Answer:
x^2+3x-3
Step-by-step explanation:
(x^2+2x-1)+(x^2+x-5)
2x^2+3x-6
(3x^2+6x-9)-(2x^2+3x-6)
x^2+3x-3
hopes this helps
Answer:
[tex]x^2 + 3x - 3[/tex]
Step-by-step explanation:
The perimeter of a triangle, can be calculated as, the sum of the sides.
So let's first assume the third side is a polynomial, and more specifically, a quadratic in the form: [tex]ax^2+bx+c[/tex]. This assumption is denoted from the fact that the perimeter only has terms up to the degree of 2, also known as x squared. The answer is also a quadratic, so it isn't an unreasonable assumption that if we add two quadratics (the ones given), and add one more quadratic, we should still have quadratic.
So, the sum of the three sides can be expressed as: [tex](x^2 + 2x - 1) + (x^2 + x - 5) + (ax^2 + bx + c)[/tex]
We can combine like terms to get:
[tex](x^2+x^2+ax^2)+(2x+x+bx)+(-1-5+c)[/tex]
Now from here, we can combine like terms (add coefficients):
[tex](2+a)x^2 + (3+b)x + (-6+c)[/tex]
From here, we simply set this equal to the given perimeter of: [tex]3x^2 + 6x-9[/tex], which gives us the equation:
[tex](2+a)x^2 + (3+b)x+(-6+c) = 3x^2 + 6x - 9[/tex]
Now from here, the coefficients need to correspond for both quadratics to be equal to each other, so that means that the following must be true:
[tex](2+a)=3\implies a = 1\\(3 + b) = 6\implies b = 3\\(-6 +c) = -9 \implies c = -3[/tex]
We now plug this into the quadratic standard form to get:
[tex]x^2 + 3x - 3[/tex]
Which is our third side!
The function g is defined by g(x)=x² +4.
Find g (5a).
g (5a) =
Answer:
25a² +
Step-by-step explanation:
5a is put in the equation replacing the previous variable and then the whole square follows and hence. g(5a) =25a²+
The graph shows the number of meters Jenny runs relative to the number of minutes she runs what is the constant of proportionality round your answer to the nearest hundredth (6,100)
Find the first three powers, A, A2, and A3, of the transition matrix below. Find the probability that state 1 changes to state 2 after three repetitions of the experiment. 0.3 0.1 0.6 A0.5 0.2 0.3 Type an integer or decimal for each matrix element.)
The probability that state 1 changes to state 2 after three repetitions of the experiment is 0.052.
The first power of the transition matrix A is simply the matrix itself:
A1 = [ 0.3 0.1 0.6 ]
[ 0.5 0.2 0.3 ]
The second power of the transition matrix is obtained by multiplying A by itself:
A2 = A1 * A1 = [ 0.30.3+0.10.5 0.30.1+0.10.2 0.30.6+0.10.3 ]
[ 0.50.3+0.20.5 0.50.1+0.20.2 0.50.6+0.20.3 ]
= [ 0.19 0.06 0.33 ]
[ 0.29 0.08 0.33 ]
The third power of the transition matrix is obtained by multiplying A2 by A:
A3 = A2 * A = [ 0.190.3+0.060.5 0.190.1+0.060.2 0.190.6+0.060.3 ]
[ 0.290.3+0.080.5 0.290.1+0.080.2 0.290.6+0.080.3 ]
= [ 0.161 0.052 0.327 ]
[ 0.247 0.068 0.327 ]
To find the probability that state 1 changes to state 2 after three repetitions of the experiment, we need to look at the second element of the first row of A3. This element is 0.052, so the probability that state 1 changes to state 2 after three repetitions of the experiment is 0.052.
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Please select ALL that apply
Answer:
1st, 3rd
Step-by-step explanation:
1st: 8-10-12=-14
2nd:10-8-12=-10, so no
3rd:yes, because it just removed the brackets
4th:8-6-12+4=-6, so no
Hope this helps u
All the expressions that are equivalent to (8 - 12 - (6 + 4)) would be,
1) 8 - (6 + 4) - 12
3) 8 - 12 - 6 - 4
Given that,
The expression is,
8 - 12 - (6 + 4)
Now, Used the concpet to simplify the expression by using operations addition, subtraction, etc.
