a Car has a 15 gallon gas tank . I f a car gets 32 miles per gallon and travels 384 miles . how much gas will be left in the tank?

Answer:

wilson swam farther by 0.4 km

Step-by-step explanation:

wilson swam 1.2km

brian swam 0.8km

1.2 - 0.8 = 0.4

Answer:

length =29m width =11m

Step-by-step explanation:

length---L

width -----W

L=3W-4

area=319sqm

area of rectangle=L × W

area of rectangle =W ×(3W - 4)=319

expanding...

3W^2 - 4W=319

3W^2 - 4W -319=0

factorize

(W-11)(3W+29)=0

W=11 or -29/3

using the positive because the negative width with a minus sign does not make sense in real life, we use 11m

width =11m

length 3W -4=3(11) -4 =29m

Answer:

A. Tossing 5 coins and getting 4 heads

Step-by-step explanation:

Compound events may be described as events whose occurence has more than one possible outcome, that is the number of possible events is more than one. From the options given above, Rolling 3 on a die, this event has only one possible outcome, which is rolling 3 ; tossing a coin and getting tails also has one obe possible outcome. Drawing 10 diamonds from a deck also focuses on one event which is drwinh diamonds. However, tossing 5 coins and getting 4 heads involves that the 5th toss will be tail. This has more than one event and thus a compound event.

Answer: A.

Step-by-step explanation:

Tossing five coins and getting four heads is a compound event as the coins and cards are different

Answer: 8

Step-by-step explanation

Answer:

$8

Step-by-step explanation:

If we just keep track of the money in the account, we can solve this pretty quickly. If the balance is -20, and we subtract another 10 from it, it gives us -30. $38 is then deposited into the account, giving us a balance of $8.

[tex]-20-10+38=8[/tex]

Answer:

(x-1)^5 (x+1)

Step-by-step explanation:

2 (x-1)^5 + (x-1)^6

Factor out (x-1)^5

2 (x-1)^5 + (x-1)^5 (x-1)

(x-1)^5( 2 + x-1)

Combine like terms

(x-1)^5 (x+1)

Answer:

A

Step-by-step explanation:

factor out (x-1)^5 and you get (x-1)^5(2+x-1)

simplify that to get (x-1)^5(x+1)

Answer:

f(x+3) = 4x + 14

Step-by-step explanation:

f(x+3) = 4(x+3) + 2

f(x+3) = 4x + 12 + 2

f(x+3) = 4x + 14

hope this helps!

Answer:

f(x)=4x+2

f(x+3) means substitute x as (x+3)

f(x+3)=4(x+3) +2

= 4x + 12 + 2

=4x+14.

OPTION C IS LEGIT

Answer:

r = -6

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Slope 3/4

This means that [tex]m = \frac{3}{4}[/tex], and thus:

[tex]y = \frac{3}{4}x + b[/tex]

(6,3)

This means that when [tex]x = 6, y = 3[/tex]. We use this to find b. So

[tex]y = \frac{3}{4}x + b[/tex]

[tex]3 = \frac{3}{4}(6) + b[/tex]

[tex]b = 3 - \frac{18}{4} = \frac{12}{4} - \frac{18}{4} = -\frac{6}{4}[/tex]

So

[tex]y = \frac{3}{4}x - \frac{6}{4} = \frac{3x - 6}{4}[/tex]

(-6, r)

r is y when [tex]x = -6[/tex]. So

[tex]y = \frac{3(-6) - 6}{4} = -6[/tex]

So r = -6.

Answer:

Area = 52.81 square inches

Step-by-step explanation:

[tex]Diameter = 8.2in\\\\Radius = \frac{diameter}{2}=\frac{8.2}{2}=4.1in\\\\Area \ of \ a \ circle = \pi r^2 = \pi \times 4.1^2 = 52.81 in^2[/tex]

Answer:

x = 3 , y = 2

Step-by-step explanation:

We need to solvd the the given exponential equation , the equation is,

[tex]\bf\implies 2^x \times 3^y = 72 [/tex]

Now write 72 as prime factors of 2 and 3 ,

[tex]\bf\implies 2^x \times 3^y = 2^3 \times 3^2 [/tex]

On comparing ,

[tex]\bf\implies x = 3 \\[/tex]

[tex]\bf\implies y = 2 [/tex]

Answer:

just another way to say problem

Step-by-step explanation:

Answer:

X2 -X1 / Y2 - Y1

Step-by-step explanation:

14- 4 / (-13) - (-4)

10/-9

Answer:

The probability of rolling a 5 is 1/6.

