(50 points) Use the spinner below. Show your work, making sure to simplify your answers. (Note: The smallest section of the circle is 1/16 of the circle.)

16. What is P(red, yellow, blue)?

17. What is P(orange, yellow)?

18. P(green, blue, purple)?

19. P(pink)?

20. P(red, orange, yellow, green, blue, purple)?

Thank you!!

Answer:

(i) - rectangular prism

(Ii) - triangular prism

(iii) - square pyramid

Step-by-step explanation:

Answer:

(-1)^2+5= 1+5=6

(0)^2+5= 0+5= 5

(1)^2+5= 1+5= 6

6+5+6= 17

x-1 + x0 + x1 = (-1)^2 + 5  + (0)^2 + 5  +  (1)^2 + 5  = 6 + 5 + 6 = 17

Answer: Infinite solutions

Step-by-step explanation:

\(8-(2x-9)=17-2x\)

Begin by distributing the negative into the parenthesis.

\(8-2x+9=17-2x\)

Combine like terms;

\(17-2x=17-2x\)

Subtract 17

\(-2x=17-17-2x\)

\(-2x=-2x\)

Add 2x

\(-2x+2x=0\\0=0\)

Equation: 8 - (2x - 9) = 17 - 2x

First, we distribute the - sign.

8 -2x + 9 = 17 - 2x

Then, we combine like terms if there any on both sides.

17 - 2x = 17 - 2x

Now, we can see the equations are equal to each other.

However, we can go a step further and solve for x.

17 - 2x = 17 - 2x

Subtract 17 from both sides.

-2x = -2x

Divide both sides by -2.

x = x

Therefore, x has no value or is 0.

There are 60 students that prefer soccer

The first step is to determine the percentage of students that prefer soccer The percentage of students that prefer soccer = 100 - (53% + 26% + 15% ) = 6%

6% of the students surveyed prefer soccer

The second step is to determine the number of students that prefer soccer

Number of students that prefer soccer = (percentage of students that prefer soccer / 100) x total number of students surveyed

\(\frac{6}{100}\) × 1000 = 60 students

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Answer:

(10 1/3, 42)

Step-by-step explanation:

a1 = 1

a2 = a1×2 + 1/3 = 2 1/3

a3 = a2×2 + 1/3 = (a1×2 + 1/3)×2 + 1/3 = a1×4 + 2/3 + 1/3 =

= 4 + 3/3 = 5

a4 = a3×2 + 1/3 = ... = 10 1/3

b1 = 0

b2 = (b1 + 1/2)×4 = (0 + 1/2)×4 = 1/2 × 4 = 2

b3 = (b2 + 1/2)×4 = ((b1 + 1/2)×4 +1/2)×4 = 16×b1 + 16/2 + 4/2=

= 16/2 + 4/2 = 8 + 2 = 10

or (to check we made no mistake)

= (2 + 1/2)×4 = 8 + 2 = 10. => all ok, no mistake

b4 = (b3 + 1/2)×4 = ... = (10 + 1/2)×4 = 40 + 2 = 42

so, the fourth ordered pair (= the fourth elements of each sequence) is therefore (10 1/3, 42)

MatricesABC DeterminantA = 0, B = -1, C = 1, D = 0AD - BC = 0 - (-1) = 1A = 1, B = 0, C = 0, D = -1AD - BC = -1 - 0 = -1A = -1, B = 0, C = 0, D = 1AD - BC = -1 - 0 = -1 and the eigenvalues of A are ±1, which implies that det(A) = ±1.

(a)A matrix that is its own inverse is called involutory. Three 2 × 2 matrices A#I such that A2 = 1 are as follows: MatricesABCDeterminantA = 0, B = -1, C = 1, D = 0AD - BC = 0 - (-1) = 1A = 1, B = 0, C = 0, D = -1AD - BC = -1 - 0 = -1A = -1, B = 0, C = 0, D = 1AD - BC = -1 - 0 = -1

(b)The determinants for such a matrix is +1 or -1. Let A be an n × n matrix such that A² = I, where I is the identity matrix of order n. Since A² = I, the characteristic polynomial of A satisfies the equation (λ − 1)(λ + 1) = 0. The eigenvalues of A are ±1. Let λ be an eigenvalue of A. Then there exists a nonzero vector v such that Av = λv. We haveA²v = IAv = λAv = λ²v.So λ²v = v, or (λ² − 1)v = 0.Since v is nonzero, we must have λ² = 1 or λ = ±1. Hence, the eigenvalues of A are ±1, which implies that det(A) = ±1.The proof is complete.

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Answer:

Option B. y=x+5

Step-by-step explanation:

If x=2 and y=7

Inserting the values into y=x+5

7=5+2

7=7

If x=3 and y=8

y=x+5

8=3+5

8=8

If x=4 and y=9

y=x+5

9=4+5

9=9

If x=5 and y=10

y=x+5

10=5+5

10=10

The five things when two parallel lines are cut by a transversal are the corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

Here we have to find the five things that happen when two parallel lines are cut by a transversal.

When two parallel lines are cut by the transversal line it will form five angles.

Corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

From the given figure:

Corresponding angle:

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

consecutive angle:

∠3 and ∠6

∠4 and ∠5

alternate interior angle:

∠3 and ∠5

∠4 and ∠6

alternate exterior angle:

∠2 and ∠8

∠1 and ∠7

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Answer: 48 in 1 hour

Step-by-step explanation:

32 divided by 40 = 0.8

0.8 times 60 = 48

hope this helped you out :))

Answer: 300

Step-by-step explanation:

30 if 3/10 (0.3) of 100

90 is 3/10 (0.3) of 300

Answer is given below in picture

I hope it helps.

This is the value of x in the equation x = 1.025 L.

To find out how much punch was added to the bowl, we need to subtract the original amount of punch (1.341 L) from the final amount of punch (2.366 L):
2.366 L - 1.341 L = 1.025 L
So, 1.025 L of punch was added to the bowl.

To find the amount of punch added to the bowl, you'll need to subtract the initial volume from the final volume. Let x be the amount of punch added. The initial volume of punch in the bowl is 1.341 L, and the final volume is 2.366 L. To calculate x, use the following equation: x = final volume - initial volume x = 2.366 L - 1.341 L x ≈ 1.025 L So, approximately 1.025 L of punch was added to the bowl to make the total volume 2.366 L.
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When procedures are mandated by third party payers, the modifier -32 (mandated services) is used. This modifier is used to indicate that a service or procedure is mandated by a third party payer, such as Medicare or Medicaid.

It is used to ensure that the service or procedure is reimbursed appropriately and to avoid denials. The use of the -32 modifier is important to accurately reflect the requirements of the payer and to avoid any potential billing or coding errors. It is important to check with the specific payer to determine if the use of this modifier is required for a particular service or procedure.

When procedures are "mandated" by third-party payers, you would use the modifier -32. This modifier indicates that a service or procedure is being performed due to specific requirements from a third-party payer. It helps to provide the necessary information for reimbursement and ensures that the claim is processed correctly by the payer. Remember to attach the modifier -32 to the appropriate procedure code on the claim form when submitting it to the third-party payer. This will help avoid any potential delays or denials in payment due to insufficient documentation.

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The matrix is a not invertible when it's column do not span because it is not linearly independent.

According to the statement

we have find that the matrix can be a invertible or not when its column is spaned.

So, For this purpose, we know that the

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

And according to the statement it is not possible for thr matrix to be invertible.

Because for matrix it is not a possible because it is not independent,

In other words, No, if the columns don't span R5 -> NOT linearly independent -> not invertible.

So, The matrix is a not invertible when it's column do not span because it is not linearly independent.

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The probability that among 10 such cars tested, 3 will average less than 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon is given by 0.0020125

Let X be the number of cars among ten that averages less than 28 miles per gallon. Let Y be the number of cars among ten that average from 28 to 32 miles per gallon. Let Z be the number of cars among ten that average more than 32 miles per gallon. We are to find P(X = 3, Y = 6, Z = 1).

Firstly, let us find the probability of getting 3 cars among 10 cars that will average less than 28 miles per gallon.

The probability of getting exactly 3 cars among 10 cars that will average less than 28 miles per gallon is given by the probability mass function:

P(X = 3) = (10C3) (0.4)³ (0.6)⁷
= (10 x 9 x 8 / 3 x 2 x 1) (0.064) (0.096)
= 0.23 (approximately)

Similarly, the probability of getting 6 cars among 10 cars that will average from 28 to 32 miles per gallon is given by the probability mass function:

P(Y = 6) = (10C6) (0.5)⁶ (0.5)⁴
= (10 x 9 x 8 x 7 x 6 x 5 / 6 x 5 x 4 x 3 x 2 x 1) (0.156) (0.063)
= 0.25 (approximately)

Finally, the probability of getting 1 car among 10 cars that will average more than 32 miles per gallon is given by the probability mass function:
P(Z = 1) = (10C1) (0.1)¹ (0.9)⁹
= (10) (0.1) (0.348)
= 0.035

Therefore, the answer is:
P(X = 3, Y = 6, Z = 1) = P(X = 3) P(Y = 6) P(Z = 1)
= 0.23 x 0.25 x 0.035
= 0.0020125 (approximately)

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The basic solutions on the interval [0,2\pi)[0,2π) for the equation 2\(\sin 2x+\sin x=12sin2x+sinx=1\) are x=\(\frac{\pi}{6}\)   and x=\(\frac{5\pi}{6}\). The correct option is c.

​

To find the solutions to the equation \(2\sin 2x+\sin x=12sin2x+sinx=1\), we can start by rearranging the equation to obtain \(2\sin 2x+\sin x-1=02sin2x+sinx−1=0.\) Next, we can apply the double angle identity for sine, which states that\(\sin 2x = 2\sin x\cos xsin2x=2sinxcosx\). By substituting this into the equation, we get 4\sin x\cos x+\sin x-1=04sinxcosx+sinx−1=0.

Now, we can factor out the common term \sin xsinx from the equation: \(\sin x(4\cos x+1)-1=0sinx(4cosx+1)−1=0.\) This equation holds true if either \(\sin x = 0sinx=0 or 4\cos x+1=14cosx+1=1.\)From \sin x = 0sinx=0, we find one solution \(x=\frac{\pi}{2}\)

​ From\(4\cos x+1=14cosx+1=1\), we have \(4\cos x = 04cosx=0\), which gives us \(\cos x = 0cosx=0\). The solutions for \(\cos x = 0cosx=0\) on the interval [0,2\pi)[0,2π) are\(x=\frac{\pi}{2} and x=\frac{3\pi}{2}.\)

​ Combining all the solutions, we have\(x=\frac{\pi}{2}, x=\frac{3\pi}{2} , x=\frac{\pi}{6}, and x=\frac{5\pi}{6}\)

​ However, we need to consider that the interval given is [0,2\pi)[0,2π), so the solutions outside this interval are not valid. Therefore, the valid solutions on the interval [0,2\pi)[0,2π) are \(x=\frac{\pi}{6} and x=\frac{5\pi}{6}\)

​

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Answer:

C my dude. have a merry christmassss

Answer:

A

Step-by-step explanation:

Both are negative, and largest is always first.

Answer:

The city's snowfall in the two-month period was above the historical average by 1/8 feet

Step-by-step explanation:

Fractions

The question provides the following information: In January, a city’s snowfall was 5/8 feet below the historical average. Let's assume the snowfall level to be positive if it's above the historical average and negative otherwise.

The data from January gives us a snowfall of -5/8 feet because it was below the average.

We also know in February, the snowfall was 3/4 foot above the historical average. Following our predefined convention, the data from February gives us a snowfall of +3/4 feet.

To know if the city's snowfall during the two-month period was above or below the historical average, we just need to add them, signs included.

If the result is negative, the two-month period showed a snowfall below the historical average.

Let's find the sum of

\(\displaystyle -\frac{5}{8}+\frac{3}{4}\)

The LCM of 4 and 8 is 8, thus:

\(\displaystyle -\frac{5}{8}+\frac{3}{4}=\frac{-5+2*3}{8}=\frac{1}{8}\)

Since this quantity is positive, we can say the city's snowfall in the two-month period was above the historical average by 1/8 feet.

Given that Owen has $1.05 in dimes and nickels. He has 3 more dimes than nickels. We are to find out how many coins of each type he has.Let us assume that Owen has x nickels.

he has x+3 dimes.Since the value of each nickel is $0.05, thus, the value of x nickels is 0.05x dollars.Since the value of each dime is $0.10, therefore, the value of (x+3) dimes is 0.10(x+3) dollars.Owen has a total of $1.05 which can be written as 105 cents.

The total number of coins is the sum of the number of nickels and the number of dimes.1. Therefore, the equation is

5x + 10(x+3) = 105.2.

Simplify the equation:5x + 10x + 30 = 10515x = 75x = 5O

wen has 5 nickels.3. Owen has x+3 dimes.

Since x = 5, then he has 5+3 = 8 dimes

.Owen has 5 nickels and 8 dimes.

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Answer:

bust stop #2 6.5 minutes

Step-by-step explanation:

Answer:

bust stop #2 6.5 minutes

Step-by-step explanation:

(i) The null hypothesis is that the mean living area of all single-family homes in the county is equal to or less than 2400 square feet. The alternative hypothesis is that the mean living area of all single-family homes in the county is greater than 2400 square feet.

(ii) The test statistic is calculated using the formula: (sample mean - hypothesized mean) / (standard deviation / square root of sample size). In this case, the test statistic is \(\frac{(2540 - 2400)}{\frac{472}{\sqrt{50} } } =2.44\)

(iii) The p-value is the probability of obtaining a sample mean as extreme or more extreme than the one observed, assuming the null hypothesis is true. Using a t-distribution with 49 degrees of freedom (since we are using a sample size of 50 and estimating the population standard deviation), we can find the p-value to be 0.009.

(iv) Using a significance level of 0.05, we can conclude that the real estate agent's claim is not true, since the p-value is less than 0.05. We reject the null hypothesis and accept the alternative hypothesis that the mean living area of all single-family homes in the county is greater than 2400 square feet. If we use a significance level of 0.01 instead, we still reject the null hypothesis since the p-value is less than 0.01.

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Answer:

Surface area of the figure = 1000 in²

Step-by-step explanation:

From the figure attached,

Two rectangular prisms A and B have been shown with the dimensions.

Surface area of a rectangular prism = 2(length + width) × height

Surface area of prism A = 2(9 + 10) × 20

                                        = 760 in²

Surface area of prism B = 2(15 + 10) × 8

                                        = 16×25

                                        = 400 in²

But one surface of prism B along the width and the same area of prism A are hidden.

Area of the hidden surfaces = 2(10 × 8)

                                               = 160 in²

Total surface area of the figure = 760 + 400 - 160

                                                    = 1000 in²

you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.

First, we know the graph of f(x), and now we want to find the graph of the function:

f(x - 3) + 5.

Remember that a horizontal translation of N units is written as:

f(x + N)

Remember that a vertical translation of N units is written as:

f(x + N)

Then the function:

f(x - 3) + 5

Is a translation of 3 units to the right and 5 units upwards.

This means that you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.

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8) The percent of people that said that Pinocchio was their favorite Disney Movie is of: 28%.

9) The percent of people that said that Pinocchio or Cars was their favorite Disney movie is of: 39%.

10) The two movies that about half the people say were their favorite is of: Pinocchio and Toy Story.

From the pizza graph, the sum of all the percentages must be of 100%, hence the Pinocchio percentage is obtained as follows:

10 + 11 + 14 + 15 + 22 + P = 100

72 + P = 100

P = 100 - 72

P = 28%.

Then the percentage for Pinocchio or Cars is of:

28 + 11 = 39%.

The percentage for Pinocchio or Toy Story is of:

28 + 22 = 50%.

(about half).

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Answer:

1.1 dollar is unit price per 100grams

Amy because Ben spend the less money then

amy get more money

Amy has more money than her brother after all transactions.

An equation is a statement that the depicts the values of two mathematical expressions as equal using an (=) sign. Example -

2x = 5

An expression is written using individual terms (either constant or variable) separated by mathematical operations. Example -

3x + 5y + 3

We have Amy who has $1275 less than her brother ben. Ben spends $550 and Amy gets $750.

Assume that the money with Ben and Amy after transactions is $x and $y respectively. Let Ben has a initial amount of $m and Amy has of $n.

n = m - 1275

After transactions -

x = m - 550

y = m - 1275 + 750 = m - 525

Now -

m - 525 > m - 550  for every value of [m].

So, now Amy has more money.

Therefore, Amy has more money than her brother after all transactions.

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The correct null hypothesis for a single sample t-test is "a. μ=c".

A single sample t-test is used to determine whether the mean of a sample is significantly different from a hypothesized value, usually denoted by "c".

The test compares the sample mean to the hypothesized value and determines whether the observed difference is large enough to reject the null hypothesis.

The null hypothesis for a single sample t-test is always that the population mean is equal to the hypothesized value, which is expressed mathematically as:

H0: μ = c

where μ is the population mean and c is the hypothesized value.

The alternative hypothesis, which represents the opposite of the null hypothesis, is that the population mean is not equal to the hypothesized value, expressed as:

Ha: μ ≠ c

If the calculated t-value from the test is larger than the critical t-value at the chosen level of significance (usually 0.05), then we reject the null hypothesis and accept the alternative hypothesis.

This means that we have sufficient evidence to conclude that the sample mean is significantly different from the hypothesized value.

On the other hand, if the calculated t-value is smaller than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the sample mean is significantly different from the hypothesized value.

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hello

101.7 * 5.45 =

if you observe you'll see a decimal point after the third number. this tells us that the answer has a three significant figure

By taking the quotient between the total distance and the distance traveled with one tank, we conclude that the correct option is B.

We know that the car holds 25 gallons, and gets 18 miles per gallon.

Then, with one tank, the distance that the car can travel is:

25*18mi = 450mi

The number of times that the tank must be filled is equal to the quotient between the total distance of the trip, and the distance traveled with one tank, it is:

1350mi/450mi = 3

This means that the tank must be filled 3 times, so the correct option is B.

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Answer:

b:)

Step-by-step explanation:

The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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