the average rate of change of g(x)=-3x^(3)+3 from x=-3 to x=3 .

Answer:

Determine Your Budget.

Check Your Credit.

View Multiple Rentals.

Consider Roommates.

Consider a Cosigner.

Gather Your References.

Check Out the Neighborhood.

Check All the Websites.

Answer:

[tex]\frac{3}{x+7}[/tex]

Step-by-step explanation:

[tex]\frac{3x-21}{x^{2} -49}[/tex]

We will start with factoring the numerator, by pulling a 3 out of each term:

3(x - 7)

We will then factor the denominator. As the denominator is a difference of perfect squares (in the form [tex]x^{2} -a^{2}[/tex]), we know that it can be factored in the form (x + a)(x - a), a being the square root of the number given. (In this case, a = 7, because the square root of 49 is 7.)

Our denominator is now:

(x + 7)(x - 7)

And our fraction is now:

[tex]\frac{3(x-7)}{(x-7)(x+7)}[/tex]

As both the numerator and denominator have the term (x-7), they will cancel, leaving us with the simplified expression:

[tex]\frac{3}{x+7}[/tex]

The mean change in Mr.60. Connor's bank account is $6.

To find the mean change in Mr. Connor's bank account, we need to add up all the changes and divide by the total number of changes.

First, we can simplify the given list of changes by combining the positive changes and the negative changes separately:

$50.25 + $50.25 = $100.50 (total positive change)

-$22.50 + (-$22.50) + (-$22.50) = -$67.50 (total negative change)

Then, we can find the total change in Mr. Connor's account by subtracting the total negative change from the total positive change:

$100.50 - $67.50 = $33.00 (total change)

Finally, we can find the mean change by dividing the total change by the number of changes:

$33.00 ÷ 5 = $6.60 (mean change)

Therefore, the mean change in Mr.60. Connor's bank account is $6.

In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is also known as the arithmetic mean or simply the average.

To find the mean of a set of numbers, you add up all the numbers in the set and then divide by the total number of numbers. For example, to find the mean of the numbers 2, 5, 7, and 10, you add them up (2 + 5 + 7 + 10 = 24) and then divide by the total number of numbers (4), which gives a mean of 6.

The mean is often used in statistics to describe the typical or average value of a data set. It is a useful measure of central tendency because it takes into account all the values in the data set, not just a few extreme values. However, the mean can be affected by outliers, or extremely high or low values in the data set that can skew the average.

There are different types of means, including the arithmetic mean, the geometric mean, and the harmonic mean, each with different methods of calculation and specific applications.

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The proper choice is D, and it provides the best-fitting regression model for the data plot under consideration.

A model that uses a linear regression has an output-input connection that is a straight line. The most straightforward to understand and even see in action in the actual world is this. Even when a relationship isn't quite linear, our brains nevertheless attempt to recognize the pattern and associate that relationship with a crude linear model.

The number of responses to a marketing effort could serve as one illustration. We might receive five responses out of 1,000 emails sent. If a linear regression can be used to describe this relationship, then we can anticipate ten responses from 2,000 emails sent. Your chart may be different, but the basic premise is the same: we link a predictor and a goal and presume that they are related.

There is typically a regression model running in the background to support a claim like this, whether it is connected to exercise, happiness, health, or any other claim.

Moreover, a mean squared error can be used to describe the model fit. In essence, this provides us with a numerical representation of how well the linear model fits.

Predicting a patient's length of hospital stay, the association between income and crime, the birth rate and education, or the relationship between sales and temperature are more serious instances of linear regression.

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Pick a positive and a negative number: 15 and -1

Since the produce of a positive and a negative number is always negative, then x * y can't be greater than 13.

Answer: TSA( TOTAL SURFACE AREA) of the cube of side 8 cm is 384 square cm.

Step-by-step explanation: We know,

the total surface area of a cube is = 6 a^2 where a is the length of the side of the cube.

Here, a = 8cm

thus TSA = 6* 8*8= 384 square cm.

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Answer:

(g ￮ h)(t) = 8t

Step-by-step explanation:

to find (g ￮ h)(t) substitute t = h(t) into g(t)

(g ￮ h)(t)

= g(h(t))

= g(4t - 2)

= 2(4t - 2) + 4

= 8t - 4 + 4

= 8t

Answer:

Step-by-step explanation:

If 20% of the test is made up of 10 open-ended questions, we can set up a proportion to find the total number of questions on the test.

Let x be the total number of questions on the test.

We can write the proportion as:

open-ended questions/total questions = 20%/100%

or

10/x = 20/100

To solve for x, we can cross-multiply to get:

10 * 100 = 20 * x

1000 = 20x

x = 50

Therefore, there are 50 total questions on the test.

The expected weight left after the next customer's order shipped is 92 pounds, and the variance of the weight left is 51.2 lb²

What is the probability mass function?

A probability mass function (PMF) is a mathematical function that describes the probability of each possible value of a discrete random variable. In simpler terms, the PMF gives the likelihood of a specific outcome occurring when you randomly select an item from a finite set of possible outcomes.

The PMF assigns a probability to each outcome, such that the sum of all probabilities equals 1. The PMF is often presented in a table or a graph to show the probabilities associated with each possible value of the random variable.

The given probability mass function (pmf) for the number of batches ordered by a randomly chosen customer, X, is:

X P(X)

0 0.3

1 0.5

2 0.1

3 0.1

To calculate the expected value of X, we use the formula:

E(X) = Σ [x * P(X=x)]

E(X) = (0 * 0.3) + (1 * 0.5) + (2 * 0.1) + (3 * 0.1)

E(X) = 0 + 0.5 + 0.2 + 0.3

E(X) = 1

To calculate the variance of X, we first need to calculate the squared values of X:

X²

0² = 0

1²  = 1

2² = 4

3² = 9

Then, we use the formula:

Var(X) = E(X²) - [E(X)]²

E(X²) = Σ [x² * P(X=x)]

E(X²) = (0² * 0.3) + (1² * 0.5) + (2² * 0.1) + (3² * 0.1)

E(X²) = 0 + 0.5 + 0.4 + 0.9

E(X²) = 1.8

Var(X) = E(X²) - [E(X)]²

Var(X) = 1.8 - 1²

Var(X) = 0.8 batches²

The expected number of pounds left after the next customer's order is shipped can be calculated as:

E(Weight left) = 100 - 8X

where X is the number of batches ordered by the next customer.

Using the formula for the expected value of X that we found earlier, we can write:

E(Weight left) = 100 - 8E(X)

E(Weight left) = 100 - 8(1)

E(Weight left) = 92 lb

To calculate the variance of the number of pounds left, we first need to find the variance of X, which we already calculated as 0.8 batches² Then, we use the formula for the variance of a linear function of a random variable:

Var(aX + b) = a² * Var(X)

where a = -8 (the negative sign indicates that the weight left decreases as X increases) and b = 100.

Var(Weight left) = (-8)² * Var(X)

Var(Weight left) = 64 * 0.8

Var(Weight left) = 51.2 lb^2

Therefore, the expected weight left after the next customer's order is shipped is 92 pounds, and the variance of the weight left is 51.2 pounds squared.

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Applying the AA Similarity theorem:

AC = 10

AB = 20

If two triangles have two corresponding congruent triangles they are similar to each other according to the AA Similarity theorem, which means their corresponding sides are proportional.

Triangles DCE and ACB are similar to each other by AA Similarity theorem, therefore:

AC/CE = BC/CD

Substitute:

AC/8 = 15/12

AC = (15 * 8)/12

AC = 10

Also,

AB/16 = 15/12

AB = (16*15)/12

AB = 20

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Using Integration, we can find out that all the fish in the lake died after 20 weeks.

Integration is the process of connecting the parts to create the whole. In the integral calculus, we find a function whose derivative is known. Integration is therefore the opposite of distinction. Integration is used to define and calculate the area enclosed by the function graph. The basic calculus methods used to address arithmetic issues are differentiation and integration.

We first determine the growth rate of the fish, let it be D.

The death rate factor S is to be multiplied by P to get the death rate, so the term is:

- SP = - k P/√P

      = - k√P

Given, birth rate, S is 0.

P' = -k√P

Now, we can separate and integrate it:

P'/√P = -k

∫dP'/√P = ∫-k dt

2√P = -kt + c

Applying the data that we have:

P (0) = 900

2 (30) = 0 + c

⇒ c = 60.

At t = 6,

P = 441

  = (21) ²

So, 2(21) = 60 - 6k

⇒ 6k = 18

⇒ k = 3.

Finally, we set t = 0 and we solve it for t:

2(0) = 60 - 3t

⇒ t = 20.

Therefore, the fish in the lake died after 20 weeks.

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Answer:

a=35

Step-by-step explanation:

5a=25×7

5a=175

5a/5=175/5

a=35

Answer: y = 10/7 x= 26/7 so A (26/7 , 10/7)

Step-by-step explanation:

since an equation for x is already given, we can plug it in to the first equation to solve for y

3(4y-2) + 2y = 14

12y - 6 +2y = 14

14y -6 = 14

14y = 20

y = 20/14

simplify

y = 10/7

plug the y we just found into the equation for x to find the value of x

x = 4(10/7) -2

x= 40/7 - 2

make both fractions

x = 40/7 -14/7

x= 26/7

hope this helps!

Answer: 6 3/4 I hope this helps

Step-by-step explanation:

27/4

Convert the improper fraction into a mixed number

6 3/4

Mixed number-A number written as a whole number and a fraction.

The reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

Vector, in mathematics, a quantity that has both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.

The reflection of a vector v in a line L can be found by projecting v onto L and then doubling the projection.

To project v onto L, we need to find the projection of v onto a vector that lies on L. Let's call this vector a. We can find a by normalizing the vector [1, -2, 2] to get:

a = [1/3, -2/3, 2/3]

Now, the projection of v onto a is given by the dot product of v and a:

proj_v_a = (v . a) * a = [(81/3) + (5(-2/3)) + (7*2/3)] * [1/3, -2/3, 2/3]

= [13/3, -26/3, 26/3]

To find the reflection of v in L, we need to double the projection and subtract it from v:

ref_v_L = 2 * proj_v_a - v

= 2 * [13/3, -26/3, 26/3] - [8, 5, 7]

= [26/3, -52/3, 52/3] - [8, 5, 7]

= [2/3, -67/3, 31/3]

Therefore, the reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

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The individual events are dependent. The probability of the combined event is of:

0.0137 = 1.37%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

As the students are chosen without replacement, the events are dependent.

The parameter values for this problem are given as follows:

N = 72 students, k = 18 seniors, n = sample size of 3.

The probability of three seniors is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,72,3,18) = \frac{C_{18,3}C_{54,0}}{C_{72,3}} = 0.0137[/tex]

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Answer:

-1

Step-by-step explanation:

g(-1)=-1

Answer: 480

Step-by-step explanation:

20 times 24 is 480

Using the given restrictions we can see that there are 37 balls on the box.

Let's assume that the total number of balls is B.

We know that in the box there are more than 25 and fewer than 40 tennis balls, so we have the inequality.

25 < B < 40

If we count in 3's, then there is one left over, so we can write:

B = 3*n + 1   (where n is an integer number)

And if we count in 5's there are 2 leftovers:

B = 5*m + 2  (where m is an integer, from this we conclude that the number ends in a 2 or a 7)

Then we have 3 restrictions:

25 < B < 40

B = 3*n + 1

B = 5*m + 2

notice that if n = 12

B = 3*12 + 1 = 37

if m = 7

B = 5*7 + 2 = 37

and 37 is a solution of the inequality, then we conclude that there are 37 balls on the box.

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The piecewise function graphed is defined as follows:

A piecewise function is a function that has multiple definitions, depending on the input x of the function.

The function in this problem has definitions for two intervals, given as follows:

For x < -5, the function is decreasing with a slope of -2, as when x increases by 1, y decays by 2, hence:

y = -2x + b.

When x = -6, y = 0, hence the intercept b is given as follows:

0 = -2(-6) + b

b = -12.

Hence:

y = -2x - 12, x < -5.

For x > 3, the function is decreasing with a slope of -1, as when x increases by 1, y decays by 1, hence:

y = -x + b.

When x = 5, y = 0, hence the intercept b is given as follows:

0 = -5 + b

b = 5.

Hence:

y = -x + 5, x > 3.

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The area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the triangle can be determined by using the midpoint formula, which states that the area of an isosceles triangle is equal to half the product of the two base lengths multiplied by the height.

In this case, the midpoint of the triangle is (3,0). This means that the triangle's base lengths are equal to 6 (the difference between the x coordinates of the midpoint and the two endpoints, 3-(-3)) and the height is equal to 6 (the difference between the y coordinates of the midpoint and the two endpoints, 3-(-3)).

Therefore, the area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

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4.3cm is the measure of the unknown side

According to the theorem, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment if two secant segments are drawn to a circle from an exterior point.

Applying the rule to the question;

3(y+3)= 2(2+9)

3y + 9 = 22

Subtract 9 from  both sides

3y = 22- 9

3y = 13

y = 13/3

y = 4.3cm

Hence the measure of y to the nearest tenth is 4.3cm

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With Scale factor=4, the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

What is the definition of scaling factor?

The Scale Factor is used to scale shapes of different sizes. Geometry teaches us about different geometrical shapes in two and three dimensions. The scale factor is a statistic that is used to compare statistics that appear comparable but have distinct scales or metrics. Consider two circles with the same shape but different radii.

The scale factor indicates how much bigger or smaller a figure is in comparison to the original figure. You may create an extended or reduced version of any original form by using a scale factor.

Now,

side of smaller square=12

area=12²=144

perimeter=12*4=48

For bigger square, as scaling factor=4

then side=12*4=48

area=48²=2304

perimeter=4*48=192

Hence,

            the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

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Answer:

B. $11

Step-by-step explanation:

At end of 4th year:

[tex]320 {e}^{.03 \times 4} = 360.80[/tex]

At end of 5th year:

[tex]320 {e}^{.03 \times 5} = 371.79[/tex]

Interest earned between end of these two years:

[tex]371.79 - 360.80 = 10.99[/tex]

It can be put as 40 / 100 as a fraction, which if you needed, it can be further simplified to 4 / 10, or even 8 / 20.

Answer:

------------------------------

As per question we have:

Find the required segment length using segment addition rule:

Using translation the graph of y = (x - 2)² - 5 is the graph of y = x² shifted 2 units to the right and 5 units down.

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To translate the graph of y = x² to y = (x - 2)² - 5, apply the following transformations -

Shift the graph to the right by 2 units.

This means that we replace x with x - 2, which moves the graph 2 units to the right.

Shift the graph down by 5 units.

This means that we subtract 5 from the entire function, which moves the graph 5 units down.

So the transformed function is -

y = (x - 2)² - 5

To see how this transformation changes the graph, compare the original function y = x² to the transformed function y = (x - 2)² - 5.

The vertex of the parabola has moved from the origin (0,0) to the point (2,-5).

Therefore, the graph is shifted using translation.

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Answer:

Step-by-step explanation:

the answer is

B

and
C

We can conclude that -

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is that Khadija, Adnan, and Husam sent a total of 80 text messages over their cell phones during the weekend. Husam sent 2 times as many messages as Adnan. Adnan sent 8 more messages than Khadija.

Assume that Khadija sent {x] messages. Then, Adnan would have send

(x + 8) messages and Husam would have sent 2(x + 8) messages. We can

write the sum as -

x + x + 8 + 2x + 16 = 80

4x + 24 = 80

4x = 56

x = 7

Messages sent by Khadija = 7

Messages sent by Adnan = 15

Messages sent by Husam = 30

Therefore, we can conclude that -

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x - intercept of line A = (1 , 0)

x - intercept of line B = (-4, 0)

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A line with no curve is called straight line.

Given,

Equation of line A

y = 6x - 6

for x - intercept y = 0

0 = 6x - 6

6x = 6

x = 6/6

x = 1

x - intercept = (1 , 0)

Given table of values on line B

x   y

-4  0

-2  -1

0   -2

By the table, when y = 0, x = -4

x- intercept of line B = (-4 , 0)

Hence, (1, 0) is x - intercept of line A.

(-4 , 0) is x - intercept of line B.

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