Find the value of c guaranteed by the Mean Value Theorem……

The width of the rectangle is 13 cm and the dimension is 26 cm x 13 cm

Given data ,

Let the length be L and width be W

Now , the width is 1/2 of the length, so we can write:

W = (1/2)L

The area of a rectangle is given by the formula:

Area = Length x Width

Given that the area is 338 square centimeters, we can write:

338 = L × W

Substituting W with (1/2)L, we have:

338 = L × (1/2)L

To solve this equation, we can multiply both sides by 2 to eliminate the fraction:

676 = L²

Taking the square root of both sides, we find:

L = √676

L = 26

So the length of the rectangle is 26 centimeters.

Substituting this value back into the equation for the width, we have:

W = (1/2)L

W = (1/2)(26)

W = 13

Hence , the dimensions of the rectangle are length = 26 centimeters and width = 13 centimeters

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The slope and y-intercept include the following:

Slope = 2.

y-intercept = -1.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the linear equation:

-6x + 3y =-3

By making y the subject of formula, we have:

3y = 6x - 3

y = 2x - 1

By comparison, the slope and the y-intercept include the following:

Slope, m = 2.

y-intercept, b = -1.

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[tex]2x^2=-8\\x^2=-4[/tex]

No real solutions.

Complex solutions:

[tex]x=\sqrt{-4} \vee x=-\sqrt{-4}\\x=2i \vee x=-2i[/tex]

Paul will spend $1,382.4 constructing the patio.

Looking at the design, we can see that the length of the patio is represented by 8 cm, and the width is represented by 6.4 cm. To convert these measurements to feet, we multiply them by the scale factor:

Length = 8 cm * 3 ft/cm = 24 ft

Width = 6.4 cm * 3 ft/cm = 19.2 ft

The area of the patio is calculated by multiplying the length and width:

Area = Length * Width = 24 ft * 19.2 ft = 460.8 ft²

The cost to construct the patio is $3 per square foot. Therefore, Paul will spend:

Cost = Area * Cost per square foot = 460.8 ft² * $3/ft² = $1,382.4

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The calculated measure of the red arc in ⊙C is 11

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

The congruent circles

From the circles, we have

Centers = C and P

Also, we have

Corresponding segments are equal segments

Using the above as a guide, we have the following:

QR = LM

Where

LM = 11

This gives

QR = 11

Hence, the value of QR is 11

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Using substitution method to solve the system of linear equation, the number of calculator is 50 and calender is 30

The collection of two or more linear equations involving the same variables is known as a system of linear equations. In this case, linear equations are first-order equations, where the maximum power of the variable is 1.

To solve this problem, we can set the variables for this;

Let;

To write the system of linear equations;

x + y = 80 ...eq(i)

12x + 10y = 900 ...eq(ii)

Part B;

Using substitution method;

From equ(i)

x + y = 80

x = 80 - y ...equ(iii)

Put equ(iii) into equ(ii)

12(80 - y) + 10y = 900

y = 30

x = 50

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Using a t-distribution with 21 degrees of freedom (since n-1 = 22-1 = 21), and a 95% confidence level, we can find the critical value from a t-table or calculator.

The critical value is ±2.080.

Rounded to three decimal places, the critical value is 2.080.

The period of the trigonometric function in this problem is given as follows:

A) 540º.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the tangent function, we have that it is similar to the sine function, that we use tan() instead of sin().

For which the parameters are given as follows:

The coefficient B for the equation is given as follows:

B = 2/3.

Hence the period of the function is given as follows:

2π/(2/3) = 3π = 540º.

