Cones A and B both have volume 48 pi cubic units but have different dimensions. Cone A has a radius of 6 units and a height of 4 units. Find one possible radius and height for Cone B. Explain how you know Cone B has the same volume as Cone A

a.  the equation showing the relationship between s and r:

6s + 2r = 21

b.  the equation that shows the rearrangement of r as a function of s:

r = (21/2) - 3s

c. If it takes Diego 1.2 seconds to spin around each time, the total time he spends spinning is r = 5.7 seconds

The equation showing the relationship between s and r: 6s + 2r = 21

The equation that shows the rearrangement of r as a function of s:

2r = 21 - 6s

r = (21/2) - 3s

c., the total time Diego spends spinning is:

6s = 6(1.2) = 7.2 seconds

Applying the equation in part (b), we can find the time he spends running:

r = (21/2) - 3s

r = (21/2) - 3(1.2)

r = 5.7 seconds

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The direct variation equation that shows the relationship between x and y, where y = 20 when x = 5, is y = 4x.

In a direct variation, the relationship between two variables can be described by the equation y = kx, where y and x are the variables and k is the constant of variation. This equation indicates that y varies directly with x, which means that as x increases or decreases, y also increases or decreases proportionally.

To find the constant of variation, we need to use the given information about the values of y and x. In this case, we are told that when x = 5, y = 20. We can substitute these values into the direct variation equation:

y = kx

20 = k(5)

To solve for k, we divide both sides by 5:

k = 20/5

Simplifying this expression, we get:

k = 4

Therefore, the direct variation equation that shows the relationship between x and y is:

y = 4x

This equation means that for any value of x, if we multiply it by 4, we will get the corresponding value of y. For example, if x = 2, then y = 4(2) = 8. If x = 10, then y = 4(10) = 40. In other words, y is always four times the value of x in a direct variation relationship.

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Step-by-step explanation:

100 - 9 = 91   seats for seven student groups

91 / 7 = 13  seats in each student group

   each student group receives   13 - 9 = 4 more seats than the roped off section

Henry had 35/6 gallons of juice, which is equivalent to 5 and 5/6 gallons.

To convert quarts to gallons, we need to know that there are 4 quarts in 1 gallon. So, we divide the number of quarts by 4 to get the number of gallons.

In this problem, we're given that Henry had 23 1/3 quarts of juice. To convert this amount to gallons, we first need to convert the mixed number to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction and then adding the numerator. This gives us:

23 1/3 = (23 × 3 + 1) / 3 = 70 / 3

Now we can divide 70/3 by 4 to get the amount of juice in gallons:

70/3 ÷ 4 = 70/3 × 1/4 = 70/12

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2 in this case. This gives us:

70/12 ÷ 2/2 = 35/6

So, Henry had 35/6 gallons of juice in total.

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For the given ellipse, the height of the ceiling at the center is 5 meters.

From the properties of an ellipse, we know that the distance from the center to one of the foci is a, and the distance from the center to one of the vertices is b. We can find these values using the equation of an ellipse:

(x²/a²) + (y²/b²) = 1

At the center of the gallery, x = 0, and we know that the major axis length is 36 meters, so b = 18 meters. We can solve for a by using the fact that the distance between the two foci is 10 meters:

2a = 36 - 10 = 26

a = 13

Therefore, the distance from the center to one of the foci is 13 meters, and the distance from the floor to the same focus is 13 - 5 = 8 meters.

Thus, the height of the ceiling at the center of the gallery is 13 - 8 = 5 meters.

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The mean IQ score in the population is approximately 98, and the standard deviation is approximately 16.

Let μ = mean and σ = standard deviation of IQ scores in population.

Then we can write the two equations as :

⇒ P(X ≤ 80) = 0.13    ...equation(1)

⇒ P(X ≥ 128) = 0.03   ...equation(2)

we standardize the data by using the formula:

⇒ Z = (X - μ)/σ,

Where Z = standard normal variable.

Using the standard normal distribution, we know that P(Z ≤ -1.126) = 0.13,

So, -1.126 = (80 - μ)/σ   .....equation(3),

and we know that P(Z ≥ 1.881) = 0.03.

So, 1.88 = (128 - μ)/σ     ...equation(4),

⇒ μ = 128 - 1.881σ,

Solving equation(3) and equation(4),

We get,

⇒ σ ≈ 16.

Substituting σ = 16 into the equation(4),

We get,

⇒ μ = 128 - 1.881×16,

⇒ μ = 98.

Therefore, the mean IQ score = 98, and standard deviation is = 16.

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Answer:

a) 183.75

b) 386.25

i believe thats right, i am very sorry if i am wrong

The density of the material is 4 g/cm³.

What is the density of the material?

Density is a physical property that describes the amount of mass per unit volume of a substance. It is typically represented by the symbol "ρ" (rho) and is calculated by dividing the mass of an object by its volume. The units of density are usually expressed as mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

Density is defined as mass per unit volume. We can use the formula:

density = mass/volume

Substituting the given values:

density = 48g / 12cm³

Simplifying:

density = 4g/cm³

Therefore, the density of the material is 4 g/cm³.

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Answer:

apples - $0,55 per pound

oranges - $0,45 per pound

Step-by-step explanation:

Let's assume, that apples cost x dollars per pound and oranges cost y dollars per pound.

Let's write 2 equations according to the given information and put them in a system:

{3x + 4y = 3,45,

{4x + 2y = 3,10;

Let's make x the subject from the 1st equation:

3x = 3,45 - 4y / : 3

x = 1,15 - 1 1/3y

Let's replace x in the 2nd equation:

[tex]4 \times(1.15 - 1 \frac{1}{3} y) + 2y = 3.10[/tex]

[tex]4.6 - \frac{16}{3} y + 2y = 3.10[/tex]

[tex] - \frac{10}{3} y = 3.10- 4.6[/tex]

[tex] - \frac{10}{3} y = - 1.5[/tex]

[tex]y = 0.45[/tex]

[tex]x = 1.15 - 1 \frac{1}{3} \times 0.45 = 0.55[/tex]

so, they are not equally likely. Thus, P(spade) = 13/52 or 1/4, and P(heart) = 13/52 or 1/4, but P(spade) ≠ P(heart).

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. The probability of an event is calculated by dividing the number of ways an event can occur by the total number of possible outcomes.

The true statements are:

P(ace) = 4/52 or 1/13

P(jack) = 4/13

P(ace) > P(king)

The false statements are:

P (numbered card) > P (face card) - this is not true since there are 12 face cards (4 jacks, 4 queens, 4 kings) and 40 numbered cards (2-10), so P(face card) = 12/52 or 3/13, and P (numbered card) = 40/52 or 10/13, which means that P (numbered card) > P (face card).

P(spade) = P(heart) - this is not true either, since there are 13 cards of each suit, but the spades and hearts are different suits, so they are not equally likely. Thus, P(spade) = 13/52 or 1/4, and P(heart) = 13/52 or 1/4, but P(spade) ≠ P(heart).

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To create the figure with the new scale of 1 unit = 3 yd. The steps are mentioned below.

Scale refers to the proportional relationship between the measurements of an object or a system and the corresponding measurements on a representation or a model of that object or system. It is commonly used in many fields, including mathematics, engineering, architecture, art, and geography.

In mathematics, scale can be expressed as a ratio or a fraction, which indicates how much the measurements on the representation or model have been reduced or enlarged relative to the actual measurements of the object or system. For example, a scale of 1:100 means that every measurement on the representation or model is 100 times smaller than the corresponding measurement on the actual object or system.

In art and architecture, scale is used to create a sense of proportion and perspective in a work. For example, an artist might use a smaller scale for a background object to make it appear farther away, while using a larger scale for a foreground object to make it appear closer.

To create the figure with the new scale of 1 unit = 3 yd. Here are the steps:

Determine the dimensions of the rectangle in yards using the original scale of 1 unit = 6 yd.

Divide the dimensions by 2 to get the new dimensions using the new scale of 1 unit = 3 yd.

Draw a rectangle on a new grid using the new dimensions.

