In an experiment, a student randomly chooses an answer to two multiple-choice questions. The first question has 4 answers to choose from, and the second question has 5 answers to choose from. How many outcomes are in the sample space? Enter your answer in the box.

Answer: #5 is 10 student tickets and 20 adult tickets

Step-by-step explanation:

Answer:

20 adult tickets sold and 15 student tickets sold

Step-by-step explanation:

Answer:

x = 4.057682724 pts

Step-by-step explanation:

A pint is equal to 473.176473 milliliters

473.176473 milliliters         1920 ml

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

1 pt                                        x pts

using cross products

473.176473  * x = 1902

 divide each side by 473.176473

x = 1920 /473.176473

x = 4.057682724 pts

U.S. liquid pint:

1 pint = 473.2 ml therefore 1 ml = 1/473.2 pints = 0.0021 pints.

1,920 ml = 1,920 · 0.0021 pints = 4.032 pints

U.S. dry pint:

1 pint = 550.6 ml therefore 1 ml = 1/550.6 pints = 0.0018 pints

1,920 ml = 1,920 · 0.0018 pints = 3.456 pints

f(x) > 0 - I and II quadrant

f(x) < 0 - III and IV quadrant

Look at the picture.

A. F(x) < 0 on the interval x < 0.     TRUE

B. F (x) > 0 on the interval x <0.      FALSE

C. F (x) < 0 on the interval 0 < x < 1.      TRUE

D. F (x) > 0 on the interval 0 < x < 1.      FALSE

E. F (x) < 0 on the interval 1 < x < 3.     FALSE

F. F (x) > 0 on the interval 1 < x < 3.      TRUE

G. F (x) < 0 on the interval x > 3.     TRUE

H. F (x) > 0 on the interval x > 3.      FALSE    

Answer:

The function is an exponential,

f(x) = A exp(log(3)x) = 2×3^x = 2(3)^x

The first point you graph for any exponential is (0,A), here (0,2). After (1,6), the next point might be (2,18).

Step-by-step explanation:

(0,2×3^0) = (0,2)

(1,2×3^1) = (1,6)

(2,2×3^2) = (2,2×9) = (2,18)

2(3)^x ought to be written 2×3^x, that is, two times three raised to the x power. x can be any real number.

Since 3 = exp(log(3)), we can substitute for 3 and write 2×exp(log(3))^x. Since exp(p)^q = exp(p×q), the function is also written 2×exp(log(3)x).

exp(x) is also written e^x. exp(x) is the unique function with exp(0)=1, and with the slope of the tangent line at exp(x) equal to exp(x). For instance, the slope at exp(0) is 1, the slope at exp(1) = e is e, slope at exp(2) is exp(2).

for A exp(b x), the slope at x is A b exp(b x).

For 3^x = exp(log(3)x), we have

3^0=1, slope log(3)

3^1=3, slope 3log(3),

3^2=9, slope 9log(3).

Step-by-step explanation: Put 2 as the exponent to get 3x3=9, then do 9x2=18. So x = 2 is y = 18 = (2,18).

The slope-intercept form:

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

m - slope

b - y-intercept

We have [tex]5x+8y=16[/tex]. Convert:

[tex]5x+8y=16[/tex]          subtract 5x from both sides

[tex]8y=-5x+16[/tex]      divide both sides by 8

[tex]\boxed{-\dfrac{5}{8}x+2}[/tex]

Answer:

Step-by-step explanation:

if ABC is a triangle then <]ABC + <}BCA +<}CAB = 180 degrees

Poof:

Draw line a through points A and B. Draw line B through point C and parallel to line a

Since line a and b are parallel <] BAC = <] B'CA and <]ABC = <}BCA'.

it is obvious that <}B'CA + <}ACB + <]BCA' = 180 degrees

Thus <]ABC + <)BCA + <)CAB = 180 degrees

Lemma:

if ABCD is quadrilateral and <)CAB = <}DCA then AB and DC are parallel.

Step-by-step explanation:

Consider a triangle ABC and let ∠A + ∠B + ∠C = 180°

Construct a straight line DE running parallel to BC and passing though A.

