If c is the number that satisfies the conclusion of the Mean Value Theorem for f(x)= x^3 - 2x^2 on the interval 0â¤xâ¤2, then c=a) 0b) 1/2c) 1d) 4/3

The missing lengths of a geometric system are listed below: AC = 114, BC = 96, BE = 3

In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if every pair of corresponding sides have the same proportion. Then, the system is described by this proportion formula:

AB / AC = AE / AD = BE / CD

18 / AC = 15 / 95 = BE / 19

Then,

18 / AC = 15 / 95

AC = 18 × (95 / 15)

AC = 114

15 / 95 = BE / 19

BE = 19 × (15 / 95)

BE = 3

Now, we determine the length of side BC:

BC = AC - AB

BC = 114 - 18

BC = 96

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In reference to the given histogram, an absence of bars signifying either 4 or 5 traffic tickets implies that no one from the selection had accumulated this amount.

It should be noted that to make sure our point is accurate, we can sum the heights of the separate bars for 3, 6 and 8 tickets which demonstrate the total people included within the survey who have acquired the relevant number of traffic citations.

The height of the bar for three violations measures out at 1.

Conversely, a measurement of 2 denotes the bar for six infringements.

An assessment of 1 has been given to the bar with regards to eight offences.

Due to the lack of representation mentioned in the histogram concerning both 4 and 5 transgressions, it confirms our inference: nobody from the selection received four or five traffic tickets.

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The quadratic equation y = x²-6x+5 is minimum because the coefficient of x² is positive.

x = [tex]\frac{-b}{2a}[/tex], but a = 1 and b = -6

therefore x = [tex]\frac{-(-6)}{2(1)}[/tex] = 3

By plugging the value in the quadratic equation above, then we have

y = (3)² - 6(3) + 5 = -4 = -4

Note that y is the y-value of the vertex.

To determine whether the function y = x^2 - 6x + 5 has a maximum or minimum value, we can use the vertex formula, which gives the x-coordinate of the vertex of a quadratic function as -b/2a.

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Answer: Either 58 or 85

Step-by-step explanation:

5 + 8 = 13
8 + 5 = 13

5 x 8 = 40

8 x 5 = 40

The test score that is 0.6 standard deviations above the mean is 111.

We can use the formula for z-score to find the test score that is 0.6 standard deviations above the mean:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we want to find x when z = 0.6, μ = 105, and σ = 10:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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The test score that is 0.6 standard deviations above the mean is 111.

To find the test score that is 0.6 standard deviations above the mean, we can use the formula

z = (x - μ) / σ

where z is the number of standard deviations from the mean,

x is the test score we want to find,

μ is the mean of the distribution (105), and

σ is the standard deviation of the distribution (10).

We know that the desired test score is 0.6 standard deviations above the mean,

so we can set z = 0.6 and solve for x:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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The value of the variables are x = -2 and y = 4

From the information given, we have that the simultaneous equations are;

4x-5y=-28

-9x-2y=10

Make 'x' the subject from equation 1

4x = -28 + 5y

x = -28 + 5y/4

Now, substitute the value in equation 2, we get;

-9(-28 + 5y/4) - 2y = 10

expand the bracket

252 - 45y/4 - 2y = 10

find the lowest common multiple

252 - 45y - 8y/4 = 10

cross multiply

252 - 45y -8y = 40

collect the like terms

-53y = -212

Make y the subject

y = 4

substitute the value

x = -28 + 5y/4

x = -28 + 20/4

x = -8/4

x = -2

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Answer:

84

Step-by-step explanation:

This is a combination problem with repetition. Since there is an unlimited number of each type of cookie, we can choose 6 cookies from a pool of 4 types of cookies.

The formula for choosing r items from n types with repetition is:

(n + r - 1)C(r)

Where C is the combination function.

Using this formula, we can calculate the number of ways to choose 6 cookies:

(4 + 6 - 1)C(6) = 9C6 = 84

Therefore, there are 84 ways for Angelina to choose 6 cookies from Sam's Kookie shop, if she can choose any combination of chocolate chip, sugar, oatmeal, and snickerdoodle cookies with unlimited supply.

An equation in slope-intercept form for the line shown in the graph is x = -1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 3)/(-1 + 1)

Slope (m) = -3/0

Slope (m) = 0.

At data point (-1, 3) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 0(x - (-1))

y - 3 = 0

y = 3.

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In linear equation, The required days for which Bryan's workout would be the same in either pool is 2 days.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Here.

Let the number of days of B'ryan workout be x, the total yard he swims be y,

According to the question,

he swims at the rec center pool, will complete a 100-yard warm-up, and then swim laps in a lane that is 39 yards long.

y = 100 + 39x

Jason swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus the main set that consists of 37 yards per lap.

y = 104 + 37x

Equating both the equation,

100 + 39x =  104 + 37x

39x - 37x =  104 - 100

2x = 4

x = 2  days

Thus, the requried days for which Bryan's workout would be the same in either pool is 2 days.

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If we throw, a coin in twice, then pay off for throw exactly two heads is $120. The expected win value in the game in 742 trials is equals to the $1669.5.

We have to two tosses a coin and we gift with payouts according to results of tossing. When we throw exactly two heads in two tosses of a coin, then pay out is $120. If not throw two heads then payout is $37… Now, number of times we play the game that is trials = 742

We have to determine value of expected value to win or loss for 742 trials. First we determine the excepted value of proposition. Total possible outcomes on two tosses of a coin = 4 = {HH,TT, HT, TH}

Probability of throwing two heads = 1/4

= 0.25

Probability of not throwing two heads

= 1 - 1/4 = 3/4 = 0.75

That is when x (pay off) = $120, P( x)

= 0.25 ; x (payout) = -$37, P( X) = 0.75. Now, the excepted value formula is written as, [tex]E( x) = \sum x× P(x) [/tex]

= $120 × 0.25 - $37 ×0.75

= $2.25

So, the expected value of win with 575 trials of gane = 2.25 × 742

= 1669.5

Hence, required excepted win value is $1669.5.

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The equation represents the total number of stars is y = 35x

The equation that represents the total number of stars earned, y, for passing x levels would be:

y = 35x

where y represents the total number of stars earned, and x represents the number of levels passed.

For example, if Marcellus and Anika passed 10 levels, they would earn:

y = 35(10) = 350 stars

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The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex.

To write the vertex form of a quadratic equation given the vertex (-4, 5) and a-value of 5, you can use the vertex form equation:

y = a(x - h)² + k

where (h, k) is the vertex and a is the a-value.

In this case, h = -4, k = 5, and a = 5. Substitute these values into the equation:

y = 5(x - (-4))² + 5

Simplify the equation:

y = 5(x + 4)² + 5

So, the vertex form of the quadratic equation is:

y = 5(x + 4)² + 5

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The vertex form of the quadratic equation is: y = 5[tex](x + 4 )^2[/tex] + 5

A quadratic equation's vertex form is provided by:

y = a[tex](x - h)^2[/tex] + k

where "a" is the coefficient of the parabola and "(h, k)" is its vertex [tex]x^2.[/tex]

Given that the vertex is (-4, 5) and a-value is 5, we can substitute the values into the vertex form equation:

h = -4

k = 5

a = 5

When we enter these numbers into the equation, we obtain:

y = 5(x -[tex](-4) ^2[/tex] + 5

Simplifying the equation, we get:

y = 5[tex](x + 4)^2[/tex] + 5

So, the vertex form of the quadratic equation is:

y = 5[tex](x + 4 )^2[/tex] + 5

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The area of the given circle is  1.76625 square feet.

Remember that the area of a circle of radius R is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know the diameter (2 times the radius) of the circle, which is 1.5ft, then the radius is:

R = 1.5ft/2 = 0.75ft

Then the area of the circle is:

A = 3.14*(0.75ft)²

A = 1.76625 ft²

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Answer:

141 degrees

Step-by-step explanation:

First find the value of the other interior angle that is not shown. To find it u add 108 n 33 which gives you 141

Then subtract 141 from 180 which gives u 39 degrees

After subtract 39 from 180 which gives you 141 degrees

A method of assigning probabilities based on historical data is called the Empirical Probability method.

Empirical probability refers to the probability of an event based on observed data or past experience.

It is also known as experimental probability because it is determined through experimentation or observation.

This approach involves analyzing past events and their outcomes to calculate the probability of a particular event happening in the future.

To calculate empirical probability, you can use the formula:
Empirical Probability = (Number of successful outcomes) / (Total number of outcomes)
In this method, you collect and analyze historical data to make predictions about future events.

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Answer: B. Fixed Annuity

Step-by-step explanation: A Fixed Annuity is a type of retirement plan where you make regular contributions to an insurance company, and in return, they guarantee a fixed payout during your retirement years. This guaranteed benefit is typically paid out as a stream of income for a specific period or for the rest of your life, depending on the terms of the annuity contract.

Unlike other retirement plans such as a 401(k), Roth IRA, or Traditional IRA, which are investment-based and subject to market fluctuations, a Fixed Annuity provides a guaranteed benefit regardless of how the financial markets perform.  This can provide peace of mind for individuals who prioritize a stable and predictable income during retirement.

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a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).

How to solve the question?

To determine the number of camp sites required for a group of 237 campers, we can divide the total number of campers by the maximum number of campers allowed per site.

237 campers ÷ 6 campers per site = 39.5

Since we cannot have a fraction of a campsite, we need to round up to the nearest whole number. This is because we need to ensure that there is enough space for all of the campers, and rounding up will ensure that we have enough sites to accommodate them.

Therefore, a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).

It is important to note that while this calculation is a good starting point, it is always a good idea to check with the campground to ensure that they can accommodate a group of this size. Additionally, the campground may have specific policies or procedures in place for reserving campsites for large groups.

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The option (3) is correct the quotient is −5x³ + x + 3.

To solve quadratic equations by factoring, we first express the quadratic polynomial into a product of factors by using middle term splitting or different identities and then set each factor equal to 0. The equation a x 2 + b x + c = 0 ( a ≠ 0 ) can be written as.

According to given question

To divide[tex]15x^5[/tex] − 3x³ − 9x² by −3x² using the factorization method, we can factor out −3x² from the expression and simplify to get:

[tex]15x^5[/tex]− 3x³ − 9x²= −3x²(−5x³ + x + 3)

Therefore, the quotient is −5x³ + x + 3.

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Thus, the value of the  x- and y-intercepts for the given linear equation is (-30, 0) and (0, 15)

A nonlinear function's intercepts can be defined algebraically or graphically. The points on a graph where a nonlinear function crosses both x and y axes are known as the intercepts.

Given that-

linear equation:  -x + 2y = 30

x-intercept: It occurs when y = 0,

-x + 2(0) = 30

-x = 30

x = -30

y-intercept: It occurs when x = 0,

-0 + 2y = 30

2y = 30

y = 15

Thus, the value of the  x- and y-intercepts for the given linear equation is (-30, 0) and (0, 15).

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According to the Equation, the provided question's conclusion is that the object strikes the top of the tree in roughly 4 seconds.

An equation is a mathematical statement that demonstrates the equality of two expressions and is typically denoted by the equals symbol (=). Equations can be used to solve issues and make predictions as well as to express a wide variety of mathematical relationships.

The formula for the distance travelled by an object under constant acceleration can be used to solve this issue:

d = 1/2 * g * t²

where:

The distance travelled is d.

Gravitational acceleration (g) is around 32.2 feet per second squared.

T is the passing of time

Since the object is being dropped in this scenario, we know that its initial height is 0 feet and its ending height is 44 feet. For the duration of the trip, we may construct the following equation:

The required time is t seconds.

h(t) = 44

Simplifying:

-16t² + 300 = 44

16t² = 300 - 44

t² = 256/16

t² = 16

When both sides are squared:

t = 4 seconds

The time it takes for the object to strike the tree's top is therefore 4 seconds.

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The complete question is,

Let's say the object lands 44 feet above the ground, at the top of a tree. You may calculate the number of seconds after being dropped by writing and solving an equation.

Answer:

Step-by-step explanation:

5

each stack of bricks weighs 163.2 pounds. So the answer is D) 163.2 pounds. we need to form equation to solve this

what is equation  ?

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), that are separated by an equal sign (=). An equation tells us that the expressions on both sides have the same value or are equivalent.

In the given question,

If there are 20 stacks with an equal number of bricks on them, let's call the number of bricks on each stack "x". Then the total number of bricks is:

total number of bricks = 20 stacks × x bricks/stack = 20x bricks

We are also told that the total weight of all the bricks is 3,264 pounds. Let's call the weight of each brick "w". Then the total weight is:

total weight = number of bricks × weight per brick = (20x) bricks × w pounds/brick

We want to find the weight of each stack of bricks, which is equal to the weight of a certain number of bricks. Let's call this weight "s". Then we have:

s pounds/stack = x bricks/stack × w pounds/brick

We can solve for "s" by using the two equations above:

total weight = (20x) bricks × w pounds/brick = 3,264 pounds

s pounds/stack = x bricks/stack × w pounds/brick

Dividing the first equation by 20x, we get:

w pounds/brick = 3,264 pounds ÷ (20x) bricks/stack = 163.2 pounds/stack

Substituting this into the second equation, we get:

s pounds/stack = x bricks/stack × 163.2 pounds/stack

Dividing both sides by x, we get:

s pounds/stack ÷ x bricks/stack = 163.2 pounds/stack

Simplifying, we get:

s pounds/brick = 163.2 pounds/stack

Therefore, each stack of bricks weighs 163.2 pounds.

So the answer is D) 163.2 pounds.

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Answer:

1) -4<x<-2

2) x<-7 or x75

3) 2<x<7

4) x<-5 or x<6

5) x<-8 or x74

Step-by-step explanation:

Answer:

24   +    28

2*2*2*3   +    2*2*7              [prime factors]

You may distribute any common ones, for example:

  4(6+7)              [that is, 2*2*(2*3 + 7)

  2(12+14)

The scale factor used to dilate triangle ABC to triangle A'B'C' is approximately 4. So, correct option is C.

To determine the scale factor used to dilate triangle ABC to triangle A'B'C', we can use the formula:

scale factor = distance(A', B') / distance(A, B)

We can choose any pair of corresponding vertices to calculate the distance, but it's usually easiest to use the endpoints of a side. Let's use points A and A', and points B and B', respectively:

distance(A', B') = √[(12 - (-12))² + (12 - (-12))²] = √(24² + 24²)  ≈ 34

distance(A, B) = √[(3 - (-3))² + (3 - (-3))²] = √(6² + 6²) = 6√2

Substituting these values into the formula, we get:

scale factor = 34 / (6√2) ≈ 4

This means that every length in triangle A'B'C' is 4 times the corresponding length in triangle ABC.

Therefore, Correct option is C.

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The area of the fiqure is 132 cm².

Area is the region bounded by a plane shape.

To calculate the area of the figure, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the area is 132 cm².

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