Please look at the picture and answer the question thank you

An exponential decay function to model the situation is f(x) = 49(0.7)^x.

The average rate of change over 1 ≤ x ≤ 4 is -7.5.

The average rate of change over 5 ≤ x ≤ 7 is -1.4.

The rate of change decreases as x increases.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since the initial value is 49 and the decay factor is 0.7, an exponential function that models the situation is given by:

f(x) = ab^x

f(x) = 49(0.7)^x

When x = 1, the value of f(x) is:

f(1) = 49(0.7)^1

f(1) = 34.3.

When x = 4, the value of f(x) is:

f(4) = 49(0.7)^4

f(4) = 11.7649.

For the average rate of change over 1 ≤ x ≤ 4, we have:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [11.7649 - 34.3]/(4 - 1)

Average rate of change = -22.5351/3

Average rate of change = -7.5

For the average rate of change over 5 ≤ x ≤ 7, we have:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [49(0.7)^7 - 49(0.7)^5]/(7 - 5)

Average rate of change = [4.0354 - 8.2354]/2

Average rate of change = -4.2/3

Average rate of change = -1.4.

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Answer:

96:144

Step-by-step explanation:

240/5=48

48*2=96

48*3=144

So your answer is 96:144

12 is the denominator because it represents the total number of times Nicanor selects a diving ring from the bag

Explaination:

Nicanor randomly selects a ring from the bag a total of 12 times. 3 times he selects a red ring, 4 times a yellow one, and 5 times a blue one.

When he selects a red ring, he selects it 3 times out of the 12 times total, which is represented as the fraction 3/12.

When he selects a yellow ring, he selects it 4 times out of the 12 times total, which is represented as the fraction 4/12.

When he selects a blue ring, he selects it 5 times out of the 12 times total, which is represented as the fraction 5/12.

Hope this helps you!

Answer:

Step-by-step explanation:

put the 2x and make it 2

Answer:

4,7

Step-by-step explanation:

4,7

Answer:24.353333333

Step-by-step explanation:

The equation of the line in point-slope form is obtained as y = -2x + 4.

What is the point-slope form?

Point-slope is the general form of a linear equation which is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

The line passes through point (x1,y1) = (0,4)

The slope of the line is m = -2.

The formula for point-slope form of equation is -

y-y1=m(x-x1)

Substituting the values in the equation -

y - 4 = -2(x - 0)

y - 4 = -2x

y = -2x + 4

Therefore, the equation is obtained as y = -2x + 4.

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Therefore , the solution of the given problem of elevation comes out to be

X = 21.23°.

When it is between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.

Here,

Given :  tan X = P/ B

tan X = 68 / 175

X  = tan⁻¹ (68 /175)

X = 21.23

Therefore , the solution of the given problem of elevation comes out to be

X = 21.23°.

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A 140-pound person will typically burn 4 calories per mile of walking at a rate of 3 miles per hour.

Walking at a pace of 3 miles per hour results in an average calorie burn of 4 for a 140-pound person. This person would therefore burn around 112 calories in a period of 30 minutes. On the other hand, a 200-pound person burns roughly 5 calories per minute, or 159 calories every 30 minutes.

An average walking speed of 3 miles per hour (or 120 steps per minute) is recommended for health reasons. That is a mile that takes 20 minutes. You must increase your pace to 4 miles per hour (135 steps per minute), or a 15-minute mile, to walk for weight loss.

Walking and running have about equal calorie burn rates per minute. Walking at 3.5 mph for 40 minutes for a 160-pound person would take 40 minutes.

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38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.

The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:

d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]

There are points that correspond to each vertex in the polygon:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:

d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }[/tex] ≤ b r/≥ d=[tex]\sqrt{(8-(-2)^{2})+(7-11)^{2} }[/tex]  ≤b r/≥

d=[tex]\sqrt{116}[/tex]

There are points that correspond to each vertex in the polygon:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So, using the distance formula and the vertex positions of side PT, we can determine its length:

P  = (-2, 11)

T  = (8, 7)

The length of PT is [tex]\sqrt{116}[/tex]

The other 4 sides are handled in the same way, and the results are as follows:

TS = [tex]\sqrt{49}[/tex]

SR = [tex]\sqrt{50}[/tex]

RQ = [tex]\sqrt{61}[/tex]

QP = [tex]\sqrt{40}[/tex]

You may calculate the perimeter by adding all the sides:[tex]\sqrt{116}[/tex]+[tex]\sqrt{49}[/tex]+[tex]\sqrt{50}[/tex]+[tex]\sqrt{61}[/tex]+[tex]\sqrt{40}[/tex] = 38.97

The solution is 39 units if you round off.

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Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given : Sue covered 2.4 km distance and

bike wheel rotated 1225 times.

Thus,

To find the value of diameter of the wheel

=>2400=2πr*1225

=> 2400/2 = πr*1225

=> 1200 = πr*1225

=>r=31

Diameter = 2*31 = 62cm

Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

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Answer: The diagonal AC of a square bisects the square and the midpoint of the diagonal is the center of the square. Since the center of the square is the midpoint of the diagonal, we can find the midpoint of AC by averaging the x-coordinates and y-coordinates of A and C.

The coordinates of the center of the square is ( (2+(-2))/2 , (4+1)/2) = (0, 2.5)

Since a square is a special case of rectangle, which means all sides are equal, the length of the side of the square is the distance between A and C.

Using the distance formula, we can find the length of the side of the square:

d = sqrt( (2-(-2))^2 + (4-1)^2 ) = sqrt(4^2 + 3^2) = sqrt(16+9) = sqrt(25) = 5

The coordinates of the vertex D can be found by subtracting half of the side length from x and y coordinates of the center point.

D(0-5/2, 2.5 - 5/2) = (-2.5, 0.5)

The coordinates of the vertex B can be found by adding half of the side length from x and y coordinates of the center point.

B(0+5/2, 2.5 + 5/2) = (2.5, 5.5)

So the remaining vertices are (2.5, 5.5) and (-2.5, 0.5)

Step-by-step explanation:

Answer:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

Step-by-step explanation:

Given exponential function:

[tex]f(x)=P(1+r)^x[/tex]

Replace f(x) with y:

[tex]y=P(1+r)^x[/tex]

Divide both sides by P:

[tex]\dfrac{y}{P}=(1+r)^x[/tex]

Take natural logs of both sides:

[tex]\ln \left(\dfrac{y}{P}\right)=\ln (1+r)^x[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)=x \ln (1+r)[/tex]

Divide both sides by x:

[tex]\dfrac{1}{x}\ln \left(\dfrac{y}{P}\right)=\ln (1+r)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)^{\frac{1}{x}}=\ln (1+r)[/tex]

Raise both sides to power of e:

[tex]\large\text{$e^{\ln \left(\frac{y}{P}\right)^{\frac{1}{x}}}=e^{\ln (1+r)}$}[/tex]

[tex]\textsf{Apply the power law}: \quad e^{\ln x}=x[/tex]

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}=1+r[/tex]

Subtract 1 from both sides:

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1=r[/tex]

Therefore, the equation to find r is:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

The value of x, given the angle measures in Triangle ABC, can be found to be 22.

Triangle ABC is a right angled triangle which means that ACB has the angle measure of 90 degrees. This means that the angle measures left will add up to :

= Sum of interior angles in triangle - Angle ACB

= 180 - 90

= 90 degrees

If the sum of 2 x and ( 3 x - 20 ) adds up to 90 degrees, the value of x would then be:

90 = 2 x + ( 3 x - 20 )

2 x + 3 x - 20 = 90

2 x + 3 x = 90 + 20

5 x = 110

x = 110 / 5

x = 22

In conclusion, the value of x is 22.

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The question is:

What is the value of x?

The required correct product is (x + 4)/(x - 4)(x  + 1) for the rational expressions.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Anderson multiplies two rational expressions with the given results.

His error is the inequivalent can't be canceled out.

The two rational expressions are given in the question, as follows:

(x² - 16)/(x² - 8x + 16) × (x + 1)/(x² + 2x + 1)

(x² - 4²)/(x² - 2 × 4 × x + 4² ) × (x + 1)/(x² + 2 × 1 × x + 1²)

(x + 4)(x - 4)/(x - 4)² × (x + 1)/(x + 1)²

(x + 4)/(x - 4)(x  + 1)

Thus, the required correct product is (x + 4)/(x - 4)(x  + 1).

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Answer:  48 square inches

Step-by-step explanation:

To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.

area of triangle L x W = 6x4=24

area of rectangle LxW =6x4=24

24+24=48

Answer:

95 6/7

Step-by-step explanation:

The perimeter can be found by adding the length and width together and then multiplying the sum by 2.

Perimeter = 2(L + W)

Where L is the length and W is the width.

So, using the given measurements:

Perimeter = 2(33 5/7+ 14 3/14) = 94 26/14

94 26/14 -> 95 12/14 -> 95 6/7

Answer:

The perimeter is [tex]95\frac{6}{7}[/tex] inches.

Step-by-step explanation:

The formula for the perimeter of a rectangle is

[tex]P=2L+2W[/tex]

We are given the length and the width. Lets evaluate the perimeter.

First lets convert the length and width to an improper fraction.

Length: [tex]33\frac{5}{7}[/tex]

To write 33 as a fraction with a common denominator, multiply by [tex]\frac{7}{7}[/tex]. Then simplify.

[tex]\frac{33*7}{7} +\frac{5}{7}[/tex]

[tex]\frac{231}{7} +\frac{5}{7}[/tex]

[tex]\frac{231+5}{7}[/tex]

[tex]\frac{236}{7}[/tex]

Width:

To write 14 as a fraction with a common denominator, multiply by [tex]\frac{14}{14}[/tex]. Then simplify.

[tex]\frac{14*14}{14} +\frac{3}{14}[/tex]

[tex]\frac{196}{14} +\frac{3}{14}[/tex]

[tex]\frac{196+3}{14}[/tex]

[tex]\frac{199}{14}[/tex]

Lets enter the 2 fractions into the perimeter equation.

[tex]P=(2*\frac{236}{7} )+(2*\frac{199}{14} )[/tex]

Simplify each term.

[tex]P=\frac{2*236}{7} +2*\frac{199}{14}[/tex]

[tex]P=\frac{472}{7} +2*\frac{199}{14}[/tex]

Factor 2 out of 14.

[tex]P=\frac{472}{7} +2*\frac{199}{2(7)}[/tex]

Cancel the common factor of 2.

[tex]P=\frac{472}{7} +\frac{199}{7}[/tex]

Combine the numerators over the common denominator.

[tex]P=\frac{472+199}{7}[/tex]

[tex]P=\frac{671}{7}[/tex]

[tex]P=95\frac{6}{7}[/tex]

The salesman needs to sell $25937.5 to reach his needed monthly income needs.

Commission, also known as sales commission, is a payment given to employees based on the sales they make.

Given that, A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250.

Monthly salary = fixed part + commission part

The fixed salary is $925.

The commission part is 8% on all sales over $1250

Let x = amount of sales, and x must be greater than $1250.

Then, the amount of sales over $1250 is x - 1250.

He earns 8% on that amount, so the commission part is 8%(x - 1250),

or 0.08(x - 1250).

Monthly salary = fixed part + commission part

Monthly salary = 925 + 0.08(x - 1250)

925 + 0.08(x - 1250) = 2900

0.08x = 2075

x = 25937.5

Therefore, he needs to sell $25937.5.

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The correct answer is x² - 7x - 18 = (x - 9)(x + 2)

Answer:

A represents f(x) and B represents g(x)

Step-by-step explanation:

choose a value for x, substitute , say x = 1 into both f(x) and g(x) , then check the values obtained on the graph.

f(x) = 100 × [tex](\frac{3}{5}) ^{1}[/tex] = 100 × [tex]\frac{3}{5}[/tex] = 20 × 3 = 60

thus (1, 60 ) is a point on the graph of f(x)

the point (1, 60 ) is on graph A

g(x) = 100 × [tex](\frac{2}{5}) ^{1}[/tex] = 100 × [tex]\frac{2}{5}[/tex] = 20 × 2 = 40

thus (1, 40 ) is a point on the graph of g(x)

the point (1, 40 ) is on graph B

The gallons of ice cream 4 machines can make is 650 gallons.

Two ice cream machines make a total of 320 gallons in a certain amount of time.

Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:

Therefore,

If 2 ice cream machine = 320 gallons

4 ice cream machine = ?

cross multiply

Hence,

gallons of ice cream made by 4 machines = 320 × 4 / 2

gallons of ice cream made by 4 machines = 1280 / 2\

Therefore,

gallons of ice cream made by 4 machines = 640 gallons

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Answer:Angle

Step-by-step explanation:

The sequence of 100, 25, 6.25, 1.5625 is geometric.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.

In essence, we multiply the numbers together and calculate their n[tex]th[/tex]root, where n is the total number of data values.

A succession of shapes are used to create geometric patterns.

Because the pattern is governed by a rule, patterns created from shapes are comparable to patterns created from numbers.

The dimensions, perimeter, area, surface area, volume, etc. of geometric shapes are determined using geometry formulas.

Mathematics' branch of geometry examines the connections between points, lines, angles, surfaces, solids' measurements, and qualities.

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to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }[/tex]

Answer:

-9

Step-by-step explanation:

The constant doesn't have a letter attached to it

The required factors of the polynomial by grouping are  (x-3)(x^2 + 2).

To factor polynomial equations, a specialized approach is called grouping. It can be applied to polynomials with four terms as well as quadratic equations. Although they differ significantly, the two approaches are comparable.The first two terms and the final two terms are combined: p(x)=(x3 - 4x2) + (3x - 12), and we then identify the shared

factors as follows: p(x) = x2(x - 4) + 3(x - 4). (x - 4).

x^3 - 3x^2 + 2x -6

(x-3)(x^2 + 2)

Thus, required factors are (x-3)(x^2 + 2).

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Answer:

1,2,3,4,6,12,18

Step-by-step explanation:

uh

Answer:all integers

Step-by-step explanation:

the correct is all integers