ASAP PLEASE! A rectangular swimming pool is 8 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2000 cubic feet. Find the dimensions of the pool.


The smaller dimension of the pool is {} ft and the larger dimension of the pool is {} ft.

The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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Answer:

<XWZ ≅ < XZW  by alternate interior angles & WZ = WZ by reflexive property

Step-by-step explanation:

Because they're parallel lines cut by a transversal. So, <W is where one angle is, and <Z is where another angle is. They both share a side as well. Always look out for those types of triangles because those are types of hidden information

The probability that the first ball drawn is a red is 8/14

the probability that the first ball drawn is a yellow is 6/13

Let A = getting a red ball

B= getting a yellow ball given that first was red ball

P( A ) = 8/14

P( B  ) = 6/ 13 (since 1 red ball is out)

A(A ∩ B)= 6/13 x 8/14 =

48/182

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

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Answer:

gradient = 2

Step-by-step explanation:

calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-5)}{2-0}[/tex] = [tex]\frac{-1+5}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

The values of x and y are x = 80° and y = 130°.

What is conservative interior angles?

When a line, referred to as the transversal line, crosses two other lines, two angles are created that are known as consecutive interior angles. Consecutive interior angles, or co-interior angles for short, are the angles formed on the inside of the two lines and on the same side of the transversal line.

Consecutive interior angle CONVERSE is another name for the same side interior angle CONVERSE.

Line line n || m

if (x - 30) + (x + 50) = 180.

x -  30 + x + 50 = 180

2x + 20 = 180

subtract 20 from both sides

2x = 160

divide both sides by 2

x = 80

IF (x - 30) + y = 180, then k || j.

(80 - 30) + y = 180

50 + y = 180

subtract 50 from both sides

y = 130

Hence, the values of x and y are x = 80° and y = 130°.

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Complete question:

Complete question is attached below,

Answer:

i found something that might help you

Step-by-step explanation:

Answer:

22x

Step-by-step explanation:

2x 2(6x+3)

2x 12x+6x

22x

The compound interest after 5 years is $7,081.916.

Compound interest:

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Here we have to find the interest earned after 5 years.

Data given:

Principle (P) = $11600

rate(r) = 10%

time(t) = 5 years.

Formula to find compound interest:

CI = P( 1 + r/100[tex])^{t}[/tex] - P

Now put the values in the formula.

CI = 11600 ( 1 + 10/100[tex])^{5}[/tex] - 11600

  = 18681.916 - 11600

  = 7081.916

Therefore the compound interest is $7081.916.

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Answer:

Step-by-step explanation:

You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).

The given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.

  [tex]f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}[/tex]

The function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.

The function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.

The x-intercept is found where the numerator of the simplified function is zero: x = -1

The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)

The function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.

The vertical asymptote is at the uncanceled denominator zero, x = -3.

The holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.

The holes are (-4, 6) and (0, 2/3).

Answer:

M+N is defined

All others not defined

Step-by-step explanation:

Two matrices can be added or subtracted if and only if they have the same dimensions i.e. they must have the exact same number of rows and number of columns

Only M and N with dimensions (4 x 2) each can be added or subtracted.

(4 x 2 ) means 4 rows and 2 columns

So the only defined operation is
M + N

All the others are not defined

Answer:

[tex]\textsf{De\:\!fined}: \quad \boxed{M + N}[/tex]

[tex]\textsf{Not\:de\:\!fined}: \quad \boxed{N - Q} \quad \boxed{Q + L} \quad \boxed{M - P}[/tex]

Step-by-step explanation:

Generally, a matrix is referred to as [tex]n\times m[/tex] where n is the number of rows and m is the number of columns.

Therefore:

Matrices can be added or subtracted only when they are the same size.

[tex]\boxed{N - Q}[/tex]

Matrices N and Q are different sizes. Therefore, the operation is not defined.

[tex]\boxed{M + N}[/tex]

Matrices M and N are the same size. Therefore, the operation is defined.

[tex]\boxed{Q + L}[/tex]

Matrices Q and L are different sizes. Therefore, the operation is not defined.

[tex]\boxed{M - P}[/tex]

Matrices M and P are different sizes. Therefore, the operation is not defined.

There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

In inferential statistics, the null hypothesis states that two possibilities are equal.

The observed difference is thought to be the sole product of chance, which is the underlying premise.

Statistical tests can be used to calculate the likelihood that the null hypothesis is true.

So,

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

As the population standard deviation is given when n > 30

So, we'll run the Z test.

Formula: [tex]z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}[/tex]

Replace the values:

[tex]\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}[/tex]

For the p-value, see the z table.

Consequently, p = 0.9927.

The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146

α = 0.1

p value< α

Thus, we disregard the null hypothesis.

Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.

Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

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Answer:

Ok this is easy you got this!

Step-by-step explanation:

Ok so, we know their over total is 98.00, we also know that the boots cost $34 each

lets start with 34+34= 68

now we are going to take that from 98

98-68=30

now because they bought two canteens we will divide 30 by 2

30 divided by 2 is 15

the cost of each canteen is $15

Using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

So, we have -9 - 9√3i:

This quantity has a modulus.

|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18

And argument θ to the effect:

tan(θ) = (-9√3) / (-9) = √3

We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:

θ = arctan(√3) - π = π/3 - π = -2π/3

The polar form is then:

18 (cos(-2π/3) + i sin(-2π/3))

And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))

Therefore, using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?

a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Answer:

18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Step-by-step explanation:

D

Answer:

There are 80 coins in her collection.

Step-by-step explanation:

We can find out how many coins are in her coin collection by first converting 5% into a fraction by moving the decimal place to the left twice. Which then we get 0.05. Then, we can set up this equation:

4 ÷ 0.05 = 80

Now, let's check our answer:

0.05 x 80 = 4.

Yep! It checks out!

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To divide complex numbers, you multiply by the conjugate of the denominator:

    [tex]\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i}[/tex]

We do this to turn the denominator into a real number.

[tex]\begin{aligned}\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i} &= \dfrac{-9+6i-18i+12i^2}{9-4i^2}\\[0.5em] &= \dfrac{-9-12i-12}{9+4}\\[0.5em] &= \dfrac{-21-12i}{13}\\[0.5em] &= -\dfrac{21}{13}-\dfrac{12}{13}i\end{aligned}[/tex]

Answer:

[tex]-\dfrac{21}{13}-\dfrac{12}{13}i[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{-3-6i}{3+2i}[/tex]

Multiply the numerator and denominator by the complex conjugate of the denominator:

[tex]\implies \dfrac{-3-6i}{3+2i} \cdot \dfrac{3-2i}{3-2i}[/tex]

Simplify:

[tex]\implies \dfrac{(-3-6i)(3-2i)}{(3+2i)(3-2i)}[/tex]

[tex]\implies \dfrac{-9+6i-18i+12i^2}{9-4i^2}[/tex]

[tex]\implies \dfrac{-9-12i+12i^2}{9-4i^2}[/tex]

Apply the imaginary number rule [tex]i^2=-1[/tex] :

[tex]\implies \dfrac{-9-12i+12(-1)}{9-4(-1)}[/tex]

[tex]\implies \dfrac{-9-12i-12}{9+4}[/tex]

[tex]\implies \dfrac{-21-12i}{13}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}:[/tex]

[tex]\implies -\dfrac{21}{13}-\dfrac{12}{13}i[/tex]

Answer: [tex]512x^3+960x^2+600x+125[/tex]

Step-by-step explanation: Start by spreading the expression out so it turns into (8x + 5)*(8x + 5)*(8x + 5). (* means multiply). Then, foil (multiply the first numbers, outside numbers, inside numbers, and last numbers to form a new expression) the first two expressions to get 64x^2+80x+25*(8x + 5). Foil that again, going through and multiplying each number from both expressions by every number in the other expression to get 512x^3+960x^2+600x+125. Hope that helps.

Answer:

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Perfect Cube Formula}\\\\$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$\\\end{minipage}}[/tex]

To find the product of the given expression, use the perfect cube formula.

Given expression:

[tex](8x + 5)^3[/tex]

Therefore:

Apply the perfect cube method:

[tex]\begin{aligned}(8x+5)^3&=(8x)^3+3(8x)^2(5)+3(8x)(5)^2+5^3\\&=8^3 \cdot x^3+3 \cdot 64x^2\cdot5+3\cdot 8x\cdot 25+125\\&=512x^3+960x^2+600x+125\end{aligned}[/tex]

From the given statement the mean mcr rt tomatometer score is significantly above fresh.  

What is tomatometer score?

The Tomatometer score represents the percentage of professional critic reviews that are positive for a given film or television show.

To find answer we need to perform hypothesis.

The mean MCU Rotten Tomatoes score is equal to or less than 75%, which is the null hypothesis.

The mean MCU Rotten Tomatoes score is more than 75%, which is the alternative hypothesis. To test this theory, we can use a one-tailed t-test.

The null hypothesis can be rejected if the p-value is less than the significance level, which is typically 0.05, at which point it can be determined that the mean MCU Rotten Tomatoes score significantly exceeds fresh.

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Answer$200+$50x

Step-by-step explanation:

Answer:

4 Months

Step-by-step explanation:

if X = total (not sure)

thats means you must do $200 / $50 = 4 Months

Answer: rate of change is 2

Step-by-step explanation:

The box's dimensions that reduce the overall cost of the materials are as follows:

L = W = 16 cm

H = 32 cm

Given,

What is the dimensions of the rectangle?

A rectangle has two dimensions: a length and a width that are both perpendicular to it. The interior of an oval or a triangle also has two dimensions.

Here,

We've got

Volume = 512 cm3 L* W * H

Sides of the box cost = 1 cent/cm²

Top and bottom cost 2 cent/cm²

Then,

Box dimensions that reduce the overall cost of materials used

We are aware of

L× W × H = 512 cm³

Where,

L stands for length, W for width, and H for height.

So, when we reduce the cost function

C(L, W, H) = (1) 1 H + (2) 1 (L + W)

Thus insert H.

Replacing H with 512/LW yields,

C(L, W) = 512(1/L, 1/W), plus 2LW

So

When both partial derivatives are 0, there will be a minimum cost.

512/L2 - 2W = dC/dL = 0

So

512/W2 - 2L = 0 for dC/dW.

L = 256/W²

Now

The answer to the aforementioned equation is

L = W = (256)⁻³ = 16cm

And

H = 512/16 = 32

H = 32 cm

Consequently, the box's measurements that reduce the overall cost of the materials utilized are:

L = W = 16 cm

H = 32 cm

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The increase in the salary for Charolette will be $251.65.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since Charolette earns 3,595 per month at her job. She will receive a 7% raise. The amount of raise will be calculated by simply multiplying the percentage that she was given for the raise in the salary by the initial salary that she was earning.

This will be illustrated thus:

= Percentage × Salary

= 7% × $3595

= $251.65

The value of $251.65 will the increase in the salary.

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The frequentist probability is objective, based on observed data, need large sample or long term frequency, and doesn't have prior knowledge.

Frequentist probability is a definition of probability that defines the probability of an event as the probability of an event being observed in a long-term or infinite experiment.

Frequentist probability is different from Bayesian probability in following points,

Thus, the statement are true for frequentist definition for the probability is doesn't have prior knowledge, need large sample, based on observed data, and objective.

Your question is incomplete, but it is general information about the frequentist definition of probability.

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Answer:

Step-by-step explanation:

Answer:

t >28= the temp is warmer than 28

t >29= the table is heavier than 29 kilos

t <29= tony is you get than 29 yrs old

t <28= tia ran the race in under 28 secs

Step-by-step explanation:

hope this helps

The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

Let the number of number of red pencils be 'x'.

Total blue pencils = 5.

Ratio = blue pencils/red pencils

5/x = 1/2

x = 5 x 2

x = 10

Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

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Answer: x = 6

Step-by-step explanation:

2x + 7 = 9x - 35

-7x + 7 = -35

-7x = -42

x=6

w should be equal to 92° to prove that r || s.

To prove whether the two lines are parallel we should know whether

So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.

From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.

The answer is w. Therefore, option a is correct.

The complete question is -

Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?

a)w

b)x

c)y

d)z

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98% of the quarters can be expected to see a profit of at least $0.5 million.

What is a standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Z score = 0.7-0.5 = 0.2

σ = 0.1

P-value from Z-Table:

P(x<0.5) = 0.97725

             ≈ 98%

Hence, 98% of the quarters can be expected to see a profit of at least $0.5 million.

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If the base of the right triangle is 6 and the perpendicular height is 8 , then the length of the hypotnuse is  10 .

In the question ,

it is given that ,

the base of the right triangle is 6 , and

the height of the perpendicular is 8 ,

let the length of the hypotnuse of the given triangle be = h

Since the triangle is a right triangle , So , it follows Pythagoras Theorem ,

that means ,

h² = 6² + 8²

h² = 36 + 64

h² = 100

Simplifying further ,

we get ,

h = 10

Therefore , the length of the hypotnuse is = 10 .

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The difference between these distances on the Earth is 3.32 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression that shows the multiplication for the same number. Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. Exponents are used to show repeated multiplication of a number by itself

Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.

The difference will be:

= 4.00x10^4 km - 6.8x10^3 km.

= 3.32 × 10⁴

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