A relay race team has 4 runners who run different parts of the race.
There are 16 students on your track team. How many ways can your coach
select students to compete in the race?

The volume of the dough will be 4200 cubic inches in about 7.9 hours later.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A bread dough doubles in size every hour and is represented by the function y = 35(2ˣ⁻¹).

Now, The volume of the dough would be 4200 cubic inches when,

4200 =  35(2ˣ⁻¹).

2ˣ⁻¹ = 4200/35.

2ˣ⁻¹ = 120.

2ˣ/2 = 120.

2ˣ = 240.

[tex]log_22^x = log_2240[/tex].

[tex]x = 7.9[/tex].

So, About 7.9 hours later.

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The distance between the points is given by the equation D = 17 units

Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

The distance from A to B is the same as the distance from B to A

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane

Given data ,

Let the distance between the points be D

Now , the equation will be

Let the first point be P ( 1 , 0 )

Let the second point be Q ( 9 , 15  )

Now , Distance between two points is the length of the line segment that connects the two points in a plane.  

And , D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( ( 9 - 1 )² + ( 15 - 0 )² )

D = √ ( 8 )² + ( 15 )²

D = √ ( 64 + 225 )

D = √289

D = 17 units

Hence , the distance is 17 units

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The two expressions 15 + 5n and 5(3 + n) are both equivalent to each other when factorized and expanded respectively.

Equivalent equations are equations which have the same value when being solved.

15 + 5n and 5(3 + n)

15 + 5n

factorize

= 5(3 + n)

5(3 + n)

open parenthesis

15 + 5n

Therefore, it can be concluded that 15 + 5n and 5(3 + n) are equivalent.

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The exponent expression that is used to express 75 as sum of the powers of 8 is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The integer 75 is written as -

[tex]2^0+2^1+2^2+2^6[/tex]

75 is expressed as sum of the powers of 2, with whole number exponents.

To find 75 expressed as sum of the powers of 8, divide the integer by 8 -

[tex]8^0=1[/tex]

[tex]8^1=8[/tex]

[tex]8^2=64[/tex]

Only one integer 2 is left to complete the sum as 75.

To find what the power value is use the equation -

[tex]8^x=2\\x=\frac{2}{8} \\x=\frac{1}{3}[/tex]

So, the last exponent is [tex]8^{\frac{1}3} }[/tex].

So the expression is [tex]8^0+8^1+8^2+8^\frac{1}{3} =75[/tex].

Therefore, the exponent expression is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].

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Answer:

[tex]2\sqrt{14}[/tex]

D.

Step-by-step explanation:

10 in half is 5

[tex]b = \sqrt{c^{2} - a^{2} }[/tex]

b = [tex]\sqrt{81 - 25}[/tex] = [tex]\sqrt{56}[/tex] = [tex]2\sqrt{14}[/tex]

Step 1: Calculate the area of a square.

The area of a square is the square of one of its sides.

Therefore, the area of the square is A = s^2, where s is the length of one side.

Step 2: Find the length of one side of the garden.

The given area is A = 52 square feet.

Substituting this value into the equation for the area of a square, we get 52 = s^2.

Step 3: Solve for s.

To solve for s, we can take the square root of both sides of the equation.

This gives us s = √52 ≈ 7.21 feet.

Therefore, the approximate length of one side of Julie's garden is 7 feet.

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. Square units are used in the measuring.

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The quadratic equation that is satisfied here is given as x^2 + 5x - 176 = 0

Let's call the two integers x and y, where x is the smaller integer (N). Then, we have:

xy = 176

and

y = x + 5

We can substitute the second equation into the first equation to get:

x(x + 5) = 176

Expanding the left side, we get:

x^2 + 5x - 176 = 0

This is a quadratic equation that N satisfies.

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Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.

Answer:

x = 23

Step-by-step explanation:

4x + 8 - 8 = 100 - 8

4x = 92

(4x) / 4 = 92 / 4

x = 23

Answer:

x = 23

Step-by-step explanation:

4x + 8 = 100 ( subtract 8 from both sides )

4x = 92 ( divide both sides by 4 )

x = 23

Answer:

∠A = 49°

Step-by-step explanation:

Vertically opposite angles are congruent.

          ∠A = ∠B

   8x - 23 = 6x - 5

Add 23 to both sides,

          8x = 6x - 5 + 23

          8x = 6x + 18

Subtract 6x from both sides,

      8x - 6x = 18

            2x = 18

Divide both sides by 2,

              x = 18 ÷ 2

             x = 9

∠A = 8x - 23

     = 8*9 - 23

     = 72 - 23

     = 49°

Answer:512

Step-by-step explanation:

8^3

The probability that a woman is having one child of each sex is 0.2548.

The probability of having two children of the same gender (either both girls or both boys) can be calculated by multiplying the probability of having a girl or a boy is (which is 1/2 or 0.5) by itself twice, as each child is independent of the other:

0.5 × 0.5 = 0.25 (probability of having either two girls or two boys)

Since the total probability of having two girls or two boys is 0.5048 as given in the question, the probability of having one child of each sex is: 0.5048 - 0.25 = 0.2548.

Therefore, the probability that a woman with two children has one child of each sex is 0.2548

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Answer:

[tex]\dfrac{9}{6}=\dfrac{8}{v}[/tex]

 Similar polygons are two polygons with same shape and different size.

In similar polygons  

To find the value f 'x'

          [tex]\dfrac{ED}{E'D'} = \dfrac{CD}{C'D'}\\\\\dfrac{9}{6}=\dfrac{8}{v}[/tex]

In other words, altering the sampling distribution in this way increases the likelihood of making a type 1 error.

The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey.

Here,

The sampling distribution is a distribution of the values of a statistic (such as the mean or median) calculated from a set of sample data. It gives us information about how the statistic is likely to vary from sample to sample, and it is used in hypothesis testing to calculate the probability of observing certain results if the null hypothesis is true.

Filtering out all values below the mean has the effect of changing the shape, location, and spread of the sampling distribution. For example, if the original sampling distribution is normally distributed with a mean of 0 and a standard deviation of 1, filtering out all values below the mean would result in a new sampling distribution with a mean greater than 0 and a standard deviation smaller than 1.

When the sampling distribution is altered, for example by filtering out all values below the mean, it can have an effect on type 1 errors. Type 1 errors occur when we reject the null hypothesis when it is actually true.

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Answer: No.

Step-by-step explanation:

      This is not a function because it fails the vertical line test.

What is the vertical line test?

      The vertical line test is a test used to check if a graph is a function. If we place a vertical line on the graph, we should be able to shift it left and right without intersecting the graph in two places at once. Since this is a circle, it fails this test and is not a function.

A graph of XY with endpoints X(-3, 1) and Y(4,-5) and its image after the set of transformations (compositions) is shown in the image attached below.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

By applying a rotation of 180° to the ordered pairs of points X and Y, the coordinates of its image (X′Y′) can be calculated as follows:

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

Ordered pair X = (-3, 1)    →     Ordered pair X' = (-(-3), -(1)) = (3, -1).

Ordered pair Y = (4, -5)    →     Ordered pair Y' = (-(4), -(-5)) = (-4, 5).

Next, we would apply a translation based on this transformation rule:

           (x, y)                    →           (x − 1, y + 1)

Ordered pair X' (3, -1)     →         (3 − 1, -1 + 1)   = X" (2, 0).

Ordered pair Y' (-4, 5)    →        (-4 − 1, 5 + 1) = Y" (-5, 6).

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Answer:

a) y = 11x

b) y = $660

Step-by-step explanation:

a) For 10 people is $110, so simply divide.

110/10 = $11 per person.

y = 11x

b) So using that, substitute 60 for x.

y = 11(60)

y = $660

A collection of clearly defined objects is referred to as a set, and the universal set is the set that includes the components of all other sets, including the null set. The letter U is used to represent the universal set.

There are n sets and a finite Universal set U.

Defining the Union A∪B : If either of the two strings has a 1 on the ith bit, then the union of the two strings will also have a 1 on the ith bit, but if both strings have a 0 on the ith bit, then the union of the two strings will also have a 0 on the ith bit.

Defining the Intersection A∩B : If there is a 1 on the ith bit of both strings, then the intersection of the two strings will also have a 1 on the ith bit, but if there is a 0 on either string's ith bit, then the intersection of the two strings will also have a 0 on the ith bit.

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There are 30 dogs in the store, and 12 cats.

Let's call the number of dogs in the store "x".

Since the sum of the number of dogs and cats is 42, we know that:

x + (x - 18) = 42

Expanding and solving for x:

2x - 18 = 42

2x = 60

x = 30

So there are 30 dogs in the store, and (30 - 18) = 12 cats.

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One water tank can be rented for 160 dollars, according to the provided statement.

The radius of a circular is the separation between its centre and perimeter. Always, the circumference is twice the radius.

The volume of the cylinder-shaped water tank is given by the formula

V = πr²h, where

r is the radius

h is the height.

Substituting the given values, we get:

V = π(4 feet)²(2 feet) = 32π cubic feet

The cost of renting the water tank is given by the product of the volume and the cost per cubic foot:

Cost = 5 dollars/cubic foot × 32π cubic feet

Multiplying these values, we get:

Cost = 160π dollars

Therefore, it costs 160π dollars to rent one water tank.

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Answer:

121 voters.

Step-by-step explanation:

To answer this question, we need to find the expected number of students who will vote 9 years from now. To do this, we will apply the 10% decrease in voting every year.

Starting with 341 students who voted this year, we decrease the number of voters by 10% every year.

After 9 years, the number of voters would be:

341 * (1 - 0.10)^9 = 341 * 0.354813389233575594 = 121.05

So, it is expected that 121 students will vote 9 years from now. Rounding to the nearest whole number, we get 121.

Therefore, the answer is 121 students.

There are 121 voters expected to vote 9 years from now.

we need to determine the expected number of students who will vote 9 years from now. To do this, we will apply the 10% decrease in voting every year.

Starting with 341 students who voted this year, we decrease the number of voters by 10% every year.

After 9 years, the number of voters would be as;

341 x (1 - 0.10)^9

= 341 x 0.354813389233575594

= 121.05

So, it is expected that 121 students will vote 9 years from now. Rounding to the nearest whole number 121.

Therefore, the answer will be 121 students.

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The mean number of web-enabled devices for the 5 students is 3.8.

Before, solving this question the

The mean, or average, of the data is the sum of all the values divided by the number of values.

In this case, the mean for the data can be calculated as the sum of the number of devices for all 5 students divided by the number of students.

The calculation is as:

mean = (4 + 3 + 5 + 5 + 2) / 5

= 19 / 5

= 3.8

So, the mean number of web-enabled devices for the 5 students is 3.8. This gives an estimate of the average number of devices that students have.

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Answer:

hi :)

Step-by-step explanation:

Answer:

[tex]\dfrac{2+n}{7}[/tex]

Step-by-step explanation:

      [tex]\dfrac{2x + nx - 2y - ny}{7x - 7y}=\dfrac{2x - 2y + nx - ny}{7x - 7y}[/tex]

                                     [tex]=\dfrac{2(x - y) + n(x - y)}{7(x - y)}\\\\\\=\dfrac{(x -y)(2 +n)}{7(x - y)}\\\\\\=\dfrac{2 +n}{7}[/tex]

Thr solution to the inequality - 3a < -5 is -6 < -5. This can be written as negative 6 less than negative 5

- 3a < -5

if a = 2

- 3a < -5

substitute into the inequality

= -3(2) < -5

= -6 < -5

Hence, the solution to the given inequality when a = 2 is negative 6 less than negative 5

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The graph of the system of inequalities representing the constraints on the given graph of the first Quadrant is given below.

Red region is x + y ≤ 11

Blue region is x + 2y ≤ 12

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Two systems of linear inequalities are:

x + y ≤ 11

x + 2y ≤ 12

The graph of the system of inequalities representing the constraints on the given graph of the first Quadrant is given below.

Thus,

The graph of the system of inequalities is given below.

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The necessary equation in the case at hand will be 40x + 50 = P, where P represents the total number of pages read and x represents the number of hours read.

A mathematical equation compares two numbers or values to a meaningful word, for instance, 6 x 4 = 12 x 2.

An equation is employed when more than one factor needs to be considered in order to fully understand or describe a situation.

So, to answer the question:

Chole has read the first fifty pages of the book.

Every hour, he reads forty pages.

For more than x hours, he reads.

The equation will then be as follows:

40x + 50 = P

P is the total number of pages read, while x denotes the number of hours spent reading.

Therefore, the necessary equation in the case at hand will be 40x + 50 = P, where P represents the total number of pages read and x represents the number of hours read.

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Answer: A and D

Step-by-step explanation:

This is the REAL correct answer.

Answer: B. The environment of the zoo may cause the lions to behave

differently than they would in a natural habitat.  

                                         and

D. The presence of the researchers may affect the lions' behavior.

Step-by-step explanation:  Studying lion behavior in zoos has limitations. The artificial environment of a zoo can affect how lions behave compared to their behavior in the wild.  Additionally, the presence of researchers may influence the lions' behavior, making it difficult to observe and understand their natural interactions.

B. The environment of the zoo may cause the lions to behave differently than they would in a natural habitat.

In a zoo, lions are confined to a limited space and are provided with a controlled environment.  This artificial setting may not accurately reflect their natural habitat and can influence their behavior.  For example, the availability of food, different social dynamics, and reduced hunting opportunities in a zoo can lead to altered behaviors that may not be representative of how lions behave in the wild.

D. The presence of the researchers may affect the lions' behavior.

When researchers observe animals in a zoo, their presence can influence the behavior of the lions.  The presence of unfamiliar humans can cause the animals to become more cautious, stressed, or exhibit abnormal behavior.  This could potentially alter the social interactions and dynamics observed by the researchers, making it challenging to accurately understand and interpret natural lion behavior.

The value of a1 in a geometric series for which Sn=21825, an=125, r=15 will be 5/9.

The formula for the nth term in a geometric series is given by:

an = a1 * r^(n-1)

Where a1 is the first term, r is the common ratio, and n is the number of terms.

We are given Sn, an and r, and we can use the formula for the sum of a geometric series to solve for n:

Sn = a1 * (1 - r^n) / (1 - r)

Substituting the given values, we get:

21825 = a1 * (1 - 15^n) / (-14)

Multiplying both sides by -14, we get:

-304350 = a1 * (1 - 15^n)

Since we are given that an = 125, we can substitute this into the formula for an and solve for n:

125 = a1 * 15^(n-1)

Substituting a1 = -304350 / (1 - 15^n) from the equation above, we get:

125 = -304350 / (1 - 15^n) * 15^(n-1)

Dividing both sides by 15^(n-1), we get:

125 * 15^(1-n) = -304350 / (1 - 15^n)

Multiplying both sides by (1 - 15^n), we get:

125 * 15^(1-n) * (1 - 15^n) = -304350

Expanding the right-hand side, we get:

125 * (15 - 15^n) = -304350

Dividing both sides by 125, we get:

15 - 15^n = -2434.8

Adding 15^n to both sides, we get:

15^n = 15 - (-2434.8) = 2449.8

Taking the natural logarithm of both sides, we get:

n * log(15) = log(2449.8)

Dividing both sides by log(15), we get:

n = log(2449.8) / log(15)

Since n is the number of terms, it must be a positive integer. The closest positive integer to this value is 3, so n = 3.

Finally, we can use the formula for an to find a1:

an = a1 * r^(n-1)

Substituting the given values and n = 3, we get:

125 = a1 * 15^(3-1)

Dividing both sides by 15^(3-1), we get:

125 / 15^2 = a1

Calculating, we get:

a1 = 125 / 15^2

= 125 / 225

= 5/9.

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Answer:

(0,-6), (2,0), and (1,-3)

Step-by-step explanation:

We are given the equation of the line, and are then asked to find points on that line that correspond to values of x and y (x,y).  We can either graph the line and look for the points, or we can solve the equation using the given value of x or y, to find the other value of y or x.  Let's do both.

Graph

See the attached graph.  The line is drawn and then the three points are located using the provided value of x or y.  

We find:

    (0,-6)

    (2,0), and

    (1,-3)

Solve

Fun, but we could also put the one given value in the equation and then solve for the other:

y = 3x - 6

----------

1.  (0,__)

y = 3x - 6

y = 3*(0) - 6

y = -6

The point is (0,-6)

2.  (__,0)

y = 3x - 6

0 = 3x - 6

-3x = -5

x = 2

The point is (2,0).

3.  (1,__)

y = 3x - 6

y=3*(1)-6

y= -3

The point is (1,-3)