Convert the following measurements.
a. 2 cubic yards to cubic feet
b. 135 cubic feet to cubic yards
c. 6,912 cubic feet to cubic inches
d. 279,936 cubic inches to cubic feet

Solve the following addition problem. Remember to carry as necessary.

7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.

Solve the following subtraction problem. Remember to borrow as necessary.

9 cu. yd. 113 cu. in. – 4 cu. ft. 129 cu. in.

Solve the following multiplication problem.

11 cu. yd. 17 cu. in. × 135

What’s the capacity of a 3 cubic foot carton in cubic inches?

The Great Pyramid was built in Egypt more than 4,000 years ago. It was built by King Khufu, or Cheops, who intended to use it as a tomb. The pyramid contains about 2,300,000 blocks of stone, each weighing 2 1⁄2 tons. Can you calculate the approximate total weight of the Great Pyramid, in pounds?

Convert the following liquid measures.
a. 5 gallons to pints
b. 128 tablespoons to fluid ounces
c. 93 pints to quarts
d. 13 quarts to cups
e. 69 teaspoons to tablespoons
f. 112 cups to gallons
g. 18 fluid ounces to teaspoons
h. 3 gallons to fluid ounces

A local dairy farmer collects 490 gallons of milk a day from his cows. He keeps 1⁄35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day? (There are 100 cents in a dollar.)

A swimming pool has a capacity of 1,386 cubic feet. One gallon of water will fill 231 cubic inches of space. How many gallons of water will it take to fill the entire pool? (Hint: Convert the capacity of the pool to cubic inches first.)

The instructions on a bottle of laundry detergent tell you to add two capfuls of detergent to each gallon of water. One capful of detergent is equal to about one tablespoon. If your washing machine holds 11 gallons of water, how many tablespoons of detergent will you need to add? How many fluid ounces of detergent?

Convert the following dry measurements.
a. 11 bushels to quarts
b. 3 pecks to pints
c. 97 quarts to bushels
d. 1,120 quarts to pecks

Twelve apple pies can be made from one bushel of apples. How many apple pies can be made from one peck of apples?

Mr. Osaka sprinkles 1.694 pints of dry, powdered plant food on his garden three times a year. In quarts, what’s the total amount of plant food he uses in one year?

Answer:

Net assest value of one share is $8 .

Option (c) is correct .

Step-by-step explanation:

As given

A mutual fund has total assets of 2.4 million dollars and 300,000 shares.

As 1 million = 1000000

Total assest value = $2.4 × 1000000

Thus

[tex]Net\ asset\ value\ of\ one\ share = \frac{2.4\times 1000000}{300000}[/tex]

Put all the values in the above

[tex]Net\ asset\ value\ of\ one\ share = \frac{24\times 1000000}{300000\times 10}[/tex]

[tex]Net\ asset\ value\ of\ one\ share = \frac{24}{3}[/tex]

Net asset value of one share = $8 .

Therefore net assest value of one share is $8 .

Option (c) is correct .

Let

[tex]A(0,0)\\B(5,1)[/tex]

we know that

the formula to calculate the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

Substitute the values in the formula

[tex]m=\frac{(1-0)}{(5-0)}[/tex]

[tex]m=\frac{1}{5}[/tex]

therefore

the answer is the option b

the slope is equal to  [tex]\frac{1}{5}[/tex]

Final answer:

Solutions to a system of linear equations are represented graphically as the intersections of lines on a graph and can be unique, infinitely many, or none. Graphical representations are essential in various applications, like economic models, and software like R facilitates solving these systems.

Explanation:

Possible solutions to a system of linear equations can be one of three types: a unique solution, infinitely many solutions, or no solution. Graphically, these solutions are represented by the intersections of lines on a graph. In the case of a unique solution, the lines intersect at exactly one point.

For example, consider two linear equations of the form y = mx + b. Graphically, each equation is represented by a straight line. Where these lines cross is the solution to the system. If both equations produce the same line, they have infinitely many solutions since every point on the line satisfies both equations.

