a number c is an eigenvalue of a if and only if the equation (a -ci)x = 0 has a nontrivial solution.

With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17\(\frac{1}{3}\)

With one third of a serving remaining, there are 17 servings total.

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Answer:

x = 2

y = -1

Step-by-step explanation:

8x + 2y = 14

2x + y = 3

In order to find the number x represents, you have to make the number of y for both equations the same. So:

8x + 2y = 14

(×2) 4x + 2y = 6 (×2)

Then, you can cancel the y off both equations, which will leave:

8x = 14

4x = 6

To find 4x, you have to find the difference between both equations, so you have to:

14 - 6 = 8

Now that the actual number 4x represents is 8, so:

4x = 8

(÷4) x = 2 (÷4)

Now to find y, substitute the letter x with 2:

2x + y = 3

2 (2) + y = 3

4 + y = 3

4 - 3 = -y

1 = -y

(× -) -1 = y (× -)

Answer: x = 2

              y = -1

Hope this helps!  :)

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Answer:

D.

Step-by-step explanation:

A polynomial is an expression that looks similar to this:

3x³+x-3

A POLYNOMIAL IN ONE VARIABLE is a polynomial that contains only one variable. Example: 5x 2 + 3x - 7.

#6

Sum of exterior angles of any polygon=360°

sides=6

Measure of one angle

Option D

#7

4ft=1cm

and

Dimensions are 8cm and 15cm

Option B

Answer:

6.  d.  m∠YXZ = 60°

7.  b.  8 cm x 15 cm

Step-by-step explanation:

Question 6

∠YXZ is the exterior angle of a regular polygon

Exterior angle of a regular polygon = 360° ÷ number of sides

⇒ ∠YXZ = 360° ÷ 6

⇒ ∠YXZ = 60°

Question 7

Scale  1 cm : 4 ft

Therefore, to convert actual dimensions in feet to sketch dimensions in centimeters, divide dimensions in feet by 4:

⇒ width = 32 ft

⇒ width = 32 ÷ 4 = 8 cm

⇒ length = 60 ft

⇒ length = 60 ÷ 4 = 15 cm

Therefore, the dimensions of the sketch are 8 cm x 15 cm

The equation of the tangent line to the curve r = 4sin(3θ) at θ = π/6 is y = (√3/2)x + √3.

To find the equation of the tangent line, we need to determine the slope of the tangent line at the given point and then use the point-slope form of a line to write the equation.

The equation of the curve is given as r = 4sin(3θ). We can convert this to Cartesian coordinates using the relationships x = rcos(θ) and y = rsin(θ).

Plugging in the given value θ = π/6, we have:

r = 4sin(3(π/6)) = 4sin(π/2) = 4.

Using the conversion formulas, we get:

x = 4cos(π/6) = 4(√3/2) = 2√3,

y = 4sin(π/6) = 4(1/2) = 2.

So the point of tangency is (2√3, 2).

To find the slope of the tangent line, we differentiate the equation of the curve with respect to θ:

dr/dθ = 12cos(3θ).

At θ = π/6, we have:

dr/dθ = 12cos(3(π/6)) = 12cos(π/2) = 0.

Since the derivative is zero, the tangent line is vertical, and its slope is undefined.

Therefore, the equation of the tangent line can be written as x = 2√3.

In terms of x and y, we can rewrite this equation as y = (√3/2)x + √3.

Hence, the equation of the tangent line to the curve r = 4sin(3θ) at θ = π/6 is y = (√3/2)x + √3.

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Answer:

Sample Space = {(ABC), (ACB), (BAC), (BCA), (CAB), (CBA)}

= 6

Instances when A is besides C {(ACB),( BAC),( BCA), ( CAB)}

=4

P( A is besides C)= 4/6

To calculate the net sales, we need to subtract the discounts, sales returns and allowances, and freight in from the gross sales.

Therefore, we have:

Net sales = Gross sales - Discounts - Sales returns and allowances - Freight in

Substituting the given values, we get:

Net sales = $50,000 - $1,800 - $4,380 - $2,750 = $41,070

Therefore, the net sales of the company are $41,070. Answer: (d).

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Answer:

answer: 521

Hope that helps!

To find the number of 5-card poker hands that have at least 3 spades from a standard deck of 52 cards, we can use a combination of methods.

These are the following steps that are needed to be followed :

First, we can find the total number of 5-card poker hands from a standard deck, which is calculated as:

C(52,5) = 2,598,960

Next, we can find the number of 5-card poker hands that have exactly 3 spades. To do this, we need to choose 3 spades from the 13 available in the deck, and 2 non-spades from the 39 remaining cards. This can be calculated as:

C(13,3) * C(39,2) = 1,098,240

We can also find the number of 5-card poker hands that have exactly 4 spades. To do this, we need to choose 4 spades from the 13 available in the deck, and 1 non-spade from the 39 remaining cards. This can be calculated as:

C(13,4) * C(39,1) = 224,850

Finally, we can find the number of 5-card poker hands that have exactly 5 spades. To do this, we need to choose all 5 spades from the 13 available in the deck. This can be calculated as:

C(13,5) = 1287

To find the total number of 5-card poker hands that have at least 3 spades, we can add up the number of hands with exactly 3 spades, exactly 4 spades, and exactly 5 spades:

1,098,240 + 224,850 + 1,287 = 1,324,377

Therefore, there are 1,324,377 5-card poker hands from a standard deck of 52 cards that have at least 3 spades.

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Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

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Answer:

Step-by-step explanation:

Use the ratio of corresponding sides of similar triangles:

Answer:

x = 108

Step-by-step explanation:

x is the height

from the Euclidian theorem we know that :

x^2 = 81*144

x^2 = 11664 find the root for both

x = 108

The probability of obtaining tails and the number 5 is 1/12

the probability of obtaining an even number is 1/2

P(heads and prime number)  1/4

Since the events are independent, the probability of obtaining tails and the number 5 is:

P(tails and 5) = P(tails) * P(5) = (1/2) * (1/6) = 1/12

The coin toss outcome is irrelevant, so the probability of obtaining an even number is:

P(even number) = 1/2

The probability of obtaining heads and a prime number is:

P(heads and prime number) = P(heads) * P(prime number) = (1/2) * (1/2) = 1/4

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Answer:

1 inch per hour

Step-by-step explanation:

1 hour it burns 1 inch

Answer:  x > -8

Step-by-step explanation:

3x - 17 < 4x -  9   subtract 3x from both sides, and add 9 to both sides

-3x + 9 < -3x + 9

0  - 8   <  x  +  0      Rewrite and reverse the sign to simplify

     x > -8

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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The probability is that two random professionals will be chosen, and the first of their IQs is greater than 115 and the second is between 115 and 130.

To find this probability, we need to consider the independence of the IQs of different professionals. This means that the outcome of one professional's IQ does not affect the outcome of another professional's IQ:

1. The probability that the first professional's IQ is greater than 115: let's assume that the probability of the first professional's IQ being greater than 115 is p1.

2. The probability that the second professional's IQ is between 115 and 130: for the distribution of IQs, let's assume that the probability of the second professional's IQ being between 115 and 130 is p2.

Since the IQs of the professionals are independent events, we can multiply the probabilities of the two events happening together to find the overall probability. Therefore, the probability that both events occur is p1 * p2.

To calculate the final probability, we need specific values for p1 and p2, which are not provided in the question. However, we can illustrate the concept using an example:
For example, if p1 is 0.6 (60% chance) and p2 is 0.3 (30% chance), then the probability of both events occurring is 0.6 * 0.3 = 0.18 or 18%.

In conclusion, the probability that two random professionals will be chosen, and the first of their IQs is greater than 115 and the second is between 115 and 130 depends on the specific values of p1 and p2.

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You could round both numbers and then multiply:

18.3 ---> 18

6.37 ---> 6

18 * 6 = 108

Help this answer helps you!

Answer:

Sample Response: Round to the greatest place value to do the math in your head. 18.3 rounds to 20, and 6.37 rounds to 6. The estimated product will be 20 times 6, which is 120.

Answer:

c = 6

Step-by-step explanation:

52 = 7 + 5(c = 3)

52 = 7 + 5c + 15

52 = 22 + 5c

-5c = 22 - 52

-5c = -30

c = \(\frac{-30}{-5}\)

c = 6

Answer:

6 hours is your answer, good luck

Answer:

6 hours

Step-by-step explanation:

In hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between two groups, or that a certain parameter is equal to a specified value. In this case, the null hypothesis is that the mean difference is 0, meaning there is no significant difference between the two groups being compared.

The alternative hypothesis (Ha), on the other hand, is a statement that contradicts the null hypothesis. It can be one-tailed (directional), indicating that the mean difference is greater than or less than 0, or two-tailed (non-directional), indicating that the mean difference is not equal to 0. So, to determine the null and alternative hypotheses in this case, we know that the null hypothesis is that the mean difference is 0. The alternative hypothesis can be either one of the following:
- Ha: The mean difference is not equal to 0 (two-tailed)
- Ha: The mean difference is greater than 0 (one-tailed)
- Ha: The mean difference is less than 0 (one-tailed)

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Sin (angle) = opposite leg / hypotenuse

Sin(x) = 2.1/4

x = arcsin(21./4)

x = 31.7 degrees

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

The given equation is 4x+2 = 12.

To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:

4x+2-2 = 12-2

4x = 10

Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.

Rewrite equation:

x = log base 4 of 10

Use the change of base formula, we can present this as:

x = \(log base 10 of 10 / log base 10 of 4\)

Simplifying:

x = 1.442114

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.

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Answer: the person above has it

Step-by-step explanation:

Answer:

One, four, and five

Step-by-step explanation:

I just got it right, and I hope you do too :)

The solution is Option A , Option D, Option E

The equation of line is y = ( - 1/2 ) x + 7/2 and the slope is m = ( -1/2 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as G = G ( -4 , 1 )

Let the second point be represented as H = H ( 2 , -2 )

The slope of the line between the points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - 1 ) / ( 2 - ( - 4 ) )

On simplifying the equation , we get

Slope m = -3 / 6

Slope m = -1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Now , the line passes through the point J ( 1 , 3 )

Substituting the values in the equation , we get

y - 3 = ( -1/2 ) ( x - 1 )

On simplifying the equation , we get

y - 3 = ( -1/2 )x + 1/2

Adding 3 on both sides of the equation , we get

y = ( -1/2 )x + 7/2

So , the equation of line is y = ( -1/2 )x + 7/2

Substitute the value of x and y in the equation , we get

Let the point be A ( -3 , 5 )

when x = -3 and y = 5

y = ( -1/2 )x + 7/2

5 = (- 1/2) (- 3) +7/2

5 = 3/2 + 7/2

5 = 10/2

5 = 5

So , the point A lies on the line

Let the point be B ( 3 , 2 )

when x = 3 and y = 2

2 = (- 1/2) (3) +7/2

2 = -3 / 2 + 7/2

2 = 4/2

2 = 2

So , the point B lies on the line

Let the point be C ( 5 , 1 )

when x = 5 and y = 1

1 = (- 1/2) (5) +7/2

1 = -5 / 2 + 7/2

1 = 2/2

1 = 1

So , the point C lies on the line

Hence , the equation of line is y = ( -1/2 )x + 7/2

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Answer:

Angle 4 and Angle 6

Step-by-step explanation:

consecutive interior angles**

The student earned a total of 6 points by correctly using definite integrals to find f(-2) and f(2), identifying the critical values and absolute minimum value of f(x) and finding f''(-5).

The student earned a total of 6 points in the problem. They earned 3 points in for using an appropriate definite integral to find f(-2), and another point for using a definite integral to find f(2). They did not earn any points.

In next part, they earned 2 points for identifying where f'(x) = 0, and identifying the absolute minimum value of f(x) at x=2. In part (d), they earned 1 point for finding f''(-5), but did not earn the second point due to a contradiction in their reasoning about the differentiability of f(x) at x=3.

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Answer:

34.5%

Step-by-step explanation: