Tom earns $3.25 per hour at the car wash plus $1.50 for each car he washes. If he wishes to earn at least $100 on a busy weekend during which he works 12 hours, what is the minimum number of cars that he must wash? Which property of equality did you use to solve this problem?

In order to achieve a bigger splash in their next trial, all the students must need to do is use a ball with a larger circumference.

Displacement and volume are defined as a dimensional object dropped into a liquid that will always displace its own volume from the liquid.

For a basketball, the circumference is a function of its volume. In other words, the larger the circumference, the larger the volume.

This defines that a basketball with a larger volume will displace more water from the pool than one with a lower volume.

Finally, to make a bigger splash, a basketball with a larger circumference would be needed.

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Answer:

each person will get 1 and 1/3 cups of ice cream

Step-by-step explanation:

Answer:

0.8 cups

Step-by-step explanation:

It would be splitting 2 quarts of ice cream with 10 people,

because including Dave.

2/10 = 1/5 = 0.8 cups

Answer:

\(y = -3x\)

Step-by-step explanation:

Given

The attached graph

Required

Determine the graph equation

To do this, we pick any 3 corresponding points of x and y

\((x_1,y_1) = (0,0)\)

\((x_2,y_2) = (2,-6)\)

\((x_3,y_3) = (-4,12)\)

The equation can then be solved using linear interpolation as follows:

\(\frac{y-y_3}{x-x_3} = \frac{y_2 - y_1}{x_2-x_1}\)

This gives:

\(\frac{y-12}{x-(-4)} = \frac{-6 -0}{2-0}\)

\(\frac{y-12}{x+4} = \frac{-6 -0}{2-0}\)

\(\frac{y-12}{x+4} = \frac{-6}{2}\)

\(\frac{y-12}{x+4} = -3\)

Multiply both sides by x + 4

\((x + 4) * \frac{y-12}{x+4} = -3 * (x + 4)\)

\(y - 12 = -3 *(x + 4)\)

Open bracket

\(y - 12 = -3x -12\)

Add 12 to both sides

\(y - 12+12 = -3x -12+12\)

\(y = -3x\)

d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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Answer:

6.   32

7.    62

8.   512

9.   675

10.  13

11.   ⅔

You should re-analyze the data to determine why your results contradicted your hypothesis if the experiment's findings did not support it. You shouldn't change the experiments, observations, or both in order to get results that support your theory.

The Scientific Method is the framework that is most frequently employed while conducting an experiment. Asking a specific question, formulating a hypothesis, conducting experiments to collect data, analyzing the data, and determining if the hypothesis is true in light of the experimental results are all hallmarks of the scientific method.

The results may be published or distributed if the data are consistent with the hypothesis. The experiment's evaluation phase includes the write-up. Regardless of what took place during the experiment, the outcomes must be reported, whether they support or refute the hypothesis.

Next, list any issues that came up throughout the trial, and then include recommendations for changes and next steps in your report. To record what happened during the experiment, a write-up is required. It becomes a part of the background literature for the topic being investigated or put to the test.

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Answer:

Step-by-step explanation:

x / 12 = 3 / 8

x = 3 / 8 x 12

x = 3 / 94

x = 32

32 / 12 = 3 / 8

Answer:

Third option: (1, 0), (2, 0), and (–3, 0)

Step-by-step explanation:

The x-intercepts are the points at which the graph of the function crosses the x-axis.

By reading the question, we can see that:

"... crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0)..."

So the x-intercepts are:

(-3, 0)

(1, 0)

(2,  0)

Then the correct option is the third one:

"(1, 0), (2, 0), and (–3, 0)"

Answer: Option 3

Step-by-step explanation: Got it right on Edge

Answer:

Step-by-step explanation:

(x - 2)/2 = 1

x - 2 = 2

x = 4

(y + 5)/2= 1

y + 5 = 2

y = -3

(4, -3) Coordinates of B

The coordinates of endpoint B is (4,-3).

