Which of these ordered pairs is a solution to the linear inequality y ≤ 2x + 5?


(–2, 5)


(–2, 4)


(0, 5)


(1, 9)

Answer:

He would would have about 40%Left on his account AKA $960 dollars.

Step-by-step explanation:

Sorry If I am Wrong.

==> 100% of his money was in the account before the bank opened in the morning.

==> As soon as they opened, Mr. Smith ran in, grabbed 60% of his money, and left with it.

==> Any time you have one whole thing ... 100% of it ... and you take away 60% of it, there's 40% of it left. That's the part you DIDN'T take.

The perimeter of the region swept out by a circle with radius 2, when translated 5 units, remains the same at 4π or approximately 12.57 units.



When a circle is translated, its center is moved without changing its shape or size. In this case, the circle with a radius of 2 is translated 5 units. Since the translation is in a straight line, the shape swept out by the circle is a larger circle with the same radius.

The perimeter of a circle is given by the formula:P = 2πr

where P is the perimeter and r is the radius.

For the original circle with a radius of 2, the perimeter is:

P1 = 2π(2) = 4π

For the translated circle with the same radius, the perimeter is also:

P2 = 2π(2) = 4π

Therefore, the perimeter of the region swept out by the circle is the same as the perimeter of the original circle, which is 4π or approximately 12.57 units.

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Answer:

you need to wash 60 cars to get atleast $300

Step-by-step explanation:

well 6 times 5 is 30

and 60 times 5 is 300

Answer:

5.00x ≥ 300

Solve: x ≥ 60

Step-by-step explanation:

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

The probability that 5 different integers randomly chosen from between 20 and 69 each have a different tens digit is 0.0000022.

To find the probability that 5 different integers randomly chosen from between 20 and 69 (inclusive) each have a different tens digit, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes.

First, let's determine the total number of possible outcomes. The range of integers between 20 and 69 (inclusive) contains 50 numbers. Therefore, there are 50 choices for the first number, 49 choices for the second number, 48 choices for the third number, 47 choices for the fourth number, and 46 choices for the fifth number. So, the total number of possible outcomes is:

50 * 49 * 48 * 47 * 46 = 54,512,400

Now, let's calculate the total number of favorable outcomes. We want each chosen number to have a different tens digit. There are 5 different tens digits in the range (2, 3, 4, 5, and 6). For the first chosen number, we have 5 choices. For the second number, we have 4 choices remaining (as one tens digit has already been used), for the third number we have 3 choices remaining, for the fourth number we have 2 choices remaining, and for the fifth number we have 1 choice remaining. So, the total number of favorable outcomes is:

5 * 4 * 3 * 2 * 1 = 120

Therefore, the probability that 5 different integers randomly chosen from between 20 and 69 each have a different tens digit is:

120 / 54,512,400 ≈ 0.0000022

This can be expressed as approximately 0.00022% or 1 in 454,270.

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The jars are nor enough because the applesauce is more than 35 cups which is what 20 glass jars can contain. Since each of the cup will hold 1 3/4 cups of applesauce.

Given data

number of cups of apple sauce = 40

number of glass jars = 20

number of cups each glass jar can hold = 1 3/4

solution

if one glass jar hold 1 3/4 cups then 20 glass jars will hold

= 20 * 1 3/4

= 35 cups

Since there are 40 available cups of apple sauce and the 20 glass jars is equivalent to 35 cups, hence the glass jars will contain 35 cups and there will be 5 cups left.

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Answer:

c) $637.50

Step-by-step explanation:

Formula: I= PRT

2500×8.5%×3 = 637.5

Answer:

uh wut's the question?

Step-by-step explanation:

Answer:

There is no question here, what did you need help with?

Answer:

8

Step-by-step explanation:

It's 8 because if you multiply youll get the answer

Answer:

-3/2x-14

Step-by-step explanation:

-2 (3/4x+7)

(3/4x) (-2/1) = -6/4x= -3/2x

(-2) (7)=-14

FINAL ANSWER:

-3/2x-14

Try Multiplication

Answer:

Distributive Property of Multiplication

Step-by-step explanation:

To expand the given expression, we'll distribute "-2" to the rest of the two terms to get them multiplied.

Answer:

C = 12.6 (rounded to the nearest tenth)

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr

R = radius

The radius is the half of a diameter, so 4/2 is 2.

C = 2π(2)

C = 12.56637061

The area of the region bounded by the curve r = 9cos(θ) and the sector 0 ≤ θ ≤ π/6 is \($27\pi/8 - 81/8\times \sqrt{3}$\)

The curve r = 9cos(θ) is a polar curve that forms a half-circle with a radius of 9/2. To find the area of the region bounded by this curve and the sector 0 ≤ θ ≤ π/6, we can use the formula for the area of a polar region:

\($A = \frac{1}{2} \int_{a}^{b} r(\theta)^2 d\theta$\)

In this case, a = 0 and b = π/6, and the curve is given by r(θ) = 9cos(θ). Substituting these values into the formula, we get:

\($A = \frac{1}{2} \int_{0}^{\frac{\pi}{6}} (9\cos(\theta))^2 d\theta$\)

Simplifying and evaluating the integral gives:

\(A = \frac{1}{2} \int_{0}^{\frac{\pi}{6}} 81\cos^2(\theta) d\theta\\\\ = \frac{1}{2}\left(\frac{81}{2}\cdot\frac{\pi}{6}+\frac{81}{4}\cdot\sin\left(\frac{\pi}{6}\right)\right)\\ \\ = \frac{27\pi}{8} - \frac{81}{8}\sqrt{3}\)

