The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?

Answer: 13/20

Step-by-step explanation: First to find the first part, we need to find a common denominator. So we must ask ourselves, which number is a multiple that both 5 and 4 have in common? The answer then would be 20. So, it would look like this:

[tex]\frac{1}{4} = \frac{?}{20}[/tex]

[tex]\frac{2}{5} = \frac{?}{20}[/tex]

So to find what "?" equals for both fractions, we must use this formula:

Amount =  Right denominator / Left denominator (1st part)

So, now we do 20 / 5 and 20 / 4

20 / 5 = 4

20 / 4 = 5

So, the 2nd part is taking the quotient from that and multiplying it by the left numerators. This would look like this:

5 * 1 = 5

4 * 2 = 8

So your "?" should look like this:

[tex]\frac{1}{4} = \frac{5}{20}[/tex]

[tex]\frac{2}{5} = \frac{8}{20}[/tex]

Then, you'd just add! So, 8 + 5 = 13 and 20 + 20 would stay that same ; 20. So your result is [tex]\frac{13}{20}[/tex]

I hope this helped!

The ratio of the the total amount spent on advertising to the amount spent on its website is 100: 49.

Now, According to the question:

There are 100 pence in one pound. Money can be written as, for example, £5.50, which means five pounds and fifty pence. The decimal point separates the pounds from the pence.

"Information available from the question"

For every pound a company spends on advertising, it spends  £0.49 pence on its website.

Ratio of the the total amount spent on advertising to the amount spent on its website is,

= 1/0.49

[tex]= \frac{1*100}{0.49*100}[/tex]

= 100/49

= 100 : 49

Therefore, the ratio of the the total amount spent on advertising to the amount spent on its website is 100: 49.

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If the price of gas increases by 5% again next week, then the price be approx 10% higher than it was originally because again shows that their is  two times increment of 5%.

Let the price of gas is x.

The price of gas is increased by 5% in a week. So after increment the price of gas = x + x × 5%

After increment the price of gas = x + 5x/100

After increment the price of gas = (100x + 5x)/100

After increment the price of gas = 105x/100

After increment the price of gas = 1.05x

The gas price again increase by 5%.

Now the price of gas after again increment = 105x/100 × 105%

The price of gas after again increment = 105x/100 × 105/100

The price of gas after again increment = 11025x/10000

The price of gas after again increment = 1.1025x

Now we find the total increment in two weeks

Percent Increment = (1.1025x - x)/x × 100

Percent Increment = 0.1025x/x × 100

Percent Increment = 0.1025 × 100

Percent Increment = 10.25%

Then we can say that approx 10% the cost of oil increased then originally.

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We can see here that ranking the four math operations in order of importance, we have:

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.

Addition (+) is the most important of the four operations because it is the foundation of all arithmetic. It is used in everyday life for basic calculations such as adding up a grocery bill or calculating the total cost of a purchase with tax. It is also used in more advanced mathematical concepts such as algebra and calculus.

Multiplication (x) is the second most important operation because it is used to find the total number of items in a group or the total area of a shape. It is also used in more advanced mathematical concepts such as solving equations and finding derivatives.

Subtraction (-) is the third most important operation because it is used to find the difference between two numbers. It is also used in more advanced mathematical concepts such as algebra and calculus.

Division (÷) is the least important of the four operations because it is a reverse operation of multiplication, which is more important and more frequently used. It is used to find the number of times one number is contained within another or the size of a group when the total size and number of groups is known.

All four math operations are important and useful in different ways, but the order of importance is based on how frequently they are used and how foundational they are to other mathematical concepts.

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The probability that there exists people who share the same birthday is 0.995.

Considering that all the 365 days are equally likely to be the birthday of a person and all the events that a person has birthday on 'y' are independent of others.

Under the said assumptions, let's say that there are n number of people in the room. If we number the people from 1 to n, then the total number of possibilities of birthdays are (365)^n.

Therefore, the possible combinations that all birthdays are different:

365 * 364 * 363 * .... * (365- n+1)

Thus, the probability that all birthdays are different is:

[tex]\frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]

To get the probability of at least two people sharing the same birthday is,

[tex]1- \frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]

= 1 - 0.0058

= 0.9942

=0.995

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The distance travelled by Yusuf in 2 hours is 104 miles.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given that, Yusuf drove 156 miles in 3 hours.

We determine the speed of Yusuf.

Speed = Distance / time

Speed = 156 miles / 3 hours

Speed = 52 miles per hour

Now, the distance travelled in 2 hours will be;

Speed = Distance / time

Distance = Speed × time

Distance = 52 miles per hour × 2 hours

Distance = 104 miles.

Therefore, the distance covered is 104 miles.

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Line a which passes (1, 4) has a constant of proportionality of 4.

Line b runs through (5, 2), with a constant of proportionality of 2/5.

The constant of proportionality is often represented by the letter "k" and it is used in a mathematical relationship known as a proportionality relationship. The proportionality relationship can be written as y = kx, where y and x are the two variables and k is the constant of proportionality.

This means that the value of y is directly proportional to the value of x and is equal to k times the value of x. The value of k can be found by dividing the value of y by the value of x, when the two variables are in proportion.

Line a passes through the (1, 4), therefore:

constant of proportionality = y/x = 4/1 = 4.

Line b passes through the (5, 2), therefore:

constant of proportionality = y/x = 2/5.

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Answer:

d

Step-by-step explanation:

The length of the north side of the house is 2x^2 + 9x - 32

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

The figure

On the figure, we have

North side = 5x - 4 + x^2 - 23 + x^2 + 4x - 5

Evaluate

North side = 2x^2 + 9x - 32

Here, we have

Length = 2x + 1

Width =  x^2 + 4x - 5

So, we have

Area = (2x + 1) * (x^2 + 4x - 5)

Area = 2x^3 + 8x^2  -10x + x^2 + 4x - 5

Area = 2x^3 + 9x^2 - 6x - 5

Here, we have

Length = 5x - 4

Width =  5x + 4

So, we have

Area = (5x - 4) * (5x + 4)

Area = 25x^2 - 16

From the figure, we have

Dimensjon = 5x - 4 by (2x + 1 + x + 6 - 5x - 4)

Dimensjon = 5x - 4 by - 2x + 3

Hence, the dimension of the bathroom is 5x - 4 by - 2x + 3

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Emmanuel weighs 150 pounds. about 2 hours will it take him to metabolize one standard drink

Every hour, the body processes one normal drink. If you have 5 standard drinks, your body will take 5 hours to absorb the alcohol.

In general, the liver can digest one ounce of liquor (or one standard drink) in one hour. If you consume more than this amount of alcohol, your system will get saturated, and the excess alcohol will accumulate in your blood and physiological tissues until it can be metabolized.

It takes your liver around an hour to break down the amount of alcohol in a standard alcoholic drink (one beer, one glass of wine, or one shot).

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The domain of the rational function in this problem is given as follows:

All real values except x = -3, x = 3, x = 4.

The domain of a function is the set composed by all the input values that the function accepts.

The function in this problem is a fraction, meaning that the denominator cannot be zero.

The denominator is given as follows:

x³ - 4x² - 9x + 36.

The roots of the denominator are given as follows:

x = -3, x = 3, x = 4.

Hence the domain is all real values except those, meaning that the second option is the correct option.

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The coordinates of the point that partitions the segment is given as :  (-3, 21)

To find the coordinates of the point on the directed line segment from (-9, 9) to (7, -7) that partitions the segment into a ratio of 3 to 5, we can use the concept of vector addition.

First, we can represent the directed line segment as a vector, with the initial point (-9, 9) being the tail, and the terminal point (7, -7) being the head. The vector representing the directed line segment is:

V = <7 - (-9), -7 - 9> = <16, -16>

To partition the segment into a ratio of 3 to 5, we can represent the partition point as a scalar multiple of the vector V:

P = (-9, 9) + (3/8)V = (-9, 9) + (3/8)(16, -16)

The scalar multiple 3/8 is used to get the partition point, it's calculated by dividing the desired ratio (3) by the sum of the ratio (3+5)

Then, we can find the x and y coordinates of the point P by applying the scalar multiple to the components of the vector:

P(x, y) = (-9, 9) + (3/8)(16, -16) = (-9, 9) + (3/8)(16, -16) = (-9 + 316/8, 9 - 3-16/8) = (-9 + 6, 9 + 12) = (-3, 21)

So the coordinates of the point on the directed line segment that partitions the segment into a ratio of 3 to 5 are (-3, 21).

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​

Answer:(−3,3)

​

Step-by-step explanation:

For Figure 2, Triangles are congruent by SSS (side side side).

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now ,

As in given figure for triangles

2 sides of both are parallel and one is common for both

Hence,

           These are congruent by SSS theorem.

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Answer:

y = 1/80

Step-by-step explanation:

[tex] \sf\frac {5}{8y} + 7 = \frac{3}{4y}- 3[/tex]

Substract 7 from both sides

[tex] \sf\frac {5}{8y} + 7 - 7 = \frac{3}{4y}- 3 - 7[/tex]

Calculate

[tex] \sf\frac {5}{8y} = \frac{3}{4y}-10[/tex]

Substract 3/4y from both sides

[tex] \sf\frac {5}{8y} - \frac{3}{4y} = \frac{3}{4y} - \frac{3}{4y} -10[/tex]

Calculate

[tex] \sf\frac {5}{8y} -\frac{3}{4y}= -10[/tex]

L.C.M = 32y²

[tex] \sf \frac{−4y}{ {32y}^{2} } = -10[/tex]

-4y/32y² Divide further

[tex] \sf \frac{ - 4}{ 32y } = -10[/tex]

Divide further

[tex] \sf \frac{ - 1}{ 8y } = -10[/tex]

Cross - multiply

[tex] \sf \: 8y \times - 10 = - 1[/tex]

Multiply

[tex] \sf \: - 80y = - 1[/tex]

Divide both sides by -80y

[tex] \sf \: \frac{ - 80y}{ - 80} = - \frac{ - 1}{ - 80} [/tex]

Calculate

[tex] \sf \: y = \frac{1}{80} [/tex]

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The problem is given as follows:
Prove: ΔLUZ ≅ ΔIDA

The triangles above can be said to be congruent because:

[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)

[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides)

[tex]\overline{UZ}[/tex] ≅ [tex]\overline{AD}[/tex] (Corresponding sides)

It is also given that:

m ∠ ULZ ≅ m ∠ ADI

since

[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)

[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides) and

m ∠ ULZ ≅ m ∠ ADI ;

We can thus conclude that the ΔLUZ  ≅ ΔIDA

When two triangles are congruent, one can be moved (through one or more stiff movements) to coincide with the other. All congruent sides and angles will be found.

The triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sections of another triangle. [Side - Angle - Side]

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The predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is $92.08 per year.

To find the predicted average rate of change of the company's sales turnover over the interval [9, 11], we need to find the slope of the line that best fits the data points provided.

The slope of the line can be calculated using the formula:

(change in y) / (change in x) = (S(x2) - S(x1)) / (x2 - x1)

We can use any two of the provided data points to find the slope. Using the data points (9, $1,061.08) and (7, $876.92), we get:

(change in y) / (change in x) = ($1,061.08 - $876.92) / (9 - 7) = $184.15 / 2 = $92.08 per year

This is the average rate of change of the company's sales turnover over the interval [9, 11]. So the answer is C. $92.08 per year.

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Awnse choice cAnswer:

Step-by-step explanation:

Answer:

72 miles

Step-by-step explanation:

its obvious

Answer:

B

Step-by-step explanation:

What you're seeing is a (x,y,z) plane.

At this point, it's just plug and play.

Looking at choice B....

(1) + (2) + (2)(3) = 1 + 2 + 6 which is indeed 9

(2)(1) + (2)(2) + 3(3) = 2 + 4 + 9 which is indeed 15

(1) + (-3) = 1 - 3 which is indeed -2

Answer:

(3x+4)+55°+85°=180°

(3x+4)+140°=180°

(3x+4)=180°-140°

(3x+4)=40°

3x+4=40

3x=40-4

3x=36

x=12

(3x+4)

(3×12)+4

=40°

The appropriate way to visualize a list of the eye colors of 120 people is pie chart and dot plot.

A pie chart is a circular statistical graphic in which the slices represent numerical proportions. In a pie chart, the arc length of each slice reflects the amount it stands for.

Pie charts can be used to show percentages of a whole group and show percentages at a particular moment. In contrast to bar graphs and line graphs, pie charts do not show changes over time.

A dot plot, also known as a strip plot or dot chart, is a simple style of data visualization in which data points are shown as dots on a graph with an x- and y-axis.

The things you and your partner choose to eat are a wonderful example.

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The following question may be like this:

What is an appropriate way to visualize a list of the eye colors of 120 people? select all that apply.

Answer: Your answer would be 2x ⋅ (2x) ⋅ 11

Step-by-step explanation: I hope this helps!

Answer:

-45

Step-by-step explanation:

f(x) = -2x² + 5

f(-5) = -2(-5)² + 5

= -2(25) + 5

= -2 × 25 + 5

= -50 + 5

= -45

Answer:

8) 27.75

10) See down below. May be 1.83 OR 123.75, depending on what your problem says

Step-by-step explanation:

Problem 8)

Let's first take apart [tex]2^{3}[/tex], which will be 8. Now, let's plug that back into the equation real quick:

12 + (8 ÷ [tex]\frac{2}{3}[/tex]) + 3.75

Since dividing a fraction can also be equal to multiplying the reciprocal of that same fraction, ÷ [tex]\frac{2}{3}[/tex] can be re-written as: * [tex]\frac{3}{2}[/tex]

Let's put that into the equation now and solve:

12 + (8 * [tex]\frac{3}{2}[/tex]) + 3.75

= 12 + 12 + 3.75

= 27.75

Problem 10) (I'm unsure if the sign after 80 is ÷ or +, but I'll do equations for both)

(If the sign after 80 is ÷, check these steps on how to solve):

Same methods as problem 8. Let's first break down [tex]4^{2}[/tex], which will be 16. Then, let's set the ÷ [tex]\frac{2}{5}[/tex] to * [tex]\frac{5}{2}[/tex] and solve:

80 ÷ (16 * [tex]\frac{5}{2}[/tex]) + 3.75

= 80 ÷ (40) + 3.75

= [tex]\frac{80}{40+3.75}[/tex]

= 1.82857

(If the sign after 80 is +, check these steps):

80 + (16 * [tex]\frac{5}{2}[/tex]) + 3.75

= 123.75

m is the angle formed by the two parallelogram sides that are next to each other. Because all angles in a parallelogram are equal, m is equal to all other angles in the parallelogram.

A parallelogram is a four-sided form having two parallel sides and four right angles on each side. Both sides are straight and opposite sides are equal in length. A parallelogram's opposing angles are also equal.

M is the angle subtended by the parallelogram JKLM. A parallelogram is a four-sided form with parallel and equal-length opposing sides. A parallelogram's angles are also equal in size. As a result, m is an angle of the parallelogram JKLM and is proportional to the other angles of the parallelogram JKLM.

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Answer:

n = √m

Step-by-step explanation:

Now we have to,

→ find the required value of n.

The equation is,

→ m = n²

Then the value of n will be,

→ m = n²

→ n² = m

→ [ n = √m ]

Hence, the value of n is √m.

If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.

If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.

The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.

Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.

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1.21 Canadian dollars is equivalent to 1 US dollar

A monetary exchange rate, also known as a foreign exchange rate, is the rate at which one currency can be exchanged for another. Exchange rates are determined by the foreign exchange market and can fluctuate based on supply and demand.

Since an automobile in Toronto sells for 25,500 Canadian dollars and the same car sells in Detroit for 21,000 US dollars.

Thus, 25,500 Canadian dollars equivalent in US dollars will be:

25,500 Canadian dollar /21,000 US dollars  = 1.21

Thus, 1.21 Canadian dollar is equivalent to 1 US dollar dollars

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Answer: 0.455

Step-by-step explanation:

I figured how to get $1? (The unit price?) so I did 4 divided by 8.8

Answer: The unit price is $2.20 per kilogram of apples

Step-by-step explanation:

Divide $8.80 with 4

8.80/4 = 2.20 per kilogram  

The set up percent equation is:

4600 = m . 5000

The percent of books that are fiction will be:

m = 92%.

Now, According to the question:

A relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Number of books in the town's library = 5,000

Number of books that are fiction= 4,600

The set up percent equation is:

4600 = m . 5000

where, m is the books' fiction

The percent of books that are fiction will be:

m = 4600/5000 × 100

m = 92%.

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The percent error in this measurement would be 16%.

1. Calculate the difference between the measured speed and the actual speed: 5 mph - 4.2 mph = 0.8 mph

2. Calculate the percent error: (0.8 mph / 4.2 mph) x 100 = 19.05%

3. Round to the nearest whole number: 19.05% = 19%

The percent error in this measurement is 19%, which means that the measured speed was 19% higher than the actual speed.

This can be caused by a variety of factors, including the radar gun being set to an incorrect sensitivity, the speed of the ball being too high for the radar gun to accurately measure, or the radar gun not being able to accurately detect the speed of the ball due to environmental factors such as wind or lighting.

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