The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?

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:

9x^2y^6 square feet.

Step-by-step explanation:

The area of a square is the length of one of its sides multiplied by itself.

If the side length of a square is -3xy^3 feet,

then the area of the square is

-3xy^3 * -3xy^3 = 9x^2y^6

Therefore, the area of the square is 9x^2y^6 square feet.

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.

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!

Kareem uses 300 milliliters of Solution B.

Let's assume Kareem uses "x" milliliters of Solution B.

Since Kareem uses twice as much Solution A as Solution B, he would use 2x milliliters of Solution A.

Solution A contains 10% alcohol, so the amount of alcohol from Solution A is (2x)(0.10) = 0.2x milliliters.

Solution B contains 15% alcohol, so the amount of alcohol from Solution B is (x)(0.15) = 0.15x milliliters.

The resulting mixture has 105 milliliters of pure alcohol, which is the sum of the alcohol from Solution A and Solution B:

0.2x + 0.15x = 105

Combining like terms:

0.35x = 105

Dividing both sides by 0.35:

x = 105 / 0.35

x = 300

Therefore, Kareem uses 300 milliliters of Solution B.

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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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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 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 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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To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

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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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)

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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The steady-state average utilization of the server is 0.3333.

a. Customer and server in the system: The two-runway airport system can be modeled as a queuing system, where the customer is the aircraft and the server is the runway. The server serves the customers by allowing them to land and take off from the runway.

The runway capacity is limited, and thus, the number of customers (aircraft) that can be served at any given time is also limited. The server also has a processing rate, which is the time required to service a single customer. In this case, the server has two processing rates, one for landing and one for takeoff.

b. Arrival rate can be tolerated if the average wait in the sky is not to exceed 3 minutes: The time to land an airplane is exponentially distributed, with a mean of 1.5 minutes. Thus, the rate at which planes arrive can be calculated using the formula λ = 1/μ, where λ is the arrival rate and μ is the mean time.

Therefore, λ = 1/1.5 = 0.6667 planes per minute. The average wait in the sky should not exceed 3 minutes. This means that the time a plane spends waiting in the queue should be less than or equal to 1.5 minutes. Using Little’s Law, the average number of customers in the system can be calculated as L = λW, where L is the number of customers, λ is the arrival rate, and W is the waiting time.

Thus, L = 0.6667 × 1.5 = 1.0 customers. Since there are two runways, the system can handle two customers at a time, which means that the utilization rate is 50%.

c. Steady-state average utilization of the server: The steady-state average utilization of the server can be calculated using the formula ρ = λ/μ, where ρ is the utilization rate, λ is the arrival rate, and μ is the service rate. In this case, the utilization rate is the same as the arrival rate since the server is always busy.

Thus, ρ = 0.6667 / 2μ = 0.3333. Since there are two runways, the total utilization rate is 0.6667, which is less than 1.0. This means that the system is not overloaded and can handle the given arrival rate. Therefore, the steady-state average utilization of the server is 0.3333.

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Answer:

b. 12 cm

Step-by-step explanation:

The perimeter of any shape is the sum of the lengths of its sides.

We can call the three sides of a triangle a, b, and c.  Thus, the perimeter, P is given by the formula:

P = a + b + c

Thus, we can plug in 3 for a, 4 for b, and 5 for c to find P, the perimeter of the triangle in centimeters:

P = 3 + 4 + 5

P = 7 + 5

P = 12

Thus, the perimeter is 12 cm (answer b.).

The solution to the inequality |1/4x - 3| - 5 ≥ 4 is x ≥ 48 or x ≤ -28. The graph of the solution is a number line with the regions to the right of 48 and to the left of -28 shaded, indicating the values of x that make the inequality true.

Part A: To solve the inequality |1/4x - 3| - 5 ≥ 4, we can follow these steps:

Step 1: Remove the absolute value brackets and rewrite the inequality as two separate inequalities:

1/4x - 3 - 5 ≥ 4   or   -(1/4x - 3) - 5 ≥ 4

Step 2: Simplify each inequality:

1/4x - 8 ≥ 4   or   -1/4x + 2 - 5 ≥ 4

Step 3: Solve each inequality separately:

1/4x ≥ 12   or   -1/4x - 3 ≥ 4

Step 4: Continue solving each inequality:

x ≥ 48   or   -1/4x ≥ 7

Step 5: Multiply both sides of the second inequality by -4, remembering to reverse the inequality sign when multiplying by a negative number:

x ≤ -28

Part B: The graph of the solution would be a number line with shaded regions. The region to the right of 48 (including 48) would be shaded to represent x ≥ 48. The region to the left of -28 (including -28) would also be shaded to represent x ≤ -28. These shaded regions represent the values of x that satisfy the inequality. The rest of the number line, between -28 and 48, would remain unshaded, indicating that those values of x do not satisfy the inequality.

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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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Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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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:

  20°

Step-by-step explanation:

You want to know the measure of external angle 1 in the diagram of a circle, secants, and chord.

The measure of each arc subtended by a chord is shown as 100°. They all have the same measure because the chords are all the same length.

The measure of the remaining arc is ...

  360° -100° -100° -100° = 60°

The measure of angle 1 is half the difference of the measures of the arcs it intercepts:

  angle 1 = 1/2(100° -60°)

  angle 1 = 20°

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The measure of the angle 1 using the appropriate angle theorem is 20°

The measure of the arc subtended by the chord is 100°. Since the length of the chord are equal, then the measure of each arc in the figure is the same.

Since we have three arcs measuring 100°

The measure of the smallest arc would be : (360 - 100) = 60°

Angle 1 = 0.5(100-60) (half the measure of intercepted arc)

Angle 1 = 0.5(40) = 20°

Hence, the measure of angle 1 is 20°

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Answer: 8  

Step-by-step explanation:

By the pythagorean theorem

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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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 calculated value of X in the circle is 6

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

The circle

The value of X can be calculated using the following intersecting secants equation

5 * (5 + 7) = x * (x + 4)

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

x * (x + 4) = 60

When solved for x, we have

x = 6

Hence, the value of X is 6

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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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One bagel costs 485 cents, equivalent to $4.85.

Let t be the price of a piece of toast in cents

Let m be the price of a muffin in cents

Let b be the price of a bagel in cents.

We will form equations to solve:

Multiply Equa 1 by 2:

4t + 2b = 630 --------- (Equ 4)

Subtract Equ 4 from Equ 3:

(t + 2b + 3m) - (4t + 2b) = 725 - 630

-t + 3m = 95

3m - t = 95 --------- (Equ 5)

Multiply Equ 2 by 2:

2b + 4m = 970 ------ (Equ 6)

Add Equ 5 and Equ 6:

(3m - t) + (2b + 4m) = 95 + 970

3m + 2b + 4m - t = 1065

6m + 2b - t = 1065 (------- Equ 7)

Now we have two equations:

Solve Equ 2 for b:

b = 485 - 2m

Substitute b in Equ 7:

6m + 2(485 - 2m) - t = 1065

6m + 970 - 4m - t = 1065

2m - t = 95 ------ (Equ 8)

Subtract Equ 8 from Equ 5:

(3m - t) - (2m - t) = 95 - 95

3m - t - 2m + t = 0

m = 0

Substitute m = 0 into Equ 2:

b + 2(0) = 485

b = 485

Therefore, one bagel costs 485 cents.

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The correct expression is: 14 - 5 = a.

To find the value of a in the equation a + 5 = 14, we can use inverse operations. Inverse operations are operations that undo each other.

Starting with the equation a + 5 = 14, the inverse operation of adding 5 is subtracting 5. By subtracting 5 from both sides of the equation, we isolate the variable a:

a + 5 - 5 = 14 - 5

This simplifies to:

a = 9

By performing the subtraction, we find that a = 9.

The answer "14 - 5 = a" correctly demonstrates the use of inverse operations to find the value of a. It shows that by subtracting 5 from both sides of the equation, we isolate the variable and determine that a is equal to 9.

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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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