Here, The expression is,
8 - 12 - (6 + 4)
8 - 12 - 10
8 - 22
- 14
For the equivalent expressions we can simplify all the equations,
Option 1,
8 - (6 + 4) - 12
8 - 10 - 12
8 - 22
- 14
So, It is equivalent to a given expression.
Option 2,
(6 + 4) - 8 - 12
10 - 8 - 12
10 - 20
- 10
So, It is not equivalent to a given expression.
Option 3,
8 - 12 - 6 - 4
8 - 12 - 10
8 - 22
- 14
So, It is equivalent to a given expression.
Option 4,
8 - 6 - 12 + 4
8 - 18 + 4
12 - 18
- 6
So, It is not equivalent to a given expression.
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Valeria invested $770 in an account paying an interest rate of 53% compounded
monthly. Zoey invested $770 in an account paying an interest rate of 5%
compounded continuously. To the nearest dollar, how much money would Zoey have
in her account when Valeria's money has tripled in value?
4
Answer:
[tex]\$856.03[/tex]
Step-by-step explanation:
Continuous Compound Interest Formula:The Continuous Compound Interest Formula is derived from the Compound Interest Formula: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], as the number of times interest is applied, goes to infinity. Through some simple algebraic manipulation, we get the formula: [tex]A = Pe^{rt}[/tex] (e is known as Euler's Number and is notation for a constant value like [tex]\pi[/tex])
Calculating Time:Since Valeria invested 770 in an account with an interest of 53% paying monthly, we want to find how much time it takes to triple her money, and then plug that into Zoey's equation.
So let's generally solve for time in the equation:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
First divide by P
[tex]\frac{A}{P} = (1 + \frac{r}{n})^{nt}[/tex]
From here, it helps to take the base 10 log of both sides, so we can apply logarithmic properties, in this case we want to bring the exponent down.
[tex]log(\frac{A}{P}) = nt * log(1 + \frac{r}{n})[/tex]
Now from here' lets divide both sides by the log (the one on the right side) and "n" to give us:
[tex]\frac{log(\frac{A}{P})}{n * log(1 + \frac{r}{n})} = t[/tex]
Now whenever we need to calculate time, we simply need to plug in these values. We're given the following information from the problem:
[tex]P = 770\\r = 0.53\\n = 12\text{ compound monthly means 12 per year}\\A= 2,310 \text{ this is just 770 * 3, since we're looking for when Valeria's money triples}[/tex]
Plugging in the values we get:
[tex]\frac{log(\frac{2310}{770})}{12*log(1+\frac{0.53}{12}}=t[/tex]
Plugging this into a calculator, gives an approximate value of:
[tex]2.1183\approx t[/tex]
Calculating Zoey's Balance:From here we simply need to plug values into the continuous compound interest formula: [tex]A=Pe^{rt}[/tex]
We're given the following information:
[tex]A = 770\\r= 0.03\\[/tex]
and we know that:
[tex]t\approx 2.1183[/tex]
since we solved for that.
So now let's just plug values into the equation!
[tex]A\approx 770 * e^{0.05 * 2.1183}\\A \approx 856.03[/tex]
So now we have our solution!
g count the worst-case number of operations performed by the following pseudocode segment. assume that all possible data sets are equally likely. preconditions: x
G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. preconditions: x
x(x + 1)/2 = O(x^2)
The pseudocode segment given has two nested for loops. The outer loop is iterating over the variable x, while the inner loop is iterating over variable i. G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. Each loop iteration is increasing the variable z by 1. In total, this will result in x*(x+1) / 2 operations being performed. This is equal to O(x^2), which is the worst-case number of operations.
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a vehicle purchased for $25,000 depreciates at a constant rate of 5%. determine the approximate value of the vehicle 12 years after purchase. round to the nearest whole dollar.
