Which of the following choices is equivalent to the equation below?

5(2x−1) = 5(5x−14)

A 2x − 1 = 5x − 14
B 5(2x − 1) = 5x − 14
C 2x − 1 = 5
D None of these choices are correct.

Answer:

Step-by-step explanation:

Answer:

a. 24.12 ft³/hr b. 0.0768 ft/hr

Step-by-step explanation:

a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.

The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out

Since volume flow rate in = P(t) and volume flow rate out = R(t),

dV/dt = P(t) - R(t)

[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]

We need to find the rate of change of volume when t = 6.

From the table when t = 6, P(6) = 47 ft³/hr

Also, substituting t = 6 into R(t), we have R(6)

[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]

[tex]\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr[/tex]

dV/dt ≅ 24.12 ft³/hr

So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr

b. How fast is the water level in the pool rising at t=6 hours?

Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet

dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.

So, dV/dt = πr²dh/dt

dh/dt = dV/dt ÷ πr²

Since dV/dt = 24.12 ft³/hr and r = 10 ft,

Substituting the values of the variables into the equation, we have that

dh/dt = dV/dt ÷ πr²

dh/dt = 24.12 ft³/hr ÷ π(10 ft)²

dh/dt = 24.12 ft³/hr ÷ 100π ft²

dh/dt = 0.2412 ft³/hr ÷ π ft²

dh/dt = 0.2412 ft³/hr

dh/dt = 0.0768 ft/hr

So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr

Answer:

50√3 square units.

Step-by-step explanation:

Let the two sides of the triangle given be 'a' and 'b'.

Let the angle between them be θ

From the question given above, the following data were obtained:

Side a = 20 units

Side b = 10√3

Angle (θ) = 30°

Area (A) =?

A = ½ × ab × Sineθ

A = ½ × 20 × 10√3 × Sine 30

A = ½ × 20 × 10√3 × ½

A = 10 × 5√3

A = 50√3 square units

Therefore, the area of the triangle is 50√3 square units

9514 1404 393

Answer:

  5, 10, 20

Step-by-step explanation:

Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...

  ((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd

  5x -5 = 4x   ⇒   x = 5

The original numbers are 5, 10, 20.

_____

After the adjustment, the arithmetic sequence is 8, 10, 12.

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

Explanation:

Let's say the shed comes in 40 equal pieces. Each piece takes the same amount of time to assemble. Why am I picking 40? Because 8*5 = 40.

This will allow us to rewrite the fractions with a common denominator.

So Jack can build 8/40 of the shed in the same amount of time Kyle can build 25/40 of the shed.

Instead of writing fractions (which honestly are a pain to deal with), I'm going to write "8 pieces" and "25 pieces" to represent "8/40" and "25/40" respectively. Just keep in mind that there are 40 pieces total.

So again, Jack can assemble 8 pieces in the time it takes Kyle to assemble 25 pieces.

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

The ultimate goal is to have Kyle assemble 40 pieces while Jack puts together some unknown number of pieces (some number between 8 and 40). Let's say it's x.

We can then form this proportion

[tex]\frac{\text{Jack's initial 8 pieces}}{\text{x pieces}}=\frac{\text{Kyle's initial 25 pieces}}{\text{goal of 40 pieces}}[/tex]

which simplifies or cleans up to

5/x = 25/40

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

Let's solve for x using cross multiplication

8/x = 25/40

8*40 = x*25

320 = 25x

25x = 320

x = 320/25

x = 12.8

So in the time it takes Kyle to assemble all 40 pieces, Jack can put together 12.8 pieces of the shed. However, we can't have Jack put together some fractional piece, because each "piece" is as small as it gets. We can't get any smaller. It would be like saying a fractional part of an atom or a lego block.

So we'll round 12.8 down to 12.

Jack can assemble 12 pieces in the time it takes Kyle to assemble 40 pieces.

Let's then convert this back to fraction form

12 pieces = 12/40 of a shed = 3/10 of a shed.

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 5x+6=2x-3[/tex]

[tex]\\ \sf\longmapsto 5x-2x=-3-6[/tex]

[tex]\\ \sf\longmapsto 3x=-9[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-9}{3}[/tex]

[tex]\\ \sf\longmapsto x=-3[/tex]

Answer:

Step-by-skfmckfmkfkfkfkfkkfkfkfkfkfkfoftep explanation:

Cl

Answer:

0.08 ; 0.16

Step-by-step explanation:

Given :

x = 32 ; n = 267 ; phat = x / n = 32 / 267 = 0.11985

The Zcritical at 95% = 1.96

The confidence interval for proportion :

C. I = Phat ± Z*√(phat(1-phat))/n

C. I = 0.11985 ± 1.96√(0.11985(1-0.11985))/267

C. I = 0.11985 ± 1.96(0.0198765)

C. I = 0.11985 ± 0.0389581

C. I = 0.08 ; 0.158

C. I = 0.08 ; 0.16

Answer:

3.) A,B,AB,O

Step-by-step explanation:

Non-numeric data refers to categorical data, or data that is not expressed quantitatively. Answers (1) and (2) contain quantitative data, so they would be eliminated as potential answer choices and therefore (4) would also be eliminated. This leaves answer (3), which does not have quantitative data and is therefore non-numeric.

Answer:

how long will it take before your investment is wort$6000?

Answer:

15.56

Step-by-step explanation:

Given the vectors ||u|| = 5√2 units, and ||v|| = 6√2 units.

||u + v|| ≈  5√2 +  6√2

||u + v|| ≈  (5+6)√2

Since √2≈ 1.4142

||u + v|| ≈   11(1.4142)

||u + v|| ≈  15.56

Hence the correct option is D

Answer: 11.05

Step-by-step explanation: got it right

Answer:

The inverse is 1/3x -2

Step-by-step explanation:

f (x) = 3x + 6

y = 3x+6

Exchange x and y

x = 3y+6

Subtract 6 from each side

x-6 = 3y+6-6

x-6 = 3y

Divide by 3

1/3x - 6/3 = y

1/3x -2 = y

The inverse is 1/3x -2

Answer:

10

Step-by-step explanation:

(-12) + (-8) +30

-(12+8)+30

-20 + 30

10

Answer:

e- 77

d- 52

f- 51

Step-by-step explanation:

Step-by-step explanation:

d=52° (,vertically opposite angle)

77+52+f=180 (linear pair)

f=180- 129

f=51°

52+51+e=180

e=180- 103

e=77°

Answer:

18

Step-by-step explanation:

6^2 plus 3^2 = 324, square root 324 =18

Answer:

[tex]\sqrt{45}[/tex]

Step-by-step explanation:

The line represents the hypotenuse of a right triangle with legs 6 and 3. For any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.

Therefore, we have:

[tex]6^2+3^2=c^2,\\c^2=36+9,\\c=\boxed{\sqrt{45}}[/tex]

Answer: x=4, -1

Step-by-step explanation:

Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.

Step 1. Replace f(x) with y.

[tex]y = x^3-7x^2+8x+16[/tex]

Step 2. To find the roots of the equation, replace y with 0 and solve.

[tex]0 = x^3-7x^2+8x+16[/tex]

Step 3. Factor the left side of the equation.

[tex](x-4)^2 (x+1)=0[/tex]

Step 4. Set x-4 equal to 0 and solve for x.

[tex]x-4=0[/tex]

Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.

[tex]x=-1[/tex]

The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].

[tex]x=4,-1[/tex]

Answer:

15

Step-by-step explanation:

Difference in distances = 75-60 = 15 miles

So Car A travels 15 miles more than Car A in an hour

Answered by Gauthmath

Answer:

0.375 dollars

Step-by-step explanation:

1 pound = 16 oz

1 oz = 1/16 pound

2 oz = 2/16

2/16 * 3 = 0.375

Answer:

x=7

Step-by-step explanation:

6x+11=7x+4

Answer:

Rational number

Step-by-step explanation:

Given

[tex]5\frac{3}{8}[/tex]

Required

The subset it belongs to

Express as improper fraction

[tex]5\frac{3}{8} = \frac{43}{8}[/tex]

The above number is rational because it is represented by the division of 2 integers, i.e. 43 and 8 are integers

Express as decimals

[tex]5\frac{3}{8} = 5.375[/tex]

The above number cannot be classified as integers or whole because it has decimal parts

Answer:

H1 : μ ≠ 20000

Step-by-step explanation:

Given that :

Population mean salary, μ = 20,000

To test if mean salary is more or less Than population mean salary, μ, this means we are testing if the mean salary is different from 20,000

Hence, the hypothesis :

Null, H0 : The mean salary is 20000

Alternative, H1 : The mean salary is not 20000

Using notation :

H0 : μ = 20000

H1 : μ ≠ 20000

Hence, alternative hypothesis is : H1 : μ ≠ 20000

Answer: 15

Step-by-step explanation:

Answer:

Following are the solution to the given points:

Step-by-step explanation:

For point a:

[tex]fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\[/tex]

[tex]=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\[/tex]

Using the PDF of the X value

[tex]fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1[/tex]

0 ; otherwise

For point b:

[tex]E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\[/tex]

[tex]= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\[/tex]

[tex]= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}[/tex]

Answer:

I think answer is E

Step-by-step explanation:

Answer:

made up of about 20 common amino acids. The proportion of these amino acids varies as a characteristic of a given protein, but all food proteins—with the exception of gelatin—contain some of each. Amino nitrogen accounts for approximately 16% of the weight of proteins. Amino acids are required for the synthesis of body protein and other important nitrogen-containing compounds, such as creatine, peptide hormones, and some neurotransmitters. Although allowances are expressed as protein, a the biological requirement is for amino acids.

Proteins and other nitrogenous compounds are being degraded and resynthesized continuously. Several times more protein is turned over daily within the body than is ordinarily consumed, indicating that reutilization of amino acids is a major feature of the economy of protein metabolism. This process of recapture is not completely efficient, and some amino acids are lost by oxidative catabolism. Metabolic products of amino acids (urea, creatinine, uric acid, and other nitrogenous products) are excreted in the urine; nitrogen is also lost in feces, sweat, and other body secretions and in sloughed skin, hair, and nails. A continuous supply of dietary amino acids is required to replace these losses, even after growth has ceased.

Amino acids consumed in excess of the amounts needed for the synthesis of nitrogenous tissue constituents are not stored but are degraded; the nitrogen is excreted as urea, and the keto acids left after removal of the amino groups are either utilized directly as sources of energy or are converted to carbohydrate or fat.

Answer:

what i dont understand

Step-by-step explanation:

Answer:

54%

Step-by-step explanation:

that is the greatest percentile given

The confidence level of 54% would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population.

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.

From the definition of the confidence interval itself, it is clear that the level with the widest interval will be the highest confidence level.

So if you need a wider interval for estimating the mean of a population from the mean and standard deviation, you need to take higher confidence level.

Out of the given options, the highest level is 54%.

Hence the confidence level is 54%.

Learn more about Confidence Interval here :

https://brainly.com/question/29680703

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Step-by-step explanation:

combination

is answer of this question