Step-by-step explanation:

There is only one 5 out of the 6 sides, therefor you can only get it once, so the probability of rolling a 5 would be 1/6.

Answer:

The answer is D. Selections of objects in which the order of the objects matters.

Step-by-step explanation:

Permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

The formula for permutation: A permutation is the choice of (r) things from a set of (n) things without replacement and where the order matters. Formula-  

[tex]nPr= \frac{n!}{(n-r)!}[/tex]

Permutation can be classified in three different categories:

Answer: 40 coins. Doesn't your profile say college?

Answer:

The coefficient of variation after the tax is imposed is 0.033

Step-by-step explanation:

Given

[tex]\mu =1000[/tex] --- mean

[tex]\sigma^2 = 1200[/tex] --- variance

[tex]tax = 10\%[/tex]

Required

The coefficient of variation

The coefficient of variation is calculated using:

[tex]CV = \frac{\sqrt{\sigma^2}}{\mu}[/tex]

After the tax, the new mean is:

[tex]\mu_{new} = \mu * (1 + tax)[/tex]

[tex]\mu_{new} = 1000 * (1 + 10\%)[/tex]

[tex]\mu_{new} = 1100[/tex]

And the new variance is:

[tex]\sigma^2_{new} = \sigma^2 * (1 + tax)[/tex]

[tex]\sigma^2_{new} = 1200 * (1 + 10\%)[/tex]

[tex]\sigma^2_{new} = 1320[/tex]

So, we have:

[tex]CV = \frac{\sqrt{\sigma^2}}{\mu}[/tex]

[tex]CV = \frac{\sqrt{1320}}{1100}[/tex]

[tex]CV = \frac{36.33}{1100}[/tex]

[tex]CV = 0.033[/tex]

Answer:

25.9 ft

Step-by-step explanation:

tan = opp/adj

tan67 = 61 / adj

adj = 61/tan67

use calculator

adj = 25.892963788785889

Rounded

25.9 ft

Answer:

I'm not sure but I did do it on a calculator so 1.515-1.56= -0.045

Answer:

20

Step-by-step explanation

7*4=28

28-4=24

4(2)=8

28-8=20

hope that helped!!

Answer:

y = 8/27

Step-by-step explanation:

given

x = 7

y = 4x*y - 4(2)

y = 4*7*y - 8

y = 28y - 8

8 = 28y - y

8 = 27y

8/27 = y

to prove

y = 4x*y - 4(2)

8/27 = 4*7*y - 8

8/27 = 28*8/27 - 8

8/27 = 224/27 - 8

8/27 = 224 - 27*8/27

8/27 = 8/27

hence it is proved that y is 8/27 .

Answer: 11.20

Step-by-step explanation:

Divide. 56.00 ÷ 5 = 11.20 therefore each shirt cost 11.20 Hope that helps!

Answer:

Divide.

Answer : option B

Step-by-step explanation:

Cost             Number of shirts

 56                      5

  x                        1

 [tex]\frac{56}{x} = \frac{5}{1}[/tex]

[tex]5 \times x = 56 \times 1\\\\x = \frac{56}{5} = 11.20[/tex]

Answer:

6

Step-by-step explanation:

We can find the sum by find all 4 terms

n=1

(-1) (( 3*1)+2) = -1 *5 = -5

n=2

(-1)^2 ( 3*2 +2) = 1(6+2) = 8

n= 3

(-1)^3 ( 3*3+2) = -1 ( 9+2) = -11

n=4

(-1)^4 (3*4 +2) = 1( 12+2) = 14

Add them together

-5+8-11+14

6

Answer:

C. 6

Step-by-step explanation:

hope this helps :)

Answer:

Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees.

Answer:

One number is 60 and the other is 7.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify and set up

Let x be one number and y be the other.

x + y = 67

x - y = 53

Step 2: Solve for x

Elimination

Step 3: Solve for y

Answer:

a) cosA=5/13   b) sinA=12/13

Step-by-step explanation:

Look at the needed angle, then use SOHCAHTOA!

