If f(x) = 3x + 7, find:
f(3) = [?]

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)

Answer:

\(20(x - y)² - 45y² = 5(2(x - y) + 3y)(2(x - y) - 3y)\)

Step-by-step explanation:

We can start by factoring out the common factor of 5 from both terms:

\(20(x - y)² - 45y² = 5(4(x - y)² - 9y²)\)

Now, we can see that we have a difference of squares in the second set of parentheses:

\(= 5(2(x - y) + 3y)(2(x - y) - 3y)\)

Therefore, the fully factorized expression is:

\(20(x - y)² - 45y² = 5(2(x - y) + 3y)(2(x - y) - 3y)\)

If the events A and B are mutually exclusive, meaning they cannot occur simultaneously, then the probability of both events occurring together is zero. In this case, the formula simplifies to P(A or B) = P(A) + P(B).

The probability that either event A or event B will occur can be calculated using the addition rule of probability. According to this rule, the probability of either event A or event B occurring is equal to the sum of the individual probabilities of each event minus the probability of both events occurring together.

In other words, P(A or B) = P(A) + P(B) - P(A and B)



However, if the events A and B are not mutually exclusive, then the probability of both events occurring together needs to be subtracted from the sum of their individual probabilities to avoid double-counting.

So, the final answer to the question "What is the probability that either event will occur?" depends on the specific probabilities of events A and B and whether they are mutually exclusive or not.

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150°

Step-by-step explanation:

360° - 210° = 150° .......

Answer:

g = 200

Step-by-step explanation:

trust me.

I big brain.

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

Step-by-step explanation:

25% = 25/100 = 0.25

Then:

Bounce 1:

160 - (160*0.25) = 160 - 40 = 120

Bounce 2:

120 - (120*0.25) = 120 - 30 = 90

Bounce 3:

90 - (90*0.25) = 90 - 22.5 = 67.5

Bounce 4:

67.5 - (67.5*0.25) = 67.5 - 16.875 = 50.625

Answer:

Circumference: 12π + 8 cm,

Area: 48 ( cm )^2

Step-by-step explanation:

This figure is composed of circles, squares, and semicircles. As you can see, the squares indicate that each semicircle should have ( 1 ) the same area, and ( 2 ) the same length ( circumference ). It would be easier to take the circumference of the figure first, as it is composed of arcs part of semicircles the same length.

Circumference of 1 semicircle = \(\frac{1}{2}\)( πd ) =  \(\frac{1}{2}\)π( 4 ) = 2π ( cm )

Circumference of Figure (composed of 6 semicircles + 2 sides of a square),

We know that 6 semicircles should be 6 \(*\) 2π, and as the sides of a square are equal - if one side is 4 cm, the other 3 are 4 cm as well. Therefore the " 2 sides of a square " should be 2

Circumference of Figure = 6 \(*\) 2π + 2 = 12π + 8 ( cm )

_____________

The area of this figure is our next target. As you can see, it is composed of 3 semicircles, and the area of 3 semicircles subtracted from the area of 3 squares. Therefore, let us calculate the area of 1 semicircle, and the area of 1 square first.

Area of 1 semicircle = 1/2π\(r^2\) = 1/2π\((2)^2\) = 2π ( cm ),

Area of 1 square = ( 4 cm )( 4 cm ) = 16 ( \(cm^2\) )

So, the area of the figure should be the following -

Area of Figure = 3 \(*\) 2π + 3( 16 - 2π ) = 48 ( cm )^2

The sample of given data is Sample 1: 1, 2, 3, 4, 5 Sample 2: 6, 7, 8, 9, 10

b)Sample 1: 1, 2, 3, 4, 5 Sample 2: 6, 7, 8, 9, 10

(a) An example of data with SS(between) = 0 and SS(within) > 0 could be the following:

Sample 1: 1, 2, 3, 4, 5

Sample 2: 6, 7, 8, 9, 10

Sample 3: 11, 12, 13, 14, 15

In this example, the means of each sample are all different from each other, but the grand mean (8) is equal to the mean of each sample. Therefore, there is no variability between the means of the samples, resulting in SS(between) = 0. However, there is still variability within each sample, resulting in SS(within) > 0.

(b) An example of data with SS(between) > 0 and SS(within) = 0 could be the following:

Sample 1: 1, 2, 3, 4, 5

Sample 2: 6, 7, 8, 9, 10

Sample 3: 11, 12, 13, 14, 15

In this example, the means of each sample are all the same (8), but the values within each sample are all different from each other. Therefore, there is variability between the means of the samples, resulting in SS(between) > 0. However, there is no variability within each sample, resulting in SS(within) = 0.

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Answer:

0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 650 pounds and a standard deviation of 20 pounds.

This means that \(\mu = 650, \sigma = 20\)

What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste?

Less than 620:

pvalue of Z when X = 620. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{620 - 650}{20}\)

\(Z = -1.5\)

\(Z = -1.5\) has a pvalue of 0.0668

More than 700:

1 subtracted by the pvalue of Z when X = 700. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{700 - 650}{20}\)

\(Z = 2.5\)

\(Z = 2.5\) has a pvalue of 0.9938

1 - 0.9938 = 0.0062

Total:

0.0668 + 0.0062 = 0.073

0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste

The graph showing the points is attached

The solutions are shown algebraically below

The solutions are f(2,5) and (4,2)

when the x or y part of the solution is substituted in the equation if the values is in line with the equation then the solution is correct

using f(2,5)

y < 1÷2x+4 = y < x/2 + 4

y < 2/2 + 4

y < 5

This is not a solution since y should be less than 5 not equal to 5

x + 2y ≥ 6 ⇒ x ≥ 6 - 2y

⇒ x ≥ 6 - 2 * 5

x ≥ 6 - 10

x ≥ -4

this is a solution 2 ≥ -4

using f(4,2)

y < x/2 + 4

y < 4/2 + 4

y < 6

This is a solution since 4 < 6

x + 2y ≥ 6 ⇒ x ≥ 6 - 2y

⇒ x ≥ 6 - 2 * 2

x ≥ 6 - 4

x ≥ 2

this is is a solution since 4 ≥ 2

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Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

7 men should be able to dig 21 wells in approximately 4.7 days.

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

We can use the formula:

Number of days = (number of wells * number of days per well) / number of men.

So, we have

Number of days per well for 2 men:

11 days / 7 wells = 1.5714 days per well.

Using the above as a guide, we have the following:

the number of days for 7 men to dig 21 wells:

21 wells * 1.5714 days per well / 7 men = 4.7142days.

Hence, the number of days is 4.7 days.

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An ordered pair which is a solution to the given system of linear equations is: (1, 4).

In order to determine which ordered pairs are valid and true solutions based on the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (0, -4), we have:

-3x + 2y = 5

-3(0) + 2(-4) = 5

0 - 8 = 5

-8 = 5 (No)

For ordered pair (-3, 5), we have:

-3x + 2y = 5

-3(-3) + 2(5) = 5

9 + 10 = 5

19 = 5 (No)

For ordered pair (1, 4), we have:

-3x + 2y = 5

-3(1) + 2(4) = 5

-3 + 8 = 5

5 = 5 (Yes)

For ordered pair (1, 4), we have:

y = 8x - 4

4 = 8(1) - 4

4 = 4 (Yes).

For ordered pair (-7, -8), we have:

-3x + 2y = 5

-3(-7) + 2(-8) = 5

21 - 16 = 5

5 = 5 (Yes)

For ordered pair (-7, -8), we have:

y = 8x - 4

-8 = 8(-7) - 4

-8 = -58 (No).

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Answer:

Money Market account

Step-by-step explanation:

Money Market accounts typically allow you to earn money at a higher interest rate than other types of savings accounts.

