I need help on this asap!

When the sphere has a radius of 5 feet, the radius is increasing at a very slow rate of 0.018 feet per minute if volume is increasing.

The volume of a sphere formula, V = (4/3)r3, must be used to determine the rate of change of the radius.

Using this formula's derivative with regard to time t, we obtain:

[tex]dV/dt = 4r2(dr/dt)[/tex].

Here, r: radius of the sphere, and we need to determine dr/dt, the rate of change of the radius when r=5. dV/dt is the rate of change of the volume, which is provided as 562 cubic feet per minute.

When we enter the provided values, we obtain:

[tex]562 = 4\pi (17)^2(dr/dt)[/tex]

0.018 feet per minute is equal to[tex]dr/dt = 562 / (4(17)2)[/tex].

As a result, the radius changes at a rate of about 0.018 feet per minute when the radius is 5 feet.

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The value of x given the following image is 13.

What is congruent angle?

When two angles have the same magnitude, they are considered congruent. In other words, they have the same angle degree. For example, if one angle measures 45 degrees, any other angle that also measures 45 degrees is congruent to it.

Congruent angles are denoted by the symbol ≅. So, if angle A and angle B have the same measure, we can write it as:

Angle A ≅ Angle B

Congruent angles have the same properties and characteristics, including being able to fit into the same spaces and be formed by the same geometric shapes. In practical terms, congruent angles are identical when placed side by side.

Finding the value of x :

Angle ABC and Angle EBD are congruent.

Value of Angle ABC is (-3x+14) degrees.

Value of Angle EBD is (-x-12) degrees.

Equating the two angles we get ,

[tex]-3x+14=-x-12[/tex]

[tex]-2x=-26[/tex]

[tex]2x=26[/tex]

[tex]x=13[/tex]

Therefore, the value of x given the following image is 13.

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Answer:

We have the equation:

-3 + sin(-3x) = -7/2

Adding 3 to both sides gives:

sin(-3x) = -1/2

The solutions for sin(x) = -1/2 are x = 7π/6 and x = 11π/6 in the interval [0, 2π).

We need to find the solutions for -3x in the interval [0, π).

For x = 7π/18, we get -3x = -7π/6, which is not in the given interval.

For x = 5π/18, we get -3x = -5π/2, which is not in the given interval.

For x = π/18, we get -3x = -π/2, which is in the given interval.

Therefore, the solution to the equation in the given interval is:

-3x = -π/2

x = π/6

First one is 6

second one is 12

third one is -8

hope this helps

Answer:

Step-by-step explanation:

x=6

x=12

x=-8

Step-by-step explanation:

Apply the power rule and multiply the exponents

The axis of symmetry of equation f(x) = x² - x³ - 4 is x = 2/3.

The axis of symmetry is a vertical line that passes through the vertex of a parabolic function, which is the highest or lowest point on the graph depending on the direction of the parabola. The equation f(x) = x² - x³ - 4 is a cubic function that can be written in standard form as:

f(x) = -x³ + x² - 4

To find the axis of symmetry, we need to first find the x-coordinate of the vertex. This can be done by taking the derivative of f(x) and setting it equal to zero:

f'(x) = -3x² + 2x = 0

x(2-3x) = 0

x = 0 or x = 2/3

Since the coefficient of the x³ term is negative, the vertex of the cubic function is a maximum. Therefore, the axis of symmetry is the vertical line passing through the x-coordinate of the vertex, which is x = 2/3.

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If a gift box is a cube that measures 8 inches by 8 inches on all sides. The lateral and surface area of the gift box without the lid is 384 square inches.

Since the gift box is a cube, all its sides have the same length of 8 inches. The lateral area of a cube is the sum of the areas of all its sides except the top and bottom faces, while the surface area includes all faces, including the top and bottom.

