A pulley that has a diameter of 8 inches is belted to a pulley that has a diameter of 12 inches. The 8-inch diameter pulley is running at 1,548 revolutions per minute. If the speeds of the pulleys vary inversely to their diameters, how many revolutions per minute does the larger pulley make?

step 1 :

BODMAS

STANDS FOR:brackets, of, division, multiplication ,addition ,subtraction.

so now you have to open the brackets then add following bodmas formula.

NOTE;THE NUMBER OR SYMBOL BEFORE THE BRACKET IS PART OF THE BRACKET.

+(-11/29) is the same -11/29

33/58-11/29=11/58

the trick really is to use BODMAS

^^

In a lottery game where a player picks six numbers and repetition is not allowed, the player has a certain number of choices for each number. The number of choices for each number depends on the range of numbers from which the player can pick.

Let's say the range of numbers from which the player can pick is 1 to 49. For the first number, the player has 49 choices, because they can pick any number from 1 to 49. However, once the player has picked their first number, they have 48 choices for their second number, because they cannot pick the same number again. For the third number, the player has 47 choices, for the fourth number, 46 choices, for the fifth number, 45 choices, and for the sixth number, 44 choices.

The total number of different combinations of six numbers that the player can pick is calculated by multiplying the number of choices for each number. This can be written as 49 x 48 x 47 x 46 x 45 x 44. The total number of combinations is 10,068,347,520.

In other words, if a player picks six numbers from a range of 1 to 49, without repetition, the player has 10,068,347,520 different combinations of numbers to pick from.

It's important to understand that repetition is not allowed in this type of lottery game, as it would greatly increase the number of combinations. Allowing repetition would mean that the player could pick the same number multiple times, which would significantly increase the number of combinations and make the game much less challenging.

In conclusion, in a lottery game where a player picks six numbers from a range of 1 to 49, without repetition, the player has 10,068,347,520 different combinations of numbers to choose from. The number of choices decreases with each number picked, as repetition is not allowed, making the game more challenging.

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The figure with the least surface area is the cube.

The surface area of a 3 dimensional figure or solid figure is the sum of the area of the whole surface.

Therefore,

surface area of the cube = 6a²

where

surface area of the cube = 6 × 6²

surface area of the cube = 6 × 36

surface area of the cube = 216 units²

surface area of the second rectangular prism = 2(lh + lw + hw)

where

Therefore,

surface area of the second rectangular prism = 2(54 + 54 + 16)

surface area of the second rectangular prism = 2(124)

surface area of the second rectangular prism = 248 units²

Therefore,

surface area of the third rectangular prism = 2(13.5 + 216 + 16)

surface area of the third rectangular prism = 2(245.5)

surface area of the third rectangular prism = 491 units²

Therefore, the least surface area is the cube.

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a. False .   6(-b+8) and 2(-3b + 4) are non equivalent expressions.

b. False .  -8h-3.5 and -0.5(16h - 7) are non equivalent expressions.

c. True . -9(k-5+ 2k - 8) and -27k + 117 are equivalent expressions.

d. False .(36m +12) and 12m + 4 are equivalent non expressions.

What are equivalent expressions ?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

What are non equivalent expressions ?

If "x" is the same for both equations, then they are equivalent. If "x" is different (i.e., the equations have different roots), then the equations are not equivalent.

Hence ,

a. False .   6(-b+8) and 2(-3b + 4) are not equivalent expressions.

b. False .  -8h-3.5 and -0.5(16h - 7) are not equivalent expressions.

c. True . -9(k-5+ 2k - 8) and -27k + 117 are equivalent expressions.

d. False .(36m +12) and 12m + 4 are equivalent not expressions.

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The length of the leg in the triangle is 11.6 units

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

The length of the other leg using Pythagorean Theorem is

Other Leg = √(Hypotenuse² - One Leg²)

So, we have

Orher Leg = √(16² - 11²)

Evaluate

Other leg = 11.6

Hence, the other leg is 11.6 units

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The x-coordinate is the a) first number of an ordered pair and represents the point's horizontal location.

An ordered pair is a composition of the x coordinate also known as abscissa and the y coordinate also known as ordinate, having two values written in a fixed order within parentheses.

The ordered pair helps to locate a point on the Cartesian plane for better visual comprehension and its numeric values in an ordered pair can be integers or fractions. It is represented as (x, y) Where, x = abscissa, the distance measure of a point from the primary axis “x” and, y = ordinate, the distance measure of a point from the secondary axis “y”

Hence, the x-coordinate is the first number of an ordered pair and represents the point's horizontal location.

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By using the quadratic regression feature of a graphing calculator a quadratic model would be;

⇒ y = 0.06x² + 0.31 x + 4

And, Your stopping distance would be if you were going 80 miles per hour is,  412.8 ft.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Speed (mph)           Stopping distance (ft)

10                                12.5

20                               36.0

30                               69.5

40                               114.0

50                               169.5

60                               249.0

70                               325.5

Now, Use the quadratic regression feature of a graphing calculator to find a quadratic model.

Hence, From the above data, we get;

⇒ y = 0.06x² + 0.31 x + 4

Hence, Your stopping distance would be if you were going 80 miles per hour is,

⇒ y = 0.06x² + 0.31 x + 4

⇒ y = 0.06(80)² + 0.31 (80) + 4

⇒ y = 384 + 24.8 + 4

⇒ y = 412.8 ft

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Answer: pi*3^2= 9pi  

pi*6=6pi

6pi*17= 102pi

102pi+9pi= 111pi in. squared

pi*6^2=36pi

pi*12=12pi

36pi+12pi*x=111pi

12pi*x=75pi

x=6.25pi

x=Height btw

Step-by-step explanation:

Pythagoras

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Plugging in numbers

[tex] {4}^{2} + {8}^{2} = {c}^{2} [/tex]

If we do the math given

[tex]16 + 64 = {c}^{2} - - - 80 = {c}^{2} [/tex]

Last but not least, we root both sides

[tex] \sqrt{80} = c[/tex]

Which means C = 8.9

Answer: 8x + 11

Step-by-step explanation:

1. Distribute the 3 on both variables. SO 3 times 2x plus 3 times 1 is (6x+3).

2. Do the same for the 2. You get (2x +8)

3.(6x+3) + (2x+8).

4. Rid the parenthesis.

5. 6x + 3 +2x + 8.

6. Combine like terms.

7. 8x + 11 is your solution.

The simplification of the given expression gives the value 2(a + b) / a(a - b).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is,

[(a + b) / 2a²] ÷ [(a - b) / 4a]

The fractional term in the denominator of the main expression can be written as the multiplication of it's reciprocal.

[tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{d}{c}[/tex]

So the expression becomes,

[tex]\frac{a+b}{2a^2}[/tex] × [tex]\frac{4a}{a-b}[/tex]

= 2(a + b) / a(a - b)

Hence the simplified form of the given expression is 2(a + b) / a(a - b).

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Answer:

20

Step-by-step explanation:

[tex]4 \times 5 = 20[/tex]

Answer:

it is C i just got a 100 on the unit test review

Step-by-step explanation:

Answer: -165.59

Step-by-step explanation: Search math w ay on the internet :)

Answer:

2. 3 and 5

3. 3 and 4

4. 3 and 2

5. 3 and 6

Answer:

E. and F.  (11 and 15).  D. is not correct since the equation says > 8, not >= to 8.

Step-by-step explanation:

3(2x-1)>5(x+1)

6x-3>5x+5

x>8

0.45 is the smallest cost per apple, the best deal can be found at Fruit Market.

Cost refers to the amount of money, time, or resources that are required to obtain, produce, or achieve something. It can refer to the expense involved in purchasing a product or service, or the investment required to start a new business, undertake a project, or undertake some other endeavor. In general, cost can be thought of as the sacrifice made in order to gain something of value.

To compare the deals, we need to find the cost per apple for each store.

For Fruit Market: 5 apples cost 2.25, so the cost per apple is 2.25 / 5 = 0.45.

For Fruitz: 8 apples cost 4.20, so the cost per apple is 4.20 / 8 = 0.525.

For Vitamin C: 12 apples cost 6.62, so the cost per apple is 6.62 / 12 = 0.55.

Since 0.45 is the smallest cost per apple, the best deal can be found at Fruit Market.

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The perimeter of the rectangle when the width is 15 inches, would therefore be 90 inches

The width of the rectangle is said to be half of the length which means that because the width is 15 inches, then the length would be:

= 2 x width

= 2 x 15

= 30 inches

As we now have the length as 30 inches and the width as 15 inches, the perimeter of the rectangle would therefore be :

= 30 + 30 + 15 + 15

= 60 + 30

= 90 inches

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The full question is:

The width of a rectangle is half of the length. What is the perimeter of the rectangle when the width is 15 inches?

The probability that the committee contains at least one man is 16/21 or 0.7619 or 76.19%.

To find the probability, we divide the number of committees that contain at least one man by the total number of possible committees.

The total number of possible committees is the number of ways to choose 3 people from the 9 total people (6 women and 3 men). This can be calculated using the combination formula C(9,3) = 9! / (3!(9 - 3)!) = 84.

The number of committees that contain at least one man is the number of committees that contain exactly 1 man plus the number of committees that contain exactly 2 men plus the number of committees that contain exactly 3 men.

Exactly 1 man: C(3,1) x C(6,2) = 45

Exactly 2 men: C(3,2) x C(6,1) = 18

Exactly 3 men: C(3,3) = 1

Adding up the results of these three calculations, we find that the number of committees that contain at least one man is

45 + 18 + 1 = 64

probability of having at least one man = 64/84 = 16/21 = 0.7619 = 76.19%

So, the probability that the committee contains at least one man is 16/21 or 0.7619 or 76.19%.

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The probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.

