The height of the yellow mark above the water is 1 foot.
This is further explained below.
How far above the water is the yellow mark?Generally, The radius of a waterwheel is 4 feet, and its center is 1 foot below the waterline.
Estimation of feet:
cos π/3 = OB/OA
1/2 = OB/4
OB = 2
t
In conclusion,A yellow mark should be placed above the water
= OB - OD
= 2 - 1
= 1 foot
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Answer:
the other answer is correct is A. 1 foot
Step-by-step explanation:
Got it right on edge
ASAP!!!
2 1/4x + 1/2x = 44
Solove for X and include all steps to get branliest.
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
How to find the square root of [tex]\sqrt{28[/tex]
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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Intelligence Quotient (IQ) scores are often reported to be normally distributed with 100.0 and standard deviation = 15.0. A random sample of 57 people is taken.
What is the probability that the mean IQ score of people in the sample is less than 987 Round your answer to 4 decimal places, if necessary.
A measure of the probability that the sample's average IQ is below 987 is 44.70 %.
Why are z-scores important?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.
Do z scores have p values?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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A pendulum is 45cm long. When the pendulum swings it travels along the arc of the circle and covers a distance of 27.5cm. Calculate the size of the angle which the pendulum travels.
The angle which the pendulum travels is 0.61 radian
What is central angle of circle ?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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pls help its urgent!!
What polynomial identity should be used to prove that 61 = 125 − 64?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes therefore, option (a) is correct.
What is a number system?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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a politician who is running for the office of governor of a state with 4 million registered voters commissions a survey. in the survey, 54% of the 5,000 registered voters interviewed say they plan to vote for her. the population of interest is the:
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 cost of renting a canoe to use on River Y costs $.40 The cost of renting a canoe to use on River Z costs $5 per hour plus a $15 deposit. The total cost, c, of renting a canoe on either river for n hours can be represented by an equation. Write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers.
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
The Great Games Company sells 9/20 of its games through its online store. What percent of the games are sold online?
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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If line q bisects KM at point V, KV = 2.5z,
and VM = 5z - 10, find KM. No
The value of KM is 20
What is segment bisector ?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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Dale has 33 carnival tickets. Its costs 7 tickets to ride the roller coaster. How many rides can he take?
Find the sum of 8x^{2}-x+98x
2
−x+9 and 8x^{2}-5x+58x
2
−5x+5.
Answer: 16x^2+144x+18
Step-by-step explanation:
The sum of two given expressions is 16x²-6x+14.
What is addition of algebraic expression?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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Triangle rst is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures? δrst ≅ δacb δrst ≅ δabc δrst ≅ δbca δrst ≅ δbac.
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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Write an expression for the volume of a cube with a side of length 3z^5 Simplify your expression
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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Lena is building a fence. She will need to dig up holes to help support the posts that hold up the fence. The holes need to have a depth of 3 1/3 feet below the ground. Each post is 10 feet long. What is the height of the part of the post that is above the ground? PLEASE HELP 100 points
The height of the part of the post that is above the ground is 10 - 3(1/3)
= 6(2/3) feet.
What is a height?Height is degree of vertical distance, both vertical extent (how "tall" some thing or a person is) or vertical position (how "high" a factor is). For example, "The peak of that constructing is 50 m" or "The peak of an aircraft in-flight is ready 10,000 m". For example, "Christopher Columbus is five foot 2 inches in vertical peak."When the time period is used to explain vertical position (of, e.g., an aircraft) from sea level, peak is greater frequently referred to as altitude.Furthermore, if the factor is connected to the Earth (e.g., a mountain peak), then altitude (peak above sea level) is referred to as elevation.In a two-dimensional Cartesian space, peak is measured alongside the vertical axis (y) among a particular factor and every other that doesn't have the identical y-value. If each factors occur to have the identical y-value, then their relative peak is zero. In the case of 3-D space, peak is measured alongside the vertical z axis, describing a distance from (or "above") the x-y plane.To learn more about height from the given link:
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Write the inequality for the statement: the difference between a number and seven eighths exceeds negative two thirds f plus 7 over 8 is greater than 2 over 3 f minus 7 over 8 is less than or equal to negative 2 over 3 f minus 7 over 8 is greater than negative 2 over 3 f minus 7 over 8 is less than negative 2 over 3
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
How to write inequality equation?Let
The unknown number = gdifference 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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DOI HAVE TO DISTRIBUTE?
2+5(x+3)-3(x-4)=x+2(2x+4)
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 ;)
Graph the polygon with the given vertices and its image after a reflection in the line y=-x . A(0, -3), B(2, 2), C(5,\0)
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).
What is the transformation of a graph?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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Suppose that R and S are points on the number line If RS= 10 and R lies at 13 where could S be located
Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at
323'What is a number line?A number line is a sequence of numbers arranged at a particular pattern in a straight line
How to find the point of S if R lies at point 13Information 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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1
10
To solve this problem, ask the question
= ?
How many tenths are in 4/5?
How many fifths are in 1/10?
How many tenths are in 1/5?
How many fifths are in 5?
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.
What is tenths and fifths?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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How to turn “the number with the units digit equal to x and the tens digit three more than the ones digit” into a algebraic problem
The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X
How to identify the place value of a digit in a number?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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A woman has a total of $8,000 to invest. She invests part of the money in an account that pays 11 % per year
and the rest in an account that pays 12% per year. If the interest earned in the first year is $920, how much did
she invest in each account?
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
Trigonometry Question!
Second Question: Calculate the value of X.
Show work needed.
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°
What is 1 as a power of 10
Answer:
Step-by-step explanation:
1 to the 10th power is 1.
what is 1+13⋅2+52−3+15−3
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
Find two functions F and G such that (f°g) (x) = h(x).
This operation is equivalent to:
[tex](f\circ g)(x)=f(g(x))[/tex]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:
[tex]g(x)=x+4[/tex]We can see that h(x) becomes:
[tex]h(x)=(g(x))^2+2g(x)[/tex]And if we substitute g(x) by x, we will get the expression of the ouside function f(x):
[tex]f(x)=x^2+2x[/tex]This way, we have:
[tex](f\circ g)(x)=(g(x))^2+2g(x)=(x+4)^2+2(x+4)=h(x)[/tex]So, the functions are:
[tex]\begin{gathered} g(x)=x+4 \\ f(x)=x^2+2x \end{gathered}[/tex]Here is an unlabeled rectangle, followed by other quadrilaterals that are labeled.
a. Select ALL quadrilaterals that are scaled copies of the unlabeled rectangle.
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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b. If Mark stays where he is and Mandy walks to him, how far must she walk?
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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1/2 - 9/4x = -2/3 solve for x and simplify your answer as much as possible
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!
Consider the points on a line segment in the coordinate plane A(-2, -4) and B(0, 8). What is the
distance from the midpoint to the origin?
A √8
B √5
C √10
D √2
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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