14. Which triangles are similar?

Answer:

  6050 square meters

Step-by-step explanation:

You want to know the largest rectangular area that can be enclosed using 220 meters of fencing for 3 sides.

For enclosure length x, the width of the enclosure is half the remaining fence: (220 -x)/2. The area is the product of length and width.

  A = (x)(220 -x)/2

This is the equation of a parabola that opens downward. Its vertex (maximum) is halfway between the zeros, which are x=0 and x=220. This means the area is maximized when x=110 and the width is (220-110)/2 = 55.

The maximum area is (110 m)(55 m) = 6050 m².

__

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The answer is 2025 sq. meter.

If you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, the largest area you can enclose is 4840 square meters. Explanation: To determine the largest possible area, we have to find out how to divide the 220 meters of fencing so that we can maximize the space enclosed by it. If one side of the rectangle is x meters long, the other side is (110 - x) meters long (because we have one straight wall to use as a side).The perimeter of the rectangle can be calculated by adding up all four sides of the rectangle. Hence:2x + (110 - x) + (110 - x) = 220We simplify the equation to solve for x:2x + 220 - 2x = 220-x = 55Therefore, one side of the rectangle is 55 meters long, and the other side is (110 - 55) = 55 meters long as well. The area of a rectangle is given by its length multiplied by its width. In this case, the area is:55 x 55 = 3025.

Therefore, the largest area that can be enclosed is 3025 square meters.

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Answer: $14,983.50

Step-by-step explanation:

If someone works 48.5 hours in a week and their regular work week is 40 hours, then they would have worked 8.5 hours of overtime.

What is meant by a week?

A week is a unit of time equal to seven days, usually beginning on Monday and ending on Sunday. It is commonly used to measure and organize time.

What is meant by hours?

Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.

According to the given information

In most cases, overtime pay is calculated as 1.5 times the employee’s regular hourly rate.

If someone works 48.5 hours in a week and their regular workweek is 40 hours, then they would have worked 8.5 hours of overtime.

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Answer:

Gabriel left $1.53 in tips.

Step-by-step explanation:

Sales tax: 9.50*0.075=0.7125

9.50+0.71=10.21

Total with Sales Tax: $10.21

Tip: 10.21*0.15=1.5315

Answer:

To solve for y in the inequality 5(2y - 1) < -15, we can simplify the expression on the left-hand side as follows:

5(2y - 1) < -15

10y - 5 < -15 // Distribute the 5 on the left side

10y < -10 // Add 5 to both sides

y < -1 // Divide both sides by 10 and flip the inequality

Therefore, the solution is y < -1.

Answer:

The formula for area of a parallelogram is A=bh

x=10.3

Step-by-step explanation:

We don't have the base but we have the height.

the base is x and the height is 5

if the area is 51.5

we should divide the height to find the base.

51.5÷5=10.3

so the base is 10.3

Check if answer is correct:

b=10.3

h=5

a= 51.5

10.3(5)=51.5

a= 51.5cm²

I hope this helps as long as you know the formula it's easy :D

Answer:

∠2 = 125°

Step-by-step explanation:

∠1 and ∠2 form a straight angle of 180° (∠3 and ∠4 aswell)

∠1 = ∠3, because they are cross angles (∠3 and ∠4 aswell)

We can write an equation according to this and find y:

(8y - 9)° = (6y + 7)°

8y - 6y = 7 + 9

2y = 16 / : 2

y = 8

∠1 = 8 × 8 - 9 = 55°

∠2 = 180° - 55° = 125°

∠3 =∠1 = 6 × 8 + 7 = 55°

∠4 = 180° - 55° = 125°

Answer:

alternate exterior angles

Step-by-step explanation:

Both x and 100° are alternate exterior angles. Therefore, by definition, x = 100°.

The sample space when 2 lollipops are randomly selected with replacement is S_with_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}

The sample space when lollipops are selected without replacement is S_without_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}.

The experiment with replacement (Part A) shows independent events because the probability of each lollipop being chosen is the same for both selections.

When selecting 2 lollipops with replacement, we put the first lollipop back into the bag before choosing the second one.  When selecting 2 lollipops without replacement, we do not put the first lollipop back into the bag before choosing the second one.

The outcome of the first event does not affect the probability of the second event.

The experiment without replacement (Part B) shows dependent events because the probability of the second lollipop being chosen is affected by the outcome of the first event. When one lollipop is removed from the bag, there are fewer options available for the second selection, and the probabilities of the remaining lollipops change.

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Answer:

quadratic

Step-by-step explanation:

see image above for explanation.

