A waterwheel has a radius of 4 feet, and the center of the wheel is 1 foot under the waterline. You notice a yellow mark at the top of the wheel. If the wheel rotates StartFraction pi Over 3 EndFraction radians, how far above the water is the yellow mark? 1 foot 2 feet 3 feet 4 feet

Hello!

So, we are given the following to solve:

[tex]\frac{1}{2}- \frac{9}{4}x=- \frac{2}{3}[/tex]

To solve this, subtract  [tex]\frac{1}{2}[/tex] from both sides.

[tex]\frac{1}{2} -\frac{9}{4}x- \frac{1}{2} =-\frac{2}{3} -\frac{1}{2}[/tex]

Simplify.

[tex]-\frac{9}{4}x= -\frac{7}{6}[/tex]

Multiply both sides by 4.

[tex]4(-\frac{9}{4}x)=4(-\frac{7}{6})[/tex]

Simplify.

[tex]-9x=-\frac{14}{3}[/tex]

Divide both sides by -9.

[tex]\frac{-9x}{-9}= \frac{-14/3}{-9}[/tex]

Finally, simplify.

[tex]x=\frac{14}{27}[/tex]

Hope this helps!

Answer:

0.026 is the value of x.

Step-by-step explanation:

sinx=p÷h

sinx=5.3÷8.2

sinx=sin0.02......

x=0.02°

A measure of the probability that the sample's average IQ is below 987 is 44.70 %.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean.

The Z-standard score's deviation measure, which the p-value is, can be regarded of as a percentile expression. So they do have p-values.

Given: IQ scores are frequently described as having a normal distribution with a mean of 100.0 and a standard deviation of 15.0. A sample of 57 persons is chosen at random.

Z-score = (X- μ)/σ

             = (98-100)/15

             = -0.1333

P value for this z score equals 0.4470 which is 44.70 %

Therefore, the probability that the average IQ of the sample's population is lower than 987 is 44.70 %.

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Answer:

16

Step-by-step explanation:

→ Add the fractions

[tex]2\frac{1}{4} +\frac{1}{2} =\frac{9}{4} +\frac{1}{2} =\frac{9}{4} +\frac{2}{4} =\frac{11}{4}[/tex]

→ Equate to 44

[tex]\frac{11}{4} x=44\\[/tex]

→ Multiply both sides by 4

11x = 176

→ Divide both sides by 11

x = 16

The volume of the cube is 27[tex]z^{15}[/tex]

A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.

Here we have to find the volume of a cube

The length of the side is 3[tex]z^{5}[/tex].

The formula for the volume of the cube = a³

where a is the length of the side.

Substituting the value of a we get,

The volume of the cube = (3[tex]z^{5}[/tex])³

                                        = 27[tex]z^{15}[/tex]

Therefore the volume of a cube is 27[tex]z^{15}[/tex].

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The value of square root of √28 will be;

⇒ 4√7 = 5.28

What is square root of a number?

A square root of a number is a value that multiplied by itself gives the same number.

Given that;

The number is,

⇒ √28

Now,

Let the value of square root of √28 is find as;

Since,

28 = 2 x 2 x 7

Hence,

⇒ √28 = √2 x 2 x 7

⇒ √28 =  2√7

⇒ √28 = 2 x 2.64

⇒ √28 = 5.28

Therefore,

The value of square root of √28 will be;

⇒ 4√7 = 5.28

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Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at

A number line is a sequence of numbers arranged at a particular pattern in a straight line

Information gotten form the question have it that"

RS= 10

R lies at 13

In a number line if R lies in point 13 and RS = 10 then we solve as follows

R + | 10 |

13 + 10 = 23

13 - 10 = 3

Hence R lies at point 3 or 13

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The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X  

The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths so on...

Given the statement as“the number with the units digit equal to x and the tens digit three more than the ones digit”

We need to convert the statement into the algebraic expression.

We know that unit digit number = X × 1

Then Tens digit number = (3 + X ) 10

Thus, the number = 30 + 10X + X

Hence, the Number = 30 + 11 X  

The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X  

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Answer:

Step-by-step explanation:

art I 5.00% per annum ------------- Amount invested =x

Part II 9.00% per annum ------------ Amount invested = y

8000

Interest----- 520.00

Part I 5.00% per annum ---x

Part II 9.00% per annum ---y

Total investment

x + 1 y= 8000 -------------1

Interest on both investments

5.00% x + 9.00% y= 520

Multiply by 100

5 x + 9 y= 52000.00 --------2

Multiply (1) by -5

we get

-5 x -5 y= -40000.00

Add this to (2)

0 x 4 y= 12000

divide by 4

y = 3000

Part I 5.00% $ 5000

Part II 9.00% $ 3000

CHECK

5000 --------- 5.00% ------- 250.00

3000 ------------- 9.00% ------- 270.00

Total -------------------- 520.00

This operation is equivalent to:

It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.

As we can see, h(x) have terms with x + 4, so if we call:

We can see that h(x) becomes:

And if we substitute g(x) by x, we will get the expression of the ouside function f(x):

This way, we have:

So, the functions are:

The angle which the pendulum travels is 0.61 radian

Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disk in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases.

Given that :A pendulum is 45cm long. When the pendulum swings it travels along the arc of the circle and covers a distance of 27.5cm.

  Central Angle =[tex]\frac{length of arc}{Radius}[/tex]

= [tex]\frac{27.5}{45}[/tex]

=0.61 radian

The angle which the pendulum travels is 0.61 radian

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Mandy must to walk a distance of 24.73 units towards Mark.

Given:

Mark is standing at 35th Street and 21st Avenue, so his location can be determined using the coordinates (35,21)

Mandy is positioned at 59th Street and 15th Avenue, hence her position's coordinates are as follows: (59,15).

We must now determine the distance Mandy must travel if Mark stays where he is and walks to meet him.

We can use the distance formula to determine this:

D = [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} -y_{1})^{2} } }[/tex]

Here,

(x₁, y₁) =  (35, 21)

(x₂, y₂) = (59, 15)

Then,

D = [tex]\sqrt{(59-35)^{2}+(21-15)^{2} }[/tex]

D = [tex]\sqrt{24^{2} +6^{2} }[/tex]

D = [tex]\sqrt{576+36}[/tex]

D = √612

D = 24.73

That is,

Mandy must to walk a distance of 24.73 units towards Mark.

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Answer:

Yes, you have to distribute.

Step-by-step explanation:

2+5(x+3)-3(x-4)=x+2(2x+4)

2+5x+15-3x+12=2(2x+4)

Add the Numbers

2+5x-3x=2(2x+4)

Combine Like Terms, Then you can rearrange the terms for simplification. You should end up with an exation looking like this:

2x+29=5x+8

Subtract 29 from both sides. Simplify, then subtract 5x from both sides.
2x-5x=5x-21-5x
Simplify, then Divide both sides by the same factor. Simplify once more then you should have
x=7

Hope this helps ;)

There are 8 tenths in 4/5, There are five fifths in 1/10, there are 2 tenths in 1/5, there are 25 fifths in 5.

The digit that follows the decimal has the place value of tenth. It stands for the digit's 1/10 position.

The fifth of a number is obtained by multiplying five occurrences of the number n together: n5 = n n n n. A number's fourth power or its square by its cube can likewise be used to create fifth powers.

a) Given 4/5, multiply the numerator and denominator by 2 to obtain the tenths. We get =4/5 2/2 =8/10 =8(1/10). Similarly, in 1/5, calculate the tenths in 1/5.

c) 525/25 = 25 is the fifth in 5.

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If the Great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%

The fraction of games sells through the online store = 9/20

Here we have to convert the simple fraction to the percentage

Simple fraction is a fraction that consist of whole number numerator and denominator. The top term in the simple fraction is called the numerator and bottom term is called denominator

The percentage is defined as the number that is expressed as the fraction of 100. It is represented by the percentage sign "%"

To convert  simple fraction to percentage, multiply the simple fraction by 100

The percent of games are sold online = (9/20)×100

= 45%

Hence, if the great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%.

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Answer:

88

Step-by-step explanation:

multiply 13 by 2 = 26

then add by 1 52 and 15

= 94

then subtract 94-6

88

Remember use Dmas while solving

Answer: 16x^2+144x+18

Step-by-step explanation:

The sum of two given expressions is 16x²-6x+14.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given expressions are 8x²-x+9 and 8x²-5x+5.

Now, sum =8x²-x+9+8x²-5x+5

Group like terms and simplify, we get

(8x²+8x²)+(-x-5x)+(9+5)

= 16x²+(-6x)+14

= 16x²-6x+14

Therefore, the sum of two given expressions is 16x²-6x+14.

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a.  4 million registered voters in the state where  the 5,000 registered voters is drawn from the pool of registered voters.

Options: a. 4 million registered voters in the state

b. 5,000 registered voters interviewed

c. 54 %,  voters interviewed who plan to vote for him

d. 46 %,  voters interviewed who plan not to vote for him

The population of interest is the group from which a sample set is collected. Here, the 5,000 registered voters is drawn from the pool of registered voters. The people surveyed are representative of the total number of voters. The population of interest here is the 4 million registered voters.

For example, if a survey is carried out to figure out the age that kids start walking, the population of interest is kids in general and not just the children who are surveyed.

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The distance from the midpoint to the origin is [tex]\sqrt{5}[/tex].

What is midpoint?

Midpoint is the point that is in the middle pf the line, and to calculate midpoint the formula is

[(x)1 + (x)2]/2, [(y)1 + (y)2]/2

given coodinates are (-2, -4) and (0, 8)

midpoint = (-2+0/2, 8-4/2)

=(-1, 2)

to find the distance from the midpoint to origin.

d= [tex]\sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{2} )^2} }[/tex]

the points are (-1,2) and (0,0)

d = [tex]\sqrt{(-1)^2+(2)^2}[/tex]

d = [tex]\sqrt{5}[/tex]

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Answer:

Step-by-step explanation:

1 to the 10th power is 1.

The value of KM is 20

A line, ray, line segment, or point that cuts a line segment at its center and divides it into two equal portions is known as a segment bisector. A segment is a section of a line with definite ends, which is also how the word segment is sometimes used. Any object or line is divided into two equal halves when it is bisected. Consequently, when two line segments cut or bisect each other at a location that divides the lines into equal halves, this is known as a segment bisector.

Given that : The line q bisects KM at point V, KV = 2.5z and VM = 5z - 10

the line q bisects KM at point V so KV = VM

KV = 2.5z

VM = 5z - 10

2.5z= 5z - 10

10 = 2.5z

4 = z

Now put the value of 4 in KV and VM

KV = 2.5(4)

VM = 5(4) - 10

KV + 10

VM = 10

KM = KV + VM
KM = 10 + 10

= 20

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The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes therefore, option (a) is correct.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

As per the given polynomial,

61 = 125 - 64

It is known that a³ = a × a × a

Therefore, 5³ = 5 × 5 × 5 = 125

And, 4³ = 4 × 4 × 4 = 64

Therefore, 61 = 5³ - 4³

Hence "The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes".

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The inequality for the statement: the difference between a number and seven eighths exceeds negative two thirds is g - 7/8 > -2/3.

The correct answer option is option c

Let

difference between a number and seven eighths

g - 7/8

difference between a number and seven eighths exceeds negative two thirds

g - 7/8 > -2/3

The options;

A. g plus 7 over 8 is greater than 2 over 3

g + 7/8 > 2/3

B. g minus 7 over 8 is less than or equal to negative 2 over 3

g - 7/8 ≤ -2/3

C. g minus 7 over 8 is greater than negative 2 over 3

g - 7/8 > -2/3

D. g minus 7 over 8 is less than negative 2 over 3

g - 7/8 < -2/3

So therefore, the inequality statement can be written as g - 7/8 > -2/3.

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Triangle RST is rotated 180° about the origin, and then translated up 3 units.  Then , ΔRST ≅ ΔBAC

We know that  To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of triangle RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC

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The quadrilateral named D, H, and E will be the scaled copies of the unlabeled rectangle.

A quadrilateral may be defined as a closed figure having four sides whereas a rectangle is a type of quadrilateral which has four sides in which any two sides are equal and the other two sides are also equal. The interior angles are 90°. The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. Now, from the question If any figure is a scaled copy, then all dimensions must be enlarged with the same factor it means length and width both must be enlarged with the same factor. So, the unlabeled rectangle has 4 grid lengths and 2 grid widths. In H length is 8 grids and width are 4 which is the multiplication of 2 by 4 and 2. Quadrilateral D and E also follow the same.

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The reflection of a coordinate about the y = x  will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

It is known that,

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Therefore,

A(0, -3) → A'(-3,0)

B(2, 2) → B'(2,2)

C(5,0) →C'(0,5)

Hence "The reflection of a coordinate about the y = x  will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5)".

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The height of the part of the post that is above the ground is 10 - 3(1/3)

= 6(2/3) feet.

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Answer:

y=40 z= 5h+15

5 hours to make the same amount of money

Step-by-step explanation:

40-15=25

25/5=5

hope this helped