Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.

Answers

Answer 1

The rate at which the water flow from the given volume is 21.72 in³/sec

What is rate at which the water flow

To find the rate at which water is being drained from the container, we first need to find the rate at which the water level is falling and then use that to calculate the volume of water being drained per unit of time.

We know that the surface level is falling at a rate of 0.9 inches per second and that the container has the shape of an inverted right circular cone. The volume of a cone is given by the formula:

V = (1/3) * π * r^2 * h

Where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.

We can use this formula to find the volume of the container when the water level is 8 inches. The radius at this point is 6 * (8/10) = 4.8 inches and the height is 8 inches.

V = (1/3) * π * (4.8 inches)^2 * 8 inches = 193.02 inches³

Now that we know the volume of the container when the water level is 8 inches, we can use the rate at which the water level is falling (0.9 inches per second) to find the rate at which the water is being drained.

The rate at which water is being drained = rate of change of volume / rate of change of height = dV/dt = dV/dh * dh/dt = -dV/dh * dH/dt

Where dV/dh is the derivative of volume with respect to height, dH/dt is the rate of change of height.

-dV/dh = -(1/3) * π * (4.8 inches)^2 = -24.13 in³

dH/dt = -0.9 inches/sec

The rate at which water is being drained = -dV/dh * dH/dt = -24.13 * -0.9 inches/sec = 21.72 in³/sec

So the rate at which water is being drained from the container is 21.72 in³/sec

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Related Questions

What is an equation of the line that passes through the point (2, 3) and is parallel to
the line x + y = 4?

Answers

The equation of the line that is parallel to x + y = 4 and passes through (2, 3) is expressed as: y = -x + 5.

How to Determine the Equations of Parallel Lines?

Two lines are parallel if and only if their slopes are equal. The equation of the line x + y = 4 is in slope-intercept form (y = mx + b), where m is the slope. The slope of this line is m = -1, as the coefficient of x is -1.

An equation of a line that is parallel to the line x + y = 4 and passes through the point (2, 3) can be written in the form y = mx + b, where m = -1.

Substituting the point (2,3) and the slope -1 into the point-slope form of a line gives:

y - 3 = -1(x - 2)

Expanding the right hand side gives:

y - 3 = -x + 2

And rearranging the equation gives the final form of the equation of the line:

y = -x + 5

So, the equation of the line that passes through the point (2, 3) and is parallel to the line x + y = 4 is y = -x + 5.

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5. THOUGHT PROVOKING
To find the arithmetic mean of n numbers, divide
the sum of the numbers by n. To find the geometric
mean of n numbers a₁, a₂, a3,..., an, take the nth
root of the product of the numbers.
geometric mean =
a₁a₂ a3 •...• An
Compare the arithmetic mean to the geometric
mean of n numbers.

Answers

Arithmetic mean deals will middle number while geometric mean deals with typical value

How to compare the different types of means

From the question, we have

Arithmetic mean and Geometric mean

The arithmetic mean is the sum of a set of numbers divided by the number of items in the set, and is often used to find the "middle" value of a dataset.

On the other hand, the geometric mean is the nth root of the product of a set of numbers and is often used to find the "typical" value of a dataset when dealing with quantities that can increase or decrease exponentially.

The above definitions imply that the difference between the arithmetic mean and geometric mean can be significant when dealing with sets of numbers that have large variations in values.

In general, the geometric mean will be less than or equal to the arithmetic mean.

Answers

Answer:

a) Domain: (-∞, 10)

b) k⁻¹(8) = 6

c) CBD

d) Range: (-∞, 7)

e) k⁻¹(0) = 4

f) x = -5

Step-by-step explanation:

Part a

The domain of the inverse of a function is the same as the range of the original function.

Therefore, the domain of the inverse function is:

(-∞, 10)

Part b

The inverse of a function is its reflection in the line y = x.

Therefore, given that function k(6) = 8 then:

k⁻¹(8) = 6

Part c

The inverse of a function is its reflection in the line y = x.

We cannot find k⁻¹(-9) since we have not been given the value of x when k(x) = -9.

Part d

The range of the inverse of a function is the same as the domain of the original function.

Therefore, the range of the inverse function is:

(-∞, 7)

Part e

The inverse of a function is its reflection in the line y = x.

