Caroline drew the blueprints of her new kitchen on a coordinate plane. The coordinates of the four corners of her square kitchen are (2, 4), (-10, 4), (-10, -8), and (2, -8). How many units long is one wall of her kitchen? If needed, create a graph to help answer the question.

The probability of winning the board game Monopoly is 32.5% if you move first. If you play 20 games of monopoly where you move first, the probability that you win at least 10 out of 20 times is 0.334.

          Monopoly is a game of chance where the probability of winning changes depending on the variables. When you move first in a game of Monopoly, the probability of winning is 32.5%. If you play 20 games of Monopoly where you move first, you need to determine the probability of winning at least ten games.

       We can determine this by using a binomial distribution. A binomial distribution is used to determine the probability of the number of successes or failures in a fixed number of independent trials.

The formula for the binomial distribution is:

      P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Where:

P(X=k) = probability of k successes
n = number of trials
k = number of successes
p = probability of success
(1-p) = probability of failure
C(n,k) = the number of combinations of n things taken k at a time.

Using this formula, we can determine the probability of winning at least ten games of Monopoly out of twenty. We need to find the probability of winning exactly ten games, eleven games, twelve games, and so on, up to twenty games. We can then add these probabilities together to get the probability of winning at least ten games.

     P(X>=10) = P(X=10) + P(X=11) + P(X=12) + ... + P(X=20)

     P(X=k) = C(20,k) * 0.325^k * 0.675^(20-k)

Therefore, the probability that you win at least 10 out of 20 times is:

         P(X>=10) = 0.334

    Hence, the answer is 0.334.

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Answer:

c 1:3

Step-by-step explanation:

2/6 divide it by 1/3 and u get 1:3

Answer: A A C D there's the answer

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Let us take this number as x, translating this description of the equation into mathematical language;

\(x^2 = 3x - 2\)

Now let us solve for x;

\(x^2 = 3x - 2,\\x^2+2=3x-2+2,\\x^2+2=3x,\\x^2+2-3x=3x-3x,\\x^2-3x+2=0,\\\\Factored = \left(x-1\right)\left(x-2\right)=0,\\Zero Factor Principle, \\x = 1, x = 2\\\\Solution - Option A\)

* Note that for the the previous problem I solved, I set up a similar equation that had two values for the width, one negative and the other positive. Now the width could only be a positive number, so there was only one solution out of the two.

Answer:

Step-by-step explanation:

First, you have to find the total number of socks. The total is 14. Now, since you choose 2 socks out of 14 in total, the probability is 2/14 or about 14%. To find the percent, just divide the numerator by the denominator. The answer you get is in decimal form. Multiply the decimal by 100. Then, there is your percent.

Answer:

first: $130

second: 165 miles

In linear equation, Cost of operating a 200-W lamp continuously for 1 week = 6.7 $

What in mathematics is a linear equation?

1 kW = 1000 W

1 week = 7 days

1 day = 24 hours

Power utility rate = R = 20 cents/(kW.h)

Power consumed by the lamp = P = 200 W = 200 x 10-3 kW = 0.2 kW

Time period the lamp is operating for = T = 1 week = 1 x (7 x 24) hours = 168 hours

Energy consumed by the lamp in 1 week = E

E = PT

E = (0.2)(168)

E = 33.6 kW.h

Cost of operating the lamp continuously for 1 week = C

C = ER

C = (33.6)(20)

C = 672 cents

Converting from cents to dollars,

C = 672 x (1/100) $

C = 6.72 $

Rounding off to two significant figures,

C = 6.7 $

Cost of operating a 200-W lamp continuously for 1 week = 6.7 $

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Ok the first thing we have to do is calculate the approximate values of each number's probability. That probability tells how often will the dice land on a certain number. To approximate it you have to divide every frequency by the total amount of times the dice was tossed. Let's do that for every number:

Now we can solve the question. For example if you want to know how many times the dice is expected to land on 4 you just need to multiply the probability for that number, which I called P(4), for the total amount of times the dice was tossed, which are 180 times:

And that's the answer for a.

For item b we need to make more operations. We are being asked how many times the dice is expected to land on a number greater than 3. For this we'll have to use the probability for all the numbers on the dice that are greater than 3: 4, 5 and 6. We'll need to add all these probabilities and multiply the result od that sum by 180:

Since 92.88 isn't a whole number we round it to 93 and that's the answer for item b.

We can repeat our calculations for item c but using the probabilities of the even numbers instead. Said numbers are 2, 4 and 6:

Rounding 83.88 we have 84, the solution to item c.

Answer:

pls like and follow my page ....thank you

Step-by-step explanation:

using elimination method...you will have it as

12x+15y =34 .............1

-6x+5y = 3 ...............2

multiply equation 1 by 6 and equation 2 by 12

72x + 90y = 204.........4

-72x + 60y = 36..........5

asd equation 2 and 1...

0x + 150y = 240

y= 240/250 ..

after getting your answer ..

substitute for y in either of equation 1 and 2 to get your x

To find the area of the region common to the circles \(r = -6\sin(\theta)\) and \(r = 3\), we need to determine the bounds of integration for \(\theta\) and then integrate the appropriate area formula.

First, let's find the values of \(\theta\) where the two circles intersect. Set the equations of the circles equal to each other:

\(-6\sin(\theta) = 3\)

Dividing both sides by -6 and taking the inverse sine:

\(\sin(\theta) = -\frac{1}{2}\)

This equation is satisfied for two values of \(\theta\) in the interval \([0, 2\pi)\): \(\theta = \frac{7\pi}{6}\) and \(\theta = \frac{11\pi}{6}\).

Now, we can calculate the area of the common region using the integral:

\[A = \int_{\theta_1}^{\theta_2} \frac{1}{2} \left((r_1)^2 - (r_2)^2\right) d\theta\]

where \(r_1 = -6\sin(\theta)\), \(r_2 = 3\), and \(\theta_1 = \frac{7\pi}{6}\), \(\theta_2 = \frac{11\pi}{6}\).

Plugging in the values and simplifying, we have:

\[A = \int_{\frac{7\pi}{6}}^{\frac{11\pi}{6}} \frac{1}{2} \left((-6\sin(\theta))^2 - 3^2\right) d\theta\]

\[A = \int_{\frac{7\pi}{6}}^{\frac{11\pi}{6}} \frac{1}{2} \left(36\sin^2(\theta) - 9\right) d\theta\]

Now, we can integrate this expression with respect to \(\theta\) over the given bounds to find the area.

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Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

There are two 1/2’s in an hour

4 in 2 hours + 0one more 1/2 makes 5 total

Answer: 5

Answer:

(2,3) becomes A'(-2,-3)

Step-by-step explanation:

Using the 180 cc rotation rule (x,y) --> (-x,-y). Points 2 and 3 become negative resulting in (-2,-3)

The first model, SAT = β₀ + β₁Income + β₂GPA + ε, included both income and GPA as predictors.

The second model, SAT = β₀ + β₁ GPA + ε, only included GPA as a predictor.

The third model, SAT = β₀ + β₁ Income + ε, solely used income as a predictor.

To examine the relationship between SAT scores and explanatory variables, three models were estimated based on the provided data. The first model, SAT = β0 + β1Income + β2GPA + ε, included both income and GPA as predictors. The second model, SAT = β0 + β1GPA + ε, only considered GPA as a predictor, while the third model, SAT = β0 + β1Income + ε, solely used income as a predictor.

The coefficients (β) of the models were estimated using statistical methods. These coefficients represent the relationship between the predictors and the SAT scores. By plugging in the mean values of the explanatory variables into the preferred model, the SAT score can be predicted. The preferred model is the one that is most appropriate for the given data and research question.

To obtain the predicted SAT score, the mean value of the explanatory variable(s) is substituted into the preferred model. The coefficients estimate the impact of the variables on the SAT score. The resulting prediction provides an estimate of the SAT score based on the mean values of the predictors.

It's important to note that the actual values of the coefficients and predictions cannot be provided without the specific values of the coefficients and mean values of the explanatory variables in the given data.

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Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

To determine the number of empty seats carried by each airline, we can set up a system of equations based on the given information.

Let's denote the number of empty seats for United Continental as "u," American as "a," and Southwest as "s." The system of equations will be u + a + s = 250 (equation 1) and 14.9u + 14.6a + 12.4s = 106,095 (equation 2). Additionally, it is given that u = 3a.

Equation 1 represents the total number of empty seats, which is 250. It states that the sum of the number of empty seats for each airline is equal to 250.

Equation 2 represents the total cost incurred by the airlines for the empty seats, which is $106,095. It states that the cost of u empty seats for United Continental (at a rate of 14.9¢ per seat-mile), plus the cost of a empty seats for American (at a rate of 14.6¢ per seat-mile), plus the cost of s empty seats for Southwest (at a rate of 12.4¢ per seat-mile) is equal to $106,095.

We are also given that u = 3a, which means the number of empty seats for United Continental is three times the number of empty seats for American.

To solve this system of equations, we can use technology such as a calculator or computer software. By solving the system, we find that u = 13,095, a = 4,365, and s = 70.

Therefore, United Continental carried 13,095 empty seats, American carried 4,365 empty seats, and Southwest carried 70 empty seats on their flights.

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Answer:

h(-2) = 13

h(5) = -1

Step-by-step explanation:

Given the function

h(x) = -2x + 9

Evaluating at x = -22

substitute x = -2

h(-2) = -2(-2) + 9

h(-2) = 4 + 9

h(-2) = 13

Therefore,

Evaluating at x = 5

Given the function

h(x) = -2x + 9

substitute x = 5

h(5) = -2(5) + 9

h(5) = -10 + 9

h(5) = -1

Therefore,

Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

Answer:

7 Inches

Explanation:

Divide:

18 ÷ 2.54 = 7.08661417323

Round:

7

- PNW

The prοbability that there will be fewer than 2 arrivals in a given minute \(P(X < 2) = e^{(-\lambda)} + \lambda * e^{(-\lambda)\)

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο determine the prοbability that there will be fewer than 2 arrivals in a given minute, we need tο knοw the arrival rate οr average number οf arrivals per minute. Withοut this infοrmatiοn, we cannοt calculate the exact prοbability.

Hοwever, we can make an assumptiοn οr use a hypοthetical scenariο fοr illustratiοn purpοses. Let's assume that the average number οf arrivals per minute is λ, where λ represents the rate parameter fοr a Pοissοn distributiοn. The Pοissοn distributiοn is cοmmοnly used tο mοdel the number οf events οccurring in a fixed interval οf time when the events happen independently and at a cοnstant average rate.

The prοbability οf having fewer than 2 arrivals in a given minute can be calculated as the sum οf the prοbabilities οf having 0 arrivals and having 1 arrival.

P(X < 2) = P(X = 0) + P(X = 1)

In a Poisson distribution, the probability of having x events occur is given by the formula:

\(P(X = x) = (e^{(-\lambda)} * \lambda ^x) / x\)

Using the assumption of λ, we can calculate the probability as:

P(X < 2) = P(X = 0) + P(X = 1) =\((e^{(-\lambda)} * \lambda^0) / 0! + (e^{(-\lambda)} * \lambda^1) / 1!\)

Simplifying further:

\(P(X < 2) = e^{(-\lambda)} + \lambda * e^{(-\lambda)\)

Please note that the value of λ is required to compute the probability accurately. Without knowing the specific value of λ, we cannot provide a numerical probability.

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Answer:

The value of t is 22

Step-by-step explanation:

Let us solve the question

In any triangle

∵ The sum of the measures of the interior angles of a triangle is 180°

∵ The angle of triangles are ∠1, ∠2, and ∠3

∴ m∠1 + m∠2 + m∠3 = 180°

∵ The three angles of the triangle are 2t, 3t, and 70°

∴ m∠1 = 2t

∴ m∠2 = 3t

∴ m∠3 = 70°

→ Substitute them in the rule above

∴ 2t + 3t + 70° = 180°

→ Add the like terms

∵ (2t + 3t) + 70 = 180

∴ 5t + 70 = 180

→ Subtract 70 from both sides

∵ 5t + 70 - 70 = 180 - 70

∴ 5t = 110

→ Divide both sides by 5

∴ t = 22

∴ The value of t is 22

Without knowing the specific data of the town, it is impossible to provide an exact probability but we can use the following formula to calculate the probability of an individual being employed full-time, given that they are between 18 and 49 years old:

P(full-time employment | age between 18 and 49) = P(full-time employment and age between 18 and 49) / P(age between 18 and 49)

To calculate this probability, we need to know the number of individuals in the town who are both employed full-time and between the ages of 18 and 49, and divide it by the total population of the town.

P(full-time employment and age between 18 and 49) = Number of individuals employed full-time and between the ages of 18 and 49 / Total population of the town

To calculate this probability, we need to know the number of individuals in the town who are between the ages of 18 and 49, and divide it by the total population of the town.

P(age between 18 and 49) = Number of individuals between the ages of 18 and 49 / Total population of the town

We can use the probabilities calculated in steps 1 and 2 to calculate the probability of an individual being employed full-time, given that they are between the ages of 18 and 49, using the formula:

P(full-time employment | age between 18 and 49) = P(full-time employment and age between 18 and 49) / P(age between 18 and 49)

For example, if there are 10,000 people in the town, and 6,000 of them are between the ages of 18 and 49, and out of those 6,000, 4,000 are employed full-time, then:

P(full-time employment and age between 18 and 49) = 4,000 / 10,000 = 0.4

P(age between 18 and 49) = 6,000 / 10,000 = 0.6

P(full-time employment | age between 18 and 49) = 0.4 / 0.6 = 0.67

Therefore, the probability that an individual is employed full-time, given that they are between the ages of 18 and 49, is 0.67 or 67%.

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Using the probability concept, it is found that:

a) P(girl) = 1/3, which means that 1/3 = 33% of the time, the first batter will be a girl.

b) P(boy) = 2/3, which means that 2/3 = 67% of the time, the first batter will be a boy.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, in a total of 15 people, 5 are girls and 10 are boys, hence:

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According to the question Chi's expectation in this game is -3/5, which means on average, he can expect to lose $0.60 per game.

To determine Chi's expectation, we need to calculate the expected value for each outcome and then sum them up.

Let's denote the event of selecting a blue chip as B and the event of selecting a red chip as R.

The probability of selecting a blue chip, P(B), can be calculated as the number of blue chips divided by the total number of chips:

P(B) = 4 / (4 + 6) = 4/10 = 2/5

The probability of selecting a red chip, P(R), can be calculated as the number of red chips divided by the total number of chips:

P(R) = 6 / (4 + 6) = 6/10 = 3/5

Now, let's calculate the expected value for each outcome:

If Chi selects a blue chip, he receives $6. So the expected value for this outcome is 6 * P(B) = 6 * (2/5) = 12/5.

If Chi selects a red chip, he gives Dolly $5. So the expected value for this outcome is -5 * P(R) = -5 * (3/5) = -15/5.

Finally, we can calculate Chi's expectation by summing up the expected values for each outcome:

Expectation = (12/5) + (-15/5) = (12 - 15) / 5 = -3/5.

Therefore, Chi's expectation in this game is -3/5, which means on average, he can expect to lose $0.60 per game.

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Answer:

Total number of books = 100

Number of books Ashley had given away after first week= n

Number of books Ashley had given away after second week= 2n

Number of books Ashley had given away after w week= wn

Books = Total - Number of Books she will give away

Books = 100 - wn

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

You can use proportions to solve this.

You are paying $116.64 for 3 gallons of paint, so you could write this as:

\frac{116.64}{3}

Since the question is asking for price PER CUP, you want to convert 3 gallons to cups. 3 gallons = 48 cups. So now you can rewrite this as:

\frac{116.64}{48 cups}

In order to find the cost per cup, you can set up a proportion that solves for the price, x

\frac{116.64}{48 cups}  = \frac{x}{1 cup}

Solve for x by cross multiplying:

48x = 116.64

x = $2.43

It costs $2.43 per cup of paint