Choose three true statements about the angles of the figure

1: Z1 and the 55* angle are adjacent

2: mZ1=55* because Z1 and the 55* angle are vertical angles

3: mZ2=125* because Z2 and the 55* angle are supplementary

4: mZ2 cannot be determined from the information

5: mZ1=180*-55*

6: mZ2=180*-55*-45*

Answer: There are 30 cubes in each layer and 3 layers. (Up to down.)

Explanation: You can multiply the x and y axis for one layer, and then count how many layers there are. There are 90 cubes in all.

I hope this helps, have a good day!

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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On solving the provided question, we can say that by unitary method Irene spend on gas =  $ 33.82

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method

Irene must pay back the money she used for gas.

Irene filled up her tank with gas for $33.82.

One gallon of gasoline costs $3.80.

There are 6.1 gallons of the petrol Irene purchased in the tank.

amount required = 15 -6.1 = 8.9 gallons

1 gallon = 3.8 dollars

8.9 gallons = $ 33.82

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Answer: No, the statement "if f(x)= x² (x≠2), then lim f(x) =4" is not correct. The limit of a function is a value that the function approaches as the input (in this case, x) gets closer and closer to some specific number. In this case, the limit of f(x) as x approaches 2 would be 4, since f(x)=x² for all values of x other than 2. However, if you ignore the x≠2 restriction and consider all values of x, then the limit of f(x) as x approaches 2 would be undefined, since f(x)=4 for x=2.

Step-by-step explanation:

Mai uses 10 ounces of cheese to make 4 pizzas, so she uses 10/4 = <<10/4=2.5>>2.5 ounces of cheese per pizza.

To make 15 pizzas, she will need 152.5 = <<152.5=37.5>>37.5 ounces of cheese.

The proportion and percentage is as follows;

[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]

A percentage represents a ratio or fraction with a denominator that is always 100 as opposed to a proportion, which asserts the equivalent of two ratios or fractions.

Given

[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & & \\ 5-6 & 50 & & \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]

To estimate the total frequency:

Total = sum f

Total = 29 + 53 + 50 + 22 + 1

Total = 155

The proportion (p) exists calculated by:

[tex]$p = \frac{f}{\text { Total }}[/tex]

The percentage (P) exists calculated by:

P = p × 100 %

For interval 7 - 8, we have:

p = 53 / 155 = 0.34

P = 0.34 × 100 % = 34 %

For interval 5 - 6, we have:

p = 50 / 155 = 0.32

P = 0.32 × 100 % = 32 %

So, the complete table is:

[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]

The complete question is:

A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs.

Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages.

Score Interval f Proportion Percentage

9â10 29 0.19 19%

7â8 53

5â6 50

3â4 22 0.14 14%

1â2 1 0.01 1%

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The Slope of log - log graph  represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .

What is Logarithm ?

The Logarithm is defined as  power to which a number must be raised to get some other number .

A log-log plot is the plot in which  both the x-axis  and y-axis use a log scale.

The plot of  logarithms of variables helps in extracting  the information about the power relationship. The case of  freely falling object is  used to illustrate a log - log plot.

A plot of the logarithm of freefall distance as a function of logarithm of time gives  a straight line of slope 2.

Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.

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Answer:

d which implies m/3 + 5 = 9

Answer:

Step-by-step explanation:

The ratio of the new area to the old area is 16:1. The correct option is the second option

From the question, we are to determine the statement that is true about the area of the circle.

First, we will determine the old area

Using the formula for calculating the area of a circle

A = πr²

Where A is the area

and r is the radius

From the given diagram,

r = 6 ft

Thus,

Old area = π × 6²

Old area = 36π ft²

Now,

If the radius is quadrupled

That is,

r = 4 × 6 ft

r = 24 ft

The new area will be

A = π × 24²

A = 576π ft²

The ratio of the new area to the old area is

576π ft² / 36π ft²

16 /1

= 16 : 1

Hence, the ratio is 16:1

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The best estimate for the circumference of a circle with 3 units radius is equal to 18 units. The correct option is A.

Given the radius of the circle is equal to 3 units.

The formula for the circumference of the circle is equal to

[tex]C=2*\pi *r[/tex].

By substituting the value of the radius and pi we will get:

[tex]C=2*3.14*3\\C=18.86[/tex].

Therefore the best estimate will be 18 units.

Complete question:

Which is the best estimate of the circumference of this circle?

radius = 3 units.

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If the total charge for yogurt is dependent on the base price of the bowl of yogurt plus the number of toppings added, the value of y at the y-intercept of the line representing this situation is  C $4.00

The y-intercept of a line is the point where the line crosses the y-axis. In this case, the y-intercept is the cost of the bowl of yogurt without any toppings. The base price of the bowl of yogurt is $4.00, so the y-intercept of the line representing this situation would have a value of $4.00.

This means that the cost of a bowl of yogurt without any toppings is $4.00. The cost of the bowl of yogurt with toppings is determined by adding the cost of the bowl of yogurt plus the cost of the toppings. Therefore, the y-intercept of the line representing this situation would have a value of $4.00.

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Answer:

B

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 2 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes

then slope of parallel line is 3

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (3, 5 ) , then

y - 5 = 3(x - 3) ← equation of parallel line in point- slope form

The option that is not true about cluster sampling is option  A: Cluster sampling has the advantage of reducing sampling variability.

Cluster sampling often leads to larger sampling variability than other types of sampling methods, such as simple random sampling or stratified sampling, because clusters may not be a representative sample of the population and the individuals within a cluster may be more similar to each other than to individuals in other clusters.

Therefore, This increases the chance that the sample will not be representative of the population, which can result in a higher level of sampling error.

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On solving the provided question, we can say that by  linear equation 10/3 pounds of peanuts and how many pounds of raisins should you use.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here,

the linear equation that is formed is  

10p +7 (10 - p) = 80

10p + 70 - 7p = 80

3p = 70

p = 10/3

10/3 pounds of peanuts and how many pounds of raisins should you use

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Probability measures how probable something is to occur.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

Probability is a measure of how likely something is to happen.

18 Marines, 10 Navy personnel, and 3 Coast Guard troops received their wings at a recent naval aviation school graduation.

Total: 18 + 10 + 3 = 31

a. 1 of each.  P = C 18 * C 10 * C 3  / C 3 31  

= (18 * 10 * 3) / 4495 = 0.120

b: 0 members of the navy = (C_{21} ^ 3)/(C_{21} ^ 3) = 1330/4495 = 0.296

c: 3 Marines.

p = (G ^ 3)/(C_{31} ^ 3) = (8 + 6)/4495 = 0.182

The complete question is

At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be

a.1 of each 0.120  b.  members of the Navy 0.296 c.  Marines 0.182.

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The value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]2[/tex]

The given equations are

                        [tex]6x+y=20\\x-4y=-5[/tex]

We need to find the value of [tex]x[/tex] and [tex]y[/tex]

First let's take equation [tex]2[/tex]  and we can simplify it

                                 [tex]x-4y=-5\\x=-5+4y[/tex]

Now, let's substitute the value of [tex]x[/tex] in equation [tex]1[/tex], that is

                     [tex]6x+y=20\\6(-5+4y)+y=20[/tex]

We can open the bracket and simplify

                       [tex]=-30+24y+y=20\\=-30+25y=20\\=25y=20+30\\=25y=50\\=y=\frac{50}{25} \\y=2[/tex]

Now we can substitute the value of [tex]y[/tex] in equation [tex]x-4y=-5[/tex]

                       [tex]x-4(2)=-5\\x-8=-5\\x=-5+8\\x=3[/tex]

The complete question is find the value of [tex]x[/tex] and [tex]y[/tex] from the given equations.

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The y-intercept of the line y = 7x -38 is -38. And the x-intercept is 0

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The equation of the line,

y-4=7(x-6)

Simplify,

y -4 = 7x - 42

y = 7x -38

And slope-intercept form:

y = mx + b,

where m is the slope and y is the intercept.

Comparing with the slope intercept form,

we get,

m = 7 and b = -38

And the x-intercept is 0

Therefore3, y-intercept is -38.

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By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 8 equal parts we can graph 3/4 on the number line, where 3/4 = 6/8, which will be equal to the sixth part from the left end.

A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

For drawing 3/4 on a number line, we will follow the following steps:

We will first draw a line and mark 0 and 1 on it.

In between 0 and 1, we will divide the total distance into 8 equal parts, where one part will represent (1/8)th portion.

As 3/4 can be written as 6/8 which will be equal to 6 parts out of those 8 parts.

Hence. by marking there we can locate 3/4 on the number line.

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The correct question should be like:
How do you plot 3/4 on number line

The slope of the linear equation that passes through the two given points is 1/7.

A general linear equation can be written in the slope-intercept form as:

y = a*x + b

Where the coefficients are:

a: the slope.

b: the y-intercept.

If a line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is equal to:

a = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that the line passes through (-10, -9) and (-3, -8), then the slope of this linear equation will be:

a = (-8 + 9)/(-3 + 10) = 1/7

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Answer:

A. x>-6

Step-by-step explanation:

x-11<2x-11+1+5

x-2x<-11+1+5+11

-x<6 (Now multiply by - )

x>-6

Answer:

0.04 < 0.1 < 1/6

Step-by-step explanation:

The probability of choosing a trix bar then a crunch bar exists 8/45.

Mathematics' field of probability deals with numerical assessments of how likely an event is to occur.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

Probability = Number of favorable outcome / Number of total outcome

Given,

Number of snicker bars = 2

Number of trix bars = 8

Number of crunch bars = 5

Total number of candy bars = 2 + 8 + 5 = 15

8 trix, so picking a trix would be 8/15

5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3

Probability of both: 8/15 x 1/3 = 8/45

Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.

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The probability of choosing a trix bar then a crunch bar exists 8/45.

Probability theory deals with numerical evaluations of the likelihood that an event will occur.

Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.

A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.

Probability = Number of favorable outcome / Number of total outcome

Given,

Number of snicker bars = 2

Number of trix bars = 8

Number of crunch bars = 5

Total number of candy bars = 2 + 8 + 5 = 15

8 trix, so picking a trix would be 8/15

5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3

Probability of both: 8/15 x 1/3 = 8/45

Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.

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Answer:

c is the independent variable and f is the dependent variable

Step-by-step explanation:

The height of the flag is 18 feets.

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Length is equal to 2 (2 + 3) the sum of the side lengths.

The sum of side length divided by (12) equals (2/5)

12 = 0.4(sum of side length) (sum of side length)

divide both sides by 0.4.

The height of the flag is calculated as side lengths plus length.

Height of flag: (30 – 12) = 18 feet

Therefore, the height of the flag is 18 feets.

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The value of 8(x + 7) is 8x + 56.

The value of 6(11 + x) is 66 + 6x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The distributive property of  multiplication over addition states that,

a x (b + c) = a x b + a x c

Now,

8 x (x + 7)

= 8 x (x) + 8 x 7

= 8x + 56

6 (11 + x)

= 6 x 11 + 6 x (x)

= 66 + 6x

Thus,

The value is 8x + 56 and 66 + 6x.

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Answer:

each book cost=222-15=207/9=22.88 dollar

The triangle ABC, along with it's image after the reflection x = -3, is given on the graph presented at the end of the answer.

The coordinates for the original vertices of the triangle are given as follows:

A(-5, -6), B(-4, -3) and C(-3,-7).

The reflection line is given as follows:

x = -3.

The reflection lines is a vertical line, meaning that for the reflected triangle, the y-coordinate remains constant, while the x-coordinate means that the triangles will be on the same distance relative to the reflected line, however on the opposite direction.

Vertex A has a x-coordinate two units left of x = -3, hence the coordinates of the image will be two units right, hence:

A'(-3 + 2, -6) = (-1, -6).

Vertex B has a x-coordinate one unit left of x = -3, hence the coordinates of the image will be one unit right, hence:

B'(-3 + 1, -3) = B'(-2,-3).

Vertex C remains at the same position, as it has a x-coordinate of -3.

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The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.

The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.

Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.

Given that ΔAED ≈ΔBEC & AC = BD.

as  ΔAED ≈ΔBEC, AD = BC     .................(1)

Now in  ΔABD and ΔBAC,

     AD = BC        

(corresponding sides of similar triangles) [from (1)]

     AB = AB        

(common side)

     AC = BD      

   (given)

∴     ΔABD ≈ΔBAC  (By SSS criteria)    

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