Matt is carpeting his bedroom. The room measures 12 feet by 14 feet. If carpet costs $2.29 per square foot, then how much will Matt spend to carpet his bedroom?

Answer:

[tex]\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10[/tex]

General Formulas and Concepts:
Calculus

Integration

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

Integration Rule [Fundamental Theorem of Calculus 1]:                                 [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

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

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

Area of a Region Formula:                                                                               [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

y = 2x + 3

x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

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Learn more about integration: https://brainly.com/question/26401241

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

Unit: Integration

Answer:

C .6 inches

Step-by-step explanation:

I'm not sure of my answer

The equation of the function in the form y=mx+b is y = 110x-2020

The standard equation of a line is expressed as:

y = mx + b

where:

m is the rate of change or slope

b is the intecept

Using the coordinate points

Determine the slope

m = 550/5

m = 110

For the intercept

280 + 110(20) + b

280 = 2200 + b

b = 180 - 2200

b = -2020

Hence the equation of the function in the form y=mx+b is y = 110x-2020

Learn more on rate of change here: https://brainly.com/question/8728504

Answer:

Approximately [tex]35.2[/tex] points.

Step-by-step explanation:

Let random variables [tex]X_{1},\, \dots,\, X_{30}[/tex] denote the score of those [tex]30[/tex] test-takers. These random variables are independently and identically distributed. In other words, the scores follow the same distribution and are independent from one other.

While the exact distribution of each score is unknown, the mean and variance of this distribution are given: [tex]\mu = 1083[/tex] and [tex]\sigma = 193[/tex].

By the Central Limit Theorem, the mean (average) [tex]\overline{X}_{n}[/tex] of a sufficiently large number of such observations would follow a normal distribution. The mean of that distribution would be [tex]\mu[/tex] (same as the mean of the observations) while the variance [tex]{\rm Var}(\overline{X}_{n})[/tex] would be [tex](\sigma^{2} / n)[/tex].

Take the square root of variance to find the value of the corresponding standard deviation:

[tex]\begin{aligned}& \sqrt{{\rm Var}(\overline{X}_{n})} \\ =\; & \sqrt{\frac{\sigma^{2}}{n}} \\ =\; & \sqrt{\frac{193^{2}}{30}}\\ \approx\; & 35.2\end{aligned}[/tex].

The area of the garden enclosed by the fencing is

A(x, y) = xy

and is constrained by its perimeter,

P = x + 2y = 200

Solve for x in the constraint equation:

x = 200 - 2y

Substitute this into the area function to get a function of one variable:

A(200 - 2y, y) = A(y) = 200y - 2y²

Differentiate A with respect to y :

dA/dy = 200 - 4y

Find the critical points of A :

200 - 4y = 0   ⇒   4y = 200   ⇒   y = 50

Compute the second derivative of A:

d²A/dy² = -4 < 0

Since the second derivative is always negative, the critical point is a local maximum.

If y = 50, then x = 200 - 2•50 = 100. So the farmer can maximize the garden area by building a (100 ft) × (50 ft) fence.

Answer:

r = 3

Step-by-step explanation:

Answer:

  150 in³

Step-by-step explanation:

We want to find half the volume of a rectangular pyramid. The volume of the whole pyramid is given by the formula ...

  V = 1//3LWH

  V = 1/3(5 in)(15 in)(12 in) = 300 in³

Then the volume of the half that is not filled with marbles is ...

  1/2V = 1/2(300 in³) = 150 in³

150 cubic inches of marbles are needed to finish filling the container.

Answer:

Given:

[tex] \: [/tex]

To Find:

[tex] \: [/tex]

Solution:

Let,

So,

length will be 2b + 3

[tex] \: [/tex]

As, we know:

[tex] \bigstar \quad {\underline{ \boxed{ \green{Perimeter = 2 ( length + breadth ) }}}} \quad \bigstar[/tex]

➝ 2[(2b + 3) + b)] = 252

➝ 2( 3b + 3 ) = 252

➝ 6b + 6 = 252

➝ b + 1 = 42

➝ b = 41

[tex] \: [/tex]

Now putting the value of b in second equation:

➝ l = 2(41) + 3 = 85

[tex] \: [/tex]

Hence,

[tex] \: [/tex]

Check:

2( l+b ) = 252

➝ 2( 85 + 41 )

➝ 2( 126 )

➝ 252

[tex] \: \: \: \: \: \: { \sf{ \mathbb{ \pink{Formula's \: for \: Perimeter}}}}[/tex]

★ Triangle = Sum of all sides

★ Square = 4 × Side

★ Rectangle = 2( l + b )

★ Circle = 2πr

Answer:

Bobby has 45 beads

Step-by-step explanation:

Let x be the number of beads Bobby has.

Then, (x + 30) is the number of beads Alvin has.

Then, 3 (x + 30) is the number of beads Cathy has.

3 (x + 30) + (x + 30) + x = 345

3x + 90 + x + 30 + x = 345

5x + 120 = 345

5x = 225

x = 45

Therefore, Bobby has 45 beads.

[tex] \sf \dashrightarrow \: - \frac{2}{5} - ( - \frac{3}{10} ) - ( - \frac{4}{7} )[/tex]

When there is a - in front of an expression in parentheses, change the sign of each term in the expression to +

[tex] \sf \dashrightarrow \: - \frac{2}{5} + \frac{3}{10} + \frac{4}{7} [/tex]

Calculate the LCM of denominators

[tex] \sf\frac{ - 28 + 21 + 40}{70} [/tex]

Calculate the difference

[tex] \bf \underline{ \underline \frac{33}{70} }[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-2}{5}-\left(-\dfrac{3}{10}\right)-\left(-\dfrac{4}{7}\right)[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-2}{5}+\dfrac{3}{10}+\dfrac{4}{7}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-28+21+40}{70}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-7+40}{70}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{33}{70}[/tex]

Answer:

[tex]x[/tex] =[tex]\frac{-2}{3}[/tex]   or   [tex]x[/tex] = -1

Step-by-step explanation:

quadratic formula⇒ -b ±[tex]\sqrt{b^{2} -4ac}[/tex] / 2a

15[tex]x[/tex]² + 22[tex]x[/tex] = -8

15[tex]x[/tex]² + 22[tex]x[/tex] +8 = 0

taking a=15, b=22 & c=8;

[tex]x[/tex] = (-22 ± [tex]\sqrt{ - 22^{2} 4 × 15 × 8}[/tex])/ 2 x 15 ⇒ (Pls note that the A~s are multiplications.. unable to insert symbols in equations)

  = (-22 ± [tex]\sqrt{484 - 480}[/tex]) / 30

  = (-22 ± [tex]\sqrt{4}[/tex]) / 30

  = (-22 ± 2) / 30

[tex]x[/tex] = [tex]\frac{-22 + 2}{30}[/tex]  or  [tex]x[/tex] =[tex]\frac{-22 - 2}{30}[/tex]

[tex]x[/tex] = -[tex]\frac{-20}{30}[/tex]    or [tex]x[/tex] = [tex]\frac{-30}{30}[/tex]

[tex]x[/tex] =[tex]\frac{-2}{3}[/tex] or [tex]x[/tex] = -1

Answer:

a starting value of -1/2 so its starts at -1/2 so lets see which ones start at that

not a

not b

yes c

this isn't a function

and no change so

not a

not b

yes c

yes d(not a function)

c

Hope This Helps!!!

Answer:

d) 4w - 2

Step-by-step explanation:

(7w-5) and (-3w+3)

(7w-5) + (-3w+3)

1(7w-5) + 1(-3w+3)

7w - 5 - 3w + 3

Combine like terms:

7w - 5 - 3w + 3

7w - 3w - 5 + 3

4w - 2

Hope this helps!

Considering the discrete distribution, it is found that the desired measures are given as follows:

a) 0.86.

b) 0.57.

c) 0.45.

d) 0.14.

e) 0.43.

f) 3.02.

g) 1.31.

According to the table, it is given by:

P(X = 1) = 0.14.

P(X = 2) = 0.29.

P(X = 3) = 0.12.

P(X = 4) = 0.31.

P(X = 5) = 0.14.

Item a:

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 1) = 1 - 0.14 = 0.86[/tex]

Item b:

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - P(X = 1) - P(X = 2) = 1 - 0.14 - 0.29 = 0.57[/tex]

Item c:

P(X > 3) = P(X = 4) + P(X = 5) = 0.31 + 0.14 = 0.45.

Item d:

P(X < 2) = P(X = 1) = 0.14.

Item e:

[tex]P(X \leq 2) = P(X = 1) + P(X = 2) = 0.14 + 0.29 = 0.43[/tex].

Item f:

The mean is given by the sum of each outcome multiplied by it's respective probability, hence:

E(X) = 0.14(1) + 0.29(2) + 0.12(3) + 0.31(4) + 0.14(5) = 3.02.

Item g:

The standard deviation is given by the square root of the sum of the difference squared of each observation and the mean, multiplied by it's respective probabilities, hence:

[tex]\sqrt{V(X)} = \sqrt{0.14(1-3.02)^2 + 0.29(2-3.02)^2 + 0.12(3-3.02)^2 + ... + 0.14(5-3.02)^2} = 1.31[/tex]

More can be learned about discrete probability distributions at https://brainly.com/question/24855677

Answer:

Step-by-step explanation:

sorry I tried but it is hard

Step-by-step explanation:

To find a, the leading coeffiecent of the quadratic is a.

So a is 2.

To find b, we must use the formula

[tex] - \frac{b}{2a} [/tex]

[tex] \frac{ - ( - 3)}{2(2)} = \frac{3}{4} [/tex]

So b=3/4.

To find c, plug in 3/4 into the function,

which we get

[tex]2( \frac{9}{16} ) - 3( \frac{3}{4} ) + 21[/tex]

[tex] \frac{9}{8} - \frac{9}{4} + 21 = \frac{9}{8} - \frac{18}{8} + 21 = - \frac{9}{8} + 21 = 19.875[/tex]

So c=19.875

the answer is 15!

Hope this helps!

Answer:

x = 8/3

Step-by-step explanation:

1. Subtract 7 from both sides.

-3x + 7 = -1

-7 -7

-------------------

-3x = -8

2. Divide both sides by -3

-3x = -8

---- ----

-3 -3

x = 8/3

Hey there!

12: 1, 2, 3, 4, 6, & 12

30: 1, 2, 3, 5, 6, 10, 15, & 30

75: 1, 3, 5, 15, 25, & 75

LIKE TERMS: 1 and 3

GCF: 3

Therefore, your answer is: 3

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Not worth 40 points. Poster is a liar.

R=15 --> 30/2 , H=320

Anyways, because you lied, I won't show my work.

Volume= 72,000pi or 226194.6711

Answer:

Ocupa los miles.

Step-by-step explanation:

400,000

30,000

2,000

70

9

Answer:

85%

Step-by-step explanation:

Johny answered [tex]\frac{17}{20}[/tex] questions correctly. To change this into percent, just multiply both the numerator and denominator by the number that makes the denominator equal 100. In this case, 5 would make 20 equal 100, so we multiply both the top and bottom by 5.

[tex]\frac{17}{20} *\frac{5}{5}=\frac{85}{100}[/tex]

Your numerator will be your percentage if the denominator is 100.

50 % =20 Learners

100%= x

x=100/50

=2

=2×20

=40 learners

was this helpful?

#1

100+200+300..10000

Now

[tex]\\ \rm\Rrightarrow S_{100}=\dfrac{100}{2}(100+10000)=50(10100)=505000[/tex]

#2

[tex]\\ \rm\Rrightarrow x^2+(x+1)^2=21[/tex]

[tex]\\ \rm\Rrightarrow x^2+x^2+2x+1=21[/tex]

[tex]\\ \rm\Rrightarrow 2x^2+2x=20[/tex]

[tex]\\ \rm\Rrightarrow x^2+x-10=0[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{1-40}}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{-39}}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm \sqrt{39}i}{2}[/tex]

Answer:

It is 3

•°•°•°

Math is poop