Ross bought a TV for $1,200. She sold it with 25% loss. How much did she lose?

Answer:

Step-by-step explanation:

In a survey of adults who set themselves some fitness targets, 5% achieved all of them, and 15% achieved some of them. Another fitness survey questions 400 adults. There are 80 people who expect to achieve all of their targets.

Percentage:

In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Given that:

5% achieve all of them

15% achieve some of them

Total percentage = 5% + 15%

                              = 20%

there are 400 adults = 400× 20%

                                    = 80% target

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Answer:

(20/4)

Step-by-step explanation:

The term "quotient" implies division, which is present in the (20/4) part of the expression.

Answer:

45 minutes

Step-by-step explanation:

20 miles in 150 minutes

Runner runes 6 miles.

150/20 = 7.5 minutes per mile

6 x 7.5 = 45 minutes

Answer:

Yes they both are equal

We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:

1. Start with the initial B&B tree, where the root node represents the original problem.

2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for

\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)

3. At each node, perform the following steps:

  - Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.

  - If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.

  - If the LP solution is integer, update the current best solution if the objective value is higher.

  - If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.

4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.

5. The node with the highest objective value among the integer feasible solutions is the optimal solution.

6. Optionally, backtrace through the tree to retrieve the optimal solution variables.

Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.

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Answer:

x = 71/5  (as an improper fraction)

x = 14 1/5 (as a proper fraction

x = 14.2 (as a decimal)

Step-by-step explanation:

It's a rectangle so the diagonals are equal

7x - 9 = 2x + 62

Subtract 2x from both sides

5x - 9 = 62

Add 9 to both sides

5x = 71

Divide both sides by 5

x = 71/5  (as an improper fraction)

x = 14 1/5 (as a proper fraction

x = 14.2 (as a decimal)

Answer:

x= 14.2

Step-by-step explanation:

BD and and AC are equal so

7x-9 = 2x+62

isolate the variable means x = 14.2

first time I had to take out pencil and paper so I hope it's right

Answer:

12 carrots

Step-by-step explanation:

If there is 3 times as much cabbages as there is carrots, and there is 36 cabbages then you would do 36/3 because of the 3 times as much.  The answer would be 12 carrots.

36/3=12

The equation that models the situation with d, the price in dollars, of one dozen bagels is given by option C. `2d = 17.98`.

Emma spent $17.98 on 2 dozen bagels. The equation that models the situation with d, the price in dollars, of one dozen bagels is given by option C. `2d = 17.98`.What are dozen bagels?A dozen bagels are 12 bagels. If Emma bought 2 dozen bagels, it means she bought 24 bagels. If you want to know the cost of one bagel, you can divide the total cost by the number of bagels she bought. So the cost of one bagel can be given by the equation;`Total cost of bagels / number of bagels bought = cost per bagel`Let us now use the given options to see which one of them represents the above equation.A. 17.98d = 2Here, we have the total cost multiplied by the cost per bagel which doesn't make sense.B. 17.98 + d = 2We can see that this equation does not have any terms to represent the number of bagels bought, it only has the total cost and the cost per dozen bagels.D. 2 + d = 17.98We can see that this equation does not have any terms to represent the total cost or the number of bagels bought. Hence it cannot represent the given situation.C. 2d = 17.98Here, we have the number of bagels multiplied by the cost per bagel to give us the total cost, which is what we need. Therefore the equation that models the situation with d, the price in dollars, of one dozen bagels is given by option C. `2d = 17.98`.

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Answer: 5/2

Step-by-step explanation:

You can use y2 - y1 / x2 - x1 to find the slope. 6 - 1/ 2 - 0 = 5/2

Answer:

g = ( x - 2 ) / 3

Step-by-step explanation:

x = 3g + 2

subtract 2 from each side

x - 2 = 3g + 2 - 2

simplify

x - 2 = 3g

Divide each side by 3

(x - 2)/3 = 3g/3

Simplify

( x - 2 ) / 3 = g

Flip equation

g = ( x - 2 ) / 3

And we are done!

Answer:

-13.5v-21.6

Step-by-step explanation:

Distribute Rule: a(b+c) = ab+ac

2.7(-5v-8)

= 2.7*(-5v) + 2.7(-8)

= -13.5v-21.6

Answer:

True; this \(x\) would indeed be a factor of \(z\).

