Karen and her friends decided to have a water balloon fight! They got 20 water balloons and used 6 liters of water to fill them all equally. How much water was in each balloon?

Given:

The logarithmic expression is:

[tex]\log_718[/tex]

To find:

The equivalent expression of given expression by using change-of-base formula.

Solution:

The change-of-base formula is:

[tex]\log_ba=\dfrac{\log_ca}{\log_cb}[/tex]

The given expression is:

[tex]\log_718[/tex]

Using the change-of-base formula, we get

[tex]\log_718=\dfrac{\log_c18}{\log_c7}[/tex]

Where, is a constant and c>0.

Let [tex]c=10[/tex], then

[tex]\log_718=\dfrac{\log_{10}18}{\log_{10}7}[/tex]

Therefore, the correct option is a.

Answer:

a

Step-by-step explanation:

bc look

Answer:

1st one

Step-by-step explanation:

Linear means straight and when you graph this one it is a straight line

Answer:

The answer is B. 9.7

Step-by-step explanation:

sin 14°=x/40

=> sin 14° X 40 = x

∴ x = 9.67≈ 9.7

Answer:

answer is 52.5

Step-by-step explanation:

hope it helps

Answer:

Obtuse triangle.

Step-by-step explanation:

A obtuse triangle has one angle that is larger than 90 degrees. There is a angle with 95 degrees.

Answer:

p - 7 = 42

Step-by-step explanation:

"Less than" might make you think of the  <  sign, but that's a mistake.  The expression  7 < p = 42  makes no sense!  In fact, that would say, "7 is less than p and p = 42."

To find 7 less than a number, you subtract 7 from the number.  You start with the number, then subtract 7.

p - 7 = 42

Answer:

[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

Given

[tex]\cos A = \frac{1}{2}[/tex]

Required

Determine [tex]\cos(\frac{1}{2}A)[/tex]

To do this, we make use of the following identity

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\cos A+1}{2}}[/tex]

Substitute: [tex]\cos A = \frac{1}{2}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{1}{2}+1}{2}}[/tex]

Solve the numerator

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{2+1}{2}}{2}}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{3}{2}}{2}}[/tex]

Rewrite as:

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{2} * \frac{1}{2}}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{4}}[/tex]

Take square roots

[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]

Answer: they both have four sides (quadrilateral)

Step-by-step explanation:

Answer:

Quarderlaterals with reflecting (or parrel) sides of the same length.

Step-by-step explanation:

Squares always have 4 equal sides

Parrallegrams always have two sides that are parrel to each other that are the same lenghth.

Answer: B

Step-by-step explanation:

the formula for area of a triangle is base times height divided by 2

to get the base do 12.3 x 2 = 24.6

24.6 x 25.6 = 629.76

629.76/2 = 314.88

the answer would be B

(sorry for saying the answer was A at first, i forgot to find the full base)

Answer:

B. 314.9m

Step-by-step explanation:

First, let's take a look at the formula of a triangle.

A=[tex]\frac{1}{2}[/tex](b * h) ALSO WRITTEN AS- A= [tex]\frac{(b*h)}{2}[/tex].

So, as you can see, there is only half the base provided. To get the other half, just multiply it by 2. You get 24.6m as the base.

The height is provided. It's 25.6m. Plug in your base and height values and slove.

A=[tex]\frac{24.6m * 25.6m}{2}[/tex]

A= [tex]\frac{629.76}{2}[/tex]

A= 314.88m

You then round to the nearest tenth.

The final answer is A=314.9m.

Answer:

The roots are x=2, 4

Step-by-step explanation:

The roots of the parabola are where the graph crosses the x axis .

The graph crosses the x axis at x=2 and x=4

The roots are x=2, 4

Answer:

2[tex]\sqrt{13}[/tex]

Step-by-step explanation:

Use the distance formula and plug in the values

d=(3−(−3))2+(2−6)2√  

d=(6)2+(−4)2√

d=36+16√

d=[tex]\sqrt{52}[/tex]

d= 2[tex]\sqrt{13}[/tex]

Answer:

59×695÷500×56677×6626

Answer:

B) 10 cm

Step-by-step explanation: since DC scaled up to 10 cm and they were both originally 6cm, RU would be 10cm.

