Sam has 60 toy cars. 20% of the cars are red.
How many cars are red?
A. 12
B. 20
C. 48
D. 40

[tex]r = \sqrt{\dfrac{3V}{\pi h}}[/tex]

Step-by-step explanation:

Multiply both sides by 3 to get

[tex]\pi r^2h = 3V[/tex]

Then divide both sides by [tex]\pi h[/tex] and you'll get

[tex]r^2 = \dfrac{3V}{\pi h}[/tex]

To solve for r , you need to take the square root of both sides to get

[tex]\sqrt{r^2} = r = \sqrt{\dfrac{3V}{\pi h}}[/tex]

[tex]-5x+3y = 10~~~~ .....(i)\\\\2x+5y =-35~~~ ....(ii)\\\\\text{Multiply equation (ii) by}~ \dfrac 35~ \text{ and do (ii) -(i)}\\\\\\\dfrac 35(2x+5y) - (-5x+3y) = \dfrac 35}(-35) - 10\\\\\implies \dfrac{6x}5 +3y + 5x -3y = -21-10 = -31\\\\\implies \dfrac{6x + 25x}5 = -31\\\\\implies 31x = -31 \times 5\\\\\implies x = -5\\\\\text{Substitute }~x=-5~ \text{in equation (ii):}\\\\2(-5) +5y =-35\\\\\implies -10 +5y = -35\\\\\implies 5y = -35 +10 = -25\\\\\implies y = - \dfrac{25}5 = -5[/tex]

[tex]\text{Hence,}~ \textbf{(x,y) = (-5, -5)}[/tex]

Answer:

Step-by-step explanation:

Sorry no one answered your question sooner. First Let x = what the daughter receives

Then 180000 - x is what the son will receive. Notice that if you add these together you get the total, 180000. You write a proportion and cross multiply to solve. Since x = 80000, the son will receive 80000. The daughter will receive 100000.

Answer:

Step-by-step explanation:

Answer:

1/15

Step-by-step explanation:

2/3 x 1/10 = 2/30 or 1/15

Answer:

1/15

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, a ) and (x₂, y₂ ) = (9, - 4 )

m = [tex]\frac{-4-a}{9-6}[/tex] = [tex]\frac{-4-a}{3}[/tex]

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

2x - 3y = 6 ( subtract 2x from both sides )

- 3y = - 2x + 6 ( divide through by - 3 )

y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Parallel lines have equal slopes , then

[tex]\frac{-4-a}{3}[/tex] = [tex]\frac{2}{3}[/tex] , so

- 4 - a = 2 ( add 4 to both sides )

-a = 6 ( multiply both sides by - 1 )

a = - 6 → A

It would cost an employee $443.52 to purchase one of these laptops at the sale.

The selling price of the laptops is $720 each. The cost price is 20 percent more than the cost price.

Cost price = Selling price - 20% of cost price

Cost price = 720 - 20% * 720 = $576

At the release, the laptops are at 23% off the store's cost. Hence:

Price of laptop at release = 576 - 23% of 576

Price of laptop at release = $443.52

It would cost an employee $443.52 to purchase one of these laptops at the sale.

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Answer:

No it does not

Step-by-step explanation:

Two points simplify to 1/6 whilst the other, 1/5

Answer:

At 1:40 pm you will reach the market.

Step-by-step explanation:

Distance (d) = 11 km

Average speed (v) = 3 km/h

Formula:

[tex] \rm Average \: speed = \dfrac{Distance}{Time} \\ \\ \rm 3 = \dfrac{11}{t} \\ \\ \rm t = \dfrac{11}{3} \\ \\ \rm t = 3 \frac{2}{3} \\ \\ \rm t = 3 hr \: 40min[/tex]

It will take 3 hours 40 minutes to reach the market.

So, if you set off for the market at 10 am you will reach market by 1:40 pm (10 am + 3hr 40min).

Answer:

g(x) = (5x + 3)/ x - 7

Step-by-step explanation:

Let g(x) = y

y = (7x + 3)/x - 5

Make x the subject

xy - 5y = 7x + 3

xy - 7x = 5y + 3

x(y - 7) = 5y + 3

x = (5y + 3)/ y - 7

Therefore, the inverse of the function = (5x + 3)/ x - 7

Answer:

Approximately [tex]\text{$0.26$ radian}[/tex] every minute.

