The probability of a defect units is 0.3174 by calculating the z-score of the greater than and less than value.
When the distribution is normal, we use the z-score formula.
Z = (X - μ)/σ
We have σ = 0.15 and units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.
μ = 10.15 - 0.15 = 9.85 + 0.15 = 10
Now, the probability that a unit is defective.
P(X ≥ 10.15)
1 subtracted by the pvalue of Z when X = 10.15
[tex]Z = \frac{10.15-10}{0.15}[/tex]
Z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
P(X ≤ 9.85)
[tex]Z = \frac{9.85-10}{0.15}[/tex]
Z = -1 has a pvalue of 0.1587
P = P(X ≥ 10.15) + P(X ≤ 9.85)
P = 0.1587 + 0.1587
P = 0.3174
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A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were defective. A store clerk generates random numbers to simulate a random sample of this shipment. The clerk lets the numbers 1 through 300 represent defective MP3 players, and the numbers 301 through 5,000 represent working MP3 players. The results are given.
2,806 623 232 3,955 3,799 657 2,140 262 844 561
Based on this sample, how many of the MP3 players might the clerk predict would be defective?
The manager would expect _________ defective players in the shipment.
The manager would expect 1000 defective players in the shipment.
How to find the defective members in a sample?A store receives a shipment of 5,000 mp3 players out of which 300 were found to be defective.
The clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players.
The results are given AS:
2,806 623 232 3,955 3,799 657 2,140 262 844 561
This means that out of the 10 samples 2 were found to be defective and 8 were in the working condition.
( Since the number 232 and 262 represent the defective mp3 players as they are the numbers which are less than or equal to 300 )
Hence, the Probability that the mp3 players were defective is:
P( defective)=2/10=1/5
Hence, out of 5000 mp3 players the number of players that clerk predict to be defective are:
P( defective)×5000
= 1/5 × 5000
= 1000.
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In ΔFGH, f = 600 cm, m∠F=32° and m∠G=12°. Find the length of h, to the nearest 10th of a centimeter.
The measure of the side FG that is h using the sine law will be 786.63 centimeters.
What is the sine law?The sine law in the triangle ΔFGH is given as,
FG / sin H = GH / sin F = FH / sin G
In ΔFGH, f = 600 cm, m∠F = 32°, and m∠G = 12°.
We know that the aggregate of the gradient of the triangle is 180°. Then the angle H is given as,
∠F + ∠G + ∠H = 180°
32° + 12° + ∠H = 180°
∠H = 136°
The length of the triangle 'h' is given as,
FG / sin H = GH / sin F
h / sin 136° = f / sin 32°
h = 600 (sin 136° / sin 32°)
h = 600 x 1.31
h = 786.63 cm
The measure of the side FG that is h using the sine law will be 786.63 centimeters.
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How many flowers, spaced every 4 feet, are needed
to surround a circular garden with a 70-foot radius?
Use 3 for π.
The numbers of flowers spaced every 4 feet, are needed
to surround a circular garden with a 70-foot radius, 105
What is circumference ?Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.
The formula for the circumference of a circle is given by:
C = 2πr,
To calculate the circumference of the circular garden, we can use the formula:
C = 2πr
where C is the circumference, π is the mathematical constant pi (approximated as 3 in this case), and r is the radius. Plugging in the given values, we have:
C = 2 x 3 x 70
= 420 feet
Now, since the flowers are spaced every 4 feet, we can divide the circumference by 4 to find the number of flowers needed:
number of flowers = C / 4
= 420 / 4
= 105
Therefore, 105 flowers spaced every 4 feet are needed to surround a circular garden with a 70-foot radius.
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What is the standard form for seven squared
Therefore, after answering the given query, we can state that the as we can multiply it as 7 multiply by 7 = 7*7 = 49.
what is multiply?Multiplication is one of the four matrix multiplication, along with arithmetic, addition, and subtraction. Multiplication in mathematics is the process of repeatedly combining subgroups of the same size. Multiplication is calculated using the formula multiplicand multiplier gives product. multiplicand: Starting number, to be more exact (factor). as a separator, use number two (factor). The result is what remains after splitting both the multiplicand and the multiplier. There are numerous additions necessary when adding numbers. similar to 5 x 4 = 5 x 5 x 5 x 5 = 20. What I did was multiply 5 by 4. Because to this, multiplication is frequently referred to as "doubling."
The standard form for seven squared is 49.
as we can multiply it as 7 multiply by 7 = 7*7 = 49.
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What is the whole fraction of a pizza that shows 6 pieces?
The whole fraction of a pizza that shows 6 pieces is 6/1 or simply 6.
The whole fraction of a pizza that shows 6 pieces is 6/6 or 1.
In a fraction, the numerator represents the number of parts being considered, and the denominator represents the total number of parts. In this case, there are 6 pieces of pizza being considered out of a total of 6 pieces, which means the fraction is 6/6. This fraction can be simplified to 1, meaning the whole pizza is represented.
So, the whole fraction of a pizza that shows 6 pieces is 1.
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DIFFERENCE OF SQUARES (DOTS)
factor: X²-100
Answer: [tex](x+10)(x-10)[/tex]
Step-by-step explanation: Difference of squares is an important element in understanding square functions. In order to identify difference of squares, the equation should be given in the form a^2-b^2. You can factor it completely when b^2 can be square rooted perfectly and write the factored expression as (a-b)(a+b) as I have done above.
How many 65 euros to dollars ?
The values of 65 euros is 76.70 US dollars.
To convert 65 euros to dollars, you need to know the current exchange rate between the two currencies. As of September 2021, the exchange rate is 1 euro = 1.18 US dollars.
To calculate the conversion, you can simply multiply the amount of euros by the exchange rate.
65 euros x 1.18 US dollars = 76.70 US dollars
Therefore, 65 euros is equivalent to 76.70 US dollars.
It's important to note that exchange rates can fluctuate, so the conversion may not be the same in the future. It's always best to check the current exchange rate before making a conversion.
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\int x^(2)(1)/(\sqrt(x^(2)-4))dx
The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].
What is integration?Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.
The integration equation is given below.
[tex]\begin{aligned} \rm I = \int _1^2 \sqrt{x^2 - 4} \ dx \end{aligned}[/tex]
We know that the formula is given as,
∫√(x² - a²) dx = (x/2)√(x² - a²) + (a² / 2) log [x + √(x² - a²)]
Then by the integration, we can write it as,
[tex]\begin{aligned} \rm I &= \int _1^2 \sqrt{x^2 - 4} \ dx \\\rm I &= \int _1^2 \sqrt{x^2 - 2^2} \dx\\\rm I &= \left [ \dfrac{x}{2}\sqrt{x^2-2^2} + \dfrac{2^2}{2} \log (x + \sqrt{x^2 - 2^2}) \right ]^2_1\\\end{aligned}[/tex]
Simplify the equation further, then we have
I = [(1/2) i√3 + 2 log (1 + 3i)]
The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].
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If Laura uses both talk and text right in equation for the cost, C what we do know of sending text and talking M minutes
A. Equation:
B. how much will it cost Laura to send 4 text and talk for 13 minutes
C. if Laura wants to send 18 texts and only has eight dollars how many minutes can she talk? Will this use all her money? if not how much money will she have left?
D. Solve equation for T.
A. The equation is given as C = 0.1T + 0.05M
B. It will cost Laura $1.05 to send 4 texts and talk for 13 minutes.
C. Laura will have $1.80 left after sending 18 texts and talking for 124 minutes.
D. The equation for T is T = (C - 0.05M) / 0.1.
Step by step explanationA. The equation for the cost, C, of sending both texts and talking for M minutes is:
C = 0.1T + 0.05M
where T is the number of texts sent.
This equation assumes that each text costs 10 cents and each minute of talk time costs 5 cents.
B. To calculate the cost of sending 4 texts and talking for 13 minutes, we can use the equation from part A:
C = 0.1T + 0.05M
C = 0.1(4) + 0.05(13)
C = 0.4 + 0.65
C = 1.05
Therefore, it will cost Laura $1.05 to send 4 texts and talk for 13 minutes.
C. To determine how many minutes Laura can talk if she wants to send 18 texts and only has eight dollars, we need to use the equation from part A and solve for M:
C = 0.1T + 0.05M
8 = 0.1(18) + 0.05M
8 = 1.8 + 0.05M
6.2 = 0.05M
M = 124
Therefore, Laura can talk for 124 minutes if she wants to send 18 texts and has eight dollars.
This will cost her $6.20, which is less than the amount of money she has, so she will have some money left over.
subtract the cost of talking and texting from the amount of money she has:
Money left = 8 - 6.20
Money left = 1.80
Therefore, Laura will have $1.80 left after sending 18 texts and talking for 124 minutes.