The value of the vehicle after 12 years of purchase will be $13,500.
Here, we are given that a vehicle purchased for $25,000 depreciates at a constant rate of 5%.
Therefore, the value of the vehicle after 1 year will reduce by-
25,000 × 5/100
= 250 × 5
= 1250
Thus, the value after 1 year will become = 25,000 - 1250 = 23750
In the same manner, the value will keep on reducing every year. Thus, the value after 12 years will become-
25,000 [tex](1- 5/100)^{12}[/tex]
= 25,000 [tex](1 - 0.05)^{12}[/tex]
= 25,000 [tex](0.95)^{12}[/tex]
= 25,000 × 0.54
= 250 × 54
= 13,500
Thus, the value of the vehicle after 12 years of purchase will be $13,500.
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Determine the most conservative sample size for the estimation of the population proportion for the following: E = 0.029, confidence level 95% Round your answer up to the nearest whole number. the absolute tolerance is +/-1
the most conservative sample size for the estimation of the population proportion is 4471, rounded up to the nearest whole number.
Using the formula n = (Zα/2)^2(p*(1-p))/E^2, where:
n = sample size
Zα/2 = z-score for 0.025 (α/2) = 1.96
p = 0.5 (assumed to be the estimated proportion of the population)
E = 0.029 (specified absolute tolerance)
n = (1.96^2)*(0.5(1-0.5))/0.029^2 = 4471
Therefore, the most conservative sample size for the estimation of the population proportion is 4471, rounded up to the nearest whole number.
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6 1/12-7/12 so basicly 6 is whole and 1 twelfth - seven twelfths
Answer:
71/12 = 5 11/12
Step-by-step explanation:
To solve this equation you first have to put the whole number with fraction (mixed number) and convert it into an improper fraction. To do this you have to multiply the whole number by the denominator which is 6 x 2 and you'd get 12 but then you still have the numerator so then you add your answer with the numerator and you'd get 12+1 which is 13. So your improper fraction is 13/2.
Now you set up your equation and you'd subtract. But your denominators are not the same so you have to figure out and find the common denominator. Which is 12. So then for 13/2 you'd multiply both of them by 6 and you'd get 78/12. And the 2nd one you'd multiply it by 1 getting 7/12.
Once you get to this point now you can properly set up the equation and subtract. You'd subtract 78/12 - 7/12 getting 71/12 or if you want it as a mixed number (whole number with fraction) then it is 5 11/12.
(I tried to explain how I got the answer...hopefully you were able to understand how I did it...)
Can someone please help me solve this question?
Answer:
Step-by-step explanation:
Shown following are several times in the history of the universe. Rank these times from left to right based on the peak wavelength in the spectrum of the cosmic microwave background, from shortest to longest.
100 million years after the Big Bang
1.5 billion years after the Big Bang
500,000 years after the Big Bang
1 million years after the Big Bang
today
Based on the highest wavelength in the cosmic microwave background spectrum, rank these eras from left to right, from shortest to longest, 500,000 years after the Big Bang.
What is the wavelength's peak?Peak Wavelength - The maximum wavelength at which a light source's radiometric emission spectrum is observed is referred to as the peak wavelength. Simply put, it represents photo-detectors rather than the human eye's perception of any emission from the light source.
What can we infer from the peak wavelength?The temperature can be calculated using the Wien displacement law and the peak wavelength. On a chromaticity diagram, the variation in apparent hue of stars at various temperatures can be traced.
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Which of the following activities would most likely result in the greatest degree of muscle soreness 12-24 hours post-exercise? (Assume the subject is new to this exercise)
Group of answer choices
1.Running 6 mph on a 10% incline (uphill)
2.running 7 mph on a flat road
3.running 6 mph on a 12% decline (downhill)
4.there would be identical degrees of soreness because it is new.
The activity that would most likely result in the greatest degree of muscle soreness 12-24 hours post-exercise is 4. there would be identical degrees of soreness because it is new.
People of every age and genders will have sore muscle mass. When you attempt a brand new bodily pastime or transfer up your exercising routine, you could enjoy delayed-onset muscle soreness (DOMS). Muscle aches can also additionally come on six to twelve hours after a exercising and last as long as forty eight hours. You experience ache because the muscle mass heal and get stronger. Sore muscle mass after exercising -It can have an effect on humans of all health levels, especially after attempting a brand new pastime or pushing your self a chunk tougher than usual. Usually your muscle mass will prevent aching in 2 to five days and also you may not want any clinical attention.
Thus, option 4 is the correct choice.
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Given below is a rectangle ABCD, with side AB parallel to the z-axis.
Find the equation of line BD.
-
B (3, 2)
Answer:
x = 3
Step-by-step explanation:
You want the equation of vertical line BD that includes point B(3, 2).
Equation of a lineThe equation of a vertical line is ...
x = c . . . . . . for some constant c
Since we want the line to go through a point B(3, 2) with x-coordinate 3, that is the value the constant must have.
x = 3 . . . . . the equation of line BD
__
Additional comment
Ordinarily, this rectangle would be named ABDC, with the vertices named in order around the figure.
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The two figures would be similar if the value of x is 31 mm. Thus option D.
On comparison of two or more shapes, they will only be similar if they all have a set of common corresponding properties. These properties may be due to their corresponding length of sides, or measure of internal or external angles.
To determine the value of x that would make the shapes to be similar, compare the corresponding sides of the shapes.
So that we have;
[tex]\frac{14.5}{29}[/tex] = [tex]\frac{15.5}{x}[/tex]
make x the subject of the formula
x = [tex]\frac{29*15.5}{14.5}[/tex]
= 31
x = 31 mm
The value of x that would make the two figures similar is 31 mm.
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Is 12 a solution to the inequality? x > 12
Answer:
Step-by-step explanation:
No because if the inequality sign had a line under it, it would mean that it could be equal to, but because it doesn't have a line under the inequality sign it isn't a solution.
Answer:
No
Step-by-step explanation:
12 is not a solution to this inequality >12 means all values greater than 12. Since 12 is not greater than 12, the answer is no.
SELF 5.32 The quality control manager of Marilyn's Cook-
Test ies is inspecting a batch of chocolate-chip cookies that
has just been baked. If the production process is in control, the
mean number of chocolate-chip parts per cookie is 6.0. What is the
probability that in any particular cookie being inspected
a. fewer than five chocolate-chip parts will be found?
b. exactly five chocolate-chip parts will be found?
c. five or more chocolate-chip parts will be found?
d. either four or five chocolate-chip parts will be found?
5.33 Refer to Problem 5.32. How many cookies in a batch of 100
should the manager expect to discard if company policy requires
that all chocolate-chip cookies sold have at least four chocolate-
chip parts?
Answer: This question is most likely assuming a poisson distribution; it is impossible to compute without some distribution clarified, as otherwise we don't have applicable information.
Poison distribution is:
(λke-k) / k!
Where k is the number of outcomes you are looking for, and λ is the accepted average number of outcomes. So, λ is 6 for this example, and we are looking for values of k to use.
Solving problem b is simply substituting the value.
Prob of 5 parts: (65e-5) / 5!, using a calculator and working it out, this approximates to 0.437.
Solving problem a can be used for c; to get a, do the above equation 5 times for k = 0, 1, 2, 3 and 4, and add them all together. Though somewhat tedious, this would lead to the solution. To get part c, you would use the property of complements:
The cumulative probability here would be 1 - (total prob of all scenarios with k = 0, 1, 2, 3, 4, 5). You can get that total probability by adding the answers to part a and b together.
Finally, regarding part d, the above work can be redone with a new formula, now (λke-k) / k! would have λ as 5. This would reduce the answer for a, but increase it for b and c, which you can verify by running the calculations.
Step-by-step explanation:
Explain how the associative property can be used to solve this problem.
8/9 / 7/5 x 3/16
The associative property states that the way in which numbers are grouped in an arithmetic expression does not affect the result of the computation. For example, in the expression (a + b) + c, the addition of a + b can be done first, and then added to c, or the addition of b + c can be done first and then added to a. The result will be the same either way.