Step-by-step explanation:

Convert the unit of velocity (kilometers-per-hour) to meters-per-minute so as to match the unit of radius (meters) and angular velocity (per-minute.)

[tex]\begin{aligned}v &= 11\; \rm km \cdot h^{-1} \\ &= 11 \times \frac{1000\; \rm m}{1\; \rm km} \times \frac{1\; \rm h}{60\; \text{minute}} \\ &\approx 183.33\; {\rm m} \cdot\text{minute}^{-1}\end{aligned}[/tex].

Calculate the circumference of this circle:

[tex]\begin{aligned}c &= 2\,\pi\, r \\ &= 2 \, \pi \times 700\; \rm m \\ &\approx 4398.2\; \rm m\end{aligned}[/tex].

Find the time required (in minutes) for this vehicle to go around this circle:

[tex]\begin{aligned}\frac{4398.2\; \rm m}{183.33\; {\rm m} \cdot \text{minute}^{-1}} \approx 23.990\; \text{minute}\end{aligned}[/tex].

A full circle corresponds to an angle of [tex]2\, \pi \; \text{radian}[/tex] ([tex]360^{\circ}[/tex].) In other words, this vehicle would have turned [tex]2\, \pi \; \text{radian}\![/tex] in approximately [tex]23.990\; \text{minute}[/tex] if it travels at a constant speed. The rate at which this vehicle turn would be:

[tex]\begin{aligned}\frac{2\, \pi}{23.990\; \text{minute}} \approx 0.26\; \text{minute}^{-1}\end{aligned}[/tex].

In general, for angular velocity [tex]\omega[/tex], radius [tex]r[/tex], and velocity [tex]v[/tex], [tex]v = \omega\, r[/tex]. After updating the units, the angular velocity of this vehicle (the rate at which it turns) may also be found as:

[tex]\begin{aligned}\omega &= \frac{v}{r} \\ &\approx \frac{183.33\; \rm m \cdot \text{minute}^{-1}}{700\; \rm m} \\ &\approx 0.26\; \text{minute}^{-1}\end{aligned}[/tex].

Answer: I'm assuming it's 20/900 because there is 900 songs in total.

Step-by-step explanation:

The probability that your favorite song is one of the 20 songs you hear that night is 1/900.

To find the probability that your favorite song is one of the 20 songs you hear that night, we can use the concept of probability.

The total number of songs in the karaoke song book is 900. Since each song is equally likely to be picked, the probability of randomly selecting your favorite song from the entire song book is 1 out of 900, or 1/900.

Now, you will hear a total of 20 songs that night. Out of those 20 songs, you want to know the probability that your favorite song is one of them. Since there is only one favorite song, the favorable outcomes are 1.

Therefore, the probability that your favorite song is one of the 20 songs you hear that night is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = 1 / 900

So, the probability that your favorite song is one of the 20 songs you hear that night is 1/900.

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The perimeter of a triangle is the sum of its side lengths.

The perimeter of triangle ACD is 40 units

Start by calculating the values of x and y, using the following equivalent ratios

[tex]6 : 4 = x - 2 : x - 4[/tex]

[tex]6 : 10 = 6 + x - 2 : y[/tex]

So, we have:

[tex]6 : 4 = x - 2 : x - 4[/tex]

Express as fraction

[tex]\frac 64 = \frac{x-2}{x-4}[/tex]

Cross multiply

[tex]6x - 24 = 4x - 8[/tex]

Collect like terms

[tex]6x - 4x = 24 - 8[/tex]

[tex]2x = 16[/tex]

Divide both sides by 2

[tex]x = 8[/tex]

Also, we have:

[tex]6 : 10 = 6 + x - 2 : y[/tex]

Express as fraction

[tex]\frac 6{10} = \frac{6 + x -2}{y}[/tex]

Substitute 8 for x

[tex]\frac 6{10} = \frac{6 + 8 -2}{y}[/tex]

[tex]\frac 6{10} = \frac{12}{y}[/tex]

Cross multiply

[tex]6y = 120[/tex]

Divide both sides by 6

[tex]y = 20[/tex]

The perimeter of triangle ACD is then calculated as:

[tex]P =6 + x - 2 + y + x - 4 + 4[/tex]

Substitute values for x and y

[tex]P =6 + 8 - 2 + 20 + 8 - 4 + 4[/tex]

[tex]P =40[/tex]

Hence, the perimeter of triangle ACD is 40 units

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Answer:

the answer is

1. 11.33

2. 5.9

3. 8.1

Answer: 31.57

Step-by-step explanation:

41% of 77 is what?

