Evaluate.
{[(12 - 36) ÷ (-12)]^2 - 20} ÷ (-4)

A. 1
B. 2
C. 4

Answer:

\(\frac{5}{12}\)

Step-by-step explanation:

Step 1: Set up the problem

Step 2: Solve

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

5/16

Step-by-step explanation:

Answer:

3/11

Step-by-step explanation:

3/11 equals 0.272727273 which is a repeating decimal.

Answer:

3/11 is C

Step-by-step explanation:

The slope of the line is undefined/ tends to infinity with the equation as

x = 6

In order to determine the slope of the line we need the values of the coordinates (x1, y1) and ( x2, y2)

Here, (x1, y1) is (6, -5) and (x2, y2) is (6, -4)

To calculate the slope of the line with two coordinates we apply the given formula,

Slope of the line = (y2 - y1)/(x2 - x1)

Slope of the line = (-4 - (-5))/(6 - 6) = 1/0

which gives the slope as undefined but from the given coordinates we can determine that the x coordinate is a constant here so the equation of the line becomes

x = 6

where the slope tends to infinity.

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Im pretty sure the answer is A but if not then it is C

This is bcuz B doesn’t make sense because the graph doesn’t say anything close to 100 rides and D doesn’t make sense either.

Hope this helped.

Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.

Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.

Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.

Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.

To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:

Cost per mile = $3.75 / 235 miles per gallon

Cost per mile = $0.016 per mile

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7.54 and 0.46 are the solutions to the given quadratic equations

Given the quadratic equation below:

x^2-18x+8=0

We need to determine the solutions to the given quadratic expression. Using the general formula below:

x = -b±√b²-4ac/2a

From the equation

a = 1

b = -18

c = 8

Substitute

x = 18±√18²-4(1)(8)/2(1)
x= 18±√324-32/2

x =18± 17.08/2

x = 35.08/2 and 0.92/2

x = 17.54 and 0.46

Hence the two solutions to the given quadratic equation are 17.54 and 0.46

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Given the polar curve described above, the value of k which is the instantaneous rate of change of r with respect to θ at θ = π equal to 15 is: 1.451 (Option B).

A polar curve is a shape that is designed using the polar coordinate system.

They are defined by points that stand at a variable distance from the pole, subject to the angle measured off the positive section of the x-axis.

Hence, given the polar curve described above, the value of k which is the instantaneous rate of change of r with respect to θ at θ = π equal to 15 is: (Option B) - 1.451

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Answer:

3) same slope

Step-by-step explanation:

If the lines are parallel then they have to have the same slope always.

Answer:

Step-by-step explanation:

Same tape length measures 63 units on top and 7 times m on bottom.

Make an equation and solve for m:

Count the boxes noted with m

Now

Boxes are equal

\(\\ \sf\longmapsto 7m=63\)

\(\\ \sf\longmapsto m=63/7\)

\(\\ \sf\longmapsto m=9\)

Answer:

\( \frac{4 + (x + 1)}{x + 1} = \frac{16}{12} \\ \\ \frac{5 + x}{x + 1} = \frac{16}{12} \\ \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11\)

Answer:

x = 11 cm

Step-by-step explanation:

Segments DE and BC are parallel (that's what the arrows tell you), so there are two similar triangles formed.

\(\triangle{ADE} \sim \triangle{ABC}\)

Corresponding sides are in proportion, so

\(\frac{AD}{AB}=\frac{12}{16}\)

The length of AB is (x + 1) + 4 = x + 5, and 12/16 simplifies to 3/4, so

\(\frac{x+1}{x+5}=\frac{3}{4}\)

"Cross multiply" to get

\(4(x+1)=3(x+5)\\4x+4=3x+15\\4x=3x+11\\x=11\)

The simplified expression is: \(11x^2 - 1.7x - 3.5\)

To simplify the expression \((7x^2 - 3x + 2.5) + (4x^2 + 1.3x - 6),\) we can combine like terms by adding the coefficients of the same degree terms.

Let's break it down:

\((7x^2 - 3x + 2.5) + (4x^2 + 1.3x - 6)\)

Combine the x^2 terms:

\(7x^2 + 4x^2 = 11x^2\)

Combine the x terms:

-3x + 1.3x = -1.7x

Combine the constant terms:

2.5 - 6 = -3.5

Putting it all together, the simplified expression is:

\(11x^2 - 1.7x - 3.5\)

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Step-by-step explanation:

7 + x = 2x, so x = 7

Answer:

fourth option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 4x ( divide both sides by 4 )

\(\frac{y}{4}\) = x

Change y back into terms of x with x as the inverse function, thus

h(x) = \(\frac{x}{4}\) = \(\frac{1}{4}\) x

Answer:

h(x)=1/4x

Step-by-step explanation:

To find the inverse of a function, switch the "x" and the "y". The f(x) can be considered as "y".

\(f(x)=4x\)

\(y=4x\)

\(x=4y\)

We want to isolate y. 4 and y are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 4.

\(\frac{x}{4} =\frac{4y}{4}\)

\(\frac{x}{4} =y\)

x/4 can be rewritten as 1/4x.

\(y=\frac{1}{4} x\)

\(h(x)=\frac{1}{4} x\)

The inverse of the function f(x)=4x is h(x)=1/4x

Answer:

See below.

