A champion bicyclist training in a flat, open area

could ride at 3 times the speed of the wind if the

wind were absent. On this particular day, she

traveled 30 miles against the wind in 2 more hours

than it took to go 40 miles with the wind on the

return trip. What is the speed of the bike in no

wind?

Answer:

35

Step-by-step explanation:

perimeter = sum of the lengths of the sides

In a parallelogram, opposite sides are congruent.

Two sides have length 7.5 cm.

We need the length of the top and bottom sides.

area = base × height

62 cm² = base × 6.2 cm

base = (62 cm²)/(6.2 cm)

base = 10 cm

Two sides have length 10 cm.

perimeter = 7.5 cm + 7.5 cm + 10 cm + 10 cm

perimeter = 35 cm

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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Solution of the given system is,

x = 8

y = 11

The given system of equation

-12x + 5y = 9 ....(i)

    y = 2x - 5  ...(ii)

Now we have to solve it by using substitution method.

So put value of y from equation (ii) into equation (i)

Therefore,

⇒ -12x + 5y = 9

⇒ -12x + 5(2x - 5) = 9

⇒ -12x + 10x - 25  = 9

⇒                    -2x  = 16

⇒                        x  = 8

Now put the values of x into (ii) we get,

⇒ y = 2x8 - 5

⇒ y = 11

Hence,

solutions be ,

x = 8

y = 11

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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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The experiment is binomial , probability that 3 out of 14 customers buy a magazine is 0.06 and the expected value is 1.036.

The experiment described is binomial because it satisfies the following conditions:

The probability that exactly 3 out of the first 14 customers buy a magazine. Using the binomial probability formula:

[tex]P(X = k) = (nCk) \times (p^k) \times {q}^{n - k} [/tex]

Where:

n = number of trials (14 in this case)

k = number of successful trials (3 in this case)

p = probability of success (7.4% or 0.074)

q = 1-p

Plugging in the values:

P(X = 3) = (14C3) × (0.074³) × 0.926¹¹

P(X= 3) = 0.0633

The expected number of customers from this sample that will buy a magazine can be calculated using the formula:

E(X) = n × p

Where:

- n is the number of trials

- p is the probability of success

Plugging in the values:

E(X) = 14 × 0.074 = 1.036

Therefore, the experiment is binomial and the expected value is 1.036.

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The graph of the inverse function is given by the image presented at the end of the answer, and the correct option is given by option 3.

The parent function for this problem is the cube function translated up two units, hence it is defined as follows:

y = x³ + 2.

To obtain the inverse function, first we must exchange the variables x and y on the definition of the function, as follows:

x = y³ + 2.

Then we must isolate the variable y, as follows:

[tex]y^3 = x + 2[/tex]

[tex]y = \sqrt[3]{x + 2}[/tex]

Which has the correct dashed graph given by option 3 on the image given.

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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

The value of f(-7) is 172.

To find the value of f(-7) for the given function f(x) = 4x^2 + 6x + 9, we substitute -7 for x in the function and evaluate it.

f(-7) = 4(-7)^2 + 6(-7) + 9

Simplifying the equation:

f(-7) = 4(49) - 42 + 9

= 196 - 42 + 9

= 163 + 9

= 172

Therefore, f(-7) = 172.

By substituting -7 into the function, we obtained the value of 172. This means that when x is equal to -7, the corresponding value of the function f(x) is 172.

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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!

Answer:

-3x² - x - 5

Step-by-step explanation:

(3x² - 7x - 4) - (6x² - 6x + 1) =
= -3x² - x - 5

b'

Let the given points be A(3,-5) and B(5,-1).

AB= sqrt of (5−3) ² +(−1+5)²

= sqrt of 4+16

= sqrt of 20

=2 sqrt of 5 units

Answer:67/24

hope it helps bye

The expression equivalent to the given numerical expression is 67/24.

The given numerical expression is 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3.

Here, 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3

= 2/3 ÷ 16+(9/12 +2/12)÷1/3

= 2/3 × 1/16 +11/12 ×3/1

= 2/48 + 33/12

= 1/24 + 33/12

= 1/24 + 66/24

= 67/24

Therefore, the expression equivalent to the given numerical expression is 67/24.

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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 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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Area of triangle A   = 13.5 square units

Area of triangle B   = 10.5 square units

Total area of figure =  24 square units

In the given figure,

It consist of two triangles

Now for triangle A :

Height = 3

Base    = 9

Since we know that,

Area of triangle = (1/2) x base x height

                          = 0.5 x 9 x 3

                          = 13.5 square units

Now for triangle B :

Height = 3

Base    = 7

Since we know that,

Area of triangle = (1/2) x base x height

                          = 0.5 x 7 x 3

                          = 10.5 square units

Now the total are of figure is sum of are of both triangles,

Therefore,

total area of figure,

⇒ 13.5 + 10.5

⇒ 24 square units

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The missing figure of question is attached below:

Answer:

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

Step-by-step explanation:

The ascending order of the rational numbers are -1.75 < -1.3 < 0.41 < 1.8

Given are the list of the rational numbers, so,

1 4/5, -7/4, 41% and -1.3

So,

1) The fraction form :-

a) 1 4/5 = 9/5

b) -7/4

c) 41% = 41/100

d) -1.3 = 13/10

2) The decimal form :-

a) 1 4/5 = 9/5 = 1.8

b) -7/4 = -1.75

c) 41% = 41/100 = 0.41

d) -1.3 = 13/10 = -1.3

3) The ascending order of the rational numbers =

You can arrange them by seeing the value and sign,

-1.75 < -1.3 < 0.41 < 1.8

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

Convert units to feet using the scale

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

Evaluate

Area = 38.5 square feet

Also, we have

Width = 2 * 1/2 * 7 feet

Width = 7 feet

For the plus-shaped logo, we have

Area = 5 * 1/2 * 1/2

Convert units to feet using the scale

Area = 5 * 1/2 * 7 * 1/2 * 7

Evaluate

Area = 61.25 square feet

Also, we have

Width = 3 * 1/2 feet * 7

Width = 10.5 feet

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

This is because its area is not up to the maximum area (40 square feet) and the width is greater than the minimum width (4 feet)

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The equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.

we have Center at (9, 5) and passes thorough (13, 7).

To find the equation of a circle with center (h, k) and a point (x, y) on the circle, we can use the standard form equation of a circle:

(x-h)² + (y-k)² = r²

So,  (x - 9)² + (y - 5)² = r

Since the circle passes through (13, 7), then

(13 - 9)² + (7 - 5)² = r²

²4 + (2)² = r²

16 + 4 = r²

20 = r²

So, the equation of circle is

(x - 9)² + (y - 5)² = 20

Therefore, the equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.

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Yes, the coefficient of a value can be negative in an exponential function.

A coefficient in mathematics is a multiplicative factor in some term of a polynomial, series, or expression; it is generally a number, although it can be any expression.

Recall that the general form of an exponential function is f(x) = a^(bx + c), where a is the base.

This can be negative or positive. But cannot be equal to zero. A negative exponential function can model the decay of a radioactive substance or, in accounting, depreciation of an asset.

Thus, it is correct to state that , the coefficient a value can be negative in an exponential function.

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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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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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Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Answer:x = {-4, 4}

explanation:

y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9. Therefore, option B is the correct answer.

Given that, trajectory can be mapped by the equation f(x) = -x² + 11x - 18.

Here, -x² + 11x - 18=0

-x² + 9x+2x - 18=0

-x(x-9)+2(x-9)=0

(x-9)(-x+2)=0

x-9=0 and -x+2=0

x=9 and x=2

Therefore, option B is the correct answer.

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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.

We are unable to determine the volumes of the individual components and the composite figure due to missing data on the radii and precise component configurations.

We must determine the volumes of the three separate parts—a cylinder, a 1 mm tall cone—in order to get the volume of the composite figure.

The 3 mm tall cone's volume is:

The formula  [tex]V = (1/3)r^{2} h,[/tex]  where r is the radius of the base and h is the height, determines the volume of a cone.

We must determine the radius because the cone's height is 3 mm. We are unable to determine the volume of the 3 mm tall cone without additional information.

Dimensions of the cylinder:

The formula V = r2h, where r is the radius of the base and h is the height, determines the volume of a cylinder.

We are unable to determine the volume of the cylinder without precise measurements for its height and radius.

Volume of the 1 mm tall cone: Once more, in order to calculate the volume of the 1 mm tall cone, we need to know the radius of the base. Without this additional information, we are unable to do so.

The composite figure's volume:

We would need to know the sizes and configurations of the different parts (cones and cylinder) within the composite figure in order to determine its volume.

We are unable to determine the volume of the composite figure without this information.

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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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