unit 7 right triangle and trigonometry quiz 7-2

The set o rates that Frank could use to finish the events within 7.5 hours is (0.75 km/h, 25 km/h, 12.5 km/h).

To determine the rates at which Frank must complete each event to finish the triathlon within 7.5 hours, we can use the formula:

time = distance / rate

where;

Let x be the rate at which Frank completes the swim,

y be the rate at which he completes the bike ride, and

z be the rate at which he completes the run.

Then, we have the following three equations:

2.25 / x + 65 / y + 20 / z = 7.5

x > 0, y > 0, z > 0

We want to find the set of rates (x, y, z) that satisfy these equations and inequalities.

Here is one possible set of rates that would allow Frank to complete the triathlon within 7.5 hours:

x = 0.5 km/hour

y = 20 km/hour

z = 10 km/hour

Using these rates, we can calculate the time it would take Frank to complete each event:

Swim: 2.25 km / 0.5 km/hour = 4.5 hours

Bike ride: 65 km / 20 km/hour = 3.25 hours

Run: 20 km / 10 km/hour = 2 hours

The total time would be:

4.5 + 3.25 + 2 = 9.75 hours

This is greater than 7.5 hours, so Frank would need to increase his rates to finish within the time limit.

Here are some possible sets of rates that would allow him to do so:

x = 0.75 km/hour, y = 25 km/hour, z = 12.5 km/hour

x = 1 km/hour, y = 30 km/hour, z = 15 km/hour

x = 1.25 km/hour, y = 35 km/hour, z = 17.5 km/hour

Using any of these sets of rates, Frank would be able to complete the triathlon within 7.5 hours.

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If the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1.

This example belongs to a word problem.

What is the unit cost of each boxed lunch?

Given that;

27 boxed lunches from a deli cost $245.70

Cost of 1 box =?

To determine the unit cost of each boxed lunch, we say;

Cost of each box = $245.70 ÷ 27

Cost of each box = $9.1

Hence, if the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1

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After dilating the triangle abc about point a by a scale factor of 1/3, the length of new side length of ac' is equals to the 3 units.

Dilation is a transformation used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image of the same shape as the original. For a scale factor k, the algebraic representation of inflation is (x, y) → (kx, ky). Here we have a triangle abc with side length, ac = 9 units

side length, cb = 9 units

side length, ab = 7 units

remove triangle abc around point a, and

factor dilation scale = 1/3

We need to determine the length of the new side ac'. Dimensions of original shape, ac × scale factor = Dimensions of new shape, ac'

=> length of ac' = 9 units × 1/3

=> length of ac' = 3 units

Hence, required length is 3 units.

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Answer:

Part A 4 Part B 20 Part C C

there are total 28 balls. 1 / 7 = 4 balls.

a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).

b) The probability that the sum of the numbers drawn is 4 is 2/9.

c) The probability that the sum of the numbers is at least 4 is 2/3.

a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:

P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)

Hence, the probability space can be written as a set, S = {1,2,3}.

b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:

P = 2/9

c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:

(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)

Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3

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The mean of the given probability distribution is 0.2007.

The probability distribution table for the given scenario can be completed as follows:

| x | P(x) |
|---|------|
| 0 | 0.8036 |
| 1 | 0.1929 |
| 2 | 0.0036 |
| 3 | 0.0000 |

The probabilities are calculated using the hypergeometric distribution formula:

P(x) = (C(N-K, n-x) * C(K, x)) / C(N, n)

Where N is the total number of items (14), K is the number of items that are not correctly calibrated (2), n is the number of items selected (3), and x is the number of items that are not correctly calibrated in the selection.

For x = 0:

P(x) = (C(14-2, 3-0) * C(2, 0)) / C(14, 3) = (C(12, 3) * C(2, 0)) / C(14, 3) = (220 * 1) / 364 = 0.8036

For x = 1:

P(x) = (C(14-2, 3-1) * C(2, 1)) / C(14, 3) = (C(12, 2) * C(2, 1)) / C(14, 3) = (66 * 2) / 364 = 0.1929

For x = 2:

P(x) = (C(14-2, 3-2) * C(2, 2)) / C(14, 3) = (C(12, 1) * C(2, 2)) / C(14, 3) = (12 * 1) / 364 = 0.0036

For x = 3:

P(x) = (C(14-2, 3-3) * C(2, 3)) / C(14, 3) = (C(12, 0) * C(2, 3)) / C(14, 3) = (1 * 0) / 364 = 0.0000

The mean of this probability distribution can be calculated by multiplying each value of x by its corresponding probability and summing the results:

mean = (0 * 0.8036) + (1 * 0.1929) + (2 * 0.0036) + (3 * 0.0000) = 0.2007

Therefore, the mean of this probability distribution is 0.2007.