Step-by-step explanation:

"\(x\) is a factor of \(y\)" means that there is a whole number \(p\) such that \(x\, p = y\).

Likewise, \(y\) is a factor of \(z\) if and only if there is a whole number \(q\) such that \(y\, q = z\).

This \(x\) would be a factor of \(z\) if there is some whole number \(r\) such that \(x\, r = z\).

The first equality \(x\, p = y\) implies that \(y\) may be substituted with \(x\, p\).

Substitute the \(y\) in the second equality \(y\, q = z\) with \((x\, p)\) to obtain:

\((x\, p)\, q = z\).

Rearrange to obtain:

\(x\, (p\, q) = z\).

The product of two whole numbers is still a whole number. Since \(p\) and \(q\) are both whole numbers, \(p\, q\) would also be a whole number.

Thus, if \(r = p\, q\), then \(x\, r = x\, (p\, q) = z\), while \(r\) would be a whole number.

Therefore, this \(x\) would indeed be a factor of \(z\).

Answer:

11.1 feet

Step-by-step explanation:

person = B  cat = C

                                          C

                                      /    |

                   /                       |     x

B /_48]________ ______|

              |____10ft____|

since we know the adjacent side but want the opposite side, we can use tan(angle)=opp/adj to solve.  (make sure to be in degrees lol)

tangent ( 48) = x/10

10 * tan(48) = x

11.1 = x

The cat is 11.1 feet high.

Answer:

B

Step-by-step explanation:

The total distance Tori will cover into outer space is almost equal to 3 × 10⁸.

What information do we have?

The equation describes distance = (3.21 × 10³)(1.13 × 10⁵)

Total distance Tori will cover into outer space = (3.21 × 10³)(1.13 × 10⁵)

Total distance Tori will cover into outer space = 3.6273 × 10³ × 10⁵

Total distance Tori will cover into outer space = 3.6273 × 10⁸

Total distance Tori will cover into outer space = 3 × 10⁸ (Almost equal).

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Answer:

C. the amount the tomato plant grows each week

Step-by-step explanation:

its height is already 23 and it grows by 2.4 each week (x)

Have a nice day! :)

Total 20 number cases should the manager order each month to server an average of 240 vashes of flowers.

Manager of a flower shop determines that an average of 240 vases of flowers is sold each month.

3 cases contain 36 vases.

so 1 case will contain 36/3 vases.

1 case will contain  = 12 vases.

How many cases of vases should the manager order each month.

Given is that 240 vashes of flowers each month is sold.

according to 12 vashes per case we need 20  cases to cover 240 vashes of flowers each month.

12* 20  = 240.

We need 20 cases here.

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The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Below is the answer

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Answer:

Step-by-step explana8tion:

80$ with that 6%

Answer:

(2x+1)(x-3)

x=-1/2,x=3

Step-by-step explanation:

Depends what method you use but I would do...

-3*2=-6

-6x+1x

-6x/2=x-3 and 1x/2= 2x+1

(2x+1)(x-3)

Now solve by equalling it to 0

2x+1=0

2x/2=-1/2

x=-1/2

x-3=0

x=3

Answer:

tanX = \(\frac{4}{3}\)

Step-by-step explanation:

tanX = \(\frac{opposite}{adjacent}\) = \(\frac{YZ}{XY}\) = \(\frac{32}{24}\) = \(\frac{4}{3}\) in simplest form

Answer:

139°

Step-by-step explanation:

According to the question

The equation is

4r+17+4r+115=180

8r+132=180

8r=48

r=6

So BYF =

4.6+115

24+115

139°

Answer:

139

Step-by-step explanation:

To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

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There are approximately 2.97 billion droplets per acre being sprayed.

To calculate the number of droplets per acre, we need to first convert the diameter of the droplets from microns to inches (since we are using acres as our unit of area). There are 25,400 microns in one inch, so the diameter of the droplets in inches is 250/25,400 = 0.0098 inches.

Next, we need to calculate the area of one droplet. The formula for the area of a circle is A = πr², so the area of one droplet is A = π(0.0049)² = 0.0000754 square inches.

Finally, we can calculate the number of droplets per acre by dividing the total area of one acre (43,560 square feet) by the area of one droplet: 43,560 / 0.0000754 = 2.97 billion droplets per acre.

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Answer:

As x decreases in value.f(x) decreases in value.......