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A frog starts jumping from the middle of a circular pond.
The pond is 12 metres across, from one side to the other.
The frog always jumps half the distance left to the edge of the pond.
How far is the frog from the edge after 3 jumps?
A 10.5m
B 75 cm
C 150 cm
D 5.25m
E 125C

Answer:

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

Let E represent the number of Eagle fans and S represent the number of Spartan fans at the start of the game.

We can set up two equations using the given information:

Now we can solve the equations.

From equation (1), we can replace E in equation (2), the solve for S:

Now find the number of Eagle fans using equation (1):

The population grow by 24.7% between the years 2004 and 2009

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

Population in 2004 = 2122

Population in 2009 = 2647

The growth of the population between the years is calculated as

Percentage = Population in 2009/Population in 2004  - 1

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

Percentage = 2647/2122 - 1

Evaluate

Percentage = 24.7%

Hence, the population grow between the years by 24.7%

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The logo that fits the requirement is the circle logo i.e. logo 1

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

The figures that represent the logos

For the circle logo, we have

Area = 3.14 * 1/2 * 1/2

Convert units to feet using the scale

Area = 22/7 * 1/2 * 1/2 * 7 * 7

Evaluate

Area = 38.5 sq feet

Also, we have

Width = 1/2 feet *7

Width = 3.5 feet

For the plus sign, we have

Area = 5 * 1/2 * 1/2

Convert units to feet using the scale

Area = 5 * 1/2 * 1/2 * 6 * 6

Evaluate

Area = 45 sq feet

Also, we have

Width = 3 * 1/2 * 6

Width = 9 feet

Hence, the logo that fits the requirement is the circle logo i.e. logo 1

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Answer:

90

Step-by-step explanation:

This type of problem is an example of combinations. In this case, in one salad, it states that you can chose between 5 bases, 3 proteins, and 6 dressings.

In this problem, you would have to multiply all numbers together.

In this case, 5(bases)x3(protiens)x6(dressings)=90

I hope this helps you!

The probability that a randomly chosen person from this group has type B is 0.4.

The probability of type AB is 0.12, and the probability of type B or type AB is 0.52.

We have,

The probability that a randomly chosen person from this group has type B is given by the number of people with blood type B divided by the total number of people in the group:

Probability of type B

= Number of people with type B / Total number of people

In this case, the number of people with blood type B is 20, and the total number of people is 50 (22 + 20 + 6 + 2).

Probability of type B = 20 / 50 = 0.4

Similarly, the probability that a randomly chosen person from this group has type AB is given by the number of people with blood type AB divided by the total number of people:

Probability of type AB = Number of people with type AB / Total number of people

In this case, the number of people with blood type AB is 6, and the total number of people is 50. Therefore,

Probability of type AB = 6 / 50 = 0.12

To find the probability that a randomly chosen person from this group has blood type B or type AB, we need to add the probabilities of both events:

Probability of type B or type AB = Probability of type B + Probability of type AB

Probability of type B or type AB = 0.4 + 0.12 = 0.52

Thus,

The probability that a randomly chosen person from this group has type B is 0.4, the probability of type AB is 0.12, and the probability of type B or type AB is 0.52.

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Answer:

sin( 3pi/4 ) = -√2/2

So, B.

Answer:

m<1 = 47 degrees

m<2 = 43 degrees

m<3 = 90 degrees

m<4  = 43 degrees

Step-by-step explanation:

The maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

To maximize the objective function z = 4x + 4y subject to the given constraints, we can solve this linear programming problem using the graphical method.

First, let's graph the feasible region determined by the constraints:

1. Graph the line 2x + 4y = 28:

  Rewrite the equation in slope-intercept form: y = -0.5x + 7

  Plot two points on the line: (0, 7) and (14, 0), and draw a line through them.

2. Graph the line 5x + 6y = 50:

  Rewrite the equation in slope-intercept form: y = (-5/6)x + (25/3)

  Plot two points on the line: (0, 25/3) and (10, 5/3), and draw a line through them.

3. Shade the region that satisfies the constraints:

  Shade the region below the line 2x + 4y ≤ 28.

  Shade the region below the line 5x + 6y ≤ 50.

  The feasible region is the intersection of the shaded regions.

Next, we evaluate the objective function at the corner points of the feasible region to determine the maximum value.

The corner points of the feasible region are:

A: (0, 7)

B: (0, 25/6)

C: (14/3, 4)

D: (10, 5/3)

Evaluate the objective function at each corner point:

z(A) = 4(0) + 4(7) = 28

z(B) = 4(0) + 4(25/6) = 50/3

z(C) = 4(14/3) + 4(4) = 92/3

z(D) = 4(10) + 4(5/3) = 140/3

The maximum value of z is obtained at z(C) = 92/3.

Therefore, the maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

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Answer:

x = 8, m2 = 78, m4 = 102, m6 = 78, m7 = 78,

Step-by-step explanation:

The distribution of the sample means will have a smaller standard deviation

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

Observations = 9

The population is not given

However by the theorem of the central limit; we understand that

The distribution of the sample means will always have a smaller standard deviation

This is because the sample mean selected from the population might not totally represent the whole population, but would have smaller standard deviation

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A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Answer:5

Step-by-step explanation:

5098

Answer:

here is the answer in the photo

Step-by-step explanation:

mark branliest

Of the $8,400 in sales, the store donated about 8% to hospitals.

To find the percentage of $8,400 that was donated to hospitals, we can set up a proportion using the given information.

Let's represent the percentage of the sales donated as x.

We can set up the proportion:

(x/100) = 672/8400

To solve for x, we can cross-multiply and then divide:

8400 * x = 672 * 100

8400x = 67200

x = 67200 / 8400

x = 8

Therefore, the store donated approximately 8% of $8,400 to hospitals.

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Answer: Answer is seen below (sorry if its confusing, this is what I got though)

Step-by-step explanation:

Answer:

Let's start by figuring out how many aliens are captured every four hours. If half of the aliens are captured every four hours, that means the number of remaining aliens is also halved every four hours. So we can use exponential decay to model the number of aliens remaining after t four-hour periods:

N(t) = N₀ (1/2)^t

where N₀ is the initial number of aliens and t is the number of four-hour periods that have passed.

The initial number of aliens is 1,300, and we want to know how many remain after 14 four-hour periods (from 2:00am to 8:00pm, a total of 16 hours with 4-hour intervals):

N(14) = 1,300 (1/2)^14

N(14) ≈ 20.16

So there will be approximately 20 aliens remaining free at 8:00pm on Wednesday. Note that the actual number may be slightly different due to rounding, and also because we assumed that the capture rate remains constant throughout the 16-hour period.

Step-by-step explanation:

Let's start by figuring out how many aliens are captured every four hours. If half of the aliens are captured every four hours, that means the number of remaining aliens is also halved every four hours. So we can use exponential decay to model the number of aliens remaining after t four-hour periods:

N(t) = N₀ (1/2)^t

where N₀ is the initial number of aliens and t is the number of four-hour periods that have passed.

The initial number of aliens is 1,300, and we want to know how many remain after 14 four-hour periods (from 2:00am to 8:00pm, a total of 16 hours with 4-hour intervals):

N(14) = 1,300 (1/2)^14

N(14) ≈ 20.16

So there will be approximately 20 aliens remaining free at 8:00pm on Wednesday. Note that the actual number may be slightly different due to rounding, and also because we assumed that the capture rate remains constant throughout the 16-hour period. please give brainliest! :D

The time needed before the doctor administers the medication again is given as follows:

d) 22.2 hours.

The exponential function giving the amount of the medicine in the patient's bloodstream after t hours is given as follows:

[tex]A(t) = 500(0.93)^t[/tex]

The medication will be applied when the amount is given as follows:

A(t) = 100.

Hence the time needed is obtained solving the exponential function as follows:

[tex]100 = 500(0.93)^t[/tex]

[tex](0.93)^t = \frac{100}{500}[/tex]

[tex](0.93)^t = 0.2[/tex]

The logarithm of base 10 is the inverse of the exponential, hence:

[tex]t = \frac{\log{0.2}}{\log{0.93}}[/tex]

t = 22.2 hours.

Which is the time needed before the doctor administers the medication again.

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Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = [tex]\frac{1-7}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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The value of the side BC is equal to 10√21 in the simplest rationalized form using the trigonometric ratio of tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the tangent of angle 60°

tan 60° = BC/(10√7) {opposite/adjacent}

BC = 10√7 × tan 60° {cross multiplication}

BC = 10√7 × √3 {tan 60 = √3}

BC = 10√21

Therefore, the value of the side BC is equal to 10√21 in the simplest rationalized form using the trigonometric ratio of tangent.

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If the girls read the book at the same time, who will finish first: A. Shonda will finish first. Her ratio of chapters to hours is 2/1. Corine's rate of chapters to hours is 3/2, and 2/1 is a greater slope than 3/2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = 2/1

Slope (m) = 2.

Based on the table, the slope is the change in y-axis with respect to the x-axis and for Shonda it is equal to 2/1 or 2. Therefore, Shonda would finish before Corine because 2/1 > 3/2.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: hello am I solving for x?

Step-by-step explanation:question

A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

The statement of the function is (b) when x > 0, the graph is positive

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

The functions f(x) and g(x)

In the graph, we can see that

The graph of the function passes through (0, 0)

This means that

When x > 0, the graph is positive

When x < 0, the graph is negative

Hence, the statement of the function is (b)

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Strength: TThe strength of the scatterplot refers to how closely the data points cluster around a line or curve. Direction: The direction of the scatterplot refers to the general trend or pattern exhibited by the data points.

To describe the scatterplot and determine an appropriate scale, we can analyze the given data set:

x: 0, 2, -5, 3, 1, -4, 8, -6, -1

y: -3, -1, -13, 3, -1, -11, 12, -15, -5

Strength: TThe strength of the scatterplot refers to how closely the data points cluster around a line or curve.

Direction: The direction of the scatterplot refers to the general trend or pattern exhibited by the data points.

Scale: The appropriate scale for the scatterplot depends on the range of values for the x and y variables. To determine the scale, we need to consider the minimum and maximum values for each variable.

For x: The minimum value is -6 and the maximum value is 8.

For y: The minimum value is -15 and the maximum value is 12.

Based on these ranges, an appropriate scale for both x and y could be chosen with intervals of 2 or 5 units, depending on the desired level of detail.

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The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.

Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.

Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.

Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.

To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.

1.2 The set model:

To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.

Step 5/5

Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:

Now we know that the perimeter of the rectangle is given by the formula:

So, for this rectangle:

54 = 2(5x + x)

Simplifying and solving for x, we get:

54 = 2(6x)

27 = 6x

x = 4.5 cm

Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm

The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

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Answer:

A=6cm

D=11,66cm

Step-by-step explanation:

A=6cm

D=6²+10²=136

D=√136

D=11,66

The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.

We have,

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

The probability that a particular song is played is 0.23,

As can be seen that the problem is of combination, so we have to choose 5 out of 7,

Calculate the combination as shown below,

⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2

⁷C₅ = 7 × 6 / 2

⁷C₅ = 21

Calculate the probability as shown below,

P = ⁷C₅  × (0.23)⁵ × (0.77)²

P = 0.008

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complete question;

During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.

Answer:

1. Find the area of the rectangle in square yards. In this case, the area is 9 yards * 3 yards = 27 square yards.

2. Convert square yards to square feet. There are 9 square feet in 1 square yard. So, the area of the rectangle in square feet is 27 square yards * 9 square feet/square yard = 243 square feet.

Therefore, the area of the rectangle floor in square feet is 243 square feet.

Answer:243

Step-by-step explanation:

(9x3) x (3x3)

27 x 9 = 243