In the expression you provided, the associative property can be used to group the terms in the following way:
(8/9 / 7/5) x 3/16
= (8/9 x 3/16) / (7/5)
Then, the division and multiplication operations can be carried out in the order that they appear, from left to right:
= (24/144) / (7/5)
= (1/6) / (7/5)
Finally, the division operation can be carried out to obtain the final result:
= (5/42)
Answer:
[tex]\frac{5x}{42}[/tex]
Step-by-step explanation:
8/9/7/5 = 8 · 5
9 x 7
Apply the fraction rule
8 x 5x x 3
9 x 7 x 16
cancel 8 x 5x x 3 5x
9 x 7 x 16 : 3 x 7 x 2
= 5x
3 x 7 x2
= 5x
3 x 7 x 2
Multiply the numbers 3 x 7 x 2 = 42
= 5x
42
Find f’(x) and simplify
Answer:
1. A
2. Simplification: (not sure)
[tex] \frac{ - 3x {}^{5} + 6x { }^{2} - 4x - 15 }{9x {}^{2} - 12x + 4 } [/tex]
Students arrive at the administrative services office at an average of one every 6 minutes, and their requests take, on average, 5 minutes to be processed. The service counter is staffed by only one clerk, judy gumshoes, who works eight hours per day. assume poisson arrivals and exponential service times. Required: (a) What percentage of time is Judy idle? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) (b) How much time, on average, does a student spend waiting in line? (Round your answer to the nearest whole number.) (c) How long is the (waiting) line on average? (Round your answer to 2 decimal places.) (d) What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Round your answer to 3 decimal places.)
There is 0.17% of the time is Judy idle.
It will take 25 minutes on average, does a student spend waiting in line.
The waiting line on average is 4.1 customers.
The probability that an arriving student will find at least one other student waiting in line is 0.68.
Given students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take on average 5 minutes to be processed.
The service counter is staffed by only one clerk, Judy gumshoes, who works eight hours per day.
Assume Poisson arrivals and exponential service times.
ProbabilityIt was said in the question Students arrive at the Administrative Services Office at an average of one every 15 minutes which means that:
λ = 60/6 = 10customers/hr
μ = average of 5 minutes = 60/5 = 12customers/hr
1) What percentage of time is Judy idle?
The percentage when Judy was idle = 1- λ/μ = 1- 0.83= 0.17
%Service time = 0.83
%idle time = 0.17
There is 0.17% of time is Judy idle.
2) How much time, on average, does a student spend waiting in line?
A student spends waiting in line then we make use of the formula below:
λ /μ(λ-μ )
= 0.41 × 60
= 25 minutes
It will take 25 minutes on average, does a student spend waiting in line.
3) How long is the waiting line on average?
To calculate How long the waiting line is on average;
average waiting time x arrival rate = 0.41hrs x 10 customers/hr = 4.1 customers
The waiting line on average is 4.1 customers.
What is the probability that an arriving student will find at least one other student waiting in line?
P1( Probability of having a customer to attend to) = 0.17 x 0.83 = 0.141
P2( Probability of having 2 customer to attend to) = 0.17 x 0.83 x 0.83 = 0.117
The probability of finding at least one customer = 1 -[ po + p1]
= 1 - 0.17 - 0.141 = 0.68
The probability that an arriving student will find at least one other student waiting in line is 0.68.
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if the lengths of the legs of a right triangle are labelled x and y, and if its hypotenuse length is labelled z, then the pythagorean theorem states
The Pythagorean for the triangle with a length of two legs x and y and the hypotenuse length as z is z²=x²+y².
The perpendicular, base (adjacent), and hypotenuse (opposite) are the names of the triangle's three sides. Perpendicular forms a right angle with the triangle base. The hypotenuse is the greatest side opposing the right angle (90 degrees) of a triangle. According to the Pythagorean Theorem, the square of the length of the hypotenuse will always result from adding the squares of the lengths of two legs of a right-angle triangle.
