Karen invested $6000 in Fund B, and $24000 in Fund A, as the weighted average of the two funds' returns is 5%, yielding a total profit of $1380, and we can use a system of equations to solve for the amounts invested in each fund.
To solve this problem, we can set up a system of equations using the information given.
Let x be the amount invested in Fund B, then the amount invested in Fund A is 4x. The total amount invested is the sum of these two amounts, so we have:
x + 4x = 5x = total amount investedThe total profit from the two funds is given as $1380, which is the sum of the profits from Fund A and Fund B.
We can express these profits using the amounts invested and the respective return rates:
0.04(4x) + 0.07(x) = 0.16x + 0.07x = 0.23x = $1380Solving for x, we find that x = $6000, which is the amount invested in Fund B. Therefore, the amount invested in Fund A is 4x = $24000.
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Write a power function (y=ax^b) whose graph passes through the points (2,5) and (6,9)
show work
Answer:
To find the values of a and b that make the power function y = ax^b pass through the points (2,5) and (6,9), we can use the following system of equations:
5 = a2^b
9 = a6^b
We need to solve for a and b in this system.
One way to do this is to divide the second equation by the first equation, which eliminates a and gives:
9/5 = (6/2)^b
Simplifying this gives:
9/5 = 3^b
Taking the logarithm of both sides (with any base) gives:
log(9/5) = log(3^b)
Using the logarithmic property that log(a^b) = b*log(a), we get:
log(9/5) = b*log(3)
Solving for b, we get:
b = log(9/5) / log(3)
Plugging this value of b into one of the original equations (e.g., the first one) gives:
5 = a*2^(log(9/5)/log(3))
Solving for a, we get:
a = 5 / 2^(log(9/5)/log(3))
Find an equation of the line passing through the given points. Express your answer in slope-intercept form. (3,9) and (3, -8) The equation of the line is (Type an expression using x as the variable.)
The equation of the line is x = 3.
To find the equation of a line passing through two points, we need to use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
m = (-8 - 9) / (3 - 3) = -17 / 0
Since the denominator is zero, this means that the slope of the line is undefined. This means that the line is vertical and has an equation of the form x = c, where c is a constant.
Since both of the given points have an x-coordinate of 3, the equation of the line is:
x = 3
So, the equation of the line passing through the given points is x = 3. This is the final answer in slope-intercept form.
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Help I don't understand
Answer:
Step-by-step explanation:
The Domain is (x) values that a certain line covers on a graph.
This line is a segment, so it has a very specific domain.
The domain is written in the form of => [tex]a\leq x\leq b[/tex]
- In which (a) and (b) are the smallest and largest numbers on the domain, respectively.
Here, the line starts at (-11,6) and goes all the way to (2,1)
From here - we take out the y-values to get that the x-values go from (-11) to (2)
That means that the domain. of this here line, is:
[tex]Domain = -11\leq x\leq 2[/tex]
Please help i got reset on the app
Write 3 3/4 feet as a single fraction greater than one.
Are these two matrices equal? Justify your answer. [[3,-1,7],[2,6,-9],[-5,4,-2]]*[[-2,-9,7],[4,6,-1],[-5,2,3]]
No, these two matrices are not equal.
The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.
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2. Which fraction is not equivalent to 25%?
(EXPLAIN WHY)
1/4
2/5
5/20
25/100
Answer:
The fraction that is not equivalent to 25% is 2/5.
To see why, we can start by converting 25% to a fraction. Recall that "percent" means "per hundred," so 25% is equal to 25/100 or 1/4.
Now, we can check each of the answer choices to see if they are equivalent to 1/4:
1/4 is already in the form of 1/4, so it is equivalent to 25%.
5/20 can be simplified by dividing both the numerator and denominator by 5, which gives 1/4. So 5/20 is also equivalent to 25%.
25/100 is the same as 1/4 (we converted 25% to 1/4 earlier), so it is equivalent to 25%.
