All categories

3 years ago

A postcard and a pen cost 150 cents in total. The postcard costs 100 cents more than the pen. How many cents does the pen cost?

Mathematics

1 answer:

nalin [4]3 years ago

5 0

Answer:

50 cents

Step-by-step explanation:

This is the equation I came up with: 150 = 100+p

Subtract 100 from 150 to leave the p alone.

50 = p

You might be interested in

Consider a population with 3 observations: 6, 10 and 12. You use simple random sampling without replacement to select a sample o

lozanna [386]

Answer:

$\dfrac{2}{3}$

Step-by-step explanation:

Given that:

The number of observations is:

6, 10, 12

If we are to use a simple random sampling without replacement, then we will have:

(6,10) (6,12) (10,12)

Here;

the sample size n = 2

The population size N = 3

For (6,10) ; The sample mean = $\dfrac{6+10}{2}$

= $\dfrac{16}{2}$

= 8

For (6,12) ; The sample mean = $\dfrac{6+12}{2}$

= $\dfrac{18}{2}$

= 9

For (10, 12) ; The sample mean = $\dfrac{10+12}{2}$

= $\dfrac{22}{2}$

= 11

The probability distribution of sample mean(x) is:

X 8 9 11

P(X=x) $\dfrac{1}{3}$ $\dfrac{1}{3}$ $\dfrac{1}{3}$

Thus, the probability that the sample mean is larger than 8 is:

P(X> 8) = P(X = 9) + P(X + 11)

P(X> 8) = $\dfrac{1}{3}+\dfrac{1}{3}$

P(X > 8) = $\dfrac{1+1}{3}$

P(X> 8) = $\dfrac{2}{3}$

5 0

3 years ago

4 5/2 in simplest form

egoroff_w [7]

4 5/2 is 6 1/2 in simplest form!

5 0

3 years ago

Read 2 more answers

The quotient for the following problems are the same:

Nitella [24]

The answer is True 1/2 divided by 4 and 4 divided by 1/2

7 0

3 years ago

Read 2 more answers

If f(x) = x3 – x2 – 3, which of the following is equal to g(x) = f(2 – x)?

Andru [333]

Answer:

-x^3+5x^2-8x+1, which is choice A

======================================

Work Shown:

f(x) = x^3 - x^2 - 3

f(x) = (x)^3 - (x)^2 - 3

f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)

f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2

f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3

f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4

f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5

f(2-x) = -x^3+5x^2-8x+1

----------

note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.

note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2

note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.

note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.

note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2

4 0

3 years ago

How many liters of a 10% antifreeze solution and a 40% antifreeze solution must be mixed to make 15 liters of a 25% solution? Ro

butalik [34]

Answer:

7.5 liters of a 10% antifreeze solution AND

7.5 liters of a 40% antifreeze solution

Step-by-step explanation:

According to the question,we were asked to find out how many liters of 10% anti freeze solution and 40% anti freeze each to make a 15 liters 25% mixture

Let’s call

the amount of liters needed of our 10% solution “x”. So, how

many liters do we need of the 40% solution? Well, there are 15

liters in total, x liters have been spoken for, so what remains

of our allotted 10 liters then, is 15-x.

Now let's solve for "x"

10% of x + 40% of (15 - x) = 25% of 15 liters

0.1x + 0.4(15 - x) = 0.25(15)

0.1x + 6 - 0.4x = 3.75

Collect the like terms and we have

0.3x = 2.25

x = 2.25 × 3

X = 7.5(Liters for the 10% anti freeze solution)

The 40% solution= 15 - 7.5 = 7.5 liters

Since "X" was used to fill for the unknown amount of 10% anti freeze solution,we have 7.5 liters of the 10% solution and another 7.5 liters for the 40% solution to end up with 15 liters of the desired 25% solution.

8 0

3 years ago