What is the average rate of change for the function on the interval (2, 3)

The length decreased by 6 cm (from 18 cm to 12 cm) and the width increased by 3 cm (from 9 cm to 12 cm) indeed form a square with an area of 135 cm², which is 27 cm² smaller than the area of the rectangle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Let's start by defining the variables we will use:

Let L be the original length of the rectangle.

Let W be the original width of the rectangle.

Let A be the area of the rectangle.

From the problem statement, we can set up the following equations:

(L - 6) = (W + 3) (the length decreased by 6 cm is equal to the width increased by 3 cm, forming a square)

(L - 6)(W + 3) - 27 = A (the area of the square is 27cm² smaller than the area of the rectangle)

Simplifying the first equation, we get:

L - W = 9

Solving for one variable in terms of the other, we can express L in terms of W:

L = W + 9

Substituting this expression into the second equation, we get:

(W + 3 - 6)(W + 3) - 27 = A

W(W + 6) - 27 = A

Expanding and simplifying, we get:

W² + 6W - 27 = A

Now, we can use the first equation to substitute for L in terms of W, and express A solely in terms of W:

A = LW

A = (W + 9)W

A = W² + 9W

Substituting this expression for A into the previous equation, we get:

W² + 6W - 27 = W² + 9W

Simplifying, we get:

3W = 27

W = 9

Substituting this value for W into the expression for L, we get:

L = W + 9 = 9 + 9 = 18

Therefore, the original length and width of the rectangle are 18 cm and 9 cm, respectively, and the area of the rectangle is:

A = LW = 18 x 9 = 162 cm²

We can check that the length decreased by 6 cm (from 18 cm to 12 cm) and the width increased by 3 cm (from 9 cm to 12 cm) indeed form a square with an area of 135 cm², which is 27 cm² smaller than the area of the rectangle.

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Answer:

252

Step-by-step explanation:

lol I take rsm too and I just guessed and checked

The required diameter of the sphere for the given volume of the sphere is equal to 12.2 cm (rounded to one decimal place)

Volume of the sphere = 944cm^3

Let us consider V be the volume of the sphere.

And r be the radius of the sphere.

The formula for the volume of a sphere is,

V = (4/3) × π × r^3

Solve for the radius of the sphere by rearranging the formula as follows,

⇒ r^3 = (3/4) × (V/π)

⇒r = [(3/4)×(V/π)]^(1/3)

Substituting V = 944 cm^3, we have,

⇒ r = [(3/4) ⇒ (944/π)]^(1/3)

⇒r ≈ 6.08 cm

⇒r ≈ 6.1 cm (rounded to one decimal place)

The diameter of the sphere is twice the radius, so the diameter is,

d = 2r

   ≈ 12.2 cm (rounded to one decimal place)

Therefore, the diameter of the sphere with a volume of 944 cm^3 to the nearest tenth of a centimeter is 12.2 cm.

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The value of the logarithm of numbers is 1/4

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given logarithm is 1 + log₇25

Simplifying this we have log₇25 = -1

Taking the logarithm of both sides we have

log₇25  = -100x

25 =7⁻¹⁰⁰ˣ

100x = 25

Dividing by 100

x = 25/100

X = 1/4

Therefore the value of the logarithm is 1/4

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There is a  there is a 3.125% chance that all five customers will give Steve a tip.

To calculate the probability of all five customers giving Steve a tip, we need to multiply the probability of one customer giving a tip (0.5) by itself five times since each customer's tip is an independent event. So, the probability is:

0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125

So, there is a 3.125% chance that all five customers will give Steve a tip.

To simulate this situation, we could use a random number generator that generates either 0 or 1, with a 50% chance of each. We could then repeat this process five times and count the number of times we get five ones (representing all five customers giving a tip). We could then use the proportion of times we get five ones out of the total number of simulations to estimate the probability of all five customers giving a tip. We would want to repeat the simulation many times to get a more accurate estimate.

