The diagram shows a prism placed on a horizontal floor
The prism has height 3 m
The volume of the prism is 18m³
The pressure on the floor due to the prism is 75 newtons/m²
Work out the force exerted by the prism on the floor.

By definite integrals, we find that the area of the region bounded by the functions f(x) and g(x) described in the statement is equal to 4.5 units.

In this problem we must determine the area between two functions, a quadratic equation f(x) and a linear equation g(x).

First, we need to determine the limits of the interval of x-values with the help of a graphing tool, represented by the points of intersection of the two functions.

The points of intersection of the two functions are (x₁, y₁) = (- 5, 4) and (x₂, y₂) = (- 2, 1), respectively. Then, the area is defined by the following definite integral:

[tex]I = \int\limits^{-2}_{-5} {[g(x) - f(x)]} \, dx[/tex]

[tex]I = \int\limits^{-2}_{- 5} {[(- x - 1) - (x + 3)^{2}]} \, dx[/tex]

[tex]I = - \frac{1}{2} \cdot [(- 2)^{2} - (- 5)^{2}] - [(- 2) - (- 5)] - (1 / 3) \cdot [(- 2 + 3)^{3} - (- 5 + 3)^{3}][/tex]

I = - (1 / 2) · (4 - 25) - 3 - (1 / 3) · (1 + 8)

I = - (1 / 2) · (- 21) - 3 - (1 / 3) · 9

I = 21 / 2 - 3 - 3

I = 21 / 2 - 6

I = 21 / 2 - 12 / 2

I = 9 / 2

I = 4.5

The area of the region represented by the definite integral introduced above is equal to 4.5 units.

The statement leads to a contradiction. Correct form is presented below:

Find the area of the region that is bounded above by the curve f(x) = (x + 3)² and the line g(x) = - x - 1 and bound above the x-axis.

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The means are the same and the standard deviations are different.

There are two lists given for which the means and the standard deviations need to be compared. So we first find the mean and standard deviation of each list one-by-one using the formulas,

Mean = (1/n)∑x

Variance = [(1/n)∑x²]- mean²

Standard deviation = √variance

List A  

x:  1      2     3      4     5      6

x²: 1      4     9    16    25     36

n = 6

Mean = (1/6)[1+2+3+4+5+6] = 21/6 = 3.5

Variance = 1/6[1+4+9+16+25+36] - 3.5² = 15.167-12.25 = 2.917

Standard deviation = √2.917 = 1.71

List B

x:  2    3    3     4     4    5

x²: 4    9    9    16   16   25

Mean = 1/6(2+3+3+4+4+5) = 21/6 = 3.5

Variance = 1/6(4+9+9+16+16+25)-3.5² = 13.167 - 12.25 = 0.917

Standard deviation = √0.917 = 0.9576

Hence the means are the same and the standard deviations are different.

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X+1 depicts horizontal linear equation as x = -1 and slope = 0.

Given that the slope is 0, it shows a horizontal linear equation.

Every point on a horizontal line has the same y-coordinate.

If two points have the same y coordinate, b, then the line's equation is y=b.

The y-intercept of the horizontal line y=b is the point (0,b). The line y=0 is the only x-intercept for horizontal lines.

Horizontal lines have zero slope.

As a result, in the slope-intercept equation y = mx + b, m = 0. The equation is Y = b, where b is the y-coordinate of the y-intercept.

A line that is perpendicular to the x-axis is referred to as a horizontal line.

The graph of a relation of the form x = 5 is a line parallel to the origin since the value of x never changes.

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Answer:

Step-by-step explanation:

c lol

The ratio is 1:8 and 1:64

Since each tile is one sixth of an inch in width and one fourth of an inch in length.

That is L1= 1/4  in addition to W1= 1/6 inches.

The real tiles are one sixth of a foot long and one tenth of a foot wide.

Since 1 foot equals 12 inches, that is in inches and inches. that is L2=2 and W2= 4/3

So, the length of the tile divided by its real length is equal to L1/L2

=(1/4)/2= 1/8

In addition, the relationship between the area of the tile in the model and the real area is given by:

(1/4 x 1/6)/ 2 x 4/3

= 1/64

Second method

Since there is a 1/8 ratio between the width of the model's tiles and their real width

As a result, there is dilatation with a scale factor of 1/8.

By virtue of dilatation, their area ratio = (1/8)^2 =1/64.

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Answer:   Take the help of the Percentage Difference From X to Y Calculator to evaluate the increase/decrease from 105 to 125 is 19.0476% on dividing the absolute value with the average value and multiplied by 100.

Step-by-step explanation:

Hope Fully this helps you

The z-scores that are the cutoffs are given as follows:

a. z = 1.645.

b. z = -1.96.

c. z = -0.51.

d. z = 0.

e. z = 0.

The z-score of a measure X of a variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we have that:

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Answer:

40

Step-by-step explanation:

2400 divided by 60 is 40

I hope this helps!

The equation of the line that passes through the point (6,-5) and has a slope of -1/6 is y = (-1/6)x  - 4.

We know that, the slope intercept form of a line is given by:-

y = mx + c

Where,

m represents the slope of the line,

c represents the y -intercept and,

(x,y) represent the coordinates of each of the ordered pairs in the line

Hence, we can write,

m = -1/6

One of the ordered pairs, (x,y) is (6,-5).

Hence, we can write,

-5 = (-1/6)*6 + c

-5 = -1 + c

c = -5 + 1

c = - 4

Hence, the equation of the line is given by:-

y = (-1/6)x  - 4

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In Mrs. Brown’s 75% percent of the class likes to dance .

What are mathematics operations?

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Given:

number of students in Mrs. Brown’s class = 24

number of students likes to dance = 18

Then to find the percent of the class likes to dance we divide 18 by 24 and multiply with 100:

percent of the class likes to dance = (18/24) x 100

percent of the class likes to dance = 75%

Therefore,  in Mrs. Brown’s 75% percent of the class likes to dance .

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Answer:75%

Step-by-step explanation:

number of students in Mrs. Brown’s class = 24

number of students likes to dance = 18

Then to find the percent of the class likes to dance we divide 18 by 24 and multiply with 100:

percent of the class likes to dance = (18/24) x 100

percent of the class likes to dance = 75%

Therefore,  in Mrs. Brown’s 75% percent of the class likes to dance.

Answer:

angle A: 75 degrees

Step-by-step explanation:

because m and n are both 180 degree angles so when you do 180-105 you get 75

a,d,e,h=105 degrees

b,c,f,g= 75

because 105+75=180

Given the point:

(-1, 4)

Let's find the equation of the line that passes through the point and is perpendicular to the line x = -4.

Here, the given line x = -4 is a vertical line that is always at x = -4.

The slope of a vertical line is undefined.

Since x = -4 is a vertical line it means the slope is undefined.

The slope of a line perpendicular to a vertical line is always zero.

Also, the line perpendicular to a vertical line must be a horizontal line.

Therefore, since the perpendincular line passes the point (-1, 4), it means the line will be:

y = 4

hereforem, the equation of the line that passes through the point (-1, 4) and is perpendicular to the line x = -4 is:

y = 4

ANSWER:

y = 4

The percent of the budget that is destined for sales is 19%, the percent for support is 28% and the percent for editorial is 3%. All together, they represent the 50% of the total budget. That 50% is equivalent to $62,500,000, to find the total annual budget divide this amount by the percent that it represents (in decimal form which is 0.5):

The total annual budget is $125,000,000.

Answer:EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

The non real roots of the polynomial x³ – 7x² + 15x – 25 = 0 are; 1 + 2i, 1 – 2i

Non real roots are simply imaginary roots.

We are told that the real roots of the equation  x³ – 7x² + 15x – 25 = 0 is 5.

Now, it means that (x - 5) is a factor of the given polynomial. Thus, we can factorize the polynomial as;

(x - 5)(x² - 2x + 5) = 0

Now, to find the non - real roots, we will use quadratic formula on (x² - 2x + 5) to get;

x = [-(-2) ± √((-2)² - (4 * 1 * 5))]/2(1)

x = (2 ± √(-16))/2

x = 1 ± 2i

x = 1 + 2i, 1 – 2i

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Answer:

c

Step-by-step explanation:

Using it's formula, it is found that the bond's yield with a face value of $5,000, yield of 7% and rate of 8%, is of 7.48%.

The bond's yield is given according to the following formula:

Yield = Annual Coupon Payment/Bond Price

These values are calculated considering the face value, the current yield and the coupon rate, all parameters which are given in this problem.

The Annual Coupon Payment is given by the multiplication of the face value and the Coupon Rate, hence:

Annual Coupon Payment = 5000 x 0.08 = $400.

The bond price is the given by the multiplication of the face value and 100% plus the yield, hence:

Bond Price = 5000 x 1.07 = $5350.

Then the bond's yield is given as follows, applying the formula:

Yield = 400/5350 = 0.0748 = 7.48%.

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When the function f is transformed to g, the equation is -45.5x

The equation of function f is given as

f(x) = 6.5x

The transformation is given as

The above transformation rule can be represented as

(x, y) = (-x, 7y)

When the above rule is applied, we have the following equation

g(x) = -7f(-x)

So, we have

g(x) = -7 * 6.5x

Evaluate

g(x) = -45.5x

The above equation is a linear function

So, the domain and the range are the set of all real values and the y-intercept is 0

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A list of fixed fees for services recorded on the encounter form is called the Superbills.

The purpose of encounter forms, often referred to as super bills, is to "document services performed by recording the diagnostic and procedure codes, which serve as the foundation for billing and receipt of payment for services." Every time a patient or customer receives a service, the provider records that service, often into medical claims software that may automate much of the subsequent procedure.

This technique entails coding (procedure codes and, if necessary, diagnostic codes), billing/invoicing, and/or transmission to the patient's or client's insurance provider. For the client's health and treatment plans as well as for proper billing, it is crucial to make sure that the appropriate information is documented. This is why encounter forms are such a crucial component of healthcare.

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In mathematics, time is characterized as a continuing and continuous series of events that take place one after another, from the past through the present and into the future.

Yolanda watched videos for 1/2 minute in all.

Time can be viewed as an ongoing and continuous series of related events that take place one after another, from the past through the present and into the future, in mathematics.

Time is used to sequence events as well as to quantify, measure, and compare the length of occurrences or the gaps between them.

Given,

Yolanda watched a video for 3/8 minutes.

She watched another video for 1/8 minute.​

Solution:

Total video watch hour = 3/8 + 1/8

Total video watch hour = 4/8

On simplifying we get,

Total video watch hour = 1/2 minutes

Yolanda watched videos for 1/2 minute in all.

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Answer: a

Step-by-step explanation:

because 140 squared = 200x=48/4

Answer

2

Step-by-step explanation:

1 + 1 =2

To find the final cost of the sales tax you need to:calculate the tax

As the sales tax is 9.75% you calculate the 9.75% of $200.00

Answer:

Yes.

Step-by-step explanation:

Divide 430/17 and you get around 25, signifying the correct answer is right in the middle of Hailey's estimation.

Given the equation that

The first and second graphs represent even function.

If f of x is equal to f of −x for all the values of x, then it is called Function. This implies that function is same for the positive x-axis and the negative x-axis. Trigonometric even function, and secant function are some of the examples of even function.

Following are the properties of an even function:

As the graph of first and second is symmetric about the y axis, therefore both represent even functions.

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Step 1

Given; What is the precise definition of a limit in calculus?

The required definition is;

Answer;

Let f be a function defined on some open interval containing a (except possibly at a).

Then the limit as x approaches a of f is L written as;

if and only if

Equation of the line passing through the point of (-20, 4) and perpendicular to the line [(2x + 5y) = 10] will be [2y = (5x + 108)].

As per the question statement, a line passes through the point of (-20, 4) and is perpendicular to the line [(2x + 5y) = 10].

We are required to determine the equation of the above-mentioned line.

To solve this question, we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)],

where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line.

Also, we need to know about the mathematical fact that, the product of the slopes of two perpendicular lines equate to (-1), i.e., if (m₁ and m₂) are the slopes of two perpendicular lines, then [(m₁ * m₂) = (-1)].

Converting [(2x + 5y) = 10] into the point-slope form of line, we get,

(2x + 5y) = 10

or, [5y = {(-2x) + 10}]

or, [y = {(-2/5)x + 2}]

Therefore, Slope of the line [(2x + 5y) = 10] is (-2/5).

Hence, slope of the line perpendicular to [(2x + 5y) = 10] is [-1/(-2/5)], i.e.,

Slope of the line perpendicular to [(2x + 5y) = 10] is (5/2).

Now, using [m = (5/2)] and (x₁, y₁) as (-20, 4), equation of the line will be

[(y - 4) = (5/2){x - (-20)}]

or, [(y - 4) = (5/2)(x + 20)]

or, [(y - 4) = (5/2x) + 50]

or, [2(y - 4) = 5x + 100]

or, [(2y - 8) = (5x + 100)]

or, [2y = (5x + 108)]

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Answer:

18.23

Hope this is right! (don't worry I did the math)

Answer:

I think it is a function???

Step-by-step explanation:

Because a graph represents a function if it impossible to draw a vertical line that intersects the graph more than once.

I'm not sure if I'm correct, let me know please.