The distance around a circular park is 88 yards.
What is the area of the park? Use 3.14 for π.
Answers
Answer:
616.25 \(yd^2\)
Step-by-step explanation:
The equation for the area of a circle is
\(A=\pi r^2\)
Since the problem does not give a value for r, it must be derived. Recall that the equation for the circumference of a circle is
\(C=2\pi r\)
Using the given value of the circumference,
\(C=88yd=2\pi r\)
So,
\(88yd=2\pi r\\\frac{88yd}{2\pi}=r\\14.01yd=r\)
Insert the derived value of r into the formula for area:
\(A=\pi r^2\\A=\pi(14.01yd)^2\\A=616.25yd^2\)
Related Questions
a function is in the form g(x)= ax2 + d. if a is greater than 1 and d is positive, which could be the graph of g(x) ?
Answers
hello
to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file
)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts
Answers
The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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Find the value of 5⁰ X 7⁰ X 3⁰
plz help asap
Answers
Answer:
5⁰ × 7⁰ × 3⁰ = 1
Step-by-step explanation:
5⁰ × 7⁰ × 3⁰ = ?
5⁰ = 1
7⁰ = 1
3⁰ = 1
1 × 1 × 1 = 1
just solve these 2 its prob easy i just too lazy to even try or think at the moment, want to go to bed...
Answers
Answer:
The correct option is 'No Solution'.
Step-by-step explanation:
Given the system of the equations
\(y=\frac{1}{2}x-1\)
\(2x-4y=12\)
solving the system of the equations
\(\begin{bmatrix}y=\frac{1}{2}x-1\\ 2x-4y=12\end{bmatrix}\)
\(\mathrm{Subsititute\:}y=\frac{1}{2}x-1\)
\(\begin{bmatrix}2x-4\left(\frac{1}{2}x-1\right)=12\end{bmatrix}\)
\(2x-4\left(\frac{1}{2}x-1\right)=12\)
\(2x-2x+4=12\)
\(4=12\)
as
4=12 is false, therefore the system of equations has no solution.
Therefore, the correct option is 'No Solution'.
Plz help me well mark brainliest if correct.......?????
Answers
Answer:
4 cm
Step-by-step explanation:
Divide the volume by the product of the length and width to calculate the height of a rectangular object.
I'll MARK THE BRAINLIEST!
The line plots show the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the previous week. A) Which statement is true about the range? B) Which statement is true about the mean?
A} The range is greater for the girls, B) The mean is less for the girls
B} The range is greater for the girls, B) The mean is greater for the girls
C} The range is greater for the boys, B) The mean is greater for the girls
D}The range is greater for the boys, B) The mean is greater for the boys
Answers
The range is greater for the girls and the mean is greater for the girls. So, correct option is B.
A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.
Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.
B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:
(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours
To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:
(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours
Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".
So, correct option is B.
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-0.16 as a fraction or a mixed number in simplest form
Answers
Answer:
1/-16
Step-by-step explanation:
Answer:
-16/100 im pretty sure
Step-by-step explanation:
.
a
There were 850 students at Fort Herriman Middle School last year. The student population is expected to
increase by 20% next year. What will the new population be?
Answers
Answer:
The population will be 1050
20% of 880 is 170 you add 880 and 170 and get 1050
please help, I need the answer
Answers
The given equation is true when a and b are integers and x is not equal to 0.
The statement "xᵃ + xᵇ = x⁽ᵃ⁺ᵇ⁾ " is always true when a=b.
In this case, the exponents of x on both sides of the equation are equal, and the equation simplifies to xᵃ + xᵃ = x²ᵃ , which holds true.
When a=b, the exponents are the same, and the equation is satisfied.
However, the statement is not always true for all values of a and b. If a and b are not equal, then the equation does not hold true in general.
The statement is also not true when a=0 and b=0, as both sides of the equation become 1, but the equation becomes 1 + 1 = 1, which is not true.
Therefore, the statement "xᵃ + xᵇ = x⁽ᵃ⁺ᵇ⁾ " is always true when a=b, but not true in general for all values of a and b.
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600% of what number is 5,580
Answers
Answer:
930
Step-by-step explanation:
600% of x = 5580
6x = 5580
x = 5580/6
x = 930
Please help me thank you
Answers
Answer:
b = 20 when a = 8.
Step-by-step explanation:
For this problem, we will simply plug the value of a=8 into the given equation for b, to find the value of b.
b = [ (a)^2 / 4 ] + 4
b = [ (8)^2 / 4 ] + 4
b = [ 64 / 4 ] + 4
b = [ 16 ] + 4
b = 20
Hence, when the value of a=8, then the value of b=20.
Cheers.
