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2 years ago

5

9. To fill up his fuel tank, Sam puts in 16.8 gallons of gas at $3.90 per gallon. How much does Sam spend on fuel? Round to the

hundredths place.

1 answer:

Verizon [17]2 years ago

8 0

Answer:

$65.52

Step-by-step explanation:

y = mx + b

y = amount spent on fuel = ?

m = price per gallon = $3.90

x = gallons = 16.8

b is not needed for this problem

y = (3.90)(16.8)

y = $65.52

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What is the value of x

Goshia [24]

Sum of all adjacent angles is 180°.

3x + 12 + x = 180
4x + 12 = 180
4x = 168
x = 42°

-----------------------------------------
Answer: x = 42°
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3 0

3 years ago

What is the derivative of the following function? f(x) = 4x^6/cos^5(x)

KIM [24]

Answer:

$f'(x) = \frac{24x^{5} \cos x + 20x^{6}\sin x}{\cos^{6}x }$

Step-by-step explanation:

We have to find the derivative of the following function:

$f(x) = \frac{4x^{6} }{\cos^{5} x }$

Now, differentiating both sides with respect to x we get,

$f'(x) = \frac{\cos^{5}x (24x^{5}) - 4x^{6}(5\cos^{4}x )(- \sin x)}{(\cos^{5}x )^{2}}$

⇒ $f'(x) = \frac{ 24x^{5} \cos x + 20 x^{6}\sin x}{\cos^{6}x }$ (Answer)

{Since, we know that, $\frac{d(mx^{n} )}{dx} = m \times n x^{(n - 1)}$ and $\frac{d(\cos^{n} x)}{dx} = n \cos^{(n - 1)} x(- \sin x)$ }

5 0

3 years ago

Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $90 per hour. The mechan

Katena32 [7]

Answer:

First mechanic worked 20 hours and second mechanic worked 5 hours

Step-by-step explanation:

Let the number of hours the first mechanic worked = $a$

Let the number of hours the second mechanic worked = $b$

Therefore, we can write 2 equations and then solve them simultaneously:

$a+b=25$

$65a+90b=1750$

Rearranging the first equation: $a=25-b$

and substituting into the second equation to find $b$ :

$65(25-b)+90b=1750$

$1625-65b+90b=1750\\
25b=125\\
b=5$

Now sub $b=5$ into the first equation to find $a$

$a+5=25\\
a=20$

Therefore, first mechanic (a) worked 20 hours and second mechanic (b) worked 5 hours

4 0

2 years ago

Will give brainliest to correct answer! Given that cos Ф=-8/17 and sin Ф is negative, determine the value of tan Ф.

Kipish [7]

Answer: option 3 is the correct answer

Step-by-step explanation:

Let us look at the various trigonometric ratios

Sin Ф = opposite side/ hypotenuse

Cos Ф = adjacent side / hypotenuse

Tan Ф = opposite side / adjacent side

Therefore, tan Ф = sin Ф / cos Ф

This means that if cos Ф=-8/17 and sin Ф is negative, then the hypotenuse is negative

To determine the adjacent side, we will apply Pythagoras theorem

Hypotenuse ^2 = opposite ^2 + adjacent ^2

-17^2 = 8^2 + adjacent^2

adjacent^2 = 289 - 64 = 225

adjacent = √225 = 15

tan Ф = 8/15

5 0

3 years ago

The mean length of 4 childrens' big finger is 14cm. The mean length of 9 adults' big finger is 16.1cm. What is the mean length (

Mamont248 [21]

Answer:

The mean length of the 13 people's big finger is 15.45 cm

Step-by-step explanation:

Given;

mean length of 4 childrens' big finger, x' = 14cm

mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm

Let the total length of the 4 childrens' big finger = t

$x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm$

Let the total length of the 9 adults' big finger = T

$x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm$

The total length of the 13 people's big finger = t + T

= 56 + 144.9

=200.9 cm

The mean length of these 13 people's big finger;

x''' = (200.9) / 13

x''' = 15.4539 cm

x''' = 15.45 cm (2 DP)

Therefore, the mean length of the 13 people's big finger is 15.45 cm

3 0

2 years ago