Find the measure of <2. 62 = [?]

Paul paid $ 25.50 for 3 cups of hot chocolate and cups of tea. The cost of each cup of tea was 2/3 the cost of each cup of hoy c

Allushta [10]

Let the cost of one cup of hot chocolate be = x

Let the cost of one cup of hot tea be = y

Paul paid $ 25.50 for 3 cups of hot chocolate and 4 cups of tea.

Equation becomes = $3x+4y=25.50$ ...(1)

As given, the cost of each cup of tea was 2/3 the cost of each cup of hot chocolate.

$y=\frac{2x}{3}$ .... (2)

Putting the value of y from (2) in (1)

$3x+4(\frac{2x}{3})=25.50$

= $3x+\frac{8x}{3}=25.50$

= $\frac{9x+8x}{3}=25.50$

= $17x=76.5$

x=4.5

$y=\frac{2x}{3}$

= $\frac{2*4.5}{3}$

y =3

Hence each cup of hot chocolate is $4.50

Each cup of tea is $3.

7 0

2 years ago

If your cell phone bill was 67.82 and there is a 1/20 late fee how much will your bill be with the late fee included?

almond37 [142]

Answer:

Assuming 1/20 is a 5% late fee:

$21.211

Step-by-step explanation:

67.82 x 1/20 = 3.391

67.82 + 3.391 = 71.211

4 0

2 years ago

Ahmed wrote two numbers. The first number has a 7 in its tenths place. The second number has a 7 with a value that is 1,000 time

Stels [109]

Answer: In the hundreds place.

Step-by-step explanation:

1. You know that the first number has a 7 in its tenths place. This means that it is after the decimal point. You can write is as following:

x.7

Where x represents the other digits.

2. The second number has a 7 with a value that is 1,000 times greater than the value of the 7 in the first number, this means that you can know the place of the 7 in the second number if you multiply the first number by 1,000, or in other words, move the decimal point three places to the rigth. Therefore:

x.7*1000=7xx

3. As you can see, the 7 is in the hundred place in the second number.

8 0

2 years ago

Read 2 more answers

A road map of the state of Texas has a scale of 0.5 miles in =50 miles. If the distance between two points in the state is 600 m

tamaranim1 [39]

Answer:

6 miles

Step-by-step explanation:

Let's set up a ratio:

$\frac{0.5}{50}=\frac{x}{600}$

We can use "cross multiplication" to solve for x

Cross multiplication is multiplying the numerator of the first fraction by the denominator of the second fraction and the denominator of the first fraction by the numerator of the second fraction.

$0.5*600=50x$

$300=50x$

Divide both sides by 50 to isolate x

$x=6$

8 0

2 years ago

Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c) Because the variance of each variable is dependent on the other.

Step-by-step explanation:

The random variable X and Y are defined as follows:

X = amount of ice cream in the box

Y = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

X + 3Y.

Compute the expected value of (X + 3Y) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (X + 3Y) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (X + 3Y) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

X - Y.

Compute the expected value of (X - Y) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (X - Y) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (X - Y) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

7 0

3 years ago