Find the quotient. Write your answer in simplest form.

1/4 ÷ 6

2/3

1 1/2

24

1/24

The volume of a right rectangular prism is given by the formula **V = l × w × h**, where **V** is the volume, **l** is the length, **w** is the width, and **h** is the height²³. The units of volume are cubic units, which means that they are the same as the units of length raised to the third power. For example, if the length is measured in meters, then the volume is measured in cubic meters (m³).

In this case, the length is 8 meters, the width is 10 meters, and the height is 5 meters. Therefore, the volume is:

**V = 8 × 10 × 5**

**V = 400 m³**

The units of volume are cubic meters (m³) because the units of length are meters (m).

Answer:

Step-by-step explanation:

The units for the volume of a right rectangular prism are cubic units because it is a measure of three-dimensional space.

In this case, the length, width, and height of the prism are all given in meters. Therefore, the volume of the prism can be expressed in cubic meters (m³).

So the volume of the right rectangular prism with a length of 8 meters, a width of 10 meters, and a height of 5 meters is:

Volume = length x width x height = 8 m x 10 m x 5 m = 400 m³.

Therefore, the volume of the prism is 400 cubic meters (m³).

Answer:

153.86 = π(r^2)

r = √(153.86/π) = 6.998 = 7 inches

d = 2r = 14 inches

Answer:

Diameter of pizza = 14 inches

Step-by-step explanation:

Pizza is shaped like a circle

If the radius of the pizza is r, the area which is the area of a circle of radius r is given by

[tex]A = \pi r^2[/tex]

Here we are given the area as 153.86 in²

153.86 = π · r²

r² = 153.86 /π

r = √( 153.86 /π )

 = 6.998 in

 ≈ 7 inches

Diameter = 2 x radius

               = 14 inches

The required sample size to construct a 95% confidence interval to estimate the proportion is 602 students.

a. To estimate the sample size needed to construct a 95% confidence interval with a maximum error of 2.5% when the past few years' graduation rate is 70%, we can use the following formula:

n = [Z² × p × (1-p)] / E²

where:

Z = the Z-value for the desired confidence level (95% in this case), which is 1.96

p = the estimated proportion of students who graduate in 4 years (70%)

E = the maximum error, which is 0.025 (2.5%)

Plugging in the values, we get:

n = [(1.96)² × 0.7 × (1-0.7)] / 0.025²

n = 381.16

Always round up to the next integer, so the sample size needed is 382.

b. To estimate the sample size needed when there is no knowledge of the typical graduation rate, we can use a conservative estimate of 50% for p. Plugging in the values, we get:

n = [1.96² × 0.5 × (1-0.5)] / 0.025²

n = 601.64

Always round up to the next integer, so the sample size needed is 602.

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The coordinates of point U’ are (0, 30).

Explain the term coordinates

Coordinates refer to a system used to locate a point in space or on a plane. They consist of a set of values, often expressed as ordered pairs or triples, which represent the position of the point along each axis. Coordinates are used in various fields, such as mathematics, geography, and physics.

According to the given information

The coordinates of point U’ are (0 , 30). Here’s how to find it:

The scale factor for Q’U’A’D’ is 6.

The coordinates of point U are (0 , 5).

To find the coordinates of point U’, we multiply the y-coordinate of U by the scale factor which gives us 5 * 6 = 30.

Therefore, the coordinates of point U’ are (0 , 30)

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Answer:

The pressure exerted by the box on the ground is given by the force divided by the area of the base. Let's convert the force from kN to N, and the area from m^2 to cm^2, for convenience:

4.7 kN = 4.7 × 10^3 N

1.9 m^2 = 1.9 × 10^4 cm^2

Now we can calculate the pressure:

pressure = force / area

pressure = (4.7 × 10^3 N) / (1.9 × 10^4 cm^2)

pressure ≈ 0.247 kN/m^2

Rounding this to 2 decimal places, we get:

pressure ≈ 0.25 kN/m^2

Therefore, the pressure exerted by the box on the ground is approximately 0.25 kN/m^2.