1. Given gross salary is = $768

Federal tax withholding = $68

Social security = 6.2% or 0.062*765 = $47.43

Medicare tax = 1.45% or 0.0145*765 = $11.09

State tax = 22% or 0.22*68 = $14.96

Now net salary = gross salary - tax deductions

[tex]765-(68+47.43+11.09+14.96)[/tex] = $623.52 (option D)

2. [tex]\frac{33500-28600}{28600}*100[/tex] = 17.13% (option D)

3. Option B.II and III

4. B.Checks are deposited in ATM's, so some retailers will not accept checks from a bank without ATM service.

5. B.Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.

6. D.Make purchases or get cash now, and pay back the bank in monthly payments.

7. A point of sale transaction occurs when an ATM withdrawal is made- yes this is right.

8. The answer is Thursday.

9. No picture given.

Without additional data, such as the percentage of those surveyed who chose football, it's impossible to determine the total number of people surveyed from the information provided. The data given only specifies that 210 individuals selected football as their favored sport to watch.

Based on the provided question, there's not enough information to determine the total number of people who were surveyed. The information given only states that 210 people picked football as their favorite sport to watch, but it does not provide the overall total number of people surveyed.

To calculate the total number of respondents, you need to know the ratio or percentage of people who chose football. For example, if you knew that football was chosen by 70% of those surveyed, you could use that information to calculate the total number of people. In this case, the equation would be 210 = 0.70 * x. Solving for x (the total number of people surveyed) would give you x = 210 / 0.70, which comes out to approximately 300 people.

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Mike need to deposit approximately $22,815 in his money market account now, which has a 1.825% interest rate compounded daily, to have $25,000 in 4 years.

To find out how much Mike should invest now, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:  
 A = the amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times interest applied per time period
t = time the money is invested for in years

In this case, Mike wants to have A = $25,000 in t = 4 years. The interest rate r is 1.825% or 1.825/100 = .01825 in decimal form, and since it is compounded daily, n = 365. So, we can plug into the formula and solve for P:
$25,000 = P(1 + .01825/365)^(365*4)

By performing the calculation, we find that P is approximately $22,815. Mike will therefore need to invest this amount in his money market account now to achieve his goal.

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Manuel's hourly rate of pay is calculated by dividing his total weekly earnings by the total hours he worked. He worked a total of 30 hours and earned $337.50, resulting in an hourly rate of $11.25.

The question asks us to calculate Manuel's hourly rate of pay based on the total amount he earned in a week and the number of hours he worked. To find the hourly rate, we need to divide the total earnings by the total number of hours worked.

Calculate the total number of hours worked in a week: 5 days a week times 6 hours each day equals 30 hours.

Divide Manuel's total earnings for the week by the total hours worked:
$337.50 divided by 30 hours equals an hourly rate of $11.25.

Answer:

4 + 0 = 4/2 = 2 would be the answer.

Step-by-step explanation:

Answer:

  1..25a

Step-by-step explanation:

a + 25%·a = a(1 + 0.25) = 1.25a

_____

Comment on percentages

The symbol "%" is a shorthand way to write "/100", so 25% = 25/100 = 0.25.

Of course, 100/100 = 100% = 1.

Adding 25% of something to 100% of it gives 125% of it, the original amount multiplied by 125/100 = 1.25.

Answer:

1.25a

Step-by-step explanation:

a + 25%·a = a(1 + 0.25) = 1.25a

_____

Comment on percentages

The symbol "%" is a shorthand way to write "/100", so 25% = 25/100 = 0.25.

Of course, 100/100 = 100% = 1.

Adding 25% of something to 100% of it gives 125% of it, the original amount multiplied by 125/100 = 1.25.

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Answer:

[tex]bh=50[/tex] for b=5 and h=10.

Step-by-step explanation:

Given : The value of b=5 and h=10.

To find : Evaluate bh ?

Solution :

As we have given bh i.e. b and h are multiplied together,

So, [tex]bh=b\times h[/tex]

Substitute, b=5 and h=10

[tex]bh=5\times 10[/tex]

[tex]bh=50[/tex]

Therefore, [tex]bh=50[/tex] for b=5 and h=10.

Answer:

True.

Step-by-step explanation:

We use law of sine to solve the triangle when two sides and angle (SSA) is given.There are different cases possible .

1)  If a < b sin A.

In this case  No possible triangles or we can say there will be zero solutions.

2) If a > b sin A.

In this case there are   Two triangles possible.In such cases at least one of the solutions will be an obtuse triangle.

3) If a = b sin A.

We have   Unique solution or one solution.This is true for a right triangle.

Hence the given statement  SSA triangle problems may have zero, one, or two solutions is True.

Answer: true

Step-by-step explanation:

Ap3x

Answer:

The correct answer is 49.1 minutes to 59.3 minutes

Step-by-step explanation:

The 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day is [49.091, 59.308].

A confidence interval (CI) is a range of estimates for an unknown parameter.

The formula for confidence interval is mean ± (standard normal variate at α level of significance)*(standard deviation)/ (√sample size)

CI = 54.2 ± 2.58 * 14/√50

CI = 54.2 ± 5.1081

CI = [49.091, 59.308]

Learn more about confidence interval here:

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The solution to the problem involves setting up and solving a system of equations derived from the distance function in 3D. The minimum point of the distance function corresponds to the point in the plane that's closest to the origin.

To find the coordinates of the point (x, y, z) on the plane z = 3x + 4y + 4 which is closest to the origin, we need to find the minimum distance from origin (0,0,0) to any point on the plane. The distance equation is given by √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]. This is simply Euclidean distance in 3D.

In this case, we can define the distance function d = √(x² + y²+ (3x + 4y + 4)²). To find the minimum distance, we take the derivative of this distance function with respect to both x and y, set them to 0, and solve the resulting equations. The solutions to these equations yield x and y. We substitute x and y into z = 3x + 4y + 4 to get z.

Finally, solving these equations we obtain the coordinates of the point (x, y, z) on the plane that is closest to the origin.

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Answer:

  (-6/13, -8/13, 2/13)

Step-by-step explanation:

You want the point on the plane z = 3x +4y +4 that is closest to the origin.

When the plane equation is written in standard form, the variable coefficients comprise a vector that is normal to the plane. The line normal to the plane and passing through the origin can be written in terms of this vector. Solving for the variable in that equation lets us find the point on the plane where the line intersects.

The standard form equation for the plane is ...

  3x +4y -z = -4 . . . . . . . subtract 4+z from the given equation

Then the normal to the plane is ...

  N = (3, 4, -1)

and the vector equation of the line through the origin is ...

  L = (0, 0, 0) +tN = (3t, 4t, -t)

The value of t that makes a point on the line satisfy the plane equation is ...

  3(3t) +4(4t) -(-t) = -4

  26t = -4

  t = -4/26 = -2/13

Then the point tN is ...

  (-2/13)(3, 4, -1) = (-6/13, -8/13, 2/13)

The point on the plane closest to the origin is (-6/13, -8/13, 2/13).

Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, BC. Using the definition of reflection, reflect BC over l. By the definition of reflection, C is the image of itself and A is the image of B. Since reflections preserve length, AC = BC.

Answer:

60 degrees, 30 degrees

Explanation:

Sun angle = 90° - Zenith angle

On September 22, the sun passes over celestial equator. Equinox occurs.

Zenith Angle = Latitude of the place

Latitude of New Orleans, US = 29.95° ≈ 30°

Latitude of  Helsinki, Finland = 60.95° ≈ 60°

Thus, the Sun angle at noon at New Orleans would be 90° - 30° = 60°

and at Helsinki, Finland would be 90° - 60° = 30°

Answer: In the picture below.

Step-by-step explanation:

The provided mathematical expressions represent the process of calculating Zhi's remaining tickets after playing 'g' games at a fair. '18 - 3g' symbolizes subtracting three times the number of games played from the initial total (18) tickets. '3(6 – g)', on the other hand, corresponds to multiplying the number of tickets per game (3) by the subtraction of already played games from total possible games (6).

The subject of this question is based on mathematical expressions and variables. In the case of Zhi's expression, 18 represents the total number of tickets she bought. 'g' corresponds to the number of games played, and 3 is the number of tickets required for each game. Therefore, '18 – 3g' means subtracting three times the number of games played (3g) from the total quantity of tickets (18), which would give us the number of tickets left.

Diego's expression, however, expresses the same idea differently. '6 – g' symbolises the number of games Zhi could play before she runs out of tickets (since 18 tickets divided by 3 tickets per game equals 6 games). The '3' outside the bracket is again the number of tickets each game requires. As such, '3(6 – g)' expresses the multiplication of the tickets needed per game (3) by the difference between the total games possible and the games already played (6-g). This, therefore, provides the same result—Zhi's remaining tickets after g games.

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