MATHEMATICS COLLEGE

A. 35/12
B. 12/37
C. 12/35
D. 35/37

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Use the SOH CAH TOA

Tangent = Opposite / adjacent

tan (a) = 35 / 12

Answer 2

Answer:

Answer:

the answer is obviously going to be a

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Type your response in the box.Janet and Patrick are buying stuffed frogs each month to give to a charity. Pattern 1 describes Janet's collection overthe first three months. Pattern 2 describes Patrick's collection. Study both patterns, and fill in the table based onyour observations.

Which expression is equivalent to 4^ 5x4^ -7÷4 ^-2?4^ -4

4^ 0

4^ 5÷4^9

(4^5)(4^-2)/4^-7

Answers

The equivalent value of the exponential equation is A = 4⁰ = 1

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = ( 4⁵ x 4⁻⁷ ) / ( 4⁻² )

Now , from the laws of exponents , we get

m⁻ᵃ = ( 1 / mᵃ )

So , A = ( 4⁵ x 4⁻⁷ ) x 4²

And , mᵃ×mᵇ = mᵃ⁺ᵇ

On further simplification , we get

A = 4⁵⁺²⁻⁷

A = 4⁰

A = 1

Hence , the exponential equation is solved

To learn more about exponents click :

brainly.com/question/28966438

#SPJ3

You have a piggy bank containing a total of 106 coins in dimes and quarters. If the piggy bank contains $17.05, how many dimes are there in the piggy bank? There are how many dimes in the piggy bank.

Answers

Answer:

63 dimes

Step-by-step explanation:

Set up a system of equations where d is the number of dimes and q is the number of quarters:

d + q = 106

0.1d + 0.25q = 17.05

Solve by elimination by multiplying the top equation by -0.25 to eliminate q:

-0.25d - 0.25q = -26.5

0.1d + 0.25q = 17.05

Add together and solve for d:

-0.15d = -9.45

d = 63

So, there were 63 dimes in the piggy bank

2,4000,000 in standard form

Answers

Answer:

24 million

Step-by-step explanation:

24,000,000 if you put it porperly

The units are, Unit, Tens, Hundreds, Thousand, Ten-Thousand, Hundred-Thousand, Million, Ten million, Hundred million Billion and so on

Rewrite each fraction with a denominator of 121212.
\dfrac{3}{4} =

Answers

Answer:

9/12

Step-by-step explanation:

First you multiply 3x12 which equal 36 then you divide 36 by 4 which equal 9 so your answer is 9/12

The average starting salary of this year's vocational school graduates is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Answers

Answer:

Minimum: $25,200

Maximum: $44,800

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu = 35000, \sigma = 5000$

What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Minimum: 50 - (95/2) = 2.5th percentile.

Maximum: 50 + (95/2) = 97.5th percentile

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

$Z = (X - \mu)/(\sigma)$

$-1.96 = (X - 35000)/(5000)$

$X - 35000 = -1.96*5000$

$X = 25200$

The minimum is $25,200

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

$Z = (X - \mu)/(\sigma)$

$1.96 = (X - 35000)/(5000)$

$X - 35000 = 1.96*5000$

$X = 44800$

The maximum is $44,800

Find the measures of the supplementary angles that satisfy each case.The measure of the first angle is 45° more than the measure of the second.
(I will make you braniliest if it is correct)

Answers

Answer:

67.5°, 107.5°

Step-by-step explanation:

For supplementary angles, their sum equals 180°.

Let x be the first angle and y be the second angle, then

x + y = 180°.

It is given that x = y + 45°.

So x + y = 180°

substituting x into the equation, we have

y + 45° + y = 180°

simplifying, we have

2y + 45° = 180°

collecting like terms, we have

2y = 180° - 45°

2y = 135°

dividing through by 2, we have

y = 135°/2

y = 67.5°

Since y = 67.5°

then x = y + 45°

x = 67.5° + 45°

x = 107.5°

Final answer:

The measures of the supplementary angles that satisfy the given conditions are 67.5° and 112.5°.

Explanation:

Let's say the measure of the second angle is x. Since the measure of the first angle is 45° more than the measure of the second, we can express the first angle as the measure of x + 45°.

By the definition of supplementary angles, we know that the sum of the measures of two supplementary angles is 180°. Therefore, we can create the following equation: x + (x + 45) = 180.

Solving this equation gives us:

Add the expressions on the left side of the equation to get: 2x + 45 = 180.
Subtract 45 from both sides of the equation to isolate the term containing x: 2x = 135.
Divide both sides of the equation by 2 to solve for x: x = 67.5°.

So, "the second angle measures 67.5°, and the first angle, being x + 45°, measures 112.5°".