2. along the route of a bicycle race, water stations are evenly spaced between the start and finish lines, as shown in the figure below. there are also repair stations evenly spaced between the start and finish lines. the rd water station is located miles after the st repair station. how long is the race in miles?

The exponential function is y = 4(0.4)^x

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

An exponential function s represented as

y = ab^x

Where

a = the y-intercept

a = -4

Also, we have

b = -0.64/-1.6

b = 0.4

So, we have

y = -4(0.4)^x

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When the parabola y = -1/20(x-3)2 + 6 has a focus of (3,1), the directrix equation is x=3.

Any points on a parabola is situated at a equal distance from both focus, a fixed point, and the hardware platform, a fixed vertical line. A parabola is a U-shaped plane curve.  Three different parabolas exist. Vertex form, leading to the formation, and intercept form seem to be the three forms. You can access a unique major element for the graph on each submission. There are two different methods to write a parabola's calculation: Form 1: y=a(x-h)2 + k. Form 2 is as wants to follow: x = a(y - k)2 + h.

given

( x-3)^2 > 0 , so -1/20(x-3)^2 < 0

when x>3 , it is decrease , when x<3 it is increase so the equation of the directrix is x =3

When the parabola y = -1/20(x-3)2 + 6 has a focus of (3,1), the directrix equation is x=3.

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The number 56 when compared to 10 is the same as 28 compared to 5.

Option- C(56)

Let x be the number when compared to 10 is same as 28 compared to 5.

So, finding the value of x by comparing the ratios of the above stated values.

Therefore,

                    [tex]\frac{x}{10} = \frac{28}{5}[/tex]

So, Cross multiplying the above equation,

                      x × 5 = 28 × 10

                       5x = 280

                        x = [tex]\frac{280}{5}[/tex]

                        x = 56

So, 56 when compared to 10 bears the same ratio as 28 compared to 5.

Option number - C

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Answer:

m= -1 1/2

Step-by-step explanation:

1st point : (-3,15)

2nd point : (1,9)

m=rise/run

= 15-9/-3-1

= 6/-4

=-1 1/2

The probability that both Bonnie and Kelly will sit courtside at the basketball game if they are the first two to choose seats is 2%.(option 2)

When the group selects their seats at random, we must take into account all possible outcomes in order to calculate this. There are a total of 11 seats, two of which face the court. 11 are there! possible methods by which the group can select their seats. There is only one option for Bonnie and Kelly to sit courtside out of these, and that is for them to select a seat courtside first. As a result, there is a one in eleven chance that Bonnie and Kelly will sit side by side in court., or 2%.

We can divide the probability by 100 to put this into percentage form. The question has been answered by this, which gives us 2%.

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Complete Question:

Bonnie and Kelly are part of a group going to a basketball game. The group has two court-side seats, five upper-level seats, and four seats in general admission. If the group randomly chooses seats, what is the probability that both Bonnie and Kelly will sit court side at the basketball game if they are the first two to choose seats? Express your answer as a percent. If necessary, round your answer to the nearest tenth.

1. 8%

2. 2%

3. 3%

4. 12%

Answer: 18

Step-by-step explanation: Solve using algebra and angles given.

Answer: 5<x

Step-by-step explanation:

Answer: x>5

Isolate the variable

Answer:

$38.70

Step-by-step explanation:

21.5% = 0.215

$180.00 times 0.215 = $38.70

So, Sally's Commission is $38.70

The perimeter of this rectangle is 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.

Let's call the length of the rectangle "L" and the width of the rectangle "W". The area of the rectangle is then L * W, and the perimeter is 2 * (L + W).

According to the problem, the number of square units in the rectangle's area is triple the number of units in its perimeter:

L * W = 3 * (2 * (L + W))

Expanding the right side and solving for L:

L * W = 6L + 6W

L * W - 6L = 6W

L * (W - 6) = 6W

L = 6W / (W - 6)

Since L and W are both positive integers and L can't be equal to W (because the rectangle can't be a square), we know that W must be greater than 6. Let's try W = 7:

L = 6 * 7 / (7 - 6) = 6 * 7 = 42

This gives us a rectangle with dimensions 42 x 7, which satisfies the conditions of the problem.

The perimeter of this rectangle is 2 * (42 + 7) = 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.

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Grace could have weighed 1.36 pounds, 1.37 pounds, 1.38 pounds, or 1.39 pounds of apples.

Let a be the number of pounds of apples.

We are told that Grace has 1.35 pounds of strawberries. It has more kilograms of apples than kilograms of strawberries.

