Kylie and Amelia go to the movie theater and purchase refreshments for their friends. Kylie spends a total of $125.50 on 12 bags of popcorn and 7 drinks. Amelia spends a total of $87.50 on 6 bags of popcorn and 8 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine AB, we would apply the Cosine trigonometric ratio

Cos θ = opposite side/hypotenuse. Therefore,

Cos 52 = 10/AB

0.616 = 10/AB

AB = 10/0.616

AB = 16.23

Answer: 16 men

32 women

38 children

Step-by-step explanation:

Let x represent the number of men in the group.

Let y represent the number if women in the group.

Let z represent the number of children in the group.

A group of 86 people consist of men women and children. This means that

x + y + z = 86 - - - - - - - - - - - - 1

There are twice as many women than there are men. It means that

x = y/2

There are 6 more children than there are women. This means that

z = y + 6

Substituting x = y/2 and z = y + 6 into equation 1, it becomes

y/2 + y + y + 6 = 86

multiplying through by 2, it becomes

y + 2y + 2y + 12 = 172

5y = 172 - 12 = 160

y = 160/5 = 32

x = y/2 = 32/2

x = 16

z = y + 6 = 32 + 6

z = 38

There are 16 men, 32 women, and 38 children in the group.

Let the number of men be M, the number of women be W, and the number of children be C.

From the given information, we have the following equations:

W = 2M (Twice as many women as men)

C = W + 6 (6 more children than women)

The total number of people is given as 86:

M + W + C = 86

Substituting the values of W and C in terms of M into the third equation, we have:

M + 2M + (2M + 6) = 86

5M + 6 = 86

5M = 80

M = 16

Substituting the value of M in the first equation, we have:

W = 2(16) = 32

Finally, substituting the value of W in the second equation, we have:

C = 32 + 6 = 38

Therefore, there are 16 men, 32 women, and 38 children in the group.

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Answer:

1/2.

Step-by-step explanation:

10m = 5n

m = 5n/10

m = n/2

m/n = n/2 * 1/n

m/n = 1/2.

Answer:1/2

Step-by-step explanation:

10m=5n

Divide both sides by 5n

10m/5n=5n/5n

2m/n=1

Therefore m/n=1/2

Answer:

Pythagorean's theorem: a²+ b²= c²

Sines: sin A = a/c, sin B = b/c.

Cosines: cos A = b/c, cos B = a/c.

Tangents: tan A = a/b, tan B = b/a.

Step-by-step explanation:

For example, if the side a = 22 and the angle A = 41°, we can use a sine and a tangent to find the hypotenuse and the other side. Since sin A = a/c, therefore c = a/sin A = 22/sin 41. Using a calculator, this is 22/0.6561 = 33.5314. Also, tan A = a/b, so b = a/tan A = 22/tan 41 = 22/0.8693 = 25.307.

Answer:

The domain is the set of all real number greater than 2.

The x-intercept = ( 10,0) and there is no y-intercept

A vertical asymptote at x = 2.

The graph of g(x) is symmetric to its inverse exponential function over the line y = x

Step-by-step explanation:

Final answer:

The correct descriptions of the function g(x) = log2 (x - 2) – 3 are: the domain is all real numbers greater than 2, there is a vertical asymptote at x = 2, and the graph is symmetric over the line y = x with relation to its exponential inverse. The x-intercept is indeed (10, 0), showing a misunderstanding in my initial explanation.

Explanation:

The question involves analyzing the properties of the function g(x) = log2 (x - 2) – 3. Let's address each statement:

Answer:

Step-by-step explanation:

9. f(g(-n))

g(-n) = -(n²+5) = -n²-5

f(g(-n)) = 2n+1 (-n²-5 )

2n(-n²-5)+1(-n²-5 )

-2n³-10n-n²-5

-2n³-n²-10n-5

n²(-2n-1) +5(2n-1)

(n²+5)(2n-1)

10. (2x+2)(x³+3)

2x(x³+3)+2(x³+3)

2x⁴ + 2x³ +6x +6

2x³(x+1)+6(x+1)

(2x³+6)(x+1

Answer:

The correct statements are:

To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement

To see the Reconciliation report, select View report after you've successfully reconciled the account.

