Alyssa went to Texas Roadhouse with her family. Their dinner bill was $59.96. How much tip will Alyssa give the waiter, if she tips
him 18%?

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Let A(t) denote the amount of salt (in kg) in the tank at time t.

At the start, there are 80 kg of salt in the tank, so A(0) = 80.

Solution flows into the tank at a rate of 8 L/min at a concentration of 0.04 kg/L, so that salt flows in at a rate of

(8 L/min) * (0.04 kg/L) = 0.32 kg/min

Solution flows out at the same rate, but its concentration depends on the amount of salt in the tank. The concentration of the solution is the proportion of salt in the liquid to the total volume of the liquid. Solution flows in and out at 8 L/min, so the volume of liquid (1000 L) stays the same. A(t) is the amount of salt in the tank, so the concentration is A(t)/1000 kg/L. Hence salt flows out at a rate of

(8 L/min) * (A(t)/1000 kg/L) = 0.008 A(t) kg/min

The net rate at which salt flows through the system is then given by the differential equation,

dA(t)/dt = 0.32 - 0.008 A(t)

(Don't forget to include the initial condition)

Answer:

Answer D

Step-by-step explanation:

First equation

5x + 5 = (-4) - 5

5x + 5 = -9

5x = -14

x = -2.8

Solvable

Second equation

4x + 5 = -435

4x = -440

x = -110

Solvable

Third equation

-4x + 5 = (-48) - 4

-4x + 5 = -52

-4x = -57

4x = 57

x = 14.25

Solvable

Fourth equation

-4x + 5 = -4x - 5

5 = -5

Not solvable

Step-by-step explanation:

Hey, there!!!

According to your question,

case i

force (f) = 60 n

acceleration due to gravity (a)= 10m/s^2

now,

force = mass × acceleration due to gravity

or, 60 = m × 10

or, 10m= 60

or, m= 60/10

Therefore, the mass is 6 kg.

now,

In case ii

mass= 6kg {Because there was no change in mass only change in force}

force= 54 n

now, acceleration due to gravity = ?

we have,

f=m×a

or, 54= 9×a

or, 9a= 54

or, a= 54/9

Therefore, the acceleration due to gravity is 6m/ s^2.

Hope it helps....

Answer:

he left 15 % of his bill as a tip

Step-by-step explanation:

7.5/50 x 100

0.15 x 100

15

Percentage

Answer:

10.5$

Step-by-step explanation:

Nearest 10 dollar: 70$

since the tip is 15% u take the 15 and divide it by a 100

amd than multiply the answer with 70$

the answer will be 10.5$

The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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The situation best modeled by the equation is 50 more than 24 times a number equals 92 more than the number

From the question, we have the following parameters that can be used in our computation:

24x + 50 = 17x + 92

Let x be a real number

So, a situation that can be derived from the equation is that

50 more than 24 times a number equals 92 more than the number

When represented as an equation, we have

24x + 50 = 17x + 92

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Answer:

10626 ways

Step-by-step explanation:

Given

Number of students = 23

Prizes = 3

Required

Number of different outcomes for the top 3

This question will be solved using permutation formula because it implies selection of 3 students from 23

\(^nP_r = \frac{n!}{(n-r)!}\)

Where n = 23 and r = 3

The formula becomes

\(^{23}P_3 = \frac{23!}{(23-3)!}\)

\(^{23}P_3 = \frac{23!}{(20)!}\)

\(^{23}P_3 = \frac{23!}{20!}\)

\(^{23}P_3 = \frac{23 * 22 * 21 * 20!}{20!}\)

\(^{23}P_3 = 23 * 22 * 21\)

\(^{23}P_3 = 10626\)

Hence, there are 10626 ways

Answer:

The painting is \(t = 10911.1 \ years \ old\)

Step-by-step explanation:

From the question we are told that

    The amount of carbon present after t year is

           \(y(t) = y_o * e ^{-0.00012t}\)    {Note ; This is the function }

Here  \(y(t)\) is the amount of carbon-14 after time t

        \(y_o\) the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

  Then it mean that

            \(y(t) = 0.27 y_o\)

So the equation is represented as

       \(0.27 y_o = y_o * e ^{-0.00012t}\)

=>    \(0.27 = * e ^{-0.00012t}\)

=>    \(ln(0.27) = -0.00012t\)

=>  \(- 1.30933 = -0.00012t\)

=>  \(t = \frac{-1.30933}{-0.00012}\)

=>   \(t = 10911.1 \ years\)

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

There are 2322432 coupons generated .

According to the question we have been given that the code contains one digit followed by four letters . That is it can be assumed as

                         code = D L L L L   where D and L represent the digits and letters.

Now total digits we have is  = 7

       total number of letters we have = 24

So we have to choose the first digit from these 7 digits. Thus there are 7 ways in which we can choose as they are repeated.

Also there are 24 ways to select the 4 letters after the digits as the letters are being repeated, that is ways =   24⁴

Therefore the number of coupons that can be generated from the combination are :

                                7*24⁴ = 7*331776

                                          = 2322432

Hence the number of coupons generated are 2322432.

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a) He needs 500 g of sugar to make apple crumble for 16 people.

b) She needs 45 g of flour to make apple crumble for 2 people.

c) 500g of apples is enough to make apple crumble for 6 people.

The amounts for this problem are obtained according to the proportions given in the problem.

For 8 people, the amount of sugar needed is of 250 g. For 16 people, the  number of people doubles, hence the amount of sugar needed will also double, as follows:

2 x 250 = 500 g.

For 2 people, the amount of each item is divided by 4, hence the amount of flour needed is given as follows:

180/4 = 45 g.

The amount of apple needed per people is of:

700/8 = 87.5 grams.

For 6 people, the amount is given as follows:

6 x 87.5 = 525 grams.

Hence 500g of apples is enough to make apple crumble for 6 people.

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Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

Answer:

48 ft²

Step-by-step explanation:

The question is only asking for the rectangular part, so you would do 12 • 4 = 48.

Answer:

The first one, 'five-twelfths'.

Answer:

\( \dfrac{5}{12} \)

Five-twelfths

Step-by-step explanation:

Usually, "of" in math means a multiplication.

5/6 of 1/2 means 5/6 times 1/2.

\( \dfrac{5}{6} \times \dfrac{1}{2} \)

To multiply fractions, multiply together the numerators and multiply together the denominators.

\(\dfrac{5}{6} \times \dfrac{1}{2} = \dfrac{5 \times 1}{6 \times 2} = \dfrac{5}{12}\)

Answer:

\( \dfrac{5}{12} \)

The values of the following functions are:

a. (f ºg)(x) = x+2

b.  (g º f)(x) = 3x + 14

c.  (f º g)(-1) = 3

d.  (g º f)(-1) = 11

Given:

f(x) = x+4 and

g(x) = 3x+2

we are asked to determine the following functions:

a.  (f º g)(x)

⇒ f(g(x))

⇒ f(3x+2)

⇒  (f º g)(x) = (3x+2)+4

= 3x+6

divide by 3

= x+2

b.  (g º f)(x)

⇒ g(f(x))

⇒ g(x+4)

⇒  (g º f)(x) = 3(x+4)+2

= 3x+12+2

= 3x+14

c.  (f º g)(-1)

⇒ f(g(-1))

⇒ f(3(-1)+2)

⇒ f(-3+2)

⇒ f(-1)

⇒  (f º g)(-1) = -1+4

= 3

d.  (g º f)(-1)

⇒ g(f(-1))

⇒ g(-1+4)

⇒ g(3)

⇒  (g º f)(-1) = 3(3)+2

= 11

Hence we get the required answer.

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Answer:

C

Step-by-step explanation:

using the rule of logarithms

log a - log b = log (\(\frac{a}{b}\) ) , then

log (\(\frac{15}{7}\) ) = log 15 - log 7

Answer:

How can you find the amount of interest owed on a loan? Simple interest is money earned on a savings account or an investment. ... (Years). I = Prt. Work with a partner. You put $100 in a savings account. ... The account earns $100 simple interest in 4 years. What is the annual interest rate? ... You put $350 in an account.

Step-by-step explanation:

Answer:

31 as it has only 2 factors which is 1 and 31

Answer:

B

Step-by-step explanation:

After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, there are 144 wοrds οn the vοcabulary list.

A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.

A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.

1/4 x = tοtal number οf wοrds Miguel has nοt memοrized

1/4 x = x - 36

x/4 = 36

x = 144

Therefοre, there are 144 wοrds οn the vοcabulary list.

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Answer:

If the tax rate = 3.9% and the product u are buying is priced at $42 Then, the amount you will pay for the object will be, $42 + 3.9/100 * 42

Step-by-step explanation:

I hope this help

- Intersecting lines are those lines which cross any of the two axis of the coordinate plane: x axis or y axis.

- Intersecting lines are also lines which intersect each other on a coordinate plane.

The previous explanations can be expressed as follow:

where the red lines are intersecting lines. You can notice that both lines intersect both axis ans also intersect each other.

FALSE: Finding non-linear correlations between two variables cannot be done using regression.

To determine the association between two quantitative variables, simple linear regression is performed. Simple linear regression can be used to determine:

Regression analysis is a mathematical technique for creating predictive models in which one or more existing independent or explanatory factors influence an unknown target variable.

The determination coefficient value serves as a measure of a regression model's fitness.

Thus, finding non-linear correlations between two variables cannot be done using regression is a incorrect statement.

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The complete question is-

Determine if the following statement is true or false:

Regression cannot be used to identify non-linear relationships between two variables.

Answers:

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

Explanation:

Answer:

32 degrees

Step-by-step explanation:

The total angle formed is 90 degrees because there is a right angle.

So, 90 - 58 = g

      32 degrees = g

Answer:

13 basketballs

Step-by-step explanation:

Answer:

The other zeros are:

1 - 2i, 1 - √5