A pizza restaurant allows you to choose any 3 of 8 toppings. How many
different ways are there to choose the toppings?
A. 56
B. 24
C. 40,320
D. 336

Answer:

105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.

Step-by-step explanation:

We are given that the compound has 6.3 x10^23 atoms of Cl.

To find how many molecules of AuCl3 are in the given compound, we divide the compound by 3, i.e;

[tex]\frac{6.3 \times 10^{23} }{3}[/tex]  =  [tex]2.1\times 10^{23}[/tex] molecules of AuCl3.

Now, as we know that 1 mole of AuCI3 has [tex]6.022 \times 10^{23}[/tex] molecules.

So, the moles that our compound has is given by;

      =  [tex]\frac{2.1 \times 10^{23} }{6.022 \times 10^{23} }[/tex]  = [tex]\frac{2.1}{6.022}[/tex]  = 0.349 mole AuCI3

Also, the molar mass of AuCI3 = 303.33 g/mole

So, the molar mass of 0.349 moles AuCI3 =  [tex]303.33 \times 0.349[/tex]

                                                                      =  105.86 g

Hence, 105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.

Answer:

$850.7

Step-by-step explanation:

Penelope has $1459.75 in her account.

She pays different amount that are given above.

i.e.

=1459.75-200.25-359.45-125-299.35

=475.7

Then she deposit $375

Now,

=475.7+375

=850.7

So, She has $850.7 in her account after she pays her bills and makes deposits.

Answer:

$805.7 OwO

Step-by-step explanation:

Answer:

x = 1 , y = 7

Step-by-step explanation:

Solve the following system:

{y = 5 x + 2 | (equation 1)

3 x = 10 - y | (equation 2)

Express the system in standard form:

{-(5 x) + y = 2 | (equation 1)

3 x + y = 10 | (equation 2)

Add 3/5 × (equation 1) to equation 2:

{-(5 x) + y = 2 | (equation 1)

0 x+(8 y)/5 = 56/5 | (equation 2)

Multiply equation 2 by 5/8:

{-(5 x) + y = 2 | (equation 1)

0 x+y = 7 | (equation 2)

Subtract equation 2 from equation 1:

{-(5 x)+0 y = -5 | (equation 1)

0 x+y = 7 | (equation 2)

Divide equation 1 by -5:

{x+0 y = 1 | (equation 1)

0 x+y = 7 | (equation 2)

Collect results:

Answer: {x = 1 , y = 7

Answer:

D) (1,7)

Step-by-step explanation:

just took the test

Anwer:3.537m

STEP BY STEP EXPLANATIOND:using SOH CAH TOA

First find the opposite

Represent the opposite with x

Tan 33° =x\10

x=10Tan 33°

x=6.494

To find m

Sin 33°=m\6.494 Sin 33°

m=3.5368

m=3.537meteres

Answer:760$ in a week because they worked 5 out of 7 days and made 152$ a day

Step-by-step explanation:

9.5 x 16 = $152

152 x 5 (only weekdays)

<!> Branliest is appreciated! <!>

Answer:

Step-by-step explanation:

You have all your x values to the left. Just take 2 and multiply one by one.

Then in order to graph it, you would take (x,y) and plot it.

For example:

y=2x

y=2(5) = 10

(5,10) - you would plot this on the graph.

1. y = 2x

x | y = 2x | y

5 | y = 2(5) | 10

3 | y = 2(3) | 6

0 | y = 2(0) | 0

-1 | y = 2(-1) | -2

-5 | y = 2(-5) | -10

2. y = 1 + 5x

x | y = 1 + 5x | y

-2 | y = 1 + 5(-2) | -9

-1 | y = 1 + 5(-1) | -4

0 | y = 1 + 5(0) | 1

2 | y = 1 + 5(2) | 11

Answer:

Time = distance/speed

max distance = 380+10 = 390 m

Max Time = 390/3.9 = 100 s

Answer:

Graph 1 shows a negative correlation, and graph 2 shows a positive correlation. This is because in graph one, as x increases, y decreases, and in graph two as x increases, y also increases.

Answer:

.84

Step-by-step explanation:

The probability that a worker chosen at random works at least 8 hours is 0.84.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

From the given graph,

Probability of 6 hours = 0.02

Probability of 7 hours = 0.11

Probability of 8 hours = 0.61

Probability of 9 hours = 0.15

Probability of 10 hours = 0.08

The probability of at least 8 hours can be obtained as illustrated below:

P(At least 8 hours) = P(8) + P(9) + P(10)

P(At least 8 hours) = 0.61 + 0.15 + 0.08

P(At least 8 hours) = 0.84

Therefore, the probability that a worker chosen at random works at least 8 hours is 0.84.

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Answer:

Their speed is 32 km/h.

Step-by-step explanation:

Since they're at the same speed, we can assign a variable to their speed called "x". When the first car increases its speed by 1 km/h, its new speed is "x + 1", while the other car decreases its speed by 10 km/h, so its new speed is "x - 10". The distance's formula can be expressed as below:

[tex]\text{distance} = \text{speed}*\text{time}\\[/tex]

With the modifications to their speed, the distance the first car covers in 2 h and the distance the second car covers in 3 h is shown below:

[tex]\text{distance}_{car1} = (x + 1)*2 \\\text{distance}_{car1} = 2*x + 2[/tex]

[tex]\text{distance}_{car2} = \text{speed}*\text{time}\\\text{distance}_{car2} = (x - 10)*3\\\text{distance}_{car2} = 3*x - 30[/tex]

Since the distance covered by them must be the same, we can find the value of x that makes the expressions equal.

[tex]2*x + 2 = 3*x - 30\\2*x - 3*x = -30 -2\\-x = -32\\x = 32[/tex]

Their speed is 32 km/h.

Answer:

B.

Step-by-step explanation:

"negative reciprocal slopes" means the lines are perpendicular, so they will always intersect.

Hence there will be exactly one solution.

B. The system will have one solution.

The slopes of perpendicular strains, or bisecting strains, are continually terrible reciprocals of each other. For instance, if the slope of a line is -five, then the slope of a line perpendicular to this line will be the negative reciprocal of -five.

If the 2 traces have exclusive slopes, then they'll intersect as soon as. consequently, the gadget of equations has exactly one answer. If the two traces have the equal slope however of kind y-intercepts, then they're parallel strains, and they'll by no means intersect.

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Answer:

-27p^2 q^2 +6p^3 -2p^4 -q^3

Step-by-step explanation:

COMBINE LIKE TERMS

Answer:

30.

Step-by-step explanation:

The initial value is the value that she starts out with.  This means that she is referring to year 0.  According to the chart, on year 0, she collected 30 shells.

The answer is 30.

Answer:

y = -5x

Step-by-step explanation:

Which of the following linear equations passes through points (-1, 5) and (1, -5)?

y = -5x

y = 5x + 10

y = -2x + 3

None of these choices are correct.

Solution:

First find slope of equation:

slope, m = (y2-y1) / (x2-x1) = (5-(-5) / (-1-1) = 10/(-2) = -5

Now substitute m in the point slope form to find the y-intercept b

y-y1 = m(x-x1)

y-5 =  5(x- -1)

y = -5(x+1) + 5

y = -5x  

Answer:

£228.

Step-by-step explanation:

We know that each tile is 20 cm by 20 cm, which works out to be an area of 400 square cm.

The floor is 3 m by 5 m, which means it is 300 cm by 500 cm. 300 * 500 = 150000 square cm in area.

To find how many tiles are necessary, we need to find out the area of the floor divided by the area of the individual tiles.

150,000 / 400 = 1,500 / 4 = 750 / 2 = 375

So, to cover the floor, you will need 375 tiles.

Since tiles come in boxes of 10, you will need to find what is 375 divided by 10 so you can know how many boxes to buy.

375 / 10 = 37.5

Since you absolutely NEED 375 tiles to cover the floor, you need that half of a box, so you will buy 38 boxes of tiles.

Each box costs £6. 38 * £6 = £228. And that is your total cost!

Hope this helps!

Answer:

3.14 square cm

Step-by-step explanation:

Since, a coin is circular in shape, hence its area would be equal to the area of a circle.

[tex]\therefore are \: of \: coin = \pi {r}^{2} \\ = 3.14 \times {1}^{2} \\ = 3.14 \times 1 \\ = 3.14 \: {cm}^{2} \\ [/tex]

Answer:

151,200

Step-by-step explanation:

The possible set of numbers will be 151200  

A permutation is an arrangement of objects in a definite order.

Given that, John want to find his bicycle's number, so he decided to write down all the possible 6-digit numbers from 0 to 9.

Here, we will use permutation to find the possible numbers,

Formula =

ⁿPₓ = n! / (n-x)!

Therefore,

¹⁰P₆ = 10! / (10-6)!

= 10! / 4!

= 10 × 9 × 8 × 7 × 6 × 5 = 151200

Hence, the possible set of numbers will be 151200  

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Answer:

36° and 54°

Step-by-step explanation:

Complementary angles are angles whose sum equals to 90°

Hence C +D = 90°

The ratio of C &D = 2:3 respectively

Sum of the ratio = 2+3 = 5

Hence we divide each of the ratio by the sum of the entire ratio and then multiply by 90°

For angle C :

2/5 × 90

2×18 = 36°

For angle D :

3/5× 90

3×18 = 54°

Hence the angles are 36° and 54° respectively

To proof that we are actually right

C+D = 90°

36+54 = 90°

Hence the answer is right.

Answer:

B. 7

Step-by-step explanation:

Answer:

y = -[tex]\frac{2}{5}[/tex]x - 1

Step-by-step explanation:

First, we can put the equation into y = mx + b form:

2x + 5y = 10

5y = -2x + 10

y = -[tex]\frac{2}{5}[/tex]x + 2

Now, we know the slope is -[tex]\frac{2}{5}[/tex]. A parallel line will have the same slope.

So, we can plug in the point (-5, 1) into the equation y = -[tex]\frac{2}{5}[/tex]x + b to find b:

1 = -[tex]\frac{2}{5}[/tex](-5) + b

1 = 2 + b

-1 = b

So, the equation will be y = -[tex]\frac{2}{5}[/tex]x - 1

Hey there! :)

Answer:

a. b = y - mx

b. x = y - b /m

c. t = I/ pr

d. t = A - p/pr

Step-by-step explanation:

a. y = mx + b (for b)

Isolate the b variable by subtracting both sides by mx:

y - mx = b.

Therefore:

b = y - mx.

b. y = mx + b (for x)

Subtract 'b' from both sides:

y - b = mx

Divide 'm' from both sides:

y - b / m = x

c. I = prt

Divide both sides by pr:

I /pr = t.

d. A = p + prt

Subtract p from both sides:

A - p = prt

Divide both sides by pr:

A - p / pr = t

X is equal to 28

Hope this helps......

Answer:

4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution

Step-by-step explanation:

Examine the system

2 x + 8 y = 15

4 x + 16 y = 30

We see that these equations are identical except for a factor of 2, and thus recognize that this system has infinitely many solutions.

Next, look at the system

2 x minus y = 18

4 x + 2 y = 38

If we divide the second equation by 2, we get the system

2x - y = 18

2x + y = 19

Combining these two equations, we get 4x = 37, which has a solution.

Third, analyze the system

4 x + 7 y = 17                =>  8x + 14y = 34

8 x minus 14 y = 36      => 8x - 14y  = 36, or 16x = 70, which has a solution

Finally, analyze the system

4 x minus 3 y = 16    => -8x + 6y = -32

8 x minus 6 y = 34   =>  8x  - 6y  = 34

If we combine these two equations, we get 0 + 0 = 2, which is, of course, impossible.  This system has no solution.

Answer:

4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution. the 4th option.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

6/2

I hope this is right :)

Answer:

8-in of snow each day

Step-by-step explanation:

Answer:

8 inches of snow each day

Step-by-step explanation:

hope this helps :)

Answer:  [tex]a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6[/tex]

                [tex]b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}[/tex]

              c) Transformations: reflection over the x-axis,

                                               vertical stretch by a factor of 3/2,

                                               horizontal shift 1 unit to the left,

                                               vertical shift 6 units up

Step-by-step explanation:

Intercept form: y = a(x - p)(x - q)

Vertex form: y = a(x - h)² + k

Standard form: y = ax² + bx + c

We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.

p = -3, q = 1, (x, y) = (-1, 6)

a(-1 + 3)(-1 -1) = 6

       a (2)(-2) = 6

                a  = -6/4

                 a = -3/2

a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:

[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]

b) Input a = -3/2 into the Intercept form and expand to get the Standard form:

[tex]y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}[/tex]

c) Use the Vertex form to identify the transformations:

[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]

Answer:

D.

Step-by-step explanation:

Original dimensions:

L = x

W = x

Now we reduce the width by 2 ft and increase the length by 2 ft.

L = x + 2

W = x - 2

The area is the product of the length and width.

A = LW = (x + 2)(x - 2)

The original length and width are 10 ft.

L = W = x = 10

A = LW = (10 + 2)(10 - 2) = 12 * 8 = 96

The new area is 96 sq ft.

Answer: D.