The error is related to spelling.
The word affects will be effects.
Let X be a normal rv with μ=300
and σ=45
the first and third quartiles of X are
The first and third quartiles of x are 269.625 and 330.375 respectively.
The interquartile range is 61.11.
How to Find Quartiles Using Mean & Standard Deviation?To get the first (Q1) and third (Q3) quartiles of a normally distributed dataset, use the following formulas:
Q1 = μ – (.675)σ
Q3 = μ + (.675)σ
μ - denotes the population mean
σ - denotes the population standard deviation.
The first quartile represents 25% of a dataset and the third quartile represents 75% of a dataset.
Using Mean and Standard Deviation, we need to determine Quartiles
Assume we have a normally distributed dataset with and = 45.
The first and third quartiles of the dataset can be calculated using the following formulas:
Q1 = μ – (.675)σ = 300 – (.675)*45 = 269.625
Q3 = μ + (.675)σ = 300 + (.675)*45 = 330.375
This means that 25% of all values in the dataset are less than 269.625 and 75% of all values in the dataset are less than 330.375.
We may also calculate the interquartile range using these numbers:
IQR = Q3 - Q1 = 330.375 - 269.265
IQR = 61.11
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Question
A coin is flipped three times, and the following list shows the possible outcomes.
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
How many outcomes include exactly one head?
Enter your answer as a number, like this: 42
The total number of possible outcomes when flipping a coin three times is 8, since there are two possible outcomes for each flip (heads or tails).
What is combination?Combination is a way of selecting items from a set where order does not matter. Combinations are written as a set of n distinct objects taken r at a time, where n is the total number of objects and r is the number of objects taken.
Of these 8 outcomes, 3 include exactly one head. These are the outcomes HHT, HTH, and THH.
The total number of possible outcomes is calculated using the formula 2ⁿ, where n represents the number of flips. In this case, n = 3, so the total number of outcomes is 2³ = 8.
To find the number of outcomes with exactly one head, we can use the formula nCr, which stands for n choose r.
This formula is used to calculate the number of combinations of r elements that can be chosen from a set of n elements.
In this case, n = 3 (the number of flips) and r = 1 (the number of heads).
This gives us 3C1 = 3, which is the number of outcomes with exactly one head.
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kevin scored a 4 over par (+4) on the first nine holes of the golf course. What does he need to score over the last nine holes to get back to a even par (0)?
Answer:
6
Step-by-step explanation:
he needs 6 points to score over the last nine holes
Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
We can find the total number of strokes Kevin needs to score over 18 holes to reach an even par.
If the par score for 18 holes is 72,
and Kevin scored 4 over par on the first nine holes
= 9 × 4 = 36 extra strokes.
Now, if the par score for the last nine holes is x, then we have:
4 + x + x + x + x + x + x + x + x = 72
4 + 8x = 72
8x = 68
x = 8.5
Therefore, Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.
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Which number is smaller?
a) 0.658 or 0.75
b) 15.604 or 15.640
c) 6.431 or 6.481
Find x, so that 7x + 2, 5x + 7 and 2x - 1 form an arithmatic sequence
please help if you want
The value of the given function at f(-6) is -14.
What is a function?A function in mathematics is a relationship between a set of inputs (the domain) and a set of outputs (the range), where each input corresponds to one specific outcome. Equations, tables, diagrams, and verbal descriptions can all be used to depict functions. They are frequently represented by the notation f(x), where x is the input variable and f is the name of the function. In many branches of mathematics, science, and engineering, functions are fundamental ideas that are used to simulate real-world occurrences and address issues in a variety of applications.
The give function is f(x) = 3x + 4.
Substitute the value of x = -6 to obtain the value of f(-6):
f(-6) = 3(-6) + 4
f(-6) = -18 + 4
f(-6) = -14
Hence, the value of the given function at f(-6) is -14.
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Find the measure of angle R,if R is a point of tangency
The measure of angle R,if R is a point of tangency is 37°.
