How many way can 3 benches and 6 lamps be chosen from a shipment of 9 benches and 14 lamps?

Answer:

5 per comic book and 12 per computer game hope this helps.

Answer:

Step-by-step explanation:

8x + 3y = 76

x  + 3y = 41

8x + 3y = 76

-x - 3y = -41

7x = 35

x = $5 comic book

3y + 5 = 41

3y = 36

y = $12 computer game

Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43

Answer:

d=2P^2

Step-by-step explanation:

Answer:

sqrt  (x2 - x1)^2 + (y2 - y1)^2

a. To calculate the gross salary per pay period, we need to divide the yearly salary by the number of pay periods in a year:

Gross salary per pay period = Yearly salary / Number of pay periods per year

Since there are 26 pay periods in a year (bi-weekly paychecks), we have:

Gross salary per pay period = $67,000 / 26 = $2,576.92

Therefore, the DON's gross salary per pay period is $2,576.92.

b. To compute the net salary per pay period, we need to take into account federal and state taxes, Social Security, and Medicare deductions, as well as any other pre-tax or post-tax deductions, such as health insurance premiums or retirement contributions.

Assuming a standard tax withholding rate of 20%, Social Security and Medicare deductions of 7.65%, and health insurance premiums of $200 per pay period, we can calculate the net salary per pay period as follows:

Net salary per pay period = Gross salary per pay period - Taxes - Social Security and Medicare - Health insurance

Net salary per pay period = $2,576.92 - ($2,576.92 x 0.20) - ($2,576.92 x 0.0765) - $200

Net salary per pay period = $2,576.92 - $515.38 - $197.02 - $200

Net salary per pay period = $1,664.52

Therefore, the DON's net salary per pay period is $1,664.52.

Based on the calculation below, the amount Max can be expected to have when he retires is $758,518.94.

The amount he will be expected to have when he retires can be calculated using the formula for calculating the future value of an ordinary annuity as follows:

FV = D * (((1 + r)^n – 1) / r) ……………………………….. (1)

Where;

FV = Future value or the expected amount when he retires = ?

D = Monthly deposit = $200

r = monthly average inflation adjusted stock market return = 7% / 12 = 0.07 / 12 = 0.00583333333333333

n = number of months = (67 -  22) * 12 = 540

Substituting the values into equation (1), we have:

FV = $200 * (((1 + 0.00583333333333333)^540 – 1) / 0.00583333333333333)

FV = $758,518.94

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Answer: (the 2s I added are for square 2)

5sq(5g2s2 - 16qs + 9)

Step-by-step explanation:

Given:

A pancake recipe asks for two and two-thirds times as much milk as flour.

Required:

We need to find the quantity of flour that would then be needed If four and two-thirds cups of milk are used.

Explanation:

Let x be the amount of flour needed.

Final answer:

The amount of flour needed was 1 and 1/4 cups.

The graph of the compound inequalities with intersection points

(2.21, -0.63) is given below.

Please see the graph attached.

A compound inequality has two inequality statements joined either by the "or" or “and.”

We have,

6x+2y<12 or x-6y>6

We can graph each inequality.

And we also need to see the intersection between the inequalities.

Let,

6x + 2y = 12____(1)

x - 6y = 6_______(2)

From (1)

x = (12 - 2y ) / 6 put in (2)

(12 - 2y) / 6 - 6y = 6

2 - 1/3y - 6y = 6

2 - 6 = (1/3)y + 6y

-4 = 19y / 3

y = -12 / 19

y = - 0.63 put in (1)

6x + 2 x (-0.63) = 12

6x = 12 + 1.26

x = 13.26 / 6

x = 2.21

The point of intersection on the graph is (2.21, -0.63).

Thus the graph of the compound inequalities with intersection points (2.21, -0.63) is given below.

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Answer:

The village market

Step-by-step explanation:

Price per can at the village market

= 2.30÷5

= $0.46

Price per can at Best Food

=5.10÷10

= $0.51

Answer:

Village market

Step-by-step explanation:

Find the unit rate at village market and Best food and compare.