EXPLANATION:

The steps to reconciling a bank account using QuickBooks Online include:

1. Click on the Gear button, then on “Tools” and then “Reconcile.”

2. Click on the drop-down menu under “Accounts” and select the account you want to reconcile.

3. Enter the “Ending balance” and “Ending date” based on your bank statement information.

4. Match transactions to your bank statement and check them off one by one.

5. Apply filters so transactions are easier to find.

6. Keep going until the “Difference” field is zero and you see the Success! page.

7. Select "View Report" from the Report period drop-down arrow to view your reconciliation report.

The two options that are correct regarding bank account reconciliation QuickBooks online are:

Quickbooks is an Accounting Application that aids in the collection, processing, analyses, and reporting of Accounting and Financial Information for organizations.

It is a tool that is very useful for business owners.

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Answer: each container has 6.68 liters.

Step-by-step explanation:

Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. This means that the total number of liters of paint in the mixture(purple paint) is

8.27 + 6.65 = 14.92 liters

She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. This means that the amount of paint that she poured inside the 2 containers is

14.92 - 1.56 = 13.36 liters.

Therefore, the number of liters of paint in each container is

13.36/2 = 6.68 liters

Answer:

The answer to your question is 1.- (-3, 4)    2.-   (3, 1)  None of the choices

Step-by-step explanation:

1.- The solution of a system of equation by the graph method is the point in which the lines cross. In this graph we observe that this point is approximately

(-3, 4).

2.-

Equation 1   x + y = 4

Equation 2  x - y = 2

Solve by the combination method

                   x + y = 4

                  x  -  y = 2

                 2x    0  = 6

                        2x = 6

Solve for x

                          x = 6/2

                          x = 3

Substitute x in equation 1 to find y

                    3 + y = 4

Solve for y

                          y = 4 - 3

                          y = 1

Solution     (3, 1)                          

Answer:

A Linear function is an equation whose graph is a straight line. It has the following form; y = a + bx.

A linear function contains one independent variable and one dependent variable. X is the independent variable and y is the dependent variable.

The answer is a) y = 3x + 5

Answer:

1. Area of a square = (x^2)^2 = x^4

(each side is x^2, area of a square = side^2

so (x^2)(x^2) = x^4 )

2. when x = 5

area = 5^4 = 625

3. when x = 10

area = 10^4 = 10000

Step-by-step explanation:

Hope its right!

Final answer:

The area of a square mural where the side length is a perfect square, represented as x², can be expressed as A = x⁴, which simplifies the concept of multiplying the side length by itself twice.

Explanation:

The area of a mural square, where the side length is a perfect square represented as x to the power of 2 (x²), is calculated by squaring the side length. Therefore, if x itself is a perfect square, the area A of the square mural is given by A = x² * x², which simplifies to A = x⁴. Since the side length is a perfect square, x could be expressed as y² where y is an integer, resulting in the area being y⁴, where y⁴ represents the side length squared twice.

Answer:

She buy 0.5 pounds of black olives and 3.5 pounds of green olives.

Step-by-step explanation:

Given:

Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives.

Black olives cost three dollars a pound. Green olives cost five dollars a pound.

She spends $15.50.

Now, to find the pounds of olives she buy.

Let the pounds of black olives be [tex]x.[/tex]

And the pounds of green olives be [tex]y.[/tex]

So, total pounds of olives:

[tex]x+y=4[/tex]

[tex]x=4-y[/tex]    ........( 1 )

As, given the cost of black olives $3 a pound.

And cost of green olives $4 a pound.

