Find the surface area of the sphere. Round your answer to the nearest hundredth.

Answer:

[tex]\boxed{f(x)=(3)(2)^x}[/tex]

Step-by-step explanation:

First, we need to substitute the coordinates of the two given points in the ecuation [tex]f(x)=ab^x[/tex]:

[tex]3=ab^{0} \qquad \textbf{ec.1}\\6=ab^{1} \qquad \textbf{ec.2}[/tex]

Remember that any number raised to the power 0 is equal to 1.  So:

[tex]3=a \qquad \textbf{ec.3}[/tex]

now, we can substitute in ec.2 and solve for b:

[tex]6=3b\\ b=2[/tex]

Finally:

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

Therefore, we have found the solution to the exercise

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Each squad has to have an equal amount of men and women. The maximum number of teams that can participate is 8.

A location in mathematics where a function has its maximum value. The value is an absolute maximum if it exceeds or is equal to all other function values. It is a relative or local maximum if it is simply greater than any neighboring point.

Number of girls = 16.

Number of boys = 20.

In order to calculate the maximum number of teams that can enter, we must determine the most prevalent criteria for both boys and girls based on the information provided. As follows:

Factors of 18 [tex]= 1, 2, 4, 8[/tex]  and 16.

Factors of 24 = [tex]1, 2, 3, 4, 6, 8, 12[/tex] and 24.

Highest common factor = 8

Therefore, the greatest number will be 8.

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The probability that during a 10-hour flight an airplane will fail to reach its intended destination or crash is

To solve this problem, we can use the binomial distribution, which gives the probability of k successes in n independent trials, each with the same probability of success p. In this case, a "success" is defined as the engine not failing, and a "failure" is defined as the engine failing.

Let X be the number of engines that fail during the flight. Since each engine can fail independently of the other engine, X follows a binomial distribution with n = 2 (the number of engines) and p = 0.21 (the probability of a single engine failing). The probability of X failures is:

P(X = 0) + P(X = 1) + P(X = 2)

where P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), and (n choose k) is the binomial coefficient.

Using this formula, we can calculate the probability of each possible value of X and add them up:

P(X = 0) = (2 choose 0) * 0.21⁰* 0.79²= 0.6241

P(X = 1) = (2 choose 1) * 0.21¹* 0.79¹= 0.32994

P(X = 2) = (2 choose 2) * 0.21² * 0.79⁰ = 0.04689

Therefore, the probability of the plane failing to reach its intended destination or crashing is:

P(X >= 1) = P(X = 1) + P(X = 2) = 0.32994 + 0.04689 = 0.37683

So the probability of the plane not making it to its destination is about 37.7%.

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The value of the angle X is 99 degrees. Option E

To determine the value of the angle, we need to note that the sum of the interior angles of a given regular polygon is determined with the formula;

(n -2)180

Such that 'n' is the number of sides of the polygon

From the information given, we have that;

The value of n = 6

Then, the sum of interior angles = (6-2)180 = 4(180)

Multiply the values

= 720

Equate the angles

x + 108 + 146 + 101 + 113 + 153 = 720

Add the values

x = 720 - 621

subtract the values

x = 99 degrees

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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:

[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 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.

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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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:

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

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

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

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

By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x). Thus, Left by 4 units is the answer.

A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The solutions of the equation are the points at which the graph of the function intersects the x-axis.

The functions, that are quadratic, f(x) and g(x) are described in the table. From the table, it can be seen that f(x) and g(x) are not equal to each other, as the values for each x are different. To match f(x) and g(x), one of the functions must be shifted.

By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x).

This can be calculated by subtracting the g(x) values from the f(x) values for each x.

For example, at x = -2, the difference between f(x) and g(x) is -32.

This difference is the same for all x values, meaning that f(x) must be shifted left by 4 units to match g(x). Thus, the correct answer is Left by 4 units.

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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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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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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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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.

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:

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.

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! :]

The length of the other  parallel side of the parallelogram (b2) is 8.3m with the area of the parallelogram 100m².

It is a four-sided shape that has two pairs of parallel lines with all sides equal in length.

The area of the parallelogram is 100m² and the height is 10m, so the base of the parallelogram is 13m. This forms a right triangle with one side of the parallelogram. To calculate the length of the other non-parallel side (b²), we can use the squaring method.

This can be expressed as:

a² + b² = c²

Where a and b are the two shorter sides of the triangle, and c is the longest side.

Substituting in the values given, we get:

x² + 10² = 13²

x²=13²-10²

x= √169-100

x = √69

x = 8.3m

Therefore, the length of the other non-parallel side of the parallelogram (b2) is 8.3m.

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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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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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Therefore , the solution of the given problem of triangle comes out to be EG  = 23.14.

A triangle is a hexagon because it has two or more extra polygon sections. Its form is a simple rectangular one. A and B are the only 2 different edges of a form that can set it apart from a regular triangular. When bounds are still not precisely collinear, Euclidean geometry produces a single section rather than a full cube. Three edges and three angles make up a triangle.

Here,

The length of EG can be determined as follows if EF = 24:

First, we calculate the length of FG using the Pythagorean theorem:

=> FG² = EF² - EG²

=> 10² = 24² - EG²

=> EG² = 24² - 10²

=> EG² = 536

=> EG = √536 ≈ 23.14

Consequently, EG 23.14 when FG = 10 and GH = 7 if E is the right angle apex of a right triangle EFG and EF = 24.

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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

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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Answer:

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

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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Zack wheeler had a war of 7. 8 in the 2021  season this means that He scored an average of 7.8 runs per game.

This means that Zack scored an average 7.8 runs per game.

An average is a single number represented as a list of numbers, usually the sum of the numbers divided by the number of numbers in the list (arithmetic mean). For example, the numbers 2, 3, 4, 7, and 9 (for a total of 25) have an average of 5. Depending on the context, the average can be another statistic, such as the median or the mode. Average personal income, for example, is often given as the median – a figure below 50% of personal income and above 50% of personal income – because the average would be higher if some personal income of billionaires were included. Therefore, it is recommended to avoid using the word "average" when referring to measures of central tendency.

Complete Question:

Zack Wheeler had a WAR of 7.8 in the 2021 season. What does this mean?

A. He scored an average of 7.8 runs per game.

B. His team won an average of 7.8 more games than other teams in MLB.

C. His team won around 7.8 more games than it would have with a replacement player.

 D. He scored around 7.8 more runs than a replacement player would have.

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