Step-by-step explanation:

a) y = 2x + 3 and y = -2x + 11

 One solution.  They are straight lines with different slopes, so they will intersect at some point.  

b) y = x + 2 and -2x + 2y = 4

  -2x + 2y = 4 can be rearranged to 2y = 2x +4 and then y = x + 4

    Both lines have the same slope, 1.  They are parallel and will never meet.  No solutions.

c) y = x - 3 and y = x + 6

 This has the same answer as c.  Parallel lines (both have slopes of 1.).  They will never meet:  no solutions.

d) y = 7 and y =3x-5

One solution.  Straight lines with different slopes (3 and 0) so they will cross at one point.  [At (4,7)]

e) y = -4x and y = -4x - 1

Same slopes.  There are no solutions.

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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a. The differential equation for the situation of a coasting boat is dv/dt = k*v^2.

b. The differential equation for the situation of a fixed population with virus infection is dN/dt = k*(P - N).

a. The rate of change of velocity (dv/dt) of a coasting boat is directly proportional to the square of its velocity (v^2). This can be represented by the differential equation dv/dt = k*v^2, where k is a constant of proportionality. This equation implies that as the velocity of the boat increases, the rate at which the velocity changes also increases, resulting in a nonlinear relationship.

b. In the scenario of a city with a fixed population P, the rate of change of the number of infected people (dN/dt) is proportional to the number of individuals who have not yet been infected (P - N). This can be expressed as the differential equation dN/dt = k*(P - N), where N represents the number of infected people and k is a constant of proportionality. This equation reflects the idea that as the number of infected individuals increases, the rate of new infections will decrease, reaching an equilibrium when N equals P. The equation assumes that the rate of transmission depends on the size of the susceptible population remaining, leading to a decreasing rate of infection over time.

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The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given the trigonometry identity;

d=94 secθ.

If the object is sighted at an angle of  25°, then;

d=94 sec25

d = 94 × 1/cos25

d = 94 × 1.1033

d = 103.71feet

If the object is sighted at an angle of  55°, then;

d=94 sec55

d = 94 × 1/cos55

d = 94 × 1.7434

d = 163.88feet

Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

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Answer: x = 10

Step-by-step explanation:ln20+ln5=2lnx

ln(20x5)=lnx^2

ln100=1nx^2

100=x^2

square root

x=10

The true solution is x = 10 of the expression ln 20 + ln 5 = 2 ln x which is correct answer would be option (B).

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

According to the problem, we will use some of the basic logarithmic properties,

Given expression,

⇒ ln 20 + ln 5 = 2 ln x

⇒ ln(20×5) = lnx²

⇒ ln100 = lnx²

Take anti logarithms on both sides,

⇒ 100 = x²

Taking the square root,

⇒ x = 10

Hence, the true solution is x = 10.

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Answer: x = - 7/12

Step-by-step explanation:

-3x + 2 - 5x - 7 = 4x + 2

=> -8x - 5 = 4x + 2

=> -12x = 7

=> x = - 7/12

The population that is most dense is the one for  5000 individuals per 200 square meters

Given the following information:

100 individuals per 100m^2

5000 individuals per200m^2

100,000 individuals per 20,000m^2

15,000 individuals per 10,000m^2

We find the population that is most dense using the formula:

Population density=(No. of people/Land area)

For 100 individuals per 100m^2,

Population density=100/100=1

For 5000 individuals per200m^2

Population density=5000/200=25

For 100,000 individuals per 20,000m^2

Population density=100,000/20,000=5

For 15,000 individuals per 10,000m^2

Population density=15,000/10,000=1.5

Hence, highest population density is 25 for 5000 individuals per200m^2  

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Answer:

p = 8000 + 2(6000)

20000

Step-by-step explanation:

Given that:

Profit in 1988 = 6000

Profit in 2003 = 8000 more Than double the profit made in 1998

Hence profit in 2003 (p) can be expressed as :

p = 8000 + 2(6000)

Hence profit in 2003

p = 8000 + 12000

p = 20,000

• We are required to find Z so that the area is to the right, this means that the area is to be positive .

• 88 % can be converted to 88/100 = 0.88

• z = 1-0.88 = 0.12

The value tha corresponds with 0.12 = 0.04775

= 0.048

using the cumulative standard normal z score of 0.12 = 0.5478

Answer: $3.96 per quart

Step-by-step explanation:

2 gallons = 8 quarts

Price per quart = 31.68/8 = $3.96

Therefore, price per quart = $3.96

Answer:

$3.36 per gallon

Step-by-step explanation:

So 2 gallons is equal to 8 quarts, so then you do $31.68 divided by 8 which gives you the answer of $3.36 per gallon

Answer:

-1 5/8

Step-by-step explanation:

Opposite of 1 5/8 is -1 5/8

Answer:

(2u+8)(2u+10) inches^2=4u^2+36u+80 inches^2

Step-by-step explanation:

I don't know what the options are. But I'll try to help you anyway. Is that variable for the width of the frame... u? We'll just use u.

So the area of a rectangle is found using length* width. To find the combined area of the mat and the photo, we need the combined length and the combined width.

combined length=u+8+u

(Think of it from the top to the bottom: the top strip has a length of u inches, 8 is given, and the bottom strip is also u inches long.) You can simplify it to get 2u+8 inches.

combined width=u+10+u=2u+10 inches

To find the area, you need to multiply these dimensions.

(2u+8)(2u+10) inches^2

I think this would be your answer for Part B, because it's factored.

I think for Part A, you need to multiply it all out.

=2u(2u+10) + 8(2u+10)

=4u^2+20u + 16u+80

=4u^2+36u+80 inches^2

Hope I could help you!

Answer: 52.64

Step-by-step explanation: add 18.9 and 33.74