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Answer:

hello

the answer is:

Sin B = CA/AB ----> Sin 65° = 5/AB ----> 0.906 = 5/AB

----> AB = 5.51

The pairs of coordinates arranged from least to greatest based on the differences between the points are:

(-1,-2) and (1,-4)

(4,1) and (2,2)

(-5,2) and (-3,-2)

(3,-4) and (-2,1)

(5,-2) and (-1,-1)

Let's calculate the differences and arrange the pairs accordingly:

(4,1) and (2,2):

Difference in x-coordinates: 4 - 2 = 2

Difference in y-coordinates: 1 - 2 = -1

(-5,2) and (-3,-2):

Difference in x-coordinates: -5 - (-3) = -2

Difference in y-coordinates: 2 - (-2) = 4

(3,-4) and (-2,1):

Difference in x-coordinates: 3 - (-2) = 5

Difference in y-coordinates: -4 - 1 = -5

(-1,-2) and (1,-4):

Difference in x-coordinates: -1 - 1 = -2

Difference in y-coordinates: -2 - (-4) = 2

(5,-2) and (-1,-1):

Difference in x-coordinates: 5 - (-1) = 6

Difference in y-coordinates: -2 - (-1) = -1

Now let's arrange them in order from least to greatest based on the differences in the points:

(3,-4) and (-2,1) (difference: 5)

(-1,-2) and (1,-4) (difference: 2)

(4,1) and (2,2) (difference: 2)

(-5,2) and (-3,-2) (difference: 4)

(5,-2) and (-1,-1) (difference: 6)

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Answer:

Impossible

Step-by-step explanation: if a cube is number from 1-6 theirs no chance of getting a number less than 1.

The three statements about the measures of center that are true include the following:

A. The mean for Group A is less than the mean for Group B.

B. The median for Group A is less than the median for Group B.

C. The mode for Group A is less than the mode for Group B.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Group A

Mean for Group A = [(1 × 5) + (2 × 4) + (3 × 1)]/(5 + 4 + 1)

Mean for Group A = (5 + 8 + 3)/10

Mean for Group A = 16/10

Mean for Group A = 1.6

Mode for Group A = 1

Median for Group A = (1 + 2)/2

Median for Group A = 3/2

Median for Group A = 1.5

Group B

Mean for Group A = [(1 × 3) + (2 × 2) + (3 × 4) + (5 × 1)]/(3 + 2 + 4 + 1)

Mean for Group A = (3 + 4 + 12 + 5)/10

Mean for Group A = 24/10

Mean for Group A = 2.4

Mode for Group B = 3

Median for Group B = (2 + 3)/2

Median for Group B = 5/2

Median for Group B = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A,B,C

Step-by-step explanation:

The probability of getting Two Tails is 0.1 or 10%.

Let's assume that '2. Tails' appeared x times.

According to the given information, 'No Tail' appeared 3x times, and '1 Tail' appeared 2 × 3x = 6x times.

The total number of tosses is 360. We can express this information in an equation:

x + 3x + 6x = 360

Simplifying the equation:

10x = 360

x = 36

Now we know that '2. Tails' appeared 36 times, 'No Tail' appeared 3x = 3 × 36 = 108 times, and '1 Tail' appeared 6x = 6 × 36 = 216 times.

To find the probability of getting Two Tails, we divide the number of times '2. Tails' appeared by the total number of tosses:

Probability of Two Tails = Number of times '2. Tails' appeared / Total number of tosses

= 36 / 360

= 0.1

Therefore, the probability of getting Two Tails is 0.1 or 10%.

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The phase shift of the trigonometric function is given as follows:

D) 90º to the left.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the cosine function, we have the same definition, we only use cos() instead of sin().

For which the parameters are given as follows:

For this problem, we have that the phase shift is of C = 90. As we are adding inside of the domain of the function, the phase shift is to the left.

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The test statistic is given as follows:

t = 2.52.

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 0.3, \mu = 0, s = 0.8, n = 45[/tex]

Hence the test statistic is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{0.3 - 0}{\frac{0.8}{\sqrt{45}}}[/tex]

t = 2.52.

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3/5 is the fraction between the numbers 1/3 and 87/100

A number line is a graphical representation of numbers that can be used to understand and visualize numerical relationships. It is a straight line that extends infinitely in both directions and is usually drawn horizontally.

Writing the fractions as percentage:

1/3 * 100 = 33.3%

87/100 = 87%

This shows that the required number must be between 33.3% and 87%

From the given options:

3/5 * 100 = 3 * 20

3/5 * 100 = 60%

Hence the value in between the numbers 1/3 and 87/100 is 3/5

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The simplified form of the expression 3 1/5x + 10 7/9 - 2 2/5x - 10 8/9 is 4/5x - 1/9.

To simplify the expression: 3 1/5x + 10 7/9 - 2 2/5x - 10 8/9, we need to perform the addition and subtraction of the terms.

First, let's focus on the x terms: 3 1/5x - 2 2/5x.

The whole numbers can be treated as fractions with a denominator of 1. Thus, we have:

(3 1/5)x - (2 2/5)x.

To perform the subtraction, we need to find a common denominator for the fractions involved, which is 5.

(3 1/5)x - (2 2/5)x = (16/5)x - (12/5)x.

Now we can subtract the terms:

(16/5)x - (12/5)x = (16 - 12)/5x.

Simplifying further:

4/5x.

Now let's simplify the whole number and fraction terms: 10 7/9 - 10 8/9.

10 - 10 = 0.

The fraction terms can be simplified by finding a common denominator, which is 9:

(7/9) - (8/9) = (-1/9).

Now we can combine all the simplified terms:

3 1/5x + 10 7/9 - 2 2/5x - 10 8/9

= (4/5x) + 0 + (-1/9)

= 4/5x - 1/9.

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The rule for (f - g)(x) is (f - g)(x) = 2x² - 11x - 3 and the value of (f - g)(-2) is 27

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

f(x) = 2x² - 3x + 4

g(x) = 8x + 7

The rule for (f - g)(x) is calculated as

(f - g)(x) = f(x) - g(x)

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

(f - g)(x) = 2x² - 3x + 4 - 8x - 7

So, we have

(f - g)(x) = 2x² - 11x - 3

Here, we have

x = -2

Substitute the known values in the (f - g)(x) = 2x² - 11x - 3, so, we have the following representation

(f - g)(-2) = 2(-2)² - 11(-2) - 3

Evaluate

(f - g)(-2) = 27

Hence, the value of (f - g)(-2) is 27

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Answer: when the value of the dollar decreases, also when demand is high.

Step-by-step explanation: economics

The expression  3m³np⁶  is a monomial

A monomial is an algebraic expression that consists of only one term.

In this case, the expression 3m³np⁶ has a single term as it is the product of constants (3), variables (m, n), and their exponents (3, 1, and 6).

Therefore, it meets the criteria of a monomial.

Hence, the expression  3m³np⁶  is a monomial

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A. The function f is injective.

B. The function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.

To prove that the function f is injective, we need to show that if f(x) = f(y), then x = y.

Let f(x) = f(y). Then we have:

x / (1 + x) = y / (1 + y)

Cross-multiplying, we get:

x(1 + y) = y(1 + x)

x + xy = y + xy

Now, subtract xy from both sides:

x = y

Since x = y when f(x) = f(y), we can conclude that the function f is injective.

(b) To prove or disprove that the function f is surjective, we need to determine whether for every y ∈ Q, there exists an x ∈ N such that f(x) = y.

Consider the case where y = 1/2. We need to find x ∈ N such that:

f(x) = x / (1 + x) = 1/2

Cross-multiplying, we get:

2x = 1 + x

Subtract x from both sides:

x = 1

In this case, there exists an x ∈ N (x = 1) such that f(x) = 1/2. However, we need to consider all y ∈ Q. Let's try another case.

Consider the case where y = 1. There is no x ∈ N that satisfies the following equation:

f(x) = x / (1 + x) = 1

Cross-multiplying, we get:

x = 1 + x

Subtract x from both sides:

0 = 1

This is a contradiction, so there is no x ∈ N such that f(x) = 1. Therefore, the function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.