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Answer:

Step-by-step explanation:

is there a height? Is the triangle with a 90 degrees angle? Is there any other conditions that are given?

Answer:

2 bus

Step-by-step explanation:

The expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student.

The expected value of a random variable represents the average value of that variable over multiple trials. In this case, x is a random variable representing the number of students on the bus carrying the randomly selected student, and y is a random variable representing the number of students on the randomly selected bus.

The expected value of x can be calculated as follows:

E[x] = (10/100)×10 + (20/100)×20 + (30/100)×30 + (40/100)×40

= 16 + 12 + 9 + 16

= 53/4

= 13.25

This means that, on average, the bus carrying the randomly selected student would have 13.25 students.

The expected value of y can be calculated as follows:

E[y] = (1/4)×10 + (1/4)×20 + (1/4)×30 + (1/4)×40

= 25

This means that, on average, the randomly selected bus would have 25 students.

As expected, the expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student. Since the number of students on the other 3 buses can vary widely, y has a higher expected value than x.

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Answer:

Step-by-step explanation:

So we know by Vertical Angles the opposite is contgruent and since j shares many angles one line its supplementry so we have

j + 76 + 90 = 180 suppl. angles there for j equals 14 degrees ( dont let the h fool you)

Step-by-step explanation:

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

Answer:

2

Step-by-step explanation:

14/2=7

34/2=17

Answer:

1.83 yards

Step-by-step explanation:

The calculatd value of the length of side WX is 1.25 cm.

Let's call the length of side WX "x".

The mid-segment of a trapezoid is the line segment connecting the midpoints of the non-parallel sides.

The length of the mid-segment is equal to the average of the lengths of the two parallel sides. In this case, the mid-segment is 2.75 cm long and connects the midpoints of sides WZ and XY.

We can use the formula for the length of the mid-segment of a trapezoid:

mid-segment length = (length of side WZ + length of side XY) / 2

Plugging in the values we know, we get:

2.75 = (x + 4.25) / 2

Multiplying both sides by 2, we get:

5.5 = x + 4.25

Subtracting 4.25 from both sides, we get:

x = 1.25

Therefore, the length of side WX is 1.25 cm.

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The correct order of the polynomial [tex]7x^3y^3 - 3xy^5 + 2x^2y^4 - x^4y^2[/tex] in descending powers of x is:

[tex]-x^4y^2 + 7x^3y^3 + 2x^2y^4 - 3xy^5[/tex]

Therefore, the answer is option A.

What is polynomial function?

A polynomial function is a mathematical function that consists of a sum of terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.

When we arrange a polynomial in descending order of powers of one of its variables, it means we are writing the terms with the highest power first, followed by terms with the next highest power, and so on until we reach the constant term (which has no variable).

In this case, the polynomial is [tex]7x^3y^3-3xy^5+2x^2y^4-x^4y^2[/tex]. To write this in descending order of powers of x, we need to start with the term that has the highest power of x, which is [tex]-x^4y^2[/tex].

Then we write the term with the next highest power of x, which is [tex]7x^3y^3[/tex]. After that, we write the term with the next highest power of x, which is [tex]2x^2y^4[/tex]. Finally, we write the term with the lowest power of x, which is [tex]-3xy^5[/tex].

So the correct order of the polynomial in descending powers of x is option A: [tex]-x^4y^2+7x^3y^3+2x^2y^4-3xy^5[/tex].

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Answer:

3.13

Step-by-step explanation:

The price of all three ropes together - $9.38

Price of one unit -9.38/3.=

3.12666 ; Nearest round figured cent would be $3.13

The best measure of center for this data would be the median, as it is less affected by outliers and works well for skewed data. To find the median, we arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5. There are 16 data points, so the median would be the average of the 8th and 9th values, which is 3.5. Therefore, the best measure of center for this data is the median, and its value is 3.5.

So the correct answer is: The median is the best measure of center, and it equals 3.5.

