Two lines intersect to form 4 angles. Angles 2 and 4 are vertical angles with angle 2 = 4x + 12 and angle 4 = 7x - 6. a) Find x. b) What is the measure of angle 2 ?

The system of equations has exactly one solution where x = 0 and y = -2. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

-5x + y = -2

y = 5x - 2            .....1

6x - y = 2

y = 6x - 2            .....2

From equations 1 and 2, then we have

6x - 2 = 5x - 2

x = 0

Then the value of y is given as,

y = 6(0) - 2

y = - 2

The system of equations has exactly one solution where x = 0 and y = -2. Then the correct option is C.

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The product that is represented with the algebra tiles is (2x + 2)(2x + 3)

From the question, we have the following parameters that can be used in our computation:

The algebra tiles

Representing the red tile with digit 1

So, we have

Vertical = 2x + 1 + 1 = 2x + 2

Horizontal = 2x + 1 + 1 + 1 = 2x + 3

The product that is represented with the algebra tiles is then calculated as

Product = Vertical * Horizontal

So, we have

Product = (2x + 2)(2x + 3)

Hence, the product is (2x + 2)(2x + 3)

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Answer:

\(List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}\)

Step-by-step explanation:

Given

\(Children = 3\)

Required

List all cases of having at least 1 girl

We have:

\(B = Boy\)

\(G = Girl\)

For 1 girl, we have:

GBB; BGB; BBG

For 2 girls, we have:

GGB; BGG; GBG

For 3 girls, we have:

GGG

Hence, the list is:

\(List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}\)

Answer: The line segments are equal in length

AC = BC = 5

Step-by-step explanation:

PLATO answer

The lateral surface area of the mailer is 234 In²

It is important to note that the formula for the lateral area of a triangular prism is expressed as;

A = (a + b+ c) h

Given that the parameters are enumerated as;

Now, substitute the values into the equation, we have;

Lateral area, A = (4 + 4 + 5) 18

Add the values

Lateral area = (13)(18)

Multiply the values

Lateral area = 234 In²

Hence, the value is 234 In²

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The values of the total rainfall over the span of the storm are:

After 1 hour, the total rainfall is 0.7 inches

After 2 hours, the total rainfall is 1.4 inches

After 3 hours, the total rainfall is  2.1 inches

After 4 hours, the total rainfall is 2.8 inches

After 5 hours, the total rainfall is 3.5 inches

After 6 hours, the total rainfall is 4.2 inches

After 7 hours, the total rainfall is 4.9 inches

After 8 hours, the total rainfall is 5.6 inches

After 9 hours, the total rainfall is 6.3 inches

After 10 hours, the total rainfall is 7 inches

After 11 hours, the total rainfall is 7.7inches

After 12 hours, the total rainfall is 8.4 inches

The amount of rainfall increases per hour. The increase in rainfall can be modelled using a linear function

A linear function is a function that has a variable that is raised to the power of 1.

An example is x + 10

The linear function that models the rainfall is 0.7 × h. Where h represents number of hours

After 1 hour, the total rainfall is 0.7 x 1 = 0.7 inches

After 2 hours, the total rainfall is 0.7 x 2 = 1.4 inches

After 3 hours, the total rainfall is 0.7 x 3 = 2.1 inches

After 4 hours, the total rainfall is 0.7 x 4 = 2.8 inches

After 5 hours, the total rainfall is 0.7 x 5 = 3.5 inches

After 6 hours, the total rainfall is 0.7 x 6 = 4.2 inches

After 7 hours, the total rainfall is 0.7 x 7 = 4.9 inches

After 8 hours, the total rainfall is 0.7 x 8 = 5.6 inches

After 9 hours, the total rainfall is 0.7 x 9 = 6.3 inches

After 10 hours, the total rainfall is 0.7 x 10 = 7 inches

After 11 hours, the total rainfall is 0.7 x 11 = 7.7inches

After 12 hours, the total rainfall is 0.7 x 12 = 8.4 inches

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Answer:

The sample size will be "\(102.5494 \sim 102\)". A further explanation is given below.

Step-by-step explanation:

Let the sample size will be:

= n

The given values are:

Standard deviation,

= 1.4

ME,

= 0.3

As we know,

⇒ \(n=(Z \frac{a}{2}\times \frac{SD}{E})^2\)

On putting the estimated values, we get

⇒    \(=(2.17\times \frac{1.4}{0 .3})^2\)

⇒    \(=(\frac{3.038}{0.3})^2\)

⇒    \(=102.5494 \sim 102\)

The equation for converting gain in decibels to a linear scale is dB → gain-multiplier: \(g=2^{\frac{d}6} }\)

gain-multiplier → dB: \(6*log_{2} g\)

The decibel is used in a wide range of applications. Decibels are especially used when referring to power or a derived measure, which values can vary in a wide range. The most prominent usage of decibels is in sound volume. So, for example, a sound of 0dB is barely hearable, whereas a vacuum cleaner on average has 75dB and a rock concert reaches about 110 dB.

