PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!

PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!

Answers

Answer 1

Answer:

75°

Step-by-step explanation:

Arc length LM is 108°, meaning that angle <K is half of the arc length, 54°.

*REMEMBER* all 3 angles inside a triangle must add up to 180° to make it a triangle.

We have angle <L, <K, and we are looking for angle <M.

51+54+?=180

105+?=180

?=75

Angle <M is 75°

Hope this helps :)


Related Questions

can someone help me solve -2√180u²v

Answers

Answer:-12 with the weird checkmark symbol then a five inside the checkmark symbol times u squared v

Step-by-step explanation:

what are 2, 3, and 4

Answers

1. The area of square C is 625 ft². 2. The perimeter of square C is 46 ft. 3. The area of square B is 1456 ft². 4. The length of square A is 4√15 ft.

What is Pythagoras theorem?

A key idea in geometry that connects the lengths of a right triangle's sides is known as the Pythagorean Theorem. It says that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides in a right triangle. It has the following mathematical expression:

a² + b² = c²

1. The area of square C can be found using the Pythagorean Theorem:

a² + b² = c²

Using the area the side is calculates as follows:

Side length of A = √225 = 15 ft

Side length of B = √400 = 20 ft

Now,

15² + 20² = c²

225 + 400 = c²

625 = c²

c = √625 = 25 ft

So the area of square C is:

Area of C = 25² = 625 ft²

2. The perimeter of square C can be found by adding up the side lengths of all three squares:

Perimeter of A = 36 ft, so each side length of A is 9 ft.

Perimeter of B = 48 ft, so each side length of B is 12 ft.

Perimeter of C = Side length of A + Side length of B + Side length of C

Perimeter of C = 9 + 12 + c

We found earlier that c = 25 ft, so we can substitute that in:

Perimeter of C = 9 + 12 + 25 = 46 ft

3. The area of square B can be found using the fact that the areas of squares A, B, and C are related by the equation:

Area of A + Area of B = Area of C

We know the area of A and the area of C, so we can solve for the area of B:

Area of A = 15² = 225 ft²

Area of C = 1681 ft²

Area of A + Area of B = Area of C

225 + Area of B = 1681

Area of B = 1456 ft²

4. Perimeter of B = 64 ft

Side length of B = 64 / 4 = 16 ft

Now we can use the Pythagorean Theorem to find the side length of C:

a² + b² = c²

a = 15 ft (side length of A)

b = 16 ft (side length of B)

c = √(a² + b²) = √(15² + 16²) = √481 = 22 ft

Finally, we can use the Pythagorean Theorem again to find the side length of A:

a² + b² = c²

b = 16 ft (side length of B)

c = 22 ft (side length of C)

a = √(c² - b²) = √(22² - 16²) = √240 = 4√15 ft

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PLS HELP ASAP 50 POINTS AND BRAINLEIST!!!
Explain how the arc BX, central angle BCX, and inscribed BNX are connected. what are the relationships between them?

Answers

Answer:

see explanation

Step-by-step explanation:

the arc BX is equal to the measure of the central angle BCX

the measure of the inscribed angle BNX is half the measure of its intercepted arc BX

the turtle is under your bed ! go look

2. Container P contains 800 ml of solution. 0.4 of the solution in container Q is poured into container P. Then,3/8 of the solution in the container P is poured into an empty container R. If the container R contains 540 ml of solution now, find the initial volume, in litres, of the solution in container Q. ​

Answers

The initial volume of the solution in container Q is 1.6 liters.

Let's first discover how a lot solution was poured from container Q into container P:

0.4 x volume of solution in container Q = 0.4Q

the total volume of solution in container P after this transfer is:

800 ml + 0.4Q ml

Subsequent, 3/8 of this overall volume in container P is poured into container R:

(3/eight) x (800 ml + 0.4Q ml) = 300 ml + 0.15Q ml

We recognise that field R includes 540 ml of solution now, so we are able to set up an equation:

300 ml + 0.15Q ml = 540 ml

Solving for Q, we get:

0.15Q ml = 240 ml

Q = 1600 ml

Consequently, the initial volume of the solution in container Q is 1.6 liters.

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What is the diameter of a sphere with a volume of
7483
m
3
,
7483 m
3
, to the nearest tenth of a meter?

