Simplify. 11 3/4-8 1/2

Answer:

Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.

To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:

14 ÷ (7/4) = 8

Therefore, Keith can paint 8 classrooms in total.

Answer:

we cant see the full picture :(

Assuming a poisson distribution, the probability of having at most 2 flaws in 450 square feet is approximately 0.062 or 6.2%.

For the probability of at most 2 flaws in 450 square feet, we can use the Poisson distribution.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events occur with a known average rate and independently of the time since the last event.

In this case, we are given that the average number of flaws in 150 square feet is two. Let's denote this average as λ (lambda).

We can calculate λ using the given information:

λ = average number of flaws in 150 square feet = 2

Now, let's find the probability of at most 2 flaws in 450 square feet. Since the area of interest is three times larger (450 square feet), we need to adjust the average accordingly:

Adjusted λ = average number of flaws in 450 square feet = λ * 3 = 2 * 3 = 6

Now we can use the Poisson distribution formula to find the probability. The formula is as follows:

P(X ≤ k) = e^(-λ) * (λ^0 / 0!) + e^(-λ) * (λ^1 / 1!) + e^(-λ) * (λ^2 / 2!) + ... + e^(-λ) * (λ^k / k!)

In this case, we need to calculate P(X ≤ 2), where X represents the number of flaws in 450 square feet and k = 2. Plugging in the values, we get:

P(X ≤ 2) = e^(-6) * (6^0 / 0!) + e^(-6) * (6^1 / 1!) + e^(-6) * (6^2 / 2!)

Calculating each term:

P(X ≤ 2) = e^(-6) * (1 / 1) + e^(-6) * (6 / 1) + e^(-6) * (36 / 2)

Now, let's calculate the exponential term:

e^(-6) ≈ 0.00248 (rounded to five decimal places)

Substituting this value into the equation:

P(X ≤ 2) ≈ 0.00248 * 1 + 0.00248 * 6 + 0.00248 * 18

Calculating each term:

P(X ≤ 2) ≈ 0.00248 + 0.01488 + 0.04464

Adding the terms together:

P(X ≤ 2) ≈ 0.062 (rounded to three decimal places)

Therefore, the probability of having at most 2 flaws in 450 square feet is approximately 0.062 or 6.2%.

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The residual associated with this individual is approximately -15.4 ounces, using the least squares estimate. This means that the actual amount of food consumed is about 15.4

We would predict that the dog would eat approximately 180.96 ounces of food in a week, based on the least squares estimate.  the residual associated with this individual is approximately -15.4 ounces, using the least squares estimate. This means that the actual amount of food consumed is about 15.4 ounces less than what would be predicted based on the regression model.

Using the given regression model, we can estimate the amount of food a dog weighing 42.4 pounds would consume in a week as:

Food Consumed = -32.86 + 5.25 × Weight

Food Consumed = -32.86 + 5.25 × 42.4

Food Consumed ≈ 180.96 ounces

Therefore, we would predict that the dog would eat approximately 180.96 ounces of food in a week, based on the least squares estimate.

To find the residual associated with a dog weighing 24.7 pounds and consuming 70 ounces of food per week, we first need to calculate the predicted value of food consumed based on the given regression model:

Food Consumed = -32.86 + 5.25 × Weight

Food Consumed = -32.86 + 5.25 × 24.7

Food Consumed ≈ 85.38 ounces

The residual is then calculated as the difference between the actual value of food consumed (70 ounces) and the predicted value (85.38 ounces):

Residual = Actual Value - Predicted Value

Residual = 70 - 85.38

Residual ≈ -15.4 ounces

Therefore, the residual associated with this individual is approximately -15.4 ounces, using the least squares estimate. This means that the actual amount of food consumed is about 15.4 ounces less than what would be predicted based on the regression model.

