The area of the regular pentagon is 60 square units
How to determine the area of the pentagon?The given parameters are
Radius, r = 5 units
Side length, l = 6 units
The area of the pentagon is calculated as
A = 1/4√[25 + 10√5] * l^2
Substitute 6 for l in the above equation
So, we have
A = 1/4√[25 + 10√5] * 6^2
Evaluate the product
A = 60 (approximated)
Hence, the area of the regular pentagon is 60 square units
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Harper desires to invest in a single mutual fund or ETF. She wants the fund to invest
50%-70% in stocks and the rest in bonds. Which fund or ETF would you recommend?
Harper should invest his funds in Hybrid Mutual Funds.
What are Hybrid Mutual Funds?Hybrid funds are mutual funds or exchange-traded funds (ETFs) that invest in securities other than stocks and bonds. They enable investors to own a combination of different elements that are typically found in two or more funds while investing in a single mutual fund. Hybrid Funds are mutual fund schemes that invest in more than one asset class, such as equity, debt, and other asset classes, depending on the scheme's investment objective. These funds invest in a variety of asset classes in order to diversify the portfolio and reduce risk.Therefore, Harper should invest his funds in Hybrid Mutual Funds.
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1. 4(-20) 2. (-8)(-5)
3. (-10)(0) 4. (-9)(-21)
5. 11(-1) 6. 18(-4)
Challenge: A scuba diver has 30 cubic feet of air in his tank and dives under the water at
3:15pm. When he resurfaced at 3:30pm, he had 12 cubic feet of air left. How many cubic
feet of air per minute did he use?
The cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
Unit rateQuantity of air in his tank = 30 cubic feetTime he dives in = 3:15pmTime he resurfaced = 3:30pmQuantity of air remaining in the tank = 12 cubic feetCubic feet of air used per minute = Difference in quantity of air in his tank / difference in time
= (30 - 12) / (3:30pm - 3:15pm)
= 18 / 15
= 1.2 cubic feet of air per minute
Therefore, the cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
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The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint
for "30+ hours." Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the
data set
Click the icon to view the pie chart
First construct the frequency distribution.
Class Frequency, f
0-4
5-9
10-14
15-19
20-24
25-29
30+
CIB
4
The frequency distribution for the given data is:
0-4: 0.0349.5-9: 0.1512.10-14: 0.2558.15-19: 0.1977.20-24: 0.1628.25-29: 0.1512.30: 0.0465.Treating the frequency distribution as a discrete distribution, we have that:
The mean is of 16.71.The standard deviation is of 10.95.What is the missing information?The pie chart is missing, but is given at the end of the answer.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
A frequency distribution is composed by the relative frequencies of each outcome. From the pie chart, we have that there is a total of 3 + 13 + 22 + 17 + 14 + 13 + 4 = 86 people, hence the frequency distribution is given as follows:
0-4: 3/86 = 0.0349.5-9: 13/86 = 0.1512.10-14: 22/86 = 0.2558.15-19: 17/86 = 0.1977.20-24: 14/86 = 0.1628.25-29: 13/86 = 0.1512.30: 4/86 = 0.0465.What are the mean and the standard deviation of a discrete distribution?The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The standard deviation of a discrete distribution is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their respective probabilities.This is relevant because we want to treat the frequency distribution as a discrete distribution, taking the midpoint of each interval, hence:
P(X = 2): 0.0349.P(X = 7): 0.1512.P(X = 12): 0.2558.P(X = 17): 0.1977.P(X = 22): 0.1628.P(X = 27): 0.1512.P(X = 32): 0.0465.Hence the mean is:
E(X) = 0.0349 x 2 + 0.1512 x 7 + 0.2558 x 12 + 0.1977 x 17 + 0.1628 x 22 + 0.1512 x 27 + 0.0465 x 32 = 16.71.
The mean is of 16.71.
The standard deviation is found as follows:
S(X) = sqrt[0.0349 x (2 - 16.71)² + 0.1512 x (7 - 16.71)² + 0.2558 x (12 - 16.71)² + 0.1977 x (17 - 16.71)² + 0.1628 x (22 - 16.71)² + 0.1512 x (27 - 16.71)² + 0.0465 x (32 - 16.71)²] = 10.95.
The standard deviation is of 10.95.
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Find the difference: 20-√80
O-12√5
O-2√5
02√5
O-2√15
Step-by-step explanation:
maybe you missed something in the problem definition or in the answer options, but the answer options do not contain any right answer to the described problem.
20 - sqrt(80) = 20 - sqrt(16×5) = 20 - 4×sqrt(5) =
= 11.05572809...
it is simple to estimate, in what dimension the result should be : 80 is very close to 81. so the sqrt(80) is also very close to the sqrt(81), which is 9.
