What is the quotient of (x³ + 3x² + 5x + 3) = (x + 1)?
O x² + 4x +9
O x² + 2x
Ox²+2x+3
O x² + 3x + 8

The approximate volume of Samuel's wooden cylinder is calculated as: 56.52 cubic inches.

The volume of a cylinder can be calculated by multiplying the circumference with the height of the cylinder.

Therefore, the volume of a cylinder is calculated as V = πr²h, where h is the height and πr² is the circumference of the cylinder.

Given the following:

Circumference = 9.42 inches

Height of the cylinder = 6 inches.

Thus, we have:

Volume of cylinder = 9.42 * 6 = 56.52 cubic inches.

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The probability of randomly selecting a girl is 0.606. the correct option is (C).

Given that, Total newborn babies = 850

No. of boys = 335

We need to find the probability of randomly selecting a girl baby from this population of 850 babies.

Let G be the no. of girls in the population. Then, G + 335 = 850=> G = 850 - 335=> G = 515

Therefore, the number of girls in the population is 515. Hence, the probability of randomly selecting a girl from the population is:

P (girl) = No. of girls / Total newborn babies= 515 / 850= 0.606

Thus, the correct option is (c) 0.606.

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Answer:

Question is not asked properly. Details missing. The data is not given.

The compared to mothers who gave birth for the first time at the age of under 30 to determine the incidence of breast cancer.

The study design used for this investigation of the association between age at first birth and breast cancer is Cohort Study.What is a cohort study?A cohort study is an analytical research approach in which a group of people with a shared trait or experience are followed over time. Cohort studies are used to determine the incidence of a disease, changes in morbidity and mortality rates, and to recognize risk factors for a disease. In this study of breast cancer, the mothers who gave birth for the first time at the age of 30 or older were considered exposed, and they were compared to mothers who gave birth for the first time at the age of under 30 to determine the incidence of breast cancer.

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Answer:

hard question

Step-by-step explanation:

Happy Thanksgiving

The parts of the algebraic expression 3x - 2 are:

3 is the coefficient of x.

x is the variable

2 is the constant term

The algebraic Expression is given as:

3x - 2

Now, some parts of algebraic expressions are coefficients, variables and constant.

Coefficient is defined as the figure or number that is attached to the variable in an algebraic expression.

The variable is the letter that can change because different numbers are used for it.

The constant is the number that stands alone and doesn't change.

Thus, in 3x - 2:

3 is the coefficient of x.

x is the variable

2 is the constant term

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Answer:

The court for 10 and under is 18 feet shorter so the area of this court is ( 78 − 18 ) × 27 = 1620 (78-18)\times27=1620 (78−18)×27=1620 square feet. Therefore, the area of this court is 2106 − 1620 = 486 2106-1620=486 2106−1620=486 square feet less than that of the regular court.

The number of products of each type that they can assemble each week to maintain maximum production are 3 Type A and 2 Type B.

In order to write a system of linear equations that could be used to model the situation, we would assign variables to the cost of component and the labour man-hours respectively as follows:

Next, we would translate the word problem into system of linear equations as follows. Since the business has $156.00 available to buy components each week, a linear equation that models the situation is given by;

36x + 24y = 156      .....equation 1.

Additionally, the total labour man-hours available each week is 96 man-hours;

16x + 24y = 96      .....equation 2.

Subtracting equation 2 from equation 1, we have:

20x = 60

x = 3.

y = (96 - 16x)/2

y = (96 - 16(3))/24

y = 48/24

y = 2.

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Answer: The odds in favor of a horse winning a race are given as 8:9, which means that the probability of the horse winning is 8/(8+9) = 8/17. Therefore, the probability of the horse winning the race is 8/17.

Step-by-step explanation:

The probability of the horse winning the race is 8/17.

The odds in favor of a horse winning a race is 8:9. To find: The probability of the horse winning the race. The odds are defined as: The odds in favor of an event = Number of ways an event can occur : Number of ways the event cannot occur.

Here, the odds in favor of a horse winning a race = 8 : 9. That means, the horse can win in 8 ways and lose in 9 ways. Therefore, the probability of the horse winning the race can be calculated as follows:

Probability of horse winning the race = Number of ways the horse can win / Total number of possible outcomes
= 8 / (8 + 9) [As total outcomes = winning outcomes + losing outcomes]
= 8 / 17
Therefore, the probability of the horse winning the race is 8/17.

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If 484 of the disks produced by the first machine are acceptable and 480 of the disks produced by the second machine are acceptable, random , 10% and large counts are met. Correct option is E.

To calculate a confidence interval for the difference between the proportions of acceptable DVDs produced by two different fabricating machines, we need to ensure that the following conditions are met:

Random: The sample of DVDs from each machine should be selected randomly, without any bias. This is important to ensure that the sample is representative of the population of all DVDs produced by each machine.

The sample size should be no more than 10% of the population of DVDs produced by each machine. This is important to ensure that the sampling distribution of the sample proportions is approximately normal.

Large counts: The number of acceptable and unacceptable DVDs in each sample should be large enough to satisfy the normal approximation to the sampling distribution of the sample proportions.

Therefore, the correct answer is (e) Random: met, 10%: met, Large Counts: met. All conditions for calculating a confidence interval for the difference between the proportions of acceptable DVDs produced by two different fabricating machines are met in this scenario.

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Answer: Greater than

Step-by-step explanation: 96 is a larger number than 1

Answer: 96 is greater than one

Step-by-step explanation:

96 is greater than one because if you plot it on a number line in would be far more than zero

the atmosphere has the smallest mass, followed by the oceans, inner core, crust, outer core, and mantle having the largest mass.

Based on the given masses, the order from least to greatest for the parts of the Earth would be:

Atmosphere (5.1 × 10¹⁸ kg)

Oceans (1.4 × 10²¹ kg)

Inner core (9.675 × 10²² kg)

Crust (2.6 × 10²² kg)

Outer core (1.835 × 10²⁴ kg)

Mantle (4.043 × 10²⁴ kg)

Therefore, the atmosphere has the smallest mass, and the list goes according oceans, inner core, crust, outer core, and mantle having the largest mass. The Earth is composed of several layers, including the crust, mantle, outer core, and inner core. The mass of the Earth is distributed unevenly among these layers, with the mantle being the most massive layer, accounting for about 84% (percentage) of the Earth's total mass. The core of the Earth is made up of the outer core and the inner core, which are predominantly composed of iron and nickel. The crust is the thin, outermost layer of the Earth, while the atmosphere is the layer of gases that surround the planet. Despite the atmosphere being the layer with the smallest mass, it plays a critical role in regulating the Earth's climate and sustaining life on the planet.

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Complete question

The mass of Earth is made up of these parts.

oceans     1.4 × 1021kg

crust      2.6 × 1022kg

atmosphere   5.1 × 1018kg

mantle     4.043 × 1024kg

outer core   1.835 × 1024kg

inner core   9.675 × 1022kg

What is the order, from least to greatest, of the masses of each part of Earth? Order the parts from least to greatest, with 1 being the smallest mass and 5 the greatest mass.

Answer:

$328.86

Step-by-step explanation:

1 dress is $8.70

42 dresses = 42 x 8.70

42 dresses = $365.40

10% of total cost = 10/100 x 356.40

36.54

Deduct the discount from the total amount

$365.40 - $36.54 = $328.86

Answer:

[tex]40 {ft}^{2} [/tex]

Step-by-step explanation:

You will get the shaded area by subtracting the smaller rectangle from the area of the larger restangle.

The larger rectangle's area would be

[tex]10 \: ft \: \times 8 \: ft = 80 \: {ft}^{2} \\ [/tex]

The smaller rectanlge's area is

[tex]5 \: ft \: \times \: 8ft \: = 40 \: {ft}^{2} [/tex]

The shaded region would be

[tex]80 - 40 = 40 {ft}^{2} [/tex]

The linear relation is (a) A the population of a town in increasing by ten people each year

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

The list of options that represent the situations

Situation A is linear because the increase in population is constant and can be represented by a linear equation (y = mx + b),

The equation would be y = 10x + b, where b is the population at year 0.

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The 95% confidence interval for the population mean IQ score is (99.62, 111.98), therefore option(A) use normal distribution

Since the sample size is greater than 30 (n=20), we can use the normal distribution to construct a confidence interval for the population mean.

We can use the formula:

Confidence Interval = sample mean ± z (standard error)

where z is the critical value from the standard normal distribution corresponding to the desired level of confidence, and the standard error is calculated as:

standard error = o / sqrt(n)

where o is the sample standard deviation and n is the sample size.

Assuming a 95% confidence level, we can find the critical value z from the standard normal distribution table or using a calculator. The critical value for a 95% confidence level is 1.96.

Substituting the values in the formula, we get:

Confidence Interval = 105.8 ± 1.96 × (15 / sqrt(20))

Confidence Interval = 105.8 ± 6.18

Therefore, the 95% confidence interval for the population mean IQ score is (99.62, 111.98).

Therefore, we can use the normal distribution to construct a confidence interval for the population mean IQ score.

Therefore, the correct option is (A) Use normal distribution.

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Answer:

X = -22

Step-by-step explanation:

WX = 1/7 WY

The length of WY = 2 - (-26) = 2 + 26 = 28

WX = 1/7WY = 28/7 = 4

X = -26 + 4 = -22

Answer:

X is at -22

Step-by-step explanation.

distance between W and Y is 28. 28/7 is 4. 4 away from w is -22.

Therefore , the solution of the given problem of triangle comes out to be triangle's length, rounded to two decimal places, is roughly 33.33 units.

A polygon is a hexagon if it has not less than one extra segment. It has a straightforward rectangle-shaped structure. Only edges A and B can differentiate something like this from an ordinary triangular shape. Despite the exact collinearity of the borders, Euclidean geometry only produces a part of the cube. Three edges and three angles make up a triangle.

Here,

Finding the length of each side and adding them together will allow us to determine the perimeter of the triangle whose points are E(12,-5), D(-1,-1), and F(7,-4).

The length of EF is given below using the distance formula:

=> √((7 - 12) ² + (4 - (- 5))² = √(25 + 81) = √(106) =  10.30

The ED is as follows:

=>  sqrt((-1 - 12)2 + (-1 - (-5))2) = sqrt(169 + 16) = sqrt(185), which is 13.60.

And DF is this long:

=>  √((7-1))² + (4-1))² = √(64+25) = √(89) = 9.43

As a result, the triangle's circumference is:

=>  10.30 + 13.60 + 9.43 ≈ 33.33

The triangle's length, rounded to two decimal places, is roughly 33.33 units.

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Answer:

x = 2 and y = 0

Step-by-step explanation:

Let's solve your system by elimination.

2x−3y=4;4x+3y=8

2x−3y=4

4x+3y=8

Add these equations to eliminate y:

6x=12

Then solve 6x=12 for x:

6x=12

x = 2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x−3y=4

Substitute 2 for x in 2x−3y=4:

(2)(2)−3y=4

−3y+4=4  (Simplify both sides of the equation)

−3y+4+−4=4+−4  (Add -4 to both sides)

−3y=0

y = 0

The particular equation of the outer ellipse is therefore: 1002x2 + 2402y2 - 2402 * 1002 = 0, the inner ellipse is therefore:502x2 + 2002y2 - 2002 * 502 = 0, Clearance= 343.29 yd and Approximate seats= 47124 seats

The plan for a new football stadium calls for the stands to be in a region defined by two concentric ellipses. The outer ellipse is to be 240 yd long and 200 yd wide. The inner ellipse is to be 200 yd long and 100 yd wide. A football field of standard dimensions, 120 yd by 160 ft, will be laid out in the center of the inner ellipse.

To find the particular equations of the two ellipses, we can make use of the following: standard form of equation of an ellipse:x2/a2 + y2/b2 = 1 The outer ellipse: Major axis = 240 yd = 480 yd/2a = 480/2 = 240 yd Minor axis = 200 yd/2b = 100 yd Now, substituting the values in the standard equation of an ellipse, we have:x2/2402 + y2/1002 = 1Multiplying both sides by 2402 * 1002, we have: 1002x2 + 2402y2 = 2402 * 1002

The particular equation of the outer ellipse is therefore: 1002x2 + 2402y2 - 2402 * 1002 = 0 The inner ellipse: Major axis = 200 yd = 400 yd/2a = 400/2 = 200 yd Minor axis = 100 yd/2b = 50 yd Now, substituting the values in the standard equation of an ellipse, we have: x2/2002 + y2/502 = 1 Multiplying both sides by 2002 * 502, we have:502x2 + 2002y2 = 2002 * 502The particular equation of the inner ellipse is therefore:502x2 + 2002y2 - 2002 * 502 = 0

The eccentricity of an ellipse is given by the formula: e = √(1 - b2/a2)For the outer ellipse: a = 240, b = 100∴ e = √(1 - 1002/2402) = √0.694 = 0.833 For the inner ellipse: a = 200, b = 50∴ e = √(1 - 502/2002) = √0.9375 = 0.968

To find the clearance between the corner of the field and the inner ellipse in the direction of the end line, we need to find the distance between the foci of the inner ellipse, which is given by: d = 2 * √(a2 - b2)where a = 200 yd and b = 50 yd. Substituting the values, we have: d = 2 * √(2002 - 502)≈ 387.29 yd The clearance between the corner of the field and the inner ellipse in the direction of the end line is approximately 387.29 - 120/2 = 343.29 yd.

The area of the stands is the area between the two ellipses. Using the formula given in the question, A = πab, where a = 240 yd/2 and b = 200 yd/2, the area is: A = π * 120 * 100 = 37,699.1 sq yd Approximate seating capacity of the stadium will be number of seats = 37,699.1 / 0.8 = 47123.88 ≈ 47124 seats.

A circle is a special case of an ellipse, where both radii are equal. In the case of a circle with radius r, the formula for the area of an ellipse is reduced to the formula for the area of a circle: A = πab = πr2 = area of a circle

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Answer:

See attached image

Step-by-step explanation:

This is how I did it

I made point A as (0,0)

Point B is 12 units right and 4 units up from A. So B is(12,4)

Point C is 8 units right and 8 units down from A so it is at (8, -8)

When dilated by 1/4 with point A as center of dilation, B coordinates are reduced by 1/4 so the image B' coordinates are (12/4, 4/4) = (3,1)

C coordinates are reduced by 1/4 so C' coordinates of image are (8/4, -8/4) = (2, -2)

The A' coordinates are unchanged at A'(0,0)

So the image is A'B'C' as shown in the blue triangle

I do not know what that other triangle is for, it plays no role in the dilation

I also realize you may have been given some other strategy for solving but this is the way I did it

I hope that works for you.

Based on according to the ratio given for PQ:QR, The length of side PS on the line is 34 inches.

We can use the ratios given to find the lengths of the other segments and then add them up to get the length of PS.

Let x be the length of QR. Then, according to the ratio given for PQ:QR, we have:

PQ:QR = 3:4

6:x = 3:4

Multiplying both sides by 4x, we get:

24 = 3x

x = 8

So, QR is 8 inches long. Now, using the ratio given for QR:RS, we have:

QR:RS = 2:5

8:y = 2:5

Multiplying both sides by 5y, we get:

40 = 2y

y = 20

So, RS is 20 inches long. Finally, we can add up the lengths of PQ, QR, and RS to get the length of PS:

PS = PQ + QR + RS

PS = 6 + 8 + 20

PS = 34

Therefore, the length of PS is 34 inches.

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Answer:

c) The vertical asymptotes are x = (-5 + √(13))/4 and x = (-5 - √(13))/4. To find them, set the denominator equal to zero and solve for x.

d) There are no holes in the function.

e) The zeros are x = 0, x = 2, and x = -3. To find them, set the numerator equal to zero and solve for x.

f) The slant asymptote is y = x + 2 - (3.5x + 1.5)/(2x^2 + 5x + 3). To find it, use long division to divide the numerator by the denominator. To find the slant asymptote of the given rational function, we use long division to divide the numerator by the denominator. The quotient of the division gives the equation of the slant asymptote.

g) The domain is (-∞, (-5 - √(13))/4) U ((-5 + √(13))/4, ∞). To find it, set the denominator not equal to zero and solve for x. To find the domain of the given rational function, we set the denominator not equal to zero and solve for x. The domain is all real numbers except the values of x that make the denominator equal to zero.

I hope this helps you! I'm sorry if it's wrong! If you need more help, ask me! :]

Answer: 10,000

Step-by-step explanation:

10^5 = 100000 and 10^-1 = 1/10, so the answer is 10000

If in a fraction the numerator is 1 less than the denominator if 1 is added to the numerator and 5 to denominator the fraction becomes 1 / 2 . The  the original fraction​ is4/5.

Let's assume that the denominator of the original fraction is x. Then, according to the problem, the numerator is x - 1.

If 1 is added to the numerator and 5 is added to the denominator, we get:

(x - 1 + 1) / (x + 5) = 1/2

Simplifying the left side of the equation, we get:

x / (x + 5) = 1/2

Multiplying both sides by 2(x + 5), we get:

2x = x + 5

Subtracting x from both sides, we get:

x = 5

So, the denominator of the original fraction is 5, and the numerator is 5 - 1 = 4.

Therefore, the original fraction is 4/5.

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Answer:

[tex]x=\frac{7}{30}[/tex]

Step-by-step explanation:

Solve for x:

[tex]x+\frac{2}{3}=\frac{9}{10}[/tex]

Subtract [tex]\frac{2}{3}[/tex] on both sides

[tex]x=\frac{7}{30}[/tex]

Answer:

X= 7/30

Step-by-step explanation:

subtract 2/3 from both sides.

X+ 2/3 = 9/10

X +2/3 -2/3 =9/10 -2/3

simplify the expression

X + 2/3 -2/3 =9/10 -2/3

X=7/30

[tex]cos \beta = \frac{adjuscent}{hypotenuse} \\ cos15 = \frac{47}{x} \\ x = \frac{47}{cos15} \\ x = 48.7[/tex]

The solution of the given problem of expression comes out to be  9x³.

There is a need for calculations like variable multiplying, splitting, joining, and currently removing. If they were combined, it would read: A mathematical formula, some data, and an equation. Values, elements, and mathematical operations like additions, subtractions, mistakes, subdivisions, but also arithmetic formulas all make up a declaration of truth. It is possible to assess and analyse words and sentences.

Here,

The following is the provided sentence's algebraic expression:

=> 9x³

where x is a numerical symbol.

Therefore , the solution of the given problem of expression comes out to be  9x³.

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Complete question:

Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.

{Nine times the difference of 8 and a number.}

Nine times the difference of 8 and a number.

Finding a line segment parallel to another segment and passing through a given point is true.

A line segment is a finite portion of a line that is bounded by two distinct points.

The statement is asking whether the following method is true or false for finding a line segment parallel to another segment and passing through a given point:

This method is called the "fold-and-copy" method, and it is a valid way to construct a segment parallel to another segment and passing through a given point. The reason this works is because when the paper is folded along the given point, the fold line is perpendicular to the original segment. When the segment is copied onto the paper on both sides of the fold, the resulting segments are also perpendicular to the fold line. Since two lines that are both perpendicular to the same line are parallel, the resulting segment is parallel to the original segment. The resulting segment also passes through the given point, since it was copied from the original segment which passes through the given point. Therefore, the statement is true.

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For the pizza box shaped in triangular prism, the volume is obtained as 58.32 cubic inches.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The volume of a triangular prism is given by the formula:

V = (1/2) × base × height × length

where the base and height are the dimensions of the triangular base and the length is the height of the prism.

In this case, the base of the prism is a right-angled triangle with base 10.8 inches and height 7.2 inches.

The area of the base can be found as -

Area = (1/2) × base × height

= (1/2) × 10.8 × 7.2

= 38.88 square inches

The length of the prism is given as 9 inches.

Therefore, the volume of the container can be calculated as -

V = (1/2) × base × height × length

= 38.88 × 1.5

= 58.32 cubic inches

Hence, the volume of the container is 58.32 cubic inches.

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