Now, the total money spends:

[tex]3x+4y=15.50[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]3(4-y)+4y=15.50[/tex]

[tex]12-3y+4y=15.50[/tex]

[tex]12+y=15.50[/tex]

Subtracting both sides by 12 we get:

[tex]y=3.5[/tex]

The green olives = 3.5 pounds.

Now, substituting the value of [tex]y[/tex] in equation (1):

[tex]x=4-y\\x=4-3.5\\x=0.5\ pounds.[/tex]

The black olives = 0.5 pounds.

Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.

Final answer:

Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party, determined by solving a system of equations representing the total weight and cost of the olives.

Explanation:

How Many Pounds of Black and Green Olives did Susan Buy?

To determine how many pounds of black and green olives Susan bought, we need to create a system of equations based on the information provided:

Let x be the number of pounds of black olives Susan bought, and let y be the number of pounds of green olives.

The first equation will represent the total weight of olives:

1. x + y = 4 (since Susan bought 4 pounds of olives in total)

The second equation will represent the total cost of olives:

2. 3x + 5y = 15.50 (because black olives cost $3 per pound and green olives cost $5 per pound)

Now, let's solve this system of equations:

Multiplying the first equation by 3 gives us a new equation:
3x + 3y = 12

Now, we subtract this new equation from the second equation to find y:

(3x + 5y = 15.50) - (3x + 3y = 12)

2y = 3.50
y = 1.75

So, Susan bought 1.75 pounds of green olives. We can now substitute y into the first equation to find x:

x + 1.75 = 4
x = 4 - 1.75
x = 2.25

Therefore, Susan bought 2.25 pounds of black olives.

In conclusion, Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party.

Answer:   [tex]\dfrac{5}{9}[/tex]

Step-by-step explanation:

When we throw a die , Total outcomes =6

When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]

Given : Three fair dice are rolled, one red, one green and one blue.

Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed

By Permutations , the number of favorable outcomes = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]

The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]

The probability that the upturned faces of the three dice are all of different numbers  is [tex]\dfrac{5}{9}[/tex] .

Answer:

Step-by-step explanation:

Triangle GHI is a right angle triangle.

From the given right angle triangle,

HI represents the hypotenuse of the right angle triangle.

With m∠H as the reference angle,

GH represents the adjacent side of the right angle triangle.

GI represents the opposite side of the right angle triangle.

To determine m∠H, we would apply

the Sine trigonometric ratio.

Sine θ = opposite side/hypotenuse. Therefore,

Sin H = 9/10 = 0.9

m∠H = Sin^-1(0.9)

m∠H = 64.2° to the nearest tenth.

the equations are:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

[tex]\[ a^2 = c^2 - b^2 \][/tex]

[tex]\[ b^2 = c^2 - a^2 \][/tex]

In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. So, we have:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

This equation represents the relationship among the side lengths of a right triangle.

Therefore, the equations are:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

[tex]\[ a^2 = c^2 - b^2 \][/tex]

[tex]\[ b^2 = c^2 - a^2 \][/tex]

This completes the three relations among a, b, andc.

The complete Question is given below:

A right triangle has side lengths of a,b , and c units. The longest side has a length of c units. Complete each equation show three relations among a,b , and c .

Type the answers in the boxes below.

c^(2)= _____

a^(2)= _____

b^(2)= _____

Answer:

Fiona is not correct because a larger part of the square is white.

Step-by-step explanation:

The blue area is much smaller making it unlikely for the coin to land in that area.

Answer:

I took this test and while it was hard I managed to get this answer correct here is the picture

I know this answers two years late, but it will help those in the future

Good luck, hope you ace the test

To graph the sine function with provided features, we calculate the period from the frequency, acknowledge the midline at y = 2, and recognize the amplitude of 2. The first maximum is at (π, 4), giving us the complete function y = 2 sin(π/2 x) + 2.

