Kevin has ​$24 to buy a gift for his cousin. He found a gift for ​$22. With 5​% sales tax added​ on, will Kevin have enough money to buy the​ gift? If​ so, how much will he​ pay?

Answer:

A)  [tex]\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx[/tex]

General Formulas and Concepts:

Calculus

Discontinuities

Integration

Step-by-step explanation:

Let's define our answer choices:

A)  [tex]\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx[/tex]

B)  [tex]\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx[/tex]

C)  [tex]\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx[/tex]

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

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

Unit:  Integration

Book: College Calculus 10e

Answer: a and c are polynomials, b is not.

Step-by-step explanation:

A polynomial p(x) is written as:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀*x⁰

where x is the variable, and the numbers aₙ, aₙ₋₁, ..., a₁, a₀ are the coefficients of the polynomial, such that aₙ is the leading coefficient, and the value of n (always a natural number) is the degree of the polynomial.

Notice that the powers need to be always natural numbers.

Now, let's analyze the options:

a) 3*x - 2

We can rewrite this as:

3*x¹ - 2*x⁰

Then this is a polynomial.

b) p² + 1/p    (in this case the variable is p)

the second term can be written as:

1/p = p⁻¹

Then we have a term with a negative power of p, this means that this is not a polynomial.

c) 3*y² - 2*y/3 + 1

Same as in the first case, we can rewrite this as:

3*y² - (2/3)*y¹ + 1*y⁰

This is a polynomial.

Answer:

The dimensions of the cube would be:

Step-by-step explanation:

For this exercise, I suppose the measure of each cube is 1 unit, because there no says what is (you can replace it for ft, in, or another unit you need). How the big cube is formed by the 100.000 cubes smaller, and how a cube has its three measures equal: base, height, and width, you only need to obtain the cubic root of the total cubes (you use cubic root because you're gonna calculate a cube, for example, if you'd wanna calculate a square, you must obtain the square root of the total cubes):

How each cube measure is 1 unit, when you calculate the volume of the cube with the value obtained, you must obtain the total of the cubes:

In this form, you know the answer 46,41588834 is the right answer. I use the number with just two decimals (46,42 approximately) but you can use the complete number if you need.

Answer:

A. the domain is all real numbers. and

B.the y-intercept is 3

Answer: 1. Add 2. Multiple both sides 3. 15

Step-by-step explanation: hope this helps

Answer: 2 = − 7

4

+ 1

4

x

1.

✔ Add

Start Fraction 7 over 4 End Fraction to both sides.

2.

✔ Multiply both sides

by 4.

The solution is x =

✔ 15

.

Step-by-step explanation: i just did it on ed

Given :

The length of Dwight's garden is 12.5 meters.

Dwight measured it but made a measurement error of 6%.

To Find :

The lowest and highest measurement Dwight could have made.

Solution :

Error in length measuring is :

[tex]\Delta \ l = 12.5\times 0.06 \\\\\Delta \ l = 0.75\ m[/tex]

Therefore, the lowest and highest measurement he could have is 12.5 - 0.75  = 11.75  meters and 12.5 + 0.75 = 13.25  meters.

Answer:

Alyssa=225

Eric=680

Step-by-step explanation:

The money Alyssa has $660 and  Eric has $245.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Alyssa has $75 less than three times Eric.

Let $x be the money Eric had.

Then Alyssa has 3x-75

Together they have $905.

So, x+3x-75=905

4x=905+75

4x=980

x=980/4

x=$245

Money Alyssa has 3x-75

= 3×245-75

= 735-75

= $660

Therefore, money Alyssa has $660 and  Eric has $245.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

a. $12.54 = $ 1.65 + c/2 + c b. $ 7.26

Step-by-step explanation:

a. What equation can you use to find the cost c of a sandwich

Let c be the cost of a whole ham sandwich. Now, the total bill = cost of drinks + cost of half a ham sandwich  + cost of a whole ham sandwich.

total bill = $ 12.54, cost of drinks = $ 1.65, cost of half a ham sandwich = c/2 and cost of a whole ham sandwich = c. So,

$12.54 = $ 1.65 + c/2 + c

b. What is the value of c

We then solve for c in the equation $12.54 = $ 1.65 + c/2 + c

collecting like terms, we have

$12.54 - $ 1.65 = c/2 + c

$ 10.89 = 3c/2

multiplying through by 2, we have

$ 10.89 × 2 = 3c

$ 21.78 = 3c

dividing through by 3, we have

c = $ 21.78/3

= $ 7.26

Answer:

Number 4 is neither, number 6 is perpendicular

Step-by-step explanation:

Answer:

4) Neither

Same y intercept means intersecting and intersecting is not an option

6) Perpedicular

A perpendicular line has a slope the reciprocal of each other like in this case

0.4= 2/5, 5/2=2.5

Answer: 153

Step-by-step explanation:

When we have a group of N elements, the total number of combinations of K elements ( K ≤ N) is:

[tex]C (N, K) = \frac{N!}{(N-k)!*K!}[/tex]

Where N! = N*(N - 1)*(N - 2)*...*2*1

In this case, we have a group of 18 people (then N = 18) and we want to see how many different combinations of 2 we can make (K = 2).

Using the above equation we get:

[tex]C(18, 2) = \frac{18!}{(18 - 2)!*2!} = \frac{18!}{16!*2!} = \frac{18*17}{2} = 9*17 = 153[/tex]

There are 153 different ways in which the manager can do this.

Answer:

i tried but all i got was like 80 percent

Step-by-step explanation:

Answer:

(3,-9)

Step-by-step explanation:

The given equations are :

−5x−3y=12 (1)

y=x−12 ....(2)

Put the value of y from equation (2) in equation (1)

−5x−3(x-12)=12

-5x-3x+36 = 12

Taking like terms together

-5x-3x = 12-36

-8x = -24

x = 3

Put the value of x in equation (2)

y=3−12

y = -9

Hence, the solution of the above equations is x = 3 and y = -9 or (3,-9).

Answer:

SU < 22 cm

Step-by-step explanation:

Answer:

Stacy made £25.2 from the 18 loaves of bread. So She made £5.20 as a profit.

Step-by-step explanation:

18 loaves of bread × £1.4 = £25.2 Round it up = £25

£25.20 - £20 = £5.20 Round it up = £5

Stacy Made about £5 as profit.

Answer:

9. 4/1 or 4. 10. 0

Step-by-step explanation:

9.

Slope- y2-y1/x2-x1

11-7/4-3= 4/1 or 4

10.

Slope-y2-y1/x2-x1

7-7/5-0= 0/5

When 0 is the numerator of the slope, then the slope is 0.

Answer:

x° = 11°

Z FGI = 60°

Step-by-step explanation:

If GH bisects Z FGI

then Z FGH = Z HGI

or, (3x - 3)° = (4x - 14)°

or, 3x° - 4x° = - 14° + 3°

or, x° = 11°

Z FGI = 33° - 3° + 44° - 14°

= 60°

Answer:

239 bags

Step-by-step explanation:

10,038/42=239

Answer:

Let x be the number

"five times a number"

5x

"six less than five times a number"

5x-6

"is at least 29" >29 (greater than or equal too)

5x - 6 > 29

5x > 35 (add +6 to both sides retains the dense if the inequality)

x>7 (divide both sides by +7 retains the sense of Inequailty)

Check:

Is 5(7) - 6 > 29?

35 - 6 > 29 ?

29 > 29? yes, they are equal.

Try 50:

Is 5(50) - 6 > 29 ?

250 - 6 > 29?

244 > 29 ? yes

Answer:

5x - 6 = 29

Answer:

15^3

Step-by-step explanation:

Since 15^4 means 15 x 15 x 15 x 15, therefore, just subtract the power 4 from one because you are dividing it by 15:

15^4 / 15 = 15^3

Answer:

140 miles

Step-by-step explanation:

Answer:

I'm guessing the angle 1 is supposed to be 74 degrees and not angle 2?

Step-by-step explanation:

Either way. Complementary angles always have a sum of 90°. 74+16=90 so it checks out

Answer:

[tex]z\left(-6.4\:-3.5x\right)=-6.4z-3.5zx[/tex]

Hence, Option 'C' is true.

Step-by-step explanation:

Given the expression

[tex]z\left(-6.4\:-3.5x\right)[/tex]

Apply distributive law:   [tex]a\left(b-c\right)=ab-ac[/tex]

Here:  [tex]a=z,\:b=-6.4,\:c=3.5x[/tex]

so the expression becomes

[tex]z\left(-6.4\:-3.5x\right)=z\left(-6.4\right)-z\cdot \:\:3.5x[/tex]

                         [tex]=-6.4z-3.5zx[/tex]                 ∵  [tex]+\left(-a\right)=-a[/tex]

Therefore,

[tex]z\left(-6.4\:-3.5x\right)=-6.4z-3.5zx[/tex]

Hence, option 'C' is true.

Answer:

Wut...?

Step-by-step explanation:

Step-by-step explanation:

Angle at Center = 2 * Angle at Circumference

Therefore B = 2A.

When B = 100°, A = 100°/2 = 50° (B),

When A = 48°, B = 2(48°) = 96°. (C)

Hey there!

The answer to your question is volume and change

The formula for volume is length x width x height, and if these change, the volume will change.

Hope it helps! Let me know if you need more help!

Answer:

about 11.5

Step-by-step explanation: i think this is right

Answer:

11.538%

Step-by-step explanation:

290 - 260 /260  x 100% = 11.538

Answer:

E and D

Step-by-step explanation:

Just make a mental line which these letters connect to each other.