How to calculate the angleWe have been given a diagram of a circle. We are asked to find the measure of angle R.
Since QR is the tangent of our given circle, so measure of angle Q will be 90 degrees as radius is perpendicular to tangent at point of tangency.
We will use angle sum property to solve for angle R as:
53 + 90 + R = 180
R = 180 - 143
R = 37°
Therefore, based on the information, it should be noted that the measure of angle R,if R is a point of tangency is 37°.
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Which deduction is optional
The deduction that is optional is C. Retirement plan deductions.
How is this deduction optional ?When contributing to a retirement plan like a 401(k) or an Individual Retirement Account (IRA), you receive deductions from your taxable income. Essentially, whatever amount of money contributed towards the retirement fund can be subtracted from your total annual income.
Consequently, the entire amount cannot then be seized for taxation purposes. Let's say, for instance that you earn $50,000 annually and contribute $5,000 into your account; this would imply your taxable revenue reduces to $45,000.
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Options for this question are:
A. State taxes B. Federal taxes C. Retirement planD. FICACan someone help me with this problem please
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
Answer:
100 grandparents
200 parents
100 children
Step-by-step explanation:
Define the variables: Let g be the number of grandparents, p be the number of parents, and c be the number of children.
Use the total number of people to set up an equation: g + p + c = 400
Use the information that there were twice as many parents as grandparents to set up another equation: p = 2g
Use the information that there were 50 more children than parents to set up a third equation: c = p + 50
Substitute the second equation into the third equation to eliminate p: c = 2g + 50
Substitute the second equation into the first equation to get an equation in terms of g only: g + 2g + c = 400
Substitute the third equation into the first equation to get another equation in terms of g only: g + 2(1/2 c - 50) + c = 400
Simplify the equations and solve for g: g = 100
Use the second equation to solve for p: p = 2g = 200
Use the third equation to solve for c: c = p + 50 = 250
Therefore, there were 100 grandparents, 200 parents, and 100 children in attendance at the family reunion! :DDDD
Given P(A) =1/3
and P(B) =5/12,
where A and B are
independent events, determine P(A n B)
The value of P(A n B) where A and B are independent event is 5/36
How to determine P(A n B)From the question, we have the following parameters that can be used in our computation:
P(A) =1/3 and P(B) =5/12,
where A and B are independent event
Since the events are independent, then we have
p(A and B) = p(A) * p(B)
Substitute the known values in the above equation, so, we have the following representation
P(A n B) = 1/3 * 5/12
Evaluate
P(A n B) = 5/36
Hence, the solution is 5/36
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Evaluating health care coverage. Jasper Bell was a self-employed window washer earning approximately $700 per week. One day, while cleaning windows on the eighth floor of the Second National Bank Building, he tripped and fell from the scaffolding to the pavement below. He sustained multiple severe injuries but miraculously survived the
accident. He was immediately rushed to the local hospital for surgery. Edward remained
there for 60 days of treatment, after which he was allowed to go home for further recuperation. During his hospital stay, he incurred the following expenses: surgeon, $7,500; physician, $2,000; hospital bill for room and board, $250 per day; nursing services, $1,200;
anesthetics, $600; wheelchair rental, $100; ambulance, $150; and drugs, $350. Jasper has a major medical policy that has a $3,000 deductible clause, an 80 percent co-insurance clause, internal limits of $180 per day on hospital room and board, and $1,500 as a maximum surgical fee. The policy provides no disability income benefits.
1. Explain the policy provisions as they relate to deductibles, co-insurance, and internal limits.
2. How much should Jasper expect to receive from the insurance company? How much must he pay out of his own pocket?
3. Would any other policies have offered Jasper additional protection? What about his inability to work while recording from his injury?
4. Based on the information presented, how would you assess Jasper’s health care insurance coverage? Explain.
1. The policy has a $3,000 deductible clause, which means that Jasper must pay the first $3,000 of his expenses before the insurance company begins to cover the remaining expenses.
2. Jasper should expect to receive $13,270 from the insurance company.
His total out of pocket expense will be $5,730.