To find the lateral area, we need to add up the areas of the four vertical sides. Since they are all the same size, we can simply multiply the area of one of them by 4. The area of one side is the height times the width, which is 8 inches by 8 inches, so the area of one side is:

8 in x 8 in = 64 sq in

Therefore, the lateral area is:

4 x 64 sq in = 256 sq in

To find the surface area, we need to add up the areas of all six faces. The area of each of the four vertical sides is still 64 square inches, so the total area of these sides is:

4 x 64 sq in = 256 sq in

The area of the top and bottom faces is also 8 in x 8 in = 64 sq in, so the total surface area is:

256 sq in + 2 x 64 sq in = 384 sq in

Therefore, the lateral area of the gift box without the lid is 256 square inches, and the surface area is 384 square inches.

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Extrapolation is a useful tool for predicting future values based on past data

Bethany used a method of predicting future values from past values known as extrapolation. Extrapolation is a powerful tool for predicting future values, but it is important to remember that it only works if the underlying trend in the data does not change. In Bethany's case, she is making an assumption that her income over the next 10 years will follow the same trend as it did in the past 5 years.

In extrapolation, the assumption is that the data points that were observed in the past will continue in the same direction and with the same intensity into the future. Therefore, extrapolation can be used to make predictions about future values even when no new data points have been collected. It is important to remember, however, that any predictions made using extrapolation are only estimates and may not be accurate.

Extrapolation is used in many different fields, such as finance, economics, medicine, engineering, and even weather forecasting. For example, stock analysts may use extrapolation to make predictions about future stock prices based on past prices. Similarly, meteorologists may use extrapolation to make predictions about future weather conditions based on historical weather data.

Overall, extrapolation is a useful tool for predicting future values based on past data. However, it is important to remember that it only works when the underlying trend in the data does not change. Additionally, any predictions made using extrapolation are only estimates and may not be accurate.

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In a direct proof of the theorem "if r and s are rational numbers, then the product of r and s is a rational number," the following assumptions or facts are typically used:

Using these facts, a direct proof of the theorem can be constructed by assuming that r and s are rational numbers and then showing that their product is also a rational number. Specifically, we can express r and s as fractions with integer numerators and denominators, multiply their numerators together to obtain the numerator of the product.

Since the numerator and denominator of the product are both integers, and the denominator is nonzero, the product is a rational number.

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According to the Vertical Angle Theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.

The opposing angles created by the junction of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.

WH ⊥ VZ at y ,

Y is the midpoint of WX

Now since only one line can pass through W and Y ,

X must lie WH

Either W-Y-X-H of W-Y-H-X.

In any case W, Y, X and H are collinear.

Since, WH ⊥ VZ ⇒ WX ⊥ VZ at Y.

m∠VYW = m∠VYX = 90°

∠VYW ≅ ∠VYX = 90°.

Next,

Y is midpoint of WX

WY = XY

WY ≅ XY

Finally, VZ bisects ∠WYX

m∠WVY = m∠XVY

∠WVY ≅ ∠XVY

Using 1, 2, 3

ΔVWY ≅ ΔVXY by Right Hypotenuse side Congruency,

Alternatively ,

using 2, 3 and

VY ≅ VY

ΔVWY ≅ ΔVXY (by SSS congruence )

Using equations,

ΔVWY ≅ ΔVXY

by SAS congruence,

ΔVEY = ΔVXY by ASA Congruence

ΔVNY ≅ ΔVXY by AAS congruence

ΔVWY ≅ ΔVXY by AAS congruence.

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If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.

If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.

Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:

3x : x = 3 : 1

To solve for x, we can cross-multiply:

3x * 1 = x * 3

3x = 3x

We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:

3x = 243

x = 81

Therefore, there are 81 students at Rolling Hills Middle School who have pets.

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Answer: 290.

Step-by-step explanation:

9,280

How many times can 32 go into 9? no times.

How many times can 32 go into 92? 2 times.

2880 remaining.

How many times can 32 go into 2? no times.

How many times can 32 go into 28? no times.

How many times can 32 go into 288? 9 times.

00 remaining.

Since there is an extra zero, you add a zero to your final answer.