Therefore, given that function k(4) = 0 then:

k⁻¹(0) = 4

Part f

The zero of the inverse function is the y-intercept of the original function. Therefore, given that k(0) = -5 then:

k⁻¹(-5) = 0

Therefore, x = -5 is a zero of k⁻¹(x).

inspect a sketch of typical solution curves to determine the points for which the initial value problem has a unique solution.

Answers

We have to find solutions for the given differential equation when

y = 0, y = 1/(k-x) and y(a) = b using ordinary differential equations.

We have dy / dx = y^2

a. let's define the given y = 1/(k-x)

derive the above equation with respect to x :

dy / dx = y' = 1/(k-x)^2

So this is the general solution.

b) We would want a singular solution that is not included in the general form. Here we could use y = 0

dy / dx = 0 = 0^2

so,this is a trivial singular solution.

c) If we have y(a) = b,

then, y = 1(k-a) = b

To find the value of k we use the other condition: y'(^2) = 4 x y(2)

1/(k-a)^2 = 4 x 1/(k-a)

k - 2 = 1/4

therefore, k = 9/4

hence we got, y = 1/(9/4 - a) = b

So the points (a, b) are of the form: (a, 1/(9/4 - a))

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The complete question is :

Find a general solution of the differential equation dy/dx=y2

b. Find a singular solution that is not included in the general solution.

c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b

49, 34, and 48 students are selected from the sophomore, junior, and senior classes with 496, 348, and 481 students respectively.

Answers

The sampling used in this situation is Stratified sampling
In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.

We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.

Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes.

This is, therefore, a stratified sampling.

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Q: 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?

what’s the geometric mean of 6 and 1/2

Answers

Answer:

1.7320508075689

Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0

Answers

The answer is x4 – 6x2 – 27 = 0 and this is a quadratic equation in the polynomials .

How to calculate and What is Quadratic equation?

This is a quartic equation because the highest degree is 4

In the second option, we have 3x⁴ = 2x, this is also another quartic equation.

In the third equation, we have 2(x + 5)⁴ + 2x² + 5 = 0, this is a quartic equation because the highest degree is 4

In the fourth equation, 6(2x + 4)² = (2x + 4) + 2

This is a quadratic equation because the highest degree is 2

In the fifth equation, we have 6x⁴ = -x² + 5 which is also another quartic equation

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x2 (a 0) for an equation to be a quadratic equation. The x2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are typically expressed as integral values rather than fractions or decimals.

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Part B
In part A, you used the exact lengths of the sides to find the exact area of the rectangle.

Suppose this rectangle represents a piece of fabric that needs to be cut for a sewing project. Which type of measurement do you think would be more appropriate to use in this situation: the exact side lengths as given in part A or decimal approximations of the side lengths?

Use complete sentences to explain your reasoning.

Answers

Approximation of decimals is a mathematical technique for finding or measuring approximations and minimizing the number of decimal places.

What is meant by decimal approximations?

A fractional representation of a real number that comes close to representing it. Any real number a can be represented by an endless number of decimal fractions.

The number of decimal places in a decimal number is the number of digits following the decimal point. A mathematical method for locating or measuring approximations and reducing the number of decimal places is known as approximation of decimals.

Any comparison that is close but not accurate to another entity is called an approximation. By rounding, one can get a good idea of a number. By rounding the values in a computation before performing the operations, a calculation can be approximated.

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bought a bag of candy for five dollars there were 20 pieces of candy in the bag what is the unit cost of each piece of candy in the bag

Answers

$0.25
Set up your proportion
$ over candy
$5 over 20 candies equals X over 1 candy. 5•1=5 5 divide by 20 = $0.25

use the definition of continuity and limits to find values of the constants a and b so that the piece-wise cubic function

Answers

The constants a and b can be found by ensuring the function is continuous and that the limits at each point match. This can be done by setting the values of a and b so that the function and its derivative are equal at each point.

To find the constants a and b for the given piece-wise cubic function, we must consider the definition of continuity and limits. Firstly, for the function to be continuous, the function and its derivative must be equal at each point. Thus, we need to set the values of a and b so that the function and its derivative are equal at the points x=1, x=2 and x=3. We can use this to create a system of equations to solve for a and b. Once we have determined the values of a and b, we can then check that the limits at each point match. This can be done by computing the left and right hand limits at each point, and ensuring they are equal. If the limits are equal, then the function is continuous and the constants a and b are correct.