3. Other policies may have offered Jasper additional protection, such as disability income benefits. This would have helped him while he was unable to work due to his injury.
4. Based on the information given, the health care insurance coverage that Jasper had appears to be adequate, given his circumstances.
What is deductible clause?The deductible clause is used by insurance companies to reduce the risk of paying out large amounts of money for small claims and to spread out the cost of insurance among policyholders.
1. The policy provisions as they relate to deductibles, co-insurance, and internal limits are as follows: The policy has a $3,000 deductible clause, which means that Jasper must pay the first $3,000 of his expenses before the insurance company begins to cover the remaining expenses. The co-insurance clause means that the insurance company will cover 80% of the remaining expenses and Jasper will be responsible for the remaining 20%.
The internal limits for hospital room and board and surgical fees are $180 and $1,500, respectively. This means that the insurance company will only cover up to $180 per day for hospital room and board and up to $1,500 for surgical fees.
2. Jasper should expect to receive $13,270 from the insurance company. He must pay $3,000 out of his own pocket to meet the deductible, and he will also be responsible for the remaining 20% of the expenses not covered by the insurance company, which amounts to $2,730.
This means that his total out of pocket expense will be $5,730.
3. Other policies may have offered Jasper additional protection, such as disability income benefits. This would have helped him while he was unable to work due to his injury.
4. Based on the information given, the health care insurance coverage that Jasper had appears to be adequate, given his circumstances.
The policy provides enough coverage to cover the majority of his medical expenses and the deductible and co-insurance amounts are reasonable. In addition, the internal limits for hospital room and board and surgical fees are within reasonable limits.
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express each set using the roster method.
a. the set of the natural odd numbers greater than 2, but less than 11
b.
{x|x (N and 4
In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10."
How to solve the question?
a. The set of natural odd numbers greater than 2, but less than 11 can be expressed using the roster method as {3, 5, 7, 9}. The set includes all the odd natural numbers between 2 and 11, excluding the endpoints, since 2 is not odd, and 11 is not less than 11.
b. The set {x|x (N and 4<x<10)} can be expressed using the roster method as {5, 6, 7, 8, 9}. The set includes all the natural numbers greater than 4 and less than 10, since x is a natural number (N) and satisfies the condition 4 < x < 10.
In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10." The vertical bar separates the description of the elements of the set (the condition) from the set itself.
The roster method and set-builder notation are both ways of describing sets, but the roster method lists all the elements of a set, while the set-builder notation describes the properties or conditions that define the set. Both methods are useful in different situations and depend on the specific context and the purpose of the set description.
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Your complete question is :-
express each set using the roster method.
a. the set of the natural odd numbers greater than 2, but less than 11
b.{x|x (N and 4
Margaret wants to determine how consistent the grades have been in history class. Margaret's quiz scores are 85, 86, 84, 88, 99, and 96.
Step 1: Find the mean. Round to the nearest whole number.
The mean is
.
Step 2: Find the distance each piece of data is from the mean.
Step 3: Find the average of the distance from Step 2. Round to the nearest whole number.
The MAD is
.
Answer: Mean = 89.67
Step-by-step explanation:
Step 1:
Calculate the sum of integers, then divide by the number (N) of scores:
Sum of scores = 538
538 ÷ 6 = 89.67
Step 2:
89.67 - 85 = 4.67
89.67 - 86 = 3.67
89.67 - 84 = 5.67
89.67 - 88 = 1.67
99 - 89.67 = 9.33
96 - 89.67 = 6.33
Step 3:
Avg = Sum / N
4.67 + 3.67 + 5.67 + 1.67 + 9.33 + 6.33 = 31.34
Avg = 31.34 / 6 = 5.223
Step 3; 2: 5
Simplify the expression x^4-x^3-3x-2 dived by (x-2), using synthetic division.
Please show work.
Help me please!!!!!!!
The p-value of the test statistic is given as follows:
0.0606
How to the p-value using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.For this problem, we are testing if the proportion is greater than a value, hence we have a right-tailed test.