Village market:

Rate per can  = 2.30 ÷ 5

                      = $ 0.46

Best food:

Rate per can = 5.10 ÷ 10

                     = 0.51

0.46 < 0.51

Buying can from village market is best buy as that is less priced

The Class width is $18 and the complete table is shown below.

To determine the class width, we divide the upper limit of the sixth class ($108) by the number of classes (6):

Class width = $108 / 6 = $18

Based on this class width, we can determine the class limits, boundaries, and midpoints for a grouped quantitative data table:

Class Limits:

$1 - $19

$20 - $38

$39 - $57

$58 - $76

$77 - $95

$96 - $114

Upper limit exceeds maximum value, so it can be adjusted.

Class Boundaries:

$0.5 - $19.5

$19.5 - $38.5

$38.5 - $57.5

$57.5 - $76.5

$76.5 - $95.5

$95.5 - $114.5

Class Midpoints:

$10

$29

$48

$67

$86

$105

Here, the upper limit of the sixth class has been adjusted to $114.5 to account for the maximum value of $108 in the data set.

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The correct statement is,

⇒ The values below the X-axis are negative values of y

We have to given that;

To find true statement for the Cartesian coordinate system.

Now, We know that;

the values below the X-axis are negative values of y

And, the values above the X-axis are positive values of y.

Thus, The correct statement is,

⇒ The values below the X-axis are negative values of y

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Answer: (760 - 676. 40) × 100 ÷ 760 = 11%

Step-by-step explanation:

Answer:

11% decrease

Step-by-step explanation:

Concepts:

Solving:

Let's find the percent change by using the formula.

1. Formula for Percent Change

2. Plug in the values of NV and OV

3. Simplify

Therefore, our percent decrease is 11% decrease.

270° counterclockwise about the origin.  Check the picture below.

The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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9514 1404 393

Answer:

  dollars per hour

Step-by-step explanation:

If m is the slope, the units of m can be found by considering the units of x and y.

  y is in dollars

  x is in hours

Then from the point of view of units, we have ...

  dollars = m × hours

  m = dollars/hours

The slope in the equation is the rental charge in dollars per hour.

Answer: 2.68

Step-by-step explanation: 0.4 + 0.68 + 1.6

ANSWER

7, 9, 11

EXPLANATION

We want to find three consecutive odd numbers.

Let the smallest number be x.

Then, the next odd number is (x + 2).

The last odd number is (x + 4).

The sum of the largest odd number and twice the smallest number is 25:

(x + 4) + 2x = 25

=> x + 4 + 2x = 25

3x + 4 = 25

3x = 25 - 4

3x = 21

x = 21 / 3

x = 7

Therefore, the three consecutive numbers are:

7

(7 + 2) = 9

(7 + 4) = 11

They are 7, 9, 11

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

You are absolutely correct on all 3

#4 ==>  27y³ + 18y² factored is 9y²(3y - 2)

Step-by-step explanation:

The kilometer-to-mile ratio is 0.621371 km/mile when represented as a unit ratio.

A unit ratio is a ratio that compares two quantities with the same unit of measure. In this case, we want to express the kilometer-to-mile ratio as a unit ratio.

We know that 4.82803 km is equivalent to 3 miles. To express this as a unit ratio, we need to compare the number of kilometers to the number of miles. We can do this by dividing both sides of the equation by the same value, such as by 3 or by 4.82803.

Let's divide both sides of the equation by 4.82803 km:

(4.82803 km) / (4.82803 km) = (3 miles) / (4.82803 km)

Simplifying this equation, we get:

1 = 0.621371 km/mile

Therefore, the kilometer-to-mile ratio expressed as a unit ratio is 0.621371 km/mile. This means that for every 1 kilometer, there are 0.621371 miles.

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\(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

The given fraction is \(1\frac{3}{4}\).

