After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 4 t-shirts, the video, and 1 stuffed animal, their total is $135.
Answers
The cost of each t-shirt is $15,the cost of each stuffed animal is $25, the cost of the video is $20.
How to calculate cost of each item?The difference between the purchases by the first and third groups is 4 t-shirts (they both buy the video and one stuffed animal; one group buys 6 t-shirts while the other buys only 2). The difference in the total cost between those two purchases is $60; that means each t-shirt costs $60/4 = $15.
Knowing the cost of each t-shirt, we can determine the costs of the other items purchased by the three groups:
1st group: 1 video and 1 stuffed animal for ($135-$90) = $45
2nd group: 1 video and 5 stuffed animals for ($175-$30) = $145
3rd group: 1 video and 1 stuffed animal for ($75-$30) = $45 (same as the 1st group; so we won't need this)
Comparing these parts of the purchases by the first and second groups shows that the extra 4 stuffed animals cost an extra $100; that means the cost of each stuffed animal is $100/4 = $25.
Now, knowing the cost of each t-shirt and each stuffed animal, we can determine the cost of the video using any one of the group's purchases. For example, the third group bought 2 t-shirts for $30 and 1 stuffed animal for $25, for a total of $55; the cost of the video is then $75-$55 = $20.
t-shirt $15; video $20; stuffed animal $25
Now let's do the formal algebra....
(1) 6t + v + a = 135
(2) 2t + v +5a = 175
(3) 2t + v + a = 75
The coefficients of both v and a are the same in equations (1) and (3), so subtracting one equation from the other lets us solve for a:
4t=60
a=15
The cost of each t-shirt is $15.
Substitute t-15 in each of the original equations:
(5) 90 + v + a = 135 --> v + a = 45
(6) 30 + v +5a = 175 --> v +5a = 145
(7) 30 + v + a = 75 --> v + a = 45 (same as (5), so we won't need this)
The coefficient of v is the same in both (5) and (6), so subtracting one equation from the other eliminates v, allowing us to find a:
4t=100
a=25
The cost of each stuffed animal is $25.
Substituting that value for a in (7) then gives us the value of v:
v+25=45
v=20
The cost of the video is $20.
The complete question is: After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135.
A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175. Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75. What is the cost of each item?
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Related Questions
how do I write two trillion ninety nine in number form?
Answers
Answer:
here
Step-by-step explanation:
2.000.000.099
istg if this doesnt show.
Answers
Sorry but I don't see anything but your words...
What am I supposed to be answering?
Answer:
Nv5 my dude
Step-by-step explanation:
The sum of two numbers is 65. The smaller number is 15 less than the larger number. What are the numbers?
Answers
Answer:
the numbers are 25 and 40
Roger earns 3% commission on sales of $9,500 as an electrical supplies wholesaler. What is his commission?
Answers
Answer:
$285
Step-by-step explanation:
So let's quickly analyze the problem, it is asking us how much Roger makes as a commission on sales if he earns 3% on sales for $9,500.
We can make the 3% into a decimal, by dividing it by a 100.
3/100=0.03
Now that we have a decimal to work with, we can multiply this to the amount of sales,
9500 x 0.03= $285 ( He earns $285 as commission for $9500)
Answer:
285 is his commission
Step-by-step explanation:
i have sent my explanation in the above picture
Suppose MarketOne is a marketing company that has small businesses for clients. MarketOne charges an upfront cost of $350 for new clients and an additional $195 per month to run and maintain the client's website. A linear equation could be used to relate the total cost, in dollars, of MarketOne's services and the number of months that the client's website is running. Which solution is viable for this situation? For full points, write the equation and show your work.
Answers
C = 195m + 350
where the constant term of 350 represents the upfront cost and the coefficient of 195 represents the monthly cost.
To check if this equation is viable for the situation, we can use some reasonable values for the number of months and see if the resulting costs make sense.
For example, if the client's website is running for 6 months, the total cost would be:
C = 195(6) + 350
C = 1,170 + 350
C = 1,520
This means that the client would pay $1,520 in total for 6 months of service from MarketOne.