20 - 9 = 11.
so, all the negative answer options are wrong by default.
and the only positive one is 2×sqrt(5) = 4.472135955...
additional thoughts :
20 = 4×5 or 4×sqrt(5)×sqrt(5)
so, we could write the problem as
4×sqrt(5)×sqrt(5) - 4×sqrt(5)
which could be simplified to either
4×sqrt(5)×(sqrt(5) - 1)
or
4×(5 - sqrt(5))
The Johnsons have accumulated a nest egg of $40,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $2400/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $3000. If local mortgage rates are 4.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)
Using the monthly payment formula, the price range of houses that they should consider is:
[$513,666.78, $592,083.48].
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are given as follows:
r = 0.045 -> r/12 = 0.045/12 = 0.00375.n = 30 x 12 = 360.The minimum price, discounting the down payment, is found when A = 2400, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]2400 = 0.00375P\frac{(1.00375)^{360}}{(1.00375)^{360} - 1}[/tex]
[tex]P = \frac{2400[(1.00375)^{360} - 1]}{0.00375 \times (1.00375)^{360}}[/tex]
P = $473,666.78.
Considering the down payment, we add $40,000, hence the minimum value of the range is: $513,666.78.
The maximum price, discounting the down payment, is found when A = 3000, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]3000 = 0.00375P\frac{(1.00375)^{360}}{(1.00375)^{360} - 1}[/tex]
[tex]P = \frac{3000[(1.00375)^{360} - 1]}{0.00375 \times (1.00375)^{360}}[/tex]
P = $592,083.48.
Considering the down payment, we add $40,000, hence the maximum value of the range is: $592,083.48.
Hence the price range is:
[$513,666.78, $592,083.48].
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The side-lengths of a triangle are increased by a scale factor of 4. Predict
how this change will affect the area.
A. The area will be one-fourth the original area.
B. The area will be 4 times greater.
C. The area will be 16 times greater.
D. The area will be increased by 4 units.
If the side-lengths of a triangle are increased by a scale factor of 4 then the area will be 16 times greater.
As given in the question,
Let 'a' be the base of the triangle
and 'h' be the height of the triangle
Area of the triangle = (1/2)×a× h
Side length increased by scale factor 4
New base = 4a
New height=4h
New area=(1/2)×4a×4h
= 16×(1/2)×a ×h
= 16 times the original area
Therefore, if the side-lengths of a triangle are increased by a scale factor of 4 then the area will be 16 times greater.
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I need to know the answer to this ASAP, which of these aren’t equivalent please help.
Answer:
b
Step-by-step explanation:
cuz remember () and no parentheses has a different meaning
a company makes a table for $15 and sells it for $19 what is the percent of markup
Answer:
126.6667%
Step-by-step explanation:
9g-6>12g+1 or 4>-2\5g+8
The solution to the given inequality is: (-∞, -7/3) ∪ (20, ∞).
How to solve a compound inequality involving the or operation?
To solve a compound inequality involving the op operation, we solve each inequality, then find the union of these solutions.
The first inequality for this problem is:
9g - 6 > 12g + 1
-3g > 7
3g < -7
g < -7/3.
The second inequality for this problem is:
-2/5g + 8 < 4
-2/5g < -4
2/5g > 4
2g > 20
g > 20
Hence the solution is:
(-∞, -7/3) ∪ (20, ∞).
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Six less than a number is four more than one-third of the number. Find the number.
Answer:
x - 6 = 1/3x + 4
x = 15
Hope this helps :)
Hope this helps :)Explanation and Check part below.
Step-by-step explanation:
1. Get the variable on one side by subtracting x.
x - 6 = 1/3x + 4
- 1 x - 1 x
- 6 = - 2/3x + 4
2. Subtract 4 which is the inverse operation of addition.
- 6 = - 2/3x + 4
- 4 - 4
- 10 = - 2/3x
3. Divide by - 2/3 which is the invers eoperation of multiplication.
- 10 = - 2/3x
- 2/3 - 2/3
(Keep,Change,Change - KCC method)
- 10 ÷ - 2/3 = - 10 × - 3/2 = 30/2 = 15
- 10 = - 2/3x
- 2/3 - 2/3
15 = x → x = 15
Check:
15 - 6 = 1/3(15) + 4
9 = 15/3 + 4
9 = 5 + 4
9 = 9
True statement.
Question 2(Multiple Choice Worth 2 points)
(Order of Operations with Radicals MC)
Evaluate quantity the square root of 36 times 3 squared minus the cube root of negative 64 end quantity divided by 2 squared.
one fourth
thirty fourths
fifty-eight fourths
seventy-eight fourths
The expression is evaluated to give 58/ 4, fifty-eight fourths. Option C
How to determine the valueFrom the information given, we have the deduction;
[tex]\frac{\sqrt{36}* 3^2 - \sqrt[3]{-64} }{2^2}[/tex]
Simply the expression;
√36 = 6
3² = 9
∛-64 = -4
2² = 4
Substitute the values into the expression
⇒ 6 × 9 - (-4)/ 4
Use the BODMAS rule, multiply first
⇒ 54 + 4/ 4
Add the numerators
⇒ 58/ 4
Thus, the expression is evaluated to give 58/ 4, fifty-eight fourths. Option C
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Answer:
58 over 4
Step-by-step explanation:
Question
If A {3,7,9,13, 22}, B = {5,7,14, 23, 31), and C= {8, 9, 15, 23, 25, 31, 33), then what is (AUB) nC?
Provide your answer below:
A pair of shoes is regularly priced at $80 and is on sale for 20% off. You have a coupon to receive an additional 15% off the sale price. How much will you pay for the shoes?
The customer would pay $54.40 for the shoes
What is the dollar value of the initial discount of 20%?
The dollar worth of the general discount of 20% of the price of $80 is determined as 20% multiplied by the shoe price
dollar worth of initial discount=20%*$80
dollar worth of the initial discount=$16
the price after the initial discount=$80-$16
the price after the initial discount=$64
The fact the customer has a coupon to receive additional 15% off the sale price means the purchase price for the customer is as computed thus:
final sale price=$64*(1-15%)
final sale price=$54.40
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4m+2mm+m2+m+3m2 simplified
4m^2+7m
I did this before
Use the information given to find a convenient class width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class width up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.) 8 classes for n = 75 measurements; minimum value = 50; maximum value = 205
Class boundaries list: 50,70,90,110,130,150,170,190,210
1. Calculate the range.
range= maximum value - minimum value= 205 - 50 =155
2. Divide the range by the number of classes.
width= [tex]\frac{155}{8}[/tex] =19.375
3. Round this number up to the nearest multiple of five.
width = 20
class boundaries: smallest class boundry= minimum value =50
difference between two class boundries= width
class boundaries list: 50,70,90,110,130,150,170,190,210
The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.
The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number the of possible values can be represented by a continuous random variable.
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5.) Joey is saving money for a car that will cost at least $2500. His grandpa gave him. $460 and he is currently saving $15 each week. Write and solve an inequality to represent the number of weeks it will take Joey to save up for his car.
Write a fraction that represents the parts
shaded red (indicated by "R") in the figure shown below.
W
R
W
W
W
w
The red-shaded part represents the fraction 2/7.
We are given an image of circle in the question which has 7 equal parts with two parts shaded red and the other five shaded white.
We have to find the fraction that represents the red shaded part of the circle.
A fraction defined as the part of the whole thing. For example, a pizza is divided into 6 equal pieces, then each piece is represented by 1/6.
We know that,
Fraction of red shaded part = Number of red parts/ Total number of parts
Here,
Number of red parts = 2
Total number of parts = 7
Hence,
Fraction of red shaded part = 2/7
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Which formula can be used to describe the sequence?
-2/3, -4, -24, -144,...
The formula that describes the sequence given i.e. [tex]\frac{-2}{3}[/tex],-4,-24,-144 (geometric sequence) is [tex](\frac{-2}{3} )(6)^{n-1}[/tex]
Geometric progression:
A geometric progression or a geometric sequence is a series, in which each word is varied by another by a common ratio. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence. It is symbolized by:
A, AR,[tex]AR^{2}[/tex],[tex]AR^{3}[/tex]...
Where A is the first term of the geometric sequence and R is the common ratio of the geometric sequence.
The general term of geometric sequence i.e. nth term =[tex]AR^{n-1}[/tex]
Given that A= [tex]\frac{-2}{3}[/tex] and R=6
As a result the general term of geometric sequence i.e. nth term =[tex](\frac{-2}{3} )(6)^{n-1}[/tex]
Therefore,The formula that describes the geometric sequence given i.e. [tex]\frac{-2}{3}[/tex],-4,-24,-144 is [tex](\frac{-2}{3} )(6)^{n-1}[/tex]
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A board game has 6 blue spaces,29 yellow spaces ,12 green spaces, and 18 red spaces. If you are equally likely to land on each space, what is the probability of landing on a green space? Give your answer as decimal rounded to the nearest thousandth.
Answer:
If you're equally likely to land on each space then you're 1 in number of spaces to land on a specific space=1/(6+29+12+18) = 1/65
there are 12 green spaces so chance of a green space is 12/65=0.185 rounded to a nearest thousandth
What is the opposite number of 2,45
Answer:
-2,45
Step-by-step explanation:
the opposite of a positive number is a negative number
Solve the equation 2a²3a-27=0
Answer:
[tex]a = \frac{ \sqrt[3]{36} }{2} [/tex]
What is the solution of the following system of equations? y-2x=-6 and y-4x=0
Answer: The answer is {y,x}={-12,-3}
Step-by-step explanation:
I mulitpuly the number on the coornate grid
Solve 2x2 + 5x = 12. (5 points)
Using the mileage chart below, find the distance between Sturgis and Hot
Springs.
The distance between the Sturgis and Hot springs is 102 miles.
We have a mileage chart,
We have to estimate the distance between Sturgis and Hot Springs.
What is mileage chart ?A chart showing distances between various points in miles is called mileage chart.
According to the question -
The horizontal row with the name Sturgis intersects the vertical column with the name Hot springs at the block representing 102 miles.
Therefore, the distance between the Sturgis and Hot springs is 102 miles.
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2
1 point
The point, (-3, 7), is on the line y = -3x+7.
True
O False
Step-by-step explanation:
in order to know if the the point is on the line plug in the x coordinate to check if it gives you the y coordinate as an output.If you plug in the x coordinate and it gives you the given y coordinate then the point is on the given line Now let us plug in the value of x=-3[tex]y = - 3( - 3) + 7 \\ y = - 9 + 7 \\ y = - 2[/tex]now if you check plugging in the given x coordinate it does not give you the given y coordinate but -2therefore the point(-3,7) is not in the line but (-3,-2) is the point in the line.PROBABILITY!!! Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 35% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below.
A) In the event of a power loss, the possibility of both generators failing is 0.1225.
B) (i) In the case of a power outage, having a functioning generator may be anticipated 87.75% of the time.
(ii) During a power outage, it may be anticipated that both generators will malfunction roughly 12.25% of the time.
Probability: The probability of an occurrence is defined as the ratio between the number of positive outcomes to a certain event and the entire number of potential outcomes.
Complementary Events: When event A is specified, the complement of that event A does not take place.
Union of two events: The term "union of two events" refers to the collection of outcomes that are either related to both occurrences or one of the two events.
The intersection of two events: The intersection of two events refers to the group of results that are related to both occurrences.
Independent Events: If the occurrence of one event does not influence the occurrence of another event, then two occurrences A and B are said to be independent events. To put it another way, if the occurrence of event A has no bearing on the occurrence of event B, then the two occurrences A and B are independent.
A) The likelihood that both generators would malfunction during a power outage is calculated as follows:
According to the data provided, emergency backup generators malfunction 35% of the time when they are required. The probability value is 0.35 in this case.
The required probability is,
P⎝|⎛Bothgeneratorsfailduringapoweroutage⎠|⎞
= ⎣⎡P(Firstgeneratorfail) × P(Secondgeneratorfail)⎦ |⎤
= 0.35 × 0.35 = 0.1225
When there is a power outage, the likelihood that both generators will fail is calculated by multiplying the likelihood that the first and second generators will fail. During a power outage, the failure of both generators may be anticipated roughly 12.25% of the time.
B) (i) The likelihood of having a functional generator during a power outage is calculated as indicated below:
The required probability is,
P⎝|⎛Workinggeneratorintheeventofapoweroutage⎠|⎞
= 1−P⎝|⎛Bothgeneratorsfailduringapoweroutage⎠|⎞ =
1−0.1225 = 0.8775
The likelihood that a generator will operate in the case of a power loss is calculated by deducting the likelihood that both generators would malfunction from the overall likelihood. In the case of a power outage, having a functioning generator may be anticipated 87.75% of the time.
(ii) The likelihood that a patient will require hospitalization or not is determined as follows:
When there is a power outage, there is a 12.25% chance that both generators will malfunction; this means that they will malfunction roughly 10% of the time.
It is obvious that it is possible to anticipate that during a power outage, both generators will fail roughly 12.25% of the time, suggesting that this probability is low enough to not have an effect on patients' health.
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find the comference of the circle
Answer:
25.12 feet (closest answer)
Step-by-step explanation:
formula circumference = 2πr
2πr
2×3.142(π)× 4 ft
=25.1327412
≈25.13(2 d.p)
closest answer in diagram is 25.12
Simplify the expression 15.6 + -13.5 .
Answer:
2.1
Step-by-step explanation:
15.6 + (-13.5) + = 2.1
Remove Parentheses (-a) = -a
Subtract the numbers: 15.6 - 13.5 = 2.1
= 2.1
What’s the correct answer answer asap for brainlist
Answer:
B.
Step-by-step explanation:
Because predict basically means to guess. So B. is saying "I guess my dad will make a healthy dinner - he does every other night!"
Answer:
B. I predict my dad will make a healthy dinner - he does every other night!
Step-by-step explanation:
Predict meaning is to estimate or believe something will happen, In answer b it makes the statement that the dad makes dinner every other night so it would be a good prediction to assume that he will be fixing a healthy dinner again.
hopefully this helps you !