Answer:

The odds against it snowing the next day can be found by subtracting the probability of it snowing (40%) from 100% (the total possible outcomes) and then expressing it as a ratio of non-snowing outcomes to snowing outcomes.

100% - 40% = 60%

The odds against it snowing the next day are 60:40 or 3:2 (simplifying the ratio).

The probability of picking a T and an N is 1/81.

The correct option is (B).

From the geometric shape we can see that the total number of different letter is = 9

that are M, A, T, H, I, S, F, U, N

Now T is one of the letter from that 9 letters.

Now if we pick T then the probability of that = 1/9

Therefore, P(T) = 1/9

now we again replace T in previous position before picking the next letter.

Again the total number of letters = 9

Again, N is one of the letter from that 9 letters.

So the probability of picking N = 1/9

Therefore, P(N) = 1/9

The required probability of picking T and N

= probability of picking T followed by picking N

= P(T)*P(N)

= (1/9)*(1/9)

= 1/(9*9)

= 1/81

Hence the correct option is (B).

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Answer:

5,234 cubic centimeters

Step-by-step explanation:

The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

Since the diameter of the bowling ball is 21.6 centimeters, the radius is half of that:

r = d/2 = 21.6/2 = 10.8 centimeters

Substituting this value into the formula, we get:

V = (4/3)πr^3 = (4/3)π(10.8)^3 ≈ 5,233.8 cubic centimeters

Rounding this to the nearest whole number, we get a measurement closest to the volume of the bowling ball of 5,234 cubic centimeters.

Your welcome

Answer:

The total amount of money in the savings account can be represented by the sum of the initial amount of money and the amount of money added each week multiplied by the number of weeks:

S = 450 + 70W

To find the total amount of money in the savings account after 17 weeks, we can substitute W = 17 into the equation:

S = 450 + 70(17)

S = 450 + 1190

S = 1640

Therefore, after 17 weeks of adding $70 to the savings account each week, the total amount of money in the account will be $1640.:)

As per the given equation, the center and radius of the circle are (-3, 2) and 12, respectively.

Radius is the distance between the center of a circle and any point on its circumference. It is half the length of the diameter of the circle.

The center-radius form of a circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

Comparing the given equation with the standard form, we have:

[tex](x + 3)^2 + (y - 2)^2 = 144[/tex]

This means that the center of the circle is (-3, 2) and the radius is the square root of 144, which is 12.

Therefore, the center and radius of the circle are (-3, 2) and 12, respectively.

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Answer:

4

Step-by-step explanation:

Let's start by assuming that the initial mass of the hydrate CoCl2 x XH2O is 100 grams. This means that the mass of the anhydrous compound CoCl2 after decomposition is 53.9 grams (since it is 53.9% of the hydrate mass).

The mass of water lost during the decomposition is therefore:

Mass of water lost = Initial mass of hydrate - Mass of anhydrous compound

Mass of water lost = 100 g - 53.9 g

Mass of water lost = 46.1 g

The molar mass of CoCl2 is 129.8 g/mol, and the molar mass of H2O is 18.0 g/mol. Therefore, the molar mass of the hydrate CoCl2 x XH2O is:

Molar mass of hydrate = Molar mass of CoCl2 + Molar mass of H2O × X

Molar mass of hydrate = 129.8 g/mol + 18.0 g/mol × X

We can set up a proportion to solve for X:

Mass of water lost / Molar mass of water = X / Molar mass of hydrate

Plugging in the values we found:

46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)

Solving for X:

46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)

2.56 mol = X / (129.8 g/mol + 18.0 g/mol × X)

2.56 mol × (129.8 g/mol + 18.0 g/mol × X) = X

331.968 g/mol × X + 46.368 g/mol × X = X

378.336 g/mol × X = X

X = 4

Therefore, the value of X in the hydrate formula CoCl2 x XH2O is 4, and the formula of the hydrate is CoCl2 x 4H2O.

The value of the expression is 9 1/4.

We have,

We can simplify the expression step by step using the order of operations (PEMDAS).

2 x (1/4 + 11/8 + 3)

First, let's add the fractions inside the parentheses:

1/4 + 11/8 = 2/8 + 11/8 = 13/8

Now we can substitute this result back into the original expression:

2 x (13/8 + 3)

Next, we add the two terms inside the parentheses:

13/8 + 3 = 13/8 + 24/8 = 37/8

Now we can substitute this result back into the expression:

2 x 37/8

Finally, we multiply the coefficient 2 by the fraction 37/8:

2 x 37/8 = 74/8 = 9 1/4

Therefore,

The value of the expression is 9 1/4.

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The equation of the function in standard form is f(x) = x² + 4x - 12.

Quadratic equation can be represented as follows:

ax² + bx + c

where

Therefore, let's write the equation of the function in standard form.

-12 = a(0)² + b(0) + c

c = -12

Let's use -1 and -15

-15 = a(-1)² + b(-1) + -12

-15 = a - b - 12

a - b = - 3

Let's use -2 and -16.

-16 =  a(-2)² + b(-2) + -12

-16 = 4a - 2b - 12

4a - 2b = -4

2a - b = -2

Therefore,

a - b = - 3

2a - b = -2

subtract the equations

a = 1

b = a + 3

b = 1 + 3

b = 4

Therefore, the equation is as follows:

f(x) = x² + 4x - 12

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Answer: 101

Step-by-step explanation:

180 - 76 - 48 = 56

180 - 56 - 23 = 101

Statistical methods are excellent for capturing quantitative data, which is numerical data that can be measured and analyzed using mathematical calculations.

These methods are commonly used in fields such as economics, psychology, and social sciences to collect, analyze, and interpret data.

In contrast, qualitative data such as opinions, attitudes, and beliefs are better captured using methods such as interviews, focus groups, and case studies.

Which two primary data kinds are there?

Data may be categorized into two main probability : quantitative and qualitative, and both are equally significant.

Why are primary and secondary data different?

Data may be obtained by social and health scientists by speaking with the subjects that interest them directly. These data they gather are referred to as primary data.

The information that has previously been obtained by someone else is another sort of data that might be useful to researchers. Secondary data is what this is.

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The formula for the amount of radioactive phosphorus remaining after "t" days is A = 9 × [tex](0.95)^t[/tex]

Radioactive decay is a process by which the nucleus of an unstable atom emits radiation in the form of particles or energy in order to reach a more stable state. In the case of radioactive phosphorus, the nucleus decays by emitting beta particles, which leads to a decrease in the number of radioactive atoms over time.

The amount of radioactive phosphorus remaining after "t" days can be calculated using the formula

A = A₀ ×  [tex](0.95)^t[/tex]

Where

A0 = initial amount of radioactive phosphorus (9 grams in this case)

A = amount of radioactive phosphorus remaining after "t" days

t = number of days

So, substituting the given values in the formula, we get

A = 9 ×  [tex](0.95)^t[/tex]

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The decimal numbers in this problem are classified as follows:

a) 7.8 is a rational number.

b) 8.25... is an irrational number.

In the context of this problem, we have that:

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Answer:

1) 3w - 10 > 4

3w > 6, so w > 2

Put a 2 below the third vertical line on

the number line. Draw and fill in the

circle over 2, then draw a line going to

the arrow on the right.

2) 2x + 4 < 8

2x < 4, so x < 2

Put a 2 below the third vertical line on

the number line. Draw (but do not fill in)

the circle over 2, then draw a line going

to the arrow on the left.

3) 3 < 1.5p - 9

1.5p > 6, so p > 4

Put a 4 below the third vertical line on

the number line. Draw (but do not fill in)

the circle over 4, then draw a line going

to the arrow on the right.

4) (b/5) + 9 < 10

b/5 < 1, so b < 5

Put a 5 below the third vertical line on

the vertical line. Draw (but do not fill in)

the circle over 5, then draw a line going

to the arrow on the left.

5)

[tex] \frac{1}{3} c - 2 \frac{1}{2} \geqslant \frac{1}{2} [/tex]

[tex] \frac{1}{3} c \geqslant 3[/tex]

[tex]c \geqslant 9[/tex]

Put a 9 below the third vertical line on the number line. Draw and fill in the circle over 9, then draw a line going to the arrow on the right.

6) (4/5)(x - 2) < 6

x - 2 < 7.5, so x < 9.5

Put a 9.5 below the third vertical line on

the number line. Draw and fill in the

circle over 9.5, then draw a line going to

the arrow on the left.

the starting numbers on the left don't start at 0. Make sure to make the graph on the x axis starts at 0

the missing angle measurement using the angle addition postulate are:

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. Angles are typically measured in degrees or radians.

According to the given information:

The angle addition postulate is a rule used to find the measure of an angle created by two adjacent angles. If two adjacent angles are known, then their sum will equal the measure of the larger angle formed by the two adjacent angles. To use the angle addition postulate, add the measures of the known adjacent angles to find the measure of the larger angle.

In the given set of angles, we are asked to use the angle addition postulate to find the missing angle measures. We can use this rule to find the missing angles by adding the measures of the known adjacent angles. By doing so, we can find the measure of the larger angle formed by the two adjacent angles. It is essential to note that this rule only applies to adjacent angles. Therefore, we can only use the angle addition postulate to find the missing angle measurements for angles that share a common vertex and side

LABC = 60 degrees (angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the larger angle formed by the two adjacent angles)L

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As per the given volume, the height of Sofia's pyramid is approximately 4.8 inches.

Sofia's model of the great pyramid has a volume of 90 cubic inches. This means that if we were to fill the pyramid with water, it would hold 90 cubic inches of water.

The formula for the volume of a pyramid is:

Volume = (1/3) x base area x height

In this case, we know that the volume of the pyramid is 90 cubic inches, and the base of the pyramid has a side length of 7.5 inches. We need to find the height of the pyramid.

We can start by plugging in the values we know into the formula for the volume of a pyramid:

90 = (1/3) x base area x height

We know the base has a side length of 7.5 inches, so the base area is:

base area = (7.5)² = 56.25 square inches

Now we can plug in the base area and solve for the height:

90 = (1/3) x 56.25 x height

270 = 56.25 x height

height = 270 / 56.25

height ≈ 4.8 inches

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The radius of the quarter circle is 1 mile.

The formula for calculating the area of a circle is given by A = πr², where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant equal to approximately 3.14.

To find the radius of a quarter circle, we first need to find the area of the circle. Since the area of a quarter circle is given as 0.785 square miles, we can calculate the area of the circle as follows:

Area of circle = 4 × Area of quarter circle

Area of circle = 4 × 0.785 square miles

Area of circle = 3.14 square miles

Now that we know the area of the circle, we can use the formula for the area of a circle to find the radius. We rearrange the formula as follows:

r² = A/π

r² = 3.14/π

r² = 1

r = √1

r = 1 mile

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If each episode is 30 minutes long (0.5 hours), then Angela can watch up to eight episodes this week.

Angela has already watched a certain number of hours of TV this week, but we don't know how many. Let's call that number "h". We know that her parents allow her to watch a maximum of 7 hours per week, so we can set up an inequality:

h + x ≤ 7

where "x" is the number of additional hours of TV Angela wants to watch, and "≤" means "less than or equal to". We can simplify this inequality by subtracting "h" from both sides:

x ≤ 7 - h

This inequality tells us the maximum number of hours of TV Angela can watch this week, based on how many hours she has already watched. Now we need to figure out how many episodes she can watch, given the length of each episode.

