5. Mrs. Walsh conducted a survey of the most popular after-school snack in the
middle school. Of the 400 students surveyed, 70 preferred muffins, 70 preferred
pretzels, 50 preferred fruit, 50 preferred yogurt, 80 preferred cheese and crackers,
and 80 preferred granola bars. Select all of the sections of a circle graph that each
represent of the entire circle.
muffins
Opretzels
fruit
yogurt
cheese and crackers
granola bars
06-1

Answer: The equation of a circle with center (a,b) and radius r is given by:

(x - a)^2 + (y - b)^2 = r^2

In this case, the center is (9,10) and the point on the circle is (7,4). To find the radius, we can use the distance formula between the center and the point on the circle:

r = sqrt((7 - 9)^2 + (4 - 10)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(40)

So, the equation of the circle is:

(x - 9)^2 + (y - 10)^2 = 40

Alternatively, we can also expand the equation to get:

x^2 - 18x + 81 + y^2 - 20y + 100 = 40

Simplifying and rearranging, we get:

x^2 + y^2 - 18x - 20y + 41 = 0

Therefore, the equation of the circle is either (x - 9)^2 + (y - 10)^2 = 40 or x^2 + y^2 - 18x - 20y + 41 = 0.

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{4}x-1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking fo the equation of a line whose slope is 4 and it passes through (-3 , 2)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y -2= 4 (x +3) \\\\\\ y-2=4x+12\implies {\Large \begin{array}{llll} y=4x+14 \end{array}}[/tex]

The compound figure has a 41 square metre surface area.

The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.

The compound figure's area can be calculated by breaking it up into smaller shapes and adding the areas of each one.

Then, divide the figure into two rectangles:

The first rectangle is 2 m by 9 m in size and has a surface area of 18 m².

The surface area of the second rectangle, which is 3 m by 7 m in size, is 21 m².

Next, we may determine the areas of the two triangles:

Due to its 2 m base and 2 m height, the first triangle has an area of 1/2 x 2 m x 2 m, = 2 m².

The second triangle has a base of 3 m and a height of 2 m, and its area is 1/2 x 3 m x 2 m = 3 m².

The two rectangles' overlap can then be subtracted:

The overlap is a rectangle that is 2 m by 3 m in size, or 6 m2, and measures 2 m by 3 m.

The total area of the compound figure is calculated by adding the areas of the two rectangles, the two triangles, and then deducting the overlap between the rectangles.

Total area is (18 m² + 21 m²) + (2 m² + 3 m²) - 6 m².

Total area: 41 m².

Hence, the compound has a 41 square metre size.

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Answer:

Sophia's paint is lighter.

Step-by-step explanation:

percent = part/whole × 100%

Sophia:

3 cups black, 4 cups white

total: 7 cups

white percent = 4/7 × 100% = 57%

Jeriel:

9 cups black, 10 cups white

total: 19 cups

white percent = 10/19 × 100% = 53%

Sophia's paint is lighter.

Answer:

170 cm³

Step-by-step explanation:

V = πr²h

= 3.14 * (3)² * 6

= 3.14 * 9 * 6

= 169.56 cm³

= 170 cm³

The number of large pieces of fabric that Lola should buy to be able to make 7 scarves is 7 larger pieces of fabric.

The number of small fabrics needed for one scarf is 8 pieces. The area of these pieces is:

= 8 pieces x ( 1 / 4 x 1 / 4 )

= 0. 5 foot ²

This means that 1 scarf needs 0. 5 foot ² of fabric.

The area of a single large piece of fabric is :

= 1 / 4 x 2

= 0. 5 foot ²

This means that 1 large piece can make 1 scarf. If 7 scarves need to be made therefore, then Lola needs 7 large pieces.

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By answering the above question, we may infer that Hence, the probability likelihood is 0.2752. (rounded to four decimal places).

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.

We may utilize the complement of the CDF to respond to this query.

For x 0, the complement of the CDF is defined as 1 - F(x) = e(-x).

Thus, the likelihood that an old ICU patient will be there for more than five days is as follows:

[tex]1 - F(5) = e^(-0.3030 * 5) = 0.2052[/tex]

Hence, the likelihood is 0.2052. (rounded to four decimal places).

We may utilize the difference between the CDF at two distinct values to get an answer to this query.

The likelihood that an old ICU patient will be there for two to four days is as follows:

[tex]F(4) - F(2) = (1 - e^(-0.3030 * 4)) - (1 - e^(-0.3030 * 2)) = e^(-0.3030 * 2) - e^(-0.3030 * 4) = 0.2752[/tex]

Hence, the likelihood is 0.2752. (rounded to four decimal places).

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The principal will need to order 108 pizzas to feed 300 students.

We may set up a proportion to determine how many pizzas are required to feed 300 students if 9 pizzas feed 25 students:

25 pupils × 9 pizzas = x pizzas / 300 students

where x is how many pizzas are required to feed 300 kids.

