find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (volume of a sphere

Answer:

7/32

Step-by-step explanation:

First we need to make the mixed fraction an improper fraction

4*7=28

28+4=32

So, the improper fraction will be 32/7

a reciprocal is the opposite of a fraction

this means we will flip this fraction over, moving the 7 to the numerator and 32 to the denominator

7/32

The inequality that describes this situation will be 6x + 2s ≤ 76

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x = number of group dance numbers

s = number of solo performances

The inequality will be 6x + 2s ≤ 76

This inequality can be read as "the total duration of the group dance numbers (6 minutes per group dance number) plus the total duration of the solo performances (2 minutes per solo performance) is less than or equal to 76 minutes."

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119 pupils, according to a Venn diagram, prefer Snickers or Reese's Peanut Butter Cups but not Twix.

In the 1880s, John Venn popularized the Venn diagram, a common type of diagram illustrating logical links between sets. In probability, logic, statistics, linguistics, and computer science, diagrams are used to teach basic set theory and to illustrate straightforward set relationships. In a Venn diagram, overlapping circles and other shapes are used to represent the connections between two or more sets of elements. Highlighting similarities and differences between components when organizing information graphically frequently proves beneficial. A space in the middle of a Venn diagram is created by the intersection of two sizable circles.

The group of students that enjoy Snickers is represented by set A.

The students who enjoy Twix are represented by set B.

The students who enjoy Reese's Peanut Butter are represented by set C. All three types of chocolate candies are favorites among 19 students.

Snickers and Reese's Peanut Butter Cups are among the 31.

Reese's Peanut Butter Cups and Snickers alone = 31 - 19 = 12

82 like Twix and Reese's Peanut Butter Cups

149 like Snickers

149 − (51 + 12 + 19) = 67 for Snickers alone.

The number of students who prefer Snickers or Reese's Peanut Butter Cups but not Twix is equal to 67 + 40 + 12.

There are 119 pupils that enjoy Snickers or Reese's Peanut Butter Cups.

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Answer:

101

Step-by-step explanation:

f(1) = 5 = 4*1 +1

f(9) = 37 = 4*9+1

f(6) = 4*6+1 = 25

f(f(6)) = f(25) = 4*25+1 =101

Answer:

  101

Step-by-step explanation:

Given the values of a linear function f(1) = 5 and f(9) = 37, you want the value of f(f(6)).

The given ordered pairs are (1, 5) and (9, 37). Using these, we can find the slope of the function to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (37 -5)/(9 -1) = 32/8 = 4

The y-intercept is ...

  b = y -mx

  b = 5 -4(1) = 1

So the function in slope-intercept form is ...

  y = mx +b

  f(x) = 4x +1

The value of f(6) is ...

  f(6) = 4·6 +1 = 25

The value of f(f(6)) is ...

  f(f(6)) = f(25) = 4·25 +1 = 101

The value of f(f(6)) is 101.

We can say that in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem.

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Other complex mathematical strategies were known to the Babylonians. For example, in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem long before Pythagoras.

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If a student in stat 121 wants to estimate the average score on the stat 121 final exam from last semester. The sample is: The 200 students interviewed.

Sample can be defined as the data or information that are randomly collected from a group of population so as to reach or drawn a conclusion.

Based on the scenario the sample will be the 200 students who took the class last semester  as the 200 students were randomly selected from a larger population so as to reach a conclusion.

Therefore we can conclude that the sample is the 200 students interviewed.

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8 feet from the end of the wall is the nearest edge of the picture.

The process of converting phrases into equations and then solving those equations is known as solving algebraic word problems.

We will only need to use one variable and fundamental arithmetic operations to create the equations we require. In a real-world situation, the variable often stands for an unknowable quantity.

We can model and resolve word problems on the test that have two overlapping groups using Venn diagrams.

Let's say that the distance from the picture to the wall is x.

Since that distance will be on both sides of the picture (it's in the exact middle), we can say that:

x+3+x=19

=> 2x+3 = 19

=>2x=16

=>x= 8

Thus, 8 feet from the end of the wall is the nearest edge of the picture.

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The distance Jon travels to work is 472.5 miles.

Let d be the distance Jon travels to work.

The time it takes to drive is 20 minutes and the time it takes to bike is 45 minutes.

The difference in speed between driving and biking is 14.5 mph.

We can set up the following equation:

20min * (14.5mph + x) = 45min * x

Solving for x gives us the average speed of Jon on the bike, which is 10.5 mph.

Now we can use the distance formula to solve for d:

d = rate * time

d = 10.5mph * 45min

d = 472.5 miles

Therefore, the distance Jon travels to work is 472.5 miles.

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For the given data the mean is 180.28 and the modal class is 177 - 185.

First finding mean:

For the class of 150 - 158, the class boundaries are 149.5 - 158.5.

Middle value = (150 + 158)/2 = 154

Frequency = 5

mean= 154 × 5 = 770

For the class 159 - 167, the class boundaries are 158.5 - 167.5

Middle value  = (159 + 167)/2 = 163

Frequency = 16

middle value.  frequency = 163 × 16 = 2608

For the class 168 - 176, the class boundaries are 167.5 - 176.5

Middle value = (168 + 176)/2 = 172

Frequency = 20

middle value.  frequency = 172 × 20 = 3440

For the class 177 - 185, the class boundaries are 176.5 - 185.

Middle value = (177 + 185)/2 = 181

Frequency = 21

middle value.  frequency  = 181 × 21 = 3801

For the class 186 - 194, the class boundaries are 185.5 - 194.5

Middle value (x_m) = (186 + 194)/2 = 190

Frequency = 20

middle value.  frequency  = 190 × 20 = 3800

For the class 195 - 203, the class boundaries are 194.5 - 203.5

Middle value  = (195 + 203)/2 =199

Frequency = 15

middle value.  frequency  = 199 × 15 = 2985

For the class 204 - 212, the class boundaries are 203.5 - 212.5

Middle value  = (204 + 212)/2=208

Frequency = 3

middle value.  frequency  = 208 × 3 = 624

Now in order to determine the mean of this group data all values calculated separately through the product of middle value and frequency will be added together and divided by the total frequency count (i.e 100).

That is

Mean =  ( 770 + 2608 + 3440 + 3801 + 3800 + 2985 + 624 ) = 18028 / 100

Mean  =   180.28

Now determine the model class:

Model class refers to the with the highest occurring frequency. So this is the class "177 - 183" having the frequency 21.

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The equation of the line that passes through the points (-6,4) and (-2,2) is y - 4 = -1/2(x + 6)

What is the equation of the line?

To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

The slope of the line can be found by using the two points:

m = (y2 - y1) / (x2 - x1)

So,

m = (2 - 4) / (-2 - (-6)) = -2/4 = -1/2

We know that the line passes through the point (-6,4) so we can substitute the values into the equation:

y - 4 = -1/2(x + 6)

Hence, the equation of the line that passes through the points (-6,4) and (-2,2) is y - 4 = -1/2(x + 6)

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Esperanza is aware of Sally's desire to avoid having to return back to school so you would not need to fret about her father, rumors, or feeling out of place.

Monkeys are often undesirable pets. Yes, for a while, some may be extremely sweet. However, the truth is that monkeys cannot live in a human home because they are too dangerous and require too much care. These concerns pertain to apes and are just as significant (chimpanzees, orangutans, and gibbons).

People and monkeys are both considered primates. But neither monkeys or indeed any other current ape species are linked to people. Yes, chimpanzees and humans both descend from apes.

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Answer:

i. To calculate the total expenses in Kenya shillings incurred by Wekhomba, we need to first convert the cost of the laptop in Uganda shillings to Kenya shillings using the exchange rate of 1 US dollar = Ush 1016. The cost of the laptop in Kenya shillings is (1,050,000/1016) = 1,032,474.40

We then need to add the transportation cost of 60 US dollars which is (60 * 1016) = 61,596 Kenya shillings.

Taxes in Kenya amounting to 55% of the cost in Uganda is (1,050,000 * 55/100) = 577,500 Uganda shillings which is (577,500/1016) = 567,715.20 in Kenya shillings.

The total expenses in Kenya shillings incurred by Wekhomba is 1,032,474.40 + 61,596 + 567,715.20 = 1,661,785.60

ii. To find the expenditure on transportation and taxes as a percentage of the total expenditure, we need to divide the sum of transportation costs and taxes by the total expenses and multiply by 100.

Expenditure on transportation and taxes is 61,596 + 567,715.20 = 629,311.20.

Expenditure on transportation and taxes as a percentage of the total expenditure = (629,311.20/1,661,785.60) * 100 = 37.9%

iii. To find the total value of the laptop in Tanzanian shillings, we first need to convert Kenya shillings to Tanzanian shillings using the exchange rate of 1Ksh = Ush 24.83 and Tsh 1 = Ksh 0.0714,

1,661,785.60 Kenya shillings is (1,661,785.60/24.83) = 668,817.51 Uganda shillings which is (668,817.51 / 0.0714) = 93,622,817.16 Tanzanian shillings

iv. To find the overall increase in value of the laptop as a percentage of the buying price, we need to divide the increase in value (total value in Tanzanian shillings - buying price) by the buying price and multiply by 100.

Overall increase in value = 93,622,817.16 - 1,050,000 = 92,572,817.16

The overall increase in value as a percentage of the buying price = (92,572,817.16/1,050,000) * 100 = 88.1%

Step-by-step explanation:

Answer:

........

Step-by-step explanation:

These two points on the number line describe that she descended by 70 units.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
She started at –5 and descended to –75.
On the number line, the difference between  -75 and -5 is given as
= -5 - (-75)
= 70

Thus, these two points on the number line describe that she descended by 70 units.

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Answer:

(7x + 5)(- x - 11)

Step-by-step explanation:

9(x - 1)² - 16(x + 2)² ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

9(x - 1)² - 16(x + 2)²

= [ 3(x - 1) ]² - [4(x + 2) ]² with a = 3(x - 1) and b = 4(x + 2)

= [ 3(x - 1) + 4(x + 2) ] [ 3(x - 1) - 4(x + 2) ] ← distribute parenthesis

= [ 3x - 3 + 4x + 8 ] [ 3x - 3 - 4x - 8 ]

= (7x + 5)(- x - 11 )

Answer:

(1, 1 )

Step-by-step explanation:

choose any value of x to substitute into the equation and solve for y

choosing x = 1 , then

- 1 + 5y = 4 ( add 1 to both sides )

5y = 5 ( divide both sides by 5 )

y = 1

then (1, 1 ) is a solution to the equation

Answer:

- x + 5 y = 4                                     (x = 6)

- ( 6 ) + 5 × 2 = 4                             (y = 2)

- 6 + 10 = 4

 4 = 4

∴ (6, 2) is an ordered pair that is a solution to the given equation .

The solution of u in the equation where u is a real number is -10.

In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line. Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolise complex numbers.

Given that u is a real number and the value of [tex]u^3 = -1000[/tex].

Take cube root on both sides of the equation:

[tex]\sqrt[3]{u^3} = \sqrt[3]{-1000} \\\\u = \sqrt[3]{(-10)(-10)(-10)} \\\\u = -10[/tex]

Hence, the value of u is -10.

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Step-by-step explanation:

remember, to transform an equation we need to apply any operation to both sides of the equation. otherwise the equality relation is destroyed.

we want to get the equating to look like " x = ..."

so, the "+ 39" is in the way.

we need to subtract 39, but as mentioned, we need to do this on both sides.

x + 39 = 74

x + 39 - 39 = 74 - 39

x = 35 in

the fig tree is therefore 35 in. that is 39 in shorter than 74 in (the orange tree).

The smallest possible whole-number length for the third side is 12

Following the Pythagorean theorem which states that the hypotenuse square is equal to the sum of the squares of the other two sides in a triangle.

This is represented as;

a² = b² + c²

Given that;

From the information given, we have that;

14² = 6² + c²

Find the square values

196 = 36 + c²

collect like terms

c² = 196 - 36

subtract the values

c² = 160

Find the square root of both sides

c = √160

c = 12. 65

Thus, the value is 12

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Answer:

the equation for the product of 12 x 8 = 96

Answer:

76
This is because, when you exceed 76 copies, the cost will be greater than 11.50 and you will not be able to afford it.

Step-by-step explanation:

To solve this inequality, you can divide both sides by 0.15: x <= 76.67

The total cost of the bridge will be (200/2) × 8 × 1000 + 50 × 10 + 500 = $90,000.

The formula for calculating the cost of a bridge is Cost = (Area of Bridge/2) × Unit Weight of Steel × Unit Price of Steel + Cost of Labor + Cost of Other Materials. By using this formula, we can determine the total cost of the bridge by considering the area of the bridge, the weight of the steel used, the price per unit of steel, the cost of labor, and the cost of other materials. For example, if the area of the bridge is 200m^2, the unit weight of steel is 8 tonnes/m^3, the unit price of steel is $1000/tonne, the cost of labor is $50 per hour, and the cost of other materials is $500, then the total cost of the bridge will be (200/2) × 8 × 1000 + 50 × 10 + 500 = $90,000. Thus, by using this formula, we can easily calculate the cost of the bridge and understand why local politicians are dragging their feet in building a new bridge.

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Answer: Editorial is data is the correct answer.

Step-by-step explanation: I took test and it is confirmed correct.

Answer:

Step-by-step explanation:

The mystery number is 9. The least common multiple of 3 and 36 is 36. When you pair 9 with 36, their least common multiple is still 36. 9 is greater than 6, but less than 12. Therefore, the mystery number is 9.

In order to have negative correlation between two variables the covariance must be negative.

What is correlation?

The degree to which two variables are linearly related is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It is a typical technique for outlining straightforward connections without stating cause and effect.

The correlation between two variables x and y is,

[tex]r = \frac{Cov(x, y)}{S_x*S_y}[/tex]

where,

Cov(x, y) is the covariance between x and y.

[tex]S_x[/tex] and [tex]S_y[/tex] respectively denotes the standard deviation of x and y.

If the correlation is negative then  r < 0.

Now r < 0

[tex]\frac{Cov(x, y)}{S_x*S_y} < 0\\Cov(x, y) < 0\\Sx > 0, S_y > 0[/tex]

If r < 0 the Cov(x, y) < 0.

In order to have negative correlation between two variables the covariance must be negative.

Hence, in order to have negative correlation between two variables the covariance must be negative.

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Answer:

---------------------------------------

Property of a parallelogram:

According to the property we have:

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P[tex](\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P[tex](\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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Answer:

standard form:

4×100,000

400,000

The distance between the two people is changing at a rate of 3.2 mi/hr.

The distance between the two people can be calculated by using the Pythagorean theorem.

Let one person be at the origin (0, 0) and the other person be at (x, y). After 15 minutes, the first person will be at (3*15, 0) and the second person will be at (2*15*cos45, 2*15*sin45).

Using the Pythagorean theorem, the distance between them can be calculated as:

d = sqrt((3*15 - 2*15*cos45)^2 + (2*15*sin45)^2) = sqrt(225 + 225) = sqrt(450) = 21.213

The rate of change of distance is given by the formula d/t, where d is the distance and t is the time.

Therefore, the rate of change of distance between the two people after 15 minutes is 21.213/15 = 3.2 mi/hr.

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