The probability of rolling a 1 with the first die and a 5 with the second die can be calculated using the joint probability formula. The joint probability formula is P(A ∩ B) = P(A) x P(B|A). In this case, A is rolling a 1 with the first die and B is rolling a 5 with the second die. P(A) is the probability of rolling a 1 with the first die, which is 1/6. P(B|A) is the probability of rolling a 5 with the second die given that a 1 was rolled with the first die, which is also 1/6. Therefore, the probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.

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The standard deviation for the given data is 5

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Given that,

the data,

X            Xₙ - X₀            (Xₙ - X₀)²

18            -7                      49

21             -4                      16

24            -1                        1

24            -1                        1

25             0                       0

31              6                      36

32            7                     49  

175                                  152

X₀  = 175/7 = 25

Variance  =    (Xₙ - X₀)²/(n-1)

                 =  152/(7-1)

                 =   25.33

Standard deviation =  √Variance

                                =  √25.33

                                =   5.03

Hence, the standard deviation is 5

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The exact values of trigonometric functions cosine and tangent are 4 / 5 and 3 / 4, respectively.

How to determine the exact value of a trigonometric function

In this question we must determine the exact value of two trigonometric functions on the basis a given value of another trigonometric function, whose quadrant is also known. According to the statement, sine is in the first quadrant, then both cosine and tangent are also positive. The value of cosine can be found by means of following trigonometric formula:

cos θ = √(1 - sin² θ)

cos θ = √[1 - (3 / 5)²]

cos θ = 4 / 5

And the exact value of tangent can be found by this formula:

tan θ = sin θ / cos θ

tan θ = (3 / 5) / (4 / 5)

tan θ = 3 / 4

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The expressions on both sides of the equal sign are examples of the product of two polynomials, and the goal is to simplify these products into the standard form of a single polynomial. To do this, we use the distributive property of multiplication over addition.

Starting with the first expression (5x-3)(8x-4). We use the distributive property to expand the product of two polynomials into a single polynomial:

(5x-3)(8x-4) =

= (5x × 8x) + (5x × -4) + (8x × -3) + (- 4 × -3) =

= 40x² - 20x - 24x + 12 =

= 40x² - 44x + 12 =

= 10x² - 11x + 3.

In a similar manner, the second expression can be expanded and simplified. We use the distributive property to expand the product of two polynomials into a single polynomial:

(2x+8)(7x+6) =

= (2x × 7x) + (2x × 6) + (8 × 7x) + (8 × 6) =

= 14x² + 12x + 56x + 48 =

= 14x² + 68x + 48 =

= 7x² + 38x +24x.

So both expressions have been simplified into the standard form of a single polynomial, and both are equal to the expressions on the right side of the equal sign.

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Histogram. is a best choice to display the data.

A histogram is a type of graph that is used to represent the distribution of continuous or discrete data by dividing the data into intervals (bins) and counting the number of data points in each bin.

In a histogram, the bins are represented by bars, and the height of each bar represents the frequency or density of the data within the corresponding interval.

In the case of the salaries of professors, a histogram would be a good choice for displaying the distribution of the salaries because it provides a visual representation of the frequency of different salary ranges and helps to identify any patterns or anomalies in the data.

By dividing the salaries into appropriate intervals, the histogram allows you to see how many professors have salaries within a particular range, and to compare the frequency of different salary ranges.

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You paid $16.05 with taxes for a meal.

The definition of the sales tax is given below.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

1) If you buy a meal from a restaurant that cost $15.00, and the tax is 7%,

then the amount of the tax is,

= 15 x 7 / 100

= $1.05

2) The sales tax:

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a traditional sales tax is imposed, collected by the shop, and forwarded to the government.

Therefore, the taxed amount is $1.05.

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The surface area of each small cylinder is 2.28 square units

The surface area of each small cylinder is:

Surface area = 2πr(h + r)

Where

r is the radius (0.25) and

h is the height (1.2).

Plugging in the values, we get:

Surface area = 2 * π * 0.25 * (1.2 + 0.25)

Surface area = 2 * π * 0.25 * 1.45

Surface area = 2.28

Each small cylinder has a surface area of 2.28 square units.

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The time in hours taken to travel from city A to city B is a continuous numerical variable.

A continuous numerical variable is a type of variable that can take on any value within a given range. It is numerical in nature, meaning it can be represented as a number, and it is continuous, meaning it can take on values at any point within a given range, not just specific, discrete values.

In the case of the time taken to travel from city A to city B, it can take on any value within a certain range of time, for example, from 0 hours to 24 hours.

This value can be any number, including a fraction of an hour, such as 3.5 hours or 4.75 hours, which are continuous values within the given range. This makes the time taken to travel a continuous numerical variable.

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The radius of the circle is 83.91 cm

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

Angle = 131 degrees

LEngth of arc = 192 cm

The length of arc is calcuulated as

Length = Angle/360 * 2pi r

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

131/360 * 2 * 22/7 * r = 192

So, we have

r = (192 * 7 * 360)/(131 * 2 * 22)

Evaluate

r = 83.91

Hence, the radius is 83.91 cm

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