Answer 5 :-
To find:-
Distance of swimmer from lifeguard.Answer:-
We are here given that the line of sight is 8ft above the ground and the angle of depression is 18° . So ,
\(\implies \angle DCA =\angle BAC = 18^o \\\)
as these are alternate interior angles.
Now in ∆ABC ,
\(\implies \tan \theta =\dfrac{p}{b}=\dfrac{BC}{AB} \\\)
\(\implies \tan 18^o =\dfrac{8\ ft}{AB} \\\)
\(\implies 0.325 = \dfrac{8\ ft }{AB}\\\)
\(\implies AB =\dfrac{8}{0.325}\ ft\\\)
\(\implies \underline{\underline{ AB = 24.61\ ft }}\\\)
Hence the horizontal distance of the swimmer from the lifeguard is 24.61 ft.
Also , there is a second distance of the swimmer from the lifeguard that is along AC ,
\(\implies \sin\theta =\dfrac{BC}{AC} \\\)
\(\implies \sin 18^o =\dfrac{8\ ft }{AC} \\\)
\(\implies AC = \dfrac{8\ ft}{\sin 18^o}=\dfrac{8}{0.309}\\\)
\(\implies \underline{\underline{ AC = 25.89 \ ft }} \\\)
Hence the distance of the swimmer from the lifeguard along AC is 25.89ft .
\(\rule{200}2\)
Answer 6 :-
To find:-
The altitude of the helicopter.Answer :-
We are here given that the angle of depression is 73° . Therefore here ,
\(\implies \angle SRP = \angle RPQ = 73^o \\\)
as they are alternate interior angles.
Now in ∆PQR , we have;
\(\implies \tan\theta = \dfrac{p}{b}=\dfrac{QR}{PQ} \\\)
\(\implies tan 73^o =\dfrac{RQ}{1200 \ ft} \\\)
\(\implies RQ = 1200\tan 73^o \ ft\\\)
\(\implies RQ = 1200 \times 3.27 \ ft \\\)
\(\implies \underline{\underline{RQ = 3924 \ ft }} \\\)
Hence the altitude of the helicopter is 3924 ft .
and we are done!
A water pipe is 3 feet below the ground. A gas pipe is 8 feet below the ground. Which pipe is
higher? EXPLAIN YOUR ANSWER
Which equation shows the relationship in the table?
Answer:
the answer world be b) y=x+15
Step-by-step explanation:
no need it's right
Is this relation a function? Justify your answer
.
11
10
9
8
7
6
5
4
3
2
.
8 9 10 11
A. Yes, because every and y-value is positive.
B. Yes, because the number of x-values is the same as the number of
p-values.
C. No, because two points with the same p-value have different -
values.
D. Yes, because every x-value has a single juvalue.
The relation given is a function because; Choice D: Yes, because every x-value has a single y-value.
Discussion:
Mathematically, a function from a set X to a set Y is an assignment of an element of Y to each element of X.
Conventionally, the set X is called the domain of the function and the set Y is called the codomain of the function.
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The amount of CO2 emitted per year A (in tons) for a vehicle that averages x miles per gallon of gas, can
be approximated by the function A(x) = 0.0089x2 – 0.815x + 22.3.
a) Determine the average rate of change of the amount of CO2 emitted in a year over the interval
[20, 25), and interpret its meaning.
Answer:
Average Rate of Change = -0.4145
It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile
Step-by-step explanation:
In order to solve this problem, we can make use of the Average Rate of Change formula, which looks like this:
\(ARC=\frac{A(25)-A(20)}{25-20}\)
So we need to start by finding what A(25) is equal to, so we get:
\(A(25)= 0.0089(25)^{2}-0.0815(25)+22.3\)
so
A(25)=7.4875
next, we can find A(20)
\(A(20)=0.0089(20)^{2}-0.0815(20)+22.3\)
so we get:
A(20)=9.56
so now we can use the average rate of change formula:
\(ARC=\frac{A(25)-A(20)}{25-20}\)
\(ARC=\frac{7.4875-9.56}{25-20}\)
ARC=-0.4145
and It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile
Morganton Company makes one product and it provided the following information to help prepare the master budget:
The budgeted selling price per unit is $60. Budgeted unit sales for June, July, August, and September are 8,600, 17,000, 19,000, and 20,000 units, respectively. All sales are on credit.
Thirty percent of credit sales are collected in the month of the sale and 70% in the following month.
The ending finished goods inventory equals 25% of the following month’s unit sales.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Each unit of finished goods requires 5 pounds of raw materials. The raw materials cost $2.40 per pound.
Thirty five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
The direct labor wage rate is $14 per hour. Each unit of finished goods requires two direct labor-hours.
The variable selling and administrative expense per unit sold is $1.80. The fixed selling and administrative expense per month is $67,000.
5. If 96,250 pounds of raw materials are needed to meet production in August, how many pounds of raw materials should be purchased in July?
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.
Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.
To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.
The payment for raw materials purchases in July (35% of X pounds) will be:
0.35 * X pounds
The payment for raw materials purchases in August (65% of X pounds) will be:
0.65 * X pounds
Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
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Let x=2. Evaluate the expression. x+4/3x enter your answer in the box
\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)
Solve x+4/3x , if x = 2.\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)
To solve this equation, at first, let's just substitute x with 2.
So, the equation becomes ⇨ 2+4/3×2
\( \tt \: \frac{x + 4}{3x} \\ \\ \tt \:\dashrightarrow \frac{(2) + 4}{3(2)} \\ \\ \tt \: Add \: 2 \: and \: 4 \: to \: get \: 6. \\ \\ \tt \: = \frac{6}{3\times 2} \\ \\ \tt \:Multiply \: 3 \: and \: 2 \: to \: get \: 6. \\ \\ \tt \:= \frac{6}{6} \\ \\\tt \: Divide \: 6 \: by \: 6 \: to \: get \: 1. \\ \\ = \boxed{ \boxed{ \bf \: 1}}\)
14
What is the interquartile range of the data shown in the box plot?
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
10
16
12
The interquartile range of the data shown in the box plot is 10.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
Arrange the given data in order.
17 18 19 20 21 22 23 24 25 26, 27 28 29 30 31 32 33 34 35 36
The interquartile range is the difference between the upper half and the lower half.
The upper half = 31.5
The lower half = 21.5
The interquartile range.
= 31.5 - 21.5
= 10
Thus,
The interquartile range is 10.
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Express your answer as a polynomial in standard form.f(3) = -2x + 5g() = +33 + 10Find: (gof)(x)
The given functions are,
\(\begin{gathered} f(x)=-2x+5^{} \\ g(x)=x^2+x+10 \end{gathered}\)The gof can be determined as,
\(\begin{gathered} \text{gof(x)}=g(f(x))| \\ =g(-2x+5) \\ =(-2x+5)^2+(-2x+5)+10 \\ =4x^2+25-20x-2x+5+10 \\ =4x^2-22x+40 \end{gathered}\)Thus, the requried value of gof is given by the above expression.
At the time of her grandson's birth, a grandmother deposits $ 11000 in an account that pays 2.5 % compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? The value of the account will be $= (Round to the nearest dollar as needed.)
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (initial amount)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
In this case:
P = $11,000
r = 2.5% = 0.025 (since it's compounded monthly, we need to divide by 12 to get the monthly rate)
n = 12 (compounded monthly)
t = 21 years
Plugging in these values, we get:
A = 11000(1 + 0.025/12)^(12*21)
A ≈ $16,180.64
Therefore, the value of the account at the child's twenty-first birthday will be approximately $16,181.
The triangle and the rectangle have the same area.
All lengths are in cm.
7x + 2
a Form an equation in x.
b Solve your equation to find x.
c Work out the area of the shapes.
1
2x + 7
The length of one side of the equilateral triangle in terms of x is 6x.
To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.
The perimeter of a rectangle is given by the formula:
Perimeter of rectangle = 2(length + width)
In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:
Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x
We are told that the equilateral triangle has the same perimeter as the rectangle.
Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.
Therefore, we have:
Perimeter of equilateral triangle = 3(side length)
Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:
3(side length) = 18x
Dividing both sides of the equation by 3, we get:
side length = 6x
Hence, the length of one side of the equilateral triangle in terms of x is 6x.
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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?
Consider all four-digit numbers that can be made from the digits 0-9 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is greater than 3000? Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability of choosing a random number from all four digit numbers that is greater than 3000 is 2333/7000 or 0.7777.
We know that:-
Total number of four digit numbers = 9*10*10*10 = 9000 (We have taken 9 because the number cannot start with 0)
Number of four digit numbers greater than 3000 = 7*10*10*10 - 1 = 7000 - 1 = 6999.
We have taken 7 because 0,1 and 2 cannot start the number.
We have subtracted 1 because 7000 would have also included 3000 and we need the number greater than 3000.
Hence, the probability of choosing a random number from all four digit numbers that is greater than 3000 = 6999/9000 = 2333/3000 ≈ 0.7777.
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What is the range of the relation below?
Answer:
D is correct
Step-by-step explanation:
2.31 (1 repeating) as a fraction
Answer:
\(\frac{231}{100}\)
This is assuming that you can simplify the 2.31 to the nearest hundredth.
what is the surface area for this figure
The surface area of the triangular prism is 313.47 cm².
Given is a triangular prism, we need to find the surface area,
A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.
Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.
so, the surface area of a triangular prism =
perimeter × length + 2 × base area
So,
SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9
= 167.67 + 145.8
= 313.47
Hence the surface area of the triangular prism is 313.47 cm².
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pls help asap!!!!!!!!
Answer:
It is possible, because the two shortest sides have to add up to be more than the longest side, and 8 + 12 = 20, which is more than the longest side of 17.
So yes, I agree with Bear.
A box contains 40 tiles, and all identical
shape and size, numbered 1 through 40. If a
person picks out a single tile from the box
without looking, what is the probability the
number on the tile will be a prime number?
Answer:
32.5%
Step-by-step explanation:
Hey there!
To find the probability we first need to find the amount of prime numbers in the 1-40 set.
Prime - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
That’s 13 prime numbers.
Fraction - 13/40
Simplified is just 13/40.
13 / 40 = .325
Percent - 32.5%
Hope this helps :)
A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
A study was conducted on the educational level of patients with AIDS, it was asume that
with ten years of education will be in group A, between 10 and 20 group B and between 20
group C. After the analysis it was realized that group A had 100 persons while group B and C had 30 persons
(a) If you decide to select based on proportion of 10% from each group how many patien
selected from each group. Show your calculation.
(b) What name can be given to the classified groups?
(c) What method of sampling was employed in the selection process?
1. State and explain the three major data collection techniques.
What is a variable?
What is a Parameter?
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.
(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.
(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.
The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.
The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.
A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
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bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
I will mark brainliest!
Answer:
1, 2
Step-by-step explanation:
that the solution to the graph,
Brainliest?
Answer:
(1, 2)
Step-by-step explanation:
The point where both line intersect is what is called the solution of the system of equations.
Therefore, in this case, the coordinate pair where both lines intersect is (1, 2).
Hope this helped! :D
This is another problem for my math class
Solve the inequality below
X + 14 > 27
Answer:
x = 14+
Step-by-step explanation:
If 14 + 14 = 28
Then
28 > 27 is true.
The table shows the unit prices for items Darryl
purchased to improve Downtown Deli.
Darryl places an order for 128 ounces of pickles, 24
loaves of bread, and 25 pounds of coffee. What is the
total cost of the order?
$
Answer:
94.85
Step-by-step explanation:
0.20x128=25.60
0.75x24=18.00
2.05x25=51.25
25.60+18.00+51.25= 94.85
Answer:
it is 94.85
explanation:
i took this applications of unit rate test trust me. :D
You purchase six municipal bonds on the first of the year. The current market value price is 103. The commission charge is $5 per bond. What is the cost of the purchasing these bonds?
a.
$6210
b.
$633
c.
$648
d.
$3090
Answer:
C
Step-by-step explanation:
(103 + 5) * 6 = 648
the answer for these questions
The triangles are similar by SSS congruence of triangles.
What is SSS congruence of triangles?
The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.
We are given two triangle ABC and PQR.
In order to see whether these are similar or not, we will use the SSS congruence of triangles.
The ratio of sides are:
⇒AB : PQ = 8 : 6
⇒AB : PQ = 4 : 3
Similarly,
⇒BC : QR = 12 : 9
⇒BC : QR = 4 : 3
Similarly,
⇒AC : PR = 12 : 9
⇒AC : PR = 4 : 3
Since, the ratio of all the sides is same so, the triangles are similar.
Hence, the triangles are similar by SSS congruence of triangles.
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Since, there are multiple questions so, the question answered above is attached below
17+b/26=30
Hdudhhwiw
Answer:
b=338
Step-by-step explanation:
17 + b/26 = 30
use inverse operations to solve:
17 + b/26 = 30
-17 -17
b/26 = 13
*26 *26
b = 338
i dont know how to do this
6x-2=4x+2
Answer:
x=2
Step-by-step explanation:
6x-2=4x+2
Move all terms with x to the left side by subtracting 4x from both sides:
2x-2=2
Move all terms without x to the right side by adding 2 to both sides:
2x=4
Divide both sides by 2 to get x by itself:
x=2
D(7,3) is the midpoint, (MP), of AB.
E(10, 4) is the MP of BC.
F(5,5) is the MP of AC
Find the coordinates of A, B, and C
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
Midpoint :
The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
x= x1+x2/2
y=y1+y2/2
Now ,
D(7,3) is the midpoint of AB.
D (x',y') = (7,3)
vertex of A = (x1,y1)
vertex of B = (x2,y2)
x' = x1+x2/2
7 = x1+x2/2
14 = x1+x2 ...1
y' = y1+y2/2
3= y1+y2/2
6= y1+y2 .....2
E (x'',y'') = (10,4)
vertex of c = (x3,y3)
vertex of B = (x2,y2)
x''= x3+x2/2
y''=y3+y2/2
20= x3+x2 ....3
8 =y3+y2.......4
F (x''',y''') = (5,5)
vertex of c = (x3,y3)
vertex of A = (x1,y1)
10= x1 +x3 ...5
10 =y1+y3 .....6
For 1 & 3 & 5
14 = x1+x2 ...1
20= x3+x2 ....3
10= x1 +x3 ...5
Add all 1 & 3 & 5
44 = 2(x1+x2+x3)
22 = (x1+x2+x3) .....7
For 1 & 7
x3 = 8
For 3 & 7
x1 = 2
For 5&7
x2 = 12
For 2 , 4 & 6
6= y1+y2 .....2
8 =y3+y2.......4
10 =y1+y3 .....6
Add all 2 & 4 & 6
24 = 2 (y1+y2+y3)
For 2 & 8
y3 = 6
For 4 & 8
y1 = 4
For 6 & 8
y2 = 2
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
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How do I solve this and what is the answer?
When the vertex of an angle ON the circumference of the circle, like the angle ∡BCD
its intercepted arc will have twice its measure. Since the angle measure is 29º, then its intercepted arc is
2 x 29º = 58º
All the angles that intercept the same arc must have the same measure for it to be always 58º.
Then, ∡BAC = 29º
Finding ∡BOCSince the angle ∡BOC vertex is on the center of the circle, it has the same measure of its intercepted arc:
Then, ∡BOC = 58º
ANSWERS: ∡BAC = 29º and ∡BOC = 58ºDUE TDYYYYY!!!!!!!??
The values that used to create the box and whisker plot
[using these values]
Minimum value: Lower whisker: 12
Q1: 23.5
Q2 (median): 36
Q3: 46
Maximum value: Upper whisker: 56
Here, we have,
Step 1: Order the data set from smallest to largest:
12, 19, 28, 32, 34, 38, 45, 47, 50, 56
Step 2: Calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3):
Q1 (25th percentile): The value that separates the lowest 25% of the data from the rest. Since we have 10 data points, the first quartile will be the average of the 2.5th and 3.5th data points. In our case, it's the average of the 2nd and 3rd data points:
Q1 = (19 + 28) / 2 = 23.5
Q2 (50th percentile or median): The value that separates the lowest 50% of the data from the rest. Since we have an even number of data points, the median will be the average of the 5th and 6th data points:
Q2 = (34 + 38) / 2 = 36
Q3 (75th percentile): The value that separates the lowest 75% of the data from the rest. Since we have 10 data points, the third quartile will be the average of the 7.5th and 8.5th data points. In our case, it's the average of the 7th and 8th data points:
Q3 = (45 + 47) / 2 = 46
Step 3: Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 46 - 23.5 = 22.5
Step 4: Determine the whiskers:
Lower whisker: The smallest value that is not smaller than Q1 - 1.5 * IQR
Upper whisker: The largest value that is not larger than Q3 + 1.5 * IQR
Lower whisker limit: 23.5 - 1.5 * 22.5 = -10
Upper whisker limit: 46 + 1.5 * 22.5 = 79.5
Our data points are all within these limits, so the lower whisker is at the smallest value, 12, and the upper whisker is at the largest value, 56.
Now, you can plot the box and whisker plot using these values:
Minimum value : Lower whisker: 12
Q1: 23.5
Q2 (median): 36
Q3: 46
Maximum value: Upper whisker: 56
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create a box and whisker plot for the following set of data
12, 19, 28, 32, 34, 38, 45, 47, 50, 56
I need help!! This is a area question
Answer:
A≈6503.88
Step-by-step explanation:
To find the area of a cirlce, you use the formula: A=(pi)r^2
You just plug in the radius (half of the diameter), punch it into the calculator and get your answer :)