This means that a is greater than 1.35. We can represent this information as an inequality as follows:

We were also told that Grace had 1.4 pounds of bananas. It has fewer kilograms of apples than kilograms of bananas. This means that a is less than 1.4. We can represent this information as an inequality:

Combining the two inequalities we get:

Therefore, Grace can be 1.36 lbs., 1.37 lbs., 1.38 lbs., or 1.39 kilos of apples.

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Volume= l*b*h

=7*5*3

=105 cubic inches

The new wage if the performance is Adequate is $23.1 per hour.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

If an employee's performance is adequate, then he will get a raise of 5%.

The employee wage is 22 per hour.

The performance is Adequate.

That means,

the wage is,

= 22 + 22x 0.05

= 23.1

Hence, $23.1 is the wage per hour.

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Answer:

Step-by-step explanation:

To solve for x in the equation 3x + 2 = 11, we'll start by subtracting 2 from both sides:

3x + 2 - 2 = 11 - 2

Simplifying the left-hand side:

3x = 9

Finally, divide both sides of the equation by 3 to find x:

(3x) / 3 = 9 / 3

x = 3

The set of range of given data is  {0,0,0,0}

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The y coordinates are the range values

range = {0,0,0,0}

The set of range of given data is  {0,0,0,0}

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The value of b/a is b/a = 91/3 {(1-b/a)²}.

Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.

And the standard form of a cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.

Given:

A cubic equation,

a³ - b³ / (a-b)³ = 91 where a and b are real numbers a>b>0.

Simplifying,

(a-b)(a²+b²+ab)/(a-b)³ = 91

(a²+b²+ab)/(a-b)² = 91

(a²+b²+ab-3ab+3ab)/(a-b)³ = 91

3ab/(a-b)² = 91

b/a = 91/3 {(a - b)²/a²}

b/a = 91/3 {(a - b/a)²}

b/a = 91/3 {(1-b/a)²}

Hence, b/a = 91/3 {(1-b/a)²}.

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Answer:

see below

Step-by-step explanation:

enter the values of -1 & -2 into the equation

so you'll get 2 equations for 2 variables: m & n

when x = -1

1-(m-2)*(-1)-3+n=0 ==> 1+m-2-3+n =0 so m+n=5

when x = -2

4-(m-2)*(-2)-3+n=0 ==> 4+2m-4-3+n =0 so 2m+n=3

use equation 2 subtract equation 1

2m=-2, so m = -1

n= 6

Answer:

Step-by-step explanation:

Given roots of x² -(m -2)x -(3 -n) = 0 are -1 and -2, you want the values of m and n.

Given roots -1 and -2 for a quadratic equation, we know its factored form is ...

  (x -(-1))(x -(-2)) = 0

  (x +1)(x +2) = 0

Then the standard form is ...

  x² +3x +2 = 0

Comparing this to the given equation, we find ...

  -(m-2) = 3   ⇒   m = -1

  -(3 -n) = 2   ⇒   n = 5

Answer:

(m,n) is (-2,2)

Step-by-step explanation:

Elimination means that we should rewrite one of the two equations as an expression of one of the variables isolated, and then use that definition isn the other equation.  It is also called "substitution."

Lets use the first equation and rewrite it so that the variable m is isolated:

3m-4n=-14

-4n = -3m-14

n = (3/4)m +(7/2)

Now use this definition of n in the second equation:

3m+2n=-2

3m+2((3/4)m +(7/2)) = -2

3m + (3/2)m + 7 = -2

4.5m = -9

m = -2

Now use m= -2 in either equation to find n.

3m-4n=-14

3(-2)-4n=-14

-6 -4n = -14

-4n = -8

n = 2

The solution of this system of equations is (-2,2).

See the attached graph, with x and y used in place of m and n.

The amount that Reuben owe after 9 years, rounded to the nearest cent is $19,252.95..

The formula compound interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = $8,000( 1 + 0.1/2 )^( 2 × 9 )

A = $8,000( 1 + 0.05 )¹⁸

A = $8,000( 1.05 )¹⁸

A = $19,252.95

Therefore, the accrued amount is $19,252.95.

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So there are ten different combinations of two pupils out of five when there are five kids in my class and I want to choose two to treat to lunch.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

To determine the number of ways to pick 2 students out of 5 to treat them to lunch, you can use the combination formula, which is given by nCr, where n is the number of items to choose from, r is the number of items to choose, and nCr is the number of combinations of n items taken r at a time. In this case, n = 5 and r = 2, so the number of ways to pick 2 students out of 5 is:

5C2 = 5! / (2! * (5 - 2)!) = 10

So, there are 10 possible combinations of 2 students out of 5 when there are 5 students in my class and I want to pick 2 to treat them to a lunch.

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Step 1: Calculate the ratio.

The ratio is 77 out of 100.

Step 2: Convert the ratio to a percent.

To convert the ratio to a percent, divide the numerator by the denominator and multiply the result by 100.

Therefore, 77 out of 100 can be written as 77/100 x 100 = 77%.

The conversion process known as "ratio to percentage" aids in turning a ratio into a percentage. As is common knowledge, two quantities of the same unit are compared using the ratio. A percentage, on the other hand, is a particular kind of ratio where the value of the sum is always equal to 100. Let's go over the formula, the value of the ratio to percentage for some of the most commonly used numbers, and several solved examples in depth in this article.

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Answer:

b > –6 and b < 6

Step-by-step explanation:

The expression "|b| > 6" means that the absolute value of b is greater than 6. Therefore, b can either be greater than 6 or less than -6. So, the equivalent expression is b > –6 and b < 6.

Answer:

88

Step-by-step explanation:

We can set up the proportion 8/1 = x/11. By cross-multiplying, we get that x = 88.

(–6,2) is the possible coordinates of point D if ΔDEF is congruent to ΔABC.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Shapes are congruent if you can turn one into the other by moving, rotating or flipping.

We can use this symbol  to show that two things are congruent.

Two triangles are congruent if and only if all the corresponding legs are congruent.

The only point that makes the corresponding legs to be congruent is

(–6,2)

because we can match these two triangles by flipping the red one two times and moving it into the blue one.

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Answer:0.625

Step-by-step explanation:

The y-intercept of the line shown is (0,4).

The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

Given;

A line passes through the point -4 comma 1 and through the y-axis at 4.

Now,

y=mx+c

1=m*-4+c

Line passes through 4 at y-axis

(0,4)

Therefore, the y intercept will be (0,4).

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Step-by-step explanation:

To find the velocity of the particle, we need to take the derivative of the position vector with respect to time.

r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j

d/dt[r(θ)] = d/dt[(a + b * cos(θ)) * i + (b * sin(θ)) * j]

d/dt[r(θ)] = (-b * sin(θ)) * i + (b * cos(θ)) * j

So, the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Answer:

Step-by-step explanation:

the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

We can quickly determine that the person has been moved by 10 miles by logical reasoning.

A mental process called logical reasoning seeks to reach a conclusion in a precise way.

By beginning with a set of premises and reasoning to a conclusion supported by these premises, it takes the shape of inferences or arguments.

Propositions, or true or false statements about the reality of a situation, are what the premises and the conclusion are.

They have a disagreement as a group.

In the sense that it seeks to develop correct arguments that any sane person would find persuasive, logical reasoning is norm-governed.

Logic is the primary academic field that studies logical reasoning.

So, using logical thinking, we can easily tell that the person is displaced by 10 miles.

(refer to the image attached below)

Therefore, we can quickly determine that the person has been moved by 10 miles by logical reasoning.

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Answer:

Sum: (3.49x10^-2) + (4.39x10^-2) = 7.88x10^-2

In standard form, this can be written as 0.0788.

Difference: (8.75x10^-8) - (3.75x10^-8) = 5x10^-8

In standard form, this can be written as 0.00000005.

Step-by-step explanation:

We got that the probability that the hand contains 4 cards of the same suit and 1 of another suit = 0.042917

In the given question the hand contains 4 cards of the same suit, and 1 of another suit and we have to find the probability of this.

As we know that in standard card deck have 4 suits and 13 ranks in each suit and each deck have total 52 cards. If 13 ranks separated then 39 cards are left.

So the probability that the hand contains 4 cards of the same suit and 1 of another suit is

Probability =  [tex]\frac{|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|}{^{52C_{5}}}[/tex]

Probability = [tex]\frac{|715 \times 39| + |715 \times 39|+|715 \times 39|+|715 \times 39|}{2,598,960}[/tex]

Probability = (27,885 + 27,885 + 27,885 + 27,885)/2,598,960

Probability = 111,540/2,598,960

Probability = 0.042917

we got that the probability that the hand contains 4 cards of the same suit and 1 of another suit = 0.042917

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The complete question is:

A 5-card hand is (randomly) drawn from a standard 52 card deck. What is the probability that the hand contains 4 cards of the same suit, and 1 of another suit?

In light of the query we've got The circle's radius is equivalent to 3.832 units.

In geometry, the perimeter is the overall area of a shape's boundary. A shape's perimeter is computed by adding the lengths of all of its sides and edges. Linear measurements like cm, metres, inch, and feet are used to express its dimensions.

The answers to our problem is that area

A = (θ/360) * π * r^2

π = 3.14

Perimeter is 24 degree, The formula for circumference is:

C = 2 x πr

Now, we can calculate the radius using the circumference:

r = C / (2 x π)

Substituting the value of C from the equation above, we get:

r = (24 / (2 x π))

Therefore, the radius of the circle is approximately equal to 3.832 units.

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