Can someone help with this

A sweater originally priced at $80 was marked down by 25%. What was the sale price of the sweater?

crimeas [40]

The original price of the sweater is $80 which is 100% of the price.
If the price is reduced by 25%, then the new price is 75% of the original price since 100% - 25% = 75%.
Now we need to find 75% of $80.

To find a percent of a number, multiply the percent by the number.
To convert a percent into a decimal, divide the percent by 100 which is the same as moving the decimal point two places to the left.

Here's how to change 75% into a decimal.
75% = 75/100 = 0.75

Here's how you calculate 75% of $80.
75% of $80 =

= 75% * 80

= 0.75 * $80

= $60

Answer: The sale price is $60.

6 0

3 years ago

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An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at le

hoa [83]

Answer:

0.999

Step-by-step explanation:

At least 1 correct means, 1 correct, 2 correct, 3 correct ... until 10 correct. That would be a long process to calculate.

Instead we use the complement rule to calculate.

$P(x\geq1)=1-P(x$

So we need to find P(x<1). So this is getting 0 answers correct, or 10 incorrect.

In true false question, probablity of correct is 1/2 and incorrect is 1/2, hence,

Probability of 10 incorrect is (1/2)^10

Thus,

$P(x\geq1)=1-(\frac{1}{2})^{10}=0.999$

So the answer is 0.999 (rounded to nearest thousandth)

3 0

2 years ago

Solve the system of equations. 6x – 3y = 3 –2x + 6y = 14

Oxana [17]

Answer:

x=2; y=3

Step-by-step explanation:

You first add 3y to both sides. Divide both sides by 6. Then subsitute to get your answer.

6 0

3 years ago

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The sum of the first natural number and 0 is 1, the sum of the first two natural numbers and 0 is 3, the sum of the first three

Kitty [74]

The sum of the first n natural numbers and 0=
n*(n+1)/2

8 0

2 years ago

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A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the

Mashcka [7]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

$\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1$

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

$\displaystyle y - y_1 = m( x - x_1)$

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

$\displaystyle y - (4.8) = 0.1(x - 10)$

Simplify:

$\displaystyle y = 0.1(x-10) + 4.8$

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

The initial volume is when t = 0. Evaluate:

$\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8$

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

$60 = 0.1(t - 10) + 4.8$

Subtract:

$55.2 = 0.1(t - 10)$

Divide:

$552 = t - 10$

Add. Therefore:

$t = 562\text{ minutes}$

It will take 562 minutes for the tank to be completely filled.

8 0

2 years ago