We can cross-multiply and simplify to find x's value:

300 kids times 9 pizzas equals 25 students (x pizzas)

2700 = 25x

x = 2700 / 25

x = 108

In order to serve 300 pupils, the principal will have to order 108 pizzas.

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We can state this by responding to the provided question As a result, the function's amplitude is 2 and its period is.

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The sine function of the form f(x) = -2sin(x) is an amplitude-scaled sine function.

The sine function's amplitude is represented by the coefficient, which in this example is -2. Hence, the function's amplitude is 2.

The equation T = 2/, where is the angular frequency, yields the period of the function. The angular frequency of a sine function is given by = 2/T.

With the function f(x) = -2sin(x) substituted, we get:

ω = 2π/T

Sin(x + ) = -2sin(x)

To solve for T, we obtain:

T = 2π/ω = 2π/(-2) = -π

We use T's absolute value as the period cannot be negative, making the function's period T =.

As a result, the function's amplitude is 2 and its period is.

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Therefore, the area of triangle XYZ is (1/2)bh = (1/2)(15)(15√3) = 225√3. Therefore, the area of triangle XYZ is 225√3.

Triangle is a three-sided polygon that has three angles and three sides. It is one of the basic shapes in geometry and is a very important concept in mathematics. It is also used in various fields, such as physics and engineering. Triangles can be classified into different types, such as right triangles, isosceles triangles, acute triangles, obtuse triangles, and equilateral triangles. Triangles are also used to form polygons, such as quadrilaterals, pentagons, and hexagons.

To find the area of triangle XYZ, we must first calculate the length of each side of triangle XYZ. The length of each side can be determined by multiplying the length of each side of triangle ABC by five.

Since all three sides of triangle ABC are equal in length, then each side of triangle XYZ will be 5 times the length of triangle ABC. Therefore, the length of each side of triangle XYZ is 5 times the side length of triangle ABC, or 15.

The area of the triangle can be calculated using the Triangle Area formula, A = (1/2)bh, where b is the base of the triangle and h is the height of the triangle. Since we know the length of each side of triangle XYZ, we can use these values to calculate the base and height of the triangle. The base of the triangle is 15, and the height of the triangle is 15√3.

Therefore, the area of triangle XYZ is (1/2)bh = (1/2)(15)(15√3) = 225√3. Therefore, the area of triangle XYZ is 225√3.

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Answer:

Below

Step-by-step explanation:

.385 liters =  385 milliliters  

   SIX of these would be   385 ml * 6 = 2310 ml

Mrs. Tempio can squirt 4 times as far as Zacarias can, therefore if Zacarias can only squirt 20 metres, Mrs. Tempio can squirt 4 * 20 = 80 metres.

Let's break down the issue to see why. We are aware of Zacarias' 20-meter squirt distance as well as Mrs. Tempio's 4-times-greater squirt distance. Thus, if we write up the following equation and assume that x is the that Mrs. Tempio may squirt:

x = 4 * 20

When we simplify this equation, we obtain:

x = 80

Mrs. Tempio can squirt 80 metres as a result.

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Answer:

A. 0.34

Step-by-step explanation:

  1.7

x 0.2

_____

   .14

+ .20

______

.34

1. Patrick makes more per hour by $6.

2. Betthany makes more per hour by $5.25

3. Tommy makes more per hour by $ 1.25.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

The rate of Change of Critters and Co

Slope= Rise/ Run

        = 15/2

        = 7.5

So, the equation is y = 7.5x

and, rate of Change of Little Paws

= (52.50-35) / (6-4)

= 17.5 / 2

= 8.75

So, the equation is y = 8.5x + 5

and, rate of Change of The Waging Tail

= 8.25

1. Patrick makes more per hour by $6.

2. Betthany makes more per hour by $5.25

3. Tommy makes more per hour by $ 1.25.

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Answer: The first box in the model is 60. The box above it is 300. The box above 20 is 70. The answer is 74.

Step-by-step explanation: Self-explanatory.

The probability of getting sum of 6 is C)5/36.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We know that,

Probability of event = number of favorable outcome/ Total outcome

When a 6 sided dice die twice then

Total number of outcome = 6*6=36

Favorable outcome is a sum of 6, Ways of obtaining a sum of 6

(1,5), (5,1), (2,4),(4,2) and (3,3). Thus, there are 5 ways in which 6 can be obtained using  rolling dice twice, Then

=> P(sum of 6 )=5/36

Hence the correct option is C)5/36.

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Answer:

58

Step-by-step explanation:

9x + 22                        x = 4

9(4) + 22

36 + 22

58

Answer:

50 % possibility or 1/2 chance

Step-by-step explanation:

2, 4, 6, 8, 10, 12, and 14 are all even and there are seven of them

21 is  the value of f(g(2)) in functions.