Now let

∠BAC = 1

∠ABC = 2

∠ACB = 3

∠DAB = 4

∠EAC = 5

Therefore we know that

∠DAB = ∠ABC (alternate angles), so 4 = 2

∠EAC = ∠ACB (alternate angles), so 5 = 3

Now line CE is straight line and we know that angle for a straight line 180°.

Thus ∠DAB + ∠BAC + ∠EAC  = 180°

or      ∠ABC + ∠BAC + ∠ACB =  180°

or          ∠A + ∠B + ∠C = 180°

Thus proved.

For a cleaning solution with a ratio of 4 cups of baking soda to 3 cups of water, each cup of water would require approximately 1.33 cups of baking soda. Hence, the correct answer is B) 4/3.

Alice's cleaning solution uses a ratio of 4 cups of baking soda to 3 cups of water. This ratio can be expressed as a fraction, 4/3. To find out how much baking soda is needed for each cup of water, we need to simplify this ratio. In other words, we divide the number of cups of baking soda by the number of cups of water.

When we divide 4 by 3, we get 1.33 (repeating). That means, for each cup of water, Alice will need approximately 1.33 cups of baking soda. So, the answer is B) 4/3.

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Answer:

The answer is x= -17/25 y= 19/5

Step-by-step explanation:

The system of equations 5x-2y=-11 and -2+5y=17 has the solution x=-1.4 and y=3.8 after substitution and simplification.

The given system of equations is 5x-2y=-11 and -2+5y=17. To solve this system, we need to isolate the variables. Let's start by cleaning up the second equation to 5y=19, you do that by adding 2 on both sides. This implies y=19/5 or y=3.8. Now, we can substitute y into the first equation: 5x - 2*(3.8) = -11. Solve this for x and you get x=-1.4. So the solution to the system of equations is x=-1.4 and y=3.8.

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There are 8 possible outcomes given.

There is only 1 chance of getting all three heads.

The probability would be 1/8 as a fraction, 0.125 as a decimal.

Answer:

The equation would be y = 8x - 38

Step-by-step explanation:

To find the equation of this new line, we first need to identify the slope of the first line. In slope-intercept form, the slope is always the coefficient of x. This makes the slope of the first equation 8. Since parallel lines have the same slope, our new slope will also be 8.

Given that and the point, we can solve for the equation using point-slope form.

y - y1 = m(x - x1)

y - 2 = 8(x - 5)

y - 2 = 8x - 40

y = 8x - 38

The equation of the line in point slope form is y = 8x - 38

The formula for calculating the equation of a line in point slope form is expressed as:

[tex]y-y_0=m(x-x_0)[/tex]

Given the equation of a line as y = 8x - 8

Slope m = 8

Point = (5, 2)

Get the required equation in point slope form as shown:

[tex]y-2=8(x-5)\\y-2 = 8x - 40\\y = 8x - 40 + 2\\y =8x-38[/tex]

Hence the equation of the line in point slope form is y = 8x - 38

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Answer:

1950 watt-hours

Step-by-step explanation:

3 days and 6 hours is equivalent to 3.25 days because there are 24 hours in a day and 6/24 or 6 out of 24 is equivalent to 6÷24 which is 0.25.

0.25 + 3= 3.25 which is the time.

Multiply 3.25 by 600 to find the watt-hours in 3 days and six hours.

Answer:52 stamps

Step-by-step explanation: He has 32 now. You subtract 6, as he bought 6 more. Then you double this as he sold half. That gives you 52

Starting with the equation (x/2) + 6 = 32, we solve for x to find that William originally had 52 stamps in his collection.

Let's use algebra to solve the problem William faced with his stamp collection. We can let the variable x represent the original number of stamps William had. According to the question, he sold half of his stamps and then bought 6 more, ending up with 32 stamps. This can be expressed as the equation (x/2) + 6 = 32. To find the original number, we solve for x:

Therefore, William started with 52 stamps in his collection before he sold any to consider buying a video game.

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Final answer:

To solve the problem, we found the finishing time of the first competitor by subtracting the range of completion times from the last finisher's time then added 4 minutes to get Ty's finishing time, which is 2:11 p.m.