\(1\frac{3}{4}\) feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because \(1\frac{3}{4}\) is the same as 1 + 3/4.

Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.

Therefore, the multiplication expression is 1 foot × \(1\frac{3}{4}\) = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.

Therefore, \(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

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Step-by-step explanation:

1ft=12in

1¾ft=x

x=12×7/4=21in

1¾ft=1¾×1 ft

Answer:

x = 13

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

sum the 6 exterior angles and equate to 360

3x + 6 + 41 + 6x - 5 + 4x + 7 + 62 + 7x - 11 = 360

20x + 100 = 360 ( subtract 100 from both sides )

20x = 260 ( divide both sides by 20 )

x = 13

The value of the given limits \(\lim_{x \to \infty} 1/x^2\) is 0,\(\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}\) is 4  ,\(\lim_{x \to \pi} sinx\\\) is 0 and \(\lim_{x \to \55} e\) is e.

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

Because the value of that function at that point doesn't define.

a)

\(\lim_{x \to \infty} 1/x^2\) by substitute limit 1/∞² = 0

b)

\(\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}\) here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)

Putting x = 2 will give the limit as 2 + 2 = 4.

c)

\(\lim_{x \to \pi} sinx\\\) herer put x to π so sinπ = 0.

c)

\(\lim_{x \to \55} e\) here no variable thus e will be the answer.

Hence "The value of \(\lim_{x \to \infty} 1/x^2\) is 0,\(\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}\) is 4  ,\(\lim_{x \to \pi} sinx\\\) is 0 and \(\lim_{x \to \55} e\) is e".

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Using substitution, the determination of equivalent expressions are is as follows:

Equivalent:

-6x+7-2x-3 and 4(-2x + 1)

10x-4(x-6)-3 and 11+ 2(x + 5) + 4x

Not Equivalent:

-3(x+1)-12 and -3(x-15).

Equivalent expressions are algebraic expressions that have the same value when the same value is used to substitute the variable.

To determine whether two expressions are equivalent, we can use 1 or 0:

1) -6x+7-2x-3 and 4(-2x + 1)

When x = 0

-6(0)+7-2(0)-3 = 7-3 = 4

When x = 0, 4(-2x + 1) becomes:

4(-2(0) + 1) = 4(1)  = 4

Thus, -6x+7-2x-3  and 4(-2x + 1) are equivalent expressions.

2) -3(x+1)-12 and -3(x-15)

When x = 0, -3(x+1)-12 becomes:

-3(0+1)-12 = -3-12 = -15

When x = 0, -3(x-15) becomes:

-3(0-15) = -3(-15)  = 45

Since -3(x+1)-12 and -3(x-15) give different results when x = 0, they are not equivalent expressions.

3) 10x-4(x-6)-3 and 11+ 2(x + 5) + 4x

When x = 0, 10x-4(x-6)-3 becomes:

10(0)-4(0-6)-3 = 24-3 = 21

When x = 0, 11+ 2(x + 5) + 4x becomes:

11+ 2(0 + 5) + 4(0) = 11+10  = 21

Since  10x-4(x-6)-3 and 11+ 2(x + 5) + 4x give the same result when x = 0, they are equivalent expressions.

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The distance between the fire and station B is 10.7miles

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The angle at A = 90- 35

= 55°

The angle at B = 90-49

= 41°

Angle at the fire = 180-(41+55)

= 180-96 = 84°

Using sine rule

sin84/13 = sin55/x

xsin84 = 13sin55

0.995x = 10.65

x = 10.65/0.995

x = 10.7 miles

Therefore the distance between the fire and station B is 10.7 miles.

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Answer:

The biggest number of groups that can be formed is 6, because six is the greatest common factor of 12 and 42. There will be 2 coaches in each group because 6 x 2 = 12 and 7 players in each group because 7 x 6 = 42.

Step-by-step explanation:

hope that helped

Answer:

Given,

length(l)=29ft

breadth(b)=18ft

now,

Area of rug=l×b

=29×18=522ft²

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162