Answer:

Step-by-step explanation:

1.  48 96 192      (multiplying by 2)

2. 30 37 44        ( adding 7)

3. 25 18 11          ( subtracting 7)

4. 110 232 456  ( adding 7, 14, 28, 56  and so on)

5. 230 470 950  (adding 15, 30, 60 120 and so on)

The answer for B is: 5÷4 cups of fruit drink are made with 1 cup of apple juice.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

For A:

We want to find the ratio of carrot juice to apple juice when 1 cup of apple juice is used. Let's represent the amount of carrot juice with "x".

So, we have the ratio:

x : 1 cup

which is equivalent to:

1÷5 cup : 3÷5 cup

To solve for x, we can set up a proportion:

1÷5 cup ÷ 3÷5 cup = x ÷ 1 cup

Simplifying the left side:

(1÷5 cup) ÷ (3÷5 cup) = (1÷5 cup) x (5÷3) = 1÷3 cup

So, the ratio of carrot juice to apple juice when 1 cup of apple juice is used is:

1÷3 cup : 1 cup

Therefore, the answer for A is: 1/3 cup of carrot juice is used for 1 cup of apple juice.

For B:

We want to find how many cups of fruit drink are made with 1 cup of apple juice. Let's represent the amount of fruit drink with "y".

So, we have the ratio:

1 cup : y

which is equivalent to:

3÷5 cup : (1÷5 cup + 3÷5 cup) = 4÷5 cup

To solve for y, we can set up a proportion:

1 cup ÷ 4÷5 cup = y ÷ 1

Simplifying the left side:

(1 cup) ÷ (4÷5 cup) = (1 cup) x (5÷4) = 5÷4 cup

So, 5/4 cups of fruit drink are made with 1 cup of apple juice.

Therefore, the answer for B is: 5÷4 cups of fruit drink are made with 1 cup of apple juice.

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Answer:

[tex]a_{n}[/tex] = 5n

Step-by-step explanation:

there is a common difference between consecutive terms, that is

10 - 5 = 15 - 10 = 20 - 15 = 5

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 5 and d = 5 , then

[tex]a_{n}[/tex] = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

The expected counts are large enough to use a chi-square distribution to calculate the p-value because the predicted-counts are at least 5, the degree-of-freedom that should be used is 2.

The "degree-of-freedom" is defined as the number of independent parameters or variables that must be specified to completely describe a system or equation.

We see that the projected counts(expected-counts) are large enough to use a chi-square distribution if all predicted counts are at least 5,

So, This condition is satisfied and it satisfies that the expected counts are large enough to use a chi-square distribution to calculate the p-value.

In the table we see that the number of categories are three : {Red, Black, Green},

So, degree of freedom is = (number of categories) - 1 = 3 - 1 = 2.

Therefore, the degree of freedom is 2.

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The given question is incomplete, the complete question is

Confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. The information table is given below.

What degrees of freedom should you use?

Answer:

1:A

2:B

3:A

that's the answer I think

The equation of the line that passes through the point (5, 0) and has a slope of 6/5 is:

y = (6/5)x - 6To find the equation of the line that passes through the point (5, 0) and has a slope of 6/5,

we will use the point-slope form of the equation of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Step 1: Plug in the given point (5, 0) as (x1, y1) and the slope (6/5) as m.
y - 0 = (6/5)(x - 5)
Step 2: Simplify the equation.
y = (6/5)(x - 5)
Step 3: Distribute the slope (6/5) on the right side.
y = (6/5)x - 6
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Answer:  9 square feet

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Given: [tex]\textsf{Keisaun needs to cover a square. One side is 3 feet}[/tex]

Find:  [tex]\textsf{We need to find how much paper he needs}[/tex]

Solution:  Using the information that was given to us we know that we need to determine the area of the square that Keisaun needs to cover.  We know that the area formula for a square is side * side.  We are also given the information that a single side of the board is measured to be 3 feet.  Therefore, using that information we can plug the value into the square area formula and solve.

Therefore, the answer to the question would be that Keisaun would need 9 square feet of paper to cover the square bulletin board.

Answer: radius is 2.5 and volume of ice cream is 58.9 cm cubed

Step-by-step explanation:

Answer:

See the picture below

Step-by-step explanation:

To graph this linear function, you need two things: slope and y-intercept.

y-intercept:

This is where the line crosses the x axis.  It will cross when x = 0. (0,b).  The b is the y-intercept.  You see this in the equation at the end.  In this case the y-intercept it 8.

Slope:

This is the change in y over the change in x.  On the graph I highlighted two points (0,8) and (1,5).  If you start at (0,8) and go to (1,5), you go straight down 3 units and 1 unit right.  This is your slope.  Going down is a negative direction and going right is a positive direction.  The slope would be the change in y over the change in x. [tex]\frac{-3}{1}[/tex] which simplified would be -3.  The slope is -3.

Helping in the name of Jesus.

Step-by-step explanation:

The GCF of 24 and 18 is '6'...factor that out to get

6 ( 4a-3b)   that is all you can do....

The exponential function are y = 10(2)^x, y = 1.270(1.389)^x, y = 5.656(0.957)^x and y = 6.567(0.870)^x.

1. (a) To find the equation of the exponential function that passes through the points (0,10) and (3,80), we can use the formula:

y = a(b)^x

where a and b are constants that we need to find.

First, we can use the point (0,10) to solve for a:

10 = a(b)^0

10 = a

Next, we can use the point (3,80) to solve for b:

80 = 10(b)^3

8 = b^3

b = 2

Therefore, the equation of the exponential function is:

y = 10(2)^x

(b) To find the equation of the exponential function that passes through the points (0.18, 2.8) and (2, 8), we can use the same formula:

y = a(b)^x

First, we can use the point (0.18, 2.8) to solve for a:

2.8 = a(b)^0.18

Next, we can use the point (2, 8) to solve for b:

8 = a(b)^2

Dividing the second equation by the first, we get:

2.857 = (b)^1.82

b = 1.389

Substituting this value of b back into one of the equations to solve for a, we get:

2.8 = a(1.389)^0.18

a = 1.270

Therefore, the equation of the exponential function is:

y = 1.270(1.389)^x

2. (a) To find the equation of the exponential function that passes through the points (2, 5.12288) and (1.92, 2.192), we can again use the formula:

y = a(b)^x

First, we can use the point (2,5.12288) to solve for a:

5.12288 = a(b)^2

Next, we can use the point (1.92,2.192) to solve for b:

2.192 = a(b)^1.92

Dividing the second equation by the first, we get:

0.427 = (b)^(0.08)

b = 0.957

Substituting this value of b back into one of the equations to solve for a, we get:

5.12288 = a(0.957)^2

a = 5.656

Therefore, the equation of the exponential function is:

y = 5.656(0.957)^x

(b) To find the equation of the exponential function that passes through the points (1.192,5) and (5,0.75), we can use the same formula:

y = a(b)^x

First, we can use the point (1.192,5) to solve for a:

5 = a(b)^1.192

Next, we can use the point (5,0.75) to solve for b:

0.75 = a(b)^5

Dividing the second equation by the first, we get:

0.149 = (b)^3.808

b = 0.870

Substituting this value of b back into one of the equations to solve for a, we get:

5 = a(0.870)^1.192

a = 6.567

Therefore, the equation of the exponential function is:

y = 6.567(0.870)^x

3. To find the equation of the exponential function that passes through the points (2.14,7) and (7,205), we can use the same formula as before:

y = a(b)^x

First, we can use the point (2.14,7) to solve for a:

7 = a(b)^2.14

Next, we can use the point (7,205) to solve for b:

205 = a(b)^7

Dividing the second equation by the first, we get:

29.285 = (b)^(4.86)

b = 5.474

Substituting this value of b back into one of the equations to solve for a, we get:

7 = a(5.474)^2.14

a = 0.00061

Therefore, the equation of the exponential function is:

y = 0.00061(5.474)^x

Rounding a and b to the nearest hundred, we get:

a = 0.0006

b = 5.47

So, the final equation of the exponential function is:

y = 0.0006(5.47)^x

We can check if the points (2.14,7) and (7,205) fall on the curve by plugging them into the equation:

y = 0.0006(5.47)^x

When x = 2.14:

y = 0.0006(5.47)^2.14 ≈ 7

When x = 7:

y = 0.0006(5.47)^7 ≈ 205

So, the points do fall on the curve, which means that the equation we found is correct.

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Hence, value of variable y in the triangle is 7.5

Triangle proportionality is a relationship that exists between the sides of a triangle when a line is drawn parallel to one side of the triangle, intersecting the other two sides. Specifically, the line divides the two sides in proportion to the length of the third side.

We know that,  if a line is drawn parallel to one side of a triangle, then the line divides the other two sides in proportion.

AB/AC=2y+5/2y+25

We know that

AB=BC=1/2AC

½=2y+5/2y+25

2y+25=4y+10

2y=15

y=7.5

value of variable y in the triangle is 7.5.

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Answer: y-3= 5/4(x-1) is the point slope form answer, y = 1.25x + 1.75 is the slope intercept form answer.

Step-by-step explanation:

The new beta-blocker medicine is effective in lowering high blood pressure.

A hypothesis test can be used to test the claim that a new beta-blocker is effective at the significance level α (significance level).

Let us define the null and alternative hypotheses as follows:

Null Hypothesis (H0):

This drug does not affect high blood pressure.

Alternative hypothesis (Ha):

The drug is effective in lowering high blood pressure.

To test this hypothesis, we can use a two-sample proportional z-test comparing rates of success (lowering blood pressure) in two independent populations (treatment and control groups).

First, we need to calculate the sample proportions and the standard errors of their differences. Let p1 = treatment group success rate,

p2 = control group success rate,

and p = pooled rate.

p1 = 157/290 = 0.541

p2 = 90/170 = 0.529

p = (157 + 90) / (290 + 170) = 0.536

The standard error of the difference in proportions can be calculated as:

SE = sqrt[p*(1-p)(1/n1 + 1/n2)]

= square[0.536(1-0.536)*(1/290 + 1/170)]

= 0.056

Then you can compute the test statistic z.

z = (p1 - p2) / SE

= (0.541 - 0.529) / 0.056

= 2.143

Finally, we can compute the p-value associated with the test statistic z, assuming a standard normal distribution.

p-value = P(Z > 2.143) = 0.0169

The p-value (0.0169) is less than the significance level α, so we neglect the null hypothesis and can say that this drug is effective in lowering high blood pressure.

The chosen importance is not specified in the question, so it is not sure if it's important at that level. If α is given, you can compare the p-value to α and make a decision based on that.  

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It will cost $1200 to cover both sides of the green roof with plants at a cost of $0.75 per square foot.

To calculate the cost of covering both sides of the green roof, we first need to find the area of the roof. We can use the formula for the area of a rectangle:

area = length x width

Since the roof is 40 feet long, we need to find the width to calculate the area. We can estimate the width from the picture, but it's not given explicitly. So, we can make a reasonable assumption that the width is the same as the length of the shorter side of the roof, which appears to be about 20 feet.

Using this assumption, we can calculate the area of one side of the roof:

area = length x width = 40 ft x 20 ft = 800 sq ft

Since there are two sides to the roof, the total area is twice this amount:

total area = 2 x 800 sq ft = 1600 sq ft

To find the total cost of covering both sides of the roof, we can multiply the area by the cost per square foot of plants:

total cost = area x cost per sq ft

= 1600 sq ft x $0.75/sq ft

= $1200

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Answer: [tex]\angle F = 44\°\\angle D= 46\°[/tex]

Step-by-step explanation:

Answer:

834

Step-by-step explanation:

5 + 3(4 - 3 + 2) x [tex]9^{2}[/tex] + 100

5 + 3(3) x 81 + 100

5 + 9 x 81 + 100

5 + 729 + 100

834

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Answer:

The first step is to calculate the total cost of energy used in two months. To do that, we need to multiply the amount of energy used by the cost per kilowatt-hour:

3550 kW•h x $0.10/kW•h = $355.00

So the total cost of energy used in two months is $355.00. This is the amount of the bill that the business will receive for its electricity usage.

Step-by-step explanation:

Answer:

To calculate the bill, we need to multiply the amount of energy used (3550 kW•h) by the cost per kW•h (10 cents).

3550 kW•h x 10 cents/kW•h = $355.00

Therefore, the bill for the business is $355.00.

Step-by-step explanation:

please pa brainliest po thanks.

The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero.

What is linear equation?

A linear equation is a mathematical equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.

What is y-intercept?

In a linear equation of the form y = mx + b, the y-intercept (b) is the point where the line intersects the y-axis.

The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero. In the context of Justine's race, the y-intercept would represent her starting distance from the finish line.

It would be the distance from the finish line when she began the race, or the distance she would have to run to reach the finish line if she started at the beginning. The slope of the line would tell you how much the distance decreases as she runs.

Together, the y-intercept and slope of the line can provide useful information for understanding and analyzing Justine's race.

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The answer of the given question based on the linear relationship is , the y-intercept gives information about Justine's initial position or starting point before she started running the race.

A linear relationship is a type of relationship between two variables where their relationship can be described by a straight line. In other words, the change in one variable is directly proportional to the change in the other variable. This means that as one variable increases or decreases, the other variable also changes in a consistent and predictable way. Linear relationships are commonly studied in mathematics, statistics, and other fields as they provide a useful framework for understanding the relationship between two variables and making predictions based on that relationship.

In the context of this linear relationship, the y-intercept represents the starting point of Justine's race. It is the point where her distance from the finish line is zero, which is the beginning of the race. Therefore, the y-intercept gives information about Justine's initial position or starting point before she started running the race.

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