MATHEMATICS HIGH SCHOOL

Cynthia has $2.15 worth of change in her pocket. She has three more nickels than quarters and twice as many dimes as quarters. How many of each type coin has she?

Answers

Answer 1

Answer:

Answer:

7 nickles

8 dimes

4 quarters

Step-by-step explanation:

d = 2q

n = q+3

25q + 10d + 5n = 215

25q + 10(2q) + 5(q + 3) = 215

25q + 20q + 5q - 15 = 215

50q = 200

q = 4

d = 2q = 8

n = q + 3 = 7

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Let f(x)=-4x+7 and g(x)=10x-6. Find f(g(x))

Suppose theta= 11pi/12. How do you use the sum identity to find the exact value of sin theta?

Answers

The better way is, first we have to find the equivalent in degrees

$2\pi=360\º$

$(11\pi)/(12)=345\º$

now we can change this value to $-15\º$

how do we get an angle like this?!

$30\º-45\º=-15\º$

then

$sin(30\º-45\º)=sin(30\º)*cos(45\º)-sin(45\º)*cos(30\º)$

$\begin{Bmatrix}sin(30\º)&=&(1)/(2)\n\nsin(45\º)&=&cos(45\º)&=&(√(2))/(2)}\end{matrix}\n\ncos(30\º)&=&(√(3))/(2)\end{matrix}$

now we replace this values

$sin(-15\º)=(1)/(2)*(√(2))/(2)-(√(2))/(2)*(√(3))/(2)$

$sin(-15\º)=(√(2))/(4)-(√(6))/(4)$

$\boxed{\boxed{sin(-15\º)=sin(345\º)=(√(2)-√(6))/(4)}}$

During a sale at the bookstore,books sold for $3 and magazines sold for $2.50.Jan spent $16 and bought a total of 6 books and magazines.how many of each did she buy

Answers

If you would like to know how many of each did Jan buy, you can calculate this using the following two equations:

b ... the number of books
m ... the number of magazines

$16 = b * $3 + m * $2.50 ... 16 = 3 * b + 2.50 * m
b + m = 6 ... b = 6 - m
__________________
16 = 3 * b + 2.50 * m

16 = 3 * (6 - m) + 2.50 * m

16 = 3 * 6 - 3 * m + 2.50 * m

16 - 18 = - 3 * m + 2.50 * m

- 2 = - 0.50 * m /0.50

m = 2 / 0.50

m = 4 magazines

b = 6 - m = 6 - 4 = 2 books

Result: Jan bought 4 magazines and 2 books.

4 magazines @ $2.50 a piece
2 books @ $3 a piece
6 in total for $16

1.5 gallons = x quarts

Answers

Given:
1.5 gallons = x quarts

1 gallon is equal to 4 quarts. 1 gal = 4 quarts

1.5 gallons * 4 quarts/gallon = 6 quarts.

There are 6 quarts in 1.5 gallons.

The value of x is 6.

Hence, 1.5 gallons = 6 quarts

The given statement is,

1.5 gallons = x quarts

Here we have to find how many quarts in 1.5 gallon

Since we know that,

A gallon is a standard measurement of volume and capacity for measuring liquids.

It is often used in Imperial systems and US customary measurement standards. Gallon is abbreviated as gal.

And we also know that,

1 gallon = 4 quarts

There for to find quantity of quarts in 1.5 gallon

Multiply both sides by 1.5 we get,

1.5 gallons = 4x1.5 quarts

= 6 quarts

Hence,

The value of x = 6,

To learn more about the measurement unit visit:

brainly.com/question/777464

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Student take an average of 45 minutes and standard deviation of 8 minutes to complete a certain statistics test. If a student is selected at random, what is the probability that the student takes more than 56 minutes to compete the test?

Answers

A standard normal table can be used to estimate what part of a normal distribution will fall within a certain range, given the number of standard deviations (or Z-Score) from the mean. 56 minutes is 11 minutes from 45, and the standard deviation is 8, so the Z-Score is 11/8 = 1.375. The lookup table gives 8.5% complementary probability (greater than the given number of standard deviations) for 1.37 and 8.4% for 1.38. Checking a graph, the part of the curve above 1.375 standard deviations should be somewhere between 5 and 10%, so this seems reasonable.

Using the point-slope formula, what is the equation of the line that passes through the points (1, 5) and (0, 0)?