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Answer:

25 length and 25width

Step-by-step explanation:

we need to find the biggest area with a perimeter of 100 and all sides need to be the same. So you divide 100 by 4 and you get 25 for width and 25 for length

Answer:

Step-by-step explanation:

In this math, we will be using the law of cosine.

a2 = b2 + c2 − 2bc cosA

This is to note that a here is actually x

a= x

b = 10

c = 9.4

cosA = cos20°

\(a = \sqrt{b^{2} +c^{2} - (2bc*cosA) }\\\\a= \sqrt{100 +88.36 - (188- 0.94)} \\\\a = \sqrt{1.3}\\\\a = 1.14\)

student can answer the questions on the test in 16,384 different ways if they answer every question.

To determine the number of ways a student can answer the questions on a multiple-choice test containing 7 questions with four possible answers for each question, we will use the multiplication principle. The multiplication principle states that if there are a number of independent choices, then the total number of possible outcomes is the product of the number of choices.
Identify the number of questions and possible answers. In this case, there are 7 questions and 4 possible answers for each question.
Calculate the number of ways to answer each question. Since there are 4 possible answers for each question, there are 4 ways to answer each of the 7 questions.
Apply the multiplication principle. To find the total number of ways to answer all 7 questions, multiply the number of ways to answer each question:
Total number of ways = (4 ways for question 1) x (4 ways for question 2) x ... x (4 ways for question 7)
Perform the calculation. Since there are 7 questions and 4 ways to answer each question, the total number of ways is:
Total number of ways = 4^7 = 16,384

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9514 1404 393

Answer:

  ∠2 = 45°

Step-by-step explanation:

Angles 1 and 2 are same-side interior angles where the transversal crosses parallel lines. That means they are supplementary angles.

  ∠1 +∠2 = 180° . . . . . supplementary angles total 180°

  135° +∠2 = 180° . . . . substitute the given value

  ∠2 = 180° -135° . . . .  subtract 135°

  ∠2 = 45°

In the given problem, the sum of \(\frac{4}{6}\) and \(\frac{4}{6}\) is \(\frac{4}{3}\).

The sum is the result of adding two or more numbers or terms. In other words, it is the process of bringing two or more numbers together to produce a new result or total. The symbol for the sum is "+".

The sum can be performed on any kind of number, including whole numbers, integers, rational numbers, real numbers, and complex numbers. The rules for addition are the same for all types of numbers.

To find the sum of \(\frac{4}{6}\) and \(\frac{4}{6}\),

\(\frac{4}{6}\) +  \(\frac{4}{6}\) = 2 \(\times \ \frac{4}{6}\)

        = \(\frac{4}{3}\).

So, \(\frac{4}{6}\) +  \(\frac{4}{6}\) = \(\frac{4}{3}\).

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The expected payout for one draw is $0.19327.

To calculate how much Mark should pay for one draw, we need to determine the probability of drawing each type of card and the corresponding payouts, and then take a weighted average.

There are 13 clubs in the deck, so the probability of drawing a club is 13/52 = 1/4. The payout for a club is $0.50.

There are 4 aces in the deck, so the probability of drawing an ace is 4/52 = 1/13. The payout for an ace is $0.65.

There is only one ace of clubs in the deck, so the probability of drawing the ace of clubs is 1/52. The payout for the ace of clubs is $0.95.

To calculate the weighted average payout, we can multiply the probability of each outcome by its corresponding payout, and then add up the products:

(1/4) x $0.50 + (1/13) x $0.65 + (1/52) x $0.95 = $0.125 + $0.05 + $0.01827

So the expected payout for one draw is $0.19327.

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Answer:

X = 35.7 Y=54.3

Step-by-step explanation:

Let the 2 angles be called X and Y were X is the smaller angle

we know that both angles are complementary therefore
X+Y=90

X = Y - 18.6 ( Given )

Y - 18.6 + Y = 90 ( substitution)

2Y = 90 + 18.6

Y = 108.6/2

Y=54.3

X= Y-18.6= 54.3-18.6 = 35.7

Check : X + Y = 35.7+54.3=90

E=mc² is the legendary equation of Albert Einstein .

