You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night, you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?

A.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.

B.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 77 hot dogs and 49 sodas.

C.
2.25x + 1.50y = 126 and x + y = 225.75 : -283.5 hot dogs and 509.25 sodas.

D.
There is not enough information

Answer:

D. y - 7 = 11(x - 5)

Step-by-step explanation:

Use point slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plug in the given slope and point:

y - y1 = m(x - x1)

y - 7 = 11(x - 5)

So, the correct answer is D. y - 7 = 11(x - 5)

Answer:

Step-by-step explanation:

For each game played the chance of winning is 0.05 and losing is 0.95.

If the student wins, they get $5 -$1 = $4, but they lose $1.

Expected value is:

It means you will make $0.75 per average game.

Answer:

21.8

Step-by-step explanation:

Step 1

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is 0 - 10. The mid-point of this class will be (0 + 10)/2 = 5.

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Step 2

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class 0 – 10, its frequency is 3.

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Step 3

We can now use the formula to calculate mean. Note that t...

Answer:

Option B, 15.6

Step-by-step explanation:

Using the Pythagoras theorem,

√(11²+11²)

= √(121+121)

= √(2×121)

= √121×√2

= 11√2

= 15.6

Answered by GAUTHMATH

Option B - 15.6 is Correct.

We have a figure in which a right angled triangle is shown with it base (b) = 11 and perpendicular(p) = 11.

We have to find the value of c or hypotenuse (h).

According to the Pythagoras theorem : for a right angled triangle -

[tex](h)^{2} = (b)^{2} +(p)^{2}[/tex]

According to the question -

[tex]b =11\\p =11\\h=c[/tex]

Substituting the values, we get -

[tex]c^{2} = (11)^{2} + (11)^{2} \\c^{2} = 121 + 121\\c^{2} =242\\c=15.55[/tex]

Rounding to nearest 10, we get -

c = 15.6

Hence , Option B is correct.

To solve more questions on Pythagoras theorem, visit the following link -

https://brainly.com/question/8587612

#SPJ2

Answer:

[tex]P_{95\%}=(0.333,0.527)[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=100[/tex]

Selected sample [tex]x=43[/tex]

Confidence Interval [tex]CI=95\%[/tex]

Significance Level [tex]\alpha=0.05[/tex]

Probability of picking nose is

[tex]P=\frac{x}{n}[/tex]

[tex]P=\frac{43}{100}[/tex]

[tex]P=0.43[/tex]

Generally the equation for standard error is mathematically given by

[tex]S.E=\sqrt{p*(1-p)}{n}[/tex]

[tex]S.E=\sqrt{0.4*(1-0.57)}{100}[/tex]

[tex]S.E=0.0495[/tex]

Therefore

The proportions 95\% interval is

[tex]P_{95\%}=[P-1.96x SE(P),P+1.96*SE(P)][/tex]

[tex]P_{95\%}=(0.43-1.96*0.0495,0.43+1.96*0.045)[/tex]

[tex]P_{95\%}=(0.333,0.527)[/tex]

Answer:

Step-by-step explanation:

the 3 in 135,864 is 30,000

if you mutiply that by 10 you get 300,000

you just need to write any number with a 3 in the hundred thousands place

1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.

Answer:

Area= 525

Step-by-step explanation:

14x9=126

3x7=21

14x27=378

126+21+378=525

on 220 acres

66 ⅔% is just ⅔ of 100%

330 * 2 / 3 = 220

Answer:

just fill in 40 squres

Step-by-step explanation:

Find the difference between each number:

-11 to -3 is +8

-3 to 5 is +8

The difference is 8

Use the following formula:

Bn = b1 + d(b -1)

Answer: bn = -11 + 8( b-1)

Answer:

The answer is "0.7616".

Step-by-step explanation:

Using formula:

[tex]\text{P( at least one de-fective) = 1 - P( all calculators work )}[/tex]

                                          [tex]= 1-(\frac{34}{48}\times \frac{33}{47}\times \frac{32}{46}\times \frac{31}{45})\\\\= 1-(\frac{34}{1}\times \frac{11}{47}\times \frac{1}{23}\times \frac{31}{45})\\\\=1-(\frac{11594}{48647})\\\\=\frac{48647-11594}{48647}\\\\=\frac{37051}{48647}\approx 0.7616[/tex]

Answer:

a) P(0) = 80

b) [tex]P(t) = 80(2.2361)^t[/tex]

c) 22,363 cells.

d) The rate of growth after 7 hours is of 18,000 bacteria per hour.

e) 9.7 hours.

Step-by-step explanation:

A bacteria culture grows with a constant relative growth rate.

This means that the population is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.

This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So

[tex]50000 = 400(1+r)^6[/tex]

[tex](1+r)^6 = \frac{50000}{400}[/tex]

[tex](1+r)^6 = 125[/tex]

[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]

[tex]1 + r = 125^{\frac{1}{6}}[/tex]

[tex]1 + r = 2.2361[/tex]

So

[tex]P(t) = P(0)(2.2361)^t[/tex]

(a) Find the initial population. P(0)

We have that P(2) = 400. We use this to find P(0). So

[tex]P(t) = P(0)(2.2361)^t[/tex]

[tex]400 = P(0)(2.2361)^2[/tex]

[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]

[tex]P(0) = 80[/tex]

So

[tex]P(t) = 80(2.2361)^t[/tex]

(b) Find an expression for the population after t hours.

[tex]P(t) = 80(2.2361)^t[/tex]

(c) Find the number of cells after 7 hours.

This is P(7). So

[tex]P(7) = 80(2.2361)^7 = 22363[/tex]

22,363 cells.

(d) Find the rate of growth after 7 hours.

We have to find the derivative when t = 7. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]

[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]

The rate of growth after 7 hours is of 18,000 bacteria per hour.

(e) When will the population reach 200,000?

This is t for which [tex]P(t) = 200000[/tex]. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]200000 = 80(2.2361)^t[/tex]

[tex](2.2361)^t = \frac{200000}{80}[/tex]

[tex](2.2361)^t = 2500[/tex]

[tex]\log{(2.2361)^t} = \log{2500}[/tex]

[tex]t\log{2.2361} = \log{2500}[/tex]

[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]

[tex]t = 9.7[/tex]

So 9.7 hours.

9514 1404 393

Answer:

  (a)  M = 0.25n +100

Step-by-step explanation:

The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).

The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...

  slope = rise/run = 25/100 kg/CD = 0.25

Then the equation describing the points on the graph will be ...

  M = 0.25n +100

Answer:

A

Step-by-step explanation:

I guess that is the answer

Answer:

When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value. The standard deviation is approximately equal to the range of the data divided by 4. That's it, simple.

Answer:

x=2

Step-by-step explanation:

you first have to make the bases the same

3^2x+1=9^2x-1

3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9

3^2x+1=3^4x-2

2x+1=4x-2

2x-4x=-2-1

-2x/-2=-4/-2

x=2

I hope this helps

Answer:

C

Step-by-step explanation:

It is 8.6 because we are finding the difference and using subtraction.  

So I did 68.8-59.9 and I got 8.6

Answer:

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The trees are arranged, so, to find the number of outcomes, the arrangements formula is used.

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

Desired outcomes:

5 sycamores(5! possible ways) and then the 5 palm trees(5! possible ways)

5 palm trees(5! possible ways) then the 5 sycamores(5! possible ways).

[tex]D = 2*5!*5![/tex]

Total outcomes:

Arrangements of 10 plants, so:

[tex]T = 10![/tex]

What is the probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other?

[tex]p = \frac{D}{T} = \frac{2*5!*5!}{10!} = 0.0079[/tex]

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Answer:

Step-by-step explanation:

It asks for the common set of A and B.

There only one element common to both the given sets:

Answer:

Step-by-step explanation:

∩ == this symbol stands for the common element/set

So according to this question you have to find the element which is common for both A and B sets.

So now you can see that only number 2 is common for both.

So, the answer is,

Answer:

B

Step-by-step explanation:

A function is a relation in which each input, x, has only one output, y.

There are two ways to determine if a relation is a function:

1. If each x-input has only one, unique y-output, then it's a function. If some x-inputs share the same y-outputs, it's not a function.

2. Vertical Line Test on Graphs:

To determine whether y is a function of x, when given a graph of relation, use the  following criterion: if every vertical line you can draw goes though only 1 point, the relation can be a function. If you can draw a vertical line that goes though more than 1 point, the relation cannot be a function.

Since we're given a graph relation, let's test both of the answers out.

If I were to draw a vertical line in a specific place on the first graph, I'd be hitting more than one point in the coordinate plane.

If I were to draw a vertical line in a specific place on the second graph, I'd only be hitting one point in the coordinate plane.

Therefore, choice B is a function.

Answer:

Step-by-step explanation:

(D+R) = 80:2 = 40

D = 40-R

(D+8) * R = 72X

Thay D=40-R

(40-R+8)*R = 72X

R=1.55, D=38.45

9514 1404 393

Answer:

  14.3%

Step-by-step explanation:

We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.

The APR is about 14.3%.

_____

The amount to be repaid is calculated using the simple interest formula:

  A = P(1 +rt) = $4900(1 +0.08·4) = $6468

Then the required monthly payment (for 48 months) is ...

  $6468/48 = $134.75

__

The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...

  A = 4900(r/12)/(1 -(1 +r/12)^-48)

In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).

_____

Additional comment

The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.

We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.

Answer:

12/40 or simplified it would be 3/10

Step-by-step explanation:

6 + 7* log base 2 of x = 21

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  (c)  A = 38.13 square inches; P = 23.42 inches

Step-by-step explanation:

The radius of the circle is half the diameter, so is 3 inches. This means the entire figure will fit in a rectangle 6 inches wide and 4+3 = 7 inches high. The perimeter of such a rectangle is ...

  P = 2(L+W) = 2(7+6) = 26 inches

The area of that rectangle is ...

  A = LW = (7)(6) = 42 square inches

Then area of the given figure is less than 42 square inches, and the perimeter is less than 26 inches. The only answer choice that matches these bounds is ...

  A = 38.13 square inches; P = 23.42 inches

having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old

100 = 10², so the sum you're considering is the sum of squared integers starting with 10.

[tex]\displaystyle 100+121+144+168+\cdots+n^2+\cdots = \boxed{\sum_{k=10}^\infty k^2}[/tex]

Answer:

Step-by-step explanation:

210=2x3x5x7

280=2x2x2x5x7

360=2x2x2x3x3x5

Answer:

210= 2×3×5×7

280=2×2×2×5×7

360=2×2×2×3×3×5

common factors=2×2×2×3×5×7=840

uncommon factors=3

L.C.M=Common factors× uncommon factors

L.C.M=840×3

L.C.M=2520

Step-by-step explanation:

i hope it will be helpful

plzz mark as brainliest

can u plz check if the question is right

Answer:

1130

Step-by-step explanation:

1109+7 = 1116

1116+7 = 1123

Adding 7 each time

1123+7 = 1130