Answer:

c = 25

Step-by-step explanation:

First, you can divide by 18 on both sides:

18 (c - 19) = 108

÷ 18             ÷18

c - 19 = 6

To isolate the variable c, you can add 19 on both sides:

c - 19 = 6

  +19   +19

c = 25

Answer:

c= 25

Step-by-step explanation:

108/18 = 6

6 +19 = 25

Answer:

 65 in

Step-by-step explanation:

Answer

A

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

Given

Simra has an 8-carat diamond

She cuts small pieces of [tex]\frac{1}{3}[/tex] carat

Suppose she cuts x pieces of diamond

[tex]\therefore x=\dfrac{8}{\frac{1}{3}}\\\\\Rightarrow x=8\times 3\\\Rightarrow x=24[/tex]

She has now 24 pieces of diamond.

Answer:

($42 × 7)  - ($8.25 × 8)

Step-by-step explanation:

Given that

Mike saves $42 a week for 7 weeks

And, his 8 day vacation, he plans to spend $8.25 each day

We need to find out the expression of how much he would have left

So,

Since the amount $42 is for a week

So for 7 weeks, it would be

= $42 × 7

And, he spends $8.25 each day,

And, for 8 days, it would be

= $8.25 × 8

So, the expression is

= ($42 × 7)  - ($8.25 × 8)

Answer:

I think it's 886.7

Step-by-step explanation:

hope this helps sorry if incorrect have a good rest of your day/night :) ❤

Answer:

d) [tex]\frac{9\pi }{4}[/tex]

Step-by-step explanation:

[tex]\frac{9\pi }{4} = 2\pi + \frac{\pi }{4}[/tex]

The correct options are a and d because -7pi/4 and 9pi/4 are the required angles.

Important infromation:

The angles [tex]\theta\pm 2n\pi [/tex] represent the same point on the unit circle as [tex]\theta[/tex].

It means,  [tex]\dfrac{\pi}{4}\pm 2n\pi [/tex] represents the same point on the unit circle as [tex]\dfrac{\pi}{4}[/tex].

The required angles are:

[tex]\left\{...,\dfrac{\pi}{4}-4\pi,\dfrac{\pi}{4}-2\pi, \dfrac{\pi}{4},\dfrac{\pi}{4}+2\pi,\dfrac{\pi}{4}+4\pi,...\right\}[/tex]

[tex]\left\{...,-\dfrac{15\pi}{4},-\dfrac{7\pi}{4}, \dfrac{\pi}{4},\dfrac{9\pi}{4},\dfrac{17\pi}{4},...\right\}[/tex]

Therefore, the correct options are a and d.

Find out more about 'Angles' here:

https://brainly.com/question/23475646

Answer:

Extrapolation, because a key that is 12 keys from middle c is outside the data set.

Step-by-step explanation:

Given

See attachment for the data set

Required

Which option answers the question

From the attached dataset, we can see that 12 is not within the range of the data set.

When one makes predictions about a datum or set of data outside the range of the original dataset, then one is extrapolating.

Hence, (d) is correct

Answer:

d

Step-by-step explanation:

trust me

Answer:96

Step-by-step explanation:

Okay first we would find the area of the triangle like we would for a regular square or rectangle right? LXW but we would divide by 2 for each of the triangle and add them up and then we’d do the bottom and this time no dividing by 2 just do LXW HOPES THIS HELPS

Answer:

x = -0.8 and 10.8

Step-by-step explanation:

Given the equation x2 – 10x – 8= 0

Using the general formula

x = -b±√b²-4ac/2a

x = -(-10)±√(-10)²-4(1)(-8)/2(1)

x = 10±√100+32/2

x =10±√132/2

x = 10±11.489/2

x = 10-11.489/2 and 10+11.489/2

x = -1.489/2 and 21.489/2

x = -0.8 and 10.8

Answer: 16 hours

Step-by-step explanation:

Given

Carla earns [tex]\$5[/tex] for each hour she works

Last week she earned $148 total including [tex]\$68[/tex] tip

So, the sum of hourly income and must be equal to the total money earned

Suppose she works for [tex]x[/tex] hours

[tex]\Rightarrow 5x+68=148[/tex]

[tex]\Rightarrow 5x=148-68\\\Rightarrow 5x=80\\\Rightarrow x=16\ \text{hours}[/tex]

Thus, she works 16 hours last week

Answer:

216 degrees.

Step-by-step explanation:

put it through the formula and set the formula equal to 6/5 pi. then solve.