A solid cylinder is cut vertically through its center. Its radius and height are 6 cm and 15 cm, respectively. What is the area of the resulting shape?

Answer: A

Step-by-step explanation:

A best represents the graph

To find all the values of b that will make the trinomial 3x^(2)-bx+12 factorable, we need to use the discriminant of the quadratic formula. The discriminant is the part of the quadratic formula under the square root: b^(2)-4ac. If the discriminant is a perfect square, then the trinomial will be factorable.

So we plug in the values of a, b, and c from the trinomial: b^(2)-4(3)(12) = b^(2)-144.

We want this to be a perfect square, so we can set it equal to a perfect square and solve for b:

b^(2)-144 = 36

b^(2) = 180

b = sqrt(180)

b = 6sqrt(5)

So one value of b that will make the trinomial factorable is 6sqrt(5).

Now we can plug this value of b back into the trinomial and factor it:

3x^(2)-6sqrt(5)x+12 = 0

(3x-6)(x-sqrt(5)) = 0

So the factors of the trinomial are (3x-6) and (x-sqrt(5)).

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Answer:

7.5 feet

Step-by-step explanation:

Divide the length value by 12 for your answer

90/12 = 7.5

There are 12 inches in a foot, so to convert inches to feet, you can divide the number of inches by 12.

Therefore, a 90-inch cage is equivalent to:

90 inches ÷ 12 inches/foot = 7.5 feet

So the bird cage is 7.5 ft.

Set B, which contains the elements 11, 15, 19, 23, 27, 31, 4n+7 and so on, is an infinite set because there exists a one-to-one correspondence between set B and a proper subset of itself, namely set F, which contains the odd integers greater than or equal to 15.

To expose that set b is infinite, we want to set up a one-to-one correspondence among set B and A proper subset of itself. Allow F to be the set of odd integers greater than or equal to 15, i. E., F = {15, 19, 23, 27, ...}.We are able to outline a characteristic f from set b to set f as follows:

f(11) = 15

f(15) = 19

f(19) = 23

f(23) = 27

f(27) = 31

f(4n+7) = 4(n+2) + 3

the first five factors of set b are mapped to the primary 5 factors of set f. For any detail 4n+7 in set b, the corresponding detail in set f is 4(n+2)+3, which is the next peculiar integer after 4n+7. It may be shown that this function is a one-to-one correspondence between set b and set f.

Consequently, given that set f is a proper subset of set b and there exists a one-to-one correspondence among them, set b should be infinite.

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Using basic arithmetic operations, we concluded that a) Bryony wrote more words in total than Arthur.

b) Bryony wrote 220 more words than Arthur.

The four basic mathematical operations are addition, subtraction, multiplication, and division.

a) In order to establish who wrote more words overall, we must total the words that each participant wrote. By dividing the typical words per minute by the total number of minutes each person worked, we may determine this:

Arthur: 65 minutes × 16 words/minute = 1040 words

Bryony: 90 minutes × 14 words/minute = 1260 words

Therefore, Bryony wrote more words in total than Arthur.

b) To find out how many more words Bryony wrote than Arthur, we can subtract Arthur's total from Bryony's total:

1260 words - 1040 words = 220 words

Hence, Bryony wrote 220 more words than Arthur.

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The area of the triangular piece of property is approximately 63,121.75 square feet.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Starting at the first corner, the surveyor walks 480 ft in the direction N36°W. We can break this down into its northward and westward components:

Northward component = 480 cos(36°)

≈ 388.75 ft

Westward component = 480 sin(36°)

≈ 295.42 ft

This takes the surveyor to the second corner of the property.

From the second corner, the surveyor walks S21°W to get to the third corner. We can again break this down into its southward and westward components:

Southward component = 480 cos(21°)

≈ 435.89 ft

Westward component = 480 sin(21°)

≈ 168.75 ft

Finally, the surveyor walks N82°E to get back to the starting point.

We can break this down into its northward and eastward components:

Northward component = 388.75 ft

Eastward component = 435.89 sin(82°)

≈ 426.04 ft

Now we have the lengths of all three sides of the triangular property:

Side 1 = 480 ft

Side 2 = √[(295.42 - (-168.75))^2 + (388.75 - 435.89)^2]

≈ 421.66 ft

Side 3 = √[(426.04 - 295.42)^2 + (388.75 - 0)^2]

≈ 296.13 ft

calculate the area of the triangular property, we can use Heron's formula:

Area = √[s(s - a)(s - b)(s - c)]

where s is the semiperimeter (half the perimeter) of the triangle,

and a, b, and c are the lengths of its sides.

s = (480 + 421.66 + 296.13)/2 ≈ 598.40

Area = √[598.40(598.40 - 480)(598.40 - 421.66)(598.40 - 296.13)]

Area ≈ 63,121.75 sq ft

Therefore, the area of the triangular piece of property is approximately 63,121.75 square feet.

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Answer:

12xphjzjhsgwghdghehdhhez7uehdyegd

Answer:

Let's first define our variables:

Let x be the number of students in each van and bus.

Using substitution:

From the problem, we know that:

High School A rented 8 vans and 8 buses, with a total of 240 students. So we can write the equation:

8x + 8x = 240

High School B rented 4 vans and 1 bus, with a total of 54 students. So we can write the equation:

4x + 1x = 54

Now, we can solve for x in one of the equations and then substitute that value into the other equation to solve for the other variable. For example, let's solve for x in the second equation:

5x = 54

x = 10.8

Now, we can substitute this value of x into the first equation to solve for the number of students in each van and bus for High School A:

8x + 8x = 240

8(10.8) + 8(10.8) = 172.8

So each van and bus for High School A has 10.8 students in it.

Using elimination:

We can rewrite the equations we used above in standard form:

8x + 8y = 240

4x + y = 54

We can eliminate y by multiplying the second equation by -8 and adding it to the first equation:

8x + 8y = 240

-32x - 8y = -432

-24x = -192

x = 8

Now, we can substitute this value of x into either equation to solve for y:

4(8) + y = 54

y = 22

So each van and bus for High School A has 8 students in it and each van and bus for High School B has 22 students in it.

Using graphing:

We can graph the two equations on the same coordinate plane and find the point where they intersect, which represents the solution:

8x + 8y = 240

4x + y = 54

To graph these equations, we can first solve for y in each equation:

y = -x + 30

y = -4x + 54

Then, we can plot these two lines on the same coordinate plane and find their intersection:

(6, 24)

So each van and bus for High School A has 6 students in it and each van and bus for High School B has 24 students in it.

Answer:

mine either hahahahahaha

As per the difference concept, the bearing of Q from P is 132°.

To find the bearing of Q from P, we need to calculate the difference between the bearing of P from Q and 180 degrees. This is because the bearing from P to Q is the opposite direction of the bearing from Q to P.

Let's use some notation to make this clearer. Let the bearing from P to Q be denoted by B(PQ), and the bearing from Q to P be denoted by B(QP). We are given that B(PQ) = 312°. To find B(QP), we use the following formula:

B(QP) = B(PQ) - 180°

We know that B(PQ) is 312°, so we can substitute this value into the formula to get:

B(QP) = 312° - 180°

B(QP) = 132°

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As a result, 6% sales tax is applied.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Percentile in mathematics is a related topic.

The price of the snowboarder with tax compared to the price of the snowboarders without tax is the differential in the sales tax.

Sales tax therefore equals $848 - $800 = $48.

We need to multiply the result by 100 to get the sales percentage of tax, which we can then divide by the price of the snowboard before taxes.

Sales tax percentage = (Sales tax / Cost without tax) x 100

= ($48 / $800) x 100

= 0.06 x 100

= 6%

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As a result, 6% sales tax is applied.

%, which is a relative figure used tο denοte hundredths οf any quantity. Since οne percent (symbοlized as 1%) is equal tο οne hundredth οf sοmething, 100 percent stands fοr everything, and 200 percent refers tο twice the amοunt specified. percentage. Percentile in mathematics is a related tοpic.

The price οf the snοwbοarder with tax cοmpared tο the price οf the snοwbοarders withοut tax is the differential in the sales tax.

Sales tax therefοre equals $848 - $800 = $48.

We need tο multiply the result by 100 tο get the sales percentage οf tax, which we can then divide by the price οf the snοwbοard befοre taxes.

Sales tax percentage = (Sales tax / Cοst withοut tax) x 100

= ($48 / $800) x 100

= 0.06 x 100

= 6%

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Answer:

7 ft is 84 inches, 3ft is 36 inches

84 - 36 = 48

cuts off 18 more inches

48 - 18 = 30 inches of rope remain

Step-by-step explanation:

The CFD shows that 17 observations (56.7%) fall between 15.8 and 16.0.

