The data below shows the colors preferred by a group of people. We want to plot this on a pie chart. What will be the central angles of each of these categories?
Red=
blue=
green=
purple=

The surface area of the cylinder is 150.72cm²

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.

The surface area of a cylinder is the addition of the area of the faces on the cylinder.

The surface area of a cylinder = 2πr(r+h)

= 2×3.14 × 3( 3+5)

= 18.84 × 8

= 150.72cm²

therefore the surface area of the cylinder is 150.72cm²

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Step-by-step explanation:

Complementary means they sum to 90 degrees.

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Substituting the values in, we have:

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Substituting the values in,

we have:2x + 7 + 18 = 90

Complementary means they sum to 90 degrees.

Thus F + G = 90.Substituting the values in,

we have:2x + 7 + 18 = 902x + 25 = 90

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65x = 32.5

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65x = 32.5

Angle F = 72 degrees

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65x = 32.5Angle

F = 72 degrees Angle G = 18 degrees

MARK AS BRANLIEST ANSWER

[tex]x^{2} +7=71 \iff x^{2} =71-7[/tex]

[tex]x^{2} = 64 \iff x^{2} = 8^{2}[/tex]

[tex]x_{1} = - 8, \ x_{2} = 8[/tex]

Note that where the conditions above subsist the height determined by the other colleague is not the same so the answer is No. To solve this problem, you need to be conversant with the Pythagorean Theorem, and Angle Bisector Theorems.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The formula for the Pythagorean Theorem is:

c² = a² + b²

where "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides (the legs) of a right triangle.

With this, we can find the c for the lower Right angle triangle on the left and B for the lower right angle triangle on the right.

Since C² = A² + B²

B = √( A²- C²)

B = √( 9.5²- 6²)

B [tex]\approx[/tex] 7.36546


To determine c on the right angle to the left,

c² = a² + b²

c = √(a² + b²)

c = √(5.5² + 7.2²)

c = 9.060353194

c [tex]\approx[/tex] 9.06

With the postulate of the Angle Bisector Theorem, we can begin to find the height of the two upper right angle triangles.

The Angle Bisector Theorem states that in a triangle, an angle bisector of a vertex of the triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

In other words, if a line segment bisects an angle of a triangle and intersects the opposite side or the extension of the opposite side, then the ratio of the lengths of the segments on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

As seen from the image, the right angles where each lady is holding is bisected. This means that we have for each Triangle Two angles and one side.

Right Angle on the Left:

90°

45°; and

7.2ft

Given the above, Since the angle opposite the height is 45 degrees, we know that the ratio of the height to the base is 1:1, or h/7.2 = 1/1.

Therefore, the height of the right triangle is:

h = 7.2 × 1

h = 7.2 ft

So the height of the right triangle is 7.2 feet.

Right Angle on the Right :

90°

45°; and

7.36546ft

Given the above, we can use the trigonometric ratios of the angles in the right triangle.

Since the angle opposite the height is 45 degrees, we know that the ratio of the height to the base is 1:1, or h/7.36546 = 1/1.

Therefore, the height of the right triangle is:

h = 7.36546 × 1

h = 7.36546 ft

So the height of the right triangle is 7.36546 feet.

So both heights approximated to the nearest tenth:

Since 7.2 ≠ 7.4, the heights are not equal.

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The value of n for the equation (1/36)n= 216 is -1.5.

The following equation is solved by the use of exponent power rule.

The step by step explanation is given below:

convert the fraction into negative exponential form,

(36∧-1)n=216

simplify using the exponent power rule,

(a∧n)∧m = a∧n×m

Covert both sides of the equation in terms with the same base,

(6 ∧2)∧-n = 6 ∧3

Simplify the equation ,

6∧2.-n = 6∧3

Corresponding exponents are equal to ,

-2n = 3

Divide both side of the equation by 2 ,

-n= 3/2

n= - 3/2.

Therefore n = -1.5.

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Answer:

75°

Step-by-step explanation:

The ratio of two adjacent angles is 3: 5

the total ratio = 3+5=8

the sum of the two adjacent angles = 120°

The measure of the larger angle

[tex] \frac{5}{8} \times 120 \\ = \frac{600}{8} \\ =75 [/tex]

Therefore the larger angle is 75°.

The inverse of the matrix is

[tex]$$\left[\begin{array}{cc}1 & -\frac{1}{2} \\-3 & 2\end{array}\right]$$[/tex]

Generally, The inverse of a [tex]$2 \times 2$[/tex] matrix can be found using the formula [tex]$\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]$[/tex] where a d-b c is the determinant.

Find the determinant.

Since the determinant is non-zero, the inverse exists.

Substitute the known values into the formula for the inverse.

[tex]\frac{1}{2}\left[\begin{array}{cc}2 & -1 \\-6 & 4\end{array}\right][/tex]

Multiply 1/2 by each element of the matrix.

[tex][\begin{array}{cc}\frac{1}{2} \cdot 2 & \frac{1}{2} \cdot-1 \\\frac{1}{2} \cdot-6 & \frac{1}{2} \cdot 4\end{array}\right][/tex]

Simplify each element in the matrix.

[tex]$$\left[\begin{array}{cc}1 & -\frac{1}{2} \\-3 & 2\end{array}\right]$$[/tex]

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The decimal number 4.3333333... is a rational and real number. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The decimal number is given below.

⇒ 4.333....

Let x = 4.333333333.., then 10x = 43.33333333...

10x - x = 43.33333.. - 4.333333...

9x = 39

x = 39/9

x = 13/3

The decimal number 4.3333333... is a rational and real number. Then the correct option is A.

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Answer:

Step-by-step explanation:

he's correct trust him The decimal number 4.3333333 is a rational and real number. Then the correct option is A.

Answer:

6 I think have a great day

The required frequency distribution table is below in the solution part.

The relative frequency of the data is the ratio of the given frequency to the total frequency in the observation.

To create a frequency distribution with 5 classes, we first need to find the range of the data, which is the difference between the largest and smallest values:

Range = 10

Next, we divide the range by the number of classes we want (5) to get the class width:

Class width = Range / Number of classes

Class width = 10 / 5

Class width = 2

Now, we can create the frequency distribution table:

Class      Frequency

0-1                5

2-3                29

4-5                16

6-7                14

8-9                 2

10-11               2

___________________

Total             73

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The scale factor required to dilate triangle ABC so that its image, A'B'C', is congruent to triangle XYZ is 1.2.

The scale factor is the ratio of corresponding sides of two similar figures. To find the scale factor, divide the length of the corresponding sides of the two triangles.

To find the scale factor between triangle ABC and triangle XYZ, divide the length of the corresponding sides of the two triangles. The length of side AC in triangle ABC is 10 cm, and the length of side XZ in triangle XYZ is 24 cm. Thus, the scale factor is 24/10, or 1.2.

Therefore, to dilate triangle ABC so that its image, A'B'C', is congruent to triangle XYZ, a scale factor of 1.2 is required.

In summary, the scale factor required to dilate triangle ABC so that its image, A'B'C', is congruent to triangle XYZ is 1.2. This is determined by dividing the length of the corresponding sides of the two triangles.

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The answer of the given question based on the probability is, probability that, in any hour, more than 3 customers will arrive is approximately 0.9227.

a experiment is the outcome of the event, the possible outcomes  are the number of times it occurrences.

To solve this problem, we will use the Poisson distribution,

we are given that the mean rate of customer arrivals is 7.1 per hour. We want to find the probability that more than 3 customers will arrive in any hour.

The Poisson distribution is defined as:

[tex]P(X = k) =(e^{(-\lambda)}*\lambda^k)/k![/tex]

where X is the random variable representing the number of events (in this case, customer arrivals), λ is the mean rate of occurrence, e is the mathematical constant e (approximately 2.71828), and k is the number of events we are interested in.

To find the probability of more than 3 customers arriving, we need to calculate the probability of 4, 5, 6, 7, 8, 9, and so on customers arriving, and add these probabilities together. This can be time-consuming, so instead we can use the complement rule and find the probability of 0, 1, 2, or 3 customers arriving, and subtract this from 1:

P(X > 3) = 1 - P(X <= 3)

To calculate P(X <= 3), we can use the Poisson distribution with λ = 7.1 and k = 0, 1, 2, and 3:

[tex]P(X = 0) = (e^{(-7.1)} * 7.1^0) / 0! = 0.000832[/tex]

[tex]P(X = 1) = (e^{(-7.1)} * 7.1^1) / 1! = 0.005904[/tex]

[tex]P(X = 2) = (e^{(-7.1)} * 7.1^2) / 2! = 0.020981[/tex]

[tex]P(X = 3) = (e^{(-7.1)} * 7.1^3) / 3! = 0.049546[/tex]

Adding these probabilities together, we get:

P(X <= 3) = 0.000832 + 0.005904 + 0.020981 + 0.049546 = 0.077263

Therefore, the probability of more than 3 customers arriving in any hour is:

P(X > 3) = 1 - P(X <= 3) = 1 - 0.077263 = 0.9227 (rounded to four decimal places)

So the probability that, in any hour, more than 3 customers will arrive is approximately 0.9227.

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Answer: 0.229659

Step-by-step explanation: Since you are converting centimeters to feet, you have to divide the centimeters by exactly, 30.48. so 7 / 30.48 equals 0.229659.

Answer:

(a) The interest on a simple interest loan is calculated using the formula:

Interest = Principal x Rate x Time

where:

Principal is the amount of the loan

Rate is the interest rate per time period

Time is the duration of the loan in the same time period as the interest rate

In this case, the principal is $8000.00, the rate is 9.00% per year, and the time is 9 months. To calculate the interest, we need to convert the time to years by dividing by 12:

Time in years = 9 months / 12 months per year = 0.75 years

Plugging in the values, we get:

Interest = $8000.00 x 0.09 x 0.75

Interest = $540.00

Therefore, the student must pay $540.00 in interest.

(b) The future value of a simple interest loan is calculated using the formula:

Future Value = Principal + Interest

In this case, the principal is $8000.00 and the interest is $540.00, so the future value is:

Future Value = $8000.00 + $540.00

Future Value = $8540.00

Therefore, the future value of the loan is $8540.00.

Step-by-step explanation:

The error occurs in step 2, because according to BODMAS we need to perform multiplication before addition.

The acronym BODMAS rule is used to keep track of the correct order of operations to perform while resolving mathematical statements. BODMAS stands for Brackets, Order of Powers or Roots, Division, Multiplication, Addition, and Subtraction. In some circumstances, the prefix "of" is used as well. This indicates that numerous operator expressions must only be spelled out in this sequence, from left to right. We begin by resolving the brackets, then go on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).

According to the BODMAS multiplication must be performed before addition.

Hence, the error occurs in step 2, because according to BODMAS we need to perform multiplication before addition.

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The two correct options for time and work problem are: (a) and (d)

(a) The restaurant can make 24 pizzas in 5 hours

(d) The restaurant can make 48 pizzas in 10 hours

Time and work are fundamental to how work is done at the moment. The time and work problem gives us the exact relationship between workers and the number of days and hours it takes to complete a task. 

Solution according to the question:

Given, the restaurant can make 12 pizzas in 2.5 hours

So, when we double the time of work, the number of pizzas will also be doubled, i.e

24(12×2) pizzas in 5(2.5 ×2), hence option (a) correct.

Also, 10 hours is four times of 2.5 hours.

Thus, in 10 hours the restaurant will make 48 pizzas, so option (d) is the other correct option.

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Sure, here's a complete table of y-values for different x-values:

x y = 9*(13)^x

0 9

1 117

2 1521

3 19773

4 256809

5 3335777

6 43363161

7 562002993

8 7304038917

9 94852405821

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. Functions are often represented using function notation, where the input is the independent variable and the output is the dependent variable. Functions are used to model relationships between different quantities or variables, and are an essential tool in many areas of mathematics, science, engineering, economics, and more. They allow us to make predictions, analyze data, and understand complex systems.

Here,

The exponential function y = 9*(13)^x means that for any given value of x, we can calculate the corresponding value of y by plugging in x and performing the calculation. The base of the exponential function is 13, which means that the function will increase rapidly as x gets larger.

For example, if x = 0, then y = 9*(13)⁰ = 91 = 9.

If x = 1, then y = 9(13)¹ = 913

= 117.

If x = 2, then y = 9(13)² = 9*169

= 1521.

And so on.

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Answer:

5 1/2

Step-by-step explanation:

1 7/8 + 3 5/8

first start by adding the whole numbers

1 + 3 = 4

then add the fractions (only add the numerators)

7/8 + 5/8 = 12/8

12/8 is the same thing as 1 4/8

1 4/8 is the same thing as 1 1/2

Now add the whole number you added above

4 + 1 1/2 = 5 1/2

So, you answer to 1 7/8 + 3 5/8 is 5 1/2

Hope this helps!

Answer: The problem statement is incomplete. It is given that one motorcyclist is traveling at a speed of 7 km/hr, but the speed of the other motorcyclist is not given. We cannot solve the problem without knowing the speed of the other motorcyclist.

Please provide additional information, such as the time taken by both motorcyclists to cover the distance, or any other information that may be relevant to the problem.

Step-by-step explanation:

The linear equations that represents the problem are c = 40d + 20, P = 6.07 + 0.17(y - 2002), c = fixed fee + 7.75p and d = -93t + 1007

To solve this problem, we need to write linear equations that represent each scenario

1. Total cost (C) to rent the trench digger for d days can be represented as:

C = 40d + 20

2. The amount of renewable power (P) produced in year y between 2002 and 2005 can be represented as:

P = 6.07 + 0.17(y - 2002)

3. The cost (C) of a birthday party for p people can be represented using the two given data points as:

For 10 people: 97.50 = fixed fee + 10(cost per person)

For 20 people: 175 = fixed fee + 20(cost per person)

Subtracting the first equation from the second equation gives:

77.50 = 10(cost per person)

Hence, the cost per person is:

cost per person = 7.75

Therefore, the rule for the cost (C) of a birthday party for p people is:

C = fixed fee + 7.75p

4. Jimmy's distance (d) from home after t hours of driving can be represented using the two given data points as:

After 3 hours: d = 740

After 6 hours: d = 461

Subtracting the first equation from the second equation gives:

d - 740 = -279

Hence, the distance (d) from home after t hours of driving can be represented as:

d = -93t + 1007

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Answer:

Step-by-step explanation:

p and q vary inversely:

If p = 18, q = 28, find k:

The equation is:

When p = 72, q is:

The percentage of temperatures for Shanghai between 46ºF and 78ºF is given as follows:

50%.

A box and whisker plots shows these five features from a data-set, listed as follows:

For Shanghai, the quartiles are given as follows:

Q1 = 46, Q3 = 78.

Hence the temperatures between 46 and 78ºF represent the interquartile range, containing the middle 50% of observations.

The problem is given by the image presented at the end of the answer.

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Answer: 4.8625

Step-by-step explanation:

The value of the sides are;

x = 6

HW = 37

AM = 32

WM = 44

It is important to note that one of the properties of an isosceles trapezoid is that the non-parallel sides are equal to each other.

From this deduction, we then have;

HW = AM

Given that;

HW = 6x + 1

AM = 3x + 19

Equate the lengths

6x + 1 = 3x + 19

collect the like terms

6x - 3x = 19 - 1

3x = 18

Make 'x' subject

x = 6

Then, HW = 37 and AM = 37

Substitute the value of x in

HA = 6x - 4 = 32

WM = 4x + 20 = 44

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The total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $11.32. The solution has been obtained by using linear equation.

What is a linear equation?