This leaves us with 2/5 as the answer choice that is not equivalent to 25%. We can see this by converting 2/5 to a percent:
2/5 = 0.4
0.4 x 100% = 40%
So 2/5 is equivalent to 40%, which is not the same as 25%.
Answer: [tex]2/5[/tex] second option
Step-by-step explanation: 1/4 is equal to 25% because if you multiply by 100 and divide by 4 that will equal 25. 5/20 simplified to 1/4 which we know is 25%, 25/100 also does too. Therefore, the answer is 2/5 because it simplifies to 40% which isn't 25%.
Are the perimeter and the side length of squares proportional?
Answer:
Yes, the perimeter and side length of a square are proportional. This is because a square has four equal sides, so if you increase the length of one side by a certain factor, the perimeter (which is the sum of all four sides) will also increase by the same factor. In other words, if you double the length of a side of a square, you will also double its perimeter. Similarly, if you reduce the length of a side by a certain factor, the perimeter will also be reduced by the same factor. This relationship holds true for all squares, regardless of their size or orientation.
Write an equation of the line passing through the point $\left(1,\ 9\right)$ that is parallel to the line $y=3x-2$ .
Equation of straight line parallel to y = 3x - 2 and passing through (1, 9) is
y = 3x + 6
What is straight line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity. A straight line is a figure formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them, and the line ends are extended to infinity.
Given,
Line y = 3x - 2
Comparing with y = mx + c
slope = 3
Line parallel to y = 3x - 2 and passing through (1, 9)
Slope of the parallel line = slope of line y = 3x - 2
slope m = 3
Equation of the line,
y - y' = m(x - x')
y - 9 = 3(x - 1)
y - 9 = 3x - 3
y = 3x + 6
Hence y = 3x + 6 is equation of line parallel to y = 3x - 2 and passing through (1, 9)
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FIRST TO ANSWER AND SHOW WORK GETS BRAINLIEST! PLEASE PLEASE PLEASE HURRY!!!!!!!!!!
Twelve cards are numbered from 1 to 12 and placed in a box. One card is selected at random and not replaced. Another card is randomly selected. What is the probability of selecting two even numbers?
PLEASE SHOW WORK!
Answer:
1/6
Step-by-step explanation:
Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.
Determine the amount needed such that when it comes time for retirement, an individual can make semiannual withdrawals in the amount of $15,265 for 35 years from an account paying 4.5% compounded semiannually. Round your answer to the nearest cent.
The individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.
What is the Present Value of an Annuity?
With a specific rate of return, or discount rate, the present value of an annuity is the current value of the future payments from an annuity. The present value of the annuity decreases as the discount rate increases.
To determine the amount needed for retirement, we can use the formula for the present value of an annuity:
[tex]PV= PMT* \frac{1-\frac{1}{(1+r)^{n} } }{r}[/tex]
where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.
In this case, PMT = $15,265, r = 4.5%/2 = 0.0225 (since the interest is compounded semi-annually), and n = 35 x 2 = 70 (since there are 70 semiannual periods in 35 years).
Plugging in these values, we get:
[tex]PV = (15,265\times(1 - (1 + 0.0225)^{(-70))) / 0.0225[/tex]
PV = $405,840.13
Therefore, the individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.
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Evaluate the expression when q = 8
11q
Answer: 88
Step-by-step explanation:
Plug 8 in for q
11 x (8) = 88
PLEASE HELP! I CAN'T DO THIS QUESTION.
plsplsplsss im struggling so bad- does anybody know how to do the attached question?
By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.
Explain about the similarity of triangles?Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.
Two triangles are comparable if the determinations of their corresponding sides are proportionate. The same is true if the lengths of two sides for one triangle are proportional to the lengths of the corresponding sides inside a triangle and the included angles are congruent.In the given statements, thus the similar triangle are:
ΔWYZ ≈ Δ WZX ≈ ΔZYX
A,
∠Y is common
∠x = ∠z = 90°
Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.
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Josue tosses a coin and spins on the spinner at the right. What are all the possible outcomes
Answer: Without knowing the specifics of the spinner, it's not possible to list all the possible outcomes.
