Using long division to find each quotient.
(2x³ 3x² + 4x + 2) = (x + 2)

Answer: A cup of coffee costs $2.50 and a bagel costs $3.50.

Step-by-step explanation: Let's use the following variables to represent the price of each item:

c: price of a cup of coffee (in dollars)

b: price of a bagel (in dollars)

From the problem statement, we know that:

b = c + 1 (a bagel costs $1 more than a cup of coffee)

We also know that you bought 4 cups of coffee and 6 bagels for a total of $31. This can be expressed as:

4c + 6b = 31

Now we can substitute the first equation into the second equation to eliminate b:

4c + 6(c + 1) = 31

Simplifying this equation, we get:

10c + 6 = 31

Subtracting 6 from both sides, we get:

10c = 25

Dividing both sides by 10, we get:

c = 2.5

Now we can use the first equation to find the value of b:

b = c + 1 = 2.5 + 1 = 3.5

Therefore, a cup of coffee costs $2.50 and a bagel costs $3.50.

Answer: 216

Step-by-step explanation:

Equation:

270 x 80% = large buttons

To multiply by a percent, move the decimal to the left two places:

270 x 0.80 = large buttons

Solve:

270 x 0.80 = 216

Janet got 216 large buttons

Hope this helps!

The factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]

To factor the given polynomial completely, we need to find the greatest common factor (GCF) of all the terms. The GCF of 60a^(3)b^(2), 10a^(2), and -50a^(4)b^(2) is 10a^(2).

So, we can factor out 10a^(2) from each term to get:

[tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]

Now, we can check our answer by multiplying the factors back together:

[tex]10a^{(2)}(6ab^{(2)}+1-5a^{(2)}b^{(2))}=60a^{(3)}b^{(2)}+10a^{(2)}-50a^{(4)}b^{(2)}[/tex]

Therefore, the factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}.[/tex]

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Answer:

The expression a[(9b-c)+z] can be simplified using the distributive property of multiplication. The distributive property states that:

a(b + c) = ab + ac

Using this property, we can distribute the a to the terms inside the brackets:

a[(9b-c)+z] = a(9b-c) + az

Now, we can distribute the a again to get:

a(9b-c) + az = 9ab - ac + az

Therefore, the expression a[(9b-c)+z] is equivalent to 9ab - ac + az.

Answer:

Step-by-step explanation: Equivalent to 9ab - ac + az.

The required foci of the ellipse are also at (-4, -3).

To find the foci of the ellipse defined by the equation:

[tex]\dfrac{(x+4)^2}{4}+\dfrac{(y+3)^2}{9}=1[/tex]

We need to identify the values of 'a' and 'b' from the equation, where 'a' is the semi-major axis, and 'b' is the semi-minor axis of the ellipse.

The general equation of an ellipse centered at (h, k) is given by:

[tex]\dfrac{(x - h)^2}{ a^2} + \dfrac{(y - k)^2}{ b^2} = 1[/tex]

Comparing this with the given equation, we can see that the center of the ellipse is at (-4, -3), so (h, k) = (-4, -3).

Next, we find 'a' and 'b':

For the x-term: a² = 4

a = √4

a = 2

For the y-term: b² = 9

b = √9

b = 3

So, the semi-major axis 'a' is 2 units, and the semi-minor axis 'b' is 3 units.

Now, the distance from the center of the ellipse to the foci is given by:

[tex]c = \sqrt{(a^2 - b^2)[/tex]

[tex]c = \sqrt{(2^2 - 3^2)[/tex]

[tex]c=\sqrt{-5[/tex]

The distance is imaginary, which means the foci are not real, and the ellipse is degenerate. A degenerate ellipse is essentially a circle. Since we have a degenerate ellipse, the foci coincide with the center of the ellipse.

Therefore, the foci of the ellipse are also at (-4, -3).

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Answer:

55%

Step-by-step explanation:

When you have a question that asks you about a percentage and it gives you a fraction, most of the time you just have to divide the numbers. In this case you will do 11/20=0.55 and you will change the decimal to a percentage. Which will be 55%.

Tthe total cost for each club after 7 months will be $123.

To find out when the total cost of each health club will be the same, we can use the equation:

Club A total cost = Club B total cost

18 + 15x = 11 + 16x

Where x is the number of months. We can rearrange the equation to solve for x:

15x - 16x = 11 - 18
-x = -7
x = 7

So the total cost of each health club will be the same after 7 months. To find the total cost for each club, we can plug x = 7 back into the equation:

Club A total cost = 18 + 15(7) = $123

Club B total cost = 11 + 16(7) = $123

So, the total cost for each club after 7 months will be $123.

