simply the following expression below.
(x^2 -3x+7)

This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.

To apply the Mean Value Theorem, we need to check if f(x) is continuous on [0,2] and differentiable on (0,2).

[tex]f(x) = x^3 - 2x^2[/tex] is a polynomial function, so it is continuous and differentiable everywhere.

Now, we can use the Mean Value Theorem, which states that there exists a number c in (0,2) such that:
[tex]f'(c) = (f(2) - f(0))/(2-0)[/tex]

First, let's find f'(x):

[tex]f'(x) = 3x^2 - 4x[/tex]

Now, we can solve for c:

f'(c) = 3c^2 - 4c

f(2) = 2^3 - 2(2^2) = -4

f(0) = 0^3 - 2(0^2) = 0

(f(2) - f(0))/(2-0) = -4/2 = -2

So, we need to solve the equation 3c^2 - 4c = -2 for c.

Rearranging, we get:

3c^2 - 4c + 2 = 0

Using the quadratic formula, we get:

c = (4 ± sqrt(16 - 24))/6

c = (4 ± 2i)/6

Since the interval is [0,2], we only need to consider real solutions.
[tex]f'(c) = 3c^2 - 4c\\f(2) = 2^3 - 2(2^2) = -4\\f(0) = 0^3 - 2(0^2) = 0\\(f(2) - f(0))/(2-0) = -4/2 = -2\\[/tex]
Therefore, c = 4/3 is not a valid solution.

To choose between the remaining options, we can test if f'(c) is positive or negative.

For c = 0, f'(0) = 0 - 0 = 0.

For [tex]c = 1/2, f'(1/2) = 3(1/2)^2 - 4(1/2) = -1/2.[/tex]

For[tex]c = 1, f'(1) = 3(1)^2 - 4(1) = -1.[/tex]
Therefore, f'(c) is negative on the interval [0,1/2] and positive on the interval [1/2,2].

This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.

Therefore, the answer is (b) 1/2.

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The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.

In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.

To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.

Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.

A hypothesis test for the population mean amount of mercury in a certain type of fish.

Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.

If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.

This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.

The hypothesis test, it is impossible to calculate the power.

It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.

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Answer:

Which number is missing?

40   38   35   31   26   20   13   5

Pattern: ( -2, -3, -4, etc)

40 - 2 = 38

38 - 3 = 35

35 - 4 = 31

31 - 5 = 26

26 - 6 = 20

20 - 7 = 13

13 - 8 = 5

Step-by-step explanation:

You're welcome.

The area of the parallelogram shown in the figure is 30 in². Option D is correct.

The area of the parallelogram is given by the following formula,
Area = base * height,

From the figure we have base = 10 in and height  = 3 in

So area can be given as,
Area = 10 * 3

Area = 30 in²

Thus, the area of the parallelogram shown in the figure is 30 in².

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The null hypothesis is that the proportion of students who have traveled abroad is still 12%, while the alternative hypothesis is that the proportion has increased and is now greater than 12%.

The appropriate null hypothesis is that the proportion of students at UW-Platteville who have traveled abroad remains the same as before the implementation of the study abroad program. The alternative hypothesis is that the proportion of students who have traveled abroad has increased after the implementation of the program.

Mathematically:

H0: p = 0.12

Ha: p > 0.12

where p is the true proportion of students at UW-Platteville who have traveled abroad.

To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:

z = (0.35 - 0.12) / sqrt((0.12 * 0.88) / 100) = 3.87

where 0.88 is the complement of 0.12, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.05 level of significance is 1.645.

Since the test statistic (3.87) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level to support the claim that the proportion of students who have traveled abroad has increased after the implementation of the study abroad program.

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The Junior class sold 165 slices of pizza.

Let x represent the number of hamburgers sold and y represent the number of slices of pizza sold.

