Sally’s Rent-A-Bike store rented 200 bicycles in June. In July, the store rented 300 bicycles. What percent of the bicycles rented in June were rented in July?

The positive difference in the time it takes for the water to travel 8 inches down the cylinder is D. 240.5 seconds

First, let's calculate the time it takes for the water to travel 8 inches down the cylinder in damp sand.

Since the water travels at a rate of 0.5 inches per second in damp sand, we can calculate the time as follows:

Time = Distance / Rate

Time = 8 inches / 0.5 inches per second

Time = 16 seconds

We know that it takes 2 seconds for the water to reach a depth of 2 inches. The total time doubles for each 1-inch increase in depth.

The total time taken for the water to travel 8 inches down the cylinder in dry sand is the sum of the time taken for each additional inch:

Total time = 2 + 4 + 8 + 16 + 32 + 64 + 128 = 256 seconds

Finally, let's find the positive difference in the amount of time taken for water to travel 8 inches down the cylinder in damp sand versus dry sand:

Difference = Time in dry sand - Time in damp sand

Difference = 256 seconds - 16 seconds

Difference = 240 seconds

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The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer:

jfi6+_4655vud

Step-by-step explanation:

Answer:

-x^2 +x +2

Step-by-step explanation:

f(x) = 4 - x^2 and g(x) = 2 - x

(f - g)(x) = 4 -x^2 - (2-x)

             =  4 -x^2 - 2+x

              = -x^2 +x +2

Answer:

2/-5

Step-by-step explanation:

The volume of the new solid with an additional layer of unit cubes on top of the prism is 16 cubic units. This can be calculated by multiplying the area of the base (4 square units) by the height (2 units) and adding the volume of the extra layer (8 cubic units).

If another layer of unit cubes is added on top of a prism, the volume of the new solid will be 8 cubic units. This can be calculated by multiplying the area of the base of the prism by its height. A prism is a 3D shape with two parallel, congruent bases. The base of this prism is a square with a side length of 2 units. The area of this square can be calculated by squaring the side length, so the area of the base is 2 x 2 = 4 square units. The height of the prism is also 2 units. When multiplied together, the volume of the prism is 4 x 2 = 8 cubic units. When another layer of unit cubes is added, this extra layer adds another 8 cubic units to the volume, making the overall volume of the new solid 8 + 8 = 16 cubic units.

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The number of caffeinated teas that the tea shop serve is 5.

Number of teas served = 25 teas.

Percentage that was caffeinated.= 20%

Therefore the number that was caffeinated will be the percentage multiplied by the number of teas. This will be:

= 20% × 25

= 0.2 × 25

= 5

Therefore, 5 are caffeinated

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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the equation of the line is y= x-4

Step-by-step explanation:

so so the first thing that you're going to do is get y alone

-x-5=y

next you're going to find your slope which in this case is negative one.

after that in order to find the equation of a parallel line you're going to find the reciprocal of the slope.

so in this case the reciprocal is one.

next you're going to substitute in the cordinates to find the y intercept

x+b=y. (-1)+b= -5. (. b is the y intercept)

b= -4

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

7 + 18 = 25 employees, which means that \(N = 25\)

7 over 50, which means that \(k = 7\)

10 dismissed, which means that \(n = 10\)

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055\)

0.055 = 5.5% probability that exactly 5 employees were over 50.

By definition of tangent,

tan(θ - x) = sin(θ - x) / cos(θ - x)

Expand the sine and cosine terms using the angle sum identities,

sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)

cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)

from which we get

tan(θ - x) = (sin(θ) cos(x) - cos(θ) sin(x)) / (cos(θ) cos(x) + sin(θ) sin(x))

Also recall the Pythagorean identity,

cos²(x) + sin²(x) = 1

from which we have two possible values for each of cos(θ) and sin(x):

cos(θ) = ± √(1 - sin²(θ)) = ± 3/5

sin(x) = ± √(1 - cos²(x)) = ± 12/13

Since there are 2 choices each for cos(θ) and sin(x), we'll have 4 possible values of tan(θ - x) :

• cos(θ) = 3/5, sin(x) = 12/13 :

tan(θ - x) = -56/33

• cos(θ) = -3/5, sin(x) = 12/13 :

tan(θ - x) = 16/63

• cos(θ) = 3/5, sin(x) = -12/13 :

tan(θ - x) = -16/63

• cos(θ) = -3/5, sin(x) = -12/13 :

tan(θ - x) = 56/33

Now

cos(ø-x)

sin(ø-x)

So

tan(ø-x)

Answer: Sir in what way would you like me to explain this

Step-by-step explanation:

Answer:

60:20

100:?x

60×x=100×20

=33.333 %

Answer:  6

Step-by-step explanation:

So he spends 25% of his 30 hours on games so 30x0.25=7.5 since 25% is equal to 0.25. He also spends 5% of the 30 hours on research. 30x0.05=1.5. 7.5-1.5=6

Answer:

Seven plus 2 divided by a number

Step-by-step explanation:

I think thats what u meAn

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer\(x = (739 - 625) / 3 = 38\) surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

\(CS = \int_0^{38} [D(x) - 25] dx\)

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

\(CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83\)

Therefore, the consumer surplus is approximately $145.83.

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Answer:

1. Expression: y = 235x

Answer: 1,175

2. The cost of the shirts is 5 dollars. Alex has 15 dollars in his wallet. He wants to buy 3 shirts. Write an expression that represents this problem.

Step-by-step explanation:

5. 235 per second

5 x 235 = 1,175

Expression: y = 235x

Answer:

1.98 meters

Step-by-step explanation:

divide 7.92 by 4

(7.92)/4

1.98

Answer:

Step-by-step explanation:

5(m-3)≥7m-2.4

5m-15≥7m-2.4

2m≤-12.6

m≤-6.1

Answer:

m>6.3

Step-by-step explanation:

Answer:v=-4

Step-by-step explanation:We move all terms to the left:

-5v+6-(26)=0

We add all the numbers together, and all the variables

-5v-20=0

We move all terms containing v to the left, all other terms to the right

-5v=20

v=20/-5

Answer: To find the probability that a person chosen at random has a median lifetime income between 1 to 2 standard deviations below the mean, we need to calculate the area under the normal distribution curve within that range.

First, let's define the variables:

μ = Mean lifetime income = $25800

σ = Standard deviation = $14000

We want to find the probability of having a median lifetime income between 1 to 2 standard deviations below the mean.

1 standard deviation below the mean would be μ - σ, and 2 standard deviations below the mean would be μ - 2σ.

μ - σ = $25800 - $14000 = $11800

μ - 2σ = $25800 - 2 * $14000 = $-2200

Next, we need to find the z-scores for these values. The z-score represents the number of standard deviations a given value is from the mean in a standard normal distribution.

For μ - σ:

z1 = (11800 - μ) / σ = (11800 - 25800) / 14000 ≈ -1.5714

For μ - 2σ:

z2 = (-2200 - μ) / σ = (-2200 - 25800) / 14000 ≈ -2.2857

Using a standard normal distribution table or a statistical software, we can find the corresponding probabilities associated with these z-scores.

The probability of having a median lifetime income between 1 to 2 standard deviations below the mean is the difference between the probabilities corresponding to z1 and z2.

P(1 to 2 standard deviations below the mean) = P(z1 < Z < z2)

You can refer to a standard normal distribution table or use statistical software (such as Excel, R, or Python) to calculate the probabilities. The exact values may vary depending on the specific table or software used.

Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Answer:

54 and 47

Step-by-step explanation:

Lets first number be "x" and second number be "y"

x = y + 7

x + y = 101

(y + 7) + y = 101

2y + 7 = 101

2y = 94

y = 47

x = 47 + 7

x = 54

Our answer are the sides 5,12 and 13 which represent a Pythagoraen triple

The sides of a triangle that would make a right-triangle are collectively called a Pythagorean triple

These measures stem from the Pythagoras theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

At any point in time, the hypotenuse refers to the longest side in the triangle

So basically, to get the correct answer from these options, if we square the longest side, and the sum of the squares of the two other sides equal the square of this longest side, the side that provides us with this would be our answer

So let us consider the options individually;

Answer:

Step-by-step explanation:

ax²+6x+c=0

disc=6²-4×a×c=36-4ac≥0,(∵ it has two real solutions.)

36-4ac≥0

36≥4ac

4ac≤36

ac≤9