What is a function, exactly?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Mathematics is rife with functions , and the sciences depend on them for constructing physical relationships.

f(x) = 2x² + x - 13

g(x) = x - 6

the value of f(g(2))

   g(2) = 2 - 6

          = -4

   f(g(2)) =  2x² + x - 13

               = 2(-4)² + 2 - 13

              = 32 - 11

               = 21

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answer is 14.

4-(2*-5)

4-(-10)

=4+10

=14.

Answer:

Step-by-step explanation:

[tex]\tt 4-2(-5)[/tex]

Follow the PEMDAS order of operations:-

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

1) Multiply and/ or divide:-

[tex]\tt 4 -\left(-10\right)[/tex]

2) Addition/Subtraction:-

_____________________

Hope this helps! :)

The multiple of the unit fraction 3/8​ is 15/40.

What is fraction ?

A fraction is a number that represents a part of a whole. It is a way of representing a quantity that is not a whole number. Fractions are written with two numbers, one above the other and separated by a horizontal line. The number above the line is called the numerator, and the number below the line is called the denominator.

To find the multiple of a fraction, you simply multiply the numerator and the denominator by the same number. For example, to find the multiple of 3/8, you can multiply both the numerator and the denominator by 2:

3/8 * 2/2 = 6/16

So the multiple of 3/8 by 2 is 6/16.

Similarly, you can find the multiple of 3/8 by any other number by multiplying both the numerator and denominator by that number. For instance, if you want to find the multiple of 3/8 by 5, you can multiply both the numerator and the denominator by 5:

3/8 * 5/5 = 15/40

Therefore, the multiple of the unit fraction 3/8​ is 15/40.

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Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.

You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. Variable x in the preceding example is equivalent to 6, as 6 + 6 = 12. We can substitute our variables with their values before evaluating the expression if we are aware of their values.

To evaluate the expression for w = 1/2, we substitute w = 1/2 into the expression:

w + 1/2w + 2

= 1/2 + 1/2(1/2) + 2 (substitute w = 1/2)

= 1/2 + 1/4 + 2 (simplify multiplication)

= 9/4 + 2 (convert 1/2 to 2/4 and add fractions)

= 17/4 (add fractions)

Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.

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There is a 2.28% chance that more than 250 books were borrowed in a week.

Probability can also be calculated using other methods, such as counting techniques and probability distributions. Probability distributions provide a way to model the behavior of random events and describe the likelihood of different outcomes occurring.

Probability has many applications in fields such as statistics, finance, engineering, and science. It is used to make predictions, analyze data, and make decisions based on uncertain information. Understanding probability is an important skill for many professions, as it allows individuals to make informed decisions and assess risk.

To solve this problem, we need to use the standard normal distribution and calculate the z-score.

First, we find the z-score:

z = (x - μ) / σ

z = (250 - 190) / 30

z = 2

We can then use a standard normal distribution table or calculator to find the probability of getting a z-score of 2 or higher.

Using a standard normal distribution table, we find that the probability of getting a z-score of 2 or higher is approximately 0.0228.

To convert this to a percentage, we multiply by 100:

0.0228 x 100 = 2.28%

Therefore, there is a 2.28% chance that more than 250 books were borrowed in a week.

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The complete question is:

The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week.

The result is not reasonably close to the value of 3/4 i.e. 0.75.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability of getting a green pea can be estimated by dividing the number of green peas by the total number of peas:

probability of green pea = number of green peas / total number of peas

In this case, the number of green peas is 439 and the total number of peas is the sum of the green and yellow peas, which is:

total number of peas = number of green peas + number of yellow peas

= 439 + 30 = 469

Therefore, the probability of getting a green pea is:

probability of green pea = 439 / 469 ≈ 0.935 or 93.5%

So, the estimated probability of getting an offspring pea that is green is approximately 93.5%.

The result is not reasonably close to the value of 3/4 i.e. 0.75.

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Answer:

Step-by-step explanation:

a. Variables:

D0 = Demand for nurses in 2000 = 2,000,000

S0 = Supply of nurses in 2000 = 1,890,000

D2020 = Projected demand for nurses in 2020 = 2,810,414

S2020 = Projected supply of nurses in 2020 = 2,001,998

Equations:

For 2000: D0 = S0

For 2020: D2020 = S2020

b. Using substitution, we can set the two equations equal to each other:

D0 = S0

2,000,000 = 1,890,000 + m(S0 - 1,890,000) (where m is the rate of increase in supply)

m = 0.063

Now we can use this value of m to find out during which year the supply of nurses was equal to the demand:

2,000,000 = 1,890,000 + 0.063(S - 1,890,000)

S = 2,013,008

Therefore, the supply of nurses was equal to the demand in the year 2013.

Answer:

river c is 2965 miles long while river d is 2565 miles long

Step-by-step explanation:

c+d=5530

400+d+d=5530

400+2d=5530

2d=5530-400

2d=5130 /:2

d=2565

c=d+400

c=2565+400

c=2965