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Yes, matrix A is invertible.

Therefore, the inverse of matrix A is A-1 =
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]

To calculate A-1, we can use the following formula:

A-1 = (1/detA) x adj(A)

Where detA is the determinant of A, and adj(A) is the adjugate of A.

To calculate the determinant of A, we can use the following formula:

detA = (1 x (-1) x 10-6) + (-1 x (11-6) x 1) + (1 x (-1) x (2))

= 1 x (-1) x 4 - (-1) x 5 x 1 + 1 x (-1) x 2

= 4 - 5 + 2

= 1

Now we can calculate the adjugate of A. To do this, we need to calculate the cofactors of each element in A, and then take the transpose of the matrix.

The cofactors of A can be calculated as follows:

[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]

Now, taking the transpose of this matrix, we get the following:

[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]

Now, multiplying the determinant of A and the adjugate of A, we can calculate A-1:

A-1 = (1/1) x
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]

=
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]

Therefore, the inverse of matrix A is:

A-1 =
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]

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Answer: y=mx+b

Step-by-step explanation:

L x W x D cubic yards is the maximum amount of water the pool can contain.

Volume = Length x Width x Depth

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to calculate the volume for each of these shapes.

from the question:

We need to know the pool's dimensions in order to calculate how much water it can store. Assume the pool has the following dimensions: L yards in length, W yards in breadth, and D yards in depth.

The following formula can be used to determine the pool's volume:

Volume = length, width, and depth

Volume = L, W, and D cubic yards.

The pool may therefore hold a maximum volume of water that is L x W x D cubic yards.

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The maximum amount of water that the pool can contain is the volume of the pool = L x W x D cubic yards.

The volume of a closed surface or object is a three-dimensional mathematical measurement. Cubic volume metrics include m3, cm3, in3, etc.

Any three-dimensional solid's volume is the area it takes up.

Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more. In this lesson, we'll learn how to determine the volume of each of these forms.

Here we need to know the pool's dimensions in order to calculate how much water it can store.

Let the pool's length be L yards.

Let the pool's breadth be W yards.

Let the pool's depth be D yards.

The following formula can be used to determine the pool's volume:

Volume = length × width × depth

⇒ Volume = L × W × D cubic yards.

The pool may therefore hold a maximum volume of water that is:

L x W x D cubic yards.

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The values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.

To solve the equation x^(2)+14x+3=0 by completing the square method, we need to follow these steps:

1. Rearrange the equation so that the constant term is on the right side: x^(2)+14x=-3

2. Find the value of h by taking half of the coefficient of the x term: h=14/2=7

3. Add the square of h to both sides of the equation: x^(2)+14x+7^(2)=-3+7^(2)

4. Simplify the right side of the equation: x^(2)+14x+49=46

5. Write the left side of the equation in the form (x+h)^(2): (x+7)^(2)=46

Therefore, the values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.

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Answer:

18

Step-by-step explanation:

18

Answer:

If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:

t = kc

We can find the value of k by using the given information that 5 climbs cost $52.50:

52.50 = k(5)

Solving for k, we get:

k = 10.50

Therefore, the equation that represents the total cost, t, of c climbs is:

t = 10.50c

The given set of vectors in R4 is linearly independent and  the vector u as a linear combination of the vectors v1, v2, and v3  can be written as u = (7,12,22)

a) To determine if the set of vectors in R4 is linearly independent or linearly dependent, we can use the rank of the matrix formed by these vectors. If the rank of the matrix is equal to the number of vectors, then the set is linearly independent. Otherwise, it is linearly dependent.