Let's call the length of each episode "e". We know that each episode is "e" hours long, and Angela can watch "x" hours of TV. So the number of episodes she can watch is:

x ÷ e

where "÷" means division. Putting it all together, we get:

Number of episodes = x ÷ e = (7 - h) ÷ e

Now let's sketch the graph of this inequality. We can plot "x" on the horizontal axis and "h" on the vertical axis, and shade in the region where the inequality is true:

[Insert graph here]

The shaded region represents all the possible values of "x" and "h" that satisfy the inequality. For example, if Angela has already watched 3 hours of TV this week (so h = 3), then the maximum number of hours she can watch is:

x ≤ 7 - h = 7 - 3 = 4

And the maximum number of episodes she can watch is:

Number of episodes = (7 - h) ÷ e = 4 ÷ e

So if each episode is 30 minutes long (0.5 hours), then Angela can watch up to:

Number of episodes = 4 ÷ 0.5 = 8

eight episodes this week.

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The formula that describes the distance Jack covered during the hike  is: S(t) = vt for v = 5 and t is the time

The form of a linear equation in slope intercept form is:'

y = mx + c

where:

m is slope

c is y-intercept

Now, the formula for distance here is:

s(t) = vt

where:

v is speed

t is time

For a speed of 2 mph and a time of 3 hours, we can arriave at:

s(3) = 2 * 3 = 6 m for 2 seconds

Similarly:

s(t) = 5t

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The arc measure is 110° and the measures in the quadrilateral are x° is 46° and y° is 163°

We have to find the measure of arc x°

We know that the Arcs can be measured in degrees.

The degree of an arc is equal to the measure of the central arc that creates the arc

The central arc measures 110°

So x° = 110°

The complete measure of the quadrilateral is 360 degrees

As x° is equal to 46°

x° =46°

Now let us find y°

46°+46°+105°+y°=360

y°=360-197

y°=163°

Hence, the arc measure is 110° and the measures in the quadrilateral are x° is 46° and y° is 163°

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For computer company hired interns from a group of 234 applicants.

a) Probability that intern had a computer science major and did not get hired is [tex] \frac{112}{234} [/tex]

b) Probability that interns had a major other than computer science is [tex] \frac{38}{234} [/tex]

c) Probability that interns had a computer science and get hired = [tex] \frac{58}{234} [/tex].

4) probability that an intern with a major other than computer science was not hired is [tex] \frac{38}{234}[/tex].

Probability is defined as the chance of occurrence of an event. It is calculated by the ratio of favourable outcomes to the total possible outcomes. We have a table data of computer company that hired interns. Total number of applicants = 234

the table shows data of the numbers of applicants who were or were not computer science majors, and the numbers of applicants who were or were not hired. Number of outcomes for an intern had a computer science major and did not get hired = 112

1) Probability that intern had a computer science major and did not get hired = [tex] \frac{112}{234} [/tex].

2) Number of interns had a major other than computer science = 38

Probability that interns had a major other than computer science = [tex] \frac{38}{234} [/tex].

3) Number of interns had a computer science major and hired = 58

Probability that interns had a computer science and get hired = [tex] \frac{58}{234} [/tex].

4) Number of interns had a major other than computer science was not hired

= 38

Probability that an intern with a major other than computer science was not hired = [tex] \frac{38}{234} [/tex]. Hence, required value is [tex] \frac{38}{234} [/tex].

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Complete question:

a computer company hired interns from a group of 234 applicants. the table shows the numbers of applicants who were or were not computer science majors, and the numbers of applicants who were or were not hired. match the probabilites with the description. column a 1. what is the probability that the intern had a computer science major and did not get hired.

2. what is the probability that the intern had a major other than computer science?

3. what is the probability that a computer science major was hired?

4. what is the probability that an intern with a major other than computer science was not hired

column b a.conditional - 36.2% b.conditional - 48.6% c.joint - 43.6% d.joint - 51.2% e.marginal - 68.3% f.marginal - 31.6%.

Answer: 300

1 year of tution and college fee: $9,500

= $9,500 × 2 = $19,000

2 years of tution and college fee: $19,000

Money already in Account = $5,000

If we deposit $100 every month for 5 years we would get $11,000 that is less than $19,000.

If we deposit $200 every month for 5 years qe would get $17,000 which is still less.

If we deposit $300 every month we would get $23,000 which is not less so the correct answer is $300.