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Evaluate the expression using the given value of the variable:[pr2]; use [p = 3], and [r = 3] .

Answers

Answer:

(pr²)

given,

p=3 r=3

(3 X 3²)

(3 X 9)

City A and City B had two different temperatures on a particular day. On that day, five times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −4° C. The following system of equations models this scenario: 5x = 8 + 3y x − 2y = −4 What was the temperature of City A and City B on that day?

Answers

The temperature of city A is 4°C.

The temperature of city B is 4°C.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4= 6 is an equation.

We have,

5x = 8 + 3y ______(1)

x − 2y = −4 _______(2)

Where x is the temperature of city A and y is the temperature of city B.

Now,

From (2),

x = -4 + 2y

Substitution in (1).

5 (-4 + 2y) = 8 + 3y

-20 + 10y = 8 + 3y

-20 - 8 = 3y - 10y

-28 = -7y

y = 4

Now,

x = -4 + 2y

x= -4 + 2 x 4

x = -4 + 8

x = 4

Thus,

The temperature of both city A and city B is 4°C.

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Look at the steps for solving the equation and choose a true statement.
3x-9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2-1
-6x + 1 = -6x + 1
C
There are infinitely many solutions to the equation.
There is no way to know if there is a solution to this equation.
The only solution to the equation is 1.
There are no solutions to the equation.
The only solution to the equation is -6.

Answers

Based on the steps for solving the equation, a true statement include the following: A. there are infinitely many solutions to the equation.

What is no solution?

In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

What are infinitely many solutions?

In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal:

3x - 9x + 1 = 2(-3x + 1) - 1

-6x + 1 = -6x + 2 - 1

-6x + 1 = -6x + 1

When x = 1, we have:

-6(1) + 1 = -6(1) + 1

-5 = -5.

When x = 2, we have:

-6(2) + 1 = -6(2) + 1

-11 = -11.

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$155 $267 $284 $194 $299 $284 $287 $179 What is the mean, median, and mode of this data set?

Answers

Answer:

Mean = 243.625

Median = 275.5

Mode = 284

Each value is exact without any rounding.

=================================================

Original data set:

$155 $267 $284 $194 $299 $284 $287 $179

Let's remove the dollar signs, and separate each item with a comma:

155,267,284,194,299,284,287,179

Then sort the values from lowest to highest.

155,179,194,267,284,284,287,299

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

To find the mean, we add up the values and divide by n = 8 since there are 8 items in the list.

(155+179+194+267+284+284+287+299)/8 = 243.625 is the mean

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

Refer to the sorted data set.

The median is the middle-most value. Because the sample size n = 8 is even, we'll have two values tied for the middle.

n/2 = 8/2 = 4

The items in slot 4 and 5 are tied for the middle.

The values in slot 4 and 5 are 267 and 284 in that exact order.

Compute the midpoint: (267+284)/2 = 275.5 is the median

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

The mode is the most frequent value. Look through the sorted data set to see that 284 shows up twice. This is the most frequent compared to the other values (that show up only once).

Therefore, the mode is 284

Side note: It's possible to have multiple modes. It's also possible to not have any modes at all.

Zac and Malcolm each wrote short stories. Zac’s story is 273 lines long. Malcolm’s story is 145 lines longer than Zac’s. How long is Malcolm’s story? Explain what operation you used to solve this problem.

Answers

Length of malcom's story is 418lines, the operation used to solve this problem is; lines of zac story+ extra lines of malcom story.

What is simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Given;

Number of lines in zac story=273

Number of lines in malcom story= 273+145

Now.

Total number of lines in malcom story

=273+145

=418

Therefore, the answer after simplification will be 418

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∠FGK and ∠KGH form a linear pair. Find m∠KGH.

Answers

Applying the linear pair definition, m<KGH = 60°.

What is a Linear Pair?

In geometry, a linear pair is a pair of adjacent angles that are supplementary, meaning that their measures add up to 180 degrees. The two angles must be adjacent, meaning that they share a common side or vertex, and they must be linear, meaning that they are formed by two intersecting lines.

Therefore:

m<FGK + m<KGH = 180

Substitute

120 + m<KGH = 180

m<KGH = 180 - 120

m<KGH = 60°

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Which graph represents an exponential decay function?

Answers

The graph that represents an exponential decay function is the second graph.

For you to determine which of the graphs represents an exponential decay, we will need to check the curve that passes through or lies on the x-axis.

we can draw a graph by putting the value of x and we are getting the value of y in this way we get the coordinates of a point

From both figures, we can see that the curve of the second graph almost lies on the x-axis as it curves downwards. This makes it an exponential decay function.

Hence the graph that represents an exponential decay function is the second graph.

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complete question is

Which description matches the function represented by this graph?

A. exponential growth

B. linear growth

C. linear decay

D. exponential decay

Answer:

B or 2

Step-by-step explanation:

The answer above is correct.

Problem Gregory forms two different numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have 3 digits, and each digit is used only once. If he adds these two numbers, what is the greatest sum Gregory can get? Show your work.

Answers

The numeric value of the greatest sum that can be obtained by Greg is given as follows:

1173.

How to obtain the greatest sum?

When two n digit numbers are added, the numbers in the equivalent positions are added with each other, that is, starting from the end of the number to the begining.

The first digit is added with the other first digits.The second digit is added with the other second digits.

For example, 21 + 32:

1 + 2 = 3.2 + 1 = 5.

Hence the sum is of 54.

Hence the greatest sum would be obtained as follows:

The first digits would be of 5 and 6.The second digits would be of 3 and 4. The third digits would be of 1 and 2.

Hence the sum would be given as follows:

642 + 531 = 1173.

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Two angles of a quadrilateral measure 130° and 195°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?

Answers

The measure of other two angles in the given quadrilateral are 10° and 25°.

What is quadrilateral?

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

Given that, two angles of a quadrilateral measure 130° and 195°.

The other two angles are in a ratio of 2:5.

So, the other two angles are 2x and 5x

Now, 130°+195°+2x+5x=360°

325°+7x=360°

7x=360°-325°

7x=35°

x=5

So, 2x=10° and 5x=25°

Therefore, the measure of other two angles in the given quadrilateral are 10° and 25°.

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1 The equation, A = P(1 + 0.037t), represents the amount of money earned on a savings account with 3.7% annual simple interest. If the amount after 5 years is equal to $1,422, what is the amount of the principal investment? $1,200 $1,422 $274.25 $294.86

Answers

The amount of the principal investment is, $1200. So option A is correct

What is simple interest?

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula; Simple Interest(I) = P × R × T/100

A = P(1 + RT)

Given that,

A = $1422

R = 3.7%

T = 5 year

P = ?

After 5 year total amount

1422 = P ( 1 + 0.037 × 5)

P = 1422/( 1 + 0.037 × 5)

= 1422/1.185

P = 1200

Hence, the principal amount is $1200

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Ages of Dogs The ages of 20 dogs in a pet shelter are shown. Construct a frequency distribution using 7 classes.
7
9
6
8
7
6
8
6
9
5
7
7
Send data to Excel
6
89
8
8
6 4 8
9
6 3
Class limits Class boundaries Frequency
3
2.5-3.5
4
3.5-4.5
4.5-5.5
5.5-6.5
6.5-7.5
7.5-8.5
8.5-9.5
Total
5

Answers

The frequency table is added below

How to determine the frequency distribution

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

7 9 6 8 7 6 8 6 9 5 7 7

6 8 9 8 8 6 4 8

When represented on a frequency table, we have

Class limits Class boundaries Frequency

2.5 - 3.5 3.0 - 4.0 0

3.5 - 4.5 4.0 - 5.0 1

4.5 - 5.5 5.0 - 6.0 1

5.5 - 6.5 6.0 - 7.0 5

6.5 - 7.5 7.0 - 8.0 4

7.5 - 8.5 8.0 - 9.0 6

8.5 - 9.5 9.0 - 10.0 3

Total 20

The class boundary is calculated as

class boundary = Class limits ± 0.5

Answers

The measures of the angles are Z = 146 degrees, X and W = 34 degrees and B = 119 degrees

How to determine the measure of the angles

Question 4

From the question, we have

<Y = 146 degrees

Because the lines XY and WZ are equal, it means that

<Z = 146

So, we have

X = W = (180 - 146)

Evaluate

X = W = 34

Question 6

Here, we have

Sum of the angles = 180 degrees

This gives

9x + 2 + 5x - 4 = 180

Evaluate the like terms

14x = 182

Divide by 14

x = 13

So, we have

B = 9 * 13 + 2

B = 119 degrees

Answers

The total cost of materials for one candle is $2 and she pays $40 for the booth for the day.

Therefore, the total cost for making and selling one candle is $2 + $12 + $40 = $54

To cover all her expenses, Leila must sell enough candles to make $54 from each candle.

She must sell 54/$12 = 4.5 candles

Therefore, Leila needs to sell at least 5 candles to cover all her expenses.

At that point, her sales and expenses will be 5 candles x $12/candle = $60

Therefore, Leila's sales and expenses will be $60 at that point.

If a shipment has at least 5% defective light bulbs, it will be replaced. If a sample of 60 light bulbs has 2 that are which statement is true? defective,
A The shipment will be replaced.
B The shipment will not be replaced.
C The shipment has 12 defective light bulbs.
D The shipment has 30 defective light bulbs.

Answers

The sample has 3.33% of defective bulbs so, B. The shipment will not be replaced.

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, If a shipment has at least 5% defective light bulbs, it will be replaced.

Now, A sample of 60 light bulbs has 2 that are defective.

Therefore, The percentage of defective bulbs is,

= (2/60)×100%.

= (1/30)×100%.

= 3.33%, So, the shipment will not be replaced.

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5x - y = -5

3x - 6y = 24

Solve using substitution

Answers

Answer:

x = -2

y = -5

Step-by-step explanation:

5x - y = -5

3x - 6y = 24

First, multiply the first equation by -6

-30x + 6y = 30

3x - 6y = 24

-27x = 54

x = -2

Now, put in -2 for x and solve for y

5(-2) - y = -5

-10 - y = -5

-y = 5

y = -5

Let's Check

5(-2) -(-5) = -5

-10 + 5 = -5

-5 = -5

So, x = -2 y = -5 is the correct answer.

Mike is buying dinner for his family. He buys 5 lemonades that each cost $1.50, and 5 hamburgers that each cost $8.25. If
the prices include tax, and he also leaves a $6 tip, how much does he spend in all? Write equations to show your work.
Write an equation for the cost of the lemonades. Select the correct choice below, and fill in the answer box to complete
your choice.
(Do not include the $ symbol in your answer.)
OA. 5x1.50 +6=
ETTE
OB. 1.50+5=
OC. 5x1.50 =
OD. 1.50+5+6=

Answers

The linear equation for the cost of lemonades is 1.50*x+6 where x=5 i.e. A and he spends $54.75 in total.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Cost of lemonade=$1.5, number of lemonades=5

Cost of hamburger=$8.25, number of hamburgers=5

Tip=$6

Hence,

Total cost=5*1.5+5*8.25+6

Total cost =$54.75

Cost of lemonades only = 5*1.5+6

In type of linear equation 1.50*x+6 where x=5

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Can someone help me please

Answers

Answer: 3 + y = 24

Step-by-step explanation: Hello!

If she rode 3 miles one day and y miles the other 6 days of the week, and in total that adds up to 24 miles, that means the equation should be addition.

3 miles + y miles = 24 miles
Monday, other 6 days, total seven days

The equation should be:
3 + y = 24

The circle graph shows the results of a national survey on the most popular afternoon activities of seventh graders. What percent of those students surveyed said that their favorite afternoon activity is playing video games?

Answers

Answer:

it is easy to add all the numbers up then you will get 77 then tell me how many number should you add to get to 100 it is easy trust me

Step-by-step explanation:

25. There were 13 gummies in a packet. Mrs. Sooklal bought a few packets of gummies. After giving 3 sweets to each of her 27 students, she has 10 gummies remaining, how many packets of gummies did she purchase?

Answers

7
27x3=81
81+10=91
91/13=7

when ur answering please just give the answer! thank uuu! :)

Answers

The equation of the exponential function is y = 0.2⋅2^x

Find the equation of the exponential function

The steps for this process are as follows:

Step 1: Set up the equation.

The equation of an exponential function has the form y = a⋅b^x

where a and b are constants and b is greater than 0 and not equal to 1.

Step 2: Find the constants.

We can use the given points to find the constants in the equation. For example, when x = 0, y = 0.2.

So we can set 0.2 = a⋅b^0.

This means that a = 0.2 and b^0 = 1,

so b = 1.

Step 3: Write the equation.

Substituting a = 0.2 and b = 1 into the equation gives us y = 0.2⋅2^x.

This is the equation of the exponential function represented by the table.

To learn more about exponential function refer :

brainly.com/question/30382041

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