5. The Toy Car Company sells toy cars for $8.00
per car and charges $3.50 for shipping.
a.

1) 3.25n

Overall cost of n gallons of gas

2)3.25n = 26

we are spending 26 dollars on 8 gallons of gas

3)40-3.25n

Ammount we have remaining after spending on n gallons of gas out of 40 dollars

4) 40-3.25n = 1.00

The maximum number of gallons of gas we can buy from 40 dollar is 13 gallons and 1 dollar is still remaining to us.

The given representations could be classified thus :

3.25n (Expression)

3.25n=26 (Equation)

40-3.25n (Expression)

40-3.25n=1.00 (Equation)

Total amount to spend = $40

Cost per gallon = $3.25

Number of gallons = n

An expression could be a variable, constant or a combination of both which is related by an operation symbol.

An equation on the other hand maybe defined as a relationship between two expressions linked by an equal to symbol.

Evaluating the representations given :

3.25n : This is an expression as it lacks an equal to sign connecting the expression. The expression means the cost of n gallons of gas.

3.25n = 26 : This is an equation as it contains two Seperate expressions connected by the equal to sign. The equation means that number of gallons of gas, n that can be purchased with $26.

40 - 3.25n : This is an expression. The amount left after purchasing n gallons from $40.

40 - 3.25n = 1.00 : This is an equation. The number of gallons of gas that can be purchased from $40 and still have $1 left.

Learn more : https://brainly.com/question/18109354

Answer:

The answers is " Option B".

Step-by-step explanation:

[tex]CI=\hat{Y}\pm t_{Critical}\times S_{e}[/tex]

Where,

[tex]\hat{Y}=[/tex] predicted value of lead content when traffic flow is 15.

[tex]\to df=n-1=8-1=7[/tex]

 [tex]95\% \ CI\ is\ (463.5, 596.3) \\\\\hat{Y}=\frac{(463.5+596.3)}{2}\\\\[/tex]

     [tex]=\frac{1059.8}{2}\\\\=529.9[/tex]

Calculating thet-critical value[tex]t_{ \{\frac{\alpha}{2},\ df \}}=-2.365[/tex]

The lower predicted value [tex]=529.9-2.365(Se)[/tex]

[tex]463.5=529.9-2.365(Se)\\\\529.9-463.5=2.365(Se)\\\\66.4=2.365(Se)\\\\Se=\frac{66.4}{2.365} \\\\Se=28.076[/tex]

When [tex]99\%[/tex] of CI use as the expected lead content: [tex]\to 529.9\pm t_{0.005,7}\times 28.076 \\\\=(529.9 \pm 3.499 \times 28.076)\\\\=(529.9 \pm 98.238)\\\\=(529.9-98.238, 529.9+98.238)\\\\=(431.662, 628.138)\\\\=(431.6, 628.1)[/tex]

Answer:

[tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}[/tex]

[tex]\displaystyle f(1) = \frac{1}{4}[/tex]

Step 2: Integration

Integrate the derivative to find function.

Our general solution is  [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex].

Step 3: Find Particular Solution

Find Integration Constant C for function using given condition.

∴ Our particular solution to the differential equation is  [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex].

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

Answer:

The roots are: 1, -7 and -7

Step-by-step explanation:

When we put x = -1 in F(x) it is equal to 0

Thus, (x + 1) is factor of given function.

When we divide F(x) by (x + 1) it gives the value (x² - 6x - 7)

Now, factorizing x² - 6x - 7 by middle term splitting.

x² - 6x - 7 = x² - 7x + x - 7

⇒ x(x - 7) + 1(x - 7)

⇒ (x + 1) (x - 7)

Thus, x³ - 5x² - 13x - 7 = (x + 1)(x + 1)(x - 7)

Thus, Roots of the given polynomial function is x = -1, -1, 7

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

The best estimate of the population mean for heart rate among football players is of 71.4 beats per minute.

Step-by-step explanation:

The best estimate for the population mean is the sample mean.

Sample mean:

Sum of all values in the sample divided by 10(size of the sample). So

[tex]\overline{x} = \frac{62+74+74+64+76+64+80+76+68+76}{10} = 71.4[/tex]

The best estimate of the population mean for heart rate among football players is of 71.4 beats per minute.

Answer: 71.4

Just a confrimation to the below anwser.

9514 1404 393

Answer:

  correct choice is marked

Step-by-step explanation:

The error is in step 2. The square root cannot be distributed to a sum.

Answer:

A.   x < -1

Step-by-step explanation:

Open circle at -1 with line to the left

A.   x < -1

Answer:

#1 Eighty-nine and 23 thousandths. #2 B.

Step-by-step explanation:

9 is more than 8. ‍♀️

Answer:

THE ANSWER IS B

Step-by-step explanation:

B mine please im so single

Answer: hello your question is incomplete attached below is the missing codes

Answer : It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement was not written in the main function

Step-by-step explanation:

It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement  should be moved to the Main

The correction  is below

{

   double* p = new double;

   hypotenuse(1.5, 2.0, p);

  cout << "The hypotenuse is " << *p << endl;

}

Answer:

a) 82.

b) So a growth factor of 0.025

c) 2.5%.

d) f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.

Step-by-step explanation:

Exponential equation of population growth:

The exponential equation for population growth has the following format:

[tex]f(x) = x(0)(1+r)^x[/tex]

In which x(0) is the initial value and r is the growth factor, as a decimal.

In this question:

In x years after 2021:

[tex]f(x) = 82(1.025)^x[/tex]

a)

This is f(0). So

[tex]f(0) = 82(1.025)^0 = 82[/tex]

So 82.

b)

We have to find r. So

[tex]1 + r = 1.025[/tex]

[tex]r = 1.025 - 1 = 0.025[/tex]

So a growth factor of 0.025.

c)

Growth factor multiplied by 100%.

So 0.025*100% = 2.5%.

d)

f(5) = population in 5 years after January 1st 2021, that is, January 1st 2026.

[tex]f(5) = 82(1.025)^5 = 93[/tex]

f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.

Answer:

240

Step-by-step explanation:

They spent $120 buying 120 items, so they have -$120. By selling the items at 3x the price, they gained the 120 back and made a profit of 240 (120 x 2).

Answer:

b

Step-by-step explanation:

Answer:

➬➬➬➬➬➬➬➬

[tex]6x+5+(11x-5)+x=180^o[/tex]

[tex]18x=180[/tex]

[tex]x=10[/tex]

☄m∠Q=105°

❆❆❆❆❆❆❆❆❆❆❆❆

hope it helps....

have a great day!!

Answer:

D.

Step-by-step explanation:

The mean is 11,000

Answer:

B

Step-by-step explanation:

Area = 1/2 × 24 × 11 × Sin(76)

Area = 12 × 11 × 0.9703

Area = 132 × 0.9703

Area = 128.0796

Area = 128.1 in^2

Answer:

15.05 is your answer.

Step-by-step explanation:

To find our answer we will first divide 8.75 by 100 since it is a percentage.  8.75 ÷ 100 = 0.0875

Now we will take 0.0875 and multiply it by 172 and we get 15.05.  Therefore, 15.05 is our answer

Hey there!

8.75% of 172

The word “of” means multiply in mathematical terms.

8.75% * 172

8.75% = 8.75/100 = 0.0875

0.0875 * 172

= 301/20

= 15.05

Answer: 301/20 OR 15.05

(BOTH ANSWERS WORK because they are both equivalent)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

You would be correct!

Step-by-step explanation:

10 × 4 = 40 40 + 15 = 55 therefore D is the answer great job!

Answer:

3 weeks

Step-by-step explanation:

Two puppies from the same litter are named Bruno Puppy Weight and Jasper. Their weights during the first  weeks are plotted on the coordinate grid. At which age did Bruno and Jasper weigh the same?

Solution:

We can see that Bruno and Jasper weight is represented by a straight line. Let y represent the weight of the puppies in ounce and x represent the age in weeks.

For Bruno:

The line passes through (1, 10) and (5, 16), hence the equation of the line is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{16-10}{5-1} (x-1)\\\\y-10=\frac{3}{2}(x-1)\\\\y=1.5x+8.5\ \ \ (1)[/tex]

For Jasper:

The line passes through (0, 12) and (3, 13), hence the equation of the line is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-12=\frac{13-12}{3-0} (x-0)\\\\y-12=\frac{1}{3}(x)\\\\y=\frac{1}{3} x+12\ \ \ (2)[/tex]

To find the age at which both puppies weighed the same, we have to solve equation 1 and 2 simultaneously. Subtract equation 1 from 2:

-1.167x + 3.5 = 0

1.167x = 3.5

x = 3

Put x = 3 in equation (2)

y = (1/3)(3) + 12 = 13

The solution is (3, 13)

Therefore both Jasper and Bruno weigh the same weight of 13 ounce at 3 weeks of age

Explanation:

To go from figure 1, to figure 2, we apply a translation (aka "shifting"). Specifically, we translate 3 units to the right and 4 units up.

To go from figure 2 to figure 3, we apply a reflection. The mirror line is vertical and it is along the shared segment of figures 2 and 3.

Answer and Step-by-step explanation:

The product of a two numbers/values is the result of multiplying two numbers/values.

So, multiply b and 3 together.

3b is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

77 boys, 65 girls

Step-by-step explanation:

x as the variable to represent amount of girls, and there are 12 more boys than girls (x+12). So the equation would be:

x + x + 12 = 142

2x + 12 = 142

x = 65

65 girls

then 65+ 12 = 77 boys

Answer:

509

Step-by-step explanation:

There are 4 prime factors of 6108

6108 ÷ 2 = 3054

3054 ÷ 2 = 1527

1527 ÷ 3 = 509

509 ÷ 509 = 1

Answer:

Step-by-step explanation:

5(2b+3)+8(b-6)

=10b+15+8b-48

=18b-33

=3(6b-11)

Answer:

Step-by-step explanation:

Given 10.43, you can 'estimate' it only by rounding off:

10.43 to the nearest tenth is 10.4.

10.43 to the nearest whole number is 10; we drop the fraction 0.43.

1

Answer:

V =65416.666666 cm^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The diameter is 50 so the radius is 1/2 of the diameter

r = 1/2 (50) = 25

V = 4/3 ( pi) (25)^3

V = 4/3 (pi) 15625

V =20833.3333 pi

Using 3.14 for pi

V =65416.666666 cm^3

Answer:

V =65416.666666 cm^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The diameter is 50 so the radius is 1/2 of the diameter

r = 1/2 (50) = 25

V = 4/3 ( pi) (25)^3

V = 4/3 (pi) 15625

V =20833.3333 pi

Using 3.14 for pi

V =65416.666666 cm^3

Answer:

I think it's option B

Answer:

see first of all it is a quadratic polynomial so it will have 2 zero alpha and beta

now , we will find value of a , b, c

so,

a= 3

b= 5

c= -2

now, sum of the zeros ( alpha + beta) =-b/a

so,-5/3

now product of zeros (alpha *beta) = c/a

so, it will we -2/3

hope you get it !