Answer:

cos A = 5/13,  sin A = 12/13

Step-by-step explanation:

Watch the picture for help.

sin A = a/c (According to the picture)

cos A = b/c (According to the picture)

Answer:

A, C and G

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the values into the trigonometric ratios:

[tex]\implies \sf \sin(25^{\circ})=\dfrac{a}{c}[/tex]

[tex]\implies \sf \cos(25^{\circ})=\dfrac{b}{c}[/tex]

[tex]\implies \sf \tan(25^{\circ})=\dfrac{a}{b}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric values} \\\\$\sin(90^{\circ}- \theta)=\cos \theta$\\$\cos(90^{\circ}- \theta)=\sin \theta$\\$\tan(90^{\circ}- \theta)=\cot \theta$\\\end{minipage}}[/tex]

Using trigonometric values and the calculated trigonometric ratios:

[tex]\begin{aligned} \sf \sin(90^{\circ}- 25^{\circ})&=\sf \cos (25^{\circ})\\\implies \sf \sin(65^{\circ}) &=\sf \dfrac{b}{c}\end{aligned}[/tex]

[tex]\begin{aligned} \sf \cos(90^{\circ}- 25^{\circ})&= \sf \sin(25^{\circ})\\\implies \sf \cos(65^{\circ}) &=\sf \dfrac{a}{c}\end{aligned}[/tex]

[tex]\begin{aligned}\sf \tan(90^{\circ}- 25^{\circ})&= \sf \cot(25^{\circ})\\\implies \sf \tan(65^{\circ}) &= \sf \dfrac{1}{\tan(25^{\circ})}\\\implies \sf \tan(65^{\circ}) & = \sf \dfrac{b}{a}\end{aligned}[/tex]

Therefore, the true equations are:

[tex]\sf A: \quad \cos(25^{\circ})=\dfrac{b}{c}[/tex]

[tex]\sf C: \quad \sin(65^{\circ})=\dfrac{b}{c}[/tex]

[tex]\sf G: \quad \sin(25^{\circ})=\cos(65^{\circ})[/tex]

Answer:

11-9=2 then, 2^3=8 , finally 8X2=16

Step-by-step explanation:

remember order of operations

Answer:

[tex]s \ne \±2[/tex]

[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]

[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]

Step-by-step explanation:

Given

[tex]3sx_1 +5x_2 = 3[/tex]

[tex]12x_1 + 5sx_2 =2[/tex]

Required

Determine the value of s

Express the equations as a matrix

[tex]A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right][/tex]

Calculate the determinant

[tex]|A|= (3s*5s -5 *12)[/tex]

[tex]|A|= (15s^2 -60)[/tex]

Factorize

[tex]|A|= 15(s^2 -4)[/tex]

Apply difference of two squares

[tex]|A|= 15(s -2)(s + 2)[/tex]

For the system to have a unique solution;

[tex]|A| =0[/tex]

So, we have:

[tex]15(s -2)(s+2) = 0[/tex]

Divide both sides by 15

[tex](s -2)(s+2) = 0[/tex]

Solve for s

[tex]s -2 = 0\ or\ s +2 = 0[/tex]

[tex]s = 2\ or\ s = -2[/tex]

The result can be combined as:

[tex]s =\±2[/tex]

Hence, the system has a unique solution when [tex]s \ne \±2[/tex]

Next, we solve for s using Cramer's rule.

We have:

[tex]mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right][/tex]

Calculate the determinant

[tex]|x_1| = (3 * 5s - 5 *2)[/tex]

[tex]|x_1| = 15s - 10[/tex]

So:

[tex]x_1 =\frac{|x_1|}{|A|}[/tex]

[tex]x_1 = \frac{15s - 10}{15(s -2)(s+2)}[/tex]

Factorize

[tex]x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}[/tex]

Divide by 5

[tex]x_1 = \frac{3s - 2}{3(s -2)(s+2)}[/tex]

[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]

Similarly:

[tex]mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right][/tex]

Calculate the determinant

[tex]|x_2| = 3s * 2 - 3 * 12[/tex]

[tex]|x_2| = 6s- 36[/tex]

So:

[tex]x_2 =\frac{|x_2|}{|A|}[/tex]

[tex]x_2 = \frac{6s- 36}{15(s -2)(s+2)}[/tex]

Factorize

[tex]x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}[/tex]

Divide by 3

[tex]x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}[/tex]

[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]

Answer:

the answer is a

Step-by-step explanation:

Answer:

9.0

Step-by-step explanation:

x = 7 / cos 39°

= 7 / 0.7771

= 9.0

Answer:

ya

Step-by-step explanation: