What is the radius of a sphere if its volume is 7,234.56 ft3 please answer it,Show work.

a. The scale factor of the dilation is 2, since the length of each side of the dilated quadrilateral is twice the length of the original quadrilateral.

A quadrilateral is a polygon with four sides and four angles. It is a two-dimensional shape with an equal number of sides and angles, as well as four vertices and four interior angles. The most common examples of quadrilaterals include rectangles, squares, parallelograms, trapezoids, and rhombuses. All quadrilaterals have two pairs of parallel sides, and all four sides must be connected. Quadrilaterals can be classified based on their side lengths and the size of their angles.

b. The ratio of the length of AB to the length of A'B' is 2:1, since the length of AB is twice the length of A'B'.
c. The measures of angle A and angle A' are equal, since the dilation is centered on the origin and therefore the angles of the dilated quadrilateral are the same as the angles of the original quadrilateral.

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The total amount of money earned by Hudson in a day on which he waits on 18 tables is $264.

The total amount of money earned by Hudson in a day on which he waits on t tables is $(30 + 13t).

Based on the information provided above, we can logically deduce that a linear equation that models the total amount of money earned by Hudson at this restaurant is represented by the following function:

y = 30 + 13t

Where:

When the number of tables he waits on that day is equal to 18, Hudson's total earnings can be calculated as follows;

y = 30 + 13t

y = 30 + 13(18)

y = $264.

When the number of tables he waits on that day is t tables, Hudson's total earnings can be calculated as follows;

y = 30 + 13t = $(30 + 13t).

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Answer:

d=-3

Step-by-step explanation:

d^3=-27

d=[tex]\sqrt[3]{-27} \\[/tex]

d=-3

Answer:

d=-3

Step-by-step explanation:

You must that 3rd root of -27, which is -3

The three classifications of fundamental skull shapes are: +

The number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification is 45, 30, and 15 degrees, respectively.

The skull is a bony structure that supports the face and protects the brain. There are several different skull shapes, which can be classified into three main categories based on their length and width: brachycephalic, mesocephalic, and dolichocephalic.

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The part (percentage) of the whole trip Tigran travels during the (first) two hours of driving is 90%

A percentage is a representation of a part of a quantity as a fraction with a denominator of a 100.

The fraction of the whole trip Tigran travels in the first hour = 2/5

The distance Tigran drove in the first hour of driving = (2/5) × 150-mile = 60-miles

The distance Tigran travels in the second hour = (5/6) × (150 - 60) = 75

The distance he drove in the second hour = 75 miles

The distance, d, Tigran travels during these two hours is therefore;

d = 60 miles + 75 miles = 135 miles

The part of the whole trip traveled in the two hours is therefore;

Part of trip = 135/150 = 9/10 = 90%

The part of the whole trip Tigran travels in these two hours is therefore, 90% of the trip

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the t-score for a 99.8% confidence interval with a sample size of 5 is 4.604.

The t-score for a 99.8% confidence interval with a sample size of 5 can be found using a t-distribution table or calculator.

Since we have a sample size of 5, the degrees of freedom (df) will be n - 1 = 4.

From the t-distribution table or calculator, the t-score for a 99.8% confidence interval with 4 degrees of freedom is approximately 4.604.

Therefore, the t-score for a 99.8% confidence interval with a sample size of 5 is 4.604.

the complete question is :

what is the value of the t score for a 99.8% confidence interval if we take a sample of size 5?

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To find the value of the ratio b/a for the 3.0 kg ball and the 1.0 kg ball placed at opposite ends of a massless beam in equilibrium, we can use the principle of moments.

Solution:

Step 1: Identify the forces and distances involved. The 3.0 kg ball has a force of 3.0g (g represents gravity) acting at distance a from the pivot point. The 1.0 kg ball has a force of 1.0g acting at distance b from the pivot point.

Step 2: Apply the principle of moments. For the system to be in equilibrium, the clockwise moment and anticlockwise moment must be equal. This means that the product of the force and distance for each ball must be equal:

3.0g × a = 1.0g × b

Step 3: Solve for the ratio b/a. First, divide both sides of the equation by g:

3.0a = 1.0b

Now, divide both sides of the equation by 3.0a:

b/a = 1/3

The value of the ratio b/a is 1/3.

The ratio is 1:3

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Yes, the quadrilateral is a parallelogram. To prove this using the distance formula method, we need to show that opposite sides of the quadrilateral are equal in length.

