Which pairs of triangles are similar? check all that apply. â–³abc ~ â–³def â–³def ~ â–³ghi â–³ghi ~ â–³abc â–³ghi ~ â–³jkl â–³jkl ~ â–³abc

(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

A scatter plot is a graph of the given points or given data.

(a)

To make a scatter plot of the data, plot the points (x,y) on a graph.

To draw the line of fit, draw a line such that the distance between the line and the plotted points is minimum.

(b) The line passes through points (7.3,0)and (0,18).

The equation of the line is given by:

[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]

Substitutes the points (x₁,y₁) = (7.3,0) and (x₂,y₂)=(0,18) into the above equation:

[tex]y-0=\frac{18-0}{0-7.3}(x-7.3)\\y=-2.5(x-7.3)\\y=-2.5x+18.3[/tex]

(c) The slope of a line of the form y=mx+c is m.

Therefore, the slope of the line y=-2.5x+18.3 is m = -2.5.

The slope indicates the change in y with respect to the change in x.

Therefore, the slope -2.5 indicates that the gamer losses 2.5 every week after getting a new game.

Hence,

(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

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The percentage increase in the area of the building from its initial space is 35% of the increase. Hence, option A is correct.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the data provided in the question,

The initial area of the building = 12,500

Increase in area of building = 16875

The percentage increase in the area will be,

% increase = (16875 - 12500)/12500 ×100

⇒  4375/12500 × 100

% increase = 35%

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Answer:

p = -1 ; p= 3

Step-by-step explanation:

10p^2 - 20p - 34 +4 = 0

10p^2 -20p - 30 = 0

10/10 p^2 - 20/10 p - 30/10 = 0

p^2 - 2p - 3 = 0

(p-3)(p+1) = 0

p = 3

p = -1

Answer:

b = 3

Step-by-step explanation:

Given that,

→ a = 27

Forming the equation,

→ 27 = 3b²

Now the value of b will be,

→ 27 = 3b²

→ b² = 27/3

→ b = √9

→ [ b = 3 ]

Hence, the value of b is 3.

⇒Given that a=27 in the equation [tex]a=3b^{2} \\[/tex] in the place of a plug in 27 and solve for b

[tex]27=3b^{2} \\\frac{27}{3} =\frac{3b^{2}}{3} \\b^{2} =9\\b^{2}-9=0\\(b+3)(b-3)=0\\b+3=0\\or\\b-3=0\\b=-3\\or\\b=3[/tex]

⇒Note b can also be -3 but the only option available as the answer is 3

∴ b=3 in this case.

For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.

Graph is attached.

As given in the question,

Given equation is equal to :

4x + 3y = 21

To get the slope intercept form of the given equation we have,

Subtract 4x from both the sides of the given equation we have,

4x + 3y - 4x = 21 - 4x

⇒ 3y = 21 - 4x

Now divide by 3 on both the sides of the equation we get,

3y / 3 = (-4/3)x + (21/3)

⇒ y = (-4/3) x + 7

Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.

When x = 0 ⇒ y = 7

y= 0 ⇒ x = 21 /4

Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by  y = (-4/3)x + 7.

Graph is attached.

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The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) the change in temperature in the house.

The heater turns on when the house is 4° below the set temperature and turns off when the house is 4° above the set temperature. The temperature is set at 68°. At 10:15 am the heater turns on, and at 10:30 am the heater turns off.

Temperature fluctuations can be modeled using the sine and cosine functions throughout the day.

The equations that can be used to model these data is of the form:

At 10:30 am the heater turned off,

⇒ 4° = A cos B(x - C)

At 10:15 am the heater turned on,

⇒68° = A cos B(x - C)

where A, B, and C are constants, y is the temperature in °C and x is the time

Thus, The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) is the change in temperature in the house.

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Answer: D

Step-by-step explanation: Took the test

Marsha deposited $5500 into savings with 5% interest rate

1st year, Marsha will earn : [tex]0.05 \times 5500 = 275[/tex]

2nd year, Marsha will earn: [tex]0.05 \times 5775 = 288.75[/tex]

3rd year, Marsha will earn: [tex]0.05 \times 6063.75 = 303.19[/tex]

4th year, Marsha will earn: [tex]0.05 \times 6366.94 = 318.35[/tex]

Answer:

Step-by-step explanation:

Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9

Using the concepts of probability, we got that that Stratified sampling is the experiment design which an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs.

In the question, actually the insurance company intends to study and understand the relationship between the health care cost of the customers and the provision of incentives for the preventative care by two groups, each having one of  two given attributes under study, which are;

a) One group consist of the customers having high health care cost and offered incentives for preventative care

b) The other group consist of the customers having only high health care cost without incentives

Therefore, the insurance company customers are stratified into the groups based on health care cost and again into the groups that have high health care cost and are offered preventative care and those that have only the high heath care cost, which is the process used to implement the stratified sampling technique.

Hence, an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs, by selecting a random sample of 200200200 of their customers and using a random number generator to select 100100100 customer account numbers to offer the incentive, the experiment design is named as  Stratified sampling.

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The length of the line segment MN given that the ratio of KL:LM:MN = 2:3:1 is; 9

We are told that the points K, L, M and N all lie on the same line segment.

Since the points lie on the same line segment, then it means that they are collinear points.

We are told that the ratio of the segments, KL:LM:MN = 2:3:1.

This means that we can find the length of MN since we are also given the total length of the whole segment, KN = 54.

Length of MN = (Individual ratio of MN ÷ the total ratio value of the 3 given segments) × length of the whole segment

Individual ratio of MN = 1

Total ratio value of the 3 given segments = 2 + 3 + 1 = 6

Length of whole segment, KN = 54

Length of MN = (1/6) * 54

Length of MN = 9

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The equation of the line is y=3x-2 where the slope is 3 and the y-intercept is -2.

A diagrammatic depiction of a set of facts is called a graph, chart, or diagram.

Graphs need to be accurate and effective in communicating information. They ought to be legible at different computer screen resolutions. Graphs should ideally be pleasing to the eye.

Please be aware that the terms graph, chart, and diagram can be imprecise and are sometimes used synonymously.

Graphs need to be accurate and effective in communicating information. They ought to be legible at different computer screen resolutions.

Given,

Slope m=3

y-intercept (c)=-2

The slope-intercept form is given as

y=mx +c

Therefore, y=3x-2

The equation of the line is y=3x-2 where the slope is 3 and the y-intercept is -2.

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The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.

Recall that the roots of quadratic equations are given by the formula;

x = {-b ± √(b² - 4ac)} / 2a

Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.

Therefore, the roots are as follows;

x = {-3 ± √(3² - 4•1•-5)} / 2(1)

x = (-3 ± √29)/2

Therefore, the required roots are;

x = (-3 + √29)/2 and x = (-3 - √29)/2

Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

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the quotient as a power. a^21/a is a^20.

What is Power?

In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.

What is quotient?

The number we obtain when we divide one number by another is the quotient.

What is exponential function?

An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Given that,

a^21/a

quotient as power = a^21/a

                             =  a^(21-1)

                             = a^20

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the required sample size for the interval estimate with a 95% level of confidence  is 385

since we are given the margin of error which is f $10 and a standard deviation which is $1,000,  and we are also given the level of confidence which is 95%

so the formula we are  referring to calculate the sample size is :

n=z(0..95)*s²/ E

here, E is the margin of error, S is the standard deviation

so z score of 0.95 is 1.96

so n = 1.96*1000^2/100

        = 384.16 ,which is almost 385

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The amount of pasta and sauce since he wants each bag to have the same amount is 16.

A factor simply means a number that can multiplied with another number which is also.a factor to get the original number.

In this case, Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive.

It should be noted that to get the number in each bag, it means that we have to find the highest common factor for both numbers. This will be:

Factors of 32 = 1, 2, 3, 4, 6, 8, 16 and 32

Factor of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Therefore, the answer is 16.

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The required diameter of the circle is given as 15 in. Option B is correct.

Given that,
The circumference of a circle is given 47.1 in, we have to determine the diameter of the circle.

Perimeter is the measure of the figure on its circumference.

Here,
As per the given condition,
First, write the formula for the circumference of the circle,
Circumference of the circle = πD
now substitute the value in the above equation,
47.1 = 3.14 D
D = 47.1/3.14
D = 15 in

Thus,  the required diameter of the circle is given as 15 in. Option B is correct.

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Total( as there is addition) feet walked by Lola is 29.25 +1.5x for the given equation.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.

Main body:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Hence Total feet walked by Lola is 29.25 +1.5x for the given equation.

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The p - value is d ) a probability .

Defining P - Value

P - Value : It is the probability of obtaining results at least as extreme as the  observed results of a statistical hypothesis test , assuming that the null hypothesis is correct . The p - value does not , in itself , establish probabilities of hypotheses . Rather , it is a tool for deciding , whether to reject null hypothesis or not .

A smaller p - value means that there is stronger evidence in favor of alternative hypothesis .

Hence , the p - value is d ) a probability .

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The number of ride tickets that were sold are 8 and the number of food tickets that were sold  are 24  .

In the question ,

it is given that

total number of tickets bought by the family at carnival = 32 tickets

total amount spent by the family of tickets = $90

let the number of ride tickets be [tex]=[/tex] x

let the number of food tickets be [tex]=[/tex] y

So , x + y = 32

x = 32 - y

cost of 1 ride ticket = $1.50

cost of 1 food ticket = $3.25

So the total cost is 1.25x + 3.25y = 90

Substituting x = 32 - y in the equation 1.5x + 3.25y = 90 ,

we get ,

1.5(32 - y) + 3.25y = 90

48 - 1.50y + 3.25y = 90

1.75y = 90 - 48

1.75y = 42

y = 24

So , x = 32 - 24 = 8

Therefore , The number of ride tickets that were sold are 8 and the number of food tickets that were sold  are 24  .