Practical version-

dB → gain-multiplier: \(g=2^{\frac{d}6} }\)

gain-multiplier → dB: \(6*log_{2} g\)

So if we set that 0 dB gain as 1.0 factor, and -∞ dB gain is 0.0 factor, it means that (if we are considering voltage gain as in a mixing desk fader) :

gain = 20.0*log10(factor)

therefore :

factor = 10^(gain/20.0)

If, as described in a comment, the 0 dB gain is at 0.65 factor, it means the ref is 0.65.

gain in dB = 20*log10(factor/0.65)

factor = 0.65*10^(gain/20.0)

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Answer:

10.67

Explanation:

We're told that P varies jointly as Q and R, this can be represented as shown below;

where k = constant of proportionality

Given P = 6, Q = 3 and R = 12, let's go ahead and solve for k;

Knowing k = 1/6, let's solve for P when Q = 4 and R = 16;

Answer:

6x^5-5x^4+6x^3-x^2+12x-31

Step-by-step explanation:

(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)

To add, combine like terms

6x^5-5x^4+6x^3-x^2+12x-43+12

6x^5-5x^4+6x^3-x^2+12x-31

Standard form means from the highest power of x to the lowest power of x

Answer: C

Step-by-step explanation: The sensitivity of a classification model is the proportion of true positives (TP) out of all actual positives (TP + false negatives (FN)). The specificity is the proportion of true negatives (TN) out of all actual negatives (TN + false positives (FP)). The accuracy is the proportion of correct predictions (TP + TN) out of the total number of predictions.

In this case, the model correctly predicted 309 players to pass, but there were actually 309 + 314 = 623 players who failed, so the number of false negatives (FN) is 314. The model correctly predicted 107 players to fail, but there were actually 107 + 270 = 377 players who passed, so the number of false positives (FP) is 270.

Therefore, the sensitivity is TP / (TP + FN) = 309 / (309 + 314) = 0.496, and the specificity is TN / (TN + FP) = 107 / (107 + 270) = 0.284. The accuracy is (TP + TN) / (TP + TN + FP + FN) = (309 + 107) / 1000 = 0.416.

Therefore, the correct answer is (C) Sensitivity = 0.496, Specificity = 0.284, Accuracy = 0.416.

Answer: 2

Step-by-step explanation: 12 x 3 first becuase pemdas

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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Step-by-step explanation:

okay  so The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.

distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Answer:

2/1

Explanation:

Given the ratio:

Divide both sides by 0.25

Thus, the ratio as a fraction in simplest form is 2/1.

Answer:

Its about a 16 percent decrease

The population in 2019 would be about 160,080

Step-by-step explanation:

So To find percent change you just do \(\frac{new-old}{old}\). No wwe get about 16 percent

Now to find the population just multipy the latest one by 0.16 and use that product to add to the population in 2013 and you’ll get 160,080

Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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Answer:

using diameter, The Area of the circle is 28.27

Step-by-step explanation:

A = 1/4(3.14)(d^2)

A = 28.27

Answer:

C

5y + 3

Step-by-step explanation:

The range of the graph of the exponential function is (b) {y | y > 0}

From the question, we have the following parameters that can be used in our computation:

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

58.9

Step-by-step explanation:

Angle A and the angle that equals 121.1° are supplementary angles meaning they add up to 180°. To find angle A, you subtract 121.1° from 180°.

Angle A =  180 - 121.1 = 58.9

Answer:

90% is close to 75

Step-by-step explanation:

90% of a number would be 3 times 30% of a number. As a result we can assume 90% of the number would be around 3(25) or 75

The expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

Using this formula

Expected value=Stock worth at $50+ Stock worth at $60+ Stock worth at $70

Where:

Stock worth at $50=40% chance

Stock worth at $60=35% chance

Stock worth at $70=25% chance

Let plug in the formula

Expected value=(40%×$50)+($35%×$60)+($25%×$70)

Expected value=$20+$21+$17.5

Expected value=$58.50

Inconclusion the expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

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The time is taken by the 8 gardeners to landscape the same garden will be 30 hours.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

It takes 5 gardeners 48 hours to landscape a garden.

Then the time taken by the 8 gardeners to landscape the same garden will be

The relationship between the gardeners and time is inversely proportional. Then we have

Let x be the time taken by the 8 gardeners. Then we have

8x = 5×48

 x = 30 hours

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Answer: 2.5 mi/hr. 7.5/3= 2.5

Step-by-step explanation:

The number of multiple-choice and short-answer questions on a test with 65 questions will be 40 and 25 respectively.

To determine the number of multiple-choice and short-answer questions on a test with 65 questions, we can set up a proportion based on the given ratio:

Multiple-choice questions : Short-answer questions = 8 : 5

Let x be the number of multiple-choice questions.

Let y be the number of short-answer questions.

Using the proportion, we can set up the following equation:

8/5 = x/y

8y = 5x

x = (8y)/5

Since the total number of questions on the test is 65, we have the equation:

x + y = 65

Substituting the expression for x from the previous equation:

(8y)/5 + y = 65

(8y + 5y)/5 = 65

13y/5 = 65

13y = 65 * 5

13y = 325

Dividing both sides by 13:

y = 325/13

y = 25

Substituting this value of y back into the equation x = (8y)/5:

x = (8 x 25)/5

x = 40

Therefore, there are 40 multiple-choice questions and 25 short-answer questions on the test with a total of 65 questions.

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