A histogram is a graph that displays the frequency of data in a given range. The cumulative frequency distribution (CFD) is a graph that displays the cumulative total of frequencies. The histogram and CFD of the given data are shown below:

The data shows a skewed distribution with most of the observations falling between 15.8 and 16.0. The data is highest at 16.0, with 11 observations falling in this range.

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In answering the question above, the solution is Zany thus has 1,533.75 expressions pounds more apples than Peter does.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

There are 412 bags of apples in all, with 10 apples in each bag, at Zany. Zany thus has a total of:

412 bags multiplied by 10 bags is 4,120 apples.

24,720 ounces is equal to 4,120 apples at 6 ounces each.

16,080 pounds divided by 24,720 ounces is 1,545 pounds.

Peter has a total of three bags of apples, or:

30 apples are equal to 3 bags times 10 bags

Each of Peter's apples weighs 6 ounces, making his total apple weight:

30 apples divided by 6 ounces each equal 180 ounces.

160 ounces / 16 ounces per pound equals 11.25 pounds.

After deducting Peter's weight from Zany's weight, we can determine how many pounds more apples Zany possesses than Peter:

11 pounds less than 1,545 pounds is 1,533.75 pounds.

Zany thus has 1,533.75 pounds more apples than Peter does.

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1. True. The CPI is not just one index, but includes a large number of groups, subgroups and selected items, such as a food index, a medical care index and an entertainment index.

2. True. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another.

The Consumer Price Index (CPI) is actually a collection of indices that measure the changes in prices of a wide range of goods and services.

The CPI includes several different groups, subgroups, and selected items, such as a food index, a medical care index, and an entertainment index.

Each of these indices is used to track the changes in prices of specific goods and services within that category.

An index number is a statistical measure that is used to compare the changes in prices, quantities, values, or other items of interest from one time period to another.

Index numbers are typically expressed as a percentage, with a base value of 100 representing the initial time period. Any changes in the index number from one time period to another reflect the percentage change in the item of interest over that time period.

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Answer:

-2

Step-by-step explanation:

Whenever you see f(x), for any number x, you plug x into the function. In your function, f(x) = -x - 1, you want to find f(1).

So, f(1) = -(1) - 1, which equals -2

The ordered pairs for the linear equation, y=3x-13 is (0,-13), (1,-10), and (2,-7).

To complete the table of ordered pairs for the linear equation y=3x-13, we need to substitute different values of x into the equation and solve for y. This will give us the ordered pairs (x,y) for the equation.

Step 1: Choose a value for x. Let's start with x=0.

Step 2: Substitute the value of x into the equation and solve for y.
y=3(0)-13
y=-13

Step 3: Write the ordered pair (x,y) for this solution. In this case, the ordered pair is (0,-13).

Step 4: Repeat steps 1-3 for different values of x. Let's try x=1 and x=2.

For x=1:
y=3(1)-13
y=-10
The ordered pair is (1,-10).

For x=2:
y=3(2)-13
y=-7
The ordered pair is (2,-7).

Step 5: Complete the table with the ordered pairs that we found.

   x        y
   0      -13

   1       -10
 
   2        -7
 

So, the table of ordered pairs for the linear equation y=3x-13 is:
(0,-13), (1,-10), and (2,-7).

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The expression (18)(-3)(-3) is not equivalent to others.

-7+(-3) is equivalent of the expression -7 - 3.

What is an expression?

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical value is referred to as a constant.

Variable: A symbol without a fixed value is referred to as a variable.

Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.

Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Take the first option:

(-9)(-3 × -6)

= (-9)(18)

= (18)(-9)  [Commutative property]

= -(-18)(-9)

Apply the associative property on (-9)(-3 × -6):

(-9)(-3 × -6)

= (-9× - 3)(-6)

= (27) (-6)

= (-6)(27)   [Commutative property]

The given expression is -7 - 3

Rewrite the above expression:

-7+(-3)

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Answer:

a) 7

b) 0.1

Step-by-step explanation:

a)

The width must be able to go up to 35.

Each square is 5 units wide.

35/5 = 7

The grid must be at least 7 squares wide.

b)

The highest y-coordinate is 1.7.