To graph a sine function with the given features, we first recognize that the frequency of 1/4π means the period (T) of the function is the reciprocal of the frequency, or 4π. The amplitude of 2 indicates the function will oscillate 2 units above and below the midline, which is represented by y = 2. Since the function is not reflected over the x-axis and has a y-intercept of (0, 2), we start at the midline. The graph will reach its first maximum at (T/4, 2 + amplitude) which is (π, 4), since one quarter of the period will place us at a peak of the sine wave. The complete sine function derived from these features would be y = 2 sin(π/2 x) + 2.

Answer:

Im pretty sure it is symmetrical-balance

Step-by-step explanation:

Answer:

symmetrical-balance.

Step-by-step explanation:

In design, the near or exact matching of left and right sides of a three-dimensional form or a two-dimensional composition.

Answer:

  the  answer  is B: 17 and one-third

Step-by-step explanation:

Answer:

option C

Step-by-step explanation:

In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon

The ration of spice mix over Cinnamon is

[tex]\frac{\frac{3}{4} }{\frac{5}{6} } =\frac{3}{4} \cdot \frac{6}{5} =\frac{9}{10}[/tex]

Let x be the spice mix per pound

make a proportion

[tex]\frac{9}{10} =\frac{1}{x}[/tex]

cross multiply

[tex]9x=10\\x=\frac{10}{9}\\x= 1 \frac{1}{9}[/tex]

option C is the answer

Answer:

-26

Step-by-step explanation:

a(6)=-2(6)-14

a(6)=-12-14

a(6)=-26

Hope this helped!

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-Shadyk

The 6th value in the sequence = an=−2n−14 = -4.3

Take n = 6

⇒  a6 = -2·6 -14 = -12-14 = -26

∴ a= [tex]\frac{-26}{6}[/tex] = -4.3

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.

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Answer:

Mona = 8, Shakira = 16

Step-by-step explanation:

S = 2m....m = S/2

2S + S = 24

3S = 24

S = 24/3

S = 8

Mona = 8

Shakira = 16

Answer:

Domain  (0, ∞)  and Range (-∞, ∞).

Step-by-step explanation:

The domain of f(x) = 0.5^x is all values of x and the range is f(x)>0  as  0.5^x  cannot be negative or zero.

In interval form this is Domain is (-∞, ∞) and Range is  (0, ∞).

So its inverse has Domain  (0, ∞)  and Range (-∞, ∞).

The requierd domain (0, ∞) and range (-∞, ∞) of the inverse of f(x) = 0.5ˣ.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The exponential function is given in the question, as follows:

f(x) = 0.5ˣ

Here the domain of f(x) = 0.5ˣ is all values of x and the range is f(x) > 0  as f(x) = 0.5ˣ  cannot be negative or zero.

In interval form, the Domain is (-∞, ∞) and the Range is (0, ∞).

As a result, its inverse has Domain (0, ∞) and Range (-∞, ∞)

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Answer:

($13,300,$46,900)

Step-by-step explanation:

We are given the following in he question:

Mean, μ = $30,100

Standard Deviation, σ = $5,600

Chebyshev's Theorem:

[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]

Thus, 89% of data lies within three standard deviation of mean.

[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]

Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)

Answer: the employee must make sales of $32000

Step-by-step explanation:

Let x represent the total sales that the employee makes in a month.

One employee of a computer store is paid a base salary of $2,000 a month plus an 8% commission on all sales over $7,000 during the month. This means that if the employee makes sales of $x in a month, his total earnings for that month would be

2000 + 8/100(x - 7000)

= 2000 + 0.08(x - 7000)

= 2000 + 0.08x - 560

= 0.08x + 1440

Therefore, for the employee to earn

a total of $4,000 for the month, the amount of sales would be

0.08x + 1440 = 4000

0.08x = 4000 - 1440

0.08x = 2560

x = 2560/0.08

x = $32000

Answer: X-intercept: 1/9

Y-intercept: 1/5

Step-by-step explanation:

Answer: Leah has 15 stickers left for herself.

