Mr. black class has a female student to male student ratio of 3:2. If Mr. Black's class has 18 girls, how many boys does he have? explain in writing how you determined your answer.

Answer:

[tex]\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&\dfrac{4}{3}\pi &2\pi \\&&\\2&\dfrac{32}{3}\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&\dfrac{256}{3}\pi &128\pi \\&&\\5&\dfrac{500}{3}\pi &250\pi\end{array}[/tex]

Step-by-step explanation:

Use formulas for the volumes:

[tex]V_{sphere}=\dfrac{4}{3}\pi r^3,\\ \\V_{cylinder}=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.[/tex]

1. When r=1,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 1^3=\dfrac{4}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 1^3=2\pi.[/tex]

2. When r=2,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 2^3=\dfrac{32}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 2^3=16\pi.[/tex]

3. When r=3,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 3^3=36\pi,\\ \\V_{cylinder}=2\pi \cdot 3^3=54\pi.[/tex]

4. When r=4,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 4^3=\dfrac{256}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 4^3=128\pi.[/tex]

5. When r=5,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 5^3=\dfrac{500}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 5^3=250\pi.[/tex]

Note that for all r,

[tex]\dfrac{V_{sphere}}{V_{cylinder}}=\dfrac{\frac{4}{3}\pi r^3}{2\pi r^3}=\dfrac{2}{3}.[/tex]

Answer:

Please, see the attached file.

Thanks.

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

hyperbola

Step-by-step explanation:

49x^ 2 - 16y^ 2 = 784

Divide each side by 784

49/784x^ 2 - 16/784y^ 2 = 784

x^2/16 - y^2/49 = 1

This is a hyperbola  centered at (0,0)

If it has subtraction, it has to be a hyperbola

Answer:

Thus, The conic which fits the given equation correctly is hyperbola

Step-by-step explanation:

The equation is given to be : 49x² - 16y² = 784

Now, we need to find the correct conic section which fits this given equation

So, to find the correct conic, we will reduce the given equation into the standard form :

So, make R.H.S. 1 by dividing each term by 784

[tex]\frac{49x^2}{784}-\frac{16y^2}{784}=\frac{784}{784}[/tex]

[tex]\implies \frac{x^2}{16}-\frac{y^2}{49}=1[/tex]

[tex]\implies\frac{x^2}{4^2}-\frac{y^2}{7^2}=1[/tex]

This is the standard equation of hyperbola, where a = 4 and b = 7

Thus, The conic which fits the given equation correctly is hyperbola

Answer:

75.00

Step-by-step explanation:

Let x be unknown number. Then

x is 100% and

60 is 80%.

Write a proportion:

[tex]\dfrac{x}{60}=\dfrac{100}{80},\\ \\x=\dfrac{60\cdot 100}{80}=75=75.00.[/tex]

The answer is C) 41 hope this helped

d. $50.94

The deposit is for 1 year (4 quarters) at an annual rate of 5% (1.25% per quarter). The table value for those parameters is 1.05094. Multiply this value by the $1000 amount Miguel deposited to find his ending balance.

... ending balance = $1000 × 1.05094 = $1050.94

Since his deposit amount was $1000, the interest earned is ...

... $1050.94 -1000.00 = $50.94

Answer:

1 min and 40 sec

Step-by-step explanation:

well for every ounce it takes 5 sec

5 x 20 = 100

I hope i did this right ^_^

Answer:

100 seconds

Step-by-step explanation:

We are given the following data in the question:

                              Time:      0       30       60       90      120      

Ounces of Bottles filled:      0        6         12         18       24

Where time is in seconds and the bottles are filled in ounces.

Amount of water filled in 30 seconds =  6 ounces

Amount of time taken to fill 1 ounce of water = [tex]\frac{30}{6}[/tex] = 5 seconds

We need to find the time to fill 20 Ounces

It is clear from the data that 18 ounces of water will fill in 90 seconds.

We have to find the time to fill 2 ounces of water.

Time taken to fill two ounces of water = [tex]2\times 5[/tex] seconds = 10 seconds.