Similarly, if the client's website is running for 12 months, the total cost would be:
C = 195(12) + 350
C = 2,340 + 350
C = 2,690
This means that the client would pay $2,690 in total for 12 months of service from MarketOne.
Based on these calculations, we can see that the linear equation is viable for the situation. The equation allows us to calculate the total cost of MarketOne's services based on the number of months the client's website is running, which is a useful tool for budgeting and planning.
Cindy, Inc. sells a product for $10 per unit. The variable expenses are $6 per unit, and the fixed expenses total $35,000 per period. By how much will net operating income change if sales are expected to increase by $40,000?
A) $16,000 increase
B) $5,000 increase
C) $24,000 increase
D) $11,000 decrease
Answers
Answer: it is a $16,000 increase
What is the value of x if 10 - 20x = 5?
Answers
Answer:♀️
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The statements which are true are that the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is a circle?
A circle is formed by all points in a plane that are at a particular distance from the center. To put it another way, it is the curve that a moving point in a plane draws to maintain a constant distance from another point.
We are given a circle whose equation is \(x^{2}\) + \(y^{2}\) - 2x - 8 = 0.
We know that the general form of a circle is \(x^{2}\) + \(y^{2}\) + 2gx + 2fy + C = 0, where (-g, -f) is the center and √\(g^{2}\) + \(f^{2}\) - C is the radius.
So, in the equation, g is -1 and f is 0.
So, the center is (1, 0) which represents that the center lies on the x - axis.
Now,
⇒ Radius = √\(g^{2}\) + \(f^{2}\) - C
⇒ Radius = √1 + 0 - (-8)
⇒ Radius = √1 + 8
⇒ Radius = √9
⇒ Radius = 3 units
So, the radius of the circle is 3 units.
Now, radius of circle x² + y² = 9 is
\(r^{2}\) = 9
r = 3
So, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Hence, the required solution has been obtained.
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The complete question has been attached below.
Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (0, b) at (0, 6) and blue line s intercepts (c, 0) at (2, 0) and (0, a) at (0, minus 4) Statements Reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality Which step of the proof contains an error? A. Step 5 B. Step 6 C. Step 2 D. Step 4
Answers
Answer:
transitive property
Step-by-step explanation:
What expression is not equivalent to 8 + (n - 4)?
A. (8 + n) - 4
B. n + 4
C. 12 + n
D. (8 - 4) + n
Answers
Which of the following could be the equation of a line parallel to the line y =4
Answers
Answer:
Since slope of line y = 0 and y = 4
Step-by-step explanation:
Given:
y = 4
Computation:
Equation of slope;
y = ax + c
So,
y = (a)(0) + 4
Since slope of line y = 0 and y = 4
Answer:
y=0
Step-by-step explanation:
i^{11} + i^{16} + i^{21} + i^{26} + i^{31}
Answers
Answer:
Below
Step-by-step explanation:
For this , I will assume i = \(\sqrt{-1}\)
i^{11} + i^{16} + i^{21} + i^{26} + i^{31} =
- i +1 +i -1 - i = - i
anyone can help with these?
Answers
Answer:
m∠B=63 degrees
AC≈23.6 units
AB≈26.4 units
Step-by-step explanation:
since the measures of ∠A and ∠C are given, we add 90 (∠C) to 27 (∠A) and x (∠B) which equals 180 by triangle angle sum theorem.
after isolating the variable, m∠B=63 degrees
we then use law of sin to find AC and AB
since \(\frac{sin(A)}{a}\) is already given, use that to find both AC and AB
the equation for AC would be: \(\frac{sin(27)}{12} =\frac{sin(63)}{AC}\)
the equation for AB would be: \(\frac{win(27)}{12} =\frac{sin(90)}{AB}\)
after isolating the variables, AC≈23.6 units and AB≈26.4 units
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)= −4.9t^2+11t+7. How many seconds does it take to reach maximum height? Enter the answer with at least 3 decimal places.
Answers
Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.
To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)
The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).
Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:
a = -4.9
b = 11
Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:
t = -11 / (2 * -4.9)
t = -11 / -9.8
t ≈ 1.122
Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.
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If Dede uses 10 cups of yellow paint, how much blue paint should she use to make this
same shade of green?
Answers
Answer:
10 cups
Step-by-step explanation:
Answer:
10 cups
Step-by-step explanation:
10 × 2 = 20
20÷2= 10
A man pulled a cart filled with stones that had a total mass of 60 kg.
He increased the amount of force used to pull the cart from 60 N to 90 N, what is the new
acceleration of the cart?
Answers
a1 = f/m
a1 = 60/60 = 1ms^-2
a2 = f2/m
a2 = 90/60
a2 = 1.5ms^-2
The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²
What is Force ?The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.
Formula of force,
F = ma
Given that,
A man pulled a cart filled with stones that had a total mass of 60 kg
He increased the amount of force used to pull the cart from 60 N to 90 N
New acceleration of cart = ?
F = ma
Old acceleration,
60 = 60a
a = 1 m/s²
New acceleration,
90 = 60a
a = 90/60
a = 3/2
a = 1.5 m/s²
Hence, the new acceleration is 1.5 m/s²
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Any help finding the 0th term of this geometric sequence?
Answers
Answer:
25,50,100 is the geometric sequence ?
A company charges it’s customer’s a monthly fee of c dollars for using x therms of natural gas using the formula c=15+0.88867x
Answers
The customer would be charged a monthly fee of $103.87 for using 100 therms of natural gas.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponents, roots, and logarithms) that are combined in a meaningful way. Expressions can be simple or complex, and they can involve one or more variables.
According to given conditions :
The formula to calculate the monthly fee charged by a company for using x therms of natural gas is:
c = 15 + 0.88867x
Here, c represents the monthly fee in dollars, and x represents the amount of natural gas used in therms.
The fixed monthly fee charged by the company is $15, and the variable fee is $0.88867 per therm of natural gas used. To calculate the monthly fee for a given value of x, we simply plug in the value of x into the formula and evaluate:
For example, if a customer uses 100 therms of natural gas in a month, the monthly fee would be:
c = 15 + 0.88867(100)
c = 15 + 88.867
c = 103.867
It's important to note that the formula assumes a linear relationship between the amount of natural gas used and the monthly fee charged by the company. In reality, the relationship may be more complex, and there may be other factors that affect the monthly fee.
Therefore, the customer would be charged a monthly fee of $103.87 for using 100 therms of natural gas.
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When you calculate (log)5, you would be finding the value of which of the following expressions?
Answers
Answer:
c
Step-by-step explanation:
log base 10 (5) is the expression
The value of the given expression can be written as log₁₀(5). which is the correct answer would be an option (C).
What is the logarithm of a number?The logarithm of a number is often used in mathematics and science to simplify calculations and to solve equations involving exponential growth or decay.
In particular, the logarithm of a number is the exponent to which another fixed number, called the base, must be raised to produce that number.
As per the question, when you calculate the logarithm of 5 to base 10, written as log₁₀(5), you are finding the exponent to which 10 must be raised to produce the number 5.
Thus, the value of the given expression can be written as log₁₀(5).
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Which of the following equations demonstrate that the set of polynomials is
not closed under the certain operations?
A. Subtraction: (3x^4+x^3)-(-2x^4+x^3)=5x^4
B. Addition: (x^2+x)+(x+1)=x^2+2x+1
C. Division: (x^2-5x+3)÷(x-2)=x-3+-3/x-2
D. Multiplication: (x^2-5x+3)(x-5)=x^3-10x^2+28x-15
Answers
9514 1404 393
Answer:
C. Division: (x^2-5x+3)÷(x-2)=x-3+-3/x-2
Step-by-step explanation:
The set of polynomials is closed under all basic arithmetic operations except division. The reciprocal of a (non-constant) polynomial is not a polynomial.
The division example shown in choice C illustrates the set is not closed under division.
-4x+3x+2x+x=17
x-4x+3x+2x=13
2x+x-4x+3x=9
3x+2x+x-4x=1
Answers
Answer:
x= 8,5
x=0
X= 2
x= -2
Step-by-step explanation:
The mean lifetime of a tire is 4242 months with a variance of 4949. If 145145 tires are sampled, what is the probability that the mean of the sample would be greater than 42.842.8 months
Answers
The above question is not correctly written
Complete Question
The mean lifetime of a tire is 42 months with a variance of 49. If 145 tires are sampled, what is the probability that the mean of the sample would be greater than 42.8 months.
Answer:
0.083793
Step-by-step explanation:
We would be using the z score formula.
z score formula = z = (x - μ)/σ/√n
where
x is the raw score = 42.8
μ is the population mean = 42
σ is the population standard deviation =
In the above question, we were given variance = 49
Standard deviation = √Variance
= √49
= 7
n = number of samples = 145
z score = z = (x - μ)/σ/√n
= (42.8 - 42)/ (7/√145)
= 0.8/ 0.581318359
= 1.37618
Approximately to 2 decimal places= 1.38
Using the z score table to find the probability.
P(x ≤ 42.8) = P(z = 1.38) = 0.91621
P(x>42.8) = 1 - P(x<42.8)
1 - 0.91621
= 0.083793
Therefore, the probability that the mean of the sample would be greater than 42.8 is 0.083793
What exponent is assumed is we just have the number ? For example what is the exponent for the following:80 1 0 0 0 1000 8
Answers
Answer: 1
\(\begin{gathered} \text{According to the law of indices} \\ x^1\text{ = x} \\ \text{Therefore,} \\ 8^1\text{ = 8} \\ \text{Where the exponent is 1} \end{gathered}\)When the same constant is added to the numbers 60, 100 and 180 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
Answers
The common ratio of the resulting sequence is 1.4.
Given that, the three terms are 60, 100 and 180.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
Let the same constant is added to the given number is x.
60+x, 100+x and 180+x
Now, the common ratio is
(100+x)/(60+x) = (180+x)/(100+x)
⇒ (100+x)(100+x)=(180+x)(60+x)
⇒ (100+x)²=10800+180x+60x+x²
⇒ 10000+200x+x²=10800+180x+60x+x²
⇒ 10000+200x=10800+180x
⇒ 20x=800
⇒ x=40
The three number are 100, 140 and 220
The common ratio is 140/100 =1.4
Therefore, the common ratio of the resulting sequence is 1.4.
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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 29, 31, 49, 37, 26, 28. Use a 0.025 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
Answers
The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.
Step 1: Set up hypotheses
H₀: The outcomes of the die are equally likely.
H₁: The outcomes of the die are not equally likely.
Step 2: Select the significance level
The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.
Step 3: Compute the test statistic
We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.
Expected frequencies (fair die):
1: 200/6 = 33.33
2: 200/6 = 33.33
3: 200/6 = 33.33
4: 200/6 = 33.33
5: 200/6 = 33.33
6: 200/6 = 33.33
Applying the chi-square formula, we get the test statistic:
χ² = ∑((observed - expected)² / expected)
Calculating this value, we get χ² ≈ 13.97.
Step 4: Determine the critical value
Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.
Step 5: Make a decision
The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.
The loaded die appears to behave differently from a fair die.
In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
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Write the equation below in standard form and then answer the following questions. If a value is a non-integer type your answer as a decimal rounded to the hundredths place. 4x^2+24x+25y^2+200y+336=0The center of the ellipse is (h,k). h= Answer and k= AnswerThe value for a is Answer . The value for b is Answer .The foci with the positive x value is the point ( Answer, Answer)The foci with the negative x value is the point ( Answer, Answer)
Answers
Given:
\(4x^2+24x+25y^2+200y+336=0\)Aim:
We need to convert the given equation into the standard form of the ellipse equation.
Explanation:
Consider the standard form of the ellipse equation.
\(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\)Consider the given equation.
\(4x^2+24x+25y^2+200y+336=0\)\(Use\text{ }336=36+400-100.\)\(4x^2+24x+25y^2+200y+36+400-100=0\)\(4x^2+24x+36+25y^2+200y+400-100=0\)Take out the common terms.
\(4(x^2+6x+9)+25(y^2+8y+16)-100=0\)Add 100 on both sides of the equation.
\(4(x^2+6x+9)+25(y^2+8y+16)-100+100=0+100\)\(4(x^2+6x+9)+25(y^2+8y+16)=100\)\(4(x^2+2\times3x+3^2)+25(y^2+2\times4y+4^2)=100\)\(\text{Use (a+b)}^2=a^2+2ab+b^2.\)\(4(x+3)^2+25(y+4)^2=100\)Divide both sides by 100.
\(\frac{4\mleft(x+3\mright)^2}{100}+\frac{25\mleft(y+4\mright)^2}{100}=\frac{100}{100}\)\(\frac{\mleft(x+3\mright)^2}{25}+\frac{\mleft(y+4\mright)^2}{4}=1\)\(\frac{\mleft(x+3\mright)^2}{5^2}+\frac{\mleft(y+4\mright)^2}{2^2}=1\)\(\frac{\mleft(x-(-3)\mright)^2}{5^2}+\frac{\mleft(y-(-4)\mright)^2}{2^2}=1\)The standard form of the given equation is
\(\frac{\mleft(x-(-3)\mright)^2}{5^2}+\frac{\mleft(y-(-4)\mright)^2}{2^2}=1\)Compare with the general form of the ellipse equation.
We get h=-3, k=-4, a=5 and b=2.
The centre of the ellipse is h= -3 and k = -4.
The value of a is 5.
The value of b is 2.
We need to find the eccentricity of the ellipse.
\(e=\sqrt[]{1-\frac{b^2}{a^2}}\)Substitute b=2 and a =5 in the formula.
\(e=\sqrt[]{1-\frac{2^2}{5^2}}=\sqrt[]{1-\frac{4}{25}}=\sqrt[]{\frac{25-4}{25}}=\sqrt[]{\frac{21}{25}}=0.9165\)\(e=0.9165\)The foci of the ellipse are
\(((h\pm a)e,0)\)Substitute h =-3, a=5 and e =0.9165 in the formula.
\(((-3\pm5)0.9165,0)\)The foci with a positive x value are the point
\(((-3+5)0.9165,0)\text{ =}(1.83,0)\)
\((1.83,0)\)
The foci with a negative x value are the point
\(((-3-5)0.9165,0)\text{ =}(-7.33,0)\)\((-7.33,0)\)- A robot's torso, arms, and head can be modeled by three separate cylinders and a sphere. The
robot's torso is 24 inches long, with a radius of 6 inches. The robot's arms are 30 inches long,
with a radius of 2 inches and the robot's head has a radius of 8 inches. What is the volume of the
body from the waist up rounded to the nearest cubic inch?
Answers
Answer:
5,236 in
Step-by-step explanation:
volume for head: 2144.66
volume for torso: 2714.34
volume for arms: 376.99
add it up and equals 5235.99, round it up to 5,236
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three statements that are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
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Look at this set of 7 numbers. 3275951 by how much would the median decrease if the number 3 were added to the set? Hurry pleaseeeeee
Answers
Carlos is baking a pie with a circumference of 56 inches. What is the area of the pie he will bake?
Answers
the area of the pie that Carol will bake will be equal to 249.51 inches².
We are given the circumference of the pie as = 56 inches.
As pie is in the shape of a circle, we will use the formula for circumference to find the radius of the circle.
2 π r = 56 inches
2 × 22 / 7 × r = 56
r = 56 × 7 / ( 22 × 2)
r = 8.91 inches.
Area of circle is given by:
π r²
Substituting the values in the formula, we get that
A = 22 / 7 (8.91)²
A = 249.51 inches²
Therefore, we get that, the area of the pie that Carol will bake will be equal to 249.51 inches².
Learn more about area here:
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