Step-by-step explanation:

Total number of stickers that Leah had initially is 50. Leah gave 1/2 of the stickers to her sister. This means that the number of stickers that Leah gave to her sister is

1/2 × 50 = 25 stickers

Of the amount left, she gave 2/5 to her friend. This means that the number of stickers that Leah gave to her friend is

2/5 × 25 = 10 stickers

Therefore, the number of stickers that Leah have left for herself is

50 - (25 + 15)

= 50 - 35

= 15

After giving away some of her stickers to her sister and friend, Leah has 15 stickers left for herself.

Leah initially had 50 stickers. She gave half of them to her sister, which left her with 50/2 = 25 stickers. Then, she gave away 2/5 of these remaining stickers to her friend.

To calculate how many she gave her friend, we multiply 25 * 2/5 = 10 stickers.

To find out how many Leah has left for herself, we subtract this from the number she had after giving stickers to her sister: 25 - 10 = 15 stickers.

So, Leah has 15 stickers left for herself.

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Answer:

1) 706.86

2) 726 cm^3

3) V= 792 km^3

4) 209.4 ft^3

Step-by-step explanation:

#4: V=πr2h

3.14 times the radius, then the height divided by 3

#3 V=lwh

V=lwh3 length times width times height divided by 3

#2 ^same as #3 steps

#1 A=πr2

pi times the radius squared

Answer:

1. 706.5

2. 726

3. 396

4. 130.8

Step-by-step explanation:

1. Area = pi × r²

= 3.14 × 15²

= 706.5 ft²

2. Volume = ⅓ × base area × height

= ⅓ × 11² × 18

= 726 cm³

3. Volume = ⅓ × base area × height

= ⅓ × ½ × 9 × 12 × 22

= 396 km³

4. radius = 10/2 = 5

Volume = ⅓ × base area × height

= ⅓ × 3.14 × 5² × 5

= 130.83333 ft³

Answer:$1035 was raised from the raffle tickets.

Step-by-step explanation:

The total number of prices available

for the lucky draw is 6. The 6 prizes cost 8 3/10 dollar each. Converting 8 3/10 = 83/10 dollar each.

The total cost of the 6 prizes would be 83/10 × 6 = 249/5 dollars

The total number of Raffle tickets that were sold is 1356. Each ticket was sold for 4/5 dollars each. The total amount from 1356 tickets would be

4/5 × 1356 = 5424/5 dollars

The total amount of money that was raised from the raffle tickets would be

5424/5 - 249/5 = 5175/5 = $1035

Answer: the total distance that the object will fall after 6 seconds is 576 feet.

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 6 seconds

a = 16 feet

d = 80 - 48 = 48 - 16 = 32

Therefore, the total distance the object will fall in 6 seconds is the sum of the first 6 terms, S6. It becomes

S6 = 6/2[2 × 16 + (6 - 1)32]

S6 = 3[32 + 32 × 5]

S6 = 3 × 192 = 576 feet

Final answer:

The total distance the penny falls in 6 seconds, according to the arithmetic sequence provided (16 feet the first second, 48 feet the second, and so on), is 576 feet.

Explanation:

The question involves calculating the total distance an object falls in a given number of seconds, according to an arithmetic sequence. In this case, the penny falls 16 feet in the first second, 48 feet in the second, and the distance increases by a constant amount each second. This is an arithmetic sequence where each term increases by 32 feet (48 - 16 = 32). To find the total distance, we sum the first six terms of the sequence.

The general formula for the nth term of an arithmetic sequence is a_n = a_1 + (n - 1) * d, where a_1 is the first term and d is the common difference. We can calculate the distance for each second and then add them up.

Here is how you calculate it:

First second: 16 feet

Second second: 16 + 32 = 48 feet

Third second: 48 + 32 = 80 feet

Fourth second: 80 + 32 = 112 feet

Fifth second: 112 + 32 = 144 feet

Sixth second: 144 + 32 = 176 feet

To find the total distance, add these values together:

Total distance = 16 + 48 + 80 + 112 + 144 + 176 = 576 feet.