Answers

The diameter of the sphere is approximately 20 meters to the nearest tenth of a meter.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since we are given the volume of the sphere, we can solve for the radius as follows:

V = (4/3)π[tex]r^{3}[/tex]

[tex]r^{3}[/tex] = (3V) / (4π)

r = [tex](3V/4\pi )^{1/3}[/tex]

Substituting the given value of the volume, we get:

r = [tex](3*7483/4\pi )^{1/3}[/tex] ≈ 10.0

Therefore, the radius of the sphere is approximately 10 meters. The diameter of the sphere is twice the radius, so the diameter is approximately:

2 x 10 ≈ 20 meters

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Question content area top
Part 1
A riverboat travels 69 km downstream in 3 hours. It travels 76 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.

Answers

The speed of the boat is 21 km/h and the speed of the stream is 2 km/h.

Alex brough a cell phone for $200 using money from his saving account he is replacing the money in his saving account at he rate of $8 per weeks he already has replaced $80 how many more weeks does alex will he have to put money in his saving account in order to replace the entire amount

Answers

Alex will have to put money in his savings account for 15 more weeks at a rate of $8 per week.

How to maintain budget on purchasing cell phone?

Alex purchased a cell phone for $200 using money from his savings account. He plans to replace the money in his savings account at the rate of $8 per week. He has already replaced $80, which means he needs to replace $120 more to have the entire amount. Since he is replacing the money at a rate of $8 per week, he will need 15 more weeks to replace the remaining amount. Therefore, he will have to put money in his savings account for 15 more weeks to replace the entire $200 he spent on the cell phone. By doing so, he will be able to maintain his savings and avoid any financial loss.

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The area of a rectangle is represented by the expression x^2-9x+14 units^2. Find the expressions that could represent the length and width of the rectangle

Answers

The expressions that could represent the length and width are (x - 2) units and (x - 7) units respectively.

To find the expressions that represent the length and width of the rectangle, we need to factor the given expression.

x² - 9x + 14 = (x - 2)(x - 7)

The length and width of the rectangle are represented by two factors of the expression.


To find the length and width of the rectangle, we need to understand the formula for the area of a rectangle, which is length multiplied by width. The given expression x²-9x+14 represents the area of the rectangle. To find the expressions that represent the length and width, we need to factor the given expression.

We can do this by finding two numbers that multiply to 14 and add up to -9. These numbers are -2 and -7. Therefore, we can factor the given expression as (x - 2)(x - 7). From this, we can see that the length of the rectangle is represented by the factor (x - 2) units and the width is represented by the factor (x - 7) units.

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Lin's smart phone was fully charged when she started school at 8:00 a. M. At 9:20 a. M. , it was 90%


charged, and at noon, it was 72% charged.


1. When do you think her battery will die?


2. Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.

Answers

1. It's impossible to determine exactly when Lin's battery will die without more information on her phone's battery capacity and usage patterns. However, we can estimate that it will likely die sometime after noon if the rate of battery drain remains constant.

2. Yes, battery life is a function of time. The longer a battery is in use, the more its charge will deplete. However, it is not necessarily a linear function as the rate of battery drain can vary depending on factors such as usage patterns, app activity, and temperature. In this specific case, it appears that the rate of battery drain may be slowing down as the percentage decrease from 90% to noon is less than the decrease from fully charged to 90%.

In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used. A linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.

Linear functions are related to linear equations.

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Find the gross income for selling 348 bushels of apples at 16.50 per bushel

Answers

The gross income for selling 348 bushels of apples at a price of $16.50 per bushel is $5,742.

The gross income is the total revenue earned from the sales of a product or service, before any expenses or deductions are taken out. To calculate gross income, we multiply the quantity of goods sold by the price per unit.

In this case, we are given that 348 bushels of apples were sold at a price of $16.50 per bushel. Multiplying these two values together gives us the total revenue earned from the sale of these apples, which is the gross income.

To calculate the gross income, we can use the formula:

Gross income = Quantity sold x Price per unit

Plugging in the given values, we get:

Gross income = 348 x $16.50

Simplifying the calculation, we get:

Gross income = $5,742

Therefore, the gross income for selling 348 bushels of apples at a price of $16.50 per bushel is $5,742.

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You're at a clothing store that dyes your clothes while you wait. The store offers
4 different articles of clothing and
3 colors.
If you randomly choose the article of clothing and the color, which of these diagrams can be used to find all of the possible outcomes?

Answers

The probability of randomly selecting an orange hat is 1/12 or 0.0833.

What is the probability of randomly selecting an orange hat?

In the sample, there are total of 4 pieces of clothing and 3 colors.

The possible outcomes is:

= 4 x 3

= 12

So, the outcomes when randomly selecting a piece of clothing and a color is 12.

From 12 possible outcomes, there is only one outcome where you end up with an orange hat.

So, the probability of randomly selecting an orange hat is:

= 1/12

= 0.0833.

Correct question "You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?"

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This mysterious hand went to the mall and saw a massage chair


that he would have to take a loan out to purchase. The total of the


loan was $6600. The bank said that he could get a simple interest


rate of 8% for 5 years. What is the total amount that the mysterious


hand will pay for the chair?

Answers

Since the loan is at a simple interest rate of 8% for 5 years, the total amount that the mysterious hand will pay is:

Total amount = Principal + Interest

where Principal is the initial amount of the loan, and Interest is the amount of interest charged on the loan.

The interest charged on the loan can be calculated using the simple interest formula:

Interest = Principal x Rate x Time

where Rate is the interest rate per year, and Time is the time period in years.

Plugging in the given values, we get:

Interest = 6600 x 0.08 x 5 = 2640

So the total amount that the mysterious hand will pay is:

Total amount = 6600 + 2640 = 9240

Therefore, the total amount that the mysterious hand will pay for the massage chair is $9,240.

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Tell whether the given value is the solution of the inequality

Answers

The solution to the inequality given is false.

Why is the solution false ?

To determine whether x = 5 is a solution of the inequality x + 3 > 12, we substitute x = 5 into the inequality and see if the resulting statement is true or false:

5 + 3 > 12

8 > 12

In this case, when we substitute x = 5 into the inequality, we get the statement 5 + 3 > 12, which simplifies to 8 > 12. This statement is false, since 8 is not greater than 12. Therefore, x = 5 is not a solution of the inequality x + 3 > 12.

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The full question is:

Tell whether the given value is a solution of the inequality X + 3 > 12; x = 5

You are shopping for a King & Queen size mattress, each of which are shaped like a rectangle. The Queen is 16 inches longer than it is wide. The King is 20 inches wider than the Queen, but has the same length. The area of the King-sized mattress is 1,600 in² larger than the Queen. Find the Area of both mattresses

Answers

The area of the King-sized mattress is 4,800 square inches and the area of the Queen-sized mattress is 3,200 square inches.

To find the dimensions of the Queen-sized mattress, let x be the width. Then, the length of the mattress is x + 16. The area of the Queen-sized mattress is x(x + 16) = x² + 16x.

Since the King-sized mattress has the same length as the Queen-sized mattress, its length is x + 16. Also, its width is 20 inches wider than the Queen-sized mattress, so its width is x + 16 + 20 = x + 36. Therefore, the area of the King-sized mattress is (x + 16)(x + 36) = x² + 52x + 576.

The area of the King-sized mattress is 1,600 square inches larger than the area of the Queen-sized mattress. So, we can set up the following equation:

x² + 52x + 576 - (x² + 16x) = 1600

Simplifying this equation, we get:

36x + 576 = 1600

36x = 1024

x = 28

Therefore, the width of the Queen-sized mattress is 28 inches and the length is 44 inches. So, its area is 3,200 square inches.

The width of the King-sized mattress is 28 + 36 = 64 inches and the length is 44 inches. So, its area is 4,800 square inches.

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Which statement completes the following



A. Consecutive interior angles

B. Alternate interior angles

C. Corresponding angles

D. Alternate exterior angles

Answers

The ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

What is alternate exterior angle?

An alternate exterior angle is an angle formed by a pair of lines and a transversal, such that the angle is located on the outside of the two lines, and on the opposite side of the transversal. More specifically, if line AB is intersected by transversal CD at point E, and angles 1 and 2 are formed as shown in the diagram below, then angle 1 and angle 2 are alternate exterior angles:

Alternate exterior angles are congruent if the two intersected lines are parallel. This means that the measure of angle 1 is equal to the measure of angle 2.

So, ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

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Blank 1 or B =

Blank 2 or P =

Blank 3 or l =

Answers

The part of the surface area equation are

Part 1 = B = Base areaPart 2 = P = Perimeter of basePart 3 = l = Height of pyramid

Completing the part of the surface area equation

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

SA = B + 1/2Pl

In the equation, we have

Part 1 = B

Part 2 = P

Part 3 = l

When the above parts are labelled, we have

Part 1 = B = Base area

Part 2 = P = Perimeter of base

Part 3 = l = Height of pyramid

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3. the sketch shows three adjacent angles. please write an equation that can be
used to determine the value of y?
28
36
please help

Answers

The value of y is 116°.

Three given Adjacent angles are 28°, 36° and y°.

When two angles are adjacent, they have a common side between them and share a common vertex where the two sides meet. The angles are said to be adjacent because they are next to each other.

We know that if a ray stands on a straight line, then the sum of adjacent angles is 180°.

So, 28° + y° + 36° = 180°

y° + 64° = 180°

Subtracting 64° from both sides.

y°- 64° = 180° - 64°

y° = 116°

Hence, the value of y is 116°.

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If JM=10 and LM=14, what is KM?

Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
KM =

Answers

The calculated value of the length of segment KM is 11.83

Calculating the length of KM

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

JM = 10

LM = 14

Using the similar triangle ratio, we have

JM/KM = KM/LM

substitute the known values in the above equation, so, we have the following representation

10/KM = KM/14

So, we have

KM^2 = 10 * 14

Evaluate

KM^2 = 140

This gives

KM = 11.8321595662

As a decimal rounded to the nearest hundredth, we have

KM = 11.83

HEnce, the value of KM is 11.83

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Tabitha bought a new SUV and obtained a loan for $29,000. The annual interest


rate is 4. 3% for 7 years. If Tabitha takes the loan for 5 years instead of 7, she will


save. 5% on the interest rate. How much less will Tabitha pay for her SUV if she


takes the loan for 5 years? *

Answers

Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.

To calculate the total amount Tabitha might pay for the SUV with a 7-year loan, we are able to use the compound interest formula for calculating the total amount of a loan, that is:

[tex]total amount = principal x (1 + interest charge)^{time}[/tex]

Wherein:

principal is the amount of the loaninterest charge is the annual interest rate Time is the length of the loan in years

With a 7-year loan, the full amount Tabitha could pay is:

[tex]total amount = $29,000 x (1 + 0.043)^{7} = $37,501.76[/tex]

To calculate the overall amount she could pay with a 5-year loan and a 5% decrease interest rate, we first need to calculate the new interest price. A 5% discount inside the interest price of 4.3% is:

New interest price = 4.3% - 5% = 3.3%

Then we can use the equal formula as before to calculate the total amount with the 5-year mortgage:

[tex]total amount = $29,000 x (1 + 0.033)^{5} = $33,093.47[/tex]

The difference in the overall amount among the two loans is:

$37,501.76 - $33,093.47 = $4,408.29

Therefore, Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.

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Qn in attachment
.
..​

Answers

Answer: d

Step-by-step explanation:

Answer:

pls mrk me brainliest

Step-by-step explanation:

(⁠ ̄⁠(⁠エ⁠)⁠ ̄⁠)⁠ノ

For the function f(x) = x^2e^7x find the critical numbers and use the First Derivative Test to find the local
maximum and minimum values and where they occur. Enter exact answers in fraction form.

Answers

For the function f(x) = x^2e^7x the critical numbers are 0 and -2/7 and using the First Derivative Test local minima at x = 0 and -2/7.

The function f(x) = x²e⁷ˣ

Differentiate the function f(x) with respect to x

f'(x) = 2xe⁷ˣ + 7x²e⁷ˣ

f'(x) = xe⁷ˣ(2 + 7x)

Now put f'(x) = 0 for critical points.

xe⁷ˣ(2 + 7x) = 0

x = 0                 2 + 7x = 0              e⁷ˣ ≠ 0

x = 0                 x = -2/7                e⁷ˣ ≠ 0

Hence, 0 and -2/7 are the critical points.

f'(x) = 2xe⁷ˣ + 14x²e⁷ˣ

Now f''(x) = 2e⁷ˣ + 14xe⁷ˣ + 28xe⁷ˣ + 98x²e⁷ˣ

f''(x) = 2e⁷ˣ + 42xe⁷ˣ + 98x²e⁷ˣ

f''(x) = 2e⁷ˣ(1 + 21x + 49x²)

Now f''(x) at x = 0

f''(0) = 2e⁷⁽⁰⁾(1 + 21(0) + 49(0)²)

f''(0) = 2(1 + 0 + 0)

f''(0) = 2 > 0

So f(x) has minima at x = 0

Local minima at x = 0 and y = 0.

Now f''(x) at x = -2/7

f''(0) = 2e⁻²(1 + 21(-2/7) + 49(-2/7)²)

f''(0) = 2e⁻²(1 - 6 + 4)

f''(0) = -2e⁻² < 0

f(x) has local minima at x = -2/7

Now y at x = -2/7 is

y = f(-2/7)

y = (-2/7)² e⁻²

y = 4/49e²

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could you give me a simple answer?

If the point (13, 10) were reflected using the X-axis as the line of reflection, what would be the image coordinates? What about (13, -20)? (13, 570)? Explain how you know.

Answers

Answer:

To gain our understanding of the plot (13, 10) on graph paper. We need to look at the picture reflecting or "flipping" that point over the x-axis. In this case, it "flips the point down"  the original point was in first quadrant or Quadrant |, the reflected point is in the fourth quadrant of Queadrant ||||.  The x coordinate would stay the same, but the new y coordinate would be the "opposite" sign of the original.  So the reflected point is (13, -10)

Step-by-step explanation:

(x, y) → (x, - y)

Reflection over x-axis for (13,-20) → (13, 20)

Technically some of the explanations is above /\

Thus the answer is, To gain our understanding of the plot (13, 10) on graph paper. We need to look at the picture reflecting or "flipping" that point over the x-axis. In this case, it "flips the point down"  the original point was in first quadrant or Quadrant |, the reflected point is in the fourth quadrant of Queadrant ||||.  The x coordinate would stay the same, but the new y coordinate would be the "opposite" sign of the original.  So the reflected point is (13, -10)

Question 1 (multiple choice worth 2 points) (10.03, 10.04 lc) which digital text feature plays music or speaking on its own? animation

interactive

elements

sound text​

Answers

Based on the given options, the digital text feature that plays music or speaking on its own is "sound." The correct option is sound.

Digital texts can incorporate various features to engage readers and enhance their experience. These features include:

1. Animation: Visual effects and motion graphics that add dynamic elements to a digital text. Animation can be used to illustrate complex concepts, tell stories, or create visual appeal.

2. Interactive elements: Components of digital texts that allow users to interact with the content, such as hyperlinks, buttons, quizzes, or navigation tools. Interactive elements can make digital texts more engaging and help users find information more efficiently.

3. Sound: Audio elements that play music, speaking, or other sounds. Sound can be used to provide additional information, create atmosphere, or guide users through a digital text.

4. Text: The written content of a digital text. Text can be formatted in various ways, such as using different fonts, colors, or layouts, to make digital texts more accessible and visually appealing.

In this case, the feature that plays music or speaking on its own is "sound." Sound elements in digital texts can enhance the user experience by providing audio feedback, creating a more immersive environment, or adding an additional layer of information.

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What is the area of triangle hgf? round your answer to the nearest tenth of a square centimeter. recall that you need to
round up if the value of the hundredth is 5 or greater.

Answers

The area of triangle HGF is 9.8 cm²

The Sides of the given triangle are 6.5 cm, 3.6 cm and 5.6 cm

We know that the area of the triangle is the half of product of base and height of the triangle.

The base of the triangle = 6.5 cm

Height of the triangle = 3.0 cm

We know that the triangle is

Area = 1/2 × base × height

= 1/2 × HF × GE

= 1/2 × 6.5 × 3.0

= 1/2 × 19.5

= 9.75

Rounding to the nearest tenth

= 9.8 cm²

Hence, the area of triangle HGF is 9.8 cm²

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Given question is incomplete, the complete question is below

What is the area of triangle HGF? Round your answer to the nearest tenth of a square centimeter. Recall that you need to round up if the value of the hundredth is 5 or greater.

Find an exponential function that passes through (2,8) and (4,128)

Answers

The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)

To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:

Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.

Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2

Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4

Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2

Step 5: Solve for 'b':
b = √16
b = 4

Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)

Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2

Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)

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Five students are going to volunteer at a food pantry tomorrow. Each student will be assigned to either the morning shift or the afternoon shift, but not both. Each shift must be covered by at least two of the five students. How many different ways can the five students be assigned?



I'll put branliest to first person

Answers

There are 20 different ways to assign five students to cover the morning and afternoon shifts at the food pantry.

How many different methods to assign 5 students?

There are different methods to solve this problem, but one possible way is to use a combination of counting techniques.

Since there are two shifts (morning and afternoon) and each shift must be covered by at least two students, there are two cases to consider:

Case 1: Two students cover the morning shift, and three students cover the afternoon shift.

Case 2: Three students cover the morning shift, and two students cover the afternoon shift.

For Case 1, we can choose two students out of five for the morning shift in C(5,2) = 10 ways, and the remaining three students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose three students out of the remaining three for the afternoon shift in C(3,3) = 1 way (since there are only three students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 1.

For Case 2, we can choose three students out of five for the morning shift in C(5,3) = 10 ways, and the remaining two students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose two students out of the remaining two for the afternoon shift in C(2,2) = 1 way (since there are only two students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 2.

The total number of ways to assign the students is the sum of the ways for Case 1 and Case 2, which is 10 + 10 = 20 ways.

Therefore, there are 20 different ways to assign the five students to cover the morning and afternoon shifts at the food pantry.

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Wesley makes spherical fish tanks with a diameter of 30cm. Kate requests a smaller tank with half the volume of the tank that Wesley usually makes. Kate tried to figure out the approximate diameter of the smaller tank, but she made a mistake. In which step did Kate first make her mistake?

Answers

Kate's mistake was in Step 2: "Divide the volume of Wesley's tank by 2." Since she wants a tank with half the volume of Wesley's tank, she should have divided the volume of Wesley's tank by 2, not the radius.

How to determine  which step did Kate first make her mistake

The correct approach would be to use the formula for the volume of a sphere:

V = (4/3)πr^3

Since Wesley's tank has a diameter of 30 cm, its radius is 15 cm. Substituting this value into the formula gives:

V = (4/3)π(15)^3

V ≈ 14,137 cm^3

To find the radius of the smaller tank with half the volume, Kate should have solved for the radius using the formula for the volume of a sphere:

(4/3)πr^3 = (1/2)(4/3)π(15)^3

Simplifying this equation gives:

r^3 = (1/2)(15)^3

r ≈ 10.8 cm

Therefore, the approximate diameter of the smaller tank should be 21.6 cm (twice the radius), not 10.8 cm.

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7. Membership at the local Sky Zone costs $189 per year and an hour costs $15 each.
Write an expression (make sure it looks like an expression, not an equation) to
represent the total cost of going to Sky Zone for the year. Evaluate the expression
(make it an equation) if you jump for 19 hours in a year. Write a "therefore"
statement. (4 marks)

Answers

189*365=68985

68985/15= $4599

Step-by-step explanation:

or $5000 if you round up

Prove that 5 to the power of 7 plus 5 to the power of 6 is divisible by 6

Answers

To prove that 5^7 + 5^6 is divisible by 6, we can factor out the common term 5^6 and apply the divisibility rule for 6. Here's the solution:

1. Factor out the common term 5^6:
5^7 + 5^6 = 5^6(5 + 1) = 5^6 * 6

2. Apply the divisibility rule for 6:
A number is divisible by 6 if it is divisible by both 2 and 3. Since 6 is already a multiple of 6 (6*1), the expression 5^6 * 6 is divisible by 6.

Thus, we have proved that 5^7 + 5^6 is divisible by 6.

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The value of a car is worth 40,000, and it declines by 3% every year. Which function best represents the the value of the hybrid car.


40000(0. 03)^t


40000(1. 03)^t

Answers

The function best represent the value of hybrid car that is worth 40000 and it declines by 3% every year is  [tex]40,000(0.97)^{t}[/tex]

The value of the car = 40,000

The value of car declines at the rate of 3% every year

function is represented as F(t)

F(t) = [tex]P( 1 - \frac{R}{100} )^{t}[/tex]

P is principal amount value of the car which is 40,000

R is rate at which it declines every year which is 3%

t is no. of year

Putting all the values in the equation we get

F(t) = [tex]40000(1-\frac{3}{100} )^{t}[/tex]

F(t) = [tex]40000(\frac{97}{100}) ^{t}[/tex]

F(t) = [tex]40000(0.97)^{t}[/tex]

The function represent the value of the hybrid car is [tex]40000(0.97)^{t}[/tex] .

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