becky spent 15% of what Chloe spent so amount spent by Becky =15% of X = .15X

Now, in total, they spent 0.15X+ X + 1.6X =2.75X which is given as £55

So , X=55/2.75 = 20

Amount spent by Amy = 1.6X = 1.6 *20 =£32

The value of x in the solution set of the inequality is -4.

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).

9(2x+1) < 9x - 18

2x+1 < x - 2

2x < x - 3

x < -3

This means that x can be any value less than -3 (but not equal to -3 since the sign is < and not ≤) . Hence, the answer is -4.

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Answer:

-4

Step-by-step explanation:
taking  test

The value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18 is -4.

Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

9(2x + 1) < 9x - 18

18x + 9 < 9x - 18

18x - 9x < -18 - 9

9x < -27

x < -3

x = (-∞, -3)

Hence, the solution set of the given inequality is the set of numbers less than -3. Among the given choices, only -4 is less than -3. Therefore, the value of x is -4.

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Answer: -4

Step-by-step explanation: edge2020

It will take 35 years to double the population

Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it. For instance, if you properly answered 68 out of 100 questions on a test, you would have received a 68% grade (68/100).

According to the given information

Let [tex]P(0)[/tex] be initial population

and K be the growth rate

Then Population of the country after t years

[tex]P = P(0)e^{Kt}[/tex]

Let x be the present population

2x will be the double of present population

And we know

The growth rate K = 0.02%

So

The value of t could be determined as follows

[tex]xe^{0.02t}=2x[/tex]

[tex]e^{0.02}=2[/tex]

[tex]0.02t=ln(2)[/tex]

Multiply both sides by 1000

0.02t × 1000 = ln(2) × 1000

Refine

20t = ln(2) × 1000

Divide both sides by 20

[tex]\frac{20t}{20}=\frac{ln(2).1000}{20}[/tex]

t = [tex]ln(2).500[/tex]

t = 0.693×50

t = 34.65 years

t = 35 years

It will take 35 years to double the population

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Yes, this statement is correct because in quadrilaterals if two lines are parallel, then the other two sides have to be equal in length.

Triangles that are equal in all ways and interchangeable are typically described as being congruent.

A triangle with equal legs, such as an isosceles triangle, may have equal legs that are also equal to the two equal legs of another triangle with equal legs, but if the included angle is different, the triangles are not congruent.

Two sides are simply equal if their lengths are the same.

When it comes to parallelograms, both opposite side pairs are equal and parallel.

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Answer:

x intercept= (1.5,0)

y intercept= (0,-2)d

Step-by-step explanation:

Rearrange the equation to be in the form y=mx+c:

4x-1=3y+5

y=(4x-6)/3

y=4/3(x)-2

y intercept= c from equation above =-2

y intercept=-2

x intercept => when y=0

sub 0=y

0=4/3(x)-2

2=4/3(x)

x=1.5

The function has no vertical asymptotes and the horizontal asymptotes of the function is y=0.

In the given question,

Consider the following function.

f(x) = e^{−x^2}

We have to find the vertical asymptote(s), x = Find the horizontal asymptote(s) or y = .

As we know that, a vertical asymptote is a line that runs vertically and guides the graph of the function but does not actually exist on it. Due to its position at an x-value that is outside of function's domain, it is difficult for the curve to ever pass it.

The function f(x) = e^{−x^2} has no undefined points. So the function has no vertical asymptotes.

The limit of the function at x→±∞ is calculated as follows:

[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = [tex]\lim_{x\rightarrow \pm\infty }[/tex]e^{−x^2}

[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = 0

So the horizontal asymptotes of the function is y=0.

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The right question is:

Consider the following function. (If an answer does not exist, enter DNE.) f(x) = e^{−x^2}. Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.)

y =

The real and imaginary parts of the three complex numbers are:

In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:

Case 1: - 7

The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.

Case 2: 5 - √(- 24)

First, we rewrite the entire expression in standard form:

5 - √(- 24)

5 - √[(- 1) · 24]

5 - √(- 1) · √24

5 - i √24

5 - i 2√6

The real part is 5 and the imaginary part is 2√6.

Case 3: (6 - i) · (6 + i)

We expand and simplify the resulting expression:

(6 - i) · (6 + i)

6 · (6 - i) + i · (6 - i)

36 - i 6 + i 6 - i²

(36 - i²)

36 + 1

37

37 + i 0

The real part is 37 and the imaginary part is 0.

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Answer:

The real and imaginary parts of the three complex numbers are:Real part: - 7, Imaginary part: 0Real part: 5, Imaginary part: 2√6Real part: 37, Imaginary part: 0How to determine the real and imaginary component of a complex number.In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:Case 1: - 7The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.Case 2: 5 - √(- 24)First, we rewrite the entire expression in standard form:5 - √(- 24)5 - √[(- 1) · 24]5 - √(- 1) · √245 - i √245 - i 2√6The real part is 5 and the imaginary part is 2√6.Case 3: (6 - i) · (6 + i)We expand and simplify the resulting expression:(6 - i) · (6 + i)6 · (6 - i) + i · (6 - i)36 - i 6 + i 6 - i²(36 - i²) 36 + 137 37 + i 0The real part is 37 and the imaginary part is 0.

Step-by-step explanation: hope this helps0^0

Answer: 18

Step-by-step explanation:

there you go <3

Answer: Median is 12, mode is 5, mean is 13.71

Step-by-step explanation:

Answer:

The median is 18

The mode is 5

The mean is 13

Step-by-step explanation:

The transformation from the parent function is a translation by 2 units right and 1 unit up

From the question, we have the following function that can be used in our computation:

f(x) = x³

g(x) = (x − 2)³ - 1

First, we have the transformation to be:

From f(x) = x³ to f'(x) = (x − 2)³

This means the function is translated right by 2 units

Next, we have:

From f'(x) = (x − 2)³ to g(x) = (x − 2)³- 1

This means the function is translated up by 1 unit

Hence, the transformation is 2 units right and 1 unit up

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The area of a rectangle is 42 quare millimeter. The length is 7 millimeter. 28 millimeters is the perimeter of the rectangle.

Perimeter = 2 × (Length + Width)

Perimeter = 2 × (7 + 6)

Perimeter = 28 millimeters

To calculate the perimeter of a rectangle, we need to multiply the length and the width of the rectangle, and then multiply that value by 2. In this case, the length is 7 millimeters, and the area is 42 square millimeters. To calculate the width, we can divide the area by the length, which is 42 divided by 7, which is equal to 6. So the width is 6 millimeters. Now we can calculate the perimeter using the formula: Perimeter = 2 × (Length + Width). Plugging in the values, we get: Perimeter = 2 × (7 + 6) = 28 millimeters.

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Answer:

Step-by-step explanation:

To find the value of z such that 0.12 of the area lies to the right of z, we need to know the distribution of the data and the total area under the curve. If the data follows a normal distribution, the area under the curve is always 1, and 0.12 of the area corresponds to a z-value of approximately 0.84.

We can use a standard normal table or a calculator to find the exact value of z. For example, using a standard normal table, we can find that the z-value corresponding to an area of 0.12 to the right of z is 0.8416.

Therefore, the value of z such that 0.12 of the area lies to the right of z is approximately 0.84.

The measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, center of dilation is P and scale factor is 1/3.

In the given triangle ABC, AB=12.4 units, AC=6.7 units and BC=12.7 units

Now, A'B'=12.4/3

A'B'= 4.1 units

A'C'=6.7/3

A'C'= 2.2 units

B'C'=12.7/3

B'C'= 4.2 units

Therefore, the measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.

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The f< [tex]f_{max}[/tex] the semicircular disk does not slip at the given instant.

The semicircular disk having a mass of 10 kg.

ω = 4 rad/s,  θ = 60 °

First we have to draw the free body diagram,

Calculate the distance AG.

[tex]$$\begin{aligned}A G & =\sqrt{O G^2+O A^2-2 \times O G \times O A \times \cos \theta} \\& =\sqrt{\left(\frac{4 \times 0.4}{3 \pi}\right)^2+0.4^2-2 \times \frac{4 \times 0.4}{3 \pi} \times 0.4 \times \cos 60^{\circ}} \\\end{aligned}$$[/tex]

=0.3477 m.

Calculate the angle ∝.

[tex]$$\begin{aligned}& \frac{\sin \alpha}{O G}=\frac{\sin 60^{\circ}}{0.3477} \\& \alpha=25.01^{\circ}\end{aligned}$$[/tex]

Calculate the normal acceleration at A.

[tex]$$\begin{aligned}a_{A, y} & =\omega^2\left(r_{A O}\right) \\& =4^2 \times 0.4 \\& =6.4 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]

Calculate the acceleration at G.

[tex]& \mathbf{a}_G=\mathbf{a}_A+\boldsymbol{\alpha} \times r_{G / A}-\omega^2\left(\mathbf{r}_{G / A}\right) \\[/tex]

[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}a_{A, x} \mathbf{i}+a_{A,} \mathbf{j}+\alpha \mathbf{k} \times A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j}) \\-\omega^2[A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j})]\end{array}\right\} \\[/tex]

[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}0+6.4 \mathbf{j}+\alpha \mathbf{k} \times 0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j}) \\-4^2[0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j})]\end{array}\right\} \\[/tex]

[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=(0.3151 \alpha-2.352) \mathbf{i}+(0.147 \alpha-1.3584) \mathbf{j}\end{aligned}$$[/tex]

Equate i coefficient:

[tex]-a_{G, x}=0.3151 \alpha-2.352[/tex][tex]-a_{G, x}=0.3151 \alpha-2.352[/tex]

Equate j coefficient:

[tex]$$-a_{G, y}=0.147 \alpha-1.3584$$[/tex]

The free body diagram and the kinematic diagram of the semicircular disk is as follows:

Calculate the mass moment of inertia of the semicircular disk about point O.

[tex]$$\begin{aligned}I_0 & =\frac{1}{2}\left(\frac{1}{2} m r^2\right) \\& =\frac{1}{2}\left(\frac{1}{2} \times 10 \times 0.4^2\right) \\& =0.4 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$[/tex]

Calculate the mass moment of inertia of the semicircular disk about point G.

[tex]$$\begin{aligned}I_G & =I_0-m(O G)^2 \\& =0.4-10\left(\frac{4 \times 0.4}{3 \pi}\right)^2 \\& =0.1118 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$\\[/tex]

Consider moment equilibrium condition about point A.

[tex]$$\begin{aligned}& \sum M_A=I_G \alpha+\sum m a_G d \\& m g(A G \sin \beta)=I_G \alpha+m a_{G, x}(A G \cos \beta)+m a_{G, y}(A G \sin \beta) \\& 10 \times 9.81\left(0.3477 \times \sin 25.01^{\circ}\right)=\left\{\begin{array}{l}0.1118 \alpha+10 a_{G, x}\left(0.3477 \cos 25.01^{\circ}\right) \\+10 a_{G, y}\left(0.3477 \sin 25.01^{\circ}\right)\end{array}\right\} \\& 0.118 \alpha+3.151 a_{G, x}+1.47 a_{G, y}=14.42\end{aligned}$$[/tex]

Solve the equations (1), (2), and (3), the values obtained are as follows:

[tex]$$\begin{aligned}& \alpha=18.04 \mathrm{rad} / \mathrm{s}^2 \\& a_{G, x}=3.333 \mathrm{~m} / \mathrm{s}^2 \\& a_{G, y}=1.294 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]

Consider the force equilibrium along the horizontal direction:

[tex]$$\begin{aligned}& \sum F_x=m a_{G, x} \\& f=m a_{G, x} \\& f=10 \times 3.33\end{aligned}$$[/tex]

f=33.33 N.

Consider the force equilibrium along the vertical direction:

[tex]$$\begin{aligned}& \sum F_y=m a_{G, y} \\& m g-N=m a_{G, y} \\& (10 \times 9.81)-N=10 \times 1.294 \\& N=85.16 \mathrm{~N}\end{aligned}$$[/tex]

Calculate the maximum frictional force at point A.

[tex]$$\begin{aligned}f_{\max } & =\mu_s N \\& =0.5 \times 85.16 \\f_{\max } & =42.58 \mathrm{~N}\end{aligned}$$[/tex]

Since, f< [tex]f_{max}[/tex]the semicircular disk does not slip at the given instant.

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Answer:

b) arithmetic

Step-by-step explanation:

Knowledge Needed

c and d are not valid sequence types.

Geometric Sequences are when the values of terms are found by multiplying the previous term's value by the same number.

Example:

1, 2, 4, 8, 16

x2

2, 6, 18, 54, 162

x3

20, 10, 5, 2.5, 1.25

x0.5

Arithmetic Sequences are when the values of terms are found by adding the previous term's value by the same number.

Example:

5, 6, 7, 8

+1

7, 19, 31, 43

+12

9, 6, 3, 0

-3

Question

Examine the sequence. From viewing the first 2 terms, we know that it can either be a geometric sequence that multiplies by 11/3 every time the term increases or an arithmetic sequence that adds 8 every time the term increases.

Looking at the 2nd and 3rd term, we know it is an arithmetic sequence because 19 is not equal to 11 times 11/3.

The slope of the roof is 0.25

What is a slope ?

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. And b is the value of b at the y-intercept (0, b).

To find slope

= 6.25 / 25

= 0.25

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Answer:

12

Step-by-step explanation:

1 -----> 3

?------>36

By make Cross

36*1/3 =12

The ratio of purple flower to white flowers is 1:1 for each friend.

A system of arrangement where objects are set at the center position.

In another words the piece that kept in the center position.

As example, for the purpose of decorating a table with flowers, we need to keep the flowers in such a way that all the flowers occupy the center position.

If we want to display a table as centerpieces with white and purple flowers, we must keep the two flowers in the same ratio to look the display more attractive.

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Answer: 6000 students

Step-by-step explanation:

First, we find the 40% that the university accept

40% = 0.4

Take 30000 times 0.4 = 12000 students got accept

Now we find the 50%

50% = 0.5

Take 12000 times 0.5 = 6000 students

6000 students would actually enroll

Answer:

68cm

Step-by-step explanation:

Because the scale factor is 2, which means the drawing is 2 times smaller than the actual airplane, multiply 34, the length of the wings tip to tip in the drawing by 2.

34 x 2 = 68

Answer: 68 meters

(Hope I'm correct, but read the explanation to make sure)

Step-by-step explanation:

Let's start with what we know. We know that the scale factor is 2, so in our model, from tip to tip, it is 34 cm. However, since the scale factor is 2:
34 * 2 = 68 meters