A bicycle club logged 9,860 miles. If the
29 members of the club each rode the
same number of miles, how many miles
did each member ride?

There are 73,440 ways can the singers finish first through fourth​.

A way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.

Given that, There are 18 finalists in a singing competition. The top four singers receive prizes.

In this case, the order is required, so we'll use permutation here. You need to pick 4 out of 18.

\(^{n} P_{r}\) = n!/(n-r)!

n = 18 and r = 4

18P4 = 18!/(18-4)!

= 18!/14!

= 73,440

Hence, there are 73,440 ways possible.

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Answer:

240 sq feet

Step-by-step explanation:

for a rectangle

area = length * width

a = 20 * 12

a = 240

240 sq feet

Answer:

The number can be expressed in multiple forms

Fraction form \(x=\frac{2962}{67}\)  or decimal form  \(x=44.21\)

Step-by-step explanation:

Lets break the problem down

"times" is multiplication *

The difference between 2 numbers is subtraction  \((x-y)\)

A number plus a number is addition \(x+y\)

\(68(x-45)=x+-98\)

Lets solve for \(x\).

Lets start on the left side.

Distribute 68 to the terms inside the parenthesis.

\(68x-3060=x+-98\)

A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.

\(68x-3060=x-98\)

Subtract \(x\) from both sides of the equation.

\(68x-3060-x=-98\)

Subtract \(x\) from \(68x\).

\(67x-3060=-98\)

Add 3060 to both sides of the equation.

\(67x=2962\)

Divide both sides of the equation by 67.

\(x=\frac{2962}{67}\) or as a decimal \(x=44.21\)

The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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The confidence interval: 59.5 to 61.5; margin of error: ± 1.0. Option B is the correct answer.

The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.

The confidence interval is given as:

x' ± 1.96 s/√n

Substituting the value of x' = 60.5, s = 5, and n = 100.

60.5 ± 1.96 (5/ √√100)

60.5 ± 1.96 (5/10)

60.5 ± 0.98

Hence, the confidence interval: 59.5 to 61.5; margin of error: ± 1.0. Option B is the correct answer.

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Answer:

See below

Step-by-step explanation:

(a) the equation

(b) If f(t) = 1000000

Therefore , the solution of the given problem of unitary method comes out to be the fence's true length is about 17.92 feet.

Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.

Here,

We can utilise the idea of proportions to determine the fence's actual length based on the scale drawing.

Given:

24 feet are represented by 3.75 inches at the given scale.

Let's establish a ratio:

=>  24 feet x 3.75 inches = 2.8 inches

where x represents the fence's real length.

If we cross-multiply, we obtain:

=>  24 feet * 2.8 inches * 3.75 inches

If we simplify, we get:

=>  3.75x = 67.2

By multiplying both sides by 3.75, we obtain:

=>  x = 67.2 / 3.75

=> × ≈ 17.92 feet

Therefore, the fence's true length is about 17.92 feet.

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Answer:

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

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

Answer:

y= 4x + 1 ???

Step-by-step explanation:

I don't know this.. I haven't gotten to this yet so this is just a guess.. Im sorry if its wrong

Answer:  it would be 128

Step-by-step explanation:

you have to find 25 times __ to equal 400 than when you do that you would have to multiply that by 8 to find how many students will travel. hope this helped. :]

The given rational function has a vertical asymptote at x = 12, and the

graph has x and y-intercept at the negative x and y-axis.

Response:

(a) The point (5, -2) is not on the graph

(b) f(x) = -1

(c) If f(x) = 2, x = 30

(d) Domain = (-∞, 12) ∪ (12, ∞)

(e) x-intercept is at x = -6, which is the point (-6, 0)

(f) The y-intercept is at y = -0.5, which is the point (0, -0.5)

(g) A zeros of f, is x = -6

The possible given function is presented as follows;

\(f(x) =\mathbf{\dfrac{x + 6}{x - 12}}\)

(a) When x = -2, we have;

\(f(-2) = \dfrac{(-2) + 6}{(-2) - 12} = \dfrac{4}{-14} = \mathbf{-\dfrac{2}{7}}\)

Therefore;

The point (\(-\frac{2}{7}\), -2) is on the graph, which gives;

(b) If x = 3, we have;

\(f(3) =\mathbf{ \dfrac{3 + 6}{3 - 12}} = \dfrac{9}{-9} =-1\)

(c)  If f(x) = 2, we have;

\(f(x) =2 = \mathbf{ \dfrac{x + 6}{x - 12}}\)