D. To solve the equation from part A for T, we can rearrange the terms:
C = 0.1T + 0.05M
0.1T = C - 0.05M
T = (C - 0.05M) / 0.1
Therefore, the equation for T is T = (C - 0.05M) / 0.1.
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Janelle is picking her activities for this year. She wants to play one sport and join one club. The sports she can play are tennis, golf, and basketball. The clubs she is considering are the speech club and the science club. How many different combinations of activities can Janelle pick?
Answer:
Step-by-step explanation:
make a tree, first list out the sports then draw two branches for the clubs (speech and science) then circle each club to each sport, like how the picture shown . You will find there are 6 ways Janelle could pick out her extracurriculars
Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. What will Arun’s total bill be?
Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. The correct answer is $68.44.
What is a restaurant?
A restaurant is a business that prepares and serves food and drinks to customers. [1] Meals are generally served and eaten on the premises, but many restaurants also offer take-out and food delivery services.
18/100 = .18
58 x .18 = 10.44
⇒ 58 + 10.44 = 68.44
Hence, Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. The correct answer is $68.44.
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Luna drove a tractor across her cornfield. The field was 480 meters across, and she drove at a constant velocity of 20 meters per minute across the field. How long did it take for Luna to drive one-quarter of the distance across the field? Write your answer as a whole number.
Answer:
Step-by-step explanation:
480 meters is the whole field.
One quarter of it is equal to 480 ÷ 4 = 120.
She is traveling 20 meters per minute.
120 ÷ 20 = 6
It takes her six minutes.
which expression cannot be factored using real numbers?
x^3+1
x^6+8
x^8-2
x^8-1
The quadratic-like polynomial x⁶ + 8 has no real roots, that is, it has two complex roots. (Correct choice: B)
What polynomial cannot be factored using real numbers?
In this problem we must determine what polynomial has no real roots. From real algebra we remember that any polynomial of the form x²ⁿ + a², where a is a positive real number, has no real numbers. That is, the factor form of the polynomial is shown below:
(xⁿ + i a) · (xⁿ - i a)
In other words, any polynomial of the form x²ⁿ + a², a > 0, has two complex roots. Now, by direct comparison, we conclude that polynomial x⁶ + 8 has no real roots.
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How do I solve for the answers
Answer:
4
Step-by-step explanation:
For a large sporting event the broadcasters sold 61 ad slots for a total revenue or $157 million. What was the mean price per as slot?
The mean price per ad slot was $______ million.
Round to one decimal place as needed
The mean price per ad slot was 26.167 million. The broadcasters made $157 million in revenue from the sale of 61 ad spaces for a significant sporting event.
TR=Price *Quantity
$157=P* 61
P=157/61=26.167
By dividing the sum of all values by the total number of values, one can determine the mean of a dataset (sometimes referred to as the arithmetic mean, which is distinct from the geometric mean). It is the most popular way to quantify central tendency and is commonly referred to as the "average". Simply dividing the total number of values in a data collection by the total number of values in the data set yields the answer. The calculation can be done with either raw data or a frequency table of the data. When someone or something is accused of having a very short fuse and being harsh, they are said to be mean.
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23. ERROR ANALYSIS Describe and correct the error in finding 40% of 75.
X
40% of 75 = 40% x 75 = 3000
The error in the solution is that the answer is written as 3000 instead of 30.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100 and it is denoted by the symbol '%'.
Percentage of a number is calculated as dividing the number with it's whole and then multiplying with 100.
We have to find the percentage of 40% of 75.
That is, the number which corresponds to the 40 parts per 100 of the number 75.
40% of 75 = 40% × 75
= (40 / 100) × 75
= 0.4 × 75
= 30
The correct percentage is 30, not 3000.
Hence the error is in the answer for which 30 is the correct answer.
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which graph suows the solution set of the inequality x^2+10x+16 / x-3 >0
The graph the depicts the solution set of the inequality is graph D. Option 4 is the correct answer.
What is solution of an inequality?There is a significant exception to the general rule that inequality manipulation is quite similar to equation manipulation.
An inequity still exists if the same amount is added to both sides.
The inequality still holds true if the same amount is subtracted from each side.
An inequality still holds true if both sides are multiplied or divided by the same positive value.
However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid.
The given inequality is x² + 10x + 16 / x-3 > 0.
Expand the quadratic equation:
x² + 8x + 2x + 16/ x-3 > 0
x(x + 8) + 2(x + 8) / x-3 > 0
(x + 2)(x + 8)/ x-3 > 0
x + 2 > 0 and (x + 8) < 0 and x - 3 > 0
x > -2 and x < -8 and x > 3
The intervals of x are:
-8 < x < -2 and x > 3
Hence, the graph the depicts the given interval is graph D. Option 4 is the correct answer.
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Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
2.25 inches
4.5 inches
6.75 inches
12.75 inches
The height of the cylindrical tub of ice cream is 6.75 inches.
What is the surface area of a cylinder?A cylinder is a 3 dimensional shape which has a curved side and two circular surfaces. The total surface area can be determined by the expression;
total surface area of a cylinder = 2πr^2 + 2πrh
where r is the radius of it circular surface, and h is its height.
Considering the given question, we have;
total surface area of a cylinder = 2πr^2 + 2πrh
But total surface area = 183.69 square inches
r = D/2
= 6/ 2
r = 3 inches
Thus,
183.69 = 2*3.14*3^2 + 2*3.14*3*h
= 56.52 + 18.84h
183.69 - 56.52 = 18.84h
127.17 = 18.84h
h = 127.17/ 18.84
= 6.75
The height of the cylindrical tub of ice cream is 6.75 inches.
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Answer: The answer is (C) 6.75
Step-by-step explanation:
The formula for Surface Area is: SA = 2πr^2 + 2πrh
Let's do the first part: 2πr^2
So you need to find the radius, which is half the diameter. 6 is the diameter so half that, and you get 3.
Now, times 3 by itself
3 * 3 = 9
And then times 9 by 2
9 * 2 = 18
And times 18 by pi, 3.14
18 * 3.14 = 56.52
Now that we have our first value, lets move on to the second part of the formula: 2πrh
So we need the diameter, and the question gives us the value of the diameter.
6 is the diameter
so times 6 by pi, 3.14
6 * 3.14 = 18.84h (leave h there because we don't know the height)
Now do this:
183.69 = 56.52 + 18.84h
You cannot add 56.52 and 18.84h because they are not like terms
So take away 56.52 from both sides
56.52 - 56.52 = 0
183.69 - 56.52 = 127.17
Now divide 127.17 by 18.84h
127.17/18.84 = 6.75 inches
Here is proof that my answer is correct. I have a photo of my results and it shows that 6.75 inches is correct. Here is the photo:
Have a an amazing day
15. Find DE.
C
24 61°
A
F
19°
D
E
The value of side DE of the triangle is 14.91 units
How to find the DE of the triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
In triangle CDF,
tan 61° = DF/24
DF = 24 * tan 61°
DF = 43.30 units
In triangle DEF,
tan 19° = DE/43.30
DE = 43.30 * tan 19°
DE = 14.91 units
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5x4> 12
AND 12x +5 ≤-4
The solution for x is x ≤ -3/4.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
To solve for x in the inequalities:
5x - 4 ≥ 12 and 12x + 5 ≤ -4
We'll solve each inequality separately:
5x - 4 ≥ 12
Adding 4 to both sides, we get:
5x ≥ 16
x ≥ 16/5
So the first inequality is solved for x as x ≥ 16/5.
Now, 12x + 5 ≤ -4
Subtracting 5 from both sides, we get:
12x ≤ -9
x≤ -9/12
x≤ -3/4
The only values of x that satisfy both inequalities are those that are less than or equal to -3/4.
Therefore, the solution for x is x ≤ -3/4.
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Can anyone write the quadratic of the equation in factored form?
The factored form of the quadratic equation is given as follows:
y = 3(x + 0.6667)(x - 6).
How to obtain the factored form of the quadratic equation?The quadratic equation for this problem is defined as follows:
3x² - 16x - 7 = 5.
3x² - 16x - 12 = 0.
The coefficients are given as follows:
a = 3, b = -16, c = -12.
Hence the discriminant is of:
D = (-16)² - 4(3)(-12)
D = 400.
Then the roots are of:
x = (16 - sqrt(400))/6 = -0.6667.x = (16 + sqrt(400))/6 = 6.Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:
y = 3(x + 0.6667)(x - 6).
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what percent of the dresses are for films not set in the 1700s?
Answer:
Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era
Pls help will mark Brainly est pls help
Step-by-step explanation:
We can find the other point using the axis of symmetry.
The axis of symmetry for a parabola passes through the x coordinate of the vertex.
So our axis of symmetry is x=4, which is a vertical line.
For any point on a parabola curve except the vertex, there will two points that share the same y value. The two x coordinates of those points midpoints should be the axis of symmetry.