41% of 77 is Y

Equation: P% * X = Y

Solving our equation for Y

Y = P% * X

Y = 41% * 77

Converting percent to decimal:

p = 41%/100 = 0.41

Y = 0.41 * 77

Y = 31.57

Answer:

final balance = 24,634.02

compound interest = 19,634.02

Step-by-step explanation: not my answer

Answer:

a. 125

Step-by-step explanation:

the angle labeled "x" is supplementary with the angle that has a measure of 55°

Supplementary angles add up to equal 180°

This means that x + 55 must equal 180

Note that we've just created an equation that we can use to solve for x.

We now solve for x using the equation we just created.

x + 55 = 180

subtract 55 from both sides

x = 125

The answer is a

Answer:

B = $140

Step-by-step explanation:

for part A, the graph is linear line with a Y intercept at (0,65) so this means that if you were to have no charms it would cost 65 dollars, since the y axis represents cost. then for every 1 increment on the x axis (number of charms) the Y value increases by 25 so the slope is [tex]\frac{25}{1}[/tex]

we also can conclude that there is no negative domain since you cannot have negative charms, and the range begins at 65 since you cannot get a bracelet for less money

for part B, y=25x+65

so for three charms, x is represented as 3 so y=25(3) +65 which is 75+65=y= $140

Answer:

y = -9x + 18.

Step-by-step explanation:

The general form is y = mx + c , where m = the slope and c = y-intercept.

[tex]\huge\boxed{Hi \: there! :)}[/tex]

We are given the slope of the line: -9.

We are also given its y-intercept: 18.

Slope-Intercept Form:

[tex]\huge\sf\{y=mx+b[/tex]

Where

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

Plug in the values:

y=-9x+18

[tex]\huge\boxed{Therefore, \: our \: equation \: is: y=-9x+18}[/tex]~An Unknown Dreamer

Good luck!

Answer:

10.

here,

h=c

b=5

p=12

,we know that,

h²=b²+p²(pythagoras theorum )

c=5²+12²

c=25+144

c=169

hence the value of c is 169.

93.06% of the race is longer than 236 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]

Given that μ = 310, σ = 50

For x > 236:

[tex]z=\frac{236-310}{50}=-1.48[/tex]

From the normal distribution table:

P(x > 236) = P(z > -1.48) = 1 - P(z < -1.48) = 1 - 0.0694 = 0.9306 =  93.06%

93.06% of the race is longer than 236 minutes.

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Answer:

rectangle= 22*9 = 198ft

triangle=11*10 = 110 ft

110+ 198 = 308 polygon

Answer:

[tex]3 {( \frac{1 - x}{2}) }^{2} = 3 \times {(1 - x)}^{2} \div {2}^{2} \\ =3 \times (1 - 2 \times 1 \times x + {x}^{2}) \div 4 \\ = 3 \times (1 - 2x + {x}^{2} ) \div 4 \\ = \frac{3}{4} (1 - 2x + {x}^{2})[/tex]

[tex] \bold \pink{ \underline{hope \: it \: helps}}[/tex]

Answer:

So we will use combinations, as it does not matter what order they get chosen in.

The combinitoric that you will plug in to your calculator is: nCr(12,7)

Therefore, the answer is 792

The statements that are true based on the scatter plot and the given equation of line of best-fit are:

Given that the correlation coefficient of -0.951, it suggests that the policy cost and ages of the men as shown in the scatter plot are strongly negatively correlated.

This means that, the lower the higher the age of the men, the lesser the cost of a car insurance policy.

The slope value in the equation, y = -315.67x + 8986.5, is -315.67, which is the average cost of a car insurance policy per year.

Therefore, the statements that are true based on the scatter plot and the given equation of line of best-fit are:

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