Find the remainder when x^2 + 3x - 11 is divided by x - 2
-13
1

-1

-11

Answer:

y=1/2x + 6

Step-by-step explanation:

Use point slope form

y-y1=m(x-x1)

y-5= 1/2 (x+2)

y-5= 1/2x + 1

y= 1/2x + 6

Answer: (1) C. 65 + 28H < 250

(2) 6

Step-by-step explanation:

Here is the correct question:

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Since the initial fee charged by the plumber is $65 and an hourly rate of $28, and Anand would like to spend no more than $250. This means that the addition of the initial fee plus the hourly fee based on number of hours worked will have to be less than $250. This can be mathematically expressed as:

= 65 + 28H < 250

That means option C is the correct answer.

Option B and D are incorrect because the greater sign was used but Anand doesn't want to spend more than $250 but the options denoted that he spent more than $250 which isn't correct.

2)'The largest whole number of hours that Anand can afford goes thus:

65 + 28H < 250

28H < 250 - 65

28H < 185

H < 185/28

H < 6.6

Therefore, the largest whole number of hours that Anand can afford is 6.

Answer: The Answer is 65+28H < 250 and the largest amount of hours is 6

Step-by-step explanation:

Answer:

b = 64°

2b = 128°

Step-by-step explanation:

use (n-2)×180 to find the total number of degrees inside a polygon where 'n' equals number of sides

hexagon has 6 sides; (6-2)×180 = 720°

528 + 3b = 720

3b = 192

b = 64

Expressed as a percentage, the average slope is approximately 0.0009%

To find the average slope of the ground between the two contours, we need to first determine the vertical distance between them in feet.

Since the contour interval is 5 ft and two adjacent contours are 0.6 inches apart, we can set up the following proportion to find the vertical distance between the contours in feet:

0.6 inches : 1 (map unit) = 5 ft : 2000 (map units)

Solving for the vertical distance in feet, we get:

0.6 inches * 5 ft / 2000 = 0.0015 ft

Therefore, the vertical distance between the two contours is 0.0015 ft.

The average slope of the ground between the contours can be found by dividing the vertical distance by the horizontal distance between the contours. Since the scale of the map is 1:2000, 1 inch on the map corresponds to 2000 inches on the ground. Therefore, the horizontal distance between the contours in feet is:

1 inch * 2000 / 12 = 166.67 ft

Thus, the average slope of the ground between the contours is:

0.0015 ft / 166.67 ft ≈ 0.000009

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Answer:

$17.1

Step-by-step explanation:

If Gianna paid $4.75, then she had $4.75 more than she has now. So, before she bought the smoothie, she had $12.35 + $4.75.

We can break this up into $12.00+$0.30+$0.05+$4.00+$0.70+$0.05.

Now, we have $16.00+$1.00+$0.10=$17.10, which is just $17.1

Answer:

x=5

Step-by-step explanation:

32 = 2^x

Rewrite 32 as 2^5

2^5 = 2^x

Since the bases are the same, the exponents are the same

5 =x

Answer:

\(x=5\)

Step-by-step explanation:

\(2^{5}=2*2*2*2*2=32\)

Hope this helps

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

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It will take Joey's family approximately 21 months to save enough money, compounded monthly at a 5% interest rate, to finance their vacation trip to the amusement park.

To determine the time it will take to save enough money, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r,

where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of periods.

Given:

Desired future value (FV) = $5000,

Monthly payment (P) = $240,

Monthly interest rate (r) = 5% / 12 = 0.05 / 12 = 0.004167.

We need to solve for the number of periods (n) in the formula. Rearranging the formula, we have:

n = log(1 + (FV * r) / P) / log(1 + r),

where log denotes the logarithm with base 10.

Plugging in the given values, we get:

n = log(1 + ($5000 * 0.004167) / $240) / log(1 + 0.004167).

Using a calculator, we find that n is approximately 20.998, which rounds up to 21.

Therefore, it will take Joey's family approximately 21 months to save enough money, compounded monthly at a 5% interest rate, to finance their vacation trip to the amusement park.

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Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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The probability distribution function that represents how long the pizza order taker takes is the norm(16.7, 3.03) seconds, which is a normal distribution with mean 16.7 and standard deviation 3.03 seconds.

The probability distribution function that represents how long the pizza order taker takes is the norm(16.7, 3.03) seconds.

What is a probability distribution function

A probability distribution function (PDF) is a formula used to describe a random variable's likelihood of occurring in a given range of values.