Answer:
20
Step-by-step explanation:
b = a^2/4 +4
Let a =8
b = 8^2 /4 +4
= 64/4 +4
= 16 +4
= 20
A large company event was held in a park on a hot day. Afterward, many of the employees got sick. Some blamed the potato salad. To investigate, a random sample of 20 sick employees and a random sample of 20 non-sick employees are selected. Each selected individual is asked if they ate the potato salad. The results are displayed in the table.
Management would like to know if there is convincing evidence that the distribution of responses about eating the potato salad differs for all employees who are sick versus those who are not sick. What are the appropriate hypotheses for this test?
H0: There is no difference in the distribution of responses among those who are and are not sick.
Ha: There is a difference in the distribution of responses among those who are and are not sick.
H0: There is a difference in the distribution of responses among those who are and are not sick.
Ha: There is no difference in the distribution of responses among those who are and are not sick.
H0: There is no difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Ha: There is a difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
H0: There is a difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Ha: There is no difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Answers
The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.
The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.
The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.
On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.
By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.
Therefore, the correct answer is:
H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.
Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.
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he probability symbol (~) represents the probability of an event happening.
True
False
Answers
It is true that the probability symbol '^' represents the probability of an event happening.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
The probability symbol '^' represents the probability of an event happening in a manner of dependent probabilities. Which describes the dependent relationship between the probability of certain events.
Thus, It is true that the probability symbol '^' represents the probability of an event happening.
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Which expression is equivalent to (4√a^2b)(3√b)?
A) 2ab√3
B) 3a^2b^2
C) 12ab
D) 12ab^2
Answers
Answer:
C) 12ab
Step-by-step explanation:
Express the given repeating decimal as a quotient of integers. If possible, reduce to lowest terms.
Answers
Answer:
4
Step-by-step explanation:
Huiling has sonme 20-cent coins and 50-cent coins. She has 4 times as many 20-cent coins as 50-cent coins. She has a total of $39. How many coins does she have altogether?
Answers
Answer: 150
Step-by-step explanation:
A choir is performing in front of an audience. A microphone is placed in front of the choir to capture sound.Which polar equation reprsents the microphone the choir is using?
Answers
Answer:
D on Edge.
Step-by-step explanation:
Got it right.
The polar equation represents the microphone the choir is using ; D. r = 2 + cos(θ)
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
It is given that a choir is performing in front of an audience. A microphone is placed in front of the choir to capture sound.
The polar equation represents the microphone the choir is using would be;
D. r = 2 + cos(θ)
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Solve the equation for h?
Answers
Answer:
h = V ÷ (πr²)
Step-by-step explanation:
V = π × r² × h
V ÷ π = r² × h
V ÷ π ÷ r² = h
h = V ÷ (πr²)
Since the right side is pi•r^2•h, you need to cancel the pi and r^2 from the right with division, just like you would if it had be V = 7•h. Division “undoes” multiplication.
So you divide both side by pi and r^2 to get:
V ÷ (pi r^2) = h
What is 1 2/3 - 5/6 ??
Answers
The Subtraction of the given fraction using the number line is 5/6.
The correct answer option is option A
How to subtract fraction?Fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction while a denominator is the lower value or bottom value of a fraction.
1 2/3 - 5/6
= 5/3 - 5/6
Find the lowest common multiple of the denominators and divide
= (10-5) / 6
= 5/6
In conclusion, 5/6 is the answer to the subtraction of fraction.
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If 2x-y=9 and 3x+4y=19, then y=
Answers
Answer:
x = 5
y = 1
Step-by-step explanation:
2x - y = 9
3x + 4y = 19
We multiply the first equation by 4
8x - 4y = 36
3x + 4y = 19
11x = 55
x = 5
Now we put 5 in for x and solve for y
2(5) - y = 9
10 - y = 9
-y = -1
y = 1
Let's Check the answer
2(5) - 1 = 9
10 - 1 = 9
9 = 9
So, x = 5 and y = 1 is the correct answer.
Help help help please in a hurry!!!!!!!!!!!!!!!!!!!
Answers
Answer:D
Step-by-step explanation:
please mark brainliest
solve the expression x + 3 = 7
Answers
Answer:
x=4
Step-by-step explanation:
think of the equation like this: you have to do the inverse(opposite) operations so for adding you would subtract it. So for the adding 3 you would subtract it from both sides of the equation and get X=4
plss help me for branleist
Answers
Answer: x=67
Step-by-step explanation:
All of the angles add up to 180 for a triangle
38 + 75 + x = 180 >combine like terms (the numbers)
113 + x = 180 >subtract 113 from both sides
x=67
Answer:
x = 67°Step-by-step explanation:
We know that,
\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)
\( \large \sf \: → x +38° + 75° = 180°\)
\( \large \sf \: → x + 113 = 180°\)
\( \large \sf→ x = 180°- 113°\)
\( \boxed{\large \bf→ x = 67° }\)
the soution to -2 (1-4x)=3x+8 is
a 6/11
b 2
c -10/7
d -2
Answers
rearrange the terms
2(1-4x)=3x+8 to this
2(-4x+1)= 3x+8. brainliest please
Note: Enter your answer and show all the steps that you use to
solve this problem in the space provided.