As we have a right-tailed test, the p-value is one subtracted by the p-value of z = 1.55, hence:
1 - 0.9394 = 0.0606
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Find the scale ratio for the following map.
1 inch on the map represents 5 miles
The scale ratio is _____
The scale ratio is therefore 1:5 miles per inch
The connection between distances on the map and their equivalent distances on the ground is expressed by the scale ratio. Here, one inch on the chart corresponds to five miles on the Earth. We must represent this connection as a fraction using the same units in order to calculate the scale ratio:
5 miles per inch.
By reducing both the numerator and denominator by one inch, we may simplify the following fraction:
1/5 of a mile per inch
The scale ratio is therefore 1:5 miles per inch. This implies that the comparable distance on the ground is 5 units long for every 1 unit of distance indicated on the map (1 inch) (5 miles).
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In Example 1, Step 3, the new principal is $279,811.47. For the second
payment, show the work to find:
1. The interest on $279,811.47.
2. The payment to principal.
3. The new balance.
The interest on $279,811.47 for the second payment is $933.04.
The payment to principal for the second payment is $403.11
The new balance after the second payment is $279,408.36.
How to calculate the valueInterest = $279,811.47 x 0.04 / 12 = $933.04
Payment to principal = Payment amount - Interest
Payment to principal = $1,336.15 - $933.04 = $403.11
New balance = Previous balance - Payment to principal
New balance = $279,811.47 - $403.11 = $279,408.36
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Please help. Will award brainliest
The dimension of the rectangular of a norman window will be 1.6803*3.3606.
What is the area of Rectangle?
In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.
Let r represents the radius, and b be the breadth.
Then, perimeter = 3.14*r+2r+2b = 12
For the dimension needed for the most light to enter we need to maximize the area.
Hence, area of the window : area of the semicircle + area of the rectangle
= [tex]\frac{3.14*r^2}{2} + 2rb[/tex]
= [tex]12r - (\frac{3.14+4}{2}) r^2[/tex]
A'(r) = 0
Therefore, [tex]r=\frac{12}{3.14+4}[/tex] which is nearly equal to 1.6803m
From this value of r we can calculate the value of b to be;
b= 1.6803m
Thus, a= 3.606m
Thus the required dimension is : 1.6803*33606
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HELP ASAP ASAP PLS PLS ALSO BRAINLIEST
The list represents the number of students who left school early in a 12-day period.
77, 84, 45, 54, 33, 37, 60, 43, 69, 73, 65, 49
Find the mean and interpret its meaning as it relates to the number of students that left school early.
The mean is about 57.4, and it represents the average number of students who left school early.
The mean is about 62.6, and it represents the average number of students who left school early.
The mean is about 57.4, and it represents the middle number of students who left school early.
The mean is about 62.6, and it represents the middle number of students who left school early.
Answer: it is A (The mean is about 57.4, and it represents the average number of students who left school early.)
Step-by-step explanation:
first you add all of the numbers then you get 689. then divide by 12 and you get 57.4
what is the width?
The length of' a rectangle is eight more than twice its width. If the length is less than 34, then
Variable:
Inequality:
Solution
the width of the rectangle is less than 13. However, we don't know the exact value of the width without additional information.
How to determine?
In a rectangle, the width refers to the shorter side and the length refers to the longer side. Let's use "w" to represent the width of the rectangle.
According to the problem, the length of the rectangle is 8 more than twice its width, which can be written as:
length = 2w + 8
The problem also tells us that the length is less than 34, so we can write an inequality:
length < 34
Substituting the first equation into the inequality, we get:
2w + 8 < 34
Subtracting 8 from both sides, we get:
2w < 26
Dividing both sides by 2, we get:
w < 13
So the width of the rectangle is less than 13. However, we don't know the exact value of the width without additional information.
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PQR is an isosceles triangle with PQ = PR M and N are points on PQ and PR such that angle MRQ = angle NQR
Prove that triangles QNR and RMQ are congruent
Triangles QNR and RMQ are congruent
What makes these triangles to be congruent?PQR is an isosceles triangle, by extension PQ = PR.
Considering the triangles QNR and RMQ:
Given that angle MRQ = angle NQR.
Likewise, angle RQM = angle RQN (since they are vertically opposite angles).
Consequently, angle MRQ = angle RQM + angle NQR = angle RQN + angle NQR = angle RNQ.
Hence, two pairs of angles that are equal:
angle MRQ = angle RNQ
angle RMQ = angle RQN
Also, PQ = PR, and for M and N are on PQ and PR at the same time, then, MQ = NR.
Through the angle-side-angle (ASA) congruence criterion, we can conclude that triangles QNR and RMQ are congruent.
Therefore, we have proved that triangles QNR and RMQ are congruent.
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Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
The total cost with 4 snacks is $59.
The total cost with x snacks is $29 + $5x.
What is the total cost?The first step is to determine the total number of people going to the movies. There are 3 people going to the movies.
The total cost spent by Ellie is the sum of the tickets and the total cost of the snacks.
Total cost = total cost of the tickets + total cost of the snacks
= (cost of one ticket x number of people going to the movie) + (number of snacks bought x price of one snack)
= (13 x 3) + ($5 x 4)
$39 + $20 = $59
Total cost if x snacks is bought: (13 x 3) + ($5 x x) = $39 + $5x
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What is the midpoint of this interval? 50 < x < 70
The midpoint of the interval is 60.
To find the midpoint of an interval, we take the average of its endpoints.
The endpoints of the interval 50 < x < 70 are 50 and 70.
Therefore, the midpoint of the interval is:
(midpoint) = (50 + 70) / 2
= 120 / 2
= 60
Hence, the midpoint of the interval is 60.
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Find the equation for the line that passes through (-1, 10) that has slope 5/7. You do not need to simplify.
Give your answer in point-slope
Answer:
y = (5/7)x + (75/7)
Step-by-step explanation:
If you ever find yourself in a math class where you have to write the equation of a line that goes through a certain point and has a certain slope, don't panic. There is a simple formula that can help you out. It's called the point-slope form and it looks like this:
y - y1 = m (x - x1)
It may look scary, but it's actually pretty easy to use. All you have to do is plug in the values that you know and solve for the ones that you don't. For example, let's say you have a line that passes through the point (-1, 10) and has a slope of 5/7. You can use the point-slope form to write the equation of the line like this:
y - 10 = (5/7) (x - (-1))
See? That wasn't so bad. Now you can simplify the equation by distributing the 5/7 and adding 10 to both sides. You get:
y = (5/7)x + (75/7)
And that's it! You have written the equation of the line in slope-intercept form, which is another way of writing the equation of a line. You can check your answer by plugging in the values of x and y from the original point and seeing if they make the equation true. If they do, you're good to go. If not, you made a mistake somewhere and you should go back and fix it.
Congratulations! You have learned how to use the point-slope form to write the equation of a line. Now you can impress your math teacher and your friends with your skills. Remember, with great power comes great responsibility.
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧
(06.03 MC)
According to the manufacturer, about 26% of sour candy in a package of Sandy's Sours are grape. What is the probability that the first grape candy chosen from the
bag will be, at least, the third candy chosen overall?
00.4524
00.5476
00.1424
O0.8576
00.4052
Answer:
The probability that the first grape candy chosen is not among the first two is:
P(not grape in first two) = (1 - 0.26) × (1 - 0.26) = 0.5764
Therefore, the probability that the first grape candy chosen will be at least the third candy chosen is:
P(grape candy chosen third or later) = 1 - P(not grape in first two) = 1 - 0.5764 = 0.4236
So, the answer is 0.4236, which is closest to 0.424. Therefore, the correct option is:
0.424
If your translation is moving 3 units to the right is that affecting your x coordinate or your y coordinate
A person ordering a certain model of car can choose any of 4 colors, either manual or automatic transmission, and
any of 6 audio systems, How many ways are there to order this model of car?
A) 48 ways
B) 44 ways
C 58 ways
D) 56 ways
There are 48 ways to order this model of car. The correct option is A
To determine the total number of ways to order this model of carWe need to multiply the number of options for each feature to get the total number of ways to order this particular car:
4 color choices
2 options (manual or automatic) for the transmission
Audio system: 6 choices
We can multiply these figures in order to find the total number of ways by applying the counting principle to multiplication:
4 × 2 × 6 = 48
Therefore, there are 48 ways to order this model of car.
Therefore, The correct option is A
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If y varies directly with x and y=88 when x=44, find x when y=4.
Answer:
x=2
Step-by-step explanation:
Simple ratio:
44/88=x/4
Simplify:
1/2=x/4
Cross multiply:
4=2x
x=2
Answer:
x = 2
Step-by-step explanation:
If y varies directly with x then:
[tex]\boxed{y \propto x \implies y=kx}[/tex]
where k is the constant of variation.
Given y = 88 when x = 44:
[tex]\implies 88=44k[/tex]
Solve for k by dividing both sides by 44:
[tex]\implies \dfrac{88}{44}=\dfrac{44k}{44}[/tex]
[tex]\implies 2=k[/tex]
[tex]\implies k=2[/tex]
Therefore, the equation is:
[tex]\boxed{y=2x}[/tex]
To find the value of x when y = 4, substitute y = 4 into the equation and solve for x:
[tex]\implies 4=2x[/tex]
[tex]\implies \dfrac{4}{2}=\dfrac{2x}{2}[/tex]
[tex]\implies 2=x[/tex]
Therefore, the value of x when y = 4 is x = 2.
Which number is larger, 2^81 or 3^49.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Brandon invests $5800 in two different accounts. The first account paid 3 %, the second account paid 8 % in interest. At the end of the first year he had earned $229 in interest. How much was in each account?
$ ___ at 3 %
$ ____ at 8 %
Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $[tex]4700[/tex] at 3% interest and $[tex]1100[/tex] at [tex]8[/tex]% interest. The total interest earned after one year is $229
How much was in each account?
Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:
[tex]x + y = 5800[/tex]
The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:
[tex]0.03x + 0.08y = 229[/tex]
We now have two equations with two unknowns:
[tex]x + y = 5800[/tex]
[tex]0.03x + 0.08y = 229[/tex]
We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.
Solve the first equation for x:
[tex]x = 5800 - y[/tex]
Substitute this expression for x into the second equation and solve for y:
[tex]0.03(5800 - y) + 0.08y = 229[/tex]
[tex]174 - 0.03y + 0.08y = 229[/tex]
[tex]0.05y = 55[/tex]
[tex]y = 1100[/tex]
Now substitute this value of y into either equation to solve for x:
[tex]x + 1100 = 5800[/tex]
[tex]x = 4700[/tex]
Therefore, Brandon invested $[tex]4700[/tex] at 3% interest and $[tex]1100[/tex] at [tex]8[/tex]% interest.
Learn more about the interest here:
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What is the surface area of a right cone with a height of 4 centimeters
and with 3 centimeters as the radius of its base?
Answer:
[tex]24\pi \: {cm}^{2} [/tex]
Step-by-step explanation:
Given:
A cone
h (height) = 4 cm
r (radius) = 3 cm
Find: A (surface area) - ?
In order to find the surface area, we have to know the length of the slant height first (use the Pythagorean theorem):
[tex] {l}^{2} = {r}^{2} + {h}^{2} [/tex]
[tex] { l}^{2} = {3}^{2} + {4}^{2} = 9 + 16 = 25[/tex]
[tex]l > 0[/tex]
[tex]l = \sqrt{25} = 5 \: cm[/tex]
Now, we can find the surface area:
[tex]a(surface) = \pi {r}^{2} + \pi \times r \times l[/tex]
[tex]a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 5 = 9\pi + 15\pi = 24\pi \: {cm}^{2} [/tex]