However, we can determine the total number of possible outcomes by multiplying the number of outcomes for each event. For example, if the coin has two possible outcomes (heads or tails) and the spinner has six possible outcomes, then the total number of possible outcomes would be:
2 (outcomes for the coin) x 6 (outcomes for the spinner) = 12 possible outcomes
If you provide me with the specific details of the spinner (such as the number of sections and what each section represents), I could list all the possible outcomes.
Step-by-step explanation:
Elisa has homework assignments in seven subjects she only has time to do five of them
Answer: What else? Is that the whole sentence to this story i dont get it?
Step-by-step explanation:
31. if ( f(x) = {x^{26}+x^{24}+2 x^{22}}{x-1} ), find f(i) where ( i ) is the imaginary unit. (a) ( -1-i ) (b) ( -1+i ) (c) \( 1-i ) (d) ( 1+i ) (e) none of these
To find f(i), we will substitute i for x in the given function and simplify:
f(i) = (i^{26} + i^{24} + 2i^{22})/(i-1)
= ((i^{22})(i^4 + i^2 + 2))/(i-1)
= ((i^{22})(1 + (-1) + 2))/(i-1)
= ((i^{22})(2))/(i-1)
= (2i^{22})/(i-1)
= (2i^{22})/((-1)(1-i))
= (2i^{22})/((-1)(1-i)) * ((1+i)/(1+i))
= (2i^{22})(1+i)/((-1)(1-i)(1+i))
= (2i^{22})(1+i)/((-1)(1^2 - i^2))
= (2i^{22})(1+i)/((-1)(1 - (-1)))
= (2i^{22})(1+i)/(2)
= i^{22} + i^{23}
= i^{22}(1 + i)
= (i^{22})(1 + i)
= (1)(1 + i)
= 1 + i
Therefore, the answer is (d) (1+i).
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a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
The average percentage change in population in California from 2000-2009 is 1.35% and population in 2015 will be 39306963.
What is average?
In mathematics, the average is a value that represents the central or typical value in a set of numbers. There are several types of averages, including the mean, median, and mode.
The mean is the most commonly used type of average, and it is calculated by adding up all the numbers in a set and then dividing the sum by the total number of numbers. For example, the mean of the set {3, 5, 8, 12} can be calculated as:
mean = (3 + 5 + 8 + 12) / 4 = 7
Now,
To calculate average of percentage change from 2000-2009
we have to add percentage change for every year
and that will be = 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93
=12.21%
then average=12.21/9=1.35%
hence,
The average percentage change in population in California from 2000-2009 is 1.35%.
The population in 2015 will be = 37000000 + (1.35)⁶ × 37000000/100
=37000000+2306963.15
=39306963
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st fit for data collected on the sales commission employees ea What is the equation of the line of best fit?
The equation of the line of best fit is a mathematical representation of the relationship between two variables. It is typically written in the form,
y = mx + b.
where m is the slope and b is the y-intercept. To find the equation of the line of best fit for a set of data, you can use a graphing calculator or statistical software to calculate the slope and y-intercept.
Alternatively, you can use the formula for the slope of a line (m = (y2 - y1)/(x2 - x1)) and the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line of best fit. Once you have the slope and y-intercept, you can plug these values into the equation y = mx + b to find the equation of the line of best fit.
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Antonio is working with a new geometric series generated by the equation A(n) =
12(1.5)n-1
S. Help Antonio find the sum of the first 15 terms of the series without just adding them all up. Show your work
below.
6. Help Antonio find the sum of the 16th through the 30th terms of the series. Show your work below.
Sum of the first 15 terms of the series given is = 10485.36
What is sequence and series?
A sequence is a collection or sequential arrangement of numbers that adheres to a predetermined order or set of criteria. A series is created by adding the terms of a sequence. In a sequence, a single sentence could appear more than once.
Sequences can be divided into two categories: endless sequences and finite sequences. By merging the terms of the sequence, series are defined. A series may, in exceptional cases, also have a sum of infinite terms.
In the given question,
Antonio is working with a new geometric series generated by the following equation:
A(n) = 12(1.5) ⁿ-1
Now to find the sum of the first 15 terms of the series,
S(n) = a{rⁿ)-1}/r-1
So, we have,
a = 12
r = 1.5
n = 15
Using the values in the equation:
S (15) = 12 (1.5¹⁵ - 1)/1.5-1
= 12 × (437.89-1)/0.5
= 12 × 873.78
= 10485.36
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(12x^(3)-9x^(2)-21x+22)-:(3x-3) Your answer should give the quotient and the remainder.
The quotient of (12x^(3)-9x^(2)-21x+22) divided by (3x-3) is 4x^2 + 6x + 7, and the remainder is 0.
To find the quotient, use long division. First, divide the highest degree term of the numerator by the highest degree term of the denominator: 12x3 ÷ 3x = 4x2. Multiply the denominator by the quotient, then subtract this product from the numerator:
12x3 - 3x(4x2) = 9x2 - 4x2 = 5x2.
Divide the highest degree term of the new numerator by the highest degree term of the denominator: 5x2 ÷ 3x = 5x. Multiply the denominator by the quotient, then subtract this product from the numerator:
9x2 - 3x(5x) = -21x - 15x = -36x.
Divide the highest degree term of the new numerator by the highest degree term of the denominator: -36x ÷ 3x = -12. Multiply the denominator by the quotient, then subtract this product from the numerator:
-21x - 3x(-12) = 22 - (-36) = 58.
Divide the highest degree term of the new numerator by the highest degree term of the denominator: 58 ÷ 3 = 19. Since the degree of the numerator is lower than the degree of the denominator, 19 is the remainder.
Therefore, the quotient of (12x3 - 9x2 - 21x + 22) divided by (3x - 3) is 4x2 + 6x + 7, and the remainder is 0.
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Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn.
Diamonds = 7 Spades = 7 Hearts = 9 Clubs = 13
Determine the experimental probability of not selecting a diamond.
P(not diamond) = 82.5%
P(not diamond) = 72.5%
P(not diamond) = 10%
P(not diamond) = 7%
Option A is correct, the experimental probability of not selecting a diamond is 82.5%.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The total number of cards drawn is 40, and the frequency of diamonds drawn is 7.
This means that the frequency of not selecting a diamond is:
40 - 7 = 33
So the experimental probability of not selecting a diamond is:
P(not diamond) = frequency of not selecting a diamond / total number of cards drawn
P(not diamond) = 33/40
P(not diamond) = 0.825
P(not diamond) = 82.5%
Therefore, the experimental probability of not selecting a diamond is 82.5%.
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HELP PLEASE QUICK ITS DUE IN A BIT
The measures of the angles in the figure are DBE = 64 degrees, CBE = 26 degrees. Others are shown below
Figure 7
The angle DBC is right angled
So, we have
17x + 13 + 32 - 2x = 90
This gives
15x + 45 = 90
So, we have
x = 3
Solving for the other angles, we have
DBE = 17 * 3 + 13 = 64
CBE = 32 - 2 * 3 = 26
Figure 8
Here, we have
5x + 29 = 9x - 15 -- alternate angles
So, we have
4x = 44
Divide
x = 11
Solving for the other angles, we have
WVZ = 9 * 4 - 15 = 21
CBE = 90 - 21 = 69
Figure 9
Here, we have
8x - 17 = 5x + 13 -- alternate angles
So, we have
3x = 30
Divide
x = 10
Solving for the other angles, we have
RTS = 5 * 10 + 13 = 63
PTQ = 90 - 63 = 27
Figure 10
Here, we have
6x + 25 + 2x + 23 = 180 -- angles on a straight line
So, we have
8x = 132
Divide
x = 16.5
Solving for the other angles, we have
EFG = 6 * 16.5 + 25 = 124
IFH = 180 - 124 = 56
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The cost of employee work stoppages is rising. Assume the average cost is now $360. If the average cost is normally distributed with a standard deviation of $88.
Required
a. What is the probability that the cost will be $260 or less
b. What is the probability that the cost will be more than $412
c. What is the probability that the cost will be between $260 and $412
So the probability of the cost being between $260 and $412 is 0.5953.
a. The probability that the cost will be $260 or less can be found by calculating the z-score and using a standard normal distribution table. The z-score is calculated as follows:
z = (x - μ)/σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 260, μ = 360, and σ = 88. So the z-score is:
z = (260 - 360)/88 = -1.14
Using a standard normal distribution table, we can find that the probability of the cost being $260 or less is 0.1271.
b. The probability that the cost will be more than $412 can be found by calculating the z-score and using a standard normal distribution table. The z-score is calculated as follows:
z = (x - μ)/σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 412, μ = 360, and σ = 88. So the z-score is:
z = (412 - 360)/88 = 0.59
Using a standard normal distribution table, we can find that the probability of the cost being more than $412 is 0.2776.
c. The probability that the cost will be between $260 and $412 can be found by subtracting the probability of the cost being $260 or less from the probability of the cost being $412 or less. Using the z-scores we calculated in parts a and b, we can find the probabilities from a standard normal distribution table:
P(x ≤ 260) = 0.1271
P(x ≤ 412) = 0.7224
P(260 < x < 412) = P(x ≤ 412) - P(x ≤ 260) = 0.7224 - 0.1271 = 0.5953
So the probability of the cost being between $260 and $412 is 0.5953.
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The proportion of Canadians with green eyes is 0.28. As part of a study of the genetic basis for skin sensitivity to sunlight, a research term collects a simple random sample of 600 Canadians. Answer the following questions to 4 places past the decimal.
a) How many people in the sample would you expect to have green eyes?
b) What is the standard deviation of the sample proportion? (Use the normal approximation from now on)
c) What is the probability that the sample proportion will exceed 0.2983?
The probability that the sample proportion will exceed 0.2983 is approximately 0.0708.
What are examples and probability?It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is half.
a) 0.28 percent of Canadians have green eyes. This ratio can be used to calculate the anticipated proportion of sample members who have green eyes:
Estimated number of green eyed individuals = Percentage of green eyed individuals * Sample size
Estimated population of those with green eyes: 600 divided by 0.28
168 persons with green eyes are anticipated.
As a result, we would anticipate that 168 members of the sample have green eyes.
b) The formula for calculating the sample proportion's standard deviation is:
Sample proportion's standard deviation is equal to sqrt[(p * (1-p)) / n].
where n is the sample size, and p is the percentage of people with green eyes (0.28). (600).
Sample proportion's standard deviation is equal to sqrt[(0.28 * (1-0.28)) / 600].
Sample proportion's standard deviation is 0.0258.
As a result, 0.0258 is the sample proportion's standard deviation.
c) We're looking for the likelihood that the sample proportion will be more than 0.2983. As the sample size is large enough to allow for the use of the normal approximation, we may use the conventional normal distribution to determine this probability.
Then, we must use the following formula to standardise the sample proportion:
z = [(P * (1 - P)] / sqrt[(p - P)]
where P is the population proportion (0.28), n is the sample size, and p is the sample proportion (0.2983) that we are interested in (600).
z = (0.2983 - 0.28) / sqrt[(0.28 * (1 - 0.28)) / 600]
z = 1.47
The chance of a standard normal variable reaching 1.47 can be calculated using a standard normal distribution table or calculator and is roughly 0.0708.
Thus, 0.0708 is about how likely it is that the sample proportion will be more than 0.2983.
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Use the diagram to fill in the blanks.
Answer: BC/FG and AE/AC
Step-by-step explanation:
The variableais jointly proportional toband the cube ofc. Ifa=127whenb=6andc=8, what is the value ofawhenb=8andc=5?Rdecimal places if necessary.
The value of a when b = 8 and c = 5 is 41.351.
What is jointly proportional ?Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.
The variable a is jointly proportional to b and the cube of c. This means that a = k*b*c^3, where k is a constant. We can use the given values to find k:
127 = k*6*8^3
127 = k*3072
k = 127/3072
k = 0.041351
Now we can use this value of k to find the value of a when b = 8 and c = 5:
a = 0.041351*8*5^3
a = 0.041351*8*125
a = 41.351
So the value of a when b = 8 and c = 5 is 41.351.
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the cost $C of transporting goods is directly proportional to the distance, d km. Given that C=100 when d=60 find
a) an equation connecting C and d
b) the cost of transporting goods for 45km
c) the distance if the cost of transporting goods is $120
Equation connecting C and d is C = 5/3 d.
What is Direct Proportion?Direct Proportion of two quantities can be defined as that when one of the quantity increases, the other one also increases and vice versa.
(a) Given that,
C is directly proportional to d.
Equation can be written as C = kd, for some constant k.
Also, given,
C=100 when d=60
100 = 60k
k = 100/60 = 10/6 = 5/3
Equation is C = 5/3 d
(b) When d = 45 km
C = 5/3 × 45 = 75
Cost of transporting goods for 45 km is $75.
(c) When C = $120,
120 = 5/3 d
d = 120 × 3/5 = 72 km
Hence the distance is 72 km when the cost of transporting goods is $120.
Hence the equation is C = 5/3 d.
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Math 1050 Written Homework - Section 5.3
1. Find an equation fro the parabola with vertex (3,5) and focus
(7,5).
The equation of the parabola is (y-5)^2=16(x-3)
To find the equation for the parabola with vertex (3,5) and focus (7,5), we can use the formula for a parabola with a horizontal axis of symmetry:
(y-k)^2=4p(x-h)
Where (h,k) is the vertex and p is the distance from the vertex to the focus.
In this case, the vertex is (3,5) and the focus is (7,5), so we have:
(y-5)^2=4p(x-3)
The distance from the vertex to the focus is 4, so p=4. Plugging this value into the equation gives us:
(y-5)^2=16(x-3)
This is the equation for the parabola with vertex (3,5) and focus (7,5).
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Duchenne muscular dystrophy (DMD) is a genetic disorder characterized by progressive muscle degeneration and weakness due to the alterations of a protein called dystrophin that helps keep muscle cells intact. A published study estimated that the average survival (i.e., duration of disease is approximately 27 years. The annual incidence of DMD is approximately 0.017% or 17 cases per 100,000 people per year. What is the prevalence of people living with DMD? You may show your answer formatted as a percentage or number of cases per 100,000 people.
Answer:
459 cases per 100,000 people.
Step-by-step explanation:
To calculate the prevalence of DMD, we need to know the number of people living with the condition at a specific point in time. We can estimate this number by multiplying the annual incidence rate by the average duration of the disease:
Prevalence = Annual incidence rate x Average duration of the disease
Annual incidence rate = 0.017% = 17 cases per 100,000 people per year
Average duration of the disease = 27 years
Therefore, the prevalence of DMD can be estimated as:
Prevalence = 17 cases per 100,000 people per year x 27 years = 459 cases per 100,000 people
So, approximately 459 people out of 100,000 are living with DMD. This can also be expressed as a percentage by multiplying the above value by 100, which gives:
Prevalence = 459 cases per 100,000 people x 100% = 0.459% of the population
Therefore, the prevalence of DMD is approximately 0.459% or 459 cases per 100,000 people.
Is the volume of the resulting sugar mixture equal, more than or less than the sum (20 mL sugar +50mL water ) of the volumes of the unmixed sugar and water?
The volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.
About water moleculesWhen sugar is dissolved in water, the sugar molecules fit into the spaces between the water molecules, resulting in a decrease in volume. To explain this further, let's use the following steps:
1. Start with 20 mL of sugar and 50 mL of water in separate containers. 2. Pour the sugar into the water.
3. Stir the mixture until the sugar is completely dissolved.
4. Measure the volume of the resulting sugar mixture. You will notice that the volume of the sugar mixture is less than the sum of the volumes of the unmixed sugar and water (70 mL).
This is because the sugar molecules are now occupying the spaces between the water molecules, resulting in a decrease in volume.
In conclusion, the volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.
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