Lauren has an above-ground pool. to keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. when the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? use π = 3.14

The surface area of the prism is 256in².

Given that the sides of the prism is 5in, 12in and 4in.

The total area occupied by the surfaces of an object is called the area.

Here, l=12in, b=5in and h=4in

Firstly, we will find the area of the base, we get

B=l×b

B=12×5

B=60in²

Now, we will find the perimeter of the base, we get

P=2(l+b)

P=2(12+5)

P=2×17

P=34in

Further, we will find the surface area of the prism by using the formula SA=2B+Ph.

Here, we will substitute the values from above, we get

SA=2×60in²+34in×4in

SA=120in²+136in²

SA=256in²

Hence, the surface area of the prism where the sides of the prism is 5in, 12in and 4in is 256in².

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The total surface area of the shape is 10053 cm²

From the question, we are to determine the surface area of the shape

The surface area of the shape = Surface area of hemispherical part + Surface are of the cylindrical part

∴ Surface area of the shape = 2πr² + 2πrh + πr²

Where r is the radius

and h is the height of the cylindrical part

From the given information.

r = 20

h = 50

Putting the parameters into the equation, we get

Surface area of the shape = 2π(20)² + 2π(20)(50) + π(20)²

Surface area of the shape = 2π×400+ 2π×1000 + π×400

Surface area of the shape = 800π+ 2000π + 400π

Surface area of the shape = 3200π cm²

Surface area of the shape = 10053.096 cm²

Surface area of the shape ≈ 10053 cm²

Hence, the total surface area of the shape is 10053 cm²

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The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

In this question,

The power function is f(x) =-2x^3

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.

Then the end behavior is

As x -> ∞,

[tex]\lim_{x \to \infty} f(x)[/tex]

⇒ [tex]\lim_{x \to \infty} -2x^{3}[/tex]

⇒ [tex]-2(\infty)^3[/tex]

⇒ - ∞

Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

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Answer:

(4 , -3)

Step-by-step explanation:

the points (3 , 5) and (3 , 7) ​have the same x-coordinates 3

then ,the line D joining them has the equation  

D : x = 3

the image of the point A(2 , -3) under reflecting about The line D ,

lie on the line ∆ perpendicular to D and passes through A.

∆ perpendicular to D then the equation of ∆ is :

∆ : y = a   ,where a is a real number.

Calculating ‘a’ :

∆ passes through A

Then

-3 = a

Therefore

the final equation of ∆ is :

∆ : y = -3

Obviously, the lines D and ∆ intersect at the point M(3 , -3)

FINAL STEP :

Calculating the coordinates of the point B(x , y) image of the point A(2 , -3)

M is the midpoint of the line segment AB :

Then

3 = (2 + x)/2 and -3 = (-3 + y)/2

Then

x = 4 and y = -3.

Step-by-step explanation:

sin∅=-3/4 in 4 quadrant which sine is negative there

using soh cah toa

sin=opp/hyp

where our opp=-3 and our hyp=4

using pythagoras theorem

hyp²=opp²+adj²

(4)²=(-3)²+adj²

16=9+adj²

16-9=adj²

adj²=7

adj=√7

from soh cah toa

cos∅=adj/hyp

cos∅=√7/4

Answer:

-4t-11

Step-by-step explanation:

rearrange the numbers

2t-6t-9+2

Add negative 2

2t-6t-11

2-6

-4t-11

a. The value of n is 3/2

b. The value of a is 8.

c. The value of p is 125

The curve is an exponential function

An exponential function is a function of the form y = axⁿ where a and n are constants

Since y = axⁿ where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p), substituting these points into the equation, we have

y = axⁿ

27 = a(2.25)ⁿ  (1)

64 = a(4)ⁿ        (2)

P = a(6.25)ⁿ     (3)

Dividing (2) by (1), we have

64/27 = a(4)ⁿ/a(2.25)ⁿ

4³/3³ = (4 ÷ 2¹/₄)ⁿ

4³/3³ = (4 ÷ ⁹/₄)ⁿ

4³/3³ = (4 ×  4/9)ⁿ

4³/3³ = (16/9)ⁿ

4³/3³ = (4²/3²)ⁿ

(4/3)³ = (4/3)²ⁿ

Equating exponents, we have

2n = 3

n = 3/2

The value of n is 3/2

Using equation (2)

64 = a(4)ⁿ        

a = 64/(4)ⁿ        

substituting n = 3/2 into the equation, we have

[tex]a = \frac{64}{4^{\frac{3}{2} } } \\= \frac{64}{(\sqrt{4 } )^{3} } \\= \frac{64}{2^{3} } \\= \frac{64}{8} \\= 8[/tex]

So, the value of a is 8.

