Answer:
The correct answer is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
If she has 6 classes, then the total hours of classes are:
[tex]\frac{6}{1}[/tex] · [tex]\frac{7}{6}[/tex] = [tex]7[/tex]
[tex]7[/tex] · [tex]\frac{1}{2}[/tex] - [tex]7[/tex] = [tex]\frac{1}{2}[/tex]
Suppose an annuity pays 4% annual interest, compounded annually. If you invest $4,500 in this annuity annually for 10 years, what percentage of the total balance is interest earned? Round your answer to the nearest hundredth of a percent. Do NOT round until you have calculated the final answer.
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]
so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.
so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]
Valentino's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found. Type of Crust Number Sold Thin crust 293 Thick crust 216 Stuffed crust 174 Pan style 195 Based on this information, of the next 3000 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do not round any intermediate calculations. pizzas X
Answer:
1120
Step-by-step explanation:
Given the information below:
The Relative Frequency of selling a pan style pizza =
Therefore, if Valentino's Pizzeria were to sell 4000 pizzas, the expected number of Pan style pizza sold will be:
Number of Pan Style Pizza Sold = Relative Frequency of pan Style Pizza Purchase X Total Number of Sales
They should expect to sell 1120 pan Style pizzas.
Find the equation of Straight line equally indined to the axes and cutting off an intercept 0-2 from the y-axis
The equation of the line is y = x - 2.
What is the equation of the line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
We have,
y-intercept(c) = −2 and
the line is equally inclined to the axis i.e., the same angle to the x-axis and y-axis(say)=θ
but the angle between the axes is 90°
2θ = 90° ⇒ θ = 45°
As slope and y-intercept are given.
The equation of a line is y = mx + c
c = -2 and
m = tan45°
as the line is equally inclined to the axes.
c = -2 and m = 1
Hence, the equation of the line is y = x - 2.
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Two functions, A and B, are described as follows: Function A y = 8x + 3 Function B The rate of change is 1 and the y-intercept is 4. How much more is the rate of change of function A than the slope of function B? (5 points) Question 12 options: 1) 1 2) 7 3) 8 4) 9
i need it now
The rate of change is 7 more of function A than the slope of function B.
What is meant by slope?Slope is calculated as the ratio of "vertical change" to "horizontal change" between any two points on a line, or any two points. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.
Since y=8x+3,
The rate of change in equation A is equal to the slope m m=8.
The rate of change, m=1, is given in equation B.
y=mx+ is the solution to equation B.
By substituting the values we get,
y=x+4
Calculate the difference between the rates of change of function A and function B.
8-1=7
Therefore, the rate of change is 7 more of function A than the slope of function B.
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The doubling period of a bacterial population is 15 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0 ?
Find the size of the bacterial population after 3 hours.
The doubling period of a bacterial population is 15 minutes. the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.
How to find the initial population?y = total amount of bacteria
a = initial bacterial at time 0
b = growth factor
t=120 minutes =15 minutes 8 times
So,
t=8
90000 = a (2)^8
90000 = a (256)
90000/256 = a
351.56 = a (initial population)
Equation:
y = 351.56 (2)t
After 3 hours (15 minutes 10 times), or at t = 10
y = 351.56 (2)^10
y= 359,997.44
Therefore the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.
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A password is required to log into a system that only recognizes numbers and letters
of the alphabet (not case sensitive). You want to create a password using 7 numbers
or letters, but cannot reuse any of them.
How many different passwords are possible?
There are total 42,072,307,200 different passwords are possible .
What are combinations ?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
Combinations can be confused with permutations. However, in permutations, the order of the selected items is essential. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.
Given: A password is required to log into a system that only recognizes numbers and letters of the alphabet
Since , there are total 26 letters and 10 numbers are possible that can be used to create a password . Hence , there are 36 character in total to be used.
Also , repetition of character is not allowed. Therefore , the chance of selecting every character decreases by 1 in comparison to its preceding character .
Chance of selecting first character = 36
Chance of selecting second character = 35
Similarly for seventh = 30
Thus , different passwords that are possible using 7 numbers or letters, without reusing any of them = 36*35*34*33*32*31*30 = 42,072,307,200 .
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Find the critical value(s) for a left-tailed z-test with a = 0.09. Include a graph with your answer.
