On a test that has a normal distribution, a score of 29 falls three standard deviations above the mean, and a score of 23 falls one standard deviation above the mean. Determine the mean of this test.

A) To calculate the total intake in milliliters, we need to convert each unit to milliliters and then sum them up:

Now, we add up the individual quantities:

30 ml (apple juice) + 120 ml (beef broth) + 60 ml (orange gelatin) + 473 ml (tea) = 683 ml

Therefore, the nurse should document 683 milliliters on the intake and output form.

B) If 450 ml was left in the 1-liter bag, that means 1 liter (1000 ml) - 450 ml = 550 ml has been infused. The nurse would document 550 milliliters on the intake and output form.

C) If 100 ml was left in the 1-liter bag, that means 1 liter (1000 ml) - 100 ml = 900 ml has been infused. The nurse would document 900 milliliters on the intake and output form.

D) The dose of Colace is given as 50 mg po bid, which means 50 milligrams (mg) is taken orally twice a day. There are 1000 milligrams in a gram, so to convert 50 mg to grams:

50 mg / 1000 = 0.05 grams

Therefore, the nurse would document 0.05 grams as the dose of Colace.

E) The patient is prescribed albuterol at 100 micrograms (mcg) per inhalation. To convert micrograms to milligrams, divide by 1000:

100 mcg / 1000 = 0.1 mg

Therefore, the patient would take 0.1 milligrams with each inhalation.

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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The equation that can be used to calculate the number of screens that fit in each warehouse is x + x⁄2 + 2x = 84.

To write an equation, the first step is to determine the number that goes after the = symbol. In this case, the number is the total of screens or 84 screens.

Moreover, we need to use the x to correctly represent the number of screens in each warehouse:

Note: Here is the question in English:

We have 84 rectangular 32-inch screens that must be accommodated in three warehouses: normal, plus and extra, with the capacity of the plus warehouse being half the capacity of the normal one and the capacity of the extra warehouse double the capacity of the normal one and the The only condition is that they be accommodated proportionally to the capacity of each warehouse.

What is the equation that allows calculating the number of screens that fit in each warehouse?

*Tip: Consider “x” as the normal warehouse

Select one:

x + 3x + 2x = 84

2x + x + x⁄4 = 32

x + x⁄2 + 2x = 84

4x + x + x/4 =32

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1. An equation for the height of the rocket after t seconds is h(t) = -16t² + 320t.

2. The time it takes for the rocket to reach a height of 0 is 20 seconds.

The time it takes to reach the top of its trajectory is 10 seconds.

The maximum height is 1,600 feet.

The time it takes to reach a height of 800 feet is 2.9 or 17.1 seconds.

Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the​ ground is related to time by the following quadratic function:

h(t) = -16t² + Vit

Part 1.

When the initial velocity is 320 feet per seconds, the height function becomes;

h(t) = -16t² + 320t

Part 2.

Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:

0 = -16t² + 320t

320t = 16t²

Time, t = 320/16

Time, t = 20 seconds.

Part 3.

Next, we would determine the maximum height of this rocket by taking the first derivate in order to determine the time (t) it takes;

h(t) = -16t² + 320t

h'(t) = -32t + 320

320 = 32t

t = 320/32 = 10 seconds.

Part 4.

The maximum height of this rocket is given by;

h(10) = -16(10)² + 320(10)

h(10) = 1,600 feet.

Part 5.

At a height of 800 feet, the time is given by;

800 = -16t² + 320t

16t² - 320t + 800 = 0

t² - 20t + 50 = 0

Time, t = 2.9 or 17.1 seconds.

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The volume of the hexagonal prism with base area of 166ft² and height of 10ft is 3320 ft³.

A hexagonal prism is simply a prism with a hexagonal base.

It has 8 faces, 18 edges, and 12 vertices.

The volume of a hexagonal prism with a base area is expresssed as:

Volume = Ab × h

Where Ab is the base area and h is the height.

From the diagram:

Base area of the hexagonal prism Ab = 166 ft²

Height h = 20 ft

Volume V = ?

Plug the given values into the above equation and solve for the volume:

Volume = Ab × h

Volume = 166 ft² ×  20 ft

Volume = 3320 ft³

Therefore, the volume of the hexagonal prism is 3320 ft³.

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The perimeter of ABCD is 46

Perimeter is a math concept that measures the total length around the outside of a shape.

This means to find the perimeter of a shape we add all the value of the sides together.

In the diagram above a circle is inscribed into a quadrilateral.

If BC is 16 and AD is 7

From point C if a straight is drawn, The shape will make a right angle triangle and CD will be the hypotenuse.

Therefore the perimeter of ABCD

P = 2(l+b)

= 2(16+7 )

= 2 × 23

= 46

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The standard deviation of the given data set is approximately 4.4. B answer in correct

To find the standard deviation of a data set, we need to follow these steps:

1. Find the mean (average) of the data set.

2. Subtract the mean from each data point and square the result.

3. Find the mean of the squared differences.

4. Take the square root of the mean of squared differences.

Let's calculate the standard deviation for the given data set: 81, 85, 82, 93, 85, 84, 95, 87, 88, 91.

Step 1: Find the mean

Mean = (81 + 85 + 82 + 93 + 85 + 84 + 95 + 87 + 88 + 91) / 10

Mean = 871 / 10

Mean = 87.1

Step 2: Subtract the mean and square the result for each data point

[tex](81 - 87.1)^2[/tex] = 36.81

(85 - 87.1)^2 = 4.41

(82 - 87.1)^2 = 26.01

(93 - 87.1)^2 = 34.81

(85 - 87.1)^2 = 4.41

(84 - 87.1)^2 = 9.61

(95 - 87.1)^2 = 62.41

(87 - 87.1)^2 = 0.01

(88 - 87.1)^2 = 0.81

[tex](91 - 87.1)^2[/tex] = 15.21

Step 3: Find the mean of the squared differences

Mean of squared differences = (36.81 + 4.41 + 26.01 + 34.81 + 4.41 + 9.61 + 62.41 + 0.01 + 0.81 + 15.21) / 10

Mean of squared differences = 194.9 / 10

Mean of squared differences = 19.49

Step 4: Take the square root of the mean of squared differences

Standard deviation = √19.49

Standard deviation ≈ 4.4 (rounded to the nearest tenth)

Therefore, the standard deviation of the given data set is approximately

4.4.

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Step-by-step explanation:

in such a case we first take the inner function (h(x)) and put it as "x" in the outer function (g(x)).

so,

g(h(x)) = sqrt(3×(3x + 5) - 4) = sqrt(9x + 15 - 4) =

= sqrt(9x + 11)

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Option A. The only graph that could represent the function with the zeros of -2 and 4 is the graph is : A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10).

The zeros of a quadratic function are the x-values where the function equals zero (where it crosses the x-axis). In this case, you mentioned that the zeros of the function are -2 and 4.

Looking at the provided options:

A. This graph crosses the x-axis at (-2, 0) and (4, 0), which are indeed the zeros of the function. Therefore, this could be a possible representation of the function.

B. This graph crosses the x-axis at (-4, 0) and (2, 0). These are not the zeros given for the function (-2 and 4), so this graph is not a possible representation of the function.

C. This graph crosses the x-axis at (-4, 0), but it never crosses at x=4. Instead, it crosses at x=2. Therefore, this is not a possible representation of the function.

D. This graph crosses the x-axis at (2, 0), but does not cross the x-axis at x=-2. Therefore, this is not a possible representation of the function.

So, the only graph that could represent the function with the zeros of -2 and 4 is the graph provided in Option A.

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The width of the galaxy is approximately[tex]1.419 \times 10^{17[/tex] kilometers.

The correct answer is option B: [tex]1.419 \times 10^{17.[/tex]

To calculate the width of the galaxy in kilometers, we need to multiply the number of light years by the distance of one light year in kilometers.

One light year [tex]= 9.46 \times 10^{12[/tex] kilometers

Galaxy width = 150,000 light years

To find the width of the galaxy in kilometers, we can use the formula:

Galaxy width in kilometers = One light year in kilometers [tex]\times[/tex] Galaxy width in light years

Galaxy width in kilometers [tex]= (9.46 \times 10^{12} km)[/tex] [tex]\times[/tex] (150,000 light years)

To multiply these numbers, we can use the rules of scientific notation. We add the exponents and multiply the coefficients:

Galaxy width in kilometers[tex]= 9.46 \times 10^{12} km \times 1.5 \times 10^5[/tex]

Multiplying the coefficients, we get:

Galaxy width in kilometers [tex]= (9.46 \times 1.5) \times (10^{12} km \times 10^5)[/tex]

Galaxy width in kilometers [tex]= 14.19 \times 10^{12}+5 km[/tex]  

Since we have the same base (10) raised to different exponents, we can add the exponents:

Galaxy width in kilometers [tex]= 14.19 \times 10^{17}km[/tex]

Therefore, the width of the galaxy is approximately [tex]1.419 \times 10^{17[/tex]  kilometers.

The correct answer is option B: [tex]1.419 \times 10^{17.[/tex]

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Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

[tex]f(x) = 2\sqrt{x+1}[/tex]   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

[tex]f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}[/tex]

2 = 2 (True).

