A triangle has sides with lengths that are

consecutive even integers. The perimeter of the

triangle is 72 centimeters. Sketch the triangle

and label the lengths of the sides, using the

variable. Find the length of the largest side.




Show work

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:

d which implies m/3 + 5 = 9

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:

The domain of a logarithm function is (0, ∞). The range of the logarithm function is all real numbers.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is f(x) = log x.

When the value of x is less than or equal to 0, then the value of log x is undefined.

The possible value of x where f(x) exists is the domain of a function.

In the given function the value of x must be greater than zero.

The domain of the function is (0,∞).

log (0.1) = -1

log (0.023) = -1.638

The value of log x can be any real number.

The possible value of the logarithm function is any real number. Thus the range of the function is (-∞, ∞).

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Answer:

Step-by-step explanation:

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 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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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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Answer:

Mary bought the most flour

Step-by-step explanation:

Ana bought 12 3/6 kg of flour

12 3/6 = 75/6 = 12.5 kg of flour

Mary has brought 14 2/8 kg of flour

14 2/8 = 114/8 = 14.25 kg of flour

Kristina bought 11 8/12 kg of flour.

11 8/12 = 140/12 = 11.66 kg of flour

So, Mary bought the most flour.

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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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

Answer:

25

Step-by-step explanation:

Given expression:

[tex]5^{1125} \times 0.2^{1123}[/tex]

Rewrite 0.2 as a fraction:

[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]

Simplify the numerator by applying the exponent rule a¹ = a:

[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]

[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]

[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]

[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 5^{1125-1123}[/tex]

Simplify the exponent:

[tex]\implies 5^{2}[/tex]

Simplify:

[tex]\implies 5 \cdot 5[/tex]

[tex]\implies 25[/tex]

Answer:

0.04 < 0.1 < 1/6

Step-by-step explanation:

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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Answer:     [tex]\frac{3}{8}[/tex]➗[tex]\frac{3}{4}[/tex]

Step-by-step explanation:  Are you looking to work out and calculate how to multiply 3/8 by 3/4? In this really simple guide, we'll teach you exactly what 3/8 times 3/4 is and walk you through the step-by-process of how to multiply two fractions together.

Answer: 1. The first graph has the x and y axis values as minutes and frequency, but the title is bicycling.

2. it's a dotted graph, which doesn't give enough information since that graph does not have to be linear, but when you have a graph like that you want a line graph.

Answer:

the other dude answered it better than i did

Step-by-step explanation:

A function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Given an equation y = 14x -4 there is an equation that is perpendicular to this given equation.

from the slope-intercept of a linear equation:

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

thus the slope of the given equation is 14

The slope of the required equation = 1/14

Since both equations are perpendicular

From the slope intercept of the required line equation of a line:

y = 1/14x + c...(2)

Since, it passes through the point (28, 16)

Thus, 16 = 1/14 *28 + c

c = 16

from equation 2

y = 1/14 x + 14

from the table, two given coordinates of a linear function are (4, 36) and (6, 56)

thus slope of the line = (y₂ - y₁) / (x₂ - x₁)

Slope of the line = 20/2 = 10

Equation of a line:

y = 10x +c

Since, it passes through the point  (4, 36)

Thus, 36 = 40 + c

c = -4

Therefore, the required equation from the table is y = 10x - 4

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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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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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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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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.

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

Answer:

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

The distance between points L and K is 4 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is gien by,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, Are two points L and K.

The coordinate points of L(- 2, 6) and K(- 2, 2).

Therefore, The distance between points L and K is,

[tex]|LK| = \sqrt{(- 2 + 2)^2 + (2 - 6)^2}[/tex].

[tex]|LK| = \sqrt{16}[/tex].

[tex]|LK| = 4[/tex].

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Answer:

-4.3

Step-by-step explanation:

It is asking for the temperature at midnight so to find out what it is. We simply subtract the starting temperature of 11.4f from 15.7 degrees

( 11.4 - 15.7 ). That would leave us with -4.3f at night.

When 392,196 is divided by 87, the answer obtained using long division is 4,508.

The mathematical procedure for splitting big numbers into several smaller groups or sections is known as long division. The dividend is the number we divide into smaller groups, while the divisor is the number through which we divide. Difficulty difficulty can be solved by breaking it down into manageable parts.

Dividend : 392,196

Divisor: 87 (number that divides)

39 / 87 = 0

392 / 87 = 4 (87x 4 = 348) - 4 is the first digit of the result

392 - 348 = 44 (remainder)

441 (next digit is one) / 87 = 5 (87x 5= 435) - 5 is the second digit

441-435 = 6 (remainder)

69 / 87 = not possible so add a 0, which is the third digit

696 / 87 = 8 (87x 8 = 696)

696- 696 = 0 (not remainder)

When 392,196 is divided by 87, the answer obtained using long division is 4,508.

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I understand that the question you are looking for is:

392,196 divided by 87 (Using long division)

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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