Continuous and discrete random variables can both be described using probability density functions (PDFs).

Probability distribution function for pizza order taker.

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To find the least integer for which the given function satisfies the condition, we need to identify the value of the variable that makes the function equal to 35.

The function provided is ()=35 2 2 4. Unfortunately, the expression seems to be incomplete or missing some information. To accurately determine the least integer, we would need additional details about the function, such as the variable involved and its equation or formula.

Without a clear understanding of the function's structure and missing information, it is not possible to generate a specific answer. Please provide the complete equation or formula for the function, including the variable and any additional parameters or constraints, so that I can assist you further in finding the least integer that satisfies the condition.

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r = 42 - 3.50m is the equation to represent, r, the amount of money remaining in Shawna's lunch account after she purchases m meals, -3.5 is the slope and 42 is y intercept.

To represent the amount of money remaining in Shawna's lunch account after she purchases m meals, we can use the equation:

r = 42 - 3.50m

r represents the amount of money remaining in Shawna's lunch account.

42 represents the initial amount of money loaded into her account at the start of the school year.

3.50 represents the cost of each meal in the school cafeteria.

m represents the number of meals Shawna has purchased.

Now let's determine the slope and y-intercept of this equation:

The slope represents the rate at which the money in Shawna's account decreases with each meal purchase.

The slope is -3.50, indicating that $3.50 is subtracted from her account for each meal.

The y-intercept represents the initial amount of money in Shawna's account, which is $42.

This is the value of r when m is 0 (before any meals are purchased).

Therefore, the slope is -3.50 and the y-intercept is 42.

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This can go on forever, we can then establish the recursive formula which states:

t(2)=t(1)+d

t(3)=t(2)+d, but t(2)=t(1)+d

t(3)=t(1)+d+d

t(3)=t(1)+2d

t(4)=t(1)+3d

Using trigonometric, Pythagorean and tangent identity, the value of tan(x + y) is 4/3

In the question given;

We can apply the trigonometric identity that tan (x + y) = (tan x + tan y)/(1 - tan x tan y).

We also know that cos x = 4/5 and cos y = 24/25.

Using the Pythagorean identity, we can find that sin x = 3/5 and sin y = 7/25.

Then, using the tangent identity, we can find that tan x = 3/4 and tan y = 7/24.

Plugging all of this into the formula for tan (x + y), we get:

tan (x + y) = (3/4 + 7/24)/(1 - (3/4)(7/24))

tan (x + y) = (4/3)

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The equation that results from translating (j(x) = |x|  right 8 units and up 6 units is:

j(x) = |x - 8| + 6

To translate the function (j(x) = |x| right 8 units and up 6 units, we need to modify the expression inside the absolute value function.

The translation right 8 units means we need to replace x with (x - 8).

The translation up 6 units means we need to add 6 to the entire expression.

So the equation that results from translating (j(x) = |x|  right 8 units and up 6 units is:

j(x) = |x - 8| + 6

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The complement of set A, denoted by ​ A`, is the collection of all elements that belong to the universal set but are not part of set A. It's not necessary to mention the universe (also known as U) if it's understood which set of elements is being referred to.

The complement of a set A is the collection of all elements that belong to the universal set but not to set A. It is denoted as ​ A` and does not include any elements that are already in set A. The universal set, also known as U, contains all possible elements and is assumed to be known. Therefore, when referring to the complement of a set, it is not necessary to mention the universal set explicitly. The complement of a set is useful in determining the set of elements that are not part of a particular set, and it can be used in various mathematical operations.

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Answer: \(x=-1 \pm \sqrt{15}\)

Step-by-step explanation:

\((x+1)^2 =15\\\\x+1 =\pm \sqrt{15}\\\\x=-1 \pm \sqrt{15}\)

The solution to the system of equations is x = 11.5 and y = -27.5.

The solution to the system of equations is x = 2 and y = 1

The solution to the system of equations is x = -12 and y = 7.

The solution to the system of equations is x = 0.5 and y = -6.

A system of linear equations can be solved graphically, by substitution, by elimination, and by the use of matrices.

To solve the system of equations:

3x + y = 7

5x + 3y = -25

We can use the method of substitution or elimination to find the values of x and y.

Let's solve it using the method of substitution:

From the first equation, we can express y in terms of x:

y = 7 - 3x

Substitute this expression for y into the second equation:

5x + 3(7 - 3x) = -25

Simplify and solve for x:

5x + 21 - 9x = -25

-4x + 21 = -25

-4x = -25 - 21

-4x = -46

x = -46 / -4

x = 11.5

Substitute the value of x back into the first equation to find y:

3(11.5) + y = 7

34.5 + y = 7

y = 7 - 34.5

y = -27.5

Therefore, the solution to the system of equations is x = 11.5 and y = -27.5.

To solve the system of equations:

2x + y = 5

3x - 3y = 3

Again, we can use the method of substitution or elimination.

Let's solve it using the method of elimination:

Multiply the first equation by 3 and the second equation by 2 to eliminate the y term:

6x + 3y = 15

6x - 6y = 6

Subtract the second equation from the first equation:

(6x + 3y) - (6x - 6y) = 15 - 6

6x + 3y - 6x + 6y = 9

9y = 9

y = 1

Substitute the value of y back into the first equation to find x:

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 2

Therefore, the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations:

2x + 3y = -3

x + 2y = 2

We can again use the method of substitution or elimination.

Let's solve it using the method of substitution:

From the second equation, we can express x in terms of y:

x = 2 - 2y

Substitute this expression for x into the first equation:

2(2 - 2y) + 3y = -3

Simplify and solve for y:

4 - 4y + 3y = -3

-y = -3 - 4

-y = -7

y = 7

Substitute the value of y back into the second equation to find x:

x + 2(7) = 2

x + 14 = 2

x = 2 - 14

x = -12

Therefore, the solution to the system of equations is x = -12 and y = 7.

To solve the system of equations:

2x - y = 7

6x - 3y = 14

Again, we can use the method of substitution or elimination.

Let's solve it using the method of elimination:

Multiply the first equation by 3 to eliminate the y term:

6x - 3y = 21

Subtract the second equation from the first equation:

(6x - 3y) - (6x - 3y) = 21 - 14

0 = 7

The resulting equation is 0 = 7, which is not possible.

Therefore, there is no solution to the system of equations. The two equations are inconsistent and do not intersect.

To solve the system of equations:

4x - y = 6

2x - y/2 = 4

We can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From the second equation, we can express y in terms of x:

y = 8x - 8

Substitute this expression for y into the first equation:

4x - (8x - 8) = 6

Simplify and solve for x:

4x - 8x + 8 = 6

-4x + 8 = 6

-4x = 6 - 8

-4x = -2

x = -2 / -4

x = 0.5

Substitute the value of x back into the second equation to find y:

2(0.5) - y/2 = 4

1 - y/2 = 4

-y/2 = 4 - 1

-y/2 = 3

-y = 6

y = -6

Therefore, the solution to the system of equations is x = 0.5 and y = -6.

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Answer:

  51 1/9 bd ft

Step-by-step explanation:

You want to know the number of board feet of wood in a beam (band girder) comprised of two 15 ft 4 inch 2×10s.

A board foot of wood is a volume that is 1 ft square and 1 inch thick, equivalent to 144 in³ or 1/12 ft³.

The attachment shows the calculation of the number of cubic feet of wood in the double beam, divided by (1/12 ft³/bd-ft) to given the number of board feet. The nominal size of the board is used for the calculation.

Of course, each inch is 1/12 ft, so the (end area) measurement in feet of a single 2×10 is (2/12 ft)×(10/12 ft).

The required band girder is 51 1/9 board feet of lumber.

__

Additional comment

We could have figured the area in square feet and multiplied that result by the number of inches of thickness. For purposes of explaining the units, we chose to use conventional volume units (ft³) and convert to board feet at the end.

  (15 1/3 ft)(5/6 ft) = 12 7/9 ft²

  (12 7/9 ft²)(4 in) = 51 1/9 ft²·in = 51 1/9 bd-ft . . . . double the 2" thickness of 1 board

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Answer:

W' = 54.4  pounds

Step-by-step explanation:

Given that,

The weight of a bag of books = 40 pounds

After picking up some books at school, the weight has increased by  36%.

We need to find the weight of the bag now. Let the new weight is W'.

So,

W' = 40 +36% of 40

i.e.

\(W'=40+\dfrac{36}{100}\times 40\\W'=54.4\ pounds\)

So, the new weight of the bag is equal to 54.4  pounds.

The distance between the base of the 11-foot ladder and the base of the wall, rounded to the nearest hundredth, is approximately 4.28 feet.

We can use the idea of right triangles that are similar to each other to solve this issue. In similar triangles, the lengths of the sides that are corresponding to each other are equal.

Let's say that there is a distance of "x" feet between the base of the wall and the base of the 11-foot ladder.