Using equation (3), we have

P = a(6.25)ⁿ     (3)

substituting the values of a and n into the equation,we have

[tex]P = 8(6.25)^{\frac{3}{2} } \\= 8(\sqrt{6.25}) ^{3} \\= 8(2.5}) ^{3} \\= 8(15.625})\\= 125[/tex]

The value of p is 125

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Answer:

angle l = 115

angle k = 115

angle j = 114

angle i = 66

Step-by-step explanation:

angle l = it is opposite to 115 so its the same

angle k = opposite opposing angles with angle l

angle j = 180-66=114 (between 2 parallel lines the sum of 2 angles is 180)

andle i = 180-114=66 (straight line = 180 degrees so subtract angle j to get i)

Answer:177

Step-by-step explanation:so for short, you need to multiply the 300 miles with the 59 precent we have and divide it to 100 this provides us the answer of miles he slept through the road trip

The number of miles they had travelled when Bentley fell asleep is 177 miles.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Bentley fell asleep 59% of the way through the trip.

The total length of the trip was 300 miles.

The number of miles

= 59% of 300

= 59/100 ×300

= 59×3

= 177 miles

Therefore, the number of miles they had travelled when Bentley fell asleep is 177 miles.

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The value of x if a, b, and c are collinear points and b is between a and c : 7

Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.

According to the given information:

if A, B, and C are col-linear points and B is between A and C

then

AB+BC=AC

AB=x+6

BC=3x-5

AC=36-x

(x+6)+(3x-5)=36-x

(x+3x)+(6-5)=36-x

4x+1=36-x

4x+x=36-1

5x=35

x=35/5

x=7

The value of x is 7

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Answer:

x = 2.4; y = 3.2

Step-by-step explanation:

y = 3x - 4

2x + y = 8

2x + 3x - 4 = 8

5x - 4 = 8

5x = 12

x = 12 / 5

x = 2.4

y = 3(2.4) - 4

y = 7.2 - 4

y = 3.2

6 possible ways to order 3 couples in a row

Given,

We have three married couples. that is six persons in total.

a, b, c, d, e, f may taken as the six persons.

Considering the statement:

Elder partner on the left, assume a, c and e as elders.

Then we have, (a, b) ------ ( 1)

                        (c, d) ------ (2)

                        (e, f) ------ (3)

There is no change in position between the couples.

So, we get three persons in total.

Possible ways to order these three persons will be like this: 3! = 3×2×1

                                                                                                        = 6

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In the given equation the value of x is 4.

According to the statement

we have given that the a equation and we have to solve that equation for x and find the value of the x.

So, For the value of x in given statement:

The given equation is

x⁴ = 256

we know that the 2 changes into the square root after rearrangement in the equation so, the equation become

(x²)² = 256

Now,

(x²) = √256

Then equation becomes

(x²) = 16

This is because the square root of the 256 is 16.

Now another square changes into square root then

x = √16

And

x = 4

So, In the given equation the value of x is 4.

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Answer:

12 square ft

Step-by-step explanation:

As given in the picture, the formula for the area of circles is A = pi*r*r. Since the radius is 2 ft and pi is approximately 3, A = 3*2*2 = 12 square ft.

Answer:

12 ft^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

The image gave us the value of the radius right away, so the question will be a lot easier to solve.

--> The reason why the radius is needed is that the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4[tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 ft^2.

The perimeter of inside of the track is 536.44m

The perimeter of a circle is also known as the circumference of the circle. The formula for calculating the circumference is expressed as:

C = 2πr

where

r is the radius

From the given diagram

r = 46/2 = 23m

C = 2(3.14)(23)
C = 144.44m

Find the perimeter of the rectangle

P = 2(l+w)

p = 2(46+150)
P = 2(196)
P =392m

The perimeter of the inside track = 144.44 + 392

The perimeter of the inside track = 536.44m

Hence the perimeter of inside of the track is 536.44m

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The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

To find the minimum value of 10x (3y/5):

Given - y = 3/(2x)

So, we want the bare minimum of,

Take the derivative to obtain:

When you set it to zero, you get:

So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.

Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

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Alpha level. the minimum P-value at which we reject the null hypothesis

That two options are identical is the null hypothesis. According to the null hypothesis, the observed difference is solely the result of chance. The probability that the null hypothesis is correct can be determined via statistical testing.

The "significance level," often known as the alpha level, must be established before performing any statistical test. The likelihood of rejecting the null hypothesis when it is true is what is meant by the term "alpha level" in statistics. The likelihood of making a poor decision is what this phrase means.

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Answer: 8π mm (in terms of π)

Step-by-step explanation:

1) The formulas for solving the circumference of a circle is πd (π times diameter).

2) 8 times π equals 8π mm.

Hopes this helps!

Answer:

12.56 [tex]mm^{2}[/tex]

Step-by-step explanation:

c = 2[tex]\pi[/tex]r

or c =[tex]\pi[/tex]D

The diameter is the measure of a line segment going from one side the circle to the other and going through the middle of the circle.  A radius is a line 1/2 a diameter.  It is a line segment that goes from the center of a circle to a point on the edge of the circle.

C = (3.14)(4)

C = 12.56

Answer:

-8

Step-by-step explanation:

y=(1/3)x

4 = (1/3)12

y=(1/3)(-24)

y= -8

If the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.

Given a function of x f(x)=1/(6x+6).

We are told to find out the value of the variable x for which the function does not lie.

Function is like a relationship between two or more variables expressed in equal to form. The values entered in a function is known as domain and the values which we get after entering of values are known as range.

f(x)=1/(6x+6)

It is in form of fraction. Fraction is a combination of numbers in which the above number is numerator and below number is denominator.

In this (6x+6) cannot be equal to 0 because if (6x+6) equal to 0 then the value of function becomes infinity.

So,

6x+6=0

6x=-6

x=-1

Hence if the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.

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89% of pebbles weigh more than 2.1 grams.

What is a percentage?

Given,

         Mean = 2.6

           SD = 0.4

As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first.

             [tex]z = \frac{x- mean}{SD}[/tex]

             [tex]z = \frac{2.1 - 2.6}{0.4}[/tex]

             [tex]z = -1.25[/tex]

Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1

So,

   [tex]P ( x < 1.25 ) = 0.10565[/tex]

This gives us the probability of P(z<-1.25) or P(x<2.1)

To find the probability of pebbles weighing more than 2.1

[tex]P ( x > 2.1 ) = 1 - P( x < 2.1 ) = 1 - 0.10565 = 0.89435[/tex]

Converting into percentage

0.89435 × 100 = 89.435 %

Rounding off to nearest percent   =89%

Therefore, 89% of pebbles weigh more than 2.1 grams.

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The vertex of the function f(x) exists (1, 5), the vertex of the function g(x) exists (-2, -3), and the vertex of the function f(x) exists maximum and the vertex of the function g(x) exists minimum.

Given:

[tex]$\mathrm{f}(\mathrm{x})=-(\mathrm{x}-1)^{2}+5$[/tex] and

[tex]$\mathrm{g}(\mathrm{x})=(\mathrm{x}-2)^{2}-3$[/tex]

The generalized equation of a parabola in the vertex form exists

[tex]$y=a(x-h)^{2}+k[/tex]

Vertex of the function f(x) exists (1, 5).

Vertex of the function g(x) exists (-2, -3).

Now, if (a > 0) then the vertex of the function exists minimum, and if (a < 0) then the vertex of the function exists maximum.

The vertex of the function f(x) exists at a maximum and the vertex of the function g(x) exists at a minimum.

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Answer:

- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.

- For the function g(x) = x^4 - 3, the vertex is a minimum point.

Step-by-step explanation:

To determine if the vertex for each function is a minimum or a maximum, we need to analyze the leading coefficient of each function.

Let's start with the function f(x) = -(x - 1)^2/5. This function is already in vertex form, where the vertex is (1, 0).

Since the leading coefficient is negative (-1/5), the graph of f(x) opens downward. In this case, the vertex is a maximum point. You can visualize it as a peak on a graph.

Now, let's move on to the function g(x) = (x^2)^2 - 3. This function can be rewritten in vertex form as g(x) = x^4 - 3.

The leading coefficient is positive (1), so the graph of g(x) opens upward. In this case, the vertex is a minimum point. You can visualize it as a valley on a graph.

In summary:

- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.

- For the function g(x) = x^4 - 3, the vertex is a minimum point.

Remember, the sign of the leading coefficient determines whether the vertex is a minimum or maximum point.

The formula for Observed Score is; Observed score (X) = True score (T) + measurement error (e)

The formula for Observed Score is;

Observed score (X) = True score (T) + measurement error (e)

1) True score is the score that would be obtained if an individual took a test an infinite amount of times and those test scores were averaged. The concept of true score is theoretical because you can't give someone something an infinite number of times.

2) Standard error of measurement is the standard deviation of multiple test scores (how far the sample mean of the data is likely to be from the true population mean).

The less random error (e) in the measure, the more the observed score X approximates the true score T.

Thus;

Observed score = True Score + Error

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Answer:

A

Step-by-step explanation:

the side opposite of the angle is related to the size of this angle. Smaller angles have less space for the line to "spread out," so it will be shorter. Vice versa, bigger angles will have opposite sides longer because of more space.

The considerations of expressions for each expressions are shown below.

To consider the expressions:

Part 1:

The answer to Part 1 is the letter B,

(7x²+16x+25)

Part 2:

The answer to Part 2 is the letter D,

(7x²-3x+8)

Part 3:

The answer to part 3 is the letter A,

(11x²+6x-6)

Part 4:

The answer to part 4 is the letter C,

(11x²-5x+13)

Therefore, the considerations of expressions for each expression are shown.

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The complete question is given below:
For each expression below, select the letter that corresponds to the equivalent expression given above.

Answer:

a.[tex]\sqrt{52}[/tex]cm or 7.21cm

b.[tex]\sqrt{170}[/tex]cm or 13.04cm

c. x= [tex]\sqrt{136}[/tex]cm or 11.66cm, y=[tex]\sqrt{191}[/tex]cm or 13.82cm

Step-by-step explanation:

a. You have to find the length of the other two sides of the triangle using the information already given. The first side is 6cm and the other is 12-9=4cm. Because it's a right-angled triangle you can use pythagoras

[tex]c^2=a^2+b^2\\x^2=6^2+4^2\\x^2=36+16\\x^2=52\\x=\sqrt{52}cm \\x=7.21cm[/tex]

b. You can use pythagoras again because it's a right-angle triangle

[tex]x^{2} =7^2+11^2\\x^2=170\\x=\sqrt{170} cm\\ = 13.04cm[/tex]

c. In this question you have to find x and y. We need to find x first using pythagoras

[tex]x^2=6^2+10^2\\x^2=136\\x=\sqrt{136}cm \\=11.66cm[/tex]

Now that we've found x we can find y using pythagoras but instead of find c, we will find another side

[tex]c^2=a^2+b^2\\19^2=\sqrt{170} ^2 + b^2\\361=170+b^2\\361-170=170+b^2-170\\191=b^2\\b=\sqrt{191}cm \\=13.82cm[/tex]

Hope this helps :)

Answer:

96 and 192

Step-by-step explanation:

This is a geometric sequence with a common ratio of 2 :

3 × 2 = 6

6 × 2 = 12

12 × 2 = 24

24 × 2 = 48

48 × 2 = 96

96 × 2 = 192

Therefore our final answers are 96 and 192

Hope this helped and have a good day

5x² + 9x - 1 is  the expression that represents a quadratic expression.

What is  quadratic expression?

A quadratic expression is of the form

ax² + bx +c = 0                    where a ≠ 0

The give options are-

9x - 2

5x² + 9x - 1

-2x³ + 8x² - 7x +1

[tex]x^{4} - 12 x^{3} + 8x^{2} - 7x +1[/tex]

From the given options, the only expression which is quadratic is

5x² + 9x - 1

wChoose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 −here a =5, b=9 and c=-1

Therefore, 5x² + 9x - 1 is  the expression that represents a quadratic expression.

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Answer:

The first option:

[tex]x^2-5x+9[/tex]

Step-by-step explanation:

Trust me I am right.

If you need work please ask!

Have a nice day!