The area of a circle is given by the formula:
A = πr^2
Where A is the area of the circle, π is approximately 3.14 and r is the radius of the circle.
Given the radius, r = 7.27m, we can substitute this into the formula and calculate the area of the circle.
A = π * 7.27^2 = π * 52.5129
A = 165.9 m^2
The area of the circle is 165.9 m^2. Rounded to 2 decimal places, the area of the circle is 165.90 m^2
Two triangular sculptures are similar. The leg of the first sculpture is 4.5 feet and the base is 7.2 feet. The leg of the second sculpture is 6 feet. What is the length of the base for the second sculpture? Show your work.
For two similar triangular sculptures having leg l1 = 4.5 ft, l2 = 6 ft, and base b1 = 7.2 ft, the measurement of b2 is 9.6 ft.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
Two triangles are similar.
Let the two similar triangles sculptures be ΔABC and ΔDEF.
The length of the leg ΔABC, AB = 4.5 feet
The length of the base of ΔABC, BC = 7.2 feet
The length of the leg ΔDEF, DE = 6 feet
The length of the base of ΔDEF, EF = x feet
To find the measure of base of ΔDEF, use the formula for indirect measurement.
According to indirect measurement the formula will be -
AB/DE = BC/EF
Substitute the values in the equation -
4.5/6 = 7.2/x
4.5 × x = 7.2 × 6
4.5x = 43.2
x = 43.2/4.5
x = 9.6
Therefore, the value for x is obtained as 9.6 feet.
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A form of nickel has a half life of 91 years. How much of a 90 gram sample is left after 290 years? 
The amount of the 90gram-sample that will remain after 290 years is 9.88 grams
How to determine the number of half-lives?We'll begin by obtaining the number of half lives that has elapsed. This can be obtained as follow:
Step1
Half-life (t½) = 91yearsTime (t) = 290 yearsNumber of half-lives (n) =?n = t / t½
n = 290 / 91
n = 3.1868
Step 2
determine the amount remaining:
Original amount (N₀) = 90 gramsNumber of half-lives (n) = 3.1868Amount remaining (N) =?The amount remain can be obtained as follow:
N = N₀ / 2^n
N = 90 / 2^3.1868
=9.88
N=9.88 grams
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The points on this graph represent a relationship between x
- and y
-values. Which statement about the relationship is true?
Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true is that: A. it cannot be proportional because a straight line through the point does not go through the origin.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
In conclusion, the relationship between the x-value and y-value isn't proportional because the straight line does not pass through the origin (0, 0).
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At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
please help
The equation that represents the proportional relationship is: k = 7.25.
What is a Proportional Relationship Equation?A proportional relationship is a relationship between two variables such that one variable is a constant multiple of the other. A proportional relationship can be represented by an equation of the form y = kx where y and x are the variables, and k is the constant of proportionality. This equation can also be written as y/x = k.
From the given information, we have:
Constant of proportionality (k) = 21.75 / 3
k = 7.25
To write the equation, substitute k = 7.25 into y = kx:
y = 7.25x
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Translate the phrase into a variable expression. Use the letter g to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.
The total number of seagulls standing on the pier and the 51 gulls in the air
The expression that represents the ratio between the total number of seagulls standing on the pier and the 51 gulls in the air is given as follows:
g/51.
How to obtain the ratio?The ratio between two amounts a and b is found applying a proportion, which is the division between them.
The amounts for this problem are given as follows:
g is the number of seagulls standing on the pier.51 is the number in the air.Hence the ratio is given as follows:
g/51.
Missing InformationThe problem asks for the expression for the ratio the total number of seagulls standing on the pier and the 51 gulls in the air.
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U.S. inflation is intentionally kept at a steady 5%, for a variety of economic reasons. Because of this, the cost
of most things is expected to increase by 5% per year, with few exceptions.
In 2009, minimum wage was set to 7.25, and has not changed since. If it had risen to meet the intended
inflation, what would minimum wage be now in 2023?