Therefore, the area of the region bounded by the curve r = 9cos(θ) and the sector 0 ≤ θ ≤ π/6 is \($27\pi/8 - 81/8\times \sqrt{3}$\)

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Given the sketch of the pool:

The total area of the Adult pool is:

According to the sketch, this is equivalent to:

Solving for x (the width of the walkway):

This is equivalent to:

The average rate of change over an interval is the same as the slope between those two values.  The formulate for slope is:

\(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

You are given the x values: x2=3 and x1=-9.  Plug in these x values to g(x) find the y values:

g(3)=3^2+5(3)-2=9+15-2=22

g(-9)=(-9)^2+5(-9)-2=81-45-2=34

Now, you can solve for m:

m=(22-34)/(3--9)

m=-12/12

m=1

Hope this helps!!

the  average rate of change of the function over the interval -9 ≤ x ≤ 3​ is -1

The average rate is the change of expression with respect to time.

Given the expression g(x)=x^2+5x-2 within the interval -9 ≤ x ≤ 3​

At the lower interval x = -9

g(-9) = (-9)²+5(-9)-2

g(-9)= 81-45-2

g(-9) = 34

At the upper interval x = 3

g(3) = (3)²+5(3)-2

g(3)= 9+15-2

g(3) = 22

The average change of the function will be expressed as:

\(\frac{\triangle y}{\triangle x} =\dfrac{g(b)-g(a)}{b-a}\\ \frac{\triangle y}{\triangle x} =\dfrac{g(3)-g(-9)}{3-(-9)}\\\frac{\triangle y}{\triangle x} =\dfrac{22-34}{12}\\\\\frac{\triangle y}{\triangle x} =\dfrac{-12}{12} \\\frac{\triangle y}{\triangle x} =-1\)

Hence the  average rate of change of the function over the interval -9 ≤ x ≤ 3​ is -1

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Answer:

ok so we can just add 20 + 45 then divide by 2

20+45=65/2=32.5

32.5

Hope This Helps!!!

Answer:

50; every week he deposits $50

Step-by-step explanation:

the slope in this equation is 50

using the formula y = mx + b with m being the slope we can tell that 50 is where the m is

this means that every week he deposits $50

The Upper control limit (UCL) for the x-bar chart is 25.5 and the Lower control limit (LCL) is 22.1.

Given that the process is sampled 28 times with a sample of size 8 resulted in ¯x=23.8 and ¯R=2.7.The central line is the mean of all of the sample means, which is the mean of the sample means, so the mean of the 28 sample means is the ¯x value. In this case, the central line is ¯x = 23.8, which is the mean of all 28 sample means of size 8. That is the main answer for this problem.

In order to calculate the Upper control limit (UCL) and Lower control limit (LCL) for the x-bar chart, you need to use the following formulas: UCL = ¯x + A2R LCL = ¯x - A2R Where A2 is the control chart factor. For a sample size of 8, the A2 factor is 0.577.So, UCL = 23.8 + (0.577 × 2.7) = 25.5 and LCL = 23.8 - (0.577 × 2.7) = 22.1.Thus, the Upper control limit (UCL) for the x-bar chart is 25.5 and the Lower control limit (LCL) is 22.1.

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The friend is correct. Split the 2D figure as indicated in the diagram below. The rectangle on the left rotates to form the cylinder. The triangle rotates to form the cone. Think of these as like a revolving door that carves out a 3D shape. Or you could think of propellers.

Answer:

Step-by-step explanation:

2x+6=x-4

x=-10

20x-8x=.....

Answer:

17 people surveyed own a cat.

Step-by-step explanation:

Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.

d = 4c

d + c + 15 = 100

4c + c + 15 = 100

5c + 15 = 100

5c = 85

c = 17

Check:

The number of dog owners is 4 * 17, or 68.

68 + 17 + 15 = 100

Answer:

Probability ≈ 0.4762

Step-by-step explanation:

See explanation below;

\(Total Number of Outcomes - 10C4,\\10 ! / 4! * ( 10 - 4 ),\\10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 6 * 5 * 4 * 3 * 2 * 1,\\\\Total Outcomes = 210,\\\\Number of Outcomes - 5C2 * 5C2,\\5C2 = 5 * 4 * 3 * 2 * 1 / 2 * 1 * ( 3 * 2 * 1 ),\\\\Number of Outcomes - ( 10 )^2 = 100,\\\\Conclusion; Probability = 100 / 210 = 0.4762\)

Solution; Probability ≈ 0.4762

since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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Answer:

75%

Step-by-step explanation:

percentage = v1 divided by v2

\(p = \frac{120}{160} = 75\%\)

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The correct statement regarding the probability of choosing a person at random who is a junior and plays video games, and whether these events are independent, is given as follows:

P(junior and video games) = 32%; The two events are not independent.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in this problem are given as follows:

Hence the probability is of:

P(junior and video games) = 48/150 = 0.32 = 32%.

The separate probabilities are given as follows:

The multiplication of these probabilities is of:

0.66 x 0.4 = 0.264.

Which is different of 0.32, hence these events are not independent.

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Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.

A system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.

A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.

In this problem, we need to define our variables and the solve the equations.

Let;

x + 2y = 31 ...eq(i)

3x + y = 38 ...eq(ii)

Solving both equations

x = 9, y = 11

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Answer:

nope x

Step-by-step explanation: