Keira divided 123. 52 by 3. 2 and got 38. 6. Without using a calculator, how could she check to determine if her answer is reasonable?

(a) The rates of changes of the volume are:

When r = 9 inches, dV/dt = 972π cubic inches per minute

When r = 36 inches, dV/dt = 15,552π cubic inches per minute

(b)  The rate of change of the volume relates to the radius through a quadratic function not a constant function.

a) We know that the formula for the volume of a sphere is V = (4/3)πr³. We can take the derivative with respect to time t to find the rate of change of volume.

dV/dt = 4πr² (dr/dt)

When r = 9 inches, we have:

dV/dt = 4π(9²)(3) = 972π cubic inches per minute

When r = 36 inches, we have:

dV/dt = 4π(36²)(3) = 15,552π cubic inches per minute

b) The rate of change of the volume of the sphere is not constant even though dr/dt is constant because the rate of change of the volume relates to the radius through a quadratic function not a constant function.

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Answer:

A.

Step-by-step explanation:

Because If you are simplifying then -3 would become -1 and -5 would become -3 and -4 would become -2 so your basically just simplifying

The cost of constructing the path at the rate of Rs. 25 per m2 would be Rs. 38,465.

To find the cost of constructing the path, we need to determine the area of the path and then multiply it by the cost per square meter.

The total diameter of the pond and the path is 21m + 3.5m + 3.5m = 28m.

So the radius of the pond is half of the diameter, which is 21m/2 = 10.5m.

The radius of the pond with the path is (21m+3.5m)/2 = 12.25m.

Area of the path = Area of the outer circle - Area of the pond

[tex]= π(12.25)^2 - π(10.5)^2[/tex]

[tex]= π[(12.25)^2 - (10.5)^2][/tex]

= 3.14 x (24.5 + 10.5) x (24.5 - 10.5)

= 3.14 x 35 x 14

= 1538.6 m2 (rounded to one decimal place)

Therefore, the cost of constructing the path at the rate of Rs. 25 per m2 would be:

Cost = Area x Rate per m2

= 1538.6 x 25

= Rs. 38,465.

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The difference between the greatest and least number of books read is 6.

A graph is a visual representation of data that displays the relationship between two or more variables. Graphs are used in many fields, including mathematics, science, economics, engineering, and social sciences, to help researchers and practitioners analyze, interpret, and communicate data effectively.

Here,

To graph the data, we can use a bar graph or a line graph, where the x-axis represents the weeks and the y-axis represents the number of books read. Each bar or point on the graph represents the number of books read in a particular week. Using the data from the table, we can create the following line graph:

To find the difference between the greatest number of books read and the least number of books read, we need to identify the highest and lowest data points on the graph. From the graph, we can see that the highest data point is 10, which corresponds to Week 1, and the lowest data point is 4, which corresponds to Week 3. Therefore, the difference between the greatest and least number of books read is:

10 - 4 = 6

So the difference is 6 books.

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Complete question:

The table shows how many books students in a class read each week for two months. Graph the data.

Week           1              2                      3

Books       10               7                     9

Read          4               5                     6

What is the difference between the greatest numb books read and the least number of books read?

Answer:

I think the answer is 4 tell me if it wasn't

The axiom AABC and ADEF shown in the figure are congruent by SAS axiom.

The SAS (Side-Angle-Side) axiom, also known as the SAS postulate or SAS congruence criterion, states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In other words, if you have two triangles with the same angle between two sides of equal length, then those triangles are congruent.

This can be written mathematically as:

If triangle ABC is congruent to triangle DEF by SAS axiom, then:

AB = DE

AC = DF

angle BAC = angle EDF

angle ABC = angle DEF

angle ACB = angle DFE

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1) To determine if the triangle is acute, obtuse, or right, we need to check if the sum of the squares of the two shorter sides is greater than, equal to, or less than the square of the longest side.

Let's first arrange the side lengths in ascending order:

28 in. < 34 in. < 42 in.

Now we can apply the Pythagorean theorem:

28² + 34² = 196 + 1156 = 1352

42² = 1764

Since 1352 is less than 1764, the sum of the squares of the two shorter sides is less than the square of the longest side. Therefore, the triangle is obtuse.


2)

We can use the tangent function to find the length of BC.

tan(B) = opposite/adjacent

We know that the opposite side of angle B is BC, and the adjacent side is AC, which is the height of the triangle. Since angle B is 45 degrees, we have:

tan(45) = BC/16

Simplifying the left side using the fact that tan(45) = 1, we get:

1 = BC/16

Multiplying both sides by 16, we get:

BC = 16

Therefore, the length of BC is 16 ft.


3)

Since the hypotenuse of each triangular quilt piece is 18 inches, we can use the Pythagorean theorem to find the length of each side. Let's call one leg of the triangle x (since the two legs will be equal), and the hypotenuse is 18. Then:

x² + x² = 18²

Simplifying:

2x² = 324

Dividing by 2:

x² = 162

Taking the square root:

x = √(162) = sqrt(2 * 3⁴)

We can simplify this by breaking it down into factors:

x = 3 * √(2) * 3

x = 9√(2)

Therefore, the length of each side of the triangular quilt piece is 9√(2) inches or 12.73 inches


4)

We can use the inverse sine function to find the angle that has a sine of 9/16. Using a calculator, we get:

sin^(-1)(9/16) ≈ 35.54°

Therefore, the missing value is approximately 35.54°

5)
We can use the inverse cosine function to find the angle that has a cosine of 7/18. Using a calculator, we get:

cos^(-1)(7/18) ≈ 61.48°

Therefore, the missing value is approximately 61.48°


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Comparing the estimated probabilities with the actual probability, we can see that Keeley had the best estimate for the probability.

a) To find out who had the best estimate for the probability of the spinner landing on 2, we need to compare their estimated probabilities with the actual results. The actual probability of the spinner landing on 2 can be found by dividing the total number of times it landed on 2 by the total number of spins.

Sam's estimated probability = 21/80 = 0.2625
Keeley's estimated probability = 20/50 = 0.4
Cody's estimated probability = 23/70 = 0.3286

The actual probability of the spinner landing on 2 = (21+20+23)/(80+50+70) = 0.315



b) To work out the estimated probability of the spinner landing on 2 by combining all of their results, we need to add up the total number of times the spinner landed on 2 and divide it by the total number of spins.

Total number of times the spinner landed on 2 = 21 + 20 + 23 = 64
Total number of spins = 80 + 50 + 70 = 200

Estimated probability of the spinner landing on 2 = 64/200 = 0.32

c) Using the combined results will give a better estimate than using only one person's results. This is because combining the results gives a larger sample size, which makes the estimate more accurate and reliable.

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Answer:22,888

Step-by-step explanation: replace x with 6 and use calculator :)

The x-coordinates range from -5 to 25, and the y-coordinates range from -4 to 5.

To choose appropriate scales for the coordinate plane, first, observe the range of x and y coordinates for the given points J(20, 3), K(25, 3), L(15, -3), M(-5, 5), and N(-5, -4).
The x-coordinates range from -5 to 25, and the y-coordinates range from -4 to 5.
For the x-axis, we can use a scale of 5 units for each grid square.

This scale will allow us to cover the entire range of x-coordinates.

The grid will have 6 squares in the positive x-direction and 2 squares in the negative x-direction.
For the y-axis, we can use a scale of 1 unit for each grid square.

This scale will allow us to cover the entire range of y-coordinates.

The grid will have 5 squares in the positive y-direction and 4 squares in the negative y-direction.
In summary, use a scale of 5 units for each grid square on the x-axis, and a scale of 1 unit for each grid square on the y-axis.

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The probability of a home for sale having a garage but no pool is 0.42.

To do this, we need to use some probability rules. One useful rule is the formula for calculating the probability of an event not occurring. This is given by:

P(not A) = 1 - P(A)

where A is the event we are interested in, and not A is the event of A not occurring.

In this case, we are interested in the probability of a home having a garage but no pool. Let's call this event GNP (short for garage no pool). Using the information given, we know that 60% of homes have garages and 18% have both garages and pools. We can use this information to calculate the probability of a home having a garage but no pool as follows:

P(GNP) = P(G) - P(G and P)

where G is the event of a home having a garage and P is the event of a home having a pool.

Substituting the values we have:

P(GNP) = 0.6 - 0.18

P(GNP) = 0.42

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The rule for this relation could be S = n² + 1.

What is relation rule?

A relation rule is a description of how two or more quantities or variables are related to each other. A relation rule can take various forms, depending on the nature of the relation and the variables involved.

For example, a relation rule can be expressed as an equation, a formula, a table, a graph, or a verbal description. In each case, the relation rule specifies the conditions under which the variables are related, and how they vary in relation to each other.

Based on the given table:

n: 1, 0, 2

S: 1, 0, 3

We can observe that when n=1, S=1; when n=0, S=0; and when n=2, S=3.

There are different possible rules that can describe this relation, but one possible rule is:

S = n² + 1

Using this rule, we can verify that it matches the given table:

Therefore, the rule for this relation could be S = n² + 1.

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Here's the tree diagram for the given scenario:

(1) The probability of getting tails and a 3 is the probability of following the path T-3, which is 1/2 x 1/4 = 1/8.

(ii) The probability of getting heads and an even number is the probability of following the path H-2 or H-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.

(iii) The probability of not getting heads and an even number is the probability of following the paths T-2 or T-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

Answer:

(16x^2 + 46x + 20)/(4x + 5) ft

Step-by-step explanation:

he area of the yard is given by (8x^2+13x+5) ft^2. The length of the yard is (8x+5) ft. The width of the yard is (8x^2+13x+5)/(8x+5) ft.

The fence is along the length and two widths of the yard. Therefore, the length of the fence is 2(8x+5) ft and the width of the fence is 2(8x^2+13x+5)/(8x+5) ft.

The total length of the fence is the sum of the length and width of the fence.

Therefore, the total length of the fence is 2(8x+5) + 2(8x^2+13x+5)/(8x+5) ft.

Simplifying the expression, we get:

2(8x+5) + 2(8x^2+13x+5)/(8x+5) = (16x^2 + 46x + 20)/(4x + 5) ft.

Therefore, Karla’s dad will need (16x^2 + 46x + 20)/(4x + 5) ft of fencing.

The rate at which the diameter decreases when the diameter is 11 cm is 4 cm/min.

To solve this question, we need to use the formula for the surface area of a sphere, A = 4πr2. Since the surface area of the snowball is decreasing at a rate of 2 cm2/min, we can set up a differential equation to calculate the rate of change of the radius with respect to time:  dA/dt = 2 cm2/min = 8π dr/dt.

We can rearrange this equation to find dr/dt, the rate at which the radius of the snowball is changing:  dr/dt = 2 cm2/(8πmin).

We then use the equation for the diameter of a circle, d = 2r, and substitute the rate of change of the radius to get the rate of change of the diameter: dd/dt = 2(dr/dt) = 2 cm2/(4πmin).

Finally, we can plug in the given diameter, 11 cm, to find the rate of decrease in diameter:  dd/dt = 11 cm/(4πmin) = 4 cm/min. Therefore, the rate at which the diameter decreases when the diameter is 11 cm is 4 cm/min.

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Answer: x^2 - 9

Step-by-step explanation:

Using percentage,

18. 78/100 of earth's atmosphere is made up of nitrogen.

19. 0.21 part of earth's atmosphere is made up of oxygen.

20. 100% of earth's atmosphere is here represented by the graph.

21. 1/100 of earth's atmosphere is made up of other gases.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."

This percent symbol can always be changed to a fraction or decimal equivalent by substituting "divided by 100."

Here in the graph as we can see,

Nitrogen = 78%

Oxygen = 21%

Other gases = 1%

Total = 100%

Fraction of nitrogen gas means, 78% in fraction = 78/100

Now, decimal of oxygen gas means, 21% in decimal = 0.21

The total percentage represented by graph = 100%

Other gases make up for 1/100 fraction of the total earth's atmosphere.

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The percentage of students scoring 84 or more in the exam is 99.18%.

Given, Mean test score = 72,

Standard deviation = 5.

We are supposed to find the percentage of students scoring 84 or more in the exam.

To find the percentage of students scoring 84 or more in the exam, we will use the following steps:

First, we need to find the z-score associated with 84.

Let us assume that z is the z-score corresponding to the value 84, then;

z = (84 - 72) / 5 = 2.4

Now, we have the value of z, we can find the percentage of students scoring 84 or more in the exam using the normal distribution table.

The percentage is the area under the normal distribution curve to the right of the z-score.

To find the area using the normal distribution table, we need to look for the value 2.4 in the z-table. Since 2.4 is not exactly listed in the z-table, we will use the value for 2.4 closest to it.

Using the z-table, the value closest to 2.4 is 0.9918.

Therefore, the percentage of students scoring 84 or more in the exam is;

P(Z > 2.4) = 0.9918 × 100 = 99.18%.

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The 2 pounds of $5.61 per pound birdseed are used in the mixture.10 - 2 = 8 pounds of $8.91 per pound birdseed are used in the mixture.

Answer:2 pounds of $5.61 per pound birdseed are used in the mixture.8 pounds of $8.91 per pound birdseed are used in the mixture.

Given information:Ten pounds of mixed birdseed sells for $8.25 per pound. The mixture is obtained from two kinds of birdseed, with one variety priced at $5.61 per pound and the other at $8.91 per pound.To find:Pounds of each variety of birdseed used in the mixture.Solution:Let 'x' be the number of pounds of the first kind birdseed used in the mixture.

Then, (10 - x) will be the number of pounds of the second kind birdseed used in the mixture.The price of the first kind of birdseed per pound is $5.61.Price of x pounds of the first kind of birdseed = 5.61x dollars.The price of the second kind of birdseed per pound is $8.91.Price of (10 - x) pounds of the second kind of birdseed = 8.91(10 - x) dollars.

The total cost of the mixture = $8.25 per pound × 10 pounds= $82.50 dollars.According to the question,$$5.61x+8.91(10-x)=82.5$$Multiply the numbers inside the brackets by multiplying with the negative sign.

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1-  (2x-4)(x+5)

Multiplying using the distributive property, we get:

(2x-4)(x+5) = 2x(x) + 2x(5) - 4(x) - 4(5)

= 2x^2 + 10x - 4x - 20

= 2x^2 + 6x - 20

Therefore, (2x-4)(x+5) simplifies to 2x^2 + 6x - 20.

2-(x-2)^2

Expanding using the formula for the square of a binomial, we get:

(x-2)^2 = x^2 - 4x + 4

Therefore, (x-2)^2 simplifies to x^2 - 4x + 4.

3- (3x+1)^2

Expanding using the formula for the square of a binomial, we get:

(3x+1)^2 = (3x)^2 + 2(3x)(1) + (1)^2

= 9x^2 + 6x + 1

Therefore, (3x+1)^2 simplifies to 9x^2 + 6x + 1.

4- (3x-1)(2x^2+5x-4)

Using the distributive property, we can multiply each term in the first polynomial by each term in the second polynomial:

(3x-1)(2x^2+5x-4) = 3x(2x^2) + 3x(5x) - 3x(4) - 1(2x^2) - 1(5x) + 1(4)

= 6x^3 + 15x^2 - 12x - 2x^2 - 5x + 4

= 6x^3 + 13x^2 - 17x + 4

Therefore, (3x-1)(2x^2+5x-4) simplifies to 6x^3 + 13x^2 - 17x + 4.

Answer:

  132 in

Step-by-step explanation:

You want to know the perimeter of a triangle after the dimensions are quadrupled.

"Quadrupled" means "multiplied by 4."

The perimeter is the sum of the lengths of the sides of the triangle:

  P = 8 +10 +15 = 33 . . . . inches

If the sides are quadrupled, it is ...

  P' = 4(8) +4(10) +4(15) = 4(8 +10 +15) = 4(33) = 132 . . . . inches

As you can see, if the sides are quadrupled, the perimeter is quadrupled.

The new perimeter is 132 inches.

The following random variable meets the criteria for a hypergeometric distribution: Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define x to be the number of adults in the sample with a graduate degree.

A hypergeometric distribution is a type of probability distribution that measures the likelihood of a particular number of successes (in this case, adults with a graduate degree) in a sample without replacement.

A random variable that meets the criteria for a hypergeometric distribution is that which meets these conditions: A sample of size n is taken from a population of size N. The population has k successes and N - k failures.

The hypergeometric distribution is used when sampling is done without replacement, where the sample size is small relative to the population size. The sample size is typically less than 10% of the population size. When you have the information of the population, you can use the hypergeometric distribution.

Out of the options provided, the random variable that meets the criteria for a hypergeometric distribution is, Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define x to be the number of adults in the sample with a graduate degree.

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Step-by-step explanation:

mean is all the numbers added together, which is 35 and divide by the amount of numbers so 35 divide 5 is 7. Mean= 7

Medial is the number in the middle so 4 is the medial. Because it is in the middle of all the numbers.

Hope this helps.

Answer:

$89.04

Step-by-step explanation:

The Great Sphinx in Egypt is 66 ft tall, based on measurements of its shadow and a 6 ft-tall person's shadow at sunrise.

Let's denote the height of the Sphinx as "h".

At sunrise, the angle of elevation from the tip of the Sphinx to the top of the sun is 90 degrees. This means that the triangles formed by the Sphinx, its shadow, and the sun are all similar.

Using this fact, we can set up a proportion between the height of the Sphinx and the length of its shadow:

h/220 = 6/x

where "x" is the length of the shadow of the 6 ft-tall person.

Solving for "x", we get:

x = (220*6)/h

We also know that the length of the shadow of the person is 20 ft, so we can set up another proportion:

h/220 = 6/20

Solving for "h", we get:

h = (220*6)/20 = 66 ft

Therefore, the height of the Great Sphinx is 66 ft.

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The complete question is:

The Great Sphinx in Egypt's shadow extends 220 feet below the summit of the structure at sunrise. An someone who is 6 feet tall and standing close to the Sphinx has a shadow that extends 20 feet from the top of their head. The Great Sphinx's height is how tall?

a) 70.0 ft

b) 66.0 ft

c) 733.3 ft

d) 54.5ft

The y-intercept is 5.5 inches, which is the initial height of the plant before it started growing.

We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, to solve the problem.

Since the plant is growing at a constant rate of 1.4 inches per day, the slope of the line that represents its growth is 1.4.

Let y be the height of the plant after x days. We know that the plant was 5.5 inches tall on day 0, so we have the point (0, 5.5) on the line.

Using the point-slope form of a linear equation, we get:

y - 5.5 = 1.4x

Simplifying, we get:

y = 1.4x + 5.5

Comparing the equation to the slope-intercept form, we see that the y-intercept is 5.5.

Therefore, the y-intercept is 5.5 inches.

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Answer:

B, $305.11

Step-by-step explanation:

since it is in annual interest, 36 months = 3 years.

use the formula for simple interest, which is x = Prt

278 * 0.0325 * 3 = 27.105

that is the interest that you gained.

then, add the original amount that you had, which was 278.

27.105+278 = 305.105

this rounds to $305.11, which is answer choice B

[tex](5x^8y^4)/(15x^3y^8) = (x^5/y^4) * (1/3)[/tex] is the fully simplified expression using only positive exponents.

To simplify [tex](5x^8y^4)/(15x^3y^8)[/tex], we can start by dividing the numerator and denominator by their greatest common factor, which is[tex]5x^3*y^4[/tex]:

[tex](5x^8y^4)/(15x^3y^8) = (x^8/x^3) * (y^4/y^8) * (1/3)[/tex]

Now we can simplify each term separately. First, [tex]x^8[/tex] divided by [tex]x^3[/tex] equals [tex]x^5[/tex], because when we divide two terms with the same base, we subtract their exponents:

[tex]x^8/x^3 = x^(8-3) = x^5[/tex]

Similarly, [tex]y^4[/tex]divided by[tex]y^8[/tex] equals [tex]1/y^4[/tex], because when we divide two terms with the same base, we subtract their exponents and change the sign:

[tex]y^4/y^8 = y^(4-8) = 1/y^4[/tex]

Finally, 1/3 is already in its simplest form. Putting it all together, we get:

[tex](5x^8y^4)/(15x^3y^8) = (x^5/y^4) * (1/3)[/tex]

This is the fully simplified expression using only positive exponents.

We can state that the original equation represents a fraction, where the numerator is the product of 15, the third power of x, and the eighth power of y, and the denominator is the product of 5, the eighth power of x, and the fourth power of y.

We then determined the numerator and denominator's largest common factor, which is 5x*3*y*4, in order to condense the formula. Using the exponentiation principles, we divided the numerator and denominator by this factor before simplifying each term. The end result is a fraction with x raised to the fifth power as the numerator, y raised to the fourth power as the denominator, and 3 as the common factor.

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Answer:

Step-by-step explanation:

Finally got it right. lol

Answer: 5.44 x 10 to the power of 8

Step-by-step explanation: