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2 years ago

10 quarters 17 dimes 40 nickels 15 pennies answer

1 answer:

4 0

If the given quantities are 10 quarters 17 dimes 40 nickels 15 pennies then the total money would be 6.35 dollars.

<h3>What is the fundamental principle of multiplication?</h3>

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Quarters are worth .25 of a dollar

10 x .25 = 2.5

Dimes are worth .10 of a dollar

17 x .10 = 1.7

Nickels are worth .05 of a dollar

40 x .05 = 2

Pennies are worth .01 of a dollar

15 x .01 = 0.15

Add this together

2.5 + 1.7 + 2 + 0.15

= 6.35

Learn more about multiplication;

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Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and

Anastaziya [24]

The problem is modelled in the first picture shown below

To work out the resultant vector, we modelled the vectors 150N and 75N as triangle AOB is shown in the second picture with AB as the resultant vector.

We use the cosine rule to work out the length AB
$AB^{2}= 75^{2}+ 150^{2}-(2*75*150*cos(60))$
$AB^{2} =28125-11250$
$AB^{2}=16875$
$AB= \sqrt{16875} =130$ (nearest whole number)

The third picture shows the full diagram of the vectors

To work out the direction of the resultant vector, we use the sin rule to find the size of angle A and angle B

Angle A
$\frac{130}{sin(60)}= \frac{75}{sin(A)}$
$130sin(A)=75sin(60)$
$sin(A)= \frac{75sin(60)}{130}$
$sin(A)=0.4996300406$
$A= sin^{-1}(0.4996300406)$
$A=30$ (rounded to nearest whole number)

Angle B
$B=180-60-30=90$

Direction is 60° toward negative x-axis

Answer: Magnitude 130N and direction 60° toward negative x-axis

3 0

3 years ago

A local artist working at the town fair makes caricatures and portraits. The caricatures cost $4 to make white

il63 [147K]

Answer:

The artist should make 15 caricatures and 30 portraits.

Step-by-step explanation:

First, we identify the variables for the problem. In this case, the variables will be:

C=number of caricatures

P= number of portraits.

Next, we can use the variables to make the inequalities that constrain the problem.

We know the artist can't spend more than $360 for supplies and we also know that it costs $4 to make a caricature and $10 to make a portrait, so:

$4C+10P\le 360$

We also know the artist has a limit of time of 20 hours, which is the same as 20*60=1200 minutes to paint. We know it takes her 20 minutes to make a caricature and 30 minutes to make a portrait, so:

$20C+30P\le 1200$

and we also know she must make a positive number of caricatures and a positive number of portraits so the other two constrains are:

$C\ge 0$

$P\ge 0$

So we can go ahead and graph them. (see attached picture)

Once we graphed the inequalities we can determine what the corners of the polygon created by the intersection of the shaded areas are, so we proceed and calculate them:

first point:

(0,0)

second point:

4(0)+10P=360

$P=\frac{360}{10}$

P=36

(0,36)

Third point:

20C+30(0)=1200

$C=\frac{1200}{20}$

C=60

(60,0)

Fourth point:

$4C+10P = 360$

$20C+30P = 1200$

We multiply the first equation by -5 so we get:

-20C-50P=-1800

20C+30P=1200

------------------------

-20P=-600

P=30

so:

20C+30(30)=1200

20C=1200-900

20C=300

C=15

(15,30)

Once we found the 4 points, we go ahead and evaluate them for the objective function. In this case, the objective function is the total amount of money she got from selling the pieces of art, so we get:

I=10C+20P

Point 1

I=10(0)+20(0)=0

Point 2

I=10(0)+20(36)=720

Point 3

I=10(60)+20(0)=600

Point 4

I=10(15)+20(30)=750

Next, we look for the greatest income which in this case will be 750 so that's why she must make 15 caricatures and 30 Portraits.

8 0

3 years ago

Question 4.

Ludmilka [50]

Answer:

9.80 m

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

<h3>setup</h3>

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

Tan = Opposite/Adjacent

Using the given values, we have ...

tan(24°) = AC/AB = (tree height)/(distance from tree)

tan(24°) = AC/(22 m)

<h3>solution</h3>

Multiplying by 22 m gives ...

tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.

5 0

2 years ago

Please help I got 20mins

Llana [10]

Answer/Step-by-step explanation:

Scale factor: 1/4

<em />

DE length: 5

<em />

BC length: 30

<em>(Because EF is the dilation) 7.5 x 4 = 30</em>

8 0

3 years ago

Factorise x^2 - 7x + 12

tamaranim1 [39]

Answer:

(x-3) (x-4)

Step-by-step explanation:

x²- 7x + 12

= x² - 3x -4x +12

=x(x-3) - 4(x-3)

=(x-3) (x-4)

8 0

2 years ago

Read 2 more answers