We can calculate the distance between each pair of points using the distance formula:

d = [tex]\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Using this formula, we get:

d(LM) = √[tex]((5 - (-1))^2 + (8 - 6)^2)[/tex] = √(36 + 4) = √(40) = 2√(10)

d(NP) = √[tex]((-8 - 0)^2 + (12 - 2)^2)[/tex] = √(64 + 100) = √(164) = 2√(41)

d(LN) = √[tex]((0 - (-1))^2 + (2 - 6)^2)[/tex] = √(1 + 16) = √(17)

d(MP) = √[tex]((-8 - 5)^2 + (12 - 8)^2[/tex]) = √(169 + 16) = √(185)

We can see that d(LM) = d(NP) and d(LN) = d(MP), which means that opposite sides of the quadrilateral are equal in length. Therefore, the quadrilateral is a parallelogram.

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175 Cm³ is the correct volume of the triangular prism.

What is prism?

A prism is a solid, three-dimensional object whose two ends are identical. It is a result of the elements of flat faces, identical bases, and equal cross-sections. Without bases, the prism's faces are parallelograms or rectangles.

                               A prism is a transparent object made of glass or another material that has been cut into precise angles and plane faces for the purpose of reflecting and analyzing light in optics. White light can be divided into its component colors, known as a spectrum, using a standard triangular prism.

V = 1/2 x B x H

Find the Base area = l x w

Base area = (10 x 5)

Base area = 50 sq.m

V = (1/2) x (50) x 7

V =  175

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The domain of the equation is {1, 3, 5, 7, 9}. and the range of the equation is {6, 8, 10, 12, 14}.

What is range and domain of a function?

The domain of a function in mathematics is the set of all possible input values (usually denoted by x) for which the function is defined. It is the set of all values of the independent variable (input) for which the function is defined.

A function's range, on the other hand, is the set of all potential output values (typically indicated by y) that the function may generate. It is the set of all values of the dependent variable (output) that the function can take.

Now,

To solve for y:

2y = 30 - 3x

y = (30 - 3x)/2

The domain of the equation is the set of all possible values of x that will make the equation valid. Since x and y are positive integers, we need to find integer solutions for x that will also result in integer values for y.

Let's look at the equation (30 - 3x)/2 = y. For y to be an integer, (30 - 3x) must be even. This means that x can only take on odd integer values between 1 and 9, inclusive. Therefore, the domain of the equation is {1, 3, 5, 7, 9}.

To find the range of the equation, we need to find the possible values of y that correspond to the values of x in the domain. We can substitute each value of x into the equation y = (30 - 3x)/2 and simplify to find the corresponding value of y.

When x = 1, y = 14

When x = 3, y = 12

When x = 5, y = 10

When x = 7, y = 8

When x = 9, y = 6

Therefore, the range of the equation is {6, 8, 10, 12, 14}.

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a continuous random variable x is normally distributed with a mean of 0 and a standard deviation of 1. the probability of an observation that lies within the range of -1.0 < x <1.0 is 0.6827.

       The explanation for normal distribution is described by two parameters, the mean (μ) and the standard deviation (σ).

         A continuous random variable X that is normally distributed has the probability density function, (X is a normally distributed variable):

                   f(x)=1σ√2π×e−12((x−μσ)2)

        A normal distribution with a mean of 0 and standard deviation of 1 is called standard normal distribution or Z-distribution. The probability for the standard normal distribution can be found using the standard normal distribution table.

   In this case, we have a continuous random variable x which is normally distributed with a mean of 0 and a standard deviation of 1. We are asked to find the probability of an observation that lies within the range of -1.0 < x < 1.0.

  In other words, we want to find: P(-1.0 < x < 1.0)

  To do this, we need to transform the interval (-1.0, 1.0) to a standard normal distribution as follows:

             Z=(X−μ)/σ = (X−0)/1

                              = X

   Next, we use a standard normal distribution table to find the probability for Z as follows:

             P(-1.0 < x < 1.0) = P(-1 < Z < 1)

                                      = P(Z < 1) - P(Z < -1)

    From the standard normal distribution table,

    We have P(Z < 1) = 0.8413 and

                   P(Z < -1) = 0.1587

   Therefore: P(-1.0 < x < 1.0) = 0.8413 - 0.1587

                                               = 0.6827

   Thus, the probability of an observation that lies within the range of -1.0 < x < 1.0 is 0.6827.

