Ask question

Ask question

All categories

3 years ago

9

In her wallet, Ms. Thompson has one-dollar, five-dollar, and ten-dollar bills, totally $171. She has the same number of five-dol

lar bills as one-dollar and ten-dollar bills put together. If she has 30 bills in all, how many bills of each denomination does she have?

2 answers:

Flauer [41]3 years ago

6 0

Answer:

She has 6 one dollar, 15 five dollar and 9 ten dollar of bills in her wallet.

Step-by-step explanation:

Consider the provided information.

Ms. Thompson has one-dollar, five-dollar, and ten-dollar bills, totally $171.

Let x represents the number of one dollar bills.

y represents the number of five dollar bills.

z represents the number of ten dollar bills.

She had one-dollar, five-dollar, and ten-dollar bills, totally $171.

$1x + 5y + 10z =171$ ......(1)

She has the same number of five-dollar bills as one-dollar and ten-dollar bills put together.

$y=x+z$ .....(2)

She has 30 bills in all.

$x+y+z=30$ ......(3)

Substitute the value of x+z in equation 3.

$y+y=30$

$y=15$

Substitute the value of y in equation 2

$15=x+z$

$15-x=z$ ......(4)

Substitute the value of y and z in equation 1.

$1x + 5(15) + 10(15-x) =171$

$x + 75 + 150-10x=171$

$54=9x$

$x=6$

Now substitute the value of x in equation 4.

$15-6=z$

$9=z$

Hence, she has 6 one dollar, 15 five dollar and 9 ten dollar of bills in her wallet.

MissTica3 years ago

5 0

Let's check. 6 one-dollars = $6 15 five-dollars = $75 9 ten-dollars = $90 Add them all up to get $171, so that is correct. Add the number of one-dollar bills and the number of ten-dollar bills together. 6 + 9 = 15, which is the number of five-dollar bills, so that is correct as well. Add all the numbers of bills together, 6 + 9 + 15 = 15 + 15 = 30, so that is correct

You might be interested in

Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is

Katarina [22]

Answer: A

Step-by-step explanation:

5 0

3 years ago

g If the economy improves, a certain stock stock will have a return of 23.4 percent. If the economy declines, the stock will hav

dusya [7]

Answer:

$E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%$

Now we can find the second central moment with this formula:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965$

And the variance is given by:

$Var(X) = E(X^2) - [E(X)]^2$

And replacing we got:

$Var(X) = 413.5965 -(11.759)^2 =275.5105$

And finally the deviation would be:

$Sd(X) = \sqrt{275.5105}= 16.599 \%$

Step-by-step explanation:

We can define the random variable of interest X as the return from a stock and we know the following conditions:

$X_1 = 23.4 , P(X_1) =0.67$ represent the result if the economy improves

$X_2 = -11.9 , P(X_1) =0.33$ represent the result if we have a recession

We want to find the standard deviation for the returns on the stock. We need to begin finding the mean with this formula:

$E(X) = \sum_{i=1}^n X_i P(X_i)$

And replacing the data given we got:

$E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%$

Now we can find the second central moment with this formula:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965$

And the variance is given by:

$Var(X) = E(X^2) - [E(X)]^2$

And replacing we got:

$Var(X) = 413.5965 -(11.759)^2 =275.5105$

And finally the deviation would be:

$Sd(X) = \sqrt{275.5105}= 16.599 \%$

7 0

3 years ago

What is 35 X (5 +150)=

ololo11 [35]

Answer: 5425

Step-by-step explanation:

7 0

3 years ago

Please answer this (photo below)

lozanna [386]

Answer:

Please see attached image for the graph

Step-by-step explanation:

To graph the elevation versus time, we start by plotting the first point at time zero (when the climb begins) when Zane is 20 meters below the edge (-20 meters). This corresponds to the point (0, -20).

One second later (1 in the horizontal axis), Zane has moved up 4 meters, now reaching -16 meters. This is the point (1, -16) on the graph.

One second later at time 2 seconds, he is another 4 meters up which corresponds to the point (2, -12) on the graph.

you can go on like this plotting more points on the graph.

Please see the attached image that illustrates this and shows the appropriate line that represents Zane's position versus time (pictured in red)

7 0

3 years ago

Simplify the product using distributive property (3p+2)(5p-1)

solniwko [45]

(3p+2)(5p-1)
=3p(5p-1)+2(5p-1)
=15p^2-3p+10p-2
=15p^2+7p-2
=C

7 0

3 years ago

Read 2 more answers