The highest point on the grid should be 2.

There are 20 vertical squares on the grid.

2/20 = 0.1

Each vertical square should be 0.1

A = 0.1

Answer:

5 and 35

Step-by-step explanation:

It's going up in tens so it must start from 5, therefore the one between 25 and 45 must be 35.

To solve the inequality -12x - 5 > 1 + 18x, we need to isolate the variable x on one side of the inequality. Here are the steps to do so:

1. Add 12x to both sides of the inequality to eliminate the -12x on the left side:
-5 > 1 + 30x

2. Subtract 1 from both sides of the inequality to eliminate the 1 on the right side:
-6 > 30x

3. Divide both sides of the inequality by 30 to isolate the variable x:
-6/30 > x

4. Simplify the fraction on the left side:
-1/5 > x

Therefore, the solution to the inequality is x < -1/5. The correct value of A is -1/5.

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The expected value of the number of tests taken is 1.92 an the variance of the number of tests taken is 1.5852 and the standard deviation is 1.259.

The expected value, variance, and standard deviation can be calculated using the following formulas:
Expected value (E) = ΣxP(x)
Variance (Var) = Σ(x - E)² P(x)
Standard deviation (SD) = √Var

a. To find the expected value of the number of tests taken, we can use the formula E = ΣxP(x), where x is the number of tests taken and P(x) is the probability of taking x tests.
E = (1)(22/50) + (2)(15/50) + (3)(8/50) + (4)(5/50)
E = 0.44 + 0.6 + 0.48 + 0.4
E = 1.92


b. To find the variance and standard deviation, we can use the formulas Var = Σ(x - E)² P(x) and SD = √Var.
Var = (1 - 1.92)²(22/50) + (2 - 1.92)² (15/50) + (3 - 1.92)² (8/50) + (4 - 1.92)^2 (5/50)
Var = 0.8464 + 0.0104 + 0.2928 + 0.4356
Var = 1.5852
SD = √1.5852
SD = 1.259

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This is the appropriate set notation for the set J, which includes all integers between -5 and -3.

The set J can be rewritten by listing its elements in the appropriate set notation. Since the set J contains all integers between -5 and -3, we can list the elements as follows:

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

J = {-5, -4}

In set notation, this can be written as:

J = {x | x is an integer and -5 <= x < -3}

Therefore, the set J can be rewritten as:

J = {-5, -4}

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The correct option for this question is B. There has been a rise in three-point shots, and players tend to score more points now.

Why it is?

The factor that makes it challenging to make a fair comparison between a current NBA star and an NBA star from the 1990s is:

B. There has been a rise in three-point shots, and players tend to score more points now.

The increase in three-point shots has significantly changed the way the game is played and the strategies used by teams, which makes it difficult to compare the performance of players from different eras.

Players in the current NBA tend to score more points because of the increased emphasis on the three-point shot, while players from the 1990s may have had different strengths and styles of play that were more effective in that era. Therefore, it is challenging to make a fair comparison between players from different eras based solely on their statistics.

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Step-by-step explanation:

Using the formula V = Pe^(rt), where P is the principal initially invested, e is the base of a natural logarithm, r is the rate of interest, and t is the time in years:

V = Pe^(rt)

We are given that P = $8290, r = 0.06 (since the annual interest rate is 6%), and t = 12 (since we want to find the value of the account after 12 years). Therefore, we can plug in these values and solve for V:

V = 8290 * e^(0.06*12)

V = 8290 * e^(0.72)

V = $17,936.34

Therefore, the amount of money in the account after 12 years, to the nearest cent, is $17,936.34.

24 buckets of gravel are needed for 4 buckets of cement when making concrete tiles using the given ratio.

What is the ratio?

The ratio is a mathematical concept that represents the relationship between two quantities or values. It is defined as the comparison of two numbers by division, where the first number is called the "antecedent" and the second number is called the "consequent."

According to the given ratio, the amount of gravel needed is 6 times the amount of cement, or 6/1.

To find out how many buckets of gravel are needed for 4 buckets of cement, we can set up a proportion:

6/1 = x/4

where x is the number of buckets of gravel needed.

To solve for x, we can cross-multiply:

6 x 4 = 1 x x

24 = x

Hence, 24 buckets of gravel are needed for 4 buckets of cement when making concrete tiles using the given ratio.

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The figure represented here is a square pyramid.

With a square base and fοur triangular sides that are cοnnected at a vertex, a square pyramid is a three-dimensiοnal geοmetric οbject. It has a pentahedrοn shape with five faces.

Fοur triangles are jοined at each vertex tο a square fοundatiοn tο fοrm a square pyramid. It has a square fοundatiοn, and triangles with a shared vertex make up its side faces.

We can get the squared pyramidal figure by fοlding the triangles οf equal size frοm all the sides.

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Using quadratic formula we get, Part A: The solutions for x are: x = (3 + √(57))/(3/2) and x = (3 - √(57))/(3/2). Part B: The first system solution is: ((3 + √(57))/(3/2), -(76 + 6√(57))/(9) + 5)  and second system solution is:                                                 ((3 - √(57))/(3/2), -(76 - 6√(57))/(9) + 5)

Part A: To solve for x, we need to first rearrange the equation so that all terms are on one side of the equal sign.  Adding (1/4)x^(2) to both sides of the equation:
-x^(2) + (1/4)x^(2) + 3x + 14 = 5

Next, combining like terms:
-(3/4)x^(2) + 3x + 14 = 5

Now, subtracting 5 from both sides:
-(3/4)x^(2) + 3x + 9 = 0

Finally, using quadratic formula to solve for x:
x = (-3 ± √(3^(2) - 4(-3/4)(9)))/(2(-3/4))

Simplifying:
x = (-3 ± √(57))/(2(-3/4))
x = (-3 ± √(57))/(-3/2)
x = (3 ± √(57))/(3/2)

Part B: To determine the system solutions, we need to plug in the values of x into the original equation and solve for y. For the first solution:
y = -(1/4)((3 + √(57))/(3/2))^(2) + 5
y = -(1/4)((9 + 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 + 6√(57))/(9/4)) + 5
y = -(19 + (3/2)√(57))/(9/4) + 5
y = -(76 + 6√(57))/(9) + 5

For the second solution:
y = -(1/4)((3 - √(57))/(3/2))^(2) + 5
y = -(1/4)((9 - 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 - 6√(57))/(9/4)) + 5
y = -(19 - (3/2)√(57))/(9/4) + 5
y = -(76 - 6√(57))/(9) + 5

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The equatiοn οf the least squares regressiοn line which mοst clοsely matches the data set is y = 3.5 x + 43.8

Tο sοlve fοr the data set, lets lοοk at the table,

X            1190         1992          1994         1996           1998

Y             45             51               57            61               75

Let the equatiοn that shοws the abοve data be

y = b + a x ---------(1)

Where, a = Σy Σx² - Σx Σxy

And, b = (Σxy - Σx Σy) / n Σx² -(Σx)²

By the abοve table,

Σx=20

Σxy = 1296

Σx² = 120

Σy=289

By substituting these values in the abοve value οf a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equatiοn (1)

We get, the equatiοn that shοws the given data is,

y = 3.5 x + 43.8

Therefοre, οptiοn 3 is cοrrect.

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a) The probability that a person spent more than $28 is of: 0.2033 = 20.33%.

b) The probability that a person spent between $9 and $21 is given as follows: 0.3608 = 36.08%.

c) The middle 95% of the amounts falls between $11.24 and $34.76.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the problem are given as follows:

[tex]\mu = 23, \sigma = 6[/tex]

The probability of a person spending more than $28 is one subtracted by the p-value of Z when X = 28, hence:

Z = (28 - 23)/6

Z = 0.83

Z = 0.83 has a p-value of 0.7967

1 - 0.7967 = 0.2033.

The probability of a person spending between $9 and $21 is given by the p-value of Z when X = 21 subtracted by the p-value of Z when X = 9, hence:

Z = (21 - 23)/6

Z = -0.33

Z = -0.33 has a p-value of 0.3707

Z = (9 - 23)/6

Z = -2.33

Z = -2.33 has a p-value of 0.0099.

0.3703 - 0.0099 = 0.3608 = 36.08%.

The middle 95% of amounts is between the 2.5th percentile(Z = -1.96) and the 97.5th percentile, Z = 1.96, hence:

-1.96 = (X - 23)/6

X - 23 = -1.96 x 6

X = 11.24.

1.96 = (X - 23)/6

X - 23 = 1.96 x 6

X = 34.76.

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