A$21.16
B $14.35
C$15.05
D$2,116,.49
What is the solution to 9|x + 8| > 45?
x < –3 or x > 13
–3 < x < 13
x < –13 or x > –3
–13 < x < –3
The inequality model of the question will be -13 > x > -3
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
9|x + 8| > 45
now when we remove the modulus there will be two terms.
|x + 8| > 45/9
|x + 8| > 5
-5>x + 8>5
-5-8>x >5-8
-13 > x > -3
Hence, the inequality model will be -13 > x > -3
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Conider the line .3x-6y=-8
Find the equation of the line that i parallel to thi line and pae through the point .4,2
Find the equation of the line that i perpendicular to thi line and pae through the point . (4,2)
The equation of the straight line perpendicular to the line 3x - 6y = - 8 is y-2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y=0.
The general equation of a straight line is -
y=mx+c
where -
m is slope of line which tells the unit rate of change of y with respect to x.
c is the y - intercept i.e., the point where the graph cuts the y axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
[tex]y=\frac{-A}{B} x-\frac{C}{B}[/tex]
Given that: -
[tex]3x-6y=8\\\\6y=3x-8\\\\y=\frac{1}{2}x-\frac{4}{3}[/tex]
then,
[tex]m=\frac{1}{2}\\\\c=\frac{4}{3}[/tex]
For a parallel line,
[tex]m=\frac{1}{2}\\and,(4,2)[/tex]
[tex]y-y_{1}=m(x-x_{1})\\\\y-2=\frac{1}{2}(x-4)\\\\2y-4=x-4\\\\y=\frac{x}{2}[/tex]
The equation of parallel line is y=0.5x
For a perpendicular line
[tex]m=2\\\\y-2=2(x-4)\\\\y-2=2x-8\\y-2x=-6\\y-2x+6=0\\[/tex]
Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y -2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y = 0.5x.
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Solve for c
a(c + b)=d
Answer:
[tex]c = \frac{d}{a} - b[/tex]
Step-by-step explanation:
Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, divide a from both sides of the equation:
[tex]a(c + b) = d\\\frac{a(c + b)}{a} = \frac{d}{a} \\c + b = \frac{d}{a}[/tex]
Next, isolate the variable, c, by subtracting b from both sides of the equation:
[tex]c + b = \frac{d}{a} \\c + b (-b) = \frac{d}{a} (-b)\\c = \frac{d}{a} - b[/tex]
[tex]c = \frac{d}{a} - b[/tex] is your answer.
~
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Answer:
c = (d/a) - b
Step-by-step explanation:
Now we have to,
→ Find the required value of c.
The equation is,
→ a(c + b) = d
This can be distributed as,
→ a(c + b) = d
→ a(b) + a(c) = d
→ ab + ac = d
Then the value of c will be,
→ a(c + b) = d
→ a × (c + b) = d
→ c + b = d/a
→ c = -b + (d/a)
→ [ c = (d/a) - b ]
Hence, value of c is (d/a) - b.
a big cruise ship dropped anchor off the caribbean island of antigua. the heavy anchor dropped into the water at a rate of 2.5 2.52, point, 5 meters per second. after 45 4545 seconds, the anchor was 40 4040 meters below the water's surface. from what height (above the water's surface) was the anchor released?
At a distance of 72.5 meters above the water's surface, the anchor was let go.
It takes 29 seconds to reach the water's surface.
The anchor dropped for 45 seconds at a speed of 2.5 m/s.
112.5 metres are equal to (2.5 m/s) x (45 s).
It must have dropped if it ended up only 40 meters under the water.
(112.5 m - 40 m) equals 72.5 m
Before it ever got to the water, it was in storage on the large cruise ship.
It took longer because it was descending at a speed of 2.5 m/s.
29 seconds are equal to 72.5 m / (2.5 m/s)
it began to drop, to get down to the water's surface.
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Jude types 1,281 characters in 7 minutes. What is her typing rate in characters per minute?
Answer:
183 charters
7 goes into 12 1 time so 12-7=5
bring down the 8 so 7x8=56 so 58-56=2
being down the 1 and you have 21. 7 goes into 21 three times.
Answer:
183 characters per minute
Step-by-step explanation:
1281 divided by 7
the value of philipine peso is less than the value of one US dollar
The mathematical statement that accurately depicts how value of philipine peso is less than the value of one US dollar is: p < d. The Option C is correct.
What is Less than Symbol all about?The Less-than symbol is used to compare two values where the first number is less than the second number, for example, in ascending order. The opening angle bracket is approximated by the less than symbol.
"<" is the symbol used to represent the less than inequality. The less than sign is a universally recognized math symbol composed of two equal measure strokes intersecting in an acute angle at the left.
For example: If given 2< 5: 2 is less than 5
Missing options "Which of the following mathematical statement represents the given situation? a. d = p b. p>d c. p <d d. none of these
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Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
The height of the trapezoid that has an area of 24 cubic cm is: 3 cm.
How to Calculate the Height of a Trapezoid?The formula for the area of a trapezoid is 1/2(a+b)h, where a and b are the lengths of the bases and h is the height.
Given that the area of the trapezoid is 24 cubic centimeters and the base lengths are 9 cm and 7 cm, we can plug in those values to the formula and solve for h:
24 = 1/2(9+7)h
24 = 1/2(16)h
24 = 8h
To find h, we divide both sides of the equation by 8:
h = 24/8
h = 3
So the height of the trapezoid is 3 cm.
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Students will present a play in an
auditorium that has 550 seats. Each
student performing in the play must
sell 12 tickets to the performance.
The remaining 370 tickets will be
sold by other students in the school.
Which equation could be used
to
find x, the number of students
performing in the play?
Answer:
550 - 12x = 370
Pop's Cycle Shop sells bicycles and tricycles. The
number of bicycles is 1 less than 4 times the number
of tricycles. All the bicycles and tricycles together have
a total of 174 wheels. How many bicycles are there?
The number of bicycles there is given as follows:
63.
How to obtain the number of bicycles?The number of bicycles and tricycles is obtained using a system of equations, for which the variables are given as follows:
Variable x: number of bicycles.Variable y: number of tricycles.The number of bicycles is 1 less than 4 times the number of tricycles, hence:
x = 4y - 1.
There is a total of 174 wheels, hence:
2x + 3y = 174.
The number of tricycles is obtained as follows:
2(4y - 1) + 3y = 174
11y = 176
y = 176/11
y = 16.
Hence the number of bicycles is of:
x = 4(16) - 1
x = 63.
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three people ann, bob and colin have a total of $1.80 between them, each having a different amount. does ann have the most money? (1) ann has $0.6 (2) bob has $0.5
Compared to Ann and Bob, Colin has more. Thus, Ann is not have most money.
In the given question, we have to find Ann have the most money or not.
Three people Ann, Bob and Colin have a total of $1.80 between them, each having a different amount.
Ann has $0.6 amount and Bob has $0.5 amount.
Ann + Bob + Colin = 1.80
0.6 + 0.5 + Colin = 1.80
1.1 + Colin = 1.80
Subtract 1.1 on both side, we get
Colin = 0.70
So Colin has $0.70.
So, Colin has more amount than Ann and Bob. So Ann does not have most money.
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00:00
A parking garage has 612 parking spaces on 4 levels. Each level has about the same number
of parking spaces. Select all of the statements that are reasonable estimates for the number
of parking spaces on each level
There are 153 parking spaces on each level of the parking garage.
Equation
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given that a parking garage has 612 parking spaces on 4 levels, and each level has about the same number of parking spaces, to determine the number of parking spaces on each level the following calculation must be performed: -
so the equation is ,
612/4 = X
153 = X
X = 153.
Thus, there are 153 parking spaces on each level of the parking garage.
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The mean per capita income is 21,604 dollars per annum with a standard deviation of 727 dollars per annum.
What is the probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected? Round your answer to four decimal places
The probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected is 65.53%.
This can be calculated using the normal distribution. The mean of the normal distribution is the population means, which in this case is 21,604 dollars per annum. The standard deviation is 727 dollars per annum. Using this information, we can calculate the z-score of 21635 dollars per annum by subtracting the population mean from it and dividing it by the standard deviation. This gives us a z-score of 0.42.
21635-21329/727=0.42
Using a z-table, we can calculate the probability of the sample means being less than 21635 dollars to be 0.6553.
This can also be written as 65.53%. This means that there is a 65.53% probability that the sample mean of 193 persons randomly selected would be less than 21635 dollars per annum.
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Josh drank 70 ounces of water yesterday.how many cups of water did he drink
Answer:
8.75
Step-by-step explanation:
what is the measure of arc BC?
130 degrees
180 degrees
65 degrees
32.5 degrees
The angle subtended by arc BC on center of circle is of 2 times 65 = 130
What is Area of circle ?
Area of circle can be defined as the product of pi and the square of radius of a circle.
Using the property that angle subtended by an arc on center is double than on circumference, you can find measure of arc BC.
The angle subtended by arc BC on center of circle is of 2 times 65 = 130
Given,
The angle subtended by arc BC on circumference is 65 degrees.
We have to find Length of arc BC
Relation between angle at center and angle at circumference by an arc:
"Angle subtended by an arc of a circle on its center is double than angle subtended by it on circumference"
Therefore , angle subtended by arc BC on center of circle is of 2 times 65 = 130 .
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PLEASE ANSWER DUE TOMORROW
The measurement of angles formed by intersecting line segments UT and WV are -
∠TXV = 25°
∠UXW = 25°
∠TXW = 155°
∠UXV = 155°
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Two line segments UT and WV are given.
The line segment UT and WV are intersecting each other at a point X.
Due to the intersection many angles are formed.
To find the measure of the angles, use the protractor.
The first angle is ∠TXV.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line UT.
The measure of ∠TXV is approximately 25°.
The second angle is ∠UXW.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line WV.
The measure of ∠UXW is approximately 25°.
The third angle is ∠TXW.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line WV.
The measure of ∠TXW is approximately 155°.
The fourth angle is ∠UXV.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line UV.
The measure of ∠UXV is approximately 155°.
Therefore, all the four angles are obtained.
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Sandra Williams bought a home with a 10. 25% adjustable rate mortgage for 25 years. She paid $9. 27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then interest rates have increased to 12. 75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11. 10 monthly per thousand on her loan. You can ignore the small amount of principal paid during the 3 years. What was the old monthly payment? $ a0 What is the new monthly payment? $ a1 What is the percent increase in her monthly payment (to the nearest tenth)? a2 %
a) The old monthly payment was = 9.27 × 50 = 463.5
b) The new monthly payment is = 11.10 × 50 = 555
c) The percent increase in his monthly payment is 1.947 %
With a 25-year, 10.25% adjustable rate mortgage, Sandra Williams purchased a property. She made monthly payments of $9.27 per thousand on his initial debt.
According to the question,
The per thousand value of $65000 is, 50000/1000 = 50
Now, the old monthly payment was = 9.27 × 50 = 463.5
She makes the decision to renew and will now make monthly loan payments of $11.10 per thousand.
So, the new monthly payment is = 11.10 × 50 = 555
The percent increase in his monthly payment is = 11.10 /9.27 - 1 × 100
⇒ 19.7411 %
And to nearest tenth it is 1.947%
Hence, the old monthly payment was = 9.27 × 50 = 463.5
The new monthly payment is = 11.10 × 50 = 555
Thus, the percent increase in his monthly payment is 1.947%.
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Find two numbers that the quotient is between.
4,096 divided by 61
The quotient is between _ and _
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
see image
The quotient from 4,096 divided by 61 is between 66 and 67.
Does someone mind helping me with this problem? Thank you!
Answer:
x=71; y=19
Step-by-step explanation:
x+y = 90 so x =90-y = 14+3y
so 90=14+4y
90-14 = 4y
76=4y
y=19
x=71
Answer:
x = 71
y = 19
Step-by-step explanation:
I solved by graphing and got (71,19) as included in the image. A more mathematical way to solve is by substitution. You try to find x with one of the equations, plug in x and then solve for y.
x + y = 90
x = 90 - y
90 - y = 14 + 3y
90 - y + y= 14 + 3y + y
90 = 14 + 4y
90 - 14= 14 + 4y - 14
76= 4y
19 = y
x + y = 90
x + (19) = 90
x + 19 - 19= 90- 19
x = 71
A movie club surveyed 200 high school students. The students were asked how often they go to the movies and whether they prefer action movies or dramas. Their responses are summarized in the following table
The percentage of students that prefer drama is 52%.
The percentage of students that go to the movies three times or more is 34%.
What are the percentages?
Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.
The percentage of students that prefer drama = (total number of students that prefer drama / total number of students surveyed) x 100
= [(70 + 34) / 200] x 100
= (104 / 200) x 100 = 52%
The percentage of students that go to the movies three times or more = (total number of students that go to the movies three times or more / total number of students surveyed) x 100
[(34 + 34) / 200] x 100
(68 / 200) x 100 = 34%
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Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef. The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese. How many different possible sandwiches does that leave Kim?
5
6
8
12
_______________________________________________________
Show your work!
The number of possible sandwiches does is 6.
What is combination ?
In arithmetic, a combination is a way of choosing gadgets from a set where the order of selection does no longer count. suppose we've got a hard and fast of 3 numbers P, Q and R. Then in what number of methods we can select two numbers from every set, is described via combination.
Given ,
Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef.
The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese.
factorial of n! = n*(n-1) !
The number of possible sandwiches does = 3!
=3*2 = 6.
Therefore, The number of possible sandwiches does is 6.
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0.75 * ( x+4)=9. what does x equal?
Answer:
x = 8
Step-by-step explanation:
0.75 * ( x+4) = 9
0.75x + 3 = 9
0.75x = 9 - 3
0.75x = 6
x = 6 / 0.75
x = 8
25% of 72 is what value? 21 18 12 7
Answer:
18
Step-by-step explanation:
To find a percent of a number, change the percent to a decimal by dividing the percent by 100 and multiply by the number.
25% of 72 =
= 25/100 × 72
= 0.25 × 72
= 18
Answer: it would be 18
Step-by-step explanation:
Simplify (s-5)³. Write your answer using only positive exponents.
The solution is…
Answer:
s³ - 15s² + 50s - 125
Step-by-step explanation:
yes
Analysis A question on a test asks students to find the speed at which a car
travels. The graph shows a proportional relationship between the distance traveled
in miles and time in hours. Anna incorrectly says that the speed of the car is 59
mile per hour. What is the speed of the car? What error might Anna have made?
The speed of the car is 59 miles per hour. Anna might have made an error by using change in y-coordinates/change in x-coordinates to find a unit rate, instead of change in x-coordinates/change in y-coordinates.
What is defined as speed?Speed is a measure of how quickly something is moving, or how quickly something can be done. It is usually measured in terms of distance traveled per unit of time, such as miles per hour or kilometers per hour. The unit of speed is Miles per hour (mph).Speed can also be measured in terms of the rate of change of a certain quantity. For example, speed can be used to measure acceleration, which is the rate of change in velocity. Speed can also be used to describe the rate of flow of a certain quantity, such as the rate of water flow in a river. Speed is also used to measure the rate at which a certain process is taking place, such as the rate at which a person is typing words. In many cases, speed is used to describe how quickly something is happening relative to something else, such as the speed of light relative to the speed of sound. Speed is an important concept in many fields, including physics, engineering, and sports.To learn more about speed refer to:
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