the mean of a normal probability distribution is 320; the standard deviation is 18. a. about 68% of the observations lie between what two values?

The measure of angle x, y and z is 85⁰, 45⁰ and 40⁰ respectively.

The measure of angle x, y and z is calculated by applying intersecting chord theorem as shown below;

Angle y is calculated as follows;

10⁰ = ¹/₂ (arc EA - AN )

10 = ¹/₂ (65 - y )

20 = 65 - y

y = 65 - 20

y = 45⁰

The value of arc angle x is calculated as follows;

165 + 65 + 45 + x = 360 (sum of angles in a circle)

275 + x = 360

x = 360 - 275

x = 85⁰

The value of angle z is calculated as follows;

z = ¹/₂ (arc GE - GN )

z = ¹/₂ (165 - 85)

z = 40⁰

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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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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%.

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).

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 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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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.

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 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 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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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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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 depth of the swimming pool s 8 feet

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

This means that

Depth = Volume/(length * width)

substitute the known values in the above equation, so, we have the following representation

Depth = 2000/(25 * 10)

Evaluate

Depth = 8

Hence, the depth is 8 feet

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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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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:

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.

To graph the line that passes through the coordinates (2, 3), (3, 4.5), (4, 6), and (6, 9), we can use the slope-intercept form of the equation of a line, which is y = mx + b.

To start, we can find the slope of the line using any two points on the line. Let's use the first and last points:

slope = (change in y) / (change in x) slope = (9 - 3) / (6 - 2) slope = 1.5

Now we can choose any of the four given points and plug in the slope to find the y-intercept, b. Let's use the second point:

4.5 = 1.5(3) + b b = 0.75

So the equation of the line is:

y = 1.5x + 0.75

To graph the line, we can plot the four given points and then connect them with a straight line. Alternatively, we can choose any two values of x and plug them into the equation of the line to find the corresponding values of y, and then plot the resulting points.

THIS LINE DOES PASS THROUGH THE ORIGIN

it is

NOT

proportional because the line passes through the origin

therefore the correct answer is:

A.

Answer:Y=-5/3x+3

y=1/3x-3

Step-by-step explanation:i don't know i searched the web

Answer:

Area of sector = (π/4)(7^2)

= 49π/4 square kilometers

= 38.5 square kilometers

Length of arc = (2π)(7)/4

= 7π/2 kilometers

= 11.0 kilometers

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:

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 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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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 coordinates of the vertex of the parabola is (-4, 4)

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

The parabola

The coordinates of the vertex of the parabola is the maximum or the minimum point of the parabola

In this case, it is a maximum and the point is (-4, 4)

Hence, the solution is (-4, 4)

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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 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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