According to the question the measure of angle 3, or m∠3, is also 19 degrees since angle 2 and angle 3 are vertical angles. So: m∠3 = m∠23 = 19°

We know that vertical angles are congruent, so if angle 21 and angle 22 are vertical angles, then:

m∠21 = m∠22

We also know that angle 22 and angle 23 are complementary angles, which means:

m∠22 + m∠23 = 90°

Substituting m∠22 with m∠21, we get:

m∠21 + m∠23 = 90°

We are given that m∠21 = 71 degrees, so we can substitute that in the equation:

71° + m∠23 = 90°

Subtracting 71° from both sides, we get:

m∠23 = 19°

Therefore, the measure of angle 3, or m∠3, is also 19 degrees since angle 2 and angle 3 are vertical angles. So:

m∠3 = m∠23 = 19°

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If integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, the probability that ad-bc is even is 10/16.

To solve the problem, we need to consider the parity of the product ad and bc separately. If both ad and bc are even, then their difference (ad-bc) is even. If both ad and bc are odd, then their difference is even as well. However, if one of ad and bc is odd and the other is even, then their difference is odd.

For ad to be even, either a or d (or both) must be even. Similarly, for bc to be even, either b or c (or both) must be even. Therefore, the probability that ad and bc are both even is the product of the probabilities that a, b, c, and d are even:

P(ad even) = P(a even)P(d even) = (1004/2008)^2 = 1/4

P(bc even) = P(b even)P(c even) = (1004/2008)^2 = 1/4

The probability that ad-bc is even is the sum of the probabilities that both ad and bc are even and that both ad and bc are odd:

P(ad-bc even) = P(ad even and bc even) + P(ad odd and bc odd)

= P(ad even)P(bc even) + P(ad odd)P(bc odd)

= 1/4 * 1/4 + 3/4 * 3/4

= 1/16 + 9/16

= 10/16

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Step-by-step explanation:

Approx  9.81 m/s^2

The area of the cutout and the coin is as follows:

(A) 9mm²

(B) 293 mm²

The size of a patch on a surface is determined by its area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The area of a plane figure is the area that its perimeter encloses.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

Area of the cutout:

A = s²

A = 3²

A = 9mm²

Area of the coin:
A = πr²

A = π9.8²

A = π9.8²

A = π96.04

A = 301.5656

Then,

301.5656 - 9

292.5656

Rounding off: 293 mm²

Therefore, the area of the cutout and the coin is as follows:

(A) 9mm²

(B) 293 mm²

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15(x+3) = 2x(12)

15x+45 = 24x

45 = 9x

x = 5

The test statistic for the given hypothesis test is 2.31, indicating a significant difference between the sample mean and the hypothesized mean. The p-value is less than 0.025, and at a significance level of 0.05, the null hypothesis is rejected, concluding that the true population mean is greater than 12. The rejection rule using the critical value is to reject the null hypothesis if the test statistic is greater than 1.645.

To compute the test statistic, we first need to calculate the standard er ror of the mean:

SE = /sqrt(n) = 4.32/sqrt(25) = 0.864

Then, we can calculate the test statistic:

z = (sample mean - hypothesized mean)/SE = (14 - 12)/0.864 = 2.315

Rounding to 2 decimals, the test statistic is 2.31.

The degrees of freedom for this test are 24 (n-1), so we can find the range for the p-value using a t-distribution table with 24 degrees of freedom. For a two-tailed test at a significance level of 0.05, the range is between 2.064 and 2.492. Since the test statistic (z = 2.31) falls outside this range, the p-value is less than 0.025.

At a significance level of 0.05, since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the true population mean is greater than 12.

The rejection rule using the critical value at a significance level of 0.05 is to reject the null hypothesis if the absolute value of the test statistic is greater than 1.96 (for a two-tailed test) or if the test statistic is greater than 1.645 (for a one-tailed test).

In this case, the test is one-tailed and the critical value is 1.645 (obtained from a t-distribution table with 24 degrees of freedom). Since the test statistic (z = 2.31) is greater than 1.645, we reject the null hypothesis.

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Let's use "w" to represent the width of the rectangle and "l" to represent the length.

According to the problem statement, the area of the rectangle is numerically equal to its perimeter, so we can write:

2(l + w) = lw

Simplifying this equation, we get:

2l + 2w = lw

Dividing both sides by 2, we get:

l + w = 0.5lw

Multiplying both sides by 2, we get:

2l + 2w = lw

Since the length of the rectangle is 5 times its width, we can write:

l = 5w

Substituting this into the previous equation, we get:

2(5w) + 2w = 5w^2

Simplifying this equation, we get:

10w + 2w = 5w^2

12w = 5w^2

Dividing both sides by w, we get:

12 = 5w

So the width of the rectangle is:

w = 12/5 = 2.4 cm

And the length of the rectangle is:

l = 5w = 12 cm

Therefore, the width of the rectangle is 2.4 cm and the length of the rectangle is 12 cm.

Answer:

Width: 2.4 cm

Length: 12 cm

Step-by-step explanation:

Let the width of the rectangle be w cm, and the length be 5w cm. The area A and perimeter P of the rectangle can be expressed as follows:

Area (A) = length × width

A = 5w × w = 5w^2 cm^2

Perimeter (P) = 2 × (length + width)

P = 2 × (5w + w) = 2 × 6w = 12w cm

According to the problem, the area is numerically equal to the perimeter:

A = P

5w^2 = 12w

To solve for w, we can rearrange the equation:

5w^2 - 12w = 0

w(5w - 12) = 0

This equation has two possible solutions:

w = 0

In this case, the width would be 0 cm, which doesn't form a valid rectangle.

5w - 12 = 0

5w = 12

w = 12/5 = 2.4 cm

For the second solution, the width is 2.4 cm. Now, we can calculate the length:

length = 5w

length = 5 × 2.4 = 12 cm

So, the width of the rectangle is 2.4 cm, and the length is 12 cm.

Answer:

x = 23

Step-by-step explanation:

180 - 100 = 80

51 + 80 = 131

180- 131=49

49= 2x +3

49 - 3= 46

46=2x

46/ 2= 23

X= 23

The derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

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

y = 6x^3

To find the derivative of y with respect to x, we can use the power rule of differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).

Using this rule, we can differentiate y = 6x^3 as follows:

dy/dx = d/dx (6x^3)

= 6 * d/dx (x^3)

= 6 * 3x^2 (applying the power rule with n=2)

= 18x^2

Therefore, the derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

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The answer of the given question based on quadratic equation is the value of c is -43.

An equation is mathematical statement that shows the two expressions are equal. It consists of two parts, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can be made up of numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

For example, the equation 2x + 3 = 7 shows that the expression 2x + 3 is equal to 7. The variable x represents an unknown quantity that can be solved for by manipulating the equation using algebraic techniques.

If the product of the roots of the quadratic equation y = 4x² + 16x + c is -43/4, we can use the fact that the product of the roots is equal to c/4 to solve for c.

So, we have:

[tex]\frac{c}{4} =-\frac{43}{4}[/tex]

Multiplying both sides by 4, we get:

c = -43

Therefore, the value of c is -43.

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From the given quadratic equation the value of c=-43.

What is quadratic equation?

Quadratic equations are second-degree algebraic expressions that is it an equation of degree 2 and are of the form ax² + bx + c = 0.

where a≠0.

Given quadratic equation is

 y= 4x² +16x+c

Comparing with the quadratic equation y= ax²+bx+c₁ we get,

a= 4, b= 16, c₁= c

Product of the roots is c₁/a

So for this problem product of the roots will be c/4

Here given the product of the roots of the given quadratic equation is -43/4

Equating both we get,

c/4= -43/4

c=-43

Hence, the value of c= -43.

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Answer:

Part 1: x = -2

Part 2: x = 56

Step-by-step explanation:

Part 1:

12x + 9 = -15

Given that-

12x + 9 = -15

12x + 9 - 9 = -15 -9                >> Subtract 9 to both sides

12x = -24

12x/12 = -24/12                    >> Divide both sides by 12

x = -2

Check Answer:

12(-2) + 9 = -15                 >> 12 × -2 = -24

-24 + 9 = -15                   >> -24 + 9 = -15

-15 = -15                        >> Correct

Part 2:

x/7 - 4 = 4

Given that-

x/7 - 4 = 4

x/7 - 4 + 4 = 4 + 4                 >> Add 4 to both sides

x/7 = 8                

7x/7 = 8 × 7                             >> Multiply both sides by 7

x = 56

Check Answer-

Substitute x in the equation the check.

56/7 - 4 = 4              >> 56/7 = 8

8 - 4 = 4                  >> 8 - 4 = 4

4 = 4                        >> Correct

RevyBreeze

To express the ans in scientific notation is 1.98 x [tex]10^{10}[/tex] text messages per month.

You must add up all of the numbers in a set and divide the result by the total amount of numbers in order to determine the average of the set of numbers. The mean is another name for this.

The steps to calculating the average are as follows:

Sum up each of the set's numbers.

Count how many numbers there are in all.

subtract the total number of numbers from the sum of the numbers.

The average (mean) is calculated using the following formula:

Average equals ((Sum of Numbers)/ (Total Number of Numbers)

To calculate the total number of text messages sent by all teenagers in the United States in a month, we can multiply the number of teenagers by the average number of text messages sent by each teenager:

Total text messages = (number of teenagers) x (average number of text messages per teenager)

Total text messages = 22,000,000 x 900

Multiplying these numbers gives us:

Total text messages = √19,800,000,000

Total text messages = 140712.473 text messages per month.

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Answer:

Step-by-step explanation:

1000 / 5 = 200

So if their 5 people they would share the money 200 hundred per person.

The answer of the given question based on the Probability is,  the experimental probability that the card selected was a K or 6 is 19/100 or 0.19.

What is  probability ?

Experimental probability is a method of determining the probability of an event occurring based on experimental data. It involves conducting an experiment or observation and recording the number of times the event of interest occurs, then calculating the ratio of the number of times the event occurred to the total number of trials or observations.

Experimental probability is often used in fields such as science, engineering, and social sciences, where empirical data is collected through experimentation or observation. It is a useful tool for making predictions and testing hypotheses based on real-world data.

The number of times a K or 6 was drawn is the sum of their respective frequencies, which is:

Frequency of K or 6 = Frequency of K + Frequency of 6 = 12 + 7 = 19

The total number of cards drawn is 100, so the experimental probability of drawing a K or 6 is:

Experimental probability = Frequency of K or 6 / Total number of cards drawn = 19 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 19/100 or 0.19, which is approximately equal to 4/21 or 0.1905 when expressed as a fraction or rounded to four decimal places.

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The experimental likelihood that the chosen card was either a K or a 6 is 13/100, or 0.13 or 13%.

The likelihood of results occurring is examined in the study of probability, which is based on the ratio of likely to improbable scenarios.

It is necessary to add the frequencies of cards K and 6 and divide by the total number of draws in order to determine the experimental probability of drawing a K or 6:

Frequency οf K οr 6 = 7 + 6 = 13

Tοtal number οf draws = 4 + 7 + 5 + 6 + 7 + 6 + 8 + 10 + 7 + 10 + 8 + 12 + 10 = 100

Experimental prοbability οf drawing a K οr 6 = Frequency οf K οr 6 / Tοtal number οf draws = 13 / 100

Therefore, the experimental likelihood that the chosen card was a K or 6 is 13/100, or 0.13 or 13%.

The correct response is 8 over 13, as that is the easiest answer to the 13/100 question.

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Answer:

ITS 15 ITS A C = 15

Step-by-step explanation:

HOPE THIS HELPS

PL Z GIVE BRAINLIEST

Absolute Value Equation for a Horizontal Line Passing Through Two Points -1/2 and 3/2.

The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:

| x - 1 | = 1/2

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