I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!

I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!
I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!

Answers

Answer 1

The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.

An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.

What is a reflection over the y-axis?

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:

(x, y)                               →              (-x, y)

Coordinate = (-1, 1/10)   →  Coordinate A' = (-(-1), 1/10) = (1, 1/10).

Furthermore, the transformation rule for the translation of a point by k units up is given by;

(x, y + k)         →  (x', y')

(1, 1/10 + k)       →  E(1, 4 1/10)

1/10 + k = 4 1/10

k = 4 1/10 - 1/10

k = 4.

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Related Questions

Susan got a prepaid debit card with 20 on it.For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 16 cents per yard. If after that purchase there was 14.88 left on the card, how many yards of ribbon did Susan buy?

Answers

Answer:

32 yards

Step-by-step explanation:

Let's see, the card started out with $20 on it, and ended up with $14.88.

To find how much she spent on ribbon, we can first subtract the 2 amounts:

20-14.88

=5.12

So, Susan spent $5.12 on ribbon.  We also know that each yard of ribbon was $0.16, so we can divide the spent amount ($5.12) by $0.16 to find out how many yards she bought:

5.12/0.16

=32

So, Susan bought 32 yards of ribbon.

Hope this helps :)

The length of the radius of a sphere is 6 inches. The length of the radius of a cone is 3 inches, and the height is 7 inches. What is the difference between the volume of the sphere and the volume of the cone?

Answers

The difference between the volume of the sphere and the volume of the cone is approximately 838.81 cubic inches.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Thus, for a sphere with a radius of 6 inches, the volume is:

V_sphere = (4/3)π(6³) = 904.78 cubic inches

The volume of a cone is given by the formula V = (1/3)πr[tex]^{2h}[/tex], where r is the radius and h is the height. Thus, for a cone with a radius of 3 inches and a height of 7 inches, the volume is:

V_cone = (1/3)π(3²)(7) = 65.97 cubic inches

Therefore, the difference between the volume of the sphere and the volume of the cone is:

V_sphere - V_cone = 904.78 - 65.97 = 838.81 cubic inches

Hence, the difference between the volume of the sphere and the volume of the cone is approximately 838.81 cubic inches.

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Write an exponential regression function to model the situation.​

Answers

The exponential regression function to model the situation above is: y = 400,000(0.841)^x

What is the explanation for the above response?

The exponential regression function to model the situation is:

y = ab^x

where,

y = flour in grams

x = number of weeks since the bakery opened

a = initial amount of flour (Y-intercept) = 400,000 grams

b = growth factor

To find the value of b, we can use any two points from the table. Let's use the first and second points.

When x = 0, y = 400,000

When x = 1, y = 336,400

Substituting these values in the equation, we get:

400,000 = ab^0

336,400 = ab^1

Simplifying these equations, we get:

a = 400,000

b = 0.841

Therefore, the exponential regression function is:

y = 400,000(0.841)^x

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Information into an equation and solve the
equation
The sum of a number n and 11 is equal to 25. Find the number n

Answers

The resultant equation is n + 11 = 25 and the number n is 14.

Algebraic equation:

An algebraic equation is a mathematical statement that equates two expressions using one or more variables. Solving a single variable equation can be done by adding or subtracting the same integer on both sides. Similarly multiplying or dividing by the same integer.

The information we have

The sum of a number n and 11 is equal to 25.

The statement can represent an equation and solve for n as follows

Here sum of two numbers indicates adding

Hence,  n + 11 = 25

To solve for n, isolate n on one side of the equation.

This can be done by subtracting 11 from both sides of the equation:

=> n + 11 - 11 = 25 - 11

=> n = 14

Therefore,

The resultant equation is n + 11 = 25 and the number n is 14.

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Ben completely filled his 20-gallon tank of gas with regular fuel for $59. 80 as he left the gas station he noticed the gas station across the street sold regular fuel for $2. 84 a gallon how much money could ben have saved per gallon if he had gone to the gas station across the street

Answers

Ben could have saved $0.15 per gallon if he had gone to the gas station across the street.

If Ben filled his 20-gallon tank of gas with regular fuel for $59.80, then the cost per gallon can be found by dividing the total cost by the number of gallons:

cost per gallon = total cost / number of gallons

cost per gallon = $59.80 / 20 gallons

cost per gallon = $2.99/gallon

If the gas station across the street sold regular fuel for $2.84 a gallon, then the amount Ben could have saved per gallon is:

savings per gallon = cost per gallon at initial station - cost per gallon at other station

savings per gallon = $2.99/gallon - $2.84/gallon

savings per gallon = $0.15/gallon

Therefore, Ben could have saved $0.15 per gallon if he had gone to the gas station across the street.

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Samantha is told that sin (O) = and tan (0)<0, and was asked to determine the value of cos (©).


• She uses the Pythagorean identity and defines it to be sin() + cos2 ( 0 )= 1.


• She substitutes į into the equation for sin (0)


• She then looks at values of sin ( ) and tan () and says that the only quadrant in which sin() is positive and


tan() is negative is the first quadrant.


Samantha determines that the answer is


cos () =


(21)

Answers

Samantha determines the answer as cos(θ) = -√(3/4).

Based on the information given, I can help you with this problem. Samantha is correct in using the Pythagorean identity and substitution, but she made an error in identifying the quadrant. Here's the correct process:

1. Given sin(θ) = 1/2 and tan(θ) < 0.
2. The correct quadrant where sin(θ) is positive and tan(θ) is negative is the second quadrant, not the first.
3. Using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
4. Substitute sin(θ) = 1/2 into the equation: (1/2)^2 + cos^2(θ) = 1.
5. Simplify: 1/4 + cos^2(θ) = 1.
6. Solve for cos^2(θ): cos^2(θ) = 3/4.
7. Since we are in the second quadrant, cos(θ) is negative: cos(θ) = -√(3/4).

Your answer: cos(θ) = -√(3/4).

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Analyze the diagram below and answer the questions that follow.
F
G
t
How many different ways can the line above be named? What are those names?
A. 2 ways; FG, GF
B. 3 ways; t, FG, GF
C. 4 ways; t, FG, FG, GF
D. 5 ways; t, FG, GF, FG GF

Answers

Answer: A. 2 ways; FG, GF

Step-by-step explanation: There are only two ways to name a line, and they are interchangeable: starting from one endpoint and naming the other endpoint second, or starting from the second endpoint and naming the first endpoint second.

2. Hamilton claimed that there are only 4 circuits that begin with the letters LTSR Q. Find them. 3. Find all four possible Hamiltonian circuits that begin with JVTSR

Answers

To find the possible Hamiltonian circuits that begin with JVTSR, we can start by constructing a path that begins with JVTSR and visits each vertex exactly once. Such a path must be of the form JVTSRX, where X is the remaining vertex.

Case 1: JVTSRQX

To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to Q are S and R. Thus, we must have X = S or X = R, and the circuits are JVTSRQS and JVTSRQR.

Case 2: JVTSRXQ

To find the possible value of X, we note that the only edges incident to X are S and L. Thus, we must have X = L, and the circuit is JVTSRLQ.

Case 3: JVTSRLX

To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to L are T and R. Thus, we must have X = R, and the circuit is JVTSRLR.

Case 4: JVTSRXL

To find the possible value of X, we note that the only edges incident to Q are S and R, and the only edges incident to X are L and S. Thus, we must have X = L, and the circuit is JVTSRQL.

Therefore, there are four possible Hamiltonian circuits that begin with JVTSR: JVTSRQS, JVTSRQR, JVTSRLQ, and JVTSRLR.

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In 2000, 1500 rabbits live in a warren in a certain area. the number of rabbits increases exponentially at a discrete rate of 7% per year. predict population in 2008&2022

Answers

The predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.

To predict the population of rabbits in the warren in 2008 and 2022, we can use the formula for exponential growth:
P(t) = P₀ (1 + r)ᵗ

Where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t is the time elapsed.

For this problem, we know that P₀ = 1500, r = 0.07 (since the growth rate is 7%), and we want to find P(8) and P(22) (since we're predicting the population in 2008 and 2022, respectively).

Using the formula, we get:
[tex]P(8) = 1500( 1 + 0.07)^{8}  = 2909[/tex]

So we can predict that there will be about 2909 rabbits in the warren in 2008.

To find P(22), we simply plug in t = 22:
[tex]P(22) = 1500 (1 + 0.07)^{22}  = 9933[/tex]

So we can predict that there will be about 9933 rabbits in the warren in 2022.

Therefore, the predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.

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A spinner with 6 equally sized slices has 6 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice?

Answers

Answer:

1

Step-by-step explanation:

Select the correct answer. team goal scored in first five minutes p 2.34% q 3.56% r 1.24% s 4.01% t 3.88% total 2.86% the probabilities of a particular soccer team scoring a goal within the first five minutes of the game are given in the table. what is the probability of a goal being scored in the first five minutes of the game, given that the team is team q? a. 1.24% b. 2.86% c. 3.56% d. insufficient data

Answers

The probability of a goal being scored in the first five minutes of the game, given that the team is team q is 1.24%. The correct option is a.

The probability of a goal being scored in the first five minutes of the game, given that the team is team q, is given by the conditional probability:

P(goal scored in first 5 min | team is q) = P(goal scored in first 5 min and team is q) / P(team is q)

From the table, we have:

P(goal scored in first 5 min and team is q) = 3.56%

P(team is q) = 3.56%

Therefore:

P(goal scored in first 5 min | team is q) = 3.56% / 3.56% = 1

This means that if we know the team is team q, the probability of a goal being scored in the first five minutes of the game is 100% (or certain). So the correct answer is (a) 1.24%.

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The velocity of a particle moving in a straight line is given by v = t(t^2 + 1)^3 + 3t. (a) Find an expression for the position s after a time t. (Use C for the constant of integration)
S =

Answers

The position of particle in a straight line with v = t(t^2 + 1)³ + 3t is (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² C.

To find an expression for the position s after a time t, we need to integrate the velocity function v with respect to time t.

Using the power rule of integration and the constant of integration C, we have:

s = ∫v dt = ∫[t(t² + 1)³ + 3t] dt

after expanding t(t² + 1)³ using binomial theorem we have-

(t^2 + 1)³ = t⁶ + 3t⁴ + 3t² + 1

Substituting this into the integral, we get:

s = ∫[t(t⁶ + 3t⁴ + 3t^2 + 1) + 3t] dt

s = ∫[t^7 + 3t⁵ + 3t³ + t + 3t] dt

s = ∫t^7 dt + 3∫t⁵ dt + 3∫t³ dt + ∫4t dt

s = (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² + C

Therefore, the expression for the position s after a time t is:

S = (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² + C, where C is the constant of integration.

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Josh and Draven can clean the JHS cafeteria in 25 minutes. Draven can clean the JHS cafeteria in 40 minutes. How long will it take Josh to do the job if he works alone?

Answers

It will take Josh about 66.67 minutes to easy the cafeteria alone.

Let's anticipate that the amount of work required to easy the cafeteria is 1 unit.

In a single minute, Josh can easy 1/x of the cafeteria (in which x is the number of mins it takes Josh to do the task alone), and Draven can clean 1/40 of the cafeteria in one minute.

When they work together, they could easy the cafeteria in 25 minutes, so in one minute they are able to easy 1/25 of the cafeteria.

The use of the fact that their combined rate is the sum in their individual rates, we are able to installation an equation:

1/x + 1/40 = 1/25

Multiplying each facets through the least common more than one of the denominators (40 * 25 * x), we get:

25 * 40 + x * 40 = x * 25

1000 + 40x = 25x

15x = 1000

x = 66.67

Therefore, it'd take Josh about 66.67 minutes to easy the cafeteria alone.

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The bulldogs, a baseball team, has nine starting players the height of the starting players are 72in 71in 78in 70in 72in 72in 73in 70in and 72 in which team best describes the data value 78 in

Answers

The value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses.

The Bulldogs, a baseball team, consists of nine starting players with varying heights. Their heights are as follows: 72 in, 71 in, 78 in, 70 in, 72 in, 72 in, 73 in, 70 in, and 72 in. To describe the data, we can analyze the presence of the 78 in height value.

In this case, the value 78 in represents the tallest player on the team. When examining this data set, it is important to understand how this value affects the overall distribution of heights among the players. One way to determine this is by calculating the mean, median, and mode of the height data.

The mean (average) height for the team is 71.22 inches, and the median (middle) value is 72 inches. The mode (most frequent) height is also 72 inches. The value 78 inches is above the mean and median values, indicating that it is an outlier, or a value that is significantly different from the majority of the other data points.

In conclusion, the value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses. However, it provides valuable information about the diversity of heights among the starting players on the team.

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During the basketball game, you record the number of rebounds from missed shots for each team. (a) describe the likelihood that your team rebounds the next missed shot. (B) how many rebounds should ur team expect to have in 15 missed shots

Answers

In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15  shots is 10.5 rebounds.

Given

Number of shots missed by the given team is 7

Total number of shots fired is 10

a) Then, moving on to the first part of the question

Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.

Then,

Probability = no of shots attended / total number of shots fired

Probability = 7 /10

Then the event is likely

b) Now the second part

Then the number of rebounds the given team expect to have in the next 15 missed shots

= 7/10 ×15

= 105/10

= 10.5 rebounds

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The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.

Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.

Which is correct regarding the angles of the triangle?

mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX

Answers

Answer:

In a triangle, the side opposite to the largest angle is the longest side, and the side opposite to the smallest angle is the shortest side. In triangle XYZ, the length of side XY is m + 8, the length of side YZ is 2m + 3, and the length of side ZX is m - 3. Since m ≥ 6, we can determine that 2m + 3 is the largest value, m + 8 is the next largest value, and m - 3 is the smallest value. Therefore, side YZ is the longest side and side ZX is the shortest side.

Since side YZ is the longest side, angle X must be the largest angle. Since side ZX is the shortest side, angle Y must be the smallest angle. Therefore, the correct ordering of the angles from smallest to largest is ∠Y < ∠Z < ∠X.

Step-by-step explanation:

You find an apartment which charges $925 a month rent. each year the rent increases by 6%.

Answers

The monthly rent for the apartment would be $1238.84 in the fifth year.

What is the monthly rent for an apartment that charges $925 initially and increases by 6% each year?

The problem states that the monthly rent for an apartment is $925. To calculate the rent for the second year, we need to increase this amount by 6%.

To do this, we first need to calculate 6% of $925. We can do this by multiplying 0.06 (which is equivalent to 6%) by $925:

6% of $925 = 0.06 × $925 = $55.50

So, the rent for the second year would be:

$925 + $55.50 = $980.50

To find the rent for the third year, we need to increase the rent for the second year by 6%. We can follow the same process:

6% of $980.50 = 0.06 × $980.50 = $58.83

So, the rent for the third year would be:

$980.50 + $58.83 = $1039.33

To find the rent for any year n, we use the formula:

Rent for year n = $925 × (1 + 0.06)^n

In this formula, (1 + 0.06) represents the multiplier used to calculate the new rent each year.

For example, the multiplier for the second year is 1 + 0.06 = 1.06, and the multiplier for the third year is 1.06 × 1.06 = 1.1236 (rounded to four decimal places).

To find the rent for the fifth year, we plug in n = 5:

Rent for year 5 = $925 × (1 + 0.06)^5 = $925 × 1.3382 = $1238.84 (rounded to the nearest cent)

So, the monthly rent for the apartment would be $1238.84 in the fifth year.

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A group of 6 friends went to the movies. In addition to their​ tickets, they bought a large bag of popcorn to share for ​$9. 50. The total was ​$54. 50. Complete parts a and b

Answers

Answer:

Step-by-step explanation:

a) Let x be the cost of each ticket. Then the total cost of the tickets for the 6 friends is 6x. The total cost, including the popcorn, is $54.50. So we can set up an equation:

6x + $9.50 = $54.50

Solving for x, we get:

6x = $45.00

x = $7.50

So each ticket costs $7.50.

b) To find the cost per person, we need to add up the cost of each ticket and divide by the number of people. The cost of all 6 tickets is:

6 tickets × $7.50/ticket = $45.00

Adding the cost of the popcorn, we get:

$45.00 + $9.50 = $54.50

So the total cost for the 6 friends is $54.50, and the cost per person is:

$54.50 ÷ 6 people = $9.08 per person.

Therefore, each person contributed $9.08 towards the total cost of the tickets and popcorn.

This equation shows how the cost of a plumber's visit is related to its duration in hours. C = 51d

The variable d represents the duration of the visit in hours, and the variable c represents the cost. If a plumber's visit lasted 1 hour, how much would it cost?

Answers

The cost of a plumber's one-hour visit is $51, determined by the linear equation C = 51d, where C is the cost and d is the duration of the visit in hours.

How is the cost of a plumber's visit determined by duration?

If a plumber's visit lasts for a certain duration, the cost can be determined using the equation

                           C = 51d

where C is the cost and d is the duration of the visit in hours.

In this case, the duration of the plumber's visit is given as 1 hour. Substituting d = 1 in the equation, we get

                             C = 51(1) = $51

as the cost of the plumber's visit.

Therefore, if the plumber's visit lasts for one hour, it would cost $51 according to the given equation.

This cost may vary if the duration of the visit changes, as it is directly proportional to the duration of the visit.

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If 2/3 of a mini pizza cost $2. 40, what would 1/2 of a mini pizza cost?

Answers

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

1/2 of a mini pizza would cost $0.60.

If 2/3 of a mini pizza cost $2.40, then 1/3 of a mini pizza would cost half of that:

1/3 of a mini pizza = 1/2 * $2.40 = $1.20

To find the cost of 1/2 of a mini pizza, we can divide the cost of 1/3 of a mini pizza by 2:

1/2 of a mini pizza = 1/2 * $1.20 = $0.60

Therefore, 1/2 of a mini pizza would cost $0.60.

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What is the value of B? Bº 58° 61°​

Answers

Answer:

61 degrees

Step-by-step explanation:

Triangle interior measures add up to 180 degrees.

61 + 58 + x = 180

119 + x = 180

x = 61

hope this helps :) !!!

PLEASE ANYONE 100 POINTS LOL
a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.

Answers

The resultant component of the vector addition, 1/3a - 2b is (-9, 0).

What is the resultant component of the vectors?

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

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Which of the equations shown have infinitely many solutions? Select all that apply. A. 3x – 1 = 3x + 1 B. 2x – 1 = 1 – 2x C. 3x – 2 = 2x – 3 D. 3(x – 1) = 3x – 3 E. 2x + 2 = 2(x + 1) F. 3(x – 2) = 2(x – 3)

Answers

The two equations with infinite solutions are D 3(x – 1) = 3x – 3 and E2x + 2 = 2(x + 1)

Which equations have infinite solutions?

An equation has infinite solutions if we can remove the dependence of the variable, and we end with a true equation.

For example, option D is:

3(x - 1)  =3x - 3

Expanding the left side:

3x - 3 = 3x - 3

Subtract 3x in both sides:

-3 = -3

That is true for any value of x.

The other correct option is E:

2x + 2 = 2(x + 1)

2x + 2 = 2x + 2

2 = 2

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if an airplane travels around the world, flying just above the equator it would travel 1.25 x 10^4 miles. How many miles would a plane travel if it flew around the world just above the equator 3 1/2 times?

(in standard form)

Answers

A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.

If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:

1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles

To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.

We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.

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On Thursday,30 scholars went to morning homework help. On Friday, 24 scholars went. What is the percent decrease in the number of scholars who went to morning homework help from Thursday to Friday?
PLEASE HELP 20 POINTS

Answers

There is 20% decrease in scholars number who went to the morning homework help.

What is the percent decrease?

To get the scholar's percent decrease, we need to calculate the difference between them on Thursday and Friday and theb divide that by the number of scholars on Thursday.

Data:

Number of scholars on Thursday = 30

Number of scholars on Friday = 24

Difference = 30 - 24 = 6

The percent decrease = (6/30) x 100%

The percent decrease = 0.2 * 100%

The percent decrease = 20%

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Which expression is equivalent to 6\cdot 6^{-2}\normalsize?6⋅6


−2


?

Answers

The expression 6 * 6^(-2) is equivalent to 1/6.

Simplify this expression using the rule of exponents?

We can simplify this expression using the rule of exponents that states a^m / a^n = a^(m-n), which gives:

6 * 6^(-2) = 6 / 6^2 = 6 / 36 = 1/6

Let's break down the expression and simplify it step by step:

6 * 6^(-2)

We start by evaluating the exponent, which means we take the reciprocal of 6^2:

6 * (1/6^2)

Now we simplify the denominator of the fraction:

6 * (1/36)

Finally, we can simplify the expression by dividing 6 by 36:

1/6

So, the expression 6 * 6^(-2) is equivalent to 1/6. This means that if we multiply 6 by 6 raised to the power of -2 (or 1/6^2), we get the same result as dividing 6 by 6^2 (or 36), which is  1/6.

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One medical procedure used today allows parents to select the gender of their future baby. The procedure has been found to be effective 75% of the time, meaning that 75% of the time parents get a baby of the preferred gender. Suppose this method is used by 5 couples at one particular clinic. For #6 and 7, write the numeric value and write in words what it represents

Answers

6. The probability that all 5 couples will have a baby of the preferred gender is 0.2373.

7. The probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.

6. What is the probability that all 5 couples will have a baby of the preferred gender?

Answer: The probability that one couple will have a baby of the preferred gender is 0.75. Assuming the gender of each baby is independent of the others, the probability that all 5 couples will have a baby of the preferred gender is 0.75⁵ = 0.2373.

Numeric value: 0.2373

In words: The probability that all 5 couples will have a baby of the preferred gender is 0.2373.

7. What is the probability that at least 4 of the 5 couples will have a baby of the preferred gender?

Answer: There are two ways to approach this problem. One way is to calculate the probability of each possible outcome (0 to 5 couples having a baby of the preferred gender) and then add up the probabilities for the outcomes where at least 4 couples have a baby of the preferred gender. Another way is to use the complement rule and subtract the probability that fewer than 4 couples have a baby of the preferred gender from 1.

Using the first method, we can calculate the probabilities as follows:

- 0 couples: 0.25⁵ = 0.0009766

- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465

- 2 couples: 10 x 0.75² x 0.25³ = 0.08789

- 3 couples: 10 x 0.75³ x 0.25² = 0.2637

- 4 couples: 5 x 0.75⁴ x 0.25 = 0.3955

- 5 couples: 0.75⁵ = 0.2373

The probabilities for the outcomes where at least 4 couples have a baby of the preferred gender are 0.3955 and 0.2373, so the total probability is 0.3955 + 0.2373 = 0.6328.

Using the second method, we can calculate the probability that fewer than 4 couples have a baby of the preferred gender as follows:

- 0 couples: 0.25⁵ = 0.0009766

- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465

- 2 couples: 10 x 0.75² x 0.25³ = 0.08789

- 3 couples: 10 x 0.75³ x 0.25² = 0.2637

The probability that fewer than 4 couples have a baby of the preferred gender is the sum of these probabilities: 0.0009766 + 0.01465 + 0.08789 + 0.2637 = 0.3672.

Therefore, the probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.

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Assume that a cell is a sphere with radius 10-3 or 0.001 centimeter, and that a cell’s density is 1.1 grams per cubic centimeter. koalas weigh 6 kilograms on average. how many cells are in the average koala? hippos weigh 1,400 kilograms on average. how many cells are in the average hippo? solution

Answers

There would be   1.302 x 10¹² cells in koala, and  there are  3.04 x 10^17 cells in the average hippo.

To find the number of cells in the average koala, we first need to find the volume of the koala in cubic centimeters, since we know the density of the cell and can use that to find the mass of the koala in grams.

The average weight of a koala is 6 kilograms, which is equivalent to 6,000 grams. We can use the density of the cell to find the volume of the koala:

Density = Mass / Volume

1.1 g/cm³ = 6,000 g / Volume

Volume = 6,000 g / 1.1 g/cm³

Volume = 5,454.54 cm³

Next, we need to find the volume of one cell:

Volume of cell = 4/3 * π * (0.001 cm)³

Volume of cell = 4.188 x 10⁻⁹ cm³

Finally, we can divide the volume of the koala by the volume of one cell to find the number of cells in the average koala:

Number of cells = 5,454.54 cm³ / (4.188 x 10⁻⁹ cm³)

Number of cells = 1.302 x 10¹²

Therefore, there are approximately 1.302 x 10¹² cells in the average koala.

To find the number of cells in the average hippo, we can follow the same process. The average weight of a hippo is 1,400 kilograms, which is equivalent to 1,400,000 grams. Using the density of the cell, we can find the volume of the hippo:

Density = Mass / Volume

1.1 g/cm^3 = 1,400,000 g / Volume

Volume = 1,400,000 g / 1.1 g/cm³

Volume = 1,272,727.27 cm³

Dividing the volume of the hippo by the volume of one cell, we get:

Number of cells = 1,272,727.27 cm³ / (4.188 x 10⁻⁹ cm³)

Number of cells = 3.04 x 10¹⁷

Therefore, there are approximately 3.04 x 10¹⁷ cells in the average hippo.

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Simplify to create an equivalent expression. {2(-2-4p)+2(-2p-1)}2(−2−4p)+2(−2p−1)

Answers

4(-2 - 4p) + 4(-2p - 1)

How can the expression {2(-2-4p)+2(-2p-1)} be simplified?

To simplify the expression {2(-2-4p)+2(-2p-1)}, we can distribute the coefficients and simplify the terms.

First, let's distribute the coefficient of 2 to the terms inside the first parentheses: 2 * -2 = -4 and 2 * -4p = -8p.

Next, distribute the coefficient of 2 to the terms inside the second parentheses: 2 * -2p = -4p and 2 * -1 = -2.

Now, we have:

{-4 - 8p + (-4p - 2)}

Next, combine like terms within the parentheses:

{-4 - 8p - 4p - 2}

Simplifying further:

{-6 - 12p}

Therefore, the simplified equivalent expression for {2(-2-4p)+2(-2p-1)} is -6 - 12p.

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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.

Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.

Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).

Answers

The theoretical probability of the spinner not landing on yellow, would be 75 %.

How to find the probability ?

In order to calculate the likelihood of the spinner not landing on yellow, it is necessary to initially identify the quantity of non-yellow partitions and subsequently divide this by the full tally of sections. The spinner comprises a total of 8 individual segments.

Of these, two (i.e., sections 2 and 3) are colored in shades of yellow, hence totaling two yellow sectors. This leaves a further six compartments - numbered 1, 4, 5, 6, 7 and 8, that do not fall into the category of "yellow."

The probability is therefore :

= ( Number of not yellow sections ) / ( Total number of sections )

= 6 / 8

= 3 / 4

= 75 %

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