One is the linear equation's degree. In linear equations with exponents greater than 1, it is clear that there are no variables. A straight line is produced by the graph's equation.

We are given that the price of grapes, g, is $2.19 per pound. The price of bananas, b, is $0.59 per pound. The price of pears, p, is $1.49 per pound.

From this, we get an equation as

Total Cost = 2.19g + 0.59b + 1.49p

Now, the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears will be

⇒Total Cost = 2.19(3) + 0.59(3) + 1.49(2)

⇒Total Cost = 6.57 + 1.77 + 2.98

⇒Total Cost = $11.32

Hence, the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears is $11.32.

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Question: The price of grapes, g, is $2.19 per pound. The price of bananas, b, is $0.59 per pound. The price of pears, p, is $1.49 per pound.

What is the total cost for 3 pounds of grapes, 3 pounds of bananas, and 2 pounds of pears?

The equation can be converted as: 2 (S - 1/2 u t) / t.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Let's start by simplifying the equation using the distributive property of multiplication:

S = 1/2 u t + 1/2 v t

Next, we can isolate the variable v by subtracting 1/2 u t from both sides of the equation:

S - 1/2 u t = 1/2 v t

Now we can multiply both sides of the equation by 2 to eliminate the fraction:

2 (S - 1/2 u t) = v t

Finally, we can solve for v by dividing both sides of the equation by t:

v = 2 (S - 1/2 u t) / t

Therefore, the solution for v is v = 2 (S - 1/2 u t) / t.

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The triangle has 3 interior angles and 3 sides, the sum of interior angles is always equal to 180 degree. The measure of the side UV of a triangle  is 4.2

on considering the length of the sides, the triangle is classified into different types

the sum of the interior angles of a triangle is always equal to 180°

given TR=2,WU=6,RS=1.4,UV=?

let UV be x,

x/1.4=6/2

cross multiply

2x=6*1.4

2x=8.4

x=8.4/2

x=4.2

hence UV=4.2

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Answer:68

Step-by-step explanation:

You can first subtract 104-36=68 so,68+36=104

Answer:

  68

Step-by-step explanation:

You want to know the number of marbles Chloe originally had in her collection if adding 36 marbles gave her a total of 104.

You can let a variable (o) represent the original number of marbles. You would choose this because the original number of marbles is what you're asked to find. It never hurts to use a variable name that reminds you of what it stands for.

The problem statement tells you that adding 36 to the original number gives a total of 104. As an equation, this looks like ...

  o + 36 = 104 . . . . . . adding 36 to o gives 104

The properties of equality tell you that you can subtract the same number from both sides of the equation without changing the value of the variable.

Here, we want the variable by itself, so we want to get rid of the added number 36. We do that by subtracting 36 from both sides of the equation:

  o +36 -36 = 104 -36 . . . . . subtract 36 from both sides

  o = 68 . . . . . . . . . . simplify

This solution tells us that Chloe originally had 68 marbles.

__

Additional comment

The way to solve this, or any, "word problem" is to read and understand the relationships the words are telling you, and what the words are asking for. Then write those relationships as math expressions, choosing variables and a procedure that will give you what the question is asking for.

Here, we could choose a variable that represents the quantity we want to find. That is not always the case.

Sometimes, you have to find an "intermediate" value that you need in order to be able to answer the ultimate question. You're not done when you find that intermediate value; you're only done when you are able to answer the question asked.

Answer:

q=2.1

Step-by-step explanation:

2q+3.07=7.27

take away 3.07 from both sides

2q=4.20

divide both sides by 2

q=2.10

q=2.1

The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The value of function is,

⇒ f (x) = 2x⁴ + x² - 10x + 1

Now, We can find all the values as;

At x = - 10;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1

⇒ f (- 10) = 20000 + 100 + 100 + 1

⇒ f (- 10) = 20201

At x = 2;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1

⇒ f (2) = 32 + 4 - 20 + 1

⇒ f (2) = 17

At x = 3;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1

⇒ f (3) = 162 + 9 - 30 + 1

⇒ f (3) = 143

Thus, The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

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