Regarding the 9-foot ladder:

The hypotenuse measurement of the ladder is 9 feet, and the adjacent side measurement of the distance is 3.5 feet. For the 11-foot ladder:

The length of the stepping stool (hypotenuse) = 11 feet

The separation from the foundation of the stepping stool to the foundation of the wall (neighboring side) = 'x' feet

Utilizing the proportion of comparing sides of comparative triangles, we can set up the accompanying extent:

9 / 3.5 = 11 / x We can cross-multiply to solve for "x":

9x = 3.5 * 11 9x = 38.5 Now divide by 9 on both sides:

x = 38.5 / 9 x  4.28 indicates that the 11-foot ladder's base is approximately 4.28 feet away from the wall's base, rounded to the nearest hundredth.

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it would be  2 people

Answer:The square root is √23 = 4.795.

Step-by-step explanation:

Answer:

3 times

Step-by-step explanation:

6-4.05= 1.95

1.95/.65=3

Answer:

3 times

Step-by-step explanation:

1) 4.05 + 0.65= 4.70

2) 4.70 + 0.65= 5.35

3) 5.35 + 0.65= 6

(a) To find the probability of selecting a blue ball, we need to consider the probabilities from both urns.

The probability of selecting the first urn is 1/2 since there are two urns and one is chosen at random. The probability of selecting a blue ball from the first urn is 6/20 (6 blue balls out of a total of 20 balls).

The probability of selecting the second urn is also 1/2. The probability of selecting a blue ball from the second urn is 12/19 (12 blue balls out of a total of 19 balls).

To find the overall probability of selecting a blue ball, we can use the law of total probability:

P(blue) = P(First Urn) * P(blue | First Urn) + P(Second Urn) * P(blue | Second Urn)

P(blue) = (1/2) * (6/20) + (1/2) * (12/19)

Simplifying the expression, we get:

P(blue) = 0.25 + 0.3158

P(blue) = 0.5658

To convert to a percentage, we multiply by 100:

P(blue) = 56.58%

(b) Given that the chosen ball is blue, we want to find the probability that it came from the first urn.

Using Bayes' theorem, we can calculate:

P(First Urn | blue) = (P(blue | First Urn) * P(First Urn)) / P(blue)

P(First Urn | blue) = (6/20 * 1/2) / 0.5658

P(First Urn | blue) = 0.15 / 0.5658

P(First Urn | blue) ≈ 0.2654

To convert to a percentage, we multiply by 100:

P(First Urn | blue) ≈ 26.54%

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Sheri should invest $2000 in mutual fund and $13,200 in bond.

Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -

1%×x + 4%×(15,200 - x) = 548

x/100 + 60,800/100 - 4x/100 = 548

60,800 - 3x = 54800

3x = 60800 - 54800

3x = 6000

x = 6000 ÷ 3

x = 2000

Amount to be invested in mutual fund = $2000

Amount to be invested in bond = 15,200 - 2000

Amount to be invested in bond = $13,200

Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.

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Answer:

Step-by-step explanation:

Given

Natoy's rectangular swimming pool has the length of 3m more than thrice its

width.

Width=w

Length =3w+3

So

Area of the rectangular swimming pool=length×width

216=(3w+3)×w

216=3w^2+3w

3w^2+3w-216=0

3(w^2+w-72)=0

W^2+w-72=0

W^2+(9-8)w-72=0

W^2+9w-8w-72=0

W(w+9)-8(w+9)=0

(W+9)(w-8)=0

Sotwo value of w are 8,-9

We take positive value for rectangular swimming so we take w=8m

Width=8m

Length=3×8+3

= 24+3

=27m

Answer:

Step-by-step explanation:

17

The player with a 39-inch vertical leap has a hang time of approximately 0.9014 seconds.

To determine the hang time of a player with a 39-inch vertical leap, we'll use the hang-time function, which relates vertical leap to hang time.

Step 1: Convert inches to feet by dividing the vertical leap by 12 (since there are 12 inches in a foot).
39 inches ÷ 12 = 3.25 feet

Step 2: Use the hang-time function formula, which is: Hang Time = √(8 × Vertical Leap ÷ Gravity), where gravity is approximately 32 feet per second².
Hang Time = √(8 × 3.25 ÷ 32)

Step 3: Calculate the hang time.
Hang Time = √(26 ÷ 32) ≈ √(0.8125) ≈ 0.9014 seconds

The player with a 39-inch vertical leap has a hang time of approximately 0.9014 seconds.

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