Explanation:

To determine the time Ty crossed the finish line, we first need to calculate when the first place finisher completed the race, given that the range of completion times was 2 hours and 36 minutes and the last competitor finished at 4:43 p.m. Then, we add 4 minutes to the first finisher's time to find out when Ty finished.

Let's calculate the finishing time of the first place finisher:

This is the time the first competitor finished the race.

Now, add 4 minutes to get Ty's finishing time:

Ty crossed the finish line at 2:11 p.m..

Answer:

One solution

Step-by-step explanation:

3/5(x+2)=x-4

I do not like working with fractions, so I will multiply by 5 on each side to clear the fractions.

5 *3/5(x+2)=5*(x-4)

3*(x+2)= 5*(x-4)

Distribute

3x+6 = 5x-20

Subtract 3x from each side

3x+6 = 5x-20

3x-3x+6 = 5x-3x-20

6 = 2x-20

Add 20 to each side

6+20 =2x-20+20

26 =2x

Divide each side by 2

26/2 = 2x/2

13=x

Answer:

5:4

Step-by-step explanation:

The original ratio would be 15:12 and then you can simplify by dividing both sides by 3. So the resulting ratio would be 5:4.

Answer:

5:4

Step-by-step explanation:

The ratio is 15:12. We can simply that by dividing both sides by 3 and get 5:4. So the simplified ration is 5:4

Everyone else will be a congruent to the first one triangle.

Answer:

One

Step-by-step explanation:

You can only make one. This shows that one triangle

Answer:

50,000

Step-by-step explanation:

Answer:

23% of 432 is 99.36

That rounds to 99

So, 99 students picked teacher for a career.

[tex]r-\text{the weight of the rocks}\\\\\dfrac{3}{7}r-\text{the weight of the truck}\\\\13.5t-\text{the weight of the truck}\\\\\text{The equation}\\\\\dfrac{3}{7}r=13.5\qquad\text{multiply both sides by}\ \dfrac{7}{3}\\\\\boxed{r=31.5\ (t)}\\\\Answer:\ The\ weight\ of\ rocks\ is\ 31.5\ tons.[/tex]

Answer:

31.5

Step-by-step explanation:

Answer: 150 jumps

Step-by-step explanation:

1 yard is = 3 ft.

100 yards is 300 ft.

300/2 = 150

Answer:150 jumps

Step-by-step explanation: so 1 yard is 3 feet.  100 times 3 is 300.

a grasshopper can jump 2 feet, so we need to divide by 2.

300ft divided by 2 is 150 jumps

Answer:

$56.97

this is the answer:)                                    

Answer: $56.97

=============================================

Explanation:

"25% off" means the buyer pays 75% of the original cost, ignoring any other taxes, fees, shipping, etc.

75% = 75/100 = 0.75

Multiply this decimal value with the original cost 72 and we get 0.75*72 = 54.

-----------

Now we compute the sales tax

5.5% = 5.5/100 = 0.055

0.055*54 = 2.97 is paid in tax

-----------

Add the sales tax ($2.97) to the discount price ($54) to get 54+2.97 = 56.97

We don't add on shipping because that is free. The sales tax is applied after the discount is done, or else it would imply that the 25% discount didn't fully go through (ie you are paying some portion of what was promised to be saved)

A shortcut is to compute: 72*0.75*1.055 = 56.97 which allows us to basically find the answer in one single step. The 1.055 refers to the 5.5% tax multiplier. A similar trick can be used if you have multiple discounts applied simultaneously.

Answer:

3/5 = .6

Step-by-step explanation:

1/2 in decimal form is .50, and 3/4 in decimal form is .75. We can choose any fraction that has the decimal form of .51 to .74. I'll choose .60.

.60 in fraction form is 60/100. We can simplify this down to 3/5.

Answer:

660

Step-by-step explanation:

first you multiply the first 10,000 by 5%. 10,000*5%=500 or 10,000*0.05=500. after you do that, you multiply the money left over by 8%, in this case the money left over is 2,000 dollars. 2,000*8%= 160. Then you add the two numbers together. 500+160= 660. and there you have your answer. Hope it helped!

Final answer:

To calculate the commission on a $12,000 car sale, compute 5% of the first $10,000 and 8% of the remaining $2,000, then add these to find the total commission of $660.

Explanation:

The question is about calculating the commission on a car sale given a two-tiered commission structure. The salesperson receives 5% commission on the first $10,000 of the sale and 8% commission on any amount over $10,000.

Step-by-step Calculation:

Calculate the commission on the first $10,000 at 5%: $10,000 * 0.05 = $500.

Calculate the commission on the remaining $2,000 at 8%: $2,000 * 0.08 = $160.

Add the two commission amounts together to get the total commission: $500 + $160 = $660.

The salesperson's total commission for selling a $12,000 car would be $660.

Final answer:

To determine the sale price with a 65% markup on a skirt bought for $4.50, calculate the markup in dollars, add it to the original cost, and round to the nearest cent to get the final price of $7.43.

Explanation:

To find the sale price of the skirt after a markup of 65%, we first calculate the amount of the markup by multiplying the cost by the markup rate. The markup on the skirt that costs $4.50 would be:

$4.50 times 0.65 = $2.925.

Now, add the markup to the original cost to find the sale price:

$4.50(original cost) + $2.925(markup) = $7.425

However, prices are not typically listed with three decimal places, so we would round to the nearest cent, making the final sale price of the skirt $7.43.

Answer:

Answer is D (got it right on plato)

Step-by-step explanation:

There are 4 of each king and queen in each standard deck of 52 cards.

4+4=8

8/52=0.1538 or 15.38%

Twenty cards are chosen from a pack of cards at random

In A there are 0 kings and 1 queen

0+1= 1; 1/20=.05 or 5%

In B there are 2 kings and 4 queens

2+4=6; 6/20=0.3

In C there are 0 kings and queens

0/20=0

In D there are 2 kings and 1 queen

2+1= 3; 3/20=0.15 or 15%

D is your answer because it is the closest to the probability (0.1538 or 15.38%)

Answer:

4 8 6 K J 7 Q 3 A K 2 5 8 9 10 2 4 A 67

Step-by-step explanation:

Answer:

60 square inches

Step-by-step explanation:

In triangle KLM, KL = LM = 13in, KM = 10in. Use the Heron's formula to find the area:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where p is half of the perimeter and a, b, c are sides lengths.

Then

[tex]\dfrac{a+b+c}{2}=\dfrac{13+13+10}{2}=18\ in[/tex]

and

[tex]A=\sqrt{18\cdot (18-13)\cdot (18-13)\cdot (18-10)}=\sqrt{18\cdot 5\cdot 5\cdot 8}=5\sqrt{9\cdot 2\cdot 4\cdot 2}=5\cdot 3\cdot 2\cdot 2=60\ in^2.[/tex]

Expand

12x - 48 + 4x + 28

Collect like terms

(12x + 4x) + (-48 + 28)

Simplify

16x - 20

Answer:

16x - 20

Step-by-step explanation:

12(x-4)+4(x+7)

Applying the distributive law to both parentheses:-

= 12x - 48 + 4x + 28

= 16x - 20  

Answer:

B) -3

Step-by-step explanation:

4 - 2x = 10

Subtract 4 from each side

4-4 - 2x = 10 -4

-2x = 6

Divide by -2

-2x/-2 = 6/-2

x = -3

Answer:

x= -3

Step-by-step explanation:

First, you would subtract 4 from both sides to isolate the -2x, which makes -2x=6. Then to isolate the x, you divide by the negative 2 (negative because the subtract sign is before it.) to get x=-3

Answer:

Price after discount = 2.4 (1-.3)

Price after discount = 2.4 (.7)

Step-by-step explanation:

We know the cost after the discount.

Price after discount = original price - original price * discount rate

Factoring out the original price

Price after discount = original price (1- discount rate)

We know the discount rate = .3 and the original price is 2.4

Price after discount = 2.4 (1-.3)

Price after discount = 2.4 (.7)

Price after discount = 1.68