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now it is given that,

Mid point of line segment = M(1,1) i.e. (x,y)

coordinates of A = (-2,5) i.e. (x₁ ,y₁ )

So we have,

x = 1

y = 1

x₁ = -2

y₁ = 5

Let the coordinates of the end point be B(x₂,y₂)

Since,

x = (x₁+x₂)/2

⇒ x₂ = 2x - x₁

Put the values we get,

⇒ x₂ = 2*1 - (-2)

⇒ x₂ = 2 + 2

⇒ x₂ = 4

Similarly,

y = (y₁+y₂)/2

⇒ y₂ = 2y- y₁

Put the values we get,

⇒ y₂ = 2*1- 5

⇒ y₂ = 2 - 5

⇒ y₂ = -3

Hence, the coordinates of endpoint B is (4,-3)

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The degree of a polynomial is the value of the highest degree of a monomial in the polynomial

The degree of the polynomial h(x) is 5

The reason the above value is correct is as follows;

Given;

A zero of a polynomial function h(x) is the imaginary number, x = 3 - 4·i

The multiplicity of the root at x = 3 - 4·i is One

The given table showing the real roots of the polynomial is presented as follows;

\(\begin{array}{|c|cc|}\mathbf{x}&&\mathbf{h(x)}\\\displaystyle -5&&0\\-2&&3\\-1&&0\\1&&2\\4&&0\\7&&6\\10&&0\end{array}\right]\)

Required:

To find the degree of the polynomial, h(x)

Solution:

The maximum number of roots of a polynomial is given by the degree of the polynomial

The number of roots is given by the number zeros

The maximum number of roots an nth degree polynomial can have = n roots

From the given table, the number of zeros = 4 (each with multiplicity of one) = The number of real roots

Therefore, the total number of roots of the polynomial = 4 + 1 = 5 = The (minimum possible) degree of the polynomial

The degree of the polynomial = 5

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The graph that shows two lines, which appear as one line shows a system of equations with infinitely many solutions. This is because two lines that are exactly the same have infinitely many points in common, and therefore infinitely many solutions.

Coexistent Lines refer to those that are merged or placed on top of each other. This pair of two overlapping lines is labeled coincident lines, and when simplified, their equations become identical.

Precise graphing of the lines and using correct equations is a crucial step towards avoiding such instances.

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Answer:

Step-by-step explanation:

Uncle Richard’s New Year’s Dinner

Answer:

-6 = n

Step-by-step explanation:

-6=2n-n

Combine like terms

-6 = n

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

Red

Step-by-step explanation:

total cost of blue divided by number of blue (22.78/2) is greater than total cost of red divided by number of red (67.80/6).

Blue unit cost: 11.39

Red unit cost: 11.30

Answer: -1

Step-by-step explanation:

The first step is to write the equation:

1/6 × -6

The second step is to solve:

1/6 × -6/1

= -6/6

= -1

This is how you get the answer -1.

I hope I helped and have a great day! ^-^

Answer:

x=44

Step-by-step explanation:

Pretty straightforward!

4-x/5 +x+2/3=6

3(4-x) + 5(x+2) = 90  (Multiply both sides of the equation by 15, a multiple of              both 5 and 3)

12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)

-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)

2x=88

x=44

Thank you for your time!

Answer: x=44

Step-by-step explanation: Pretty straightforward!

4-x/5 +x+2/3=6

3(4-x) + 5(x+2) = 90  (Multiply both sides of the equation by 15, a multiple of              both 5 and 3)

12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)

-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)

2x=88

x=44

Thank you for your time!

The probability that a contestant will win exactly 2 times in 5 games of selecting one box out of six identical boxes, each containing one prize placed randomly after each game, is approximately 0.016

To solve this problem, we can use the binomial distribution formula

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

Where

X is the number of successes (in this case, winning the prize) in n trials

k is the number of successes we want to calculate the probability for (in this case, 2)

n is the total number of trials (in this case, 5)

p is the probability of success in each trial (in this case, 1/6, since there is one prize in six boxes)

So, plugging in the values

P(X = 2) = (5 choose 2) × (1/6)^2 × (5/6)^3

= 10 × 1/36 × 125/216

= 125/7776

≈ 0.016

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The given question is incomplete, the complete question is:

In a carnival game there are six identical boxes, one of which contains a prize. A contestant wins by selecting the box containing the prize. After each game the old prize is removed and another prize is placed at random in one of the six boxes. If a contestant plays the game 5 times calculate the probability that he will win exactly 2 times and then match n, r, and p with the correct responses.

Answer:

288.4m

Step-by-step explanation:

This track is split into a rectangle and two semi-circles.

We can find the length of the semi-circles by finding its circumference with the formula \(2\pi r\).

\(2\cdot3.14\cdot30\\188.4\)

However this is half a circle, so:

\(188.4\div2=94.2\).

There are two semi-circles.

\(94.2\cdot2=188.4\)

Since there are two legs of 50m each, we add 100 to 188.4

\(188.4+100=288.4\)m

Hope this helped!

Answer:

Step-by-step explanation:

To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.

For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.

15 * 2π ≈ 94.2477796077

We add that to 100m and get:

194.2477796077

Answer:

j=15

Step-by-step explanation:

Let's set up an equation:

2j+7=37

Subtract both sides by 7

2j=30

Divide both sides by 2

j=15

Answer:

15

Step-by-step explanation:

37=2j+7

so subract 7 from both sides

30=2j

then divide by 2 on each side

j=15

Answer:

268$

I did math for it it should be okay

According to the information, we can infer that A. 1: Real, Rational, Integer, Whole, Natural, B. 5.1: Real, Rational, C. √(-142): Non-real, D. \(\pi\) (Pi): Irrational, Real, E. 2/3: Rational, Real, F. ∛(-27): Non-real, G. 0.671: Real, Rational, H. 3√7: Irrational, Real, I. 0: Real, Rational, Integer, Whole, Natural, J. -√16: Real, Rational.

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Answer:

A, The value of g(-2) is smaller than the value of g(4).

Step-by-step explanation:

The others DO NOT make sense.

Answer:

the last one

Step-by-step explanation:

6 1/2

First you find a common denominator. 1/4 = 3/12 and 1/3 = 4/12.

3/12 + 4/12 + 11/12 = 18/12.

18/12 = 6 6/12 = 6 1/2

Answer:18/12 or 1 1/2

Step-by-step explanation:

First you have to make all of the denominators the same by finding a common denominator which is 12. Then you multiply the whatever number you need to get to twelve by the top and bottom. Once all of the denominators are the same then you add.

1/4=3/12(multiply top and bottom by three), 1/3=4/12(multiply by 4), 11/12 stays the same.

The greatest common factor of 72 and 4 is 4.

Answer:4

Step-by-step explanation:

72÷2=36

4÷2=2

36÷2=18

2÷2=1

2×2=4

Answer is 4

The researcher randomly selected and interviewed fifty male and fifty female teachers can be categorized as:

iii. random - The selection of teachers is done randomly, without any specific criteria or pattern.

To solve the absolute-value inequality |8 - x| ≥ 5, we can consider two cases:

Case 1: (8 - x) ≥ 5

To solve this inequality, we have:

8 - x ≥ 5

-x ≥ 5 - 8

-x ≥ -3 (multiplying by -1 and reversing the inequality)

x ≤ 3 (dividing by -1 and reversing the inequality)

Case 2: -(8 - x) ≥ 5

To solve this inequality, we have:

-8 + x ≥ 5

x ≥ 5 + 8

x ≥ 13

Combining the solutions from both cases, we have:

x ≤ 3 or x ≥ 13

So, the solution to the absolute-value inequality |8 - x| ≥ 5 is x ≤ 3 or x ≥ 13.

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Answer:

C because its the only one that fits the question its asking. 12-6 8-4 4-2

Step-by-step explanation:

Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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The marina is 6. 3 miles from the boat

The direction must it sail to head directly back to the marina Is due south

From the information given, we have that;

The boat sails 6 miles north

then, the boat sails then 2 miles northeast

Using the Pythagorean theorem which states that the square of the longest leg of a triangle is equal to the sum of the squares of the other two sides of that triangle.

Then, we have to substitute the values, we get;

d² = 6² + 2²

Find the square values, we have;

d² = 36 + 4

d² = 40

Find the square root of both sides

d = 6. 3 miles

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