Given the length of one leg is x and the length of another leg is y. The length of the hypotenuse is z. Then, by the Pythagorean Theorem, z²=x²+y².
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Rate. Base
Social Security 6.20%. $128,400
Medicare. 1.45. No base
A. $74.40
B. $744
C. $72.40
D. $47.40
33. Based on the schedule shown, calculate Social Security tax for Betsy at $1,200
Answer: The correct answer is therefore A) $74.40.
Step-by-step explanation: To calculate Social Security tax for Betsy at $1,200, we need to find the amount of tax that is due on that amount of income. According to the schedule, Social Security tax is applied at a rate of 6.2% on income up to $128,400. Therefore, the amount of tax due on $1,200 of income would be $1,200 x 6.2% = $<<12006.2.01=74.4>>74.4.
How to write the fractions in its simplest form?
Step-by-step explanation:
---------------------
MaryLou made some money on her investments. She made twice as much money on her investment at 8% than on her 5% investment. In all, she made $600 in one year. How much did she have invested at each percentage rate?
Answer:
{1073, 6829}
Step-by-step explanation:
PLEASE HELP: How does the graph of f(x) = |x| compare with the graph of g(x) = −2|x|? Select all that apply.
The graph of the function f(x) = |x| and g(x) = −2|x| is attached below, the function f(x) = |x| is always positive whereas the function g(x) = −2|x| is always negative.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
The given functions are,
f(x) = |x| and g(x) = −2|x|
Here, the graph of the modulus function f(x) = |x| is always on the positive y-axis as the range of the function is always positive,
Whereas, the graph of g(x) = −2|x| is always on the negative y-axis, as the range of the function is negative.
Put the values of x in the function, and calculate the value of the function mark the values of x in the x-axis and the values of the function in y and then join all the points to get the graph.
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a) If 3/5 of the 595 students are seventh graders, and 5/8 of them participated in the competition, about how many seventh graders participated in the competition? Describe the process you used to find your answer. (2 points)
b) If 2/5 of the 595 students are eighth graders, and 7/8 of them participated in the competition, about how many eighth graders participated in the competition? Describe the process you used to find your answer. (2 points).
c) About how many total students participated? Describe the process you used to find your answer. (2 points) Using the process shown above, I added 206 and 215 to get 421 total participants
PLEASE NOW!!!
The number of students who participate in competition for each grade are 223 and 208 and their sum is 431.
What is a fraction?A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.
The number a is called as the numerator and b is the denominator.
(a) The total number of students are 595.
Then, the number of students in seventh grade is 3/5 × 595 = 357
Now, the number of students participated in competition is given as,
5/8 × 357
⇒ 223.125
Since, the number of students cannot be a decimal, it is taken as 223.
(b) The number of students in eighth grade is 2/5 × 595 = 238
Now, the number of students participated in competition is given as,
7/8 × 238
⇒ 208.25
Since, the number of students cannot be a decimal, it is taken as 208.
(c) The total number of students participating in competition is given as,
⇒ 223 + 208 = 431
Hence, the required number of students for 7th and 8th grade and their sum are given as 223, 208 and 431 respectively.
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For the following exercises, determine whether the vector field is conservative and, if it is, find the potential function. 106. F(x, y) = (6x + 5y)i + (5x + 4yj
f(x, y) = 3x + 2y + C
To know if a vector field is conservative, we have to check if it is the gradient of a scalar function.
The gradient of the function f(x, y) is given by
∇f(x, y) = (∂f/∂x, ∂f/∂y)
If a vector field F(x, y) is the gradient of a scalar function f(x, y), then the following conditions must be satisfied:
F(x, y) = ∇f(x, y)
Whether a given vector field satisfies this condition can be checked by taking the partial derivative with respect to x and y.
∂F/∂x = ∂(6x + 5y)/∂x = 6
∂F/∂y = ∂(5x + 4y)/∂y = 4
The partial derivative of a given vector field is the constant, the gradient of the scalar function. So vector fields are conservative and we can find a potential function f(x, y) such that F(x, y) = ∇f(x, y).
To find the potential function, we can integrate the partial derivative of F(x, y) with respect to x and y.
f(x, y) = ∫∂F/∂xdx + ∫∂F/∂ydy
= ∫6dx + ∫4dy
= 3x + 2y + C
where C is the constant of integration. So the potential function for a given vector field is
f(x, y) = 3x + 2y + C
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The angles of a triangle have measures of 34 degrees, 71 degrees, and 75
degrees. Classify the triangle by the angle measures and by sides.
a. By angle:_____
b. By side:______
Answer:
a. acute triangle (all the angles measure less than 90 degrees)
b. scalene triangle (none of the angles are congruent, so none of the sides are congruent)
On a recent restaurant survey, 45% of customers preferred sport drinks over soft drinks. Of those who preferred sport drinks, 58% also preferred coffee over tea, while 46% of those who enjoy soft drinks preferred tea over coffee.
What percentage of all customers prefer soft drinks and coffee? Round your answer to the nearest whole percentage.
19%
30%
46%
58%
The percentage of all customers who prefer soft drinks and coffee if 45% of customers preferred sports drinks over soft drinks, is 58%, so option D is correct.
What is set?A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter.
Given:
45% of customers preferred sports drinks over soft drinks, n(S) = 45%,
58% also preferred coffee to tea, n(C) = 58 %
46% of those who enjoy soft drinks preferred tea to coffee, n(C∩S) = 46%
Calculate the percentage of all customers who prefer soft drinks and coffee as shown below,
n(C∪S) = n(S) + n(C) - n(C∩S)
n(C∪S) = 45 + 58 - 46
n(C∪S) = 58%
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Answer:
30%.
Step-by-step explanation:
In simple terms, you have to divide 100/55, and 100/54, and multiply the two answers, which leaves you with 0.297. rounding to 0.3, which is 30%
Each page of a top-secret report on aliens requires 2 KB of space in digital format. What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds 4*10^6 KB?
Write your answer in scientific notation, and round to one decimal place. ______ pages
The maximum number of pages the report can have in scientific notation is equal to 2.0×10⁶ pages.
Scientific Notation is the expression in which numbers are written in the powers of 10 so that their expression can be used in calculation and also it makes calculation easy. To find the maximum number of pages the report can have, we need to divide the size of the USB drive, which is 4×10⁶ KB, by the size of each page, which is 2 KB/page. Doing this gives us:
4×10⁶ KB / 2 KB/page = 2×10⁶ pages
Rounding to one decimal place gives us: 2,000,000.0 pages
So, the maximum number of pages the report can have is 2,000,000.0 pages. In scientific notation, this is: 2.0×10⁶ pages.
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our new magazine initially sells 400 copies per month. research indicates that a vigorous advertising campaign could increase sales by 30% each month if our market were unlimited. but research also indicates that magazine sales in our area are unlikely to exceed 2000 per month. make a logistic model of projected magazine sales. (use t as your variable. round b to three decimal places.)
The logistic model of the projected magazine sales is P = e¹⁰⁰⁰/1+e¹⁰⁰⁰
What is meant by logistic model?
In math, logistic model refers a statistical analysis method to predict a binary outcome, such as yes or no, based on prior observations of a data set.
Here we have given that our new magazine initially sells 400 copies per month. research indicates that a vigorous advertising campaign could increase sales by 30% each month if our market were unlimited. but research also indicates that magazine sales in our area are unlikely to exceed 2000 per month.
Here we need to make a logistic model of projected magazine sales.
As per the formula of logistic model, while we looking into the given question, we identified the values,
a = 400
x = 30% => 0.3
b = 2000
Then the logistic model of the given situation is written as,
=> P = e⁴⁰⁰⁺⁰°³ˣ²⁰⁰⁰/ 1 + e⁴⁰⁰⁺⁰°³ˣ²⁰⁰⁰
=> P = e¹⁰⁰⁰/1+e¹⁰⁰⁰
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