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Answer:

y-b-3=x

Step-by-step explanation:

I got this answer off of gauth math so it should be right

The ratio of girls to boys in the class is 3:7.

To calculate the ratio of girls to boys in the class, we need to determine the number of girls in the class.

Given that there are 50 students in total and 35 of them are boys, we can find the number of girls by subtracting the number of boys from the total number of students:

Number of girls = Total number of students - Number of boys

Number of girls = 50 - 35

Number of girls = 15

Now that we know there are 15 girls in the class and 35 boys, we can calculate the ratio of girls to boys.

Ratio of girls to boys = Number of girls / Number of boys

Ratio of girls to boys = 15 / 35

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 5:

Ratio of girls to boys = (15 ÷ 5) / (35 ÷ 5)

Ratio of girls to boys = 3 / 7

This means that for every 3 girls, there are 7 boys in the class. The ratio provides a relative comparison of the number of girls to the number of boys, helping to understand the gender distribution within the class.

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Answer:

When a 3D figure is cut to create a cross-section parallel to the base, the direction of the perpendicular is vertical. This means that the cross-section will be perpendicular to the base and will have a vertical orientation.

A. The population mean is approximately 7.9 pounds.

B. The population proportion of packages is approximately 0.301.

C. The margin of error of the manager's study is 6.22%.

D. The manager will need to study approximately 10,298 packages.

A. To calculate the population mean, find the sum of the weights and divide it by the total number of packages.

Calculate the sum of the weights and the total number of packages:

Sum of weights = (0.5 x 5) + (1 x 16) + (2 x 28) + (3 x 22) + (4 x 17) + (5 x 98) + (8 x 13) + (10 x 73) + (12 x 5) + (15 x 2) + (20 x 4) + (25 x 9)

Sum of weights = 2.5 + 16 + 56 + 66 + 68 + 490 + 104 + 730 + 60 + 30 + 80 + 225

Sum of weights = 2316.5

Total number of packages = 5 + 16 + 28 + 22 + 17 + 98 + 13 + 73 + 5 + 2 + 4 + 9

Total number of packages = 292

Population mean = Sum of weights / Total number of packages

Population mean = 2316.5 / 292

Population mean ≈ 7.9 (rounded to the nearest tenth)

Therefore, the population mean is approximately 7.9 pounds.

B. To find the population proportion of packages that weigh less than 5 pounds:

Number of packages that weigh less than 5 pounds = 5 + 16 + 28 + 22 + 17

Number of packages that weigh less than 5 pounds = 88

Population proportion = Number of packages that weigh less than 5 pounds / Total number of packages

Population proportion = 88 / 292

Population proportion ≈ 0.301 (rounded to three decimal places)

Therefore, the population proportion of packages that weigh less than 5 pounds is approximately 0.301.

C. To find the margin of error of the manager's study, calculate the standard deviation of the weights. In this case, estimate the margin of error using a formula called the margin of error formula for proportions:

Margin of error = Z × √((p × (1 - p)) / n)

where, Z = z-score corresponding to the desired level of confidence, p = estimated proportion, and n = sample size (in this case, the total number of packages).

Using a standard normal distribution table, find the z-score corresponding to a 95% confidence level, which is commonly used:

Z ≈ 1.96

Margin of error = 1.96 × √((0.301 × (1 - 0.301)) / 292)

Calculating the expression inside the square root:

√((0.301 × (1 - 0.301)) / 292) ≈ 0.0317

Margin of error = 1.96 × 0.0317

Margin of error ≈ 0.0622 (rounded to four decimal places)

Therefore, the margin of error of the manager's study is approximately 0.0622 or 6.22%.

D. To determine the number of packages the manager needs to study in order to have a margin of error of only ±2%:

Margin of error = Z × √((p × (1 - p)) / n)

Given that the desired margin of error is ±2%, substitute the values:

±2% = Z × √((p × (1 - p)) / n)

Since the margin of error is the same on both sides, consider it as ±0.02 (in decimal form).

0.02 = Z × √((p × (1 - p)) / n)

Use the z-score corresponding to a 95% confidence level, which is 1.96.

0.02 = 1.96 × √((0.301 × (1 - 0.301)) / n)

Solve for n:

√((0.301 × (1 - 0.301)) / n) = 0.02 / 1.96

Squaring both sides:

(0.301 × (1 - 0.301)) / n = (0.02 / 1.96)²

Calculating the right side:

(0.02 / 1.96)² ≈ 0.000020408

Now solve for n:

(0.301 × (1 - 0.301)) / n ≈ 0.000020408

Multiplying both sides by n:

0.301 × (1 - 0.301) ≈ 0.000020408 × n

Simplifying:

0.301 - (0.301 × 0.301) ≈ 0.000020408 × n

0.301 - 0.090601 ≈ 0.000020408 × n

0.210399 ≈ 0.000020408 × n

Dividing both sides by 0.000020408:

n ≈ 0.210399 / 0.000020408

n ≈ 10,297.6

Therefore, the manager will need to study approximately 10,298 packages in order to have a margin of error of only ±2%.