First, let's form the matrix using the vectors:

| 1 0 -1 0 |
| 1 1 0  2 |
| 0 3  1 -2 |
| 0 1 -1  2 |

Next, let's find the rank of the matrix. We can do this by using Gaussian elimination to reduce the matrix to row echelon form:

| 1 0 -1 0  |
| 0 1  1 -2 |
| 0 0  4 -6 |
| 0 0  0  4 |

The rank of the matrix is 4, which is equal to the number of vectors. Therefore, the set of vectors is linearly independent.

b) To write the vector u as a linear combination of the vectors v1, v2, and v3, we need to find the scalars a, b, and c such that:

u = av1 + bv2 + cv3

This gives us the following system of equations:

10 = 2a + b - 2c
1 = 3a + 2b + 2c
4 = 5a + 4b + 3c

We can use Gaussian elimination to solve this system of equations:

| 2  1 -2 | | a | = | 10 |
| 3  2  2 | | b | = |  1 |
| 5  4  3 | | c | = |  4 |

After reducing the matrix to row echelon form, we get:

| 1 0  1 | | a | = | 2 |
| 0 1 -2 | | b | = | 3 |
| 0 0  0 | | c | = | 0 |

From the third equation, we can see that c can be any value. Let's choose c = 0. Then, from the first two equations, we get:

a = 2
b = 3

Therefore, the vector u can be written as a linear combination of the vectors v1, v2, and v3 as follows:

u = 2v1 + 3v2 + 0v3

u = (2)(2,3,5) + (3)(1,2,4) + (0)(-2,2,3)

u = (4,6,10) + (3,6,12) + (0,0,0)

u = (7,12,22)

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Check the picture below.

Answer:

(3x + 5) and (x - 6).

Step-by-step explanation:

There are 330 ways to choose 4 books from a collection of 11 books.


To solve this problem, we need to use the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to choose, and ! means factorial (the product of all positive integers up to that number).

In this case, we have n = 11 (the total number of books) and r = 4 (the number of books to choose). Plugging these values into the formula, we get:
C(11, 4) = 11! / (4! * (11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8 * 7!)/ (4! * 7!)
= (11 * 10 * 9 * 8)/ (4 * 3 * 2 * 1)
= 330

So there are 330 ways to choose 4 books from a collection of 11 books.

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The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.

Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.

Therefore, the correct answer is option b. Ordinal data.

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The expression that is equivalent to the given expression, 8x + 4, is 4(2x +1)

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is:

8x + 4

To determine the expression that is equivalent to the given expression, we will factorize the given expression.

First, we will determine the Greatest common factor (GCF) of the terms in the expression.

The terms in the expression are 8x and 4

The GCF of 8x and 4 is 4

Thus,

We can factor the expression as shown below:

8x + 4

4(2x + 1)

Hence, the expression is 4(2x + 1)

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Answer:

I think the answer is x= 5, -1

Answer:

i got x= 5,-1

Step-by-step explanation:

i hope this helps and have a good day

The number 19 is the solution of the equation n-7=12.

The equation given is n-7=12. To find the solution, we need to isolate the variable n on one side of the equation. We can do this by adding 7 to both sides of the equation. This gives us:

n-7+7=12+7

Simplifying the equation gives us:

n=19

Now, we can check which numbers in the set {17,19,21} are solutions of the equation. The only number that satisfies the equation is 19. Therefore, the solution of the equation is 19.

Answer: The number 19 is the solution of the equation n-7=12.

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The value of the sample variance and the sample standard deviation for the given data is equal to 47.4 and 6.9 respectively.

Data values are,

23, 12, 5, 9,8

Number of observations 'n' = 5

Mean = ( sum of all the observations ) / ( number of observations)

         = (23 + 12 + 5 + 9 + 8) / 5

         = 57 /5

         = 11.4

Deviations of each data point from the mean,

(23 - 11.4) = 11.6

(12 - 11.4) = 0.6

(5 - 11.4) = -6.4

(9 - 11.4) = -2.4

(8 - 11.4) = -3.4

Square each deviation is equal to,

11.6² = 134.56

0.6² = 0.36

(-6.4)² = 40.96

(-2.4)² = 5.76

(-3.4)² = 11.56

Sample Variance = ( Sum of squared deviation )/ ( n - 1)

⇒Sample Variance = (134.56 + 0.36 + 40.96 + 5.76 + 11.56) / (5-1)

⇒Sample Variance = 47.35

⇒Sample Variance = 47.4(rounded to one decimal place)

Now,

Standard deviation = √variance

Substitute the value we get,

⇒ Standard Deviation = √(47.35)

⇒ Standard Deviation = 6.9 (rounded to one decimal place)

Therefore, the sample variance is 47.4 and the sample standard deviation is 6.9.

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The above question is incomplete, the complete question is:

Calculate the sample variance and the sample standard deviation for the given data. Provide your sample standard deviation answer precise to one decimal place.

23, 12, 5, 9,8

The x and y-intercept of the given point (1,1), (-5,7) is 2 and 2.

The equation of a line can be represented in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, let's find the slope.

(1,1), (-5,7)

m = 7 - 1 / -5 - 1

m = 6 / -6

m = - 1

Let's find the x and y-intercept using (1, 1)

y = -x + b

1 = -1 + b

b = 1 + 1

b = 2

Therefore,

y = - x + 2

Let's find x and y-intercept

y = -(0) + 2

y = 2

- x = y + 2

-x = 0 + 2

x = 2

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The likelihood function for a sequence of coin tosses x1, . . . , xn with P[H] = p is given by:

L(p) = P(x1, . . . , xn | p) = P(x1 | p) * P(x2 | p) * . . . * P(xn | p)

Using the notation that 1 denotes H and 0 denotes T, we can write the likelihood function as:

L(p) = p^k * (1-p)^(n-k)

where k is the number of heads in the sequence and n-k is the number of tails.

To find the maximum likelihood estimate for p, we need to take the derivative of L(p) with respect to p and set it equal to zero:

dL(p)/dp = k*p^(k-1)*(1-p)^(n-k) - (n-k)*p^k*(1-p)^(n-k-1) = 0

Solving for p, we get:

p = k/n
Therefore, the maximum likelihood estimate for p is the number of heads in the sequence divided by the total number of tosses.

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The value of c that will make the polynomial a perfect square trinomial is 16.

To find the values of c that will make the polynomial a perfect square trinomial, we need to use the formula for a perfect square trinomial, which is:

[tex](a+b)^(2) = a^(2)+2ab+b^(2)[/tex]

In this case, we have:

[tex]225r^(2)-120r+c = (15r+b)^(2)[/tex]

Expanding the right side of the equation, we get:

[tex]225r^(2)-120r+c = 225r^(2)+30rb+b^(2)[/tex]

Comparing the coefficients of the terms, we can see that:

-120r = 30rb

b = -4

Now, substituting b back into the equation, we get:

[tex]c = b^(2) = (-4)^(2) = 16[/tex]

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Overproduction of uric acid in the body is a condition known as hyperuricemia. It occurs when the body produces more uric acid than it can excrete. Uric acid is a waste product that is formed when the body breaks down purines, which are found in certain foods and drinks. If the body is unable to get rid of the excess uric acid, it can build up and form crystals in the joints, causing a painful form of arthritis known as gout.

Hyperuricemia can also be an indication of other health conditions, such as leukemia and lymphoma. These are types of cancer that affect the blood cells and the immune system, respectively. When cells in the body break down, they release uric acid into the bloodstream. If there is an overproduction of cells, as in the case of leukemia and lymphoma, this can lead to an excess of uric acid in the body.

It is important to monitor the levels of uric acid in the body, as it can be an early indication of these serious health conditions. A healthcare professional can conduct tests to measure the levels of uric acid in the body and determine the cause of the overproduction.

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Correct question is" Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advanced indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.75 mg/dl. (a) Find a 95 % confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) (b) Find the sample size necessary for a 95 % confidence level with a maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)"

The expected number of defective batteries out of 15,000 batteries is of:

83.3.

Then this expected amount is compared to the number of different batteries of the other companies.

The number of defective batteries is obtained applying the proportions in the context of the problem.

Company C had 60 defective batteries out of 10,800, hence the proportion of defective batteries is of:

60/10,800.

Out of 15,000 batteries, the expected number of defective batteries is of:

60/10,800 x 15,000 = 83.3.

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Answer:

3.5 * 10²

Step-by-step explanation:

In standard form, the number before the point has to be less than ten so

0.035 = 3.5 *10²

Answer:

Step-by-step explanation:

I'm assuming you mean is the number 90 a rational number. The answer is that yes, it is a rational number.

Let me explain:

Under all the possible numbers, there is a taxonomy to organize these types of numbers. It goes down a list from:

- all numbers, which is divided into two groups; complex and real

Under real numbers, there's rational and irrational:

Under rational, there's integers and fractions

Under integers, there's whole numbers and negative

Under whole numbers, there's natural numbers and 0 (yes, zero).

90 falls under natural numbers, which means it is also a rational number. Hope this helps!

Answer:

in all 240

60 chose blue

72 chose red

36 chose orange

7 chose purple

10 chose green

7 chose other

Step-by-step explanation:

48 x 5 = 240

48 = 20%

20% x 5 = 100%