So,
If we know (0,-6) and the vertex is 4, let's find the other point
[tex]( \frac{0 + b}{2} = 4[/tex]
[tex]b = 8[/tex]
So our other point is
(8,-6).
So the answer to #1 is we found point (8,-6) by using the axis of symmetry. By reflecting the point (0,-6) about the vertical line x=4, we end up getting the point (8,-6)
To find q, q(x) has the same vertex, so it is (4,10).
We know the axis of symmetry is x=4, we also know the y intercept is 18 so we have point (0,18)
Using the axis of symmetry we will get (8,18).
So the graphs above are the graphs of p and q
The graph facing upwards is q
The graph facing downwards is p.
For #2, you can say we know the vertex is (4,10) and using the y intercept and axis of symmetry we found the other point on the curve.
I don't fully see the table but if the other coordinates have a higher y value, the vertex is a minimum.
Else, of the other coordinates have a lower y value, the vertex is a maximum.
-3x + 3 < 6
Please help I don’t know what it is
Answer:
x > - 1
How to find your answer:
-3x + 3 < 6 (Move the constant to the right)
-3x < 6 - 3 (now calculate)
-3x < 3 (divide both sides)
x > -1
I hope this helped.
Marvin lives in stormwind city and works as an engineer in the city of ironforge. In the morning, he has 3 33 transportation options (teleport, ride a dragon, or walk) to work, and in the evening he has the same 3 33 choices for his trip home. If marvin randomly chooses his method of travel in the morning and in the evening, what is the probability that he teleports at least once per day?.
The probability that he teleports at least once per day is [tex]\frac{5}{9}[/tex].
the Marvin must select one of the three transportation alternatives at random.
The likelihood of selecting any one of the three alternatives is the same since the selection is random.
The likelihood of successful teleportation on the first try is:
[tex]P_t=\frac{1}{3}[/tex]
Consequently, the likelihood that you do not teleport is
q=1-p
q=1-[tex]\frac{1}{3}[/tex]
q=[tex]\frac{2}{3}[/tex]
The likelihood that the Marvin won't teleport when leaving for work and returning from work is as follows:
P=[tex]\frac{2}{3}[/tex]×[tex]\frac{2}{3}[/tex]
P=[tex]\frac{4}{9}[/tex]
As a result, the probability that someone will teleport at least once is:
P=1-[tex]\frac{4}{9}[/tex]
P=[tex]\frac{5}{9}[/tex]
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What is the Soil Texture Triangle ?
Based on the ratios of sand, silt, and clay particles contained in a soil sample, soil scientists and farmers use the soil texture triangle to categorize and define the texture of soil. It is a graphic representation of the system for classifying soil textures.
Agricultural experts and soil scientists utilize the Soil Texture Triangle, a graphic representation, to categorize soil according to its texture. The triangle's three portions stand in for the three major categories of soil particles: sand, silt, and clay.
Based on the proportion of each type of particle present in a soil sample, the Soil Texture Triangle can be used to determine the texture of the soil. A soil scientist can rapidly categorize a soil as sandy, loamy, or clayey by plotting the percentage of sand, silt, and clay on the triangle.
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The graph shows the number of game systems sold
since 2015. Based on this information, which function
best models the number of game systems sold in
millions x years since 2015?
Step-by-step explanation:
so, for x = 0, y = 30.5
that means the first answer is out.
for x = 1, y = 21.35
so, only
y = 30.5(0.7)^x
can be right.
all other functions have an y-value of way over 30.5 (because the factor of 30.5 is larger than 1).
and to verify :
30.5 × 0.7¹ = 30.5 × 0.7 = 21.35
correct.
How many minutes are in 3 5/12 hours
Answer:
205
Step-by-step explanation:
3hrs is 180 min
5/12 hours is just 25 min
180+25=205
Answer:
205 minutes
Step-by-step explanation:
*60 minutes = 1 hour
3 x 60 = 180
5/12 x 60 = 5/12 x 60/1 = 300/12 = 25
180 + 25 = 205 minutes
A square lawn has an area of 1922 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?
A.43.84 B.21.92 C.62 D.31
The radius of the circle is 21.92 feet
What is the radius of the circle?From the question, we have the following parameters that can be used in our computation:
A square lawn has an area of 1922 square feet
This means that
Area = 1922
Take the square root of both sides to determine the side length
side length = 43.84
This represents the circle diameter
So, we divide by 2
radius = 21.92
Hence, the radius is 21.92
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What is the equation of this graph