Total time taken to fill 20 ounces of water =  990 + 10 = 100 seconds =  1 Minute 40 Seconds

Answer:

speed = (3/8 mi)/(3/5 h)

Step-by-step explanation:

... speed = distance/time

Fill in the given values:

... speed = (3/8 mi)/(3/5 h)

_____

Comment on units

You can use the units to provide both guidance and assurance. You know speed is generally expressed in miles per hour. If you consider "per" to mean "divided by", this expression of units tells you speed is calculated by dividing miles by hours.

If you leave the units with the numbers, as we have above, they enter into the calculation the same way any variable might. You can do the arithemetic with the numbers, and you can indicate the arithmetic with the units (just as you would with any variables). Here, the result of evaluating the equation would be ...

[tex]\displaystyle\frac{\frac{3}{8}\,\text{mi}}{\frac{3}{5}\,\text{h}}=\frac{\frac{3}{8}}{\frac{3}{5}}\,\frac{\text{mi}}{\text{h}}=\frac{5}{8}\,\text{mi/h}[/tex]

The fact that the units come out mi/h (the units of speed) provides assurance that you probably did the math correctly.

Answer:

three eighths over three fifths = five eighths mile per hour

Step-by-step explanation:

A. -59,048

The first pair of terms sums to -8; the second pair to -72. Each pair after that sums to a value 9 times the previous one. Then the sum of 10 terms is ...

... (-8) + (-72) + (-648) + (-5832) + (-52488)

Before you even add this up, you know the answer choice is A. The sum is ...

... -59, 048

_____

Using the formula

The formula for the sum of a geometric series is ...

... S = a1·(r^n -1)/(r -1) . . . . . where a1 = 4 is the initial term, r=-3 is the common ratio, and n=10 is the number of terms.

Filling in the values and doing the arithmetic, we have ...

... S = 4·((-3)^10 -1)/(-3-1) = 4·(59,049 -1)/(-4) = -59,048

Answer:

-59,048

Step-by-step explanation:

60%

The percent change can be found from ...

... ((new value)/(old value) -1) × 100%

... (1520/950 -1) × 100% . . . . . . filling in your numbers

... (1.6 - 1) × 100% = 60% . . . . . . simplify

Attendance this year was 60% higher than last year.

Answer:

C.) 0.9656

Step-by-step explanation:

Using a z-table look for -1.82 and we obtain : 0.0344.  So what's the probability that z > -1.82 is the same as saying when is z > 0.0344? Since we're talking about probabilities of an outcome from ranging from 0% to 100% meaning 0 through 1 in decimals then:

1 - 0.0344 = 0.9656

So the probability that z>-1.82 is C.) 0.9656

Using the normal distribution, it is found that there is a 0.9656 probability that z is greater than -1.82, option B.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

z = -1.82 has a p-value of 0.0344.

1 - 0.0344 = 0.9656.

0.9656 probability that z is greater than -1.82, option B.

A similar problem is given at https://brainly.com/question/5954134

Answer:

y = ($0.5/ch) x + $10

Step-by-step explanation:

Let

x = number of chores

y = allowance

The relationship between y and x can be expressed in a linear equation in the slope-intercept form.

y = mx + b

where

m is the slope

b is the y-intercept

We have the ordered pairs (8, 14) and (12, 16). We can calculate the slope using the following expression.

m = Δy/Δx = $16-$14/12ch-8ch = $0.5/ch

The equation is

y = ($0.5/ch) x + b

We will replace the first point in the previous equation.

$14 = ($0.5/ch) 8ch + b

b = $10

The final equation is

y = ($0.5/ch) x + $10

This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50. The final equation is y = ($0.5/ch) x + $10.

We are given that Hari's allowance varies depending on the number of chores he does.

We are also given two points, (8, 14) and (12, 16), that represent the relationship between the number of chores and the allowance.

We can use these two points to find the slope of the line.

The slope is equal to rise over run, which in this case is equal to

$16 - $14 / 12 - 8 = 0.5/ch.