Answer: the answer is 21 percent

Step-by-step explanation:

when you have 16 of 52 which is all of the colors together then it will give you 21%

Answer:

21% or 4/13

Step-by-step explanation:

when you have 16 of 52 which is all of the colors together, then it will give you 21%

For fractions, you have 16 of 52, then you can simplify the fraction down to 4/13. Giving you the answer of a simplified fraction.

Using the formula of the area of the circle, we know that the base area of the barrel is 3.14 ft² respectively.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

In the center of a circle, equal chords subtend equal angles.

The chord is divided in half by the radius drawn perpendicular to it.

Different-sized circles are comparable.

Rectangles, trapezoids, triangles, squares, and kites can all be encircled by circles.

So, the area of the base of the barrel would be taken out by the formula of the circle:

Radius = 2/2

Radius = 1ft

Now, area:
= πr²

= π1²

= π1

= 3.14*1

= 3.14 ft²

Therefore, using the formula of the area of the circle, we know that the base area of the barrel is 3.14 ft² respectively.

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The line of sight distance using the angle of depression 13° is derived to be 2222.71 m to the nearest hundredth meters.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the tower and the complementary angle 77°, we shall represent the line of sight distance for the television camera to the base of the stadium with x so that;

cos 77° = 500/x {adjacent/hypotenuse}

note that 90° - 13° = 77°

x = 500/ cos 77° {cross multiplication}

x = 2,222.7057.

Therefore, the line of sight distance for the television camera to the base of the stadium to the nearest hundredth meters is equal to 2,222.71. Using the trigonometric ratio of cosine for the angle 77° which is complementary to the angle of depression 13°

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in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

How to calculate the rate?

To answer these questions, we need to calculate the population and food supply at different points in time and compare them.

Let's first calculate the population after t years:

Population after t years = 2,000,000 * (1 + 4%) raise to the power t

And the food supply after t years:

Food supply after t years = 4,000,000 + 0.5 million * t

Now, let's answer the first question:

If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?

If the country doubles its initial food supply, the new food supply would be 8,000,000, and it would still increase at a rate of 0.5 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%)^t = 8,000,000 + 0.5 million * t

Solving for t, we get t ≈ 17.77 years.

So, in approximately 18 years, the population would exceed the food supply, even if the country doubles its initial food supply and maintains a constant rate of increase in the supply adequate for an additional 0.5 million people per year.

Now, let's answer the second question:

If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?

If the country doubles the rate at which its food supply increases, the new rate would be 1 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%) raise to the power t  = 16,000,000 + 1 million * t

Solving for t, we get t ≈ 21.96 years.

So, in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

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Answer:

bar chart

Step-by-step explanation:

you are right box plot, histogram and a circle graph aren't the right ones

The surface area of the triangular prism is 544 square inches.

A prism is a three-dimensional structure with two bases that are parallel and congruent and joined by lateral faces, which are a series of parallelograms or rectangles. All of the angles between the lateral faces and the bases are equal, and they are perpendicular to one another. The name of the prism is determined by the shape of the bases, such as triangular bases for a triangular prism, rectangular bases for a rectangular prism, and hexagonal bases for a hexagonal prism.

The surface area of the triangular prism is given by the formula:

SA = bh + (b1 + b2 + b3)l

Here, b = 12, h = 8, b1 = 10 + b2 = 10, b3 = 12 and l = 14.

Substituting the values we have:

SA = (12)(8) + (10 + 10 + 12)(14)

SA = 96 + (32)(14)

SA = 544 square inches.

Hence, the surface area of the triangular prism is 544 square inches.

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Answer: 10 feet > 3 yards

Step-by-step explanation:

if 1 yard = 3 feet

then 3 yards = 9 feet

so 10 feet > 3yards

For numbers 1-6, using the order of operations to evaluate each expression is given as follows:

[tex](8.15 x 4 + 5) x 3.2 = 120.32\\12 + 5 + 32 x 2.2 = 87.4\\17 + 8 x (2.7 + 6) - 3 = 83.6\\38.9 - 2.3 x 1.5 + 2.6 = 37.05\\0.2 x (5 - 0.7) + 1.8 + 2 = 4.66\\5 + (8.06 - 12.5 + 2) = 4.56[/tex]

A pοlynοmial equatiοn is an equatiοn in which a pοlynοmial expressiοn is set equal tο anοther expressiοn οr tο zerο. It is an algebraic equatiοn that invοlves οne οr mοre terms in which the variables are raised tο a pοsitive integer pοwer and multiplied tοgether. The degree οf the pοlynοmial is the highest pοwer οf the variable in the pοlynοmial equatiοn.

(8.15 x 4/5) x 3.2

= (6.52) x 3.2 (Perfοrming multiplicatiοn befοre divisiοn)

= 20.86

2. 12/5+32 x 2.2

= 2.4 + 70.4 (Perfοrming multiplicatiοn befοre additiοn)

= 72.8

3. 17+8 x (2.7/6)-3

= 17 + 1.2 - 3.0 (Perfοrming divisiοn befοre multiplicatiοn and subtractiοn)

= 15.2

4. 38.9 - 2.3 x 1.5 + 2.6

= 38.9 - 3.45 + 2.6 (Perfοrming multiplicatiοn befοre subtractiοn)

= 37.05

5. 0.2 x (5 - 0.7) + 1.8 / 2

= 0.2 x 4.3 + 0.9 (Perfοrming subtractiοn inside the parentheses)

= 1.12

6. 21.5/5+(8.06-12.5/2)

= 4.3 + 1.53 (Perfοrming divisiοn befοre subtractiοn and additiοn inside the parentheses)

= 5.83

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a.) The mode for the chart is 24.

b.) The probability that the winning score will be 25 = 7/50

C.)The probability that the winning score will be 23 or more = 37/50.

The number of times the game is played = 50 times

The number of games that showed the score of 25= 7

The probability of winning a score of 25 = 7/50

The scores that are 23 and above; 10+14+7+4+2= 37

The probability of winning a score of 23 and above = 37/50

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We would expect around 3 students to have an IQ of 140 or above at Hogwarts School of Witchcraft and Wizardry.

Based on the given information, we can use the normal distribution formula to calculate the number of students expected to have an IQ of 140 or above.

To explain this, we can use the following steps:

1. Calculate the z-score for an IQ of 140 using the formula: z = (x - μ) / σ where x is the IQ score, μ is the mean IQ score and σ is the standard deviation.

2. Look up the probability of a z-score of 2.67 or above using a standard normal distribution table or calculator. This gives us the proportion of the population with an IQ of 140 or above.

3. Multiply the proportion by the total number of students to get the expected number of students with an IQ of 140 or above.

Since we cannot have a fraction of a student, we can round this to the nearest whole number to get the final answer.

Therefore, we would expect around 3 students to have an IQ of 140 or above at Hogwarts School of Witchcraft and Wizardry.

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Answer:

x = 40

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

65 + 75 + x = 180

140 + x = 180 ( subtract 140 from both sides )

x = 40

Answer: x = 40

Step-by-step explanation:

In a triangle, all the angles add up to 180 degrees.

In this case, 65 + 75 + x = 180.

Add the 65 and 75 together using column addition:

65

+75

-------

140

Now, the equation is 140 + x = 180

Subtract 140 from both sides:

x = 40

Therefore, x is 40.

Answer:

18x + 12y ≤ 50

Step-by-step explanation:

Let x be the number of large popcoms and y be the number of small popcoms.

The cost of a large popcom is $18, and the cost of a small popcom is $12. The total cost of purchasing x large popcoms and y small popcoms is given by:

Total cost = 18x + 12y

The problem states that Jarvis has $50 in his wallet to pay for the popcoms. Therefore, we can write the following inequality:

18x + 12y ≤ 50

This inequality represents the situation where Jarvis and his family want to purchase popcoms, and Jarvis has $50 to spend. The inequality ensures that the total cost of the popcoms does not exceed $50.

The prompt on fractions is given as follows:

1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10

3) (1/3) ÷ 5 = 1/15

4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

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

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.


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The area of the rectangular section in the garden is Area = (x₂ - x₁) x (y₂ - y₁)

Now, let's look at the rectangular section of the garden represented by the coordinate plane. We are told that the section is represented by Rectangle JKLM. The four corners of this rectangle can be represented by their respective coordinates:

Point J: (x₁, y₁)

Point K: (x₂, y₁)

Point L: (x₂, y₂)

Point M: (x₁, y₂)

To find the area of this rectangle, we need to use the formula:

Area = length x width

The length of the rectangle is the distance between points J and K, which is given by:

Length = x₂ - x₁

The width of the rectangle is the distance between points J and M, which is given by:

Width = y₂ - y₁

Therefore, the area of the rectangle is:

Area = (x₂ - x₁) x (y₂ - y₁)

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Complete Question:

Gina is growing lettuce in a section of a garden. She represents this section with Rectangle JKLM. Each unit in the coordinate plane represents 1 foot.

What is the area of the section where lettuce grows?

The time interval when the object is speeding up is t > 2, and the time interval when the object is slowing down is 1 < t < 2.

Given that

S(t) = 2t³ - 3t² - 12t + 8

Differentiate to get the velocity function

v(t) = 6t² - 6t - 12

Differentiate to get the acceleration function

a(t) = 12t - 6

To determine the time intervals when the object is slowing down or speeding up, we need to examine the sign of the velocity and acceleration functions.

The object is speeding up when the velocity function is positive and the acceleration function is also positive.

This occurs when t > 2 (graphically)

Similarly, the object is slowing down at t < 2

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The data set which consists of 900 values that follow a standard normal distribution with a mean of 90 and a standard deviation of 8 has 480 values that lie between 86 and 98.

We need to determine how many values in the data set lie between 86 and 98. The formula for calculating the Z-score is as follows: Z = (X - μ) / σwhereX = the value of interestμ = the meanσ = the standard deviation

Using this formula, we can find the Z-scores for the lower and upper bounds of the range as follows:Z lower = (86 - 90) / 8 = -0.5Z upper = (98 - 90) / 8 = 1.0We can then look up these Z-scores in the standard normal distribution table to find the corresponding probabilities.

Using the table, the probability of a Z-score being less than -0.5 is 0.3085, and the probability of a Z-score being less than 1.0 is 0.8413. Therefore, the probability of a Z-score being between -0.5 and 1.0 is:0.8413 - 0.3085 = 0.5328

Finally, we can convert this probability to the number of values in the data set that lie between 86 and 98 by multiplying it by the total number of values in the data set:900 x 0.5328 = 479.52 values

Therefore, there are approximately 480 values in the data set that lie between 86 and 98.

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The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.

When measuring the area of a shape, we are determining the amount of surface the shape takes up.

To calculate the area enclosed by each fence, we must multiply the length and width of each.

The area enclosed by the wood fence is

6 1/2 x 2 1/4 = 14 7/8 square yards,

and the area enclosed by the metal fence is

2 3/4 x 2 1/2 = 6 7/8 square yards.

To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:

14 7/8 / 6 7/8 = 7 3/4.

This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.

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Option B) 1,390,072 is correct. The population of the city after 12 years can be calculated using the formula for compound interest.

To calculate the population of a city after 12 years using the formula for compound interest, we first need to identify the initial population (P0), the annual interest rate (r), and the number of years (n). We can then plug these values into the formula P = P0(1 + r/100)ⁿ. In this case, the initial population is given as 909327, the annual interest rate is 3.6%, and the number of years is 12. By substituting these values into the formula, we get P = 909327 * (1 + 3.6/100)¹² ≈ 1390072, which represents the population of the city after 12 years. Therefore, option B) 1,390,072 is the correct answer.

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Complete question:

The most recent census for a city indicated that there were 909,327 residents. the population of the city is expected to increase at an annual rate of 3.6 percent each year for the next 12 years. what will the population be at that time?

A) 1,491,958

B) 1,390,072

C) 1,440,114