The total amount from sales: 1.35x + 0.75y = 292.50

They sold 40 more slices of pizza than hamburgers: y = x + 40

Now, we'll solve the system of equations using the substitution method:

Substitute the second equation into the first equation:
1.35x + 0.75(x + 40) = 292.50

Distribute $0.75 through the parentheses:
1.35x + 0.75x + 30 = 292.50

Combine like terms:
2.10x + 30 = 292.50

Subtract 30 from both sides of the equation:
2.10x = 262.50

Divide both sides by 2.10 to solve for x:
x = 125

Now that we know there were 125 hamburgers sold, we can use the second equation to find the number of slices of pizza sold:

y = x + 40
y = 125 + 40
y = 165
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Answer:

The solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).

Step-by-step explanation:

To solve the equation x^2 = 4x + 41, we can first rearrange it as x^2 - 4x - 41 = 0.

Next, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -4, and c = -41.

Substituting these values into the formula, we get:

x = (4 ± sqrt((-4)^2 - 4(1)(-41))) / 2(1)

Simplifying:

x = (4 ± sqrt(176)) / 2

x = (4 ± 4sqrt(11)) / 2

x = 2 ± 2sqrt(11)

Therefore, the solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).

Answer:

b. sin X and c. cos Y

Step-by-step explanation:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

sin Y = 32/40 incorrect

sin X = 24/40 correct

cos Y = 24/40 correct

cos X =32/40 incorrect

So the answers are sin  X and cos Y

The best prediction is that the college will have about 480 students who prefer cookies.

According to the table, 27 out of 225 students prefer cookies. To find the prediction for the number of cookies the college will need, we can set up a proportion:

27/225 = x/4000

Where x is the predicted number of students who prefer cookies.

Solving for x, we get:

x = (27/225) * 4000

x ≈ 480

Therefore, the best prediction is that the college will have about 480 students who prefer cookies.

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A statement 'The function f(x)=log0. 75x is decreasing' is True.

We know that a function, y = f(x) is a decreasing function when (dy/dx) ≤ 0 for all such values of interval (a, b).

Consider a function  f(x)=log(0.75^x)

We write a function f(x) as,

f(x) = log(0.75^x)

f(x) = log[(3/x)^x]

f(x) = log([tex]\frac{3^x}{4^x}[/tex])

Now we find the derivative of above function with respect to x.

f'(x) = d/dx [ log([tex]\frac{3^x}{4^x}[/tex])]

f'(x) = [tex]1/(\frac{3^x}{4^x} )[/tex] [d/dx ([tex]\frac{3^x}{4^x}[/tex])]

f'(x) = [tex](\frac{4^x}{3^x})[\frac{4^x[3^xlog(3)]-3^x[4^xlog(4)]}{4^{2x}} ][/tex]

f'(x) = log(3) - log(4)

f'(x) = -0.1249

f'(x) < 0

So, the function f(x) is a decreasing function.

Thus the statement is True.

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The measure of the missing angle in the cyclic quadrilateral is 104°

From the question, we are to determine the measure of the inscribed angle in the given diagram

In the given diagram, we have a cyclic quadrilateral.

From one of the circle theorems, we known that

The sum of the opposite angles of cyclic quadrilateral are supplementary. That is they sum up to 180 degrees.

Let the unknown angle measure be x,

Then,

We can write that

x + 76°  = 180°

x = 180° - 76°

x = 104°

Hence, the missing angle measure is 104°

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Answer:

  The measure of angle AOC is double the measure of angle ABC.

Step-by-step explanation:

You want to know the relationship between central angle AOC in circle O and inscribed angle ABC subtending the same arc AC.

The measure of an inscribed angle is half the measure of the arc it intercepts. The measure of a central angle is exactly equal to the measure of the arc it intercepts. (That's how the arc measure is determined.)

Hence, the measure of angle AOC is double the measure of angle ABC.

__

Additional comment

  Inscribed : central = 1 : 2

  Central : inscribed = 2 : 1

You need to be a little careful of the wording of the relationship. Which is double and which is half can be confused when it's written in words. On a diagram, the angle with its vertex in the center will obviously be larger than the one with its vertex on the circle.

The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, decrypt to "E" and "N" respectively. Therefore, the decrypted plaintext is "CSPAEN".

what is decrypted plaintext ?

