What is the difference of the fractions? Use the number line to help find the answer.
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Answer:

Step-by-step explanation:

Given this information, we can determine the maximum number of units of each product (A, B, and C) that can be produced with the given quantity of resources (M1, M2, and M3). To do this, we can use the formula:

Maximum number of units of product = Minimum of (available quantity of resource / resource required per unit of product)

For example, to find the maximum number of units of product A that can be produced, we take the minimum of the following three values:

(71,000 units of M1 / 3 units of M1 per unit of A) = 23,666.67 units of A

(81,000 units of M2 / 2 units of M2 per unit of A) = 40,500 units of A

(92,000 units of M3 / 6 units of M3 per unit of A) = 15,333.33 units of A

So the maximum number of units of A that can be produced is 15,333.33 units.

Similarly, we can find the maximum number of units of B and C that can be produced:

(71,000 units of M1 / 3 units of M1 per unit of B) = 23,666.67 units of B

(81,000 units of M2 / 2 units of M2 per unit of B) = 40,500 units of B

(92,000 units of M3 / 4 units of M3 per unit of B) = 23,000 units of B

So the maximum number of units of B that can be produced is 23,000 units.

(71,000 units of M1 / 5 units of M1 per unit of C) = 14,200 units of C

(81,000 units of M2 / 7 units of M2 per unit of C) = 11,571.43 units of C

(92,000 units of M3 / 4 units of M3 per unit of C) = 23,000 units of C

So the maximum number of units of C that can be produced is 11,571.43 units.

It is important to note that these calculations are based on the assumption that all resources are used fully and no resources are left over.

The average speed for the given situation is 56 mph.

Given that, Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Now, distance = Speed × Time

= 60 × 3

= 180 miles

She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.

Now, Time = 30/40

= 0.75 hours

Total time =3+0.75=3.75 and total distance =180+30=210

Then average speed = 210/3.75

= 56 mph

Therefore, the average speed for the given situation is 56 mph.

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Answer:

B) f(x) ≥ 3x + 4

g of x is less than or equal to negative one half times x minus 5

Step-by-step explanation:

From the above graph,  

If point B is the solution of the system of inequalities, then point B must satisfies both inequalities  

We can see from the graph that

Point B is located above (≥) the boundary line for f(x) and is also below (≤) the boundary line for g(x).

So we can say,

Point b satisfies the inequalities

Therefore,  

The system is  

f(x) ≥ (3x+4)

g(x) ≤ (-1/2x -5)

Your Welcome

Answer:

45/49

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

9/14 * 10/7 = 90/98

divide the numerator and the denominator by 2.

90 * 2 = 45

98 * 2 = 49

45/49

Answer:

3xy

Step-by-step explanation:

Answer10:

Step-by-step explanation:

10

Answer:

8ft and 16ft

Step-by-step explanation:

you guess and check till you reach the answer

1+23         5+19

2+22        6+18

3+21         7+17

4+20        8+16

Given:

Radius of cone, r=5mm.

Slant height of the cone, l=18mm.

The Surface area of cone formula is,

Therefore, the surface area of the given cone is,

Therefore, the surface area of the given cone is,

Hence, the lateral surface area of the cone ,

The total surface area of the cone formula is,

Therefore,

Therefore, the correct option is D.

Answer:

8

Step-by-step explanation:

\( a = 1 - \sqrt{2} \)

\( (a - \dfrac{1}{a})^3 = \)

\( = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 \)

\( = (\dfrac{a^2 - 1}{a})^3 \)

\( = (\dfrac{(a + 1)(a - 1)}{a})^3 \)

\( = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 \)

\(= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3\)

\(= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3\)

\(= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3\)

\(= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3\)

\( = 2^3 \)

\( = 8 \)

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

Answer:

2ft

Step-by-step explanation:

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For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

The utilization of two or more additional numbers that compares is known as the ratio.

The ratio of red to blue in purple 1 and purple 2 will be 1:2 and 1:3, respectively. The table is given below.

Purple #1              Purple #2

Red: Blue             Red: Blue

  1      2                    1      3

 2      4                   2      6

 3      6                   3      9

For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

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All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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28/4 or 7

Well, I looked it up. Ain't gonna lie

Answer:

$4.09 for 4kg

Step-by-step explanation:

4.09/4 is less than 6.19/6

Answer:

4.09 for 4kg

it would be a better deal bc it will b 1.0225 for each and for 6 it would be 1.0316

Hope this helps

When solving a linear system of equations, you are looking for the points of intersection between the equations

From the question, we have the following parameters that can be used in our computation:

Solving a system of linear equations

Also, we have the following from the options

The general rile is that

Slope = rate of change

x and y intercepts = when y and x equals 0

points of intersection = solution to the system

Hence, you are looking for the points of intersection between the equations

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Question

When solving a linear system of equations, you are looking for which of the following?

Slope

y-intercept

x-intercept

Points of intersection

In the given exponent 5², 5 is the base and 2 is the exponent. Therefore, the correct answer is option B.

The given exponent is 5².

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

Example of exponents is x³, where x is the base and 3 is the exponent.

Here, in the exponent 5², 5 is the base and 2 is the exponent.

Therefore, the correct answer is option B.

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Answer: 26,400 feet

Step-by-step explanation:

If one mile is 5,280 feet, then we multiply the number of miles by that.

So, we would do 5,280 x 5, which equals 26,400 feet.

Answer:

e = 72, f = 36

Step-by-step explanation:

The triangle shown is an isosceles triangle, so angle e is 72 degrees. We know that the interior angles of a triangle adds up to 180 degrees so:

72 + 72 + f = 180
144 + f = 180
f = 36
Hope this helps :)

Combine like terms

Answer:

8x

Step-by-step explanation:

Given expression:

As we know, any negative integer being added by itself is 0. [-2y + 2y = 0]

Collect like terms and simplify;

Therefore, 8x is the simplified term.

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Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Part A: Grocery Store: unit price = $1.65 (Tomatoes)

Farmer's Market: unit price  = $1.75

Part B: Grocery Store offers a better deal because the unit price is less.

Unit price is defined as the price for one of something. For example, if 10 oranges cost $50, the unit price will be $50/10 = $5 i.e.  $5 for one orange.

PART A:

Let's choose tomatoes

Grocery Store

8 tomatoes for $13.20

Unit price = $13.20/8 = $1.65

10 tomatoes for $17.50

Unit price = $17.50/10 = $1.75

Part B:

The location that offers a better deal is Grocery Store. This is because the unit price is less.

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Check the picture below.

so the hexagonal prism is really just a hexagon with six 8x27 rectangles, let's simply get the area of all and sum them up.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} p=perimeter\\ a=apothem\\[-0.5em] \hrulefill\\ p=\stackrel{8\times 6}{48}\\ a=6.9 \end{cases}\implies A=\cfrac{1}{2}(6.9)(48)\implies A=165.6 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{six rectangles} }{(6)(8)(27)}~~ + ~~\stackrel{ \textit{hexgonal face} }{165.6}}\implies 1296+165.6\implies \text{\LARGE 1461.6}~in^2\)

The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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The expectation value is given by:

In this case we just have two options, each with probability 1/2, and the values of x are 2 and 9; then we have:

Therefore, the expectation is $6.5

The total monthly payment for both mortgages will be the sum of the monthly payments for each mortgage, which is $848.27 + $294.41 = $1,142.68.

Nicole's 80/20 mortgage means that she took out two mortgages to cover the cost of the house: one for 80% of the total cost and another for 20%. We can start by finding the amount of the first mortgage as follows:

80% of $205,000 = 0.8 x $205,000 = $164,000

So the amount of Nicole's first mortgage is $164,000.

To find out what her monthly payments will be, we need to calculate the monthly payments for each mortgage separately using the given interest rates and loan terms. For the first mortgage:

Loan amount: $164,000

Interest rate: 4.65% per year

Loan term: 30 years (or 360 months)

Using a mortgage calculator or formula, we can calculate the monthly payment for the first mortgage:

Monthly Payment = (Loan amount x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Loan term in months))

where Monthly interest rate = Annual interest rate / 12

Plugging in the values for the first mortgage, we get:

Monthly interest rate = 4.65% / 12 = 0.003875

Monthly Payment = (164000 x 0.003875) / (1 - (1 + 0.003875)^(-360)) = $848.27

So Nicole's monthly payment for the first mortgage is $848.27.

We can repeat the same calculation for the second mortgage, which has the following details:

Loan amount: $41,000 (20% of $205,000)

Interest rate: 7.525% per year

Loan term: 30 years (or 360 months)

Using the same formula, we get:

Monthly interest rate = 7.525% / 12 = 0.006271

Monthly Payment = (41000 x 0.006271) / (1 - (1 + 0.006271)^(-360)) = $294.41

So Nicole's monthly payment for the second mortgage is $294.41.

Note that the total monthly payment for both mortgages will be the sum of the monthly payments for each mortgage, which is $848.27 + $294.41 = $1,142.68.

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