If you want to place the rectangle in a specific location on the grid, you can use the coordinates on the grid to position it.

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Answer:

20 percent

Step-by-step explanation:

5/25=0.2

Answer:

25/30 which reduces to 5/6

Step-by-step explanation:

There is a net total of 30 students (25 for musical and 5 for play)

It's asking for the probability of someone who wants to do a musical getting selected, which would be 25 kids out of 30. Which reduces to 5/6

The percentage of students who do not wear glasses is 30%.

Thirty-five out of 50 students in a class wear glasses. The percentage of students in the class who do not wear glasses is: 30%.Explanation:Given data: The total number of students in the class = 50Number of students who wear glasses = 35. We have to calculate the percentage of students who do not wear glasses.Total students = 50Number of students who wear glasses = 35.

So, the number of students who do not wear glasses = Total students - Number of students who wear glasses= 50 - 35 = 15Percentage of students who do not wear glasses = (Number of students who do not wear glasses / Total students) x 100= (15 / 50) x 100= 0.3 x 100= 30%.

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List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.

List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.

The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").

Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.

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Answer:

List 4

Step-by-step explanation:

List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

What is sample?

In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.

According to question:

List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.

The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").

Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.

The base οf the triangle is 5 centimeters and the height οf the triangle is 20 centimeters.

In geοmetry, a triangle is a three-sided pοlygοn that cοnsists οf three line segments οr sides and three angles.

Let's denοte the base οf the triangle by "b" and the height by "h". We knοw that the area οf the triangle is 50 square centimetres, sο we can use the fοrmula fοr the area οf a triangle tο set up an equatiοn:

[tex]Area = (1/2) * base * height[/tex]

Substituting the given values, we get:

[tex]50 = (1/2) * b * h[/tex]

We also know that the height of the triangle is four times the base:

h = 4b

We can substitute this expression for "h" into the equation for the area:

[tex]50 = (1/2) * b * (4b)[/tex]

[tex]50 = 2b^2[/tex]

Dividing both sides by 2, we get:

[tex]25 = b^2[/tex]

Taking the square rοοt οf bοth sides, we get:

b = 5

Sο the base οf the triangIe is 5 centimeters. Using the expressiοn fοr the height in terms οf the base, we can find the height:

h = 4b = 4(5) = 20

Sο the height οf the triangIe is 20 centimeters.

Hence, the base οf the triangIe is 5 centimeters and the height οf the triangIe is 20 centimeters.

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Answer:

24

Step-by-step explanation:

Because it has to be a equal side and 24 is even

and plus 24 is

Observational errors, Random errors, Systematic errors, Instrumental limitations and Personal factors are the causes for measurement error.

The difference between measured value and true value is known as error. Causes for measurement error are as follows:

Errors in the experiment can be due to various reasons like observational errors, random errors, systematic errors, errors due to instrumental limitations, and errors due to personal factors.

The difference between measured value and true value is known as error.

The following are the causes of measurement error:

Observational Errors

Observational errors are errors that occur during observation. These errors may occur due to factors such as lack of attention, inadequate experience, and poor eyesight.

Random Errors

Random errors are caused by factors that are unpredictable or random. These errors cannot be removed from the data because they are the result of random fluctuations. For example, when a thermometer is being used, the thermometer might display different temperatures for different readings.

Systematic Errors

Systematic errors are those errors that are caused by a defect in the measuring instrument or an improper calibration of the instrument. These errors can be removed by carefully calibrating the instrument and then performing the measurement.

Instrumental Limitations

Instrumental limitations are caused by the limitations of the measuring instrument. These errors can be minimized by selecting the appropriate instrument for the measurement task.

Personal Factors

Personal factors are errors that are caused by the individual performing the measurement. These errors can be minimized by providing proper training and ensuring that the individual is experienced in the field of measurement.

The above causes lead to the errors in the experiment. Hence, care must be taken to minimize these errors so that the results obtained are accurate.

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Answer:

x equals [tex]\frac{11}{2}[/tex]

Hope this helps!

Step-by-step explanation:

Cross multiply to get ( 4x + 8 = 6x - 3 )  =  ( 2x = 11 ) = ( x = [tex]\frac{11}{2}[/tex] ).