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The 90% confidence interval for the population proportion of adults who made a New Year's resolution is approximately 0.523 to 0.554, while the 95% confidence interval is approximately 0.517 to 0.559.

To construct 90% and 95% confidence intervals for the population proportion based on the survey results of 1220 adults who made a New Year's resolution out of a total of 2267 adults, we can use the formula for confidence intervals for a proportion.

Calculate the sample proportion:

The sample proportion is the number of individuals who made a New Year's resolution divided by the total sample size.

Sample proportion [tex]\hat{p}[/tex]  = 1220 / 2267 = 0.5386

Determine the standard error:

The standard error measures the variability of the sample proportion and is calculated using the formula:

Standard error[tex](SE) = \sqrt{((\hat{p } \times (1 - \hat{p})) / n) }[/tex]

where n is the sample size.

Calculate the margin of error:

The margin of error represents the range within which the true population proportion is likely to fall.

It depends on the desired level of confidence and is calculated by multiplying the standard error by the appropriate critical value from the standard normal distribution.

For a 90% confidence interval, the critical value is 1.645.

For a 95% confidence interval, the critical value is 1.96.

Margin of error = Critical value [tex]\times[/tex] Standard error

Construct the confidence intervals:

The confidence interval is calculated by adding and subtracting the margin of error from the sample proportion.

For the 90% confidence interval: [tex]\hat{p}[/tex] ± Margin of error

For the 95% confidence interval: [tex]\hat{p}[/tex]  ± Margin of error

Using these steps and the provided information, we can construct the confidence intervals for the population proportion.

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259.25π in² is the surface area of the cone

The surface area of a cone can be calculated using the formula SA = πr² + πrl

where r is the radius and l is the slant height.

Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.

The slant height (l) is given as 22 inches.

Substituting these values into the formula:

Surface Area = π(8.5)² + π(8.5)(22)

= 72.25π + 187π

= 259.25π

Therefore, the surface area of the cone is 259.25π in²

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The experimental probability of the computer generating a 3 or a 5 is given as follows:

20%.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes in the table is given as follows:

90.

The desired number of outcomes is given as follows:

10 + 8 = 18.

Hence the experimental probability is given as follows:

p = 18/90 = 0.2 = 20%.

The problem is given by the image presented at the end of the answer.

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The depth of water when the tank is on its side is 4.2 cm.

We are given that;

tank measurement is 13*8*17

Now,

A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.

To find the volume of water in the tank when it is upright. To do this, you multiply the depth of water by the area of the base:

Volume = Depth * Area Volume = 9 cm * (13 cm * 8 cm) Volume = 936 cm^3

This volume does not change when you put the tank on its side. However, the area of the base does change. Depending on which side you put the tank on, the area of the base will be either 13 cm by 17 cm or 8 cm by 17 cm. Let’s assume you put the tank on its longer side, so that the area of the base is 13 cm by 17 cm.

Now, you can find the depth of water by dividing the volume by the area:

Depth = Volume / Area Depth = 936 cm^3 / (13 cm * 17 cm) Depth= 4.2 cm

Therefore, by the cube answer will be 4.2cm.

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The final volume of the gas is 8 litres when the pressure is 55 kilo pascals.

Boyle's law simply states that "the volume of any given quantity of gas is inversely proportional to its pressure as long as temperature remains constant.

Boyle's law is expressed as;

P₁V₁ = P₂V₂

Where P₁ is Initial Pressure, V₁ is Initial volume, P₂ is Final Pressure and V₂ is Final volume.

Given that:

Plug the given values into the above formula and solve for the final volume:

88 kPa × 5L = 55 kPa × V₂

V₂ = 440 / 55

V₂ = 8 L

Therefore, the final volume is 8 litres.

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Answer:

Step-by-step explanation:

x° + 2x° + 9° = 180°

3x° + 9° = 180°

x° + 3° = 60°

x = 57°

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