In the formula

Here

E stands for energy emitted.

m stands for mass

c stands for speed of light

Answer:

Equation of Special Relativity

\(\large \text{$ E=mc^2 $}\)

where:

Albert Einstein's famous equation demonstrates the relationship between mass and energy.

It is vital when using this equation that all components are converted (where necessary) into the SI units given above.  Therefore, mass must be measured in kilograms and energy must be measured in Joules.

Joules is an SI measurement for energy and is measured as kilograms x meters squared per seconds squared →  \(\sf kg \times m^2s^{-2}\)

The SI base units are the standard units of measurement defined by the International System of Units (SI).

A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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Answer:

y - 1 = 1/6x + 1 <<< Point slope form

y = 1/6x + 2 <<< slope intercept form

Either one works unless the question specifies the form of the equation

Step-by-step explanation:

Point slope form: (y - y1) = m(x - x1)

Given: (-6,1) ; m = 1/6

(y - 1) = 1/6(x - (-6))

y - 1 = 1/6x + 1 <<< Point slope form

y = 1/6x + 2 <<< slope intercept form: y = mx + b

The first three terms of the Maclaurin series for f(x) = e^x * ln(1 - x) are: f(x) ≈ -x - (3x^2)/2 - (5x^3)/6

To find the first three terms of the Maclaurin series for f(x) = e^x * ln(1 - x), we will first find the Maclaurin series for each individual function and then use power series multiplication.

1. Maclaurin series for e^x:
e^x = 1 + x + (x^2)/2! + ...

2. Maclaurin series for ln(1 - x):
ln(1 - x) = -x - (x^2)/2 - (x^3)/3 - ...

Now, we will multiply the two Maclaurin series:

f(x) = (1 + x + (x^2)/2! + ...) * (-x - (x^2)/2 - (x^3)/3 - ...)

To find the first three terms, we only need to consider the following multiplications:
- (1 * -x)
- (1 * -(x^2)/2) and (x * -x)
- (1 * -(x^3)/3) and (x * -(x^2)/2)

Performing these multiplications:

- (1 * -x) = -x
- (1 * -(x^2)/2) + (x * -x) = -(x^2)/2 - x^2 = -3x^2/2
- (1 * -(x^3)/3) + (x * -(x^2)/2) = -(x^3)/3 - (x^3)/2 = -5x^3/6

So, the first three terms of the Maclaurin series for f(x) = e^x * ln(1 - x) are:

f(x) ≈ -x - (3x^2)/2 - (5x^3)/6

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Answer:

10/13

Step-by-step explanation:

total candies = 62

yellow and green candies = 20

P (yellow or green candies) = 20/62

=> 10/13

Answer: lesser x = 3.76 & greater x = 8.24

Step-by-step explanation: just took the test

For the given quadratic equation lesser x=3.765 and greater x=8.235.

The given quadratic equation is (x-6)²-5=0.

We need to find the solutions from least to greatest.

The formula to find the solution to the quadratic equation is \(x=\frac{-b\pm\sqrt{b^{2}-4ac }}{2a}\).

Now, (x-6)²-5=0 can be written as x²-12x+31=0

Here, a=1, b=-12 and c=31

x=(12±√20)/2

⇒x=(12±4.47)/2

⇒x=3.765 or x=8.235

Therefore, lesser x=3.765 and greater x=8.235.

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Answer:

GB = 7

BE = 10.5

AG = 10

DG = 5

FG = 3·x

CF = 9·x

Step-by-step explanation:

The given parameters are;

The centroid of the ΔABC = G

Segments CF, BE, and AD are median lines

EG = 3.5 Given

∴ EG = 1/3 × BE by definition of the properties of median line

∴ BE = 3 × EG = 3 × 3.5 = 10.5

BE = 10.5

GB = 2/3 × BE = 2/3 × 10.5 = 7 by definition of the properties of median line BE

GB = 7

Similarly;

Given that AD = 15, AG = 2/3 × AD = 2/3 × 15 = 10 by definition of the properties of median line AD

AD = 10

DG = 1/3 × AD = 1/3 × 15 = 5 by definition of the properties of median line AD

DG = 5

Similarly;

Given  CG = 6·x

FG = 1/3 × CF

CF = 3 × FG

CG = 2/3 × CF = 2/3 × 3 × FG

∴ CG = 2 × FG

FG = CG/2 = 6·x/

2 = 3·x

FG = 3·x

CF = 3 × FG = CF = 3 × 3 × x = 9·x

CF = 9·x

Well I can't be for sure but I know for a fact its not set IV it's not possible to make a triangle out of all right angles. Set II, well, that isn't right either. You can't make a triangle out of all obtuse angles. Like the right angle one, its not possible you can only use one obtuse or right angle in a triangle other wise it's not going to be a triangle. I'd say go try Set III since that would most likely make an equilateral triangle.

Answer:

Each term in pattern B is 9 less than the corresponding term in pattern A.

Answer:

400 tiles

Step-by-step explanation:

Calculate the area of each tile, in m^2:

30 cm = 0.30 m

(0.30 m)^2 = 9.0 x 10^-2 m^2

Divide this into the total area:

(36m^2)/(9.0 x 10^-2 m^2)= 400 tiles

====

Another approach is to note that 6m^2 could be envisioned as a square with sides of 6 m.  Calculate the tiles needed to stretch along one side:

6 m = 600 cm

600 cm/30 cm  = 20 tiles

It takes 20 tiles to cover one direction

It would also take 20 tiles for the other direction, so a mosaic of 20 by 20 tiles would cover the 36 m^2.

20 x 20 = 400 tiles

Answer:

Remember that the slope of perpendicular lines are negative reciprocals of each other.Step-by-step explanation:y = 1 - 2x     the slope is -2     the value of the x term.So the slope of the new line using point (- 1, 2)  is  1/2.Now use y = mx + b where y = -1, x = 2, and m = 1/2 .y = mx + b-1 = 1/2(2) + b                solve for "b", the y-intersect-1 =  1 + b-2 = bThe line that is perpendicular to y = 1 - 2x  is  y = 1/2x - 2

Step-by-step explanation:

Answer:

Negative.

Step-by-step explanation:

b is above zero. So, it is positive.

c is below zero. So, it is negative.

A positive divided by negative number results in negative.

Answer:

B. negative

Step-by-step explanation:

-2 is negative. That's why.

Answer:

\(\frac{4}{5}\)

Step-by-step explanation:

Step 1: Write the equation

\(\frac{5k}{6}\) + \(\frac{2}{3}\) = \(\frac{4}{3}\)

Step 2: Multiply each term by the lowest common multiple (lcm)

lcm of the denominators 6 and 3 = 6

Step 3:

6x\(\frac{5k}{6}\) + 6x\(\frac{2}{3}\) = 6x\(\frac{4}{3}\)

Next

5k + 4 = 8

5k = 8 - 4

5k = 4

Divide through by 5

k = \(\frac{4}{5}\)

Answer:

565656÷8=p

So the answer is 637:D

Answer:

times by 1.17

Step-by-step explanation:

hope this helps!

please give me a brainliest!!<3

Answer: 0.017

Step-by-step explanation:

1.7% = 0.017

The relation between the exponential and the logarithm is used. Then the expression \(e^{\ln3}\) is given as 3.

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

The expression is given below.

\(\rightarrow e^{\ln3}\)

We know the formula

\(\rm e^{\ln x} = x\)

Then the expression can be written as

\(e^{\ln3} = 3\)

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The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.

To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:

First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.

Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.

The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.

The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.

The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.

Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:

V = ∫[a, b] 2πrh dy

Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).

Substituting t

he values of r and h into the integral, we have:

V = ∫[0, 9] 2πy(y) dy

Simplifying, we get:

V = 2π ∫[0, 9] y^2 dy

Evaluating the integral, we have:

V = 2π [y^3/3] from 0 to 9

V = 2π [(9^3/3) - (0^3/3)]

V = 2π [(729/3) - 0]

V = 2π (243)

V = 486π

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Answer:

Explanation:

Given the expression;

simplifying;

we have;

Therefore;

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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