2a) x = 77 - 2y (option A)

2b) y = 77/2 - x/2

2a) 2x + 4y - 31 = 123

To solve for x, first we need to collect like terms

Add 31 to both sides:

2x + 4y - 31 + 31 = 123 + 31

2x + 4y = 154

Next we move 4y to the other side by subtracting 4y from both sides:

2x + 4y - 4y = 154 - 4y

2x = 154 - 4y

Divide both sides by 2:

2x/2 = 1/2 (154 - 4y)

x = 154/2 - 4y/2

x = 77 - 2y (option A)

2b) To solve for y using the first equation, we will collect like terms

2x + 4y - 31 = 123

Add 31 to both sides:

2x + 4y - 31 + 31 = 123 + 31

2x + 4y = 154

subtract 2x from both sides:

2x - 2x + 4y = 154 - 2x

4y = 154 - 2x

divide both sides by 4:

Answer:

13

Step-by-step explanation:

Hypotenuse is c

so c^2 = a^2 + b^2

c^2 = 5^2 + 12^2

c^2 = 25 + 144 = 169

c^2 = 13^2

c = 13

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

---------------

Let the numbers be s and l.

We are given that:

Set up equations:

Eliminate l:

Solve for s:

Find l:

ANSWER;

6/ 2(1+2)

= 6/ 2(3)

= 6/ 2X3

= 6/6

= 1

Answer:

6 ÷ 2 [1 + 2]

= 6 ÷ 2 + 4

= 6 ÷ 6

= 1

Answer: There are 9 mangoes left in the basket.

Step-by-step explanation:

(2/5) * 15 = 6.

15 - 6 = 9.

The correct option is (D). On average, the number of breakdowns per day varies from the mean by about 0.28.

Because standard deviation represents the typical distance between each data point and the mean.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.

So, the correct answer is On average, the number of breakdowns per day varies from the mean by about 0.28.

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Answer:

i think it would be $80 (brainliest??)

Step-by-step explanation:

jane had a total of $200 BEFORE she spent on 2 games

1. $40

2. $40

3. $40

4. $40

5.$40

2 games = $80

3 games = $120 (money she had left)

Answer:

Step-by-step explanation:

(a+b)(a-b)=a^2-b^2

Answer:

The answer is A. 88.

Step-by-step explanation:

To solve for the measure of angle ( \(e\) ), start by noticing that 92 degrees and   ( \(e\) ) sum up to 180 degrees, which makes them supplementary angles.

Two angles are said to be supplementary angles if they add up to 180 degrees. Supplementary angles form a straight angle (180 degrees) when they are put together. In other words, angle 1 and angle 2 are supplementary, if Angle 1 + Angle 2 = 180 degrees.

Since angle 92 degrees and angle ( \(e\) ) sum up to 180 degrees, the equation will look like \(92\)°\(+e=180\)°. To solve the equation, start by subtracting 92 degrees from both sides, and the equation will look like \(e=88\)°. The final answer will be that the measure of angle ( \(e\) ) is 88 degrees.

Answer:

88

Step-by-step explanation:

√(a² + b²)²  - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.

                                An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

we have AB as a, AD as b and the angle between them is theta.

So using the cosine rule, we have

  BD = √a² + b² - 2abcosθ

So now consider the triangle ABC

Here AB is a, BC is b and the angle is 180-theta

So using cosine rule, we get AC as

   AC = √a² + b² - 2abcosθ( 180 - θ )

    AC = √a² + b² - 2ab(-cosθ )

    AC = √a² + b² - 2abcosθ

Now we have the two diagonals AC and BD. So multiplying, we get

 AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ

Simplifying, we get

AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)

AC × BD = √(a² + b²)² - (2abcosθ)²

AC × BD = √(a² + b²)²  - 4a²b²cos²θ

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Answer:

295 square feet

Step-by-step explanation:

Break the figure up into 3 rectangles, and then find the area of each rectangle and add all areas together.

15*3=45

19*10=190

15*4=60

45+190+60=295

Answer:26 *15*4*5*3=23400

Step-by-step explanation: Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.