Answer:

11/2 or 5.5 (5 1/2 mixed)

Step-by-step explanation:

Cross multiplication ( a/b = c/d = a*d = c*b

(x+2)*4 = 3(2x-1) =

4x + 8 = 6x - 3

Move -3 to the left side (becomes positive since it is a negative)

4x + 8 + 3 = 6x

Move 4x to the other side

8+3 = 6x - 4x

Combine Like Terms

11 = 2x

Divide by 2

11/2 = x

Answer: a) Lower limit: (13.1 - 0.05) - (18.7 + 0.05) = -5.65 cm

Upper limit: (13.1 + 0.05) - (18.7 - 0.05) = -4.95 cm

Therefore, the lower limit of the difference is -5.65 cm and the upper limit is -4.95 cm.

b) Lower limit: (0.55 - 0.005) - (0.093 + 0.005) = 0.447 km

Upper limit: (0.55 + 0.005) - (0.093 - 0.005) = 0.457 km

Therefore, the lower limit of the difference is 0.447 km and the upper limit is 0.457 km.

c) Lower limit: (2539 - 0.5) - (1.229 + 0.001) = 2537.27

Upper limit: (2539 + 0.5) - (1.229 - 0.001) = 2541.27

Therefore, the lower limit of the difference is 2537.27 and the upper limit is 2541.27.

d) Lower limit: (8.3 - 0.1) - (15.9 + 0.1) = -7.7 m

Upper limit: (8.3 + 0.1) - (15.9 - 0.1) = -7.3 m

Therefore, the lower limit of the difference is -7.7 m and the upper limit is -7.3 m.

Step-by-step explanation: omg u made me so tired

For the given cyclic quadrilateral the missing values of  x is 82°,  y is 130° and z = 118°

In trigonometry, a set of fundamental identities is referred to as the "Circle identities" and connects the six trigonometric functions of an angle in a right-angled triangle.

Here given a quadrilateral inside the circle, we know that,

Sum of opposite angle of cyclic quadrilateral is 180 degree;

Then, x + 98° = 180°

          x = 82°

Opposite angle of 76° will be;  180° - 76° = 104°

Radius are same in ΔAOB, (See the below figure)

Then, a + a + 34° = 180°

          a = 73°

then, ∠OBC = 98° - a = 25°

and in ΔCOB, 25° + 25° + y° = 180°

Then, y = 130°

and in ΔDOA,  

∠OAD = 104° - 73° = 31°

Then, z = 118°

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Simplify figure for understanding-

The main effects of the independent variables, and failing to consider them can lead to incomplete or incorrect conclusions about the relationships between variables.

When researchers are interested in whether the effect of the original independent variable on a dependent variable depends on the level of another independent variable, they are interested in the concept of an interaction effect. An interaction effect occurs when the effect of one independent variable on dependent variable changes depending on the level of another independent variable.

In other words, the effect of one independent variable is different at different levels of the other independent variable. Interactions are important to consider because they can change the interpretation of the main effects of the independent variables, and failing to consider them can lead to incomplete or incorrect conclusions about the relationships between variables.

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The new location of Point A is (3, 5). This is because the x-coordinate remains unchanged, while the y-coordinate is inverted, making it positive.

Point A is located at (3, -5). To reflect this point over the x-axis, we need to calculate the new coordinates. First, we will note that the x-coordinate remains unchanged. This means that the new x-coordinate is 3. Secondly, we will note that the y-coordinate needs to be flipped, meaning it will become positive. To do this, we will take the opposite of the original y-coordinate. Since the original y-coordinate is -5, the new y-coordinate will be 5. Therefore, the new location of Point A is (3, 5).

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The measure of abd is (0.3x+67) and the measure of cbd is (0.1x+41), the value of x is 130.

Abd is an abbreviation for the term "abdomen." It is used to describe the part of the body located between the chest and the pelvis, and contains many vital organs including the stomach, intestines, pancreas, and liver. Abd is often used in medical terminology, particularly when referring to conditions that affect the abdomen such as appendicitis or diverticulitis.

The measure of ABD is (0.3x+67) and the measure of CBD is (0.1x+41). Since the two angles are supplementary (they add up to 180 degrees), we can set the two equations equal to each other and solve for x.
0.3x + 67 = 0.1x + 41
Subtracting 0.1x from both sides of the equation, we get:
0.2x = 26
Dividing both sides of the equation by 0.2, we get:
x = 130
Therefore, the value of x is 130.

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If The measure of abd is (0.3x+67) and the measure of cbd is (0.1x+41) then the value of x is 180.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the value of x, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

We know that the sum of angles ABD and CBD is equal to angle ABC, which is 180 degrees.

So we can set up the following equation:

ABD + CBD = ABC

(0.3x + 67) + (0.1x + 41) = 180

Simplifying the equation, we get:

0.4x + 108 = 180

Subtracting 108 from both sides, we get:

0.4x = 72

Dividing both sides by 0.4, we get:

x = 180

Therefore, the value of x is 180.

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Estimated value of median is 44.7.

The graphic representation of data points arranged into specified ranges is called a histogram. The histogram, which re assembles a bar graph in appearance, contain a data series into an intuitive visual by collecting numerals data points and organizing them into logical bins or range

The middle value in a arrange  ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

l =  lower limit of median class, n = number of observations, f =  frequency of  median class, and h = class size. Median = [l + ((n/2) - cf)/f]h (assuming equal size classes).

According to question ,n =60 then median class = 25 to 45 because [tex]\frac{n}{2}[/tex]=30

l=25, f=7.5 ,cf =0.5 ,h = [tex]\frac{45-25}{4}[/tex]=5

so, median =

[tex]25+[\frac{(30-0.5)}{7.5}]*5\\44.7[/tex]

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Answer:

85

Step-by-step explanation:

13(6)+7=85

:)

Answer:

85

Step-by-step explanation:

Let's calculate the working hours of the first 6 days:

[tex]13 * 6 = 78[/tex] hours

Now let's add that to the last 7 hours she worked:

[tex]78 + 7 = \fbox{85}[/tex] hours

Answer: $21.15

Step-by-step explanation:

The insurance company will pay a total of  $70,000 in damages as insurance.

What exactly is insurance?

Insurance is a contract between an individual or entity (the insured) and an insurance company (the insurer) in which the insurer agrees to provide financial protection or compensation to the insured in any loss or damage. The insured typically pays a premium to the insurer in exchange for this protection. Insurance policies can provide coverage for various risks, such as accidents, illness, property damage, and liability.

Now,

Theresa's insurance policy covers up to $25,000 for bodily injury per person, up to $50,000 total for bodily injury per accident, and up to $25,000 for property damage per accident.

For bodily injury, the insurance will cover $25,000 for the first passenger, $10,000 for the second passenger, and $10,000 for Theresa's son, which adds up to $45,000. Since this is below the $50,000 total for bodily injury per accident, the insurance will cover all the bodily injury damages.

For property damage, the insurance will cover up to $25,000 per accident. Since the total property damage is $18,000 + $7,500 = $25,500, which is above the $25,000 coverage limit, the insurance will only pay out $25,000.

Therefore, the insurance company will pay a total of $45,000 + $25,000 = $70,000 in damages.

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The inequality that models the story is n ≥ 8

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to)

The number of charms Aaliyah might add to the necklace is represented by n. Since she plans to put at least as many charms on the necklace as the bracelet, we can use the inequality symbol "≥" to indicate this relationship.

So, the inequality that models the story is

n ≥ 8

This inequality states that the number of charms added to the necklace (n) must be greater than or equal to 8, which is the number of charms Aaliyah added to the bracelet.

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Answer: 25 divided by 5 plus 6 times 2 minus 4 and 5 tenths

Step-by-step explanation: order of operations, PE(MD)(AS)

Check the picture below.

so since ST is bisecting at the vertex T, that means that T will end up with twin angles and thus both triangles the yellow and green one since both are sharing the hypotenuse ST, both triangles are congruent by the HA theorem, and thus CPCTC.