2·(x - 12) = x + 6

2·x - x = 6 + 2 × 12 = 30

x = 30

(d) The  domain which is the list of possible x-values, which is expressed as follows;

Domain; -∞ < x < 12, and 12 < x < ∞

Which gives;

(e) The x-intercepts are;

\(0 = \mathbf{ \dfrac{x + 6}{x - 12}}\)

(f) The y-intercept

\(At \ the \ y-intercept, \ f(x) = \dfrac{0 + 6}{0 - 12} = -\dfrac{1}{2} = \mathbf{ -0.5}\)

(g) The zeros of the graph, f, are the points at which the graph crosses the x-axis which at the point x = -6

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Answer:

g(3−2x)=12x2−36x+29

Step-by-step explanation:

Do you need step by step?

Answer:

\(f(x) = 3 {x}^{9 } + 7x ^{5} + 32x ^{2} + 7\)

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Diagonals of a Parallelogram

Given the parallelogram STUV, it can be proven that the diagonals VT and SU bisect each other, that is, they define a point Z where:

SZ = ZU

VZ = ZT

We are given the following lengths:

SZ = 5

VT = 14

Since:

SZ = ZU

It follows that:

ZU = 5

The total length of the diagonal VT is cut in half by point Z, which defines the lengths:

VZ = 14/2 = 7

ZT = VZ = 7

Finally, since SU is the total length of the diagonal, then:

SU = SZ + ZU = 5 + 5 = 10

Summarinzing:

ZU = 5

SU = 10

VZ = 7

ZT = 7

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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ANSWER:

STEP-BY-STEP EXPLANATION:

To determine the probability we must calculate the following number of combinations:

Combination formula:

Number of ways of selecting 5 numbers out of 24 is C(24, 5)

Number fo ways of selecting 4 numbers out of 10 is C(10, 4):

So number of ways of selecting five numbers is:

Out of these possible ways, one one is for jackpot so

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

Answer:

\((i+2)^4\)

Step-by-step explanation:

assuming the equation is \((\sqrt{2+i})^8\) this simplifies to \((i+2)^4\) where i =\(\sqrt{-1}\)

Step-by-step explanation:

\(( \sqrt{2 + i} ) {}^{8} = (2 + i) {}^{ \frac{1}{2} \times8 } \)

\((2 + i) {}^{4} \)

Split this up

\((2 + i) {}^{2} \times (2 + i) {}^{2} \)

Use the Perfect Square Trinomial

\((a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} \)

\((2 { }^{2} + 2(2)i + {i}^{2} )(2 {}^{2} + 2(2)i + {i}^{2} \)

\( {i}^{2} = - 1\)

so

\((3 + 4i)(3 + 4i)\)

\(9 + 24i - 16\)

\( - 7 + 24i\)

For B>0, the graph of y = sin Bx will have a period of (2π/B) units. The period of a sine function is the length of one complete cycle of the function.

The period of a trigonometric function is the length of one complete cycle of the function.

For the sine function, this is the distance between two consecutive points at which the sine value is equal to zero, or the distance between two consecutive maxima or minima. In this case, the graph of y = sin Bx is multiplied by a factor of B, which will stretch or compress the graph along the x-axis by a factor of B.

Therefore, the period of the graph will be (2π/B) units.

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Answer:

Isosceles right triangle

Step-by-step explanation:

Step-by-step explanation:

Isosceles Right Triangle

Five bottles of orange juice cost $5.05.

To answer this question, we first need to find out the price of one bottle of juice. As we know that Mia bought 10 bottles for $10.10 total, the price of one bottle of juice can be found by dividing the total cost by the number of bottles. So, $10.10 divided by 10 equals $1.01. This means that each bottle of orange juice costs $1.01.

Now that we know the cost of one bottle of juice, we can calculate the cost for 5 bottles. This can easily be done by multiplying the cost of one bottle by 5. Therefore, $1.01 multiplied by 5 equals $5.05.

So, five bottles of orange juice cost $5.05.

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Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

Answer:

32,500

Step-by-step explanation:

22,750 = .70x. (Paid 70% since it was 30% discount)

divide both sides by .70

x = 32,500

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

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The limits of the function for this problem are given as follows:

In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.

At x = -2, we have that:

As the lateral limits are equal, lim x -> -2 f(x) = 3.

At x = 1, we have that:

As the lateral limits are different, the lim x -> 1 f(x) does not exist.

At x = 4, we have that:

As the lateral limits are equal, lim x -> 4 f(x) = -3.

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Answer:

D is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

y=48

Step-by-step explanation:

180-135=55-7=y=48

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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