Factorize the expression, 10ab (a − 2b)³ +24ab² (3a − 6b)²

Answer:

[tex]t = 31.29[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccc}{Stick} & {25.8} & {26.9} & {26.2} & {25.3} & {26.7}& {26.1} \ \\ {Liquid} & {16.9} & {17.4} & {16.8} & {16.2} & {17.3}& {16.8} \ \end{array}[/tex]

Required

Determine the test statistic

Let the dataset of stick be A and Liquid be B.

We start by calculating the mean of each dataset;

[tex]\bar x =\frac{\sum x}{n}[/tex]

n, in both datasets in 6

For A

[tex]\bar x_A =\frac{25.8+26.9+26.2+25.3+26.7+26.1}{6}[/tex]

[tex]\bar x_A =\frac{157}{6}[/tex]

[tex]\bar x_A =26.17[/tex]

For B

[tex]\bar x_B =\frac{16.9+17.4+16.8+16.2+17.3+16.8}{6}[/tex]

[tex]\bar x_B =\frac{101.4}{6}[/tex]

[tex]\bar x_B =16.9[/tex]

Next, calculate the sample standard deviation

This is calculated using:

[tex]s = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

For A

[tex]s_A = \sqrt{\frac{\sum(x - \bar x_A)^2}{n-1}}[/tex]

[tex]s_A = \sqrt{\frac{(25.8-26.17)^2+(26.9-26.17)^2+(26.2-26.17)^2+(25.3-26.17)^2+(26.7-26.17)^2+(26.1-26.17)^2}{6-1}}[/tex]

[tex]s_A = \sqrt{\frac{1.7134}{5}}[/tex]

[tex]s_A = \sqrt{0.34268}[/tex]

[tex]s_A = 0.5854[/tex]  

For B

[tex]s_B = \sqrt{\frac{\sum(x - \bar x_B)^2}{n-1}}[/tex]

[tex]s_B = \sqrt{\frac{(16.9 - 16.9)^2+(17.4- 16.9)^2+(16.8- 16.9)^2+(16.2- 16.9)^2+(17.3- 16.9)^2+(16.8- 16.9)^2}{6-1}}[/tex]

[tex]s_B = \sqrt{\frac{0.92}{5}}[/tex]

[tex]s_B = \sqrt{0.184}[/tex]

[tex]s_B = 0.4290[/tex]

Calculate the pooled variance

[tex]S_p^2 = \frac{(n_A - 1)*s_A^2 + (n_B - 1)*s_B^2}{(n_A+n_B-2)}[/tex]

[tex]S_p^2 = \frac{(6 - 1)*0.5854^2 + (6 - 1)*0.4290^2}{(6+6-2)}[/tex]

[tex]S_p^2 = \frac{2.6336708}{10}[/tex]

[tex]S_p^2 = 0.2634[/tex]

Lastly, calculate the test statistic using:

[tex]t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_B)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]

We set

[tex]\mu_A = \mu_B[/tex]

So, we have:

[tex]t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_A)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]

[tex]t = \frac{(\bar x_A - \bar x_B) }{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]

The equation becomes

[tex]t = \frac{(26.17 - 16.9) }{\sqrt{0.2634/6 +0.2634/6}}[/tex]

[tex]t = \frac{9.27}{\sqrt{0.0878}}[/tex]

[tex]t = \frac{9.27}{0.2963}[/tex]

[tex]t = 31.29[/tex]

The test statistic is 31.29

Answer:ANSWER would either be 120π or about 376.8

Step-by-step explanation:

A=2πrh+2πr2

A=2π*6*8+2π*6*2

A=96π+24π

A= 120π

or

A≈376.8

ANSWER would either be 120π or about 376.8

Answer: the real answer is 527.788 the top answer is wrong I did it and it said it was wrong

Step-by-step explanation:

Answer:

X ~ N(27, 4) ;

xbar ~ N(27, 0.1026) ;

0.5 ;

0.5

Step-by-step explanation:

Probability distribution of X : N(μ, σ²)

μ = 27 ; σ = 2

X ~ N(μ, σ²) = X ~ N(27, 2²) ;X ~ N(27, 4)

Distribution is approximately normal ; μ = xbar ; xbar = 27

(Standard Error)² = (σ/√n)²= (2/√39)² = 0.1026

xbar ~ N(μ, σ²) = xbar ~ N(27, 2²) ; xbar ~ N(27, 0.1026)

Probability that a randomly selected individual found a job in less than 27 weeks :

P(X < 27) :

Obtain the Zscore :

Z = (x - μ) / σ

Z = (27 - 27) / 2 = 0/2

Z = 0

P(Z < 0) = 0.5

D.) n = 36

P(X < 27) :

Obtain the Zscore :

Z = (x - μ) / σ/√n

Z = (27 - 27) / (2/√36) = 0/0.33333

Z = 0

P(Z < 0) = 0.5

The area of the forest after 15 years will be 2189.4

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

i = The initial area of the forest = 4200km

r = Per year decrease is = 4.25%

n = Number of years = 15

The required formula is

The area of forest will be

A = i (1-r)^n

A = 4200(1-0.425)^15

A= 2189.4

Hence, the area of the forest will be 2189.4

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Answer:

14, 3!

Step-by-step explanation:

It is very complicated to explain.

Answer:

A.

domestic: 316 / 96 / 412

international: 76 / 51 / 127

total: 392 / 147 / 539

B. 51 its the smallest number

C. I don't know what association means but 76.2% of domestic flights land on time and 63% of international flights land on time so id say its positive

By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

What is the value of 1meter in terms of centimeter ?

1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .

Given,

1 meter= 3.28 feet

1 Liter= 0.26 gallons

1 kilogram = 2.20 pounds

we know that ,

1yard = 0.0009144 km

so ,

26.794 yard = 26.794*0.0009144 km

= 0.024500

Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

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There are 3,024 different ways 1,214 can be shown.

Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given 1,214

since there are 4 places in the digit,

so 4 values less than 10 can be solved by

9, 8, 7, and 6

so by permutation to find ⁹P₄ = 9!/(9 - 4)!

= (9 x 8 x 7 x 6 x5!)/5!

⁹P₄  = 3,024

Hence there are 3,024 different ways.

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I believe that is a negative linear association.

9514 1404 393

Answer:

  (b)  -3

Step-by-step explanation:

It can work well to rewrite the equation as powers of 2.

  [tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\\\\(2^2)^x=(2^{-3})^{x+5}\qquad\text{as powers of 2}\\\\2x=-3(x+5)\qquad\text{equate exponents}\\\\5x=-15\qquad\text{add $3x$}\\\\\boxed{x=-3}\qquad\text{divide by 5}[/tex]

__

Check

  4^-3 = (1/8)^(-3+5)   ⇒   1/64 = (1/8)^2 . . . . true

The area of the parallelogram is 72 square units. Option B

The formula for calculating the area of a parallelogram is expressed as;

A = bh

Given that;

From the information given, we have that;

Now, substitute the values

x + y = 8 + 4

add the values

x + y = base = 12 units

h = 6 units

Now, substitute the values into the formula, we get;

Area, A = 12(6)

multiply the values

Area, A = 72 square units

Hence, the value is 72 square units

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Answer:

c = 52 yards

Step-by-step explanation:

You have to use the Pythagorean theorem to solve this question.

[tex]a^2+b^2=c^2[/tex]

The hypotenuse is longest side of a triangle.

Lets substitute in our values:

[tex]20^2+48^2=c^2[/tex]

Lets simplify this to:

[tex]400 + 2304 = 2704[/tex]

Now we need to find the square root of 2704:

[tex]\sqrt{2704}=52[/tex]

Therefore, the hypotenuse is 52 yards long.

Answer:

(a) The next tide will occur at 6:55pm

(b) [tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

(c) The height is: 2.904ft

Step-by-step explanation:

Given

[tex]T_1 = 12hr:25min[/tex] --- difference between high tides'

Solving (a): The next time a high tide will occur

From the question, we have that:

[tex]High =6:30am[/tex] --- The time a high tide occur

The next time it will occur is the sum of High and T1

i.e.

[tex]Next = High + T_1[/tex]

[tex]Next = 6:30am + 12hr : 25min[/tex]

Add the minutes

[tex]Next = 6:55am + 12hr[/tex]

Add the hours

[tex]Next = 6:55pm[/tex]

Solving (b): The sinusoidal function

Given

[tex]High\ Tide = 5.86[/tex]

[tex]Low\ Tide = -0.38[/tex]

[tex]T = 12hr:25min[/tex] -- difference between consecutive tides

[tex]Shift = 6.5hr[/tex]

The sinusoidal function is represented as:

[tex]y = A\cos(w(x - C)) + B[/tex]

Where

[tex]A = Amplitude[/tex]

[tex]A = \frac{1}{2}(High\ Tide - Low\ Tide)[/tex]

[tex]A = \frac{1}{2}(5.86 - -0.38)[/tex]

[tex]A = \frac{1}{2}(6.24)[/tex]

[tex]A = 3.12[/tex]

[tex]B = Mean[/tex]

[tex]B = \frac{1}{2}(High\ Tide + Low\ Tide)[/tex]

[tex]B = \frac{1}{2}(5.86 - 0.38)[/tex]

[tex]B = \frac{1}{2}(5.48)[/tex]

[tex]B = 2.74[/tex]

[tex]w = Period[/tex]

[tex]w = \frac{2\pi}{T}[/tex]

[tex]w = \frac{2\pi}{12:25}[/tex]

Convert to hours

[tex]w = \frac{2\pi}{12\frac{25}{60}}[/tex]

Simplify

[tex]w = \frac{2\pi}{12\frac{5}{12}}[/tex]

As improper fraction

[tex]w = \frac{2\pi}{\frac{149}{12}}[/tex]

Rewrite as:

[tex]w = \frac{2\pi*12}{149}[/tex]

[tex]w = \frac{24\pi}{149}[/tex]

[tex]C = shift[/tex]

[tex]C=6.5[/tex]

So, we have:

[tex]y = A\cos(w(x - C)) + B[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

Solving (c): The height at 3pm

At 3pm, the value of x is:

[tex]x=3:00pm - 6:30am[/tex]

[tex]x=9.5hrs[/tex]

So, we have:

[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(9.5 - 6.5)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(3)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{72\pi}{149}) + 2.74[/tex]

[tex]y = 3.12 *0.0527 + 2.74[/tex]

[tex]y = 2.904ft[/tex]

Answer:

The cost is #15.90

Step-by-step explanation:

See comment for complete question

Given

[tex]P \to Potato[/tex]

[tex]C \to Carrot[/tex]

[tex]3P + 2C = 5.08[/tex]

[tex]P = 1.24[/tex]

Required

[tex]12P + 1\frac{1}{2}C = ??[/tex]

First, we solve for C

Substitute [tex]P = 1.24[/tex] in [tex]3P + 2C = 5.08[/tex]

[tex]3 * 1.24 + 2C = 5.08[/tex]

[tex]3.72 + 2C = 5.08[/tex]

Collect like terms

[tex]2C = 5.08 - 3.72[/tex]

[tex]2C = 1.36[/tex]

Solve for C

[tex]C = \frac{1.36}{2}[/tex]

[tex]C = 0.68[/tex]

So, we have:

[tex]P = 1.24[/tex]

[tex]C = 0.68[/tex]

[tex]12P + 1\frac{1}{2}C = ??[/tex] becomes

[tex]12P + 1\frac{1}{2}C = 12*1.24 + 1\frac{1}{2}*0.68[/tex]

[tex]12P + 1\frac{1}{2}C = 14.88 + 1.02[/tex]

[tex]12P + 1\frac{1}{2}C = 15.90[/tex]

Answer:

both are b

Step-by-step explanation:

the point is equal to -2 because there is a point on -2 and with 20 it b because 2 time 10 is 20 +26 makes 46 which makes 43 less than 46

The equation of the least squares regression line for the data set is (b) ŷ = -2.984x + 112.38

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

Volunteer 15 11 22 35 18 41 27 18

Trees 77 99 4 11 44 14 2 90

Using a graphing calculator, we have the following calculation summary

The regression equation is represented as

ŷ = bX + a

Where

b = SP/SSX = -2213.88/741.88 = -2.98416

a = MY - bMX = 42.63 - (-2.98*23.38) = 112.37978

So, we have

ŷ = -2.98416X + 112.37978

Approximate

ŷ = -2.984x + 112.38

Hence, the equation  is ŷ = -2.984x + 112.38

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Answer:

x = 120°

y = 60°

Step-by-step explanation:

✔️since, lines l and m, area parallel, therefore,

x = 120° (they are corresponding angles having matching corners. Thus, corresponding angles are congruent to each other)

✔️x + y = 180° (linear pair angles)

Plug in the value of x

120 + y = 180

Subtract 120 from each side of the equation

y = 180 - 120

y = 60°

Answer:

10+12x

Step-by-step explanation:

9−4x+2x+8x+1+6x

(9+1)+(−4x+2x+8x+6x)

10+12x

Answer:

To solve this problem, we can set up the following equation:

2L + 2W = 64

We are told that the length of the rectangle is two more than double the width, so we can write the following equation:

L = 2W + 2

Substituting this equation into the first equation, we get:

2(2W + 2) + 2W = 64

Simplifying this equation, we get:

6W + 4 = 64

Subtracting 4 from both sides, we get:

6W = 60

Dividing both sides by 6, we get:

W = 10

The width of the rectangle is 10 feet.

To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:

L = 2(10) + 2

= 20 + 2

= 22

The length of the rectangle is 22 feet.

Therefore, the dimensions of the rectangle are 10 feet by 22 feet.

Step-by-step explanation:

Answer:

y = 2x + 7

Step-by-step explanation:

y + 1 = 2 ( x + 4 )

y = 2x + 8 - 1

y = 2x + 7

The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.

Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:

For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).

If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:

r = (2 · 5) : (3 · 4)

r = 10 : 12

Finally, we simplify the resulting expression:

r = 5 : 6

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Answer:

B. 1/6

D. 3/12

F. 4 3/11

PLEASE MARK BRAINLIEST

On solving the provided question, we can say that - in the linear equation y = 1/2x + 5, slope, m = 1/2

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here,

in the linear equation =>

y = +1/2x + 5

on comparing with y = mx +c

slope, m = 1/2

and, c= +5

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Answer:

steps below (C)

Step-by-step explanation:

1. x³ -> (x+1)³   ... horizontal translation left 1 unit

2. (x+1)³ -> -(x+1)³  .... reflection over x axis

3. -(x+1)³ -> -(x+1)³ + 1  ... vertical translation up 1 unit

Answer:

i think its c though im not sure

Step-by-step explanation:

Answer:

700 i think-

Step-by-step explanation:

Answer:

Step-by-step explanation:

???

Answer:

the answer is 38

Step-by-step explanation:

because one of the angles is 90 and the other one is 45, so the other angle is 45 too

so.. this is an isosceles triangle