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To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

The cost of each sandwich, given the number that was sold and the profit made was  $15.

Let S be the price of a sandwich and A be the price of a salad.

From the lunch sale, we know:

14 S + 14 A = $280

From the evening sale, we know:

42S + 154 A = $ 1400

Simplify the first equation by dividing through by 14:

S + A = $20

Solving this equation for S gives:

S = $20 - A

Substitute this equation into the second equation:

42 ( $20 - A ) + 154 A = $1400

$ 840 - 42 A + 154 A = $1400

112A = $560

A = $5

Substitute A = $5 into the first equation:

S + $5 = $20

S = $15

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The calculated value of the function g(0) from the graph is 1

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

The graph

The value of g(0) implies that

We calculate g(x) when x = 0

To calculate g(0) from the graph, we look at the point where x = 0 from the graph

Using the above as a guide, we have the following:

y = g(0)

From the graph, we can see that

When x = 0, the value of g(x) is 1

This means that

y = g(0) = 1

It can also be interpreted as the y-intercept of the function

Hence, the value of the function g(0) is 1

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The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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To find the distance of Earth and Mars from the sun using the given formula, we need to substitute the respective values of n into the equation and simplify the expression. Let's calculate them:

For Earth (n = 3, as it is the third planet from the sun):

d = 9,275,200[3(2n − 2) + 4]

d = 9,275,200[3(2*3 − 2) + 4]

d = 9,275,200[3(6 − 2) + 4]

d = 9,275,200[3(4) + 4]

d = 9,275,200[12 + 4]

d = 9,275,200[16]

d = 148,403,200

The distance of Earth from the sun is approximately 148,403,200 miles.

For Mars (n = 4, as it is the fourth planet from the sun):

d = 9,275,200[3(2n − 2) + 4]

d = 9,275,200[3(2*4 − 2) + 4]

d = 9,275,200[3(8 − 2) + 4]

d = 9,275,200[3(6) + 4]

d = 9,275,200[18 + 4]

d = 9,275,200[22]

d = 204,055,200

The distance of Mars from the sun is approximately 204,055,200 miles.

Therefore, the distances are as follows:

Earth: 1.48 ✕ 10^8 mi (148,000,000 miles)

Mars: 2.04 ✕ 10^8 mi (204,000,000 miles)

Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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The volume of the figure is 3300 ft³.

We have,

The figure is a composite of two rectangular boxes.

Now,

Rectangular box volume.

= length x width x height

Now,

One rectanglular box.

= (20 + 4) x 25 x³5

=  24 x 25 x 5

= 3000 ft²

Another rectangular box.

= 4 x 25 x (8 - 5)

= 4 x 25 x 3

= 300 ft³

Now,

The volume of the figure.

= 3000 + 300

= 3300 ft³

Thus,

The volume of the figure is 3300 ft³.

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The number of times that it would land in orange is 20 times. Option B

The likelihood or chance that a particular occurrence or outcome will occur is quantified by probability. It gauges the level of uncertainty surrounding an occurrence. A value between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express the probability of an event.

We have that;

Total number of times = 100

Fraction of orange = 1/5

Times landed in orange = 1/5 * 100

= 20 times

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The histogram that matches the data sets above would be histogram D. That is option D.

Histogram is defined as the type of representation of data that involves the use of bars that have the same width but different lengths according to the frequency of each data set represented.

From the data given above, the frequency of distribution is given below as follows:

0-4= 1

5-9 = 6

10-14 = 2

15-19 = 4

Therefore, the best histogram that will represent the given data set above would be histogram D.

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The answers are:

27. P(6) = 0.2 , 28. P(even number) = 0.6 , 29. P(6) = 1/10 , 30. P(even number) = 5/10 = 0.5

The experimental probability of getting a 6 is 0.2, because 2 out of 50 displays were 6s.

The experimental probability of getting an even number is 0.6, because 30 out of 50 displays were even numbers.

The theoretical probability of getting a 6 is 1/10, because there is 1 chance out of 10 that the calculator will display a 6.

The theoretical probability of getting an even number is 5/10, because there are 5 chances out of 10 that the calculator will display an even number.

As you can see, the experimental probabilities are close to the theoretical probabilities. This is because the calculator was programmed to randomly display a digit from 0 to 9, so the results should be evenly distributed. However, there is always some chance of variation, so the experimental probabilities may not be exactly equal to the theoretical probabilities.

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