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The tangent function has asymptotes because it is defined as the ratio of the sine and cosine

The tangent function has asymptotes because it is defined as the ratio of the sine and cosine functions:

tan(x) = sin(x) / cos(x)

When the cosine function approaches zero, the denominator of the tangent function becomes very small, and the tangent function grows to infinity or negative infinity. Therefore, the tangent function has vertical asymptotes where the cosine function is equal to zero.

In contrast, the sine and cosine functions do not have vertical asymptotes because they are periodic functions that oscillate between -1 and 1. They do have horizontal asymptotes at positive and negative infinity, but these are not vertical asymptotes.

Note that the tangent function is not defined at the points where the cosine function is equal to zero because the division by zero is undefined. This also contributes to the existence of the vertical asymptotes in the tangent function.

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Solving a system of equations we can see that the correct option is A.

Here we can define the variables:

g = snacks in one pack of granola bars.

f = snacks in one pack of fruit rolls.

And we can write a system of equations like:

10g + 6f = 152

7g + 12f = 200

If we take the difference between two times the first equation and the second, we will get:

2*(10g + 6f) - (7g + 12f) = 2*152 - 200

13g = 104

g = 104/13 = 8

There are 8 snacks in a pack of granola, and with that value we can find f.

10g + 6f = 152

6f = 152 -10g

f = (152 - 10*8)/6 = 12

We conclude that the correct option is A.

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Answer:

Step-by-step explanation:

1 mile = 1609 meters

24 miles = 38624 meters

So, Adam drives 38624 meters.

The ratios for the similar triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The length of one side of one triangle is 4 times that of the corresponding side of the other, hence the constant of the proportional relationship for the side lengths is given as follows:

k = 4.

The perimeter is measured in units, just like the side lengths, while the area is measured in units squared, hence the ratios are given as follows:

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Answer:

Given as steps.

Step-by-step explanation:

Step 2: Opposite angles of a parallelogram are Equal
Step 4 ( After " Definition of a parallelogram"): Given
Step 5: ASA congruency Property / Therom
Step 6: CPCTC


P.S: It is ASA congruency Therom as both angles are adjacent to the side they are trying to prove.


Hope It Helps!

Based on the information provided, the total Diane will need to pay is $11.6.

Let's start by calculating the total from the items she ordered, the process is shown below:

Now, let´s apply the coupon by using the 10% as a reference:

12.05 x 0.9 (she will paid only 90%) = $10.845

Finally, let's calculate the tax by using its percentage and let's add it:

$10.845 x 0.0775 = $0.84

$10.845 + $0.84 = $11.6

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Answer:

No, it is not reasonable. The scaled drawing would be 12 inches wide by 30 inches tall.

Step-by-step explanation:

First, scale down the sides. 48in divided by 4 is 12in , and 120 in divided by 4 is 30 in. So no, it would not fit on her paper.

In triangle ABC, if AB is parallel to QR and if AP:PB=BR:RC, then PQ is parallel to BC.

Since AB is parallel to QR, we can use the alternate interior angles theorem to conclude that ∠PAB = ∠QBR and ∠PBA = ∠QRB.

Also, since AP:PB=BR:RC, we can let AP=x and PB=y, so that BR=z and RC=w. Then we have:

Cross-multiplying, we get:

Now consider triangles ABP and QBR. By the angle-angle similarity theorem, we have that these triangles are similar. So:

Substituting our values for PB and BR, we get:

Cross-multiplying, we get:

Similarly, considering triangles APC and RCB, we can use the angle-angle similarity theorem to conclude that these triangles are also similar. So:

Substituting our values for RC and RB, we get:

Cross-multiplying, we get:

Now, let's consider the ratio of the lengths of PQ and BC. We have:

Substituting in the values we found earlier for ABz, QBy, ACz, and RBw, we get:

Using the fact that ABz = QBy and ACz = RBw (which we found earlier), we can simplify this expression to:

This means that PQ and BC are parallel, which is what we wanted to prove.

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As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.

Finding a value of a single unit or the ratio of two values, then using this value to determine the value of a bigger or smaller number, is the unitary method, a problem-solving strategy used in mathematics. The unit method, single unit method, and percentage method are additional names for the unitary approach. The unitary method, which can be used to address issues in a number of disciplines including mathematics, algebra, geometry, and physics, entails using a ratio, proportion, or factor. The approach is founded on the proportionality concept, according to which two ratios or quantities are proportional if they have the same ratio or proportion.

given

Three and a half pounds of apples, which can be expressed as a mixed amount or an incorrect fraction, were harvested by the Martinez family:

3 1/2 = 7/2

Ana selected one-fourth of those apples, so the quantity she selected can be calculated by dividing by the total number of apples selected by the Martinez family:

1/4 × 7/2 = (1 × 7)/(4 × 2) = 7/8

As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.

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Answer: Let's call the first term of the arithmetic progression "a" and the common difference "d". Then we can use the following formulas to find the second, fifth, and seventh terms:

- The second term is a + d.

- The fifth term is a + 4d.

- The seventh term is a + 6d.

We are given that the sum of the second and seventh terms is 25:

(a + d) + (a + 6d) = 25

Simplifying this equation, we get:

2a + 7d = 25 ...(1)

We are also given that the fifth term is 15:

a + 4d = 15 ...(2)

Now we can solve for the common difference "d" by using equations (1) and (2) to form a system of two equations in two variables. One way to do this is to solve equation (2) for "a" in terms of "d", and then substitute that expression for "a" into equation (1):

a = 15 - 4d ...(3)

Substituting equation (3) into equation (1), we get:

2(15 - 4d) + 7d = 25

Simplifying this equation, we get:

30 - 8d + 7d = 25

Solving for "d", we get:

d = -5

Therefore, the common difference is -5.

Step-by-step explanation:

Answer:b

Step-by-step explanation:

The strengths and weaknesses of the data will help to identify the areas that need to be improved.

The steps that are to be taken to apply hypothesis tests to the case of Bayview University are given below:Open the dataset of Bayview University and read the case in its entirety at the end of Chapter 9. After opening the dataset of Bayview University, read the case in its entirety at the end of Chapter 9. It is important to read the case carefully in order to understand it properly. This is the first step that is to be taken in order to apply hypothesis tests to the case of Bayview University.

Use descriptive statistics to summarize the data and comment on your findings. Once the case has been read carefully, descriptive statistics are to be used to summarize the data. Descriptive statistics are statistical techniques that are used to describe and summarize the data. They are used to summarize the data in a way that is meaningful and easy to understand. The descriptive statistics will help to identify the central tendency and the variability of the data. After summarizing the data, comments are to be made on the findings. These comments will help to identify the strengths and weaknesses of the data. The strengths and weaknesses of the data will help to identify the areas that need to be improved.

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As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) equation exceeds the size of T, which contradicts the premise that T has the greatest area.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.  

The area of a triangle in hyperbolic geometry is determined by the formula:

Area = K ∙ (α + β + γ - π)

where K is a constant that depends on the curvature of the space and,, and are the triangle's angles.

we want to emphasise the expression + + -.

Consider the following two situations:

Case 1: T has angles that add up to be less than.

Moreover, the total of the areas of triangles PTA, PTB, and PTC is larger than the area of T since their angles add up to more than T's angles. As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) exceeds the size of T, which contradicts the premise that T has the greatest area.

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The values of x and y are 7 and 6 respectively

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.

The area of a rectangle = l× w

The perimeter of rectangle = 2(l+b)

length = x

breadth = x+y

57 = x(x+y)

44 = 2( x+(x+y)

therefore ;

57 = x²+y. equation 1

44 = 4x + 2y equation 2

from equation 2, y = 22-2x

substitute 22-2x for y in equation 1

57 = x²+22-2x

57 -22= x²-2x

x²-2x -35 = 0

(x²-7x)(+5x -35 )= 0

x( x-7) 5( x-7) = 0

x+5 = 0

x-7 = 0

therefore x = -5 or 7

but we are going to take the positive answer for x

57 = 7²+y

y = 55-49

y = 6

therefore the value of x and y are 7 and 6 respectively

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The relatiοnship in the given diagram is nοt a functiοn, because fοr each input there is nοt exactly οne οutput. Sο Optiοn A is cοrrect

Functiοn is a relatiοn between a set οf inputs and a set οf οutputs which are permissible. In a functiοn, fοr particular values οf x we will get οnly a single image in y. It is denοted by f(x).

Vertical line test:-

Whenever we want tο check whether a given expressiοn is a functiοn οr nοt we can apply a vertical line test, in this test we check fοr a single image οf x , we are getting a single image οr mοre.

If we get mοre images then it will nοt be a functiοn.

Fοr example, let us take, y² = 4ax

y = ±√4ax

Fοr single value οf x we get twο values οf y

Hence, it will nοt be a functiοn.

Given that,

Values οf x and values οf y

In given diagram,

fοr x = 0,

there are twο values οf y, -4 and -2

but accοrding tο definitiοn οf y, it shοuld give οnly οne value

Hence, it is nοt a functiοn

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Answer:

E

Step-by-step explanation:

NO

Random sampling is the correct answer. Which is option (A).

Sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is referred to as Random sampling.

What is sampling?

In statistics, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Sampling is frequently employed in social science research. The method employed to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is known as random sampling.

Content-loaded sampling refers to a form of sampling that is more sophisticated than simple random sampling.

In order to form a sample, it involves first determining which variables (or characteristics) are essential to the study, and then choosing people based on those variables, hence the name "content-loaded."On the other hand, in Stratified sampling, the population is divided into subgroups (strata) based on one or more characteristics that are expected to impact the study's outcomes. The proportion of people chosen from each group should reflect the group's percentage of the overall population.

Snowball sampling is a method for selecting a sample of individuals by locating others who share the characteristics being studied and asking them to suggest additional individuals who might participate in the study. Among the given options, (A) random sampling is the correct answer.

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When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.

Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.

When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.

Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.

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Therefore , the solution of the given problem of probability comes out to be  the likelihood that they have four girls is 1/15.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.

Here,

Given that the family has at least one girl, we can use Bayes' theorem to determine the likelihood that they have four girls:

=> P(4 girls | at least one girl) = P(4 girls)

=> Times P(at least one girl | 4 girls) / P. (at least one girl)

Additionally, we are aware that the probability of having at least one female is

=> P(at least one girl = 1 - P(no girls) = 1 - (1/2)4 = 15/16.

The likelihood of not having any females is equal to the likelihood of having four boys,

which is

=>  (1/2)4 = 1/16.

Given that all four of the children are female, the likelihood of producing girls is one.

Combining everything, we have:

=> P(4 females | a girl)

=> 1 * (1/16) / (15/16) = 1/15

Given that the household has at least one girl, the likelihood that they have four girls is 1/15.

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Here some examples of math by using Mr. Maxs life outside the classroom.

One example of math in Mr. Max's life outside the classroom could be calculating the amount of gas needed to fill up his car's tank before a road trip. This involves using basic arithmetic operations such as addition, subtraction, multiplication, and division to calculate the total distance he intends to travel, the fuel efficiency of his car, and the capacity of the fuel tank. By doing so, he can estimate the amount of gas needed for the trip and plan accordingly. Additionally, he may also use math to calculate the cost of the gas based on the current price per gallon or liter, and decide on the most cost-effective way to fill up his tank.

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complete question is:

What is one example of math in Mr. Max's life outside the classroom? 10. Is math everywhere, as Bobby believes? Support your answer with evidence.

Answer:

12%

Step-by-step explanation:

147/ 1225 x 100/ 1

0.12 x 100 = 12%

Answer:

Therefore, 147 is 12% of 1225.

The difference between the total and the initial contribution, which is: Interest [tex]= $5,409.09 - $5,000, I[/tex] nterest $409.09, is the amount of interest earned. Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.

We can use the compound interest calculation to determine how much money Lupita will receive after 48 months:

Where: [tex]A = P(1 + r/n)(nt)[/tex] A represents the whole sum after t years.

P represents the primary sum.

The yearly interest rate is r.

Given that interest is compounded yearly, [tex]P = $5,000, r = 0.02, n = 1,[/tex]and[tex]t = 48/12 = 4[/tex] (since the time is given in months, we need to convert to years by dividing by 12).

Hence, the equation is: [tex]A = $5,000(1 + 0.02/1)^(1*4)[/tex]

[tex]A = $5,000(1.02)^4\sA ≈ $5,409.09[/tex]

The amount that differs between the total and the original deposit that represents interest earned is: Interest equals [tex]$5,000 - $5,409.09$409.09[/tex] in interest

Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.

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let's move like the crab, backwards.

B)

profit is simply the surplus amount or 3.75 - 2.50 = 1.25.

A)

since the item was bought for $2.50, that's our origin amount, and thus that's our 100%, what's 1.25 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 2.50 & 100\\ 1.25& x \end{array} \implies \cfrac{2.50}{1.25}~~=~~\cfrac{100}{x} \\\\\\ 2.5x=125\implies x=\cfrac{125}{2.5}\implies x=50[/tex]