The decrypted plaintext is the original message that was encrypted using a cipher, which has now been converted back to its original form using the appropriate decryption technique.

In the given question,

The given ciphertext "ZYJGKNO" can be decrypted using a times-11 cipher as follows:

The first letter "Z" becomes the third letter in the alphabet when shifted by 11 positions, so it decrypts to "C".

The second letter "Y" becomes the 24th letter in the alphabet when shifted by 11 positions, so it decrypts to "T".

The third letter "J" becomes the 18th letter in the alphabet when shifted by 11 positions, so it decrypts to "S".

The fourth and fifth letters "GK" become the 16th and 10th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "P" and "A" respectively.

The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "E" and "N" respectively.

Therefore, the decrypted plaintext is "CSPAEN".

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Value of side CD = x=3

When two triangles are  are referred to as similar figures when they share the same shape but different  in size.

given that CB and ED are perpendicular to AD,

in triangle ABC and ADE

∠A=∠A (common angle )

∠B=∠D (both are 90 degree)

ΔABC≈ ΔADE by angle-angle similarity .

and we know that when two triangle are similar then their corresponding sides are with in the same ratio or proportional.

so ,here we proved that triangle ABC and ADE are similar,

then ,

[tex]\frac{BC}{ED}=\frac{AB}{AD}[/tex]

[tex]\frac{x}{5}=\frac{9}{9+6}[/tex]

[tex]\frac{x}{5} =\frac{9}{15}\\ X=3[/tex]

x=3

from above result ,value of side CB =x=3

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Well, a diameter is double the radius. The radius is given in the image.

So, 2+2 = 4

The interior angles measure 160° and the exterior measure 200°

The sum of the interior angles of a polygon of n sides is:

(n - 2)*180

here n = 18

(18 - 2)*180 = 2880

divide that by the number of sides

2880/18 = 160°

That is the measure of each interior angle, and the exteriors are such that the sum is 360, then:

a + 160 = 360

a = 360 - 160 = 200

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Answer: 228.8cm

Step-by-step explanation:

Hope this helps! :)

Answer:

Eqation a and 15

Step-by-step explanation:

because 5 pears all cut into thirds is 15 slices 5 times 3 is 15

Supplementary angles are angles that add up to 180°. Angle 6 is a right angle, so it's worth 90°. This means that the other angle(s) have to be 90° as well.

As you can see, the other angle with 90° is angle 3, thus, making it the correct answer.

The function best models the data in the table is y=-0.6x+132 (option a).

The table shows the minimum target heart rates by age, which implies that as a person ages, their heart rate should be maintained within a certain range during exercise to achieve optimal cardiovascular benefits. In order to determine the target heart rate for a given age, we need a mathematical function that can accurately model the data in the table.

This is a linear function, which means that it assumes a constant rate of change in the target heart rate as age increases.

However, the data in the table shows that the target heart rate decreases gradually with age. Therefore, this function does  accurately model the data and is a suitable option.

Hence (a) is the right one.

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Complete Question:

Age x (year)                           Minimum Target Heart Rates by Age

30                                                                114

35                                                                 111

40                                                                108

45                                                                105

50                                                                102

Which function best models the data in the table?

a) y=-0.6x+132

b) y=(x-30)²+114

c) y= 19/30x

If the price of the packet of chips decreases by 12%, the new price will be:

New price = $9.99 - (12/100) x $9.99

New price = $9.99 - $1.199

New price = $8.791

Therefore, the new price of the packet of chips will be $8.791.

To measure a length of 10 meters without any measuring devices from 100 meters rope is fold the rope ten times and 10th fold of 100 m rope is equals to 10 m.

Total Length of rope = 100 meters

We need to measure a length of 10 meters without using any measuring devices. The ways that we can use to measure the required length includes only fold or manipulate the rope, but you cannot cut or mark it. Now, we use the division arithmetic operation to measure the length. The factors of 100 is written as 100 = 2×2× 5×5 = 10× 10

If we divide 100 by 10 then results 10 as quotient and 0 as remainder. So, the rope with length 100 meters is divided into 10 parts of 10 meters length of rope. But we cannot cut the rope, so folds the rope ten times ( i.e, first half -half then again half into half-half). Therefore, the last fold is measure of length 10 meters.

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Answer:

4/7

Step-by-step explanation:

1-3/7

7/7 -3/7

4/7

Answer:

CT is the perpendicular bisector of AB

Step-by-step explanation:

calculate the segments using x = 2

AT = 2x + 3 = 2(2) + 3 = 4 + 3 = 7

BT = x + 5 = 2 + 5 = 7

thus AT = BT

CT = 3x - 1 = 3(2) - 1 = 6 - 1 = 5

DT = 4x + 1 = 4(2) + 1 = 8 + 1 = 9

thus CT ≠ DT

∠ ATD = 41x + 8 = 41(2) + 8 = 82 + 8 = 90°

Thus CT is the perpendicular bisector of AB

Answer:

c = 56°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

120° is an exterior angle of the triangle , then

c + 64° = 120° ( subtract 64° from both sides )

c = 56°

According to this research, options B and D appear to be the most slope plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).  

It is impossible to establish which equation is the best model of the data without the actual data. However, we may analyse each possibility based only on the facts provided:

A. y= 2.2 - (1.1%): This equation appears to contain a constant term and a negative slope, making it unsuitable for predicting plant height over time.

B. y= 0.5x + 1.8: The positive slope of this equation indicates that the plant's height rises with time. The constant term of 1.8 might represent the plant's beginning height, while the coefficient of 0.5 could reflect the plant's growth rate.

C. y= 2.0 • (1.4%): This equation appears to contain a constant term and a positive slope, but the percentage term is not obvious how it links to the data.

D. y = 0.7 x + 2.1: This equation, like option B, has a positive slope and a constant term. The coefficient of 0.7 might reflect the plant's growth rate, while the constant term of 2.1 could represent the plant's original height.

According to this research, options B and D appear to be the most plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.

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The compound inequality that has no solution is d) m + 9 < 8 and -2m ≥ 10.

A compound inequality combines two or more inequalities using the logical connectives "and" or "or".

Compound inequalities are used to describe a range of values that satisfy multiple conditions simultaneously.

In the given compound inequality, the first inequality states that m + 9 is less than 8, which can be rewritten as m < -1.

The second inequality states that -2m is greater than or equal to 10, which can be rewritten as -2m ≥ 10.

However, the two inequalities cannot be true at the same time because if m is less than -1, then -2m would be greater than 2, and therefore cannot be greater than or equal to 10.

So there is no value of m that satisfies both inequalities simultaneously, resulting in no solution.

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The roots (if any) are determined by the values of x that make f(x) = 0. To find them, we solve the quadratic equation associated with the function.

A quadratic equation is an equation of the form:

ax² + bx + c = 0

where a, b, and c are constants. For a quadratic function of the form:

f(x) = ax² + bx + c

the roots are the values of x that satisfy the equation f(x) = 0. To find the roots, we set f(x) equal to zero and solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

If the discriminant (b² - 4ac) is negative, then the quadratic equation has no real roots, and the function f(x) does not intersect the x-axis. If the discriminant is zero, then the quadratic equation has one real root, and the function f(x) touches the x-axis at that point. If the discriminant is positive, then the quadratic equation has two real roots, and the function f(x) intersects the x-axis at those points.

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Answer:

If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:

15 boys - 9 girls = 6 more boys than girls.

Step-by-step explanation:

The area of the regular pentagon is  490 square units

The formula used for calculating the area of a regular pentagon is expressed with the equation

A = 1/2 pa

Such that the parameters are;

From the information given, we have that;

Perimeter = 5s

Substitute the values,

Perimeter = 5(14)

multiply the values

Perimeter = 70 units

Now, substitute the value into the formula

Area = 1/2 × 70(14)

Area = 980/2

Divide the values

Area = 490 square units

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