Answer:-1.34
Step-by-step explanation:
8. The Pinkerton Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $50 million on a large-scale, integrated plant that will provide an expected cash flow stream of $8 million per year for 20 years. Plan B calls for the expenditure of $15 million to build a somewhat less efficient, more Labor-intensive plant that has an expected cash flow stream of $3.4 million per year for 20 years. The firm's cost of capital is 10%. a. Calculate each project's NPV and IRR. (4 marks) b. Set up a Project A by showing the cash flows that will exist if the firm goes with the large plant rather than the smaller plant. What are the NPV and the IRR for this Project A? (3 marks) c. Give a logical explanation, based on reinvestment rates and opportunity costs, as to why the NPV method is better than the IRR method when the firm's cost of capital is constant at some value such as 10%. (3 marks)
What is a NPV net present value ?
The difference between the current value of cash inflows and withdrawals over a period of time is known as net present value (NPV). To evaluate the profitability of a proposed investment or project, NPV is used in capital budgeting and investment planning.
Using the appropriate discount rate, computations are performed to determine the current value of a stream of future payments, or NPV. Projects that have a positive NPV are generally worthwhile pursuing, whereas those that have a negative NPV are not.
The current worth of a stream of payments from a business, project, or investment is determined using net present value (NPV).You must predict the timing and size of future cash flows in order to determine NPV, and you must choose a discount rate that is equal to the least allowable rate of return.Your cost of capital or the rewards offered by substitute investments with equivalent risk may be reflected in the discount rate.Positive NPV indicates that the rate of return on a project or investment will be higher than the discount rate.1.
NPV of project A = [tex]-50+\frac{8}{/(1.10)^1} +\frac{8}{(1.10)^2} \frac{8}{(1.10)^3} +\frac{8}{(1.10)^4} +\frac{8}{(1.10)^5} +\frac{8}{(1.10)^6} +\frac{8}{(1.10)^7} +\frac{8}{(1.10)^8} +\frac{8}{(1.10)^9} +\frac{8}{(1.10)^1^0} +\frac{8}{(1.10)^1^1} +\frac{8}{(1.10)^1^2} +\frac{8}{(1.10)^1^3} +\frac{8}{(1.10)^1^4} +\frac{8}{(1.10)^1^5} +\frac{8}{(1.10)^1^6} +\frac{8}{(1.10)^1^7} +\frac{8}{(1.10)^1^8} +\frac{8}{(1.10)^1^9} +\frac{8}{(1.10)^2^0}[/tex]
=$18.11
2.
NPV of project B = [tex]-15+\frac{3.4}{/(1.10)^1} +\frac{3.4}{(1.10)^2} \frac{3.4}{(1.10)^3} +\frac{3.4}{(1.10)^4} +\frac{3.4}{(1.10)^5} +\frac{3.4}{(1.10)^6} +\frac{3.4}{(1.10)^7} +\frac{3.4}{(1.10)^8} +\frac{3.4}{(1.10)^9} +\frac{3.4}{(1.10)^1^0} +\frac{3.4}{(1.10)^1^1} +\frac{3.4}{(1.10)^1^2} +\frac{3.4}{(1.10)^1^3} +\frac{3.4}{(1.10)^1^4} +\frac{3.4}{(1.10)^1^5} +\frac{3.4}{(1.10)^1^6} +\frac{3.4}{(1.10)^1^7} +\frac{3.4}{(1.10)^1^8} +\frac{3.4}{(1.10)^1^9} +\frac{3.4}{(1.10)^2^0}[/tex]
= $13.95
Use function IRR in excel as = IRR(-50,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8)
= 15.03% is the IRR for A.
Use function IRR in excel as = IRR(-15,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4)
= 22.26% is the IRR for B.
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Expand the log completely
Answer:
1/3log₂(x) +1/3log₂(y) +1/3log₂(z)
Step-by-step explanation:
You want the complete expansion of ...
[tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}[/tex]
Relevant rulesThe rules of logs and exponents relevant to this expansion are ...
[tex]\log_b{(xy)}=\log_b{(x)}+\log_b{(y)}\\\\\log_b{(x^a)}=a\cdot\log_b{(x)}\\\\\sqrt[n]{\vphantom{b}a}=a^{\frac{1}{n}}[/tex]
ExpansionApplying these rules to the given expression, we get ...
[tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}=\log_2{((xyz)^{\frac{1}{3}})}=\dfrac{1}{3}\log_2{(xyz)}\\\\=\boxed{\dfrac{1}{3}\log_2{(x)}+\dfrac{1}{3}\log_2{(y)}+\dfrac{1}{3}\log_2{(z)}}[/tex]
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Answer:
a. 18.5 million
b. 2002
Step-by-step explanation:
Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.
Population in 2000The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.
A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5
The population in 2000 was 18.5 million.
Year of 26.6 millionWe can solve for t to find the year in which the population reached 26.6 million:
26.6 = 18.5·e^(0.1708t)
26.6/18.5 = e^(0.1708t)
ln(266/185) = 0.1708t
t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000
The population will reach 26.6 million in the year 2002.