You have a credit card with a balance of $1,367.90 at a 9.5%
APR. You pay $400.00 each month on the due date until the
card is paid off. How many months does it take to pay off the
card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
. the mathematical steps for solving the problem
demonstrating mathematical reasoning
Answers
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.
To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:
Step 1: Calculate the monthly interest rate.
The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):
Monthly interest rate = 9.5% / 12 = 0.0079167
Step 2: Determine the monthly payment.
The monthly payment is given as $400.
Step 3: Calculate the interest and principal paid each month.
The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.
Principal paid = Monthly payment - Interest paid
Step 4: Track the remaining balance each month.
Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.
Step 5: Repeat Steps 3 and 4 until the balance reaches zero.
Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.
Step 6: Determine the total number of months and the total amount paid.
Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.
Let's calculate the number of months and the total amount paid, including interest:
Month 1:
Interest paid = 0.0079167 * $1,367.90 = $10.84
Principal paid = $400 - $10.84 = $389.16
New balance = $1,367.90 - $389.16 = $978.74
Month 2:
Interest paid = 0.0079167 * $978.74 = $7.75
Principal paid = $400 - $7.75 = $392.25
New balance = $978.74 - $392.25 = $586.49
Month 3:
Interest paid = 0.0079167 * $586.49 = $4.64
Principal paid = $400 - $4.64 = $395.36
New balance = $586.49 - $395.36 = $191.13
Month 4:
Interest paid = 0.0079167 * $191.13 = $1.51
Principal paid = $400 - $1.51 = $398.49
New balance = $191.13 - $398.49 = -$207.36 (Paid off)
It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:
Total amount paid = 4 * $400 = $1600
Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.
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Make a tree diagram that shows the sample space of rolling a cube with facesnumbered 1 through 6 and flipping a fair coin. Using this tree diagram, what isthe probability of rolling the number 5 and the coin landing heads up?
Answers
Draw tree diagram for rolling cube and flipping the coin.
The number of observation in sample space is 12.
The possible outcome for number 5 and coin with head up is 1.
Determine the probability for number 5 and coin with head up.
\(P=\frac{1}{12}\)So probability for number 5 and coin with head up is 1/12.
Directions: Solve the following. Show your solution.
1. Diane has clay in a can. Its radius is 6 cm while its height is 10 cm. She wanted to transfer some of her clay to her cone-shaped container. What is the volume of the cone to be filled up if it has the same radius and height with
Pls do it with a solution
Answers
the volume of the cone to be filled up if it has the same radius and height with is 376. 6 cm³
How to determine the volumeTo determine the volume, we need to know the formula for the volume of a cone.
The formula for the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are expressed as;
V is the volume of the coner is the radius of the coneh is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 10/3
Find the square value
Multiply the value, we have;
Volume = 1130. 4/3
Divide the values
Volume = 376. 6 cm³
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Shawn bought 3 items at the grocery store that cost $3.35, $6.85, and $2.90. After paying the cashier, Shawn received $2.15 in change.
How much did Shawn give the cashier to pay for his purchase?
Answers
Answer: Shawn payed the cashier $15.25
Step-by-step explanation:
( I WILL BE GIVING EXTRA POINTS AND BRAINLIEST TO WHO EVER HELPS ME!! :D)
A recipe needs two and one sixth cups of walnuts and eight and one eighth cups of peanuts. How many cups of nuts are needed for the recipe in all?
A) ten and two fourteenths cups
B) ten and fourteen forty eighths cups
C) eleven and fourteen forty eighths cups
D) eleven and two fourteenths cups
(Here is an image if needed) :
Answers
Answer:
B I think
Step-by-step explanation:
Eight eighths in one cup. Took that and multiplied that and added the single eighth. Six sixths in one cup. Took that and multiplied that and added the single sixth again. Added the total up and got 10.2916666667. Rounded. Hope this helps!
Answer:
b
Step-by-step explanation:
Could I get some help with this? Thanks! Here’s the question to go along with it.
For each diagram, calculate the value of x. Show your work and include an explanation of what you used (definitions and theorems) to solve the problem. If not possible, state why.
Answers
Based on the two (2) parallel lines m||n, the value of x is equal to 4.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
In Geometry, when two (2) parallel lines are cut by a transversal, the pair of vertically opposite angles that are formed would always be equal to each other. In this context, we have the following;
m∠2 = m∠3
7x - 3 = x + 21
7x - x = 21 + 3
6x = 24
x = 24/6
x = 4.
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