We can now plug the slope and one of the points into the slope-intercept form of the equation to find the value of b, the y-intercept.

We will use the point (8, 14).

y = mx + b

14 = ($0.5/ch) 8ch + b

14 = $4 + b

b = $10

The final equation is y = ($0.5/ch) x + $10.

This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50.

Learn more about slope-intercept form here:

https://brainly.com/question/22057368

#SPJ3

Answer:

x=8

Step-by-step explanation:

Since this is  an isosceles triangle, the angles in the triangle are 4x, 4x, and 84.  The sum of the three angles in a triangle are 180.

4x+4x+ 84 = 180

Combine like terms

8x+84 = 180

Subtract 84 from each side

8x+84-84 = 180 - 84

8x = 96

Divide each side by 8

8x/8 = 96/12

x = 8

Evan has the most in his beaker.

This is because:

0.75 < 0.8 < 1.05 < 1.2.

Answer:

Step-by-step explanation:

14 cows

46 turkeys

If all the animals were turkeys, there would be 120 legs. There are 28 more than that. Replacing a turkey with a cow adds 2 legs, so there must be 14 such replacements.

There are 14 cows and 46 turkeys.

_____

Check

14×4 + 46×2 = 56 + 92 = 148 . . . . legs

14 + 46 = 60 . . . . . . heads

x-intercept: -4

y-intercept: +1

The x-axis is the horizontal line on the graph with "x" marked at the right end. It is also identified by the "0" among the numbers on the vertical scale at the left side of the graph.

You can consider the x-axis to be a number line. The numbers on that number line are those of the horizontal sequence of numbers at the bottom of the graph. (On many graphs, they're shown adjacent to the x-axis in the middle of the page. That's not the case here.) These numbers are the x-coordinate of any point with the corresponding horizontal position.

The x-intercept is where the blue line crosses the x-axis. It is marked with a dot on the vertical line that has -4 at the bottom. That -4 is the x-coordinate of the x-intercept, the value the problem is asking for.

___

The y-axis is the vertical line on the graph with "y" marked at the top end. It is also identified by the "0" among the numbers on the horizontal scale at the bottom of the graph.

You can consider the y-axis to be a number line. The numbers on that number line are those of the vertical sequence of numbers at the left side of the graph. (On many graphs, they're shown adjacent to the y-axis in the middle of the page. That's not the case here.) These numbers are the y-coordinate of any point with the corresponding vertical position.

The y-intercept is where the blue line crosses the y-axis. It is marked with a dot on the horizontal line that has 1 at the left side. That 1 is the y-coordinate of the y-intercept, the value the problem is asking for.

___

The (x, y) coordinates of the x-intercept are (-4, 0). The y-coordinate is always zero, because that is the definition of x-intercept: the x-coordinate of the point on the graph where y=0.

The (x, y) coordinates of the y-intercept are (0, 1). The x-coordinate is always zero, because that is the definition of y-intercept: the y-coordinate of the point on the graph where x=0.

Answer:

24p

Step-by-step explanation:

This is the difference of 2 squares:-  a^2 - b^2 = (a + b)(a - b).

So here we have:-

(2p + 3)^2 - (2p - 3)^2

= (2p + 3 + (2p - 3))(2p + 3 - (2p - 3))

= (2p + 3 + 2p - 3)(2p + 3 - 2p + 3

= 4p * 6

= 24p   (answer)

Final answer:

To simplify the expression (2p+3)² - (2p-3)², apply the difference of squares formula to get ((2p+3) + (2p-3)) * ((2p+3) - (2p-3)), which simplifies to 24p.

Explanation:

To simplify the expression (2p+3)² - (2p-3)², we need to apply the difference of squares formula, which is

a² - b² = (a+b)(a-b).

Here, a is (2p+3) and b is (2p-3). The result will be the product of the sum and difference of a and b.

Let's perform the simplification step-by-step:

Simplify both products:
 (4p) * (6)

Finally, multiply the results to get the simplified expression:
24p

The simplified result of the expression (2p+3)² - (2p-3)² is 24p.

Answer:

1636.4 ft/min

Step-by-step explanation:

Multiply by the conversion factors that change the units you have to the units you want.

(200 yd)/(22 s) × (3 ft/yd) × (60 s/min) = 18000/11 ft/min ≈ 1636.4 ft/min

Answer:

15 ft²

Step-by-step explanation:

The volume of a cone is given in terms of the base area (B) and height (h) by the formula ...

... V = (1/3)Bh

Putting in the given numbers, you have ...

... 35 ft³ = (1/3)B(7 ft)

... B = (35·3/7) ft² = 15 ft² . . . . . . solve for B

Answer:

14 bags

Step-by-step explanation:

If you earn $17, to find the number of bags substitute 17 for y in the equation y=0.50x+10. Then use inverse operations to solve for x.

17 = 0.50x+10               Subtract 10 from both sides.

17-10 = 0.50x

7=0.50x                        Divide both sides by 0.50

7/0.50 = x

14 =x

Answer:

Helen's salary increased more.

Step-by-step explanation:

We know that Clint's salary increased from ​$24000 to $36000 over a​ three-year period.​

So the increase in Clint's salary will be = 36000 - 24000 = $12000

While Helen's salary increased from ​$29000 to $43, 500 over the same period of 3 years.

So the increase in Helen's salary will be = 43500 - 29000 = $14500

Therefore, in absolute terms, Helen's salary has increased more.

Answer:

See attached

Step-by-step explanation:

For each increase of 1 in the index, the function value doubles. The size of the function value rapidly exceeds the limit of any linear grid.

We've shown a few points plotted. Perhaps it will give you the idea of what you need to do.

Answer:

The index starts at 1, so the domain of the function is D = {1, 2, 3, 4, 5, 6, . . .}. The sequence is based on the add 3 rule. So, to get more terms of the sequence, add 3 to the last term to get the next one. The range values include the terms of the sequence, so the range is R = {1, 4, 7, 10, 13, 16, . . .}.

To graph the function of this sequence on a coordinate plane, pair the domain values with the corresponding range values to get {(1, 1), (2, 4), (3, 7), (4, 10), (5, 13), (6, 16), . . .}. Then plot these points on the graph.

Step-by-step explanation:

The third-degree polynomial with – 3 and 2 as its only zeros is x³ + x² – 8x – 12, which can be factored as (x+3)(x-2)(x-2).

A third-degree polynomial with – 3 and 2 as its only zeros must be in the format of A(x+3)(x-2)(x-C), where A and C are constants, and C is possibly another zero of the polynomial.

Given the four options, the only polynomial that fits this format and has – 3 and 2 as zeros is x³ + x² – 8x – 12.

To verify, we can factor it: (x+3)(x-2)(x-2), which shows that 2 is a zero of multiplicity 2, and – 3 is also a zero.

There are no other real zeros besides these, so it is the correct polynomial.

Answer:

4 cm

Step-by-step explanation:

The midpoint segment has length ...

... L = AB/2 + BC + CD/2 = 16 cm

The entire segment has length ...

... AD = AB + BC + CD = 28 cm

If we subtract AD from 2L, we have ...

... 2L - AD - 2L = 2(AB/2 +BC + CD/2) - (AB +BC +CD) = 2(16 cm) -28 cm = 4 cm

... AB +2BC + CD -AB -BC -CD = 4 cm . . . . remove parentheses

... BC = 4 cm . . . . simplify

Answer:

5 weeks

Step-by-step explanation:

John creates apps at the rate ...

... (3 apps)/(6 weeks) = 1/2 app/week

Ben creates apps at the rate ...

... (3 apps)/(2 weeks) = 3/2 app/week

Together, they create ...

... (1/2) app/week + (3/2) app/week = 2 app/week

So, the time for 10 apps is ...

... (10 app)/(2 app/week) = 5 week

_____

Comment on the problem

If the guys actually work at a uniform rate like this, the result after 5 weeks will be 9 completed apps and 2 half-completed apps. Their rate is 10 apps in 5 weeks, but their actual output in that time period may not be 10 completed apps.

One should beware of the "mythical man-month." Rates of job completion depend on many factors. Individual average rates cannot always be summed when folks "work together."

Answer:

The baseball team plays 25 games

Step-by-step explanation:

If they have lost 5 games and that is 20 %, we can make a ratio.

games/ total = 20/100

5              20

------ = -----------

total        100

Using cross products

5*100 = 20*total

500 = 20* total

Divide by 20 on each side

500/20 = 20/20 * total

25 = total

Answer:

its D which is also 25 games

Step-by-step explanation:

The problem is symmetrical, so proof for ΔCDG can serve as a model for proof for ΔCEH.

∠DGA ≅ ∠DCA ≅ 90° . . . . given

∠GAD ≅ ∠CAD . . . . definition of angle bisector AD

AD ≅ AD . . . . reflexive property

ΔDGA ≅ ΔDCA . . . . AAS congruence theorem

CD ≅ GD . . . . CPCTC

∴ ΔCDG is isosceles . . . . definition of isosceles triangle (2 sides congruent)

_____

To do the same for ΔCEH, replace "D" with "E", replace "G" with "H", and replace "A" with "B". The rest of the logic applies.

Answer:

Step-by-step explanation:

1. For this sort of question a graphing calculator or spreadsheet are suitable tools. The attached shows the linear regression line to have the equation ...

... y = 0.937976x + 12.765

where x is years since 2000, and y is average tuition cost in thousands.

2. The y-intercept is the year-2000 tuition: $12,765.

3. Evaluating the formula for x=20 gives y ≈ 31.524, so the year-2020 tuition is expected to be $31,524.

4. The slope is the rate of change of tuition with respect to number of years. It is the average increase per year (in thousands). It amounts to about $938 per year.

5. [not a math question]

Answer:

Answer - 160

Step-by-step explanation:

2L+2W = 430

L = 3W-5

2(3W-5)+2W = 430

6W-10+2W = 430

8W = 440

W = 55 and L = 3(55)-5 = 160

Answer:

Length = 160 and width = 55 yards

Step-by-step explanation:

Perimeter =  2L + 2W  where L = the length and W = the width.

L = 3W - 5   (given).

So substituting for L is the formula for the perimeter:-

2(3W - 5) + 2W = 430

6W - 10 + 2W = 430

8W = 440

W = 55 yards.

So the Length L = [430 - 2(55]) / 2  = 160 yards.

Answer:

HL Congruence Theorem

Step-by-step explanation:

Answer:

HL congruence theorem

Step-by-step explanation:

Given that WZX is an isosceles triangle with sides WX=WZ

Also given that WY is altitude on side XZ

Consider triangles WXY and WZY

WX=WZ             Given

WY=WY             REflexive property

Angle wyz =angle wyx     Right angle

Hence by HL congruence theorem, since one leg and hypotenuse are equal we get the two triangles to be congruent.

Answer:

3 gallons? haha

Step-by-step explanation:

The question did not make that much sense but the only amount of anything given in the question was 3 gallons.

The questions says the maid gets 3 gallons of milk from the cow everyday. SO if we are wondering how much she makes in one day it has to be 3 gallons because it does not give any other information...

Assuming the traditional context of 'The Twelve Days of Christmas' with 8 maids a-milking, each maid gets 3 gallons of milk from her cow, so they would collectively get 24 gallons of milk in one day.

The student is asking how much milk the maids a-milking would get in one day if each maid gets 3 gallons of milk from her cow. To find the total amount of milk gathered by the maids in one day, we need to know the number of maids a-milking. Assuming a traditional context of the song 'The Twelve Days of Christmas', there are 8 maids a-milking. Therefore, the calculation would be:

8 maids x 3 gallons per maid = 24 gallons

So, the maids a-milking would get a total of 24 gallons of milk in one day.

It is important to note that the unit of measurement appropriate for such a quantity of milk is gallons, which is useful for larger capacities, such as the amount produced by a dairy farm operation.