__
Additional comment
The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.
(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)
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Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 8 years. Assume that money is worth 5.4%, compounded quarterly. (Round your answer to the nearest cent.)
Present Value of Annuity = $4,000 × 26.1948 = $104779.2
What is a present value?
The worth of an anticipated revenue stream assessed as of the valuation date is known as the present value in the fields of economics and finance.
Here, we have
Where , Annuity Amount = $4,000
n = No. of periods = 8 years × 4 quarters per year = 32 periods but since the first payment is at beginning of the quarter,
Then, n = 31 when considered for PVAF
r = 5.4% / 4 quarters = 1.35%,
Present value of Annuity = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n, r)
PVAF(n₀,r) when the first payment is at beginning of n i.e.
n₀ = 1 + { [1-(1+r)^ -n ]/r }
= 1 + { [1-(1+0.0135)^ {-31}]/0.0135 }
= 1 + [ (1 - 0.65987 ) ] / 0.0135]
= 1 + 25.1948
= 26.1948
PVAF(32,35%) = 26.1948
Hence, Present Value of Annuity = $4,000 × 26.1948 = $104779.2
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Write a quadratic function to model the graph to the right.
f(x)=____
f(x) = x² + 2x + 2
Solution:
Given vertex (1,1)
a = 1
Formula of quadratic equation is :
y = a(x + b)² + c
where, a =1, x=x, b = x1, c = y1
Substituting the values in the equation, we get
y = x² + 2x + 2
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A quadratic function to model the graph to the right is f(x) = x² + 2x + 2
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Solution:
Given vertex (1,1)
a = 1
Formula of quadratic equation is :
y = a(x + b)² + c
where, a =1, x=x, b = x1, c = y1
Substituting the values in the equation, we get
y = x² + 2x + 2
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Book b is twice as long as book a. book c is 30 pages longer then book b. together the three books have 280 pages.
I just need help with question number 10
It has to be solved algebraically Can someone please help me with this problem
Answer:
book c has 130 pages
Step-by-step explanation:
let book a = x pages
book b = 2x
book c = 2x + 30
according to the question:
x + 2x +2x + 30 = 280
5x + 30 = 280
5x = 280-30
5x = 250
x = 250/5
x = 50
thus book c has 2(50) + 30 = 130 pages
There are five questions listed below. Each question includes the quantity 22. Match the 22 in each question on the left to which part of the problem it represents on the right -- the base, percent, or amount. Some answer options on the right will be used more than once.
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.Using concepts of percentage,
3 is 16.63% of 22.
22 is 13.41% of 164.
0.88 is 4% of 22.
8 is 22% of 36.36.
1.1 is 5% of 22.
A percentage is a number or ratio expressed as a fraction of 100.
Let 3 be x% of 22.
=x/100*22=3
=x=3*100/22=13.63
3 is 13.63% of 22.
Let 22 be y % of 164.
=y/100*164=22
=y=22*100/164=13.41
13.41% of 164 is 22.
4% of 22 = 0.88
=4/100*22=0.88
Let 8 is 22% of z.
=22/100*z=8
=8*100/22=36.36
5% of 22 = 1.1
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A bag contains 7 green marbles, 3 yellow marbles and 10 black marbles. If a green marble is drawn, you win $20. If a yellow marble is drawn, you win $30. If a black marble is drawn, you lose $15. It costs $1 to play. What are you expected winnings over time?
Step-by-step explanation:
chances of winning $20=7/20
chances of winning $30=3/20
chances of winning $15=1/2
Equation that passes through 4,-3 and -4,7
Need help!!!! with geomtry
Answer: n=11 m=3
Step-by-step explanation:
2n+2=3n-9
n=11
3m+6=n+4
3m+6=11+4
3m+6=15
3m=9
m=3
Which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answer:
c
...................
Answer:
the answer is the option C
As part of a school science project, Jacob bought some bulbs for a total of $18. The cost of each bulb was $3. How many bulbs did Jacob buy?
Step One: Write an equation with the variable x
Step Two: Solve your equation.
Equation:
Solution: x=
Place the numbers in order from greatest to least 1 3/4 , 5.25 , -5/2 , -8.345
Answer: 5.25>1 3/4>-5/2>-8.345
Step-by-step explanation:
Question 12 of 25
Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Boys
Girls
Total
Play a sport
95
76
171
Do not play a
sport
45
59
104
Total
overe pot independent because Nair) 0.10
140
135
275
Are being a girl and playing a sport independent events? Why or why not?
Being a female and participating in sports are independent events for the provided data because P(girl) = P(girl participates in sports)
What are independent events?These are the occurrences that are independent of other occurrences.
Occurrences A and B are independent events when the likelihood of one occurring is unaffected by the occurrence of the other.
Probability of independent events formula:
"P(A∩B) = if A and B are independent occurrences P(A).P(B)
What exactly is probability?Finding the chance that an event will occur is the focus of this area of mathematics."
P(A) = n(A)/n(S), where n(A) is the number of positive outcomes and n(S) is the total number of possible outcomes for an event A.
For given question,
We have been given a table that shows the results broken down by gender.
Play sports Do not play sports Total
Boy 95 45 140
Girl 76 59 135
Total 171 104 275
Using the definition of probability:
⇒ P(girl) = Number of girls/ Number of students
⇒ P(girl) = 135/275
⇒ P(girl) = 0.49 ....................(1)
Now we find the probability of girls that play a sport.
Using the definition of probability:
P(girl plays a sport)
= Number of girls who plays a sport/ number of students who plays a sport
= 76/ 171
= 0.44 ......................(2)
From (1) and (2),
P(girl) = P(girl plays a sport)
Thus, being a girl and playing a sport are Independent events.
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5. Find all the solutions to the equation x²e^x– 2xe^x – 3e^x =0.
Answer:
[tex]x = 3, -1[/tex]
Explanation:
math
I need an answer pls
Answer:
y=3x^2 - 2x + 5
Step-by-step explanation:
The easiest way to find the answer to this question would be to just plug the different x values into the equations. If you take the equations and plug in x and it gives out the correct f(x) value, then the answer would be correct.
For example, plugging -3 into y=3x^2 - 2x + 5 gives you 10. Plugging in 0 gives 5. Plugging in 2 gives 13.
What is the equation of the line that is normal to the curve y^2+Inx=19 at the point (e^3,-4)
The equation of the line that is normal to the curve y² + ln(x) = 19 at the point (e³, -4) is given as follows:
y + 4 = -8e³(x - e³).
How to obtain the equation of the line normal to the curve?The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:
y - y' = m(x - x').
The derivative of the function is found applying implicit differentiation, as follows:
2y dy/dx + 1/x = 0
dy/dx = -1/(2xy).
At x = e³, y = -4, the numeric value of the derivative is given as follows:
dy/dx = e^(-3)/8.
The normal line is perpendicular to the tangent line, hence it's slope is calculated as follows:
m x e^(-3)/8 = -1.
m = -8e³.
Then the equation of the line normal to the curve at the point is given as follows:
y + 4 = -8e³(x - e³).
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Decide whether a line with the given slope slants upward or downward or is horizontal or vertical.
m = ½
Answer: Slants upwards.
Step-by-step explanation:
This is a positive slope, so the line with this given slope will slant upwards. For every increase of one in y, there is a positive change of 2 in x. See attached for a visual example, if the graph was y = ½x.
3. For the graph above, what is the approximate y-value of the point of intersection?
0-1
04
03
02
Answer: 02
Step-by-step explanation: w
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After 25 years, Sample left will be 100g if nearest hundred...ig...
You need a car for 5 days. A car rental company offers customers two rate plans. With Plan A, the
customer pays $25 per day plus $0.15 per mile driven. With Plan B the customer pays $150 for the week,
even if the car is returned early, with no per-mile charge. Which payment plan would you select if you
plan to drive a total of 100 miles?
Suppose the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points. It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students. Find what scores should be assigned A’s and B’s.
82.9 score should be assigned for A’s and 74.4 should be assigned for B’s
In this question we have been given the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points.
It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students.
We need to find what scores should be assigned A’s and B’s.
μ = 70, σ = 10
Using standard normal table,
P(X > x) = 10%
P(X > x) = 0.10
1 - P(X ≤ x) = 0.10
P(X ≤ x) =1−0.10
=0.90
Using standard normal z table,
(x - 70)/10 = 1.29
x = 82.9 (score for A’s)
Now, P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)
P(X>x) = 0.33
1 - P(X ≤ x) = 0.33
P(X ≤ x) = 1 - 0.33
= 0.67
Using standard normal z table,
(x - 70)/10 = 0.44
x = 74.4 (score for B’s)
Therefore, the score for A = 82.9 and the score for B = 74.4
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Target charges $4.40 for 8 sodas. Walmart charges $7.08 for 12 sodas. Which store has
the best unit price? How much cheaper is it?
Answer:
Target
Step-by-step explanation:
$4.40/8 is 0.55 and $7.08/12 is 0.59