The given question is incomplete , the complete question is

A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets store. How many of each type of ticket were sold ?

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Answer:

[tex]-3[/tex]

Step-by-step:

[tex]8+ (-3) + (-8)[/tex]

1  ) Combine like terms...

[tex]=5 - 8[/tex]

2 ) Solve...

[tex]= - 3[/tex]

Hope this helps! :)

Answer:

3/5x 150

= 450/5

= 90

150+90

= 240 ans

Answer:

triangle CBA is congruent to triangle CDA

The triangles are not congruent

There will be infinite number of states and paths when the state space is (x,y) as the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane.

The collection of every possible setup for a system is its state space. It is a common abstraction in the study of artificial intelligence and game theory because it can be used to reason about the behavior of a specific system. A state space is typically introduced into a system description without being given any thought to its precise physical meaning. However, it is well known that choosing an appropriate state space representation makes it simpler for us to comprehend or control a system's property.

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Answer:

Reflection

Step-by-step explanation:

Reflection is like looking at yourself through a mirror, so it would be the same for sound.

Tell me if this is correct.!

Answer:

Reflection

Step-by-step explanation:

i took this quiz

The slope Using the formula will be h = -100t + 4000

This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.

If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.

If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.

Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:

h = -100t + 4000 which appears to be choice a.

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The correlation coefficient can be used to get a better understanding and to determine the extent of a strong relation between two variables.

In a statistical setting, two or more variables are said to be connected if their values fluctuate in such a way that as the value of one variable rise or falls, the value of the other variable does the same (although it may be in the opposite direction).

For instance, there is a relationship between the two variables "hours worked" and "revenue earned" if a rise in hours worked is correlated with an increase in income earned. When considering the two factors "price" and "purchasing power," the ability of a person to purchase items reduces as the price of those goods rises (assuming a constant income).

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The axis of symmetry is the line that is relative is vertical goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line that is relative the graph of a equation that is quadratic two mirror images.

Equation of the Axis of Symmetry of a Parabola:

The equation for the axis of symmetry of a parabola can be expressed as:

[tex]x=\frac{-b}{2a}[/tex]

Remember that every quadratic function can be written in the standard form [tex]y = ax^{2}+bx+c[/tex] . The graph of a quadratic function is called a parabola, where every point on that parabola represents an x and a y that solves the quadratic function.

The vertex of a quadratic function is the highest or lowest point on the graph. The coordinate of the vertex of the parabola, then, is the x and y solution for the lowest or highest point of the parabola.

Calculating the Axis of Symmetry of a Parabola:

Again, the axis of symmetry of the parabola is the line on the graph that passes through the vertex of the parabola and splits the graph into two symmetrical sides.

It is expressed as:

[tex]x=\frac{-b}{2a}[/tex]

Or x = -2 after you substitute in the values for a and b.

Finding the Vertex of a Parabola:

To find the actual coordinates for the vertex of the parabola, simply substitute the x value into the polynomial expression to find the corresponding y value. Remember, each point on the quadratic graph is a solution to the equation.

When we continue with the previous example, we know that x = -2.

We substitute that value for x in the original quadratic function.

[tex]y=x^{2} +4x+3\\y=(-2)^{2}+4(-2)+3\\ y=4+(-8)+3[/tex]

Solving it gives us y = -1. We now know that the vertex of the parabola is the coordinate (-2, -1). Finding the vertex of a parabola couldn’t be easier.

How To Find Axis of Symmetry?

Here's what you need to remember: Whether you’re after the axis of symmetry or the full coordinates of the vertex of the parabola, use this formula to start graphing a quadratic equation.

[tex]x=\frac{-b}{2a}[/tex]

Solving for x gives you the axis of symmetry. This line of symmetry will intersect with the parabola at its vertex, where x is the coordinate you just calculated and y is the coordinate when you substitute x back into the quadratic equation,

[tex]y = ax^{2}+bx+c[/tex].

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When binomial distribution is used, the probability that at least 275 rooms are occupied is 0.96

Option b. is correct

We have the following parameters:

sample, n=300

proportions of rooms reserved, p=6%

We first get the sample mean,

Sample mean=n*p

                       =300*6%

                        =18

Now, we get population mean according to binomial distribution, μ'

μ=n-sample mean

   =300-18

   =282

We get the standard deviation, σ

σ=(sample mean*(1-p))^1/2

 =(18*(1-6%))^1/2

 =4.11

We now, calculate z-score:

z=(x-μ)/σ, given x should be at least 275

z=(275-282)/4.11

 =-1.703

Now, we have p(x>275)=p(z>-1.703)

From z-score of probabilities, we have p(z>-1.703) as 0.95572

So, p(x>275)=0.95572

                    =0.96

Hence, the probability that at least 275 rooms are occupied is 0.96

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