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However, sin⁻¹ is defined to return an angle between -90° and 90°, so it returns the angle that is closest to 30° (which is 30° in this case).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.

Here,

If sin 30° = 0.5, then sin⁻¹(0.5) is the angle whose sine is 0.5. In other words, we are looking for the angle whose sine is 0.5. Since sin 30° = 0.5, we know that one possible answer is 30 degrees. However, there are other angles that also have a sine of 0.5. One way to find the other angles is to use the inverse sine function, denoted as sin⁻¹. This function takes a value between -1 and 1 as its input and returns an angle between -90° and 90° as its output. So, if we want to find sin⁻¹(0.5), we are asking: what angle has a sine of 0.5?

The answer is: sin⁻¹(0.5) = 30°.

Note that there are other angles that also have a sine of 0.5, such as 150°, 390°, etc.

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Complete question:

Using the equality above, copy and complete the following:

The value of sin⁻¹ (0.5)​ when sin 30° = 0.5.

By reducing −16/5 ⋅ (−15/56) in lowest term, the answer is 6/7.

To perform the indicated operation and reduce the result to lowest terms, we need to multiply the two fractions:

(-16/5) x (-15/56) = (16 x 15) / (5 x 56)

(when we multiply two negative numbers, the result is positive)

= 240 / 280

Now we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 40:

240 / 280 = (240 ÷ 40) / (280 ÷ 40) = 6/7

Therefore, -16/5 ⋅ (-15/56) = 6/7 in lowest terms.

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By permutation and combination, Maximum 171 number of different  2 - person teams are possible.

Provide an example of permutation and combination?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.

                       As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.

Total number of ways to choose different 2 person out of 19 person.

                     = ¹⁹C₂

              = 19!/2! (19 - 2)!

              =  19!/2!   17!

             = 19 * 18 * 17!/2 * 1 * 17!

            = 19 * 7

              = 171

Hence, maximum 171 number of different  2 - person teams are possible.

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The rate of increase of the number of bacteria is 1200/2 = 600 bacteria/hour.

To find the rate of increase of the number of bacteria in a culture, we can use the formula

rate of change = change in number of bacteria/time elapsed.

In this case, the change in number of bacteria is 1800-600 = 1200, and the time elapsed is 2 hours.

Thus, the rate of increase of the number of bacteria is 1200/2 = 600 bacteria/hour.

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Answer: 0.48

Step-by-step explanation:

× 0.1 = ÷10

÷ 0.1 = ×10

× 0.01 = ÷100

÷ 0.01 = ×100

So, we do=

4.8 x 0.1 = 4.8 ÷ 10

= 0.48

So our answer is 0.48

37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

The area between 550 and 725 on a standardized test of educational achievement is equal to the percentage of students whose scores fall within one standard deviation (or 68%) of the mean score of 600. This can be expressed mathematically as:

Percentage = (725 - 550) / (2 * 50) = 37.5 / 100 = 37.5%

To explain in more detail, a standard deviation is a measure of the spread of a dataset around its mean value. The mean value in this case is 600, and the standard deviation is 50. Therefore, one standard deviation from the mean is calculated by subtracting or adding the standard deviation (50) from the mean (600), giving a range of 550 to 650.

Since the area in question spans across two standard deviations (550 to 725), the area is calculated by subtracting the lower range (550) from the upper range (725) and then dividing it by two standard deviations (100). This gives us the area, which is 37.5%.

To summarize, 37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

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The family-sized box requires 130 more square inches of cardboard than the regular-sized box, has an additional 228 cubic inches of cereal capacity, and costs less per cubic inch of cereal.

To calculate the additional square inches of cardboard needed for the family-sized box, we need to find the difference in surface area between the regular-sized box and the family-sized box.

The regular-sized box has a surface area of 2 x 6 + 2 x 11 + 6 x 11 = 104 square inches.

The family-sized box has a surface area of 2 x 8 + 2 x 15 + 3 x 15 + 3 x 8 + 3 x 15 = 234 square inches.

Therefore, the additional square inches of cardboard needed for the family-sized box is 234 - 104 = 130 square inches.

B. To find how many more cubic inches of cereal fit in the family-sized box than the regular-sized box, we need to calculate the difference in volume between the two boxes.

The regular-sized box has a volume of 2 x 6 x 11 = 132 cubic inches.

The family-sized box has a volume of 3 x 8 x 15 = 360 cubic inches.

Therefore, the additional cubic inches of cereal that fit in the family-sized box is 360 - 132 = 228 cubic inches.

C. To determine which cereal costs less per cubic inch of cereal, we need to divide the cost of each box by its respective volume.

The regular-sized box costs $3.99 for 132 cubic inches of cereal, which gives us a cost of $0.03 per cubic inch.

The family-sized box costs $5.69 for 360 cubic inches of cereal, which gives us a cost of $0.02 per cubic inch.

Therefore, the family-sized box costs less per cubic inch of cereal.

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There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

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Answer:

Apparently it's 4800 according to desmos.

Step-by-step explanation:

Step-by-step explanation:

x y

-3 150

-2 300

-1 600

0 4800

As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.

Answer:

[tex]y = \frac{2}{7} x - \frac{20}{7} [/tex]

Step-by-step explanation:

[tex] - 2 = \frac{2}{7} (3) + b[/tex]

[tex] - \frac{14}{7} = \frac{6}{7} + b [/tex]

[tex]b = - \frac{20}{7} [/tex]

[tex] y = \frac{2}{7} x - \frac{20}{7} [/tex]

Answer:

between 15 and 16

Step-by-step explanation:

31÷2=15.5 meaning 15.5 is between 15 and 16

The correct option for the given radical equation is option C. The value after operation is equal to 1.

Given radical expression:

[tex]\frac{x+4}{4+x}[/tex]

Now, we know that the addition is commutative.

Using commutative property, 4+x = x+4,

So,

[tex]\frac{x+4}{x+4}[/tex]

Both numerator and denominator has same value, hence they could be cancelled.

[tex]\frac{x+4}{4+x}[/tex] = [tex]\frac{x+4}{x+4}[/tex]

[tex]\frac{x+4}{x+4}[/tex] = 1.

Therefore, the value which is equivalent to x+4/4+x is equal to 1.

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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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Answer:L x b

              98ft x 56ft =5488

                                  =5488 / $3.75= $1463.47

Step-by-step explanation: Play ground is more like a rectangle so we use the formula for the rectrectangle to get total area . A=Lxb

Divide  the total with the cost since it say each per sqr feet

A=lxb

98x56=5488

5488/3.75= 1463.47

The value of h in the given parallelogram is 6 units, which can be found by using the formula for the area of a parallelogram.

In the given parallelogram, we can see that the base is 12 units long and the distance between the base and the opposite side is 6 units.

To find the value of h (the height or distance between the base and the opposite side), we can use the formula for the area of a parallelogram which is:

Area = base x height

Since we know the area of the parallelogram is 72 square units (given in the diagram), we can plug in the values we know and solve for h:

72 = 12 x h

h = 72/12

h = 6

Therefore, the value of h in the parallelogram is 6 units.

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By the 46th day, there are 400 water lilies in the pond. the estimate you made: a). close to 46 (or exactly right) because it was estimated well.

We know that the regression equation is: y = 3.915(1.106)ˣ and that the pond can hold 400 water lilies.

y = 3.915(1.106)ˣ

Here, y is equal to the number of water lilies the pond can hold.

So, y = 400

And,  x is the required time taken.

So,

400 = 3.915(1.106)ˣ

⇒ (1.106)ˣ = 400/3.915    

⇒ (1.106)ˣ = 102.17

Taking logarithm on both sides, we get

log (1.106)ˣ = log (102.17)

⇒ x log (1.106) = log (102.17) .............. [log aˣ = x loga]

⇒ x = [log (102.17)/log (1.106)]    

⇒ x = 45.92

x ≅ 46

So, the pond will take 46 days to become full.

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Complete question:

Regression equation: y = 3.915(1.106)ˣ . The pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day.

Answer:

b

Step-by-step explanation:

just did it

Answer: c

Step-by-step explanation:

The number of solutions on the graph is zero.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

to determine the number of solutions:

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

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Answer:

Choice B:  distance from home to library is length of HL

HL = 75      see calculations below

Step-by-step explanation:

use points (0,0) and (2.1, 7.2) to find HL:

HL = √(2.1 - 0)² + (7.2 - 0)² = √4.4 + 51.8 = √56.25 = 7.5

Answer:

[tex]26a - 10 = 2(13a - 5)[/tex]