Today 4 friends went out for lunch. Their total bill was $24.80, including tax and gratuity. They decided to split the bill equally and each paid with a $10 bill. How much money will each person get back

Proportionately, the number of minutes it should take to complete 4 levels is B. 120 minutes.

Proportion is the ratio between one value and another.

Proportions show the relative amount of a variable or value contained in the whole or another variable.

Proportions as fractional values are depicted using fractions, decimals, or percentages.

Number         Time

of Levels       (hours)

4                        ?

5                      2.5

The proportion of hours for level 5 = 0.5 (2.5/5) for each level.

If every level takes 0.5 hours or 30 minutes, level 4 will take 2 hours (0.5 x 4).

Or:

If level 5 takes 2.5 hours, level 4 will take 2 hours (2.5/5 x 4).

Thus, proportionately, to complete level 4 will take Option B.

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A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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The domain and range and the type of relation should be determined as follows;

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

Based on relations 3 and 4, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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Given:

Out of 200 people sampled, 174 had kids Based on this, construct a 90% confidence interval for the true population proportion of people with kids.

Required:

We need to find the confidence interval.

Explanation:

The proportion of the mean is

The standard error of the sample is

Assuming a normal distribution, look for the z-score associated with a 0.95 cumulative probability.

z-score = 1.645

The confidence interval is 0.87+0.0395 and 0.87-0.0395.

Final answer:

Answer:

216 dollars

Step-by-step explanation:

24yd*3= 72 feet*3= 216 dollars

if my answer helps please mark as brainliest.

Answer:

72$

Step-by-step explanation:

24*3.00

Answer:

Step-by-step explanation:

When they ask you to solve graphically they want you to construct those functions and note where the two lines intersect as that is the solution to the system of equations. Solving mathematically they will be equal when y=y so we can say

x-4=-x+6 add x to both sides

2x-4=6. add 4 to each side

2x=10. divide each side by 2

x=5, since y=x-4

y=5-4

y=1

So the lines will intersect at the point (5,1)

The best interpretation for the expression 85h + 75 is;

The charge for each hour worked is $85

The initial charge before commencement of work per hour is $75

The general formula of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, the slope may also be called the rate of change of the output with the input while the y-intercept represents the initial value or the value of the output when the input is zero.

Now, we are given the equation for total bill as;

T = 85h + 75

where h is number of hours worked

Thus;

The charge for each hour worked is $85

The initial charge will be $75 before commencement of work per hour.

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Answer:

y = 3 cot (1x)?

Step-by-step explanation:

The nth term of the sequence -3, 0, 5, 10, 25, 5, 47 can be represented by the piecewise function:

nth term =

-3 + (n - 1) * 5, if n mod 5 ≤ 5

5 + (n - 1) * 15, if n mod 5 > 5

To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Upon analyzing the given sequence -3, 0, 5, 10, 25, 5, 47, we can observe the following:

The sequence starts with -3 and increases by 5 each time, except for the 5th term, where it increases by 15 (from 10 to 25). After the 5th term, the sequence starts again with 5 and continues to increase by 15 each time.

Based on this pattern, we can divide the sequence into two parts:

Part 1: -3, 0, 5, 10, 25 (increasing by 5 each time)

Part 2: 5, 20, 35, 50, 65 (increasing by 15 each time)

Now, to determine the nth term, we can consider the formula for arithmetic sequences:

nth term = first term + (n - 1) * common difference

For Part 1, the first term is -3 and the common difference is 5. Thus, the nth term for Part 1 is given by:

nth term = -3 + (n - 1) * 5

For Part 2, the first term is 5 and the common difference is 15. Therefore, the nth term for Part 2 can be expressed as:

nth term = 5 + (n - 1) * 15

However, since the sequence alternates between Part 1 and Part 2, we need to determine which part the nth term falls into. For that, we can use modular arithmetic:

If n mod 5 is less than or equal to 5, then the nth term is from Part 1.

If n mod 5 is greater than 5, then the nth term is from Part 2.

Let's calculate a few terms to illustrate this:

For n = 1, the sequence starts with -3, so the 1st term is -3.

For n = 2, we are still in Part 1, so the 2nd term is 0.

For n = 3, Part 1 continues, so the 3rd term is 5.

For n = 4, we are still in Part 1, so the 4th term is 10.

For n = 5, Part 1 ends, and the 5th term is 25.

For n = 6, the sequence starts with 5 in Part 2, so the 6th term is 5.

For n = 7, Part 2 continues, so the 7th term is 20.

For n = 8, we are still in Part 2, so the 8th term is 35.

Based on this analysis, we can conclude that the nth term for the given sequence is:

If n mod 5 ≤ 5:

nth term = -3 + (n - 1) * 5

If n mod 5 > 5:

nth term = 5 + (n - 1) * 15

Therefore, depending on the value of n and the remainder when divided by 5, we can use the appropriate formula to calculate the nth term.

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Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Triangle PKE: ∠PKE = 16°, ∠PEK = 90°, and ∠EKP = 74°.

Triangle PMN: ∠PMN = 135°, ∠PKN = 8°, and ∠PKM = 37°.

To find the measures of all angles of triangles PKE and PMN in rhombus MPKN, follow these steps:

In a rhombus, all sides are equal in length, and the diagonals bisect each other at a right angle. Therefore, ∠PEK = 90°.

Since we know that one of the angles of triangle PKE is 16°, let's assume this angle is ∠PKE.

Now, we can find the third angle of triangle PKE.

The sum of the angles in any triangle is 180°,

so ∠EKP = 180° - (90° + 16°) = 180° - 106° = 74°.

In a rhombus, the diagonals bisect the angles.

So, ∠PKM = ∠EKP / 2 = 74° / 2 = 37°.

Similarly, ∠PKN = ∠PKE / 2 = 16° / 2 = 8°.

Finally, we can find the third angle of triangle PMN. Since ∠MPN is the supplementary angle to ∠K, ∠MPN = 180° - ∠K.

And ∠K = ∠PKM + ∠PKN = 37° + 8° = 45°. So, ∠MPN = 180° - 45° = 135°.

In summary, the measures of all angles of triangles PKE and PMN in rhombus MPKN are as follows

- Triangle PKE: ∠PKE = 16°, ∠PEK = 90°, and ∠EKP = 74°.

- Triangle PMN: ∠PMN = 135°, ∠PKN = 8°, and ∠PKM = 37°.

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No, the events A and B are not independent because the two events are dependent as drawing of the draw by first person affects probability of drawing the straw by the second person.

In the given question, eight friends are drawing straws. The one who picks the short straw must cook dinner for the others.

We have to determine whether the events A and B are independent.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.

The two events are dependent as drawing of the draw by first person affects probability of drawing the straw by the second person.

Hence, the events A and B are not independent.

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Answer:

-4/3

Step-by-step explanation:

slope is rise/run

we go down 4 hence the negative four, and over 3

-4/3

In this exercise we will use the differential equations to calculate finances, we find that:

a) \(Profit = (x - 3)f(x)\)

b) \(P' = f(x) + (x - 1) f'(x)\)

c) \(P' = 29400\)

The cost of producing the items is the total expenses of production while the revenue is the amount of money generated from selling the item.

a)Then using the given formula and substituting for the known values ​​we find that;

\(Cost = \ cost \ of \ producing \ one \ item * number \ of \ items \ produced\\Cost = $3 * f(x) = 3f(x)\\Revenue = selling \ price \ of \ one \ item * number \ of \ items \ produced\\Revenue = x * f(x) = xf(x)\\Profit = Revenue - Cost = xf(x) - 3f(x)\\Profit = (x - 3)f(x)\)

b) Applying knowledge of differential equations we find that:

\(P' = d/dx(xf(x) - 3f(x) )\\P' = f(x) + xf'(x) - f'(x)\\P' = f(x) + (x - 1) f'(x)\)

c)Substituting the known values ​​into the formula given above, we find that:

\(f(x) = 3000, x = $45, f'(x) = -600 items / 1$\\P' = 3000 + (45 - 1)(-600)\\P' = 3000 + 26400\\P' = 29400\)

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Answer:

\( \sf \: \frac{5 - 3 \sqrt{2} }{3} \)

Step-by-step explanation:

Given expression,

→ (5/3) - √2

Let's simplify the expression,

→ (5/3) - √2

→ (5/3) - ((√2 × 3)/(1 × 3))

→ (5/3) - (3√2/3)

→ (5 - 3√2)/3

Hence, answer is (5 - 3√2)/3.

Answer:

\(\dfrac{15+5\sqrt{2}}{7}\)

Step-by-step explanation:

Given rational expression:

\(\dfrac{5}{3-\sqrt{2}}\)

To write the given rational expression in its simplest form we need to rationalise the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of an expression is where we change the sign in the middle of the two terms.  Therefore, the conjugate of the denominator of the given expression is:

Multiply the numerator and denominator by the conjugate of the denominator:

\(\dfrac{5}{3-\sqrt{2}} \cdot \dfrac{3+\sqrt{2}}{3+\sqrt{2}}\)

Simplify:

\(\implies \dfrac{5(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}\)

\(\implies \dfrac{15+5\sqrt{2}}{9+3\sqrt{2}-3\sqrt{2}-2}\)

\(\implies \dfrac{15+5\sqrt{2}}{9-2}\)

\(\implies \dfrac{15+5\sqrt{2}}{7}\)

The simplification of the given value in  simplest form and can not be an improper fraction is 52/15.

An object's portion of the total or group is represented by a fraction. The fractional bar is a horizontal bar that divides a fraction's numerator (the top number) and denominator (the bottom number). The total number of items in a group or the number of equally divided equal pieces of the whole is represented by the denominator.

The given value is 3 1/15 + 0.4 , then we can convert to proper fraction as :

3 1/15 = 46/15

Then we  can convert as;

0.4 = 4/10 =2/5

Then add together;  46/15 + 2/5

= 52/15

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Answer:

Step-by-step explanation:

$126-$70 =

The p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis. There is insufficient evidence to support the claim p-value greater than the significance level 0.05.

Consider the above given that

⇒\(& \alpha=0.05 \quad \mathrm{n}=34 \mathrm{~s}^2=0.0005 \\\)

⇒\(H_{0} : \sigma^2 \leq 0.0004 \\\)

⇒\(H_{a} : \sigma^2 > 0.0004\)

The null and alternative hypothesis test statistic:

⇒\(& \mathrm{x}^2=\left(\frac{\mathrm{n}-1}{\sigma^2}\right) \mathrm{s}^2 \\\)

\(& =\left(\frac{34-1}{0.0004}\right) 0.0005 \\\)

⇒\(& \mathrm{x}^2=\left(\frac{33}{0.004}\right) \times 0.0005 \\\)

\(& =82,500 \times 0.0005 \\\)

⇒\(& \mathrm{x}^2=41.25\)

⇒\(h_{0} : $\sigma^2$ is that or equal to $0.0004$\)

⇒\(h_{a} : $\sigma^2$ is greater that $0.0004$\)

⇒p value=p(z>41.25)

⇒p value=0.1533

By using P Value from Chi-Square Calculator

⇒p value=0.1533

⇒P value >0.05

Fail to reject the null hypothesis.

Therefore, the p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis.

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The competitive advantage of some small Americans factories such as in tolerance contract manufacturing lies in their ability to produce parts with very narrow requirements, or tolerances, that are typical in the aerospace industry. consider a product with specifications that call for a maximum variance in the lengths of the parts of 0.0004. suppose the sample variance for 34 parts turns out to be \(s^{2}=0.0005\) . use \(\alpha=0.05\) , to test whether population variance specification is violated.

\(H_{0} \\H_{a}\)

Test statistic:

The p-value is-------.

The value of the function operation f - g(x) is 3x² + x

Function operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.

Addition and subtraction of functions:

A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.

Multiplication of functions:

Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.

Composition of functions:

Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.

In this problem, we have two functions which are;

The value of (f - g)(x) = 3x² + x

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Answer:

10

Step-by-step explanation:

Let us find the exact number of donors of gold and bronze respectively given there are 40 in total.

Gold: 45% of 40 = 45/100 *40 = 18 donors

Bronze: 20% of 40 = 20/100 *40 = 8 donors

18 donors - 8 donors = 10 more donors

I hope this helps! :)

Answer:

The sample size will be "\(102.5494 \sim 102\)". A further explanation is given below.

Step-by-step explanation:

Let the sample size will be:

= n

The given values are:

Standard deviation,

= 1.4

ME,

= 0.3

As we know,

⇒ \(n=(Z \frac{a}{2}\times \frac{SD}{E})^2\)

On putting the estimated values, we get

⇒    \(=(2.17\times \frac{1.4}{0 .3})^2\)

⇒    \(=(\frac{3.038}{0.3})^2\)

⇒    \(=102.5494 \sim 102\)

Answer:

the answer is 1.6%

Step-by-step explanation:

0.016 × 100/100 =

0.016 × 100% =

(0.016 × 100)% =

1.6%

hope this helps : )

Answer:

\(1.6\%\)

Step-by-step explanation:

\(0.016 = \frac{16}{1000} \)

let's write this fraction as a percentage

\( \frac{16}{1000} \times 100\% \\ = 1.6\%\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

2 staircases

Step-by-step explanation:

3 : 36

1 : 12

2 : 24

If katie can build three staircases to make 36 obstacles against the other player. Then 2 staircases will she need to make 24 obstacles

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

katie can build three staircases to make 36 obstacles against the other player

We need to find the number of staircases she need to make 24 obstacles.

Let us form a proportional relationship.

Consider x as the number of staircases will she need to make 24 obstacles

3/36=x/24

Apply cross multiplication

3×24=36x

72=36x

Divide both sides by 36

x=2

Hence Katie should have 2 staircases to make 24 obstacles.

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The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

Answer:

12\(x^{3}\)+9\(x^{2}\)-23x+5

Step-by-step explanation:

the answer is C I think hopeful these helps

BRAINLYY PLZZZ

Answer:

B heppppppp tarada ejejjejejeje

Answer: It’s probably C

Step-by-step explanation: