Challenge: A scuba diver has 30 cubic feet of air in his tank and dives under the water at
3:15pm. When he resurfaced at 3:30pm, he had 12 cubic feet of air left. How many cubic
feet of air per minute did he use?

You need 8 cups of juice for 12 cups of seltzer.

Representing the first statement in ratio form. So, number of cups of juice: number of cups of seltzer = 2:3. Similarly, for second statement, let the number of cups of juice be x.

Forming the equation with ratio on both sides -

2:3 = x:12

Writing the mentioned equation as fraction to solve for the value of x

x = (2 × 12)/3

Performing multiplication in numerator to find the value of x

x = 24/3

Dividing the numerator and denominator by 3 to find the value of x

x = 8

Therefore, 8 cups of juice is needed for 12 cups of seltzer.

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The solution of the logarithmic equation is approximately 5.66 .

The logarithm is a simpler way to write a exponential equation.

The exponential equation nˣ = b is written as logₙ b = x ( read as logarithm of b to the base of n is equal to x).

The various properties of logarithm are:

The given equation is :

log₂ x = 2.5

This equation is of the form  logₐ b=n

We know that from the properties of logarithm logₐ b=n is equivalent to aⁿ=b.

So the given equation can be written as

[tex]x=2^{2.5}[/tex]

Solving we get

x=5.6568....

or, x≈5.66

Therefore the logarithm equation has a solution for x where the value of x is approximately 5.66.

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Answer:

NOT possible to draw

Step-by-step explanation:

Answer:

graph the following

x=-1 y =5

it look like a two line

Step-by-step explanation:

Answer:

157.41

Step-by-step explanation:

It can be identified that, given the figure, there is a rectangle and 2 semicircles.

Let's find the area of the rectangle first: A=L*w

Plugging in the given values => A=7.5*15.1 which equals 113.25.

Now the area for the semicircles: 1/2(3.14*r^2)

First, we need to find the radius. To find the radius, you just have to divide the diameter by 2. So, 7.5/2=3.75.

We can plug square the radius which is 3.75 and plug it into the formula: 1/2(3.14*3.75^2)=>22.078125.

22.078125 is the area of only one semicircle so we need to multiply it by 2 because we have two semicircles. So, we get 44.15625.

Finally, we can add them all up to find the total area of the figure: 113.25+44.15625=157.40625.

Rounding to the nearest hundredth=>157.41

Answer:

( x , y , z) = ( 1 , 3 , - 2)

the solution

Answer:

100,000

Step-by-step explanation

week 1: 10

week 2: 10x10= 100

week 3: 100x10=1,000

week 4: 1,000x10=10,000

week 5: 10,000x10= 100,000

Have an amazing day/night!!

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

Answer: 120 degrees (originally said 150 degrees, but thats a weird ladder)

Step-by-step explanation: 6 x 4 = 24, 6 x 60 = 360, 4 = 60, 10 x 2 = 20, 4 x 5 = 20, 60 x 5 = 300. 20 / 2 = 10, 300 / 2 = 150, 150 / 1.17 = 120 most likely

Answer:

0.5

Step-by-step explanation:

Answer: the answer is 0.5 or 1/2

Step-by-step explanation:

The slope of line: 1. m= 6 , 2. m= -6 , 3. m= 2.5,  4. m= .5

The slope of the line :

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

Tan θ = Δy/Δx can also represent the slope of the line

So, tan θ to be the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.

If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:

Slope,

m = Change in y-coordinates/Change in x-coordinates

m = (y2 – y1)/(x2 – x1)

Therefore, based on the above formula, we can easily calculate the slope of a line between two points.

In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,

Slope, m = Rise/Run

1.

(-1,-1) & (0,5)

m = (y2 – y1)/(x2 – x1)

m = (5 – (-1)) /(0– (-1))

m = (5 +1)/(0 +1)

m = (6)/(1)

m = 6

2.

(3,5) & (4,-1)

m = (-1 – 5)/(4 – 3)

m = (-6)/(1)

m = -6

3.

(2,1)  & (4,6)

m = (6 – 1)/(4 – 2)

m = (5)/(2)

m = 2.5

4.

(-5,-2) & (3,2)

m = (2 – (-2))/(3 – (-5))

m = (2 +2/(3 +5)

m = (4)/(8)

m = (2/(4)

m = (1)/(2)

m = 0.5

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$10000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]10000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies 10000=P(1.0125)^{16} \\\\\\ \cfrac{10000}{(1.0125)^{16}}=P\implies 8197.46\approx P[/tex]

Answer:

1/6(x) = 16

Step-by-step explanation:

You can just solve for x which goes as follows:

6 * 1/6 = 6 * 16 - Multiply both sides by 6.

x = 96

Answer:

x=96

Step-by-step explanation:

To figure out the weight of the person on the moon we would need to take their weight and divide by 6. we don't know the weight so it's x. We know the final weight so the x divided by 6 should be 16.

this translates to:

x/6=16

x=16*6

x=96

Using set builder notation, the domain of the given function is;

{x | x ≠ 5}

The domain is all values of x that makes the given expression undefined.

The given expression is;

y = (1 - 7x)/8 - 1/|3x - 15|

To find the value of x that will make the expression undefined, it means that we will equate the denominator to zero to get;

|3x - 15| = 0

Thus;

3x = 15

x = 15/3

x = 5

Thus, using set builder notation, the domain of the given function is;

{x | x ≠ 5}

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Answer:

no

Step-by-step explanation:

Functions are wavy lines

Answer:

yes

Step-by-step explanation:

The solution to this equation is x = -3

The equation is given as

5x + 3 = 2x - 6

Collect the like terms

5x - 2x = -3 - 6

Evaluate the like terms

3x = -9

Divide both sides by 3

x = -3

Hence, the solution to this equation is x = -3

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The value when it was purchased is  $160,000 in linear equation.

What in mathematics is a linear equation?

Let the original price be = x

Decreased value  = 0.35

Current value = 104000

x - 0.35x  = 104000

0.65x = 104000

x = 104000/0.65

x = 160,000

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X²-X+6

X+6

In the given picture with 4 lines l, m and r, s. The l and m, r and s line are parallel lines.

Given that,

There is a picture with 4 lines l, m and r, s.

We have to check that those lines are parallel or not

To check that the line are parallel we have a condition.

If two lines are cut by the transversal and corresponding angles are congruent then we can say that those 2 lines are parallel.

In the figure we can see that ∠2 and∠6 are congruent.

So, we can say that lines r and s are parallel lines.

Similarly,

In the figure we can see that ∠1 and∠7 are congruent.

So, we can say that lines l and m are parallel lines.

Therefore, the l and m, r and s line are parallel lines.

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Answer:

9, 18, 27, 36, 45

Step-by-step explanation:

multiples is like finding the factors. like 1*9=9 and 2*9=18, 9*3=27, 4*9=36, 9*5=45

The rate of change of the linear equation that has the given points on its graph is; -2.

The rate of change of a linear function can be determined by using the following formula:

Rate of change = change in y / change in x = y2 - y1 / x2 - x1.

Given the following points on a graph of a linear function:

​(−5​,4​) = (x1, y1)

​(−2​,−2​) = (x2, y2)

Plug in the values

Rate of change = change in y / change in x = (-2 - 4) / (-2 -(-5))

Rate of change = -6 / 3

Rate of change = -2 / 1

Rate of change = -2

Thus, the rate of change of the linear equation that has the given points on its graph is; -2.

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Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

You can use the Pythagorean Theorem, which is [tex]a^{2}+ b^{2}= c^{2}[/tex]. So the the distance from -9 to -5 is 4 and the distance from 8 to 6 is 2.

So [tex]4^{2} +2^{2} =c^{2}[/tex]. Which equals [tex]20=c^{2}[/tex].

Then you square root [tex]c^{2}[/tex] to make it c, then you do that to the other side. So you have [tex]\sqrt{20}=c[/tex].

Which equals [tex]2\sqrt{5}[/tex].

Or you can use the Distance Formula, which is [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex].

The [tex]x_{1}[/tex] is -5 and the [tex]x_{2}[/tex] is -9. The [tex]y_{1}[/tex] is 6 and the [tex]y_{2}[/tex] is 8. When you plug that in you get [tex]\sqrt{(-9--5)^{2} +(8-6))^{2} }[/tex]. When you simplify that you get [tex]\sqrt{20}[/tex].

Which equals [tex]2\sqrt{5}[/tex].

Using the binomial distribution, there is a 0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.

For each adult, there are only two possible outcomes, either they received the vaccine or they did not. The probability of an adult receiving the vaccine is independent of any other adult, hence the binomial distribution is used to solve this question.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, we have that:

The probability that exactly 20 adults received a flu vaccine is P(X = 20), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 20) = C_{50,20}.(0.371)^{20}.(0.629)^{30} = 0.1094[/tex]

0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.

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Answer:

360 million written in scientific notation is 3.6 × 108.

Step-by-step explanation:

Answer:

Kinetic energy

Step-by-step explanation:

because when something is in motion it gains kinetic energy

Answer:

5/11

Step-by-step explanation:

make sure next time to say how much books do you have I have answered a similar question with this wording so I hope this helps :))

When Lydia buys 4 jewelry sets, the amount spent is $24.

From the information given, we are told that Michelle is preparing for her birthday and that each set is $5 and shipping is $4 flat. If Lydia buys 4 jewelry sets.

Therefore, the equation will be:

4 + (5 × x)

where x = number of set

4 + 5x

4 + (5 × 4)

= 4 + 20

= $24

The amount is $24.

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Answer:

hope this explanation helps you

Answer:

[tex]\textsf{b)} \quad -\dfrac{3\sqrt{13}}{13}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\textsf{If}\; \tan(\theta)=-\dfrac{2}{3} \implies \sf O=2 \; \textsf{and} \; A=3.[/tex]

Use Pythagoras Theorem to calculate the length of the hypotenuse:

[tex]\sf \implies O^2+A^2=H^2[/tex]

[tex]\implies \sf H=\sqrt{O^2+A^2}[/tex]

[tex]\implies \textsf{H}=\sqrt{2^2+3^2}[/tex]

[tex]\implies \textsf{H}=\sqrt{13}[/tex]

Therefore, substituting the values of A and H into the cosine ratio:

[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}[/tex]

[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}\cdot \dfrac{\sqrt{13}}{\sqrt{13}}[/tex]

[tex]\implies \cos \theta=\dfrac{3\sqrt{13}}{13}[/tex]

As the terminal side of the angle is in Quadrant II, and cosine is negative in Quadrants II and III, the exact value of cos(θ) is:

[tex]\implies \cos \theta=-\dfrac{3\sqrt{13}}{13}[/tex]

The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.

The information illustrates that the project manager is calculating work forecasts and he manager's team completed 4/5 of a job in 16 days.

Therefore, the amount that was done each day will be:

= 4/5 ÷ 16

= 4/5 × 1/16

= 4/80

= 1/20

Therefore, the error that the manager made was that the manager divided 5/4 by 16 instead of dividing 4/5 by 16. This was the reason that he got 5/64.

Therefore, the correct option is B.

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The weight represents the 42nd percentile.

=6.712

This is further explained below.

Generally, the given data is

8.3,6.5,6,6,5,4,6.7,6.5,8: 1,9.2,6.4,8 0,6.8,9.0,8.7,9.3,8.0

The ascending order of the data is

5.4,6.0,6.4,6.5,6.5,6.7,6.8,8.0,8.0,8.1,8.3,8.7,9.0

n=15.

42ndPercentile

=P_{42}

[tex]=42\left(\frac{n+1}{100}\right)^{\text {th }} \text { term } \\[/tex]

[tex]&=42\left(\frac{16}{100}\right) \text { th term } \\[/tex]

=6.72th term

=6th+0.72(72nd -6th) term

=6.7+0.72(6.8-6.7)

=6.712

In conclusion, the weight represents the 42nd percentile.

=6.712

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