Answer:
Because of absence of options, I have listed statements that are true; according to the model.
Step-by-step explanation:
To answer this, we find all possible explanations to the model. First, we know that:
X = time in office (in days)
Y = approval rating (in percentage)
The constant term in the model is 70
So the true statements that can be derived are:
(A) Y is inversely related to X. This is obvious because of the difference in sign of the coefficient of Y and that of X.
The coefficient of Y is +1
The coefficient of X is -0.01
Y has a positive coefficient while X has a negative coefficient.
The inverse relationship hence implies that the more days the politician spends in office, the less his percentage approval rating (and vice versa)!
Testing;
If X = 10 days, Y = 69.9%
If X = 20 days, Y = 69.8%
If X is 30 days, Y = 69.7%
(B) The rate at which approval rating drops is very slow; compared to the increase in number of days in office. A 10 day increase in number of days in office only results in a 0.1 or 10% decrease in percentage approval ratings.
(C) The longer a politician stays in office, the less his approval rating.
(D) The percentage approval rating is greatly influenced or increased by the constant term 70
The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, what warranty should be provided so that the company is replacing at most 5% of their toasters sold?
Answer:
A warranty of 4.32 years should be provided.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 5.8, \sigma = 0.9[/tex]
What warranty should be provided so that the company is replacing at most 5% of their toasters sold?
The warranty should be the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 5.8}{0.9}[/tex]
[tex]X - 5.8 = -1.645*0.9[/tex]
[tex]X = 4.32[/tex]
A warranty of 4.32 years should be provided.
The mean gross annual incomes of certified welders are normally distributed with the mean of $26,589 and a standard deviation of $2,659. The ship building association wishes to find out whether their welders earn more or less than $26,589 annually. The alternate hypothesis is that the mean is not $26,589. Which of the following is the alternate hypothesis? a. H1: <$26,589 b. H1: -$26,589 с. HI:T-826,589 d. Hi: -326,589
Answer:
And based on the claim the system of hypothesis are:
Null hypothesis: [tex] \mu = 26589[/tex]
Alternative hypothesis: [tex] \mu \neq 26589[/tex]
And the best alternative would be:
b. [tex]H_1: \neq $26,589[/tex]
Step-by-step explanation:
For this case we want to test the hypotheis that the true mean is different from 26859. We have the following info given:
[tex] \bar X = 26589[/tex] represent the sample mean
[tex] \sigma =2659[/tex] represent the population deviation
And based on the claim the system of hypothesis are:
Null hypothesis: [tex] \mu = 26589[/tex]
Alternative hypothesis: [tex] \mu \neq 26589[/tex]
And the best alternative would be:
b. [tex]H_1: \neq $26,589[/tex]
Find the surface area of the rectangular prism above using its net below
Answer:
82cm²
See explanation below
Step-by-step explanation:
The question is incomplete without the diagram of the rectangular prism and it's dimensions. We are to determine the surface area of the rectangular prism using it's net.
I would show you how to determine it using diagram below.
Find attached the diagram used in solving the question as well as the net obtained from the diagram.
Solution:
A net diagram is a 2-dimensional representation of a 3-dimensional solid in which case the solid is unfolded.
The net gives the total area of the sides and faces of the 3 dimensional figure.
The units of the diagram used are all in cm.
Using net diagram:
Area A = Area B = length × height = hl
Area C = Area D = width × length= wl
Area E = Area of F = height × width = hw
surface area of the rectangular prism = 2(wl + hl + hw)
w = width = 2cm
l= length = 7cm
h = height = 3cm
Insert the values in the formular
A = 2(2×7 + 3×7 + 2×3)
A = 2(14+21+6)
A = 2(41) = 82cm²
Surface area of the rectangular prism = 82cm²
Answer: a picture would help
Step-by-step explanation:
lol
Please answer this correctly
Answer:
t=13
Step-by-step explanation:
the ratio of the shorter sides is t/4 and the ratio of the longer sides is 26/8 so t=26×4/8=104/8=13
Answer: t=13in
Step-by-step explanation: As you can see in the smaller square, the number 4 is in the place of the letter t. Which means that the width (4) is half of the longitud (8). Therefore, in the bigger square all you need to do it divide the longitud (26) by two, to find the width (t). Which is equal to 13in.
I hope you found this answer helpful! If you did, give it a five-star rating and I thanks! It would really mean a lot.
(Even a brainliest if you feel like it ;D!)
How do I do this problem? Two similar pyramids have matching sides in the ratio 5:7. If the surface area of the larger pyramid is 441 cm^2. find the surface area of
the smaller pyramid.
S Area
cm²
Answer:
Surface area of the smaller pyramid will be 225 cm²
Step-by-step explanation:
Two similar pyramids have their matching or corresponding sides in the ratio of 5 : 7.
In other words,
[tex]\frac{\text{One side of the smaller pyramid}}{\text{One side of the larger pyramid}}[/tex] = [tex]\frac{5}{7}[/tex]
Therefore, [tex]\frac{\text{Surface area of the smaller pyramid}}{\text{Surface area of the larger pyramid}}[/tex] = [tex](\frac{5}{7})^{2}[/tex]
[tex]\frac{S_{\text{small}}}{S_{\text{large}}}=\frac{25}{49}[/tex]
[tex]\frac{S_{\text{small}}}{441}=\frac{25}{49}[/tex]
[tex]S_{\text{Small}}=\frac{441\times 25}{49}[/tex]
= 225 cm²
Therefore, surface area of the smaller pyramid will be 225 cm².
what number is to be multiplied with 1/3 to get 1/21
Answer:
1/7
Step-by-step explanation:
Since we do not know the number let us use the alphabet A to represent the unknown number
A × 1/3= 1/21
A/3= 1/21
Cross multiply both sides
A×21= 3×1
21A= 3
Divide both sides by the coefficient of A which is 21
21A/21=3/21
A=1/7
Hence the unknown number is 1/7
Answer:
The number to multiply with 1/3 to get 1/21 is 1/7.
Step-by-step explanation:
The question wants us to find the number you can multiply with 1/3 to get 1/21. The number is unknown but when you multiply that unknown number by 1/3 your answer should be 1/21.
Let
the number to be multiplied with = a
Therefore,
1/3 × a = 1/21
a/3 = 1/21
cross multiply
21a = 3
divide both sides by 21
a = 3/21
a = 1/7
The number to multiply with 1/3 to get 1/21 is 1/7.
In a blind taste test, do people prefer pâté or dog food? To investigate, Bohannon et al. (2010) presented 1818 college‑educated adults with unlabeled samples of dog food (Newman's Own Organics Canned Turkey & Chicken) and four meat products meant for humans (duck liver mousse, pork liver pâté, liverwurst, and Spam). Participants were asked to rank their preferences. Two of 1818 participants ranked the dog food first, whereas the other 1616 participants chose one of the other items. Based on these results, can you conclude that people are less likely to prefer dog food over all human food than would be expected by chance? Use the significance level ????=0.05.level α=0.05. C
Answer:
The conclusion is that people are less likely to prefer dog food over all human food than would be expected by chance
Step-by-step explanation:
From the question we are told that
The sample size for first sample is [tex]n_1 = 18[/tex]
The sample size for second sample is [tex]n_2 = 18[/tex]
The number that ranked the dog food first [tex]d = 2[/tex]
The number that chose one of the other items is [tex]h = 16[/tex]
The sample proportion for first sample is
[tex]p(d) = \frac{d}{n}[/tex]
=> [tex]p(d) = \frac{2}{18}[/tex]
=> [tex]p(d) = 0.11[/tex]
The sample proportion for second sample is
[tex]p(h) = \frac{h}{n}[/tex]
[tex]p(h) = \frac{16}{18}[/tex]
[tex]p(h) = 0.8889[/tex]
The value of the pooled proportion is evaluated as
[tex]\= p = \frac{h+d}{18 +18}[/tex]
[tex]\= p = \frac{2+16}{18 +18}[/tex]
[tex]\= p = 0.5[/tex]
[tex]H0: p(d) = p(h)[/tex]
[tex]Ha : p(d) < p(h)[/tex]
Test statistics
[tex]z = \frac{(p(d)) - (p(h))}{\sqrt{\= p (1- \= p) (\frac{1}{n_1} + \frac{1}{n_2} )} }[/tex]
[tex]z = \frac{ 0.1111 - 0.8889}{\sqrt{0.5 (1- 0.5) (\frac{1}{18} + \frac{1}{18} )} }[/tex]
[tex]z = -4.67[/tex]
So since the test statistics is within the rejection region for the left tailed test
The null hypothesis is rejected
The conclusion is that people are less likely to prefer dog food over all human food than would be expected by chance
To generate new leads for business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3500, and the average first-year commission for each new account opened is $5000. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.
a. Determine the equation for computing Gustin's profit per seminar, given values of the relevant parameters.
b. What type of random variable is the number of new accounts opened?
c. Construct a spreadsheet simulation model to analyze the profitability of Gustin's seminars. Would you recommend that Gustin continue running the seminars?
d. How large of an audience does Gustin need before a seminar's expected profit is greater than zero?
Answer:
(A) The equation for computing Gustin's profit per seminar; given the values of the relevant parameters is:
π = 0.01AC - 3500
Where π = profit per seminar
A = attendance per seminar
C = commission earning per new account opened
(B) A continuous random variable
(C) No
(D) An audience of 71 persons
STEP BY STEP EXPLANATION:
(A) Profit is equal to total revenue minus total cost.
TR = PAC
Where P = probability that an attendee will open a new account
A = number of attendees per seminar
C = commission Gustin gets from each new account opened.
TC = $3,500
Where cost of organizing 1 seminar is constant at $3,500
So the function for profit per seminar is given thus:
π = TR - TC = 0.01AC - 3500
(B) There are 2 types of random variable; discrete random variable and continuous random variable
We say the number of new accounts opened (NNAO) is a continuous random variable because it is not specific. It is a function of both P and A. It depends on both P and A.
From the profit function or equation we have, we can see that you can't derive the exact NNAO per attendee. It is based on probability so if you were to measure it distinctly, you would have a very minimal value.
Discrete random variables occur in specific intervals e.g. 4, 5, 6,... while continuous random variables occur over an interval; e.g. 4.01, 4.02, 4.03,...
(C) Constructing a spreadsheet simulation model to analyze the profitability of Gustin's seminars, I would not recommend that Gustin continue running the seminars!
(D) The question points to A; which is the total attendance per seminar.
So if we calculate profit with the values given in the full question, we see that profit is negative, hence Gustin is running at a loss with 25 people attending one seminar.
π = (0.01 × 25 × 5000) - 3500
π = -$2,250
So, to make a profit greater than zero, we first check how many attendees it takes for TR to equal TC or for Profit to equal 0.
We set pie π to zero.
0 = (0.01 × 5000 × A) - 3500
0 = 50A - 3500
50A = 3500
A = 70 attendees
So Gustin needs an audience of more than 70 persons before a seminars expected profit will be greater than zero.
Explain how to find the relationship between two quantities, x and y, in a table. How can you use the relationship to calculate the missing values in the table?
Explanation:
In general, for arbitrary (x, y) pairs, the problem is called an "interpolation" problem. There are a variety of methods of creating interpolation polynomials, or using other functions (not polynomials) to fit a function to a set of points. Much has been written on this subject. We suspect this general case is not what you're interested in.
__
For the usual sorts of tables we see in algebra problems, the relationships are usually polynomial of low degree (linear, quadratic, cubic), or exponential. There may be scale factors and/or translation involved relative to some parent function. Often, the values of x are evenly spaced, which makes the problem simpler.
Polynomial relations
If the x-values are evenly-spaced. then you can determine the nature of the relationship (of those listed in the previous paragraph) by looking at the differences of y-values.
"First differences" are the differences of y-values corresponding to adjacent sequential x-values. For x = 1, 2, 3, 4 and corresponding y = 3, 6, 11, 18 the "first differences" would be 6-3=3, 11-6=5, and 18-11=7. These first differences are not constant. If they were, they would indicate the relation is linear and could be described by a polynomial of first degree.
"Second differences" are the differences of the first differences. In our example, they are 5-3=2 and 7-5=2. These second differences are constant, indicating the relation can be described by a second-degree polynomial, a quadratic.
In general, if the the N-th differences are constant, the relation can be described by a polynomial of N-th degree.
You can always find the polynomial by using the given values to find its coefficients. In our example, we know the polynomial is a quadratic, so we can write it as ...
y = ax^2 +bx +c
and we can fill in values of x and y to get three equations in a, b, c:
3 = a(1^2) +b(1) +c
6 = a(2^2) +b(2) +c
11 = a(3^2) +b(3) +c
These can be solved by any of the usual methods to find (a, b, c) = (1, 0, 2), so the relation is ...
y = x^2 +2
__
Exponential relations
If the first differences have a common ratio, that is an indication the relation is exponential. Again, you can write a general form equation for the relation, then fill in x- and y-values to find the specific coefficients. A form that may work for this is ...
y = a·b^x +c
"c" will represent the horizontal asymptote of the function. Then the initial value (for x=0) will be a+c. If the y-values have a common ratio, then c=0.
__
Finding missing table values
Once you have found the relation, you use it to find missing table values (or any other values of interest). You do this by filling in the information that you know, then solve for the values you don't know.
Using the above example, if we want to find the y-value that corresponds to x=6, we can put 6 where x is:
y = x^2 +2
y = 6^2 +2 = 36 +2 = 38 . . . . (6, 38) is the (x, y) pair
If we want to find the x-value that corresponds to y=27, we can put 27 where y is:
27 = x^2 +2
25 = x^2 . . . . subtract 2
5 = x . . . . . . . take the square root*
_____
* In this example, x = -5 also corresponds to y = 27. In this example, our table uses positive values for x. In other cases, the domain of the relation may include negative values of x. You need to evaluate how the table is constructed to see if that suggests one solution or the other. In this example problem, we have the table ...
(x, y) = (1, 3), (2, 6), (3, 11), (4, 18), (__, 27), (6, __)
so it seems likely that the first blank (x) will be between 4 and 6, and the second blank (y) will be more than 27.
Here is your answer | To determine the relationship between quantities, you must determine what to do to the x-values to make them into y-values. The correct operation must turn every x-value into the corresponding y- value in the table. Once you know the relationship, you can use the same operation on all of the x-values that have unknown y-values.
Elizabeth is returning to the United states from Canada. She charges the remaining 300 canadian dollars she has to $250 US dollars. What was $1 US dollar worth in canadian dollars? I got 75000 what did I do wrong?
Answer:
1 us dollar would be worth $0.8333333 Canadian dollars
Step-by-step explanation:
i don't know what you did wrong but you would divide 250/300 to get the amount it's worth. I guess you tried to multiply it, don't do that.
What’s the correct answer for this? Select the ones that apply
A volleyball is an example of a____a0.
Answer:
sphere
Step-by-step explanation:
A volleyball is a three dimensional object
It is a three dimensional circle which is called a sphere
Answer:
sphere
Step-by-step explanation:
hope this helps:]
what is archieves meaning
Answer:
the meaning is "a collection of historical documents or records providing information about a place, institution, or group of people."
Step-by-step explanation:
hope this helped and plz mark me as brainliest!
Answer:
a collection of historical documents or records providing information about a place, institution, or group of people
Step-by-step explanation:
Jack uses triangles in the construction of bridges, such as the one shown below
. What is the measure of Angle g
Answer:
61
Step-by-step explanation:
i got it right
Answer:
The one above me is correct
Step-by-step explanation:
Hillel is juggling flaming torches to raise money for charity. His initial appearence raises $500, and he raises $15 for each minuter of juggling performance. The amount R of money Hillel raises is a function of t, the length of his performance in minutes. write the functions formula
Answer:
r(t) = 15t+500
Step-by-step explanation:
Since the amount of money (r) is a function of the time (t) we will make it the y-value. t is how much time and he gets $15 a minute so we multiply t by 15. 500 is how much he gets paid for doing it. If he showed up and just left, he would still get 500.
Answer:
R=15t+500
Step-by-step explanation:
I have the same question
I promise brainliest for the first to answer. If you roll two number cubes, what is the probability of their sum being 9 or higher? 5/12 1/6 5/36 5/18
Answer:
maybe 3/5
Step-by-step explanation:
I hope it's right
0.38, 1.52)
3
4
Over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear
function?
x = 0 to x= 3
x = 0 to x= 1.79
x=0.38 to x = 1.79
x= 1.79 to x - 3
Mark this and return
Save and Exit
Next
Submit
e here to search
Answer:
The best correct option is C
x = 1.79 to x = 3
Step-by-step explanation:
Making the sport off all little thing that crowed. They are still grouped into 7. Option C is theost appropriate.
Answer:
An exponential function and a linear function are graphed below
Over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?
a) x=0 to x=3
b) x=0 to x=1.79
c) x=0.38 to x= 1.79
d) x= 1.79 to x=3 <<<<<<< correct answer
Step-by-step explanation:
EDGE 2021
A committee of six is to be chosen randomly from 50 people, 20 of whom support Party X and 30 support Party Y. What is the probability that the majority of the committee will be Party Y supporters
Ok to choose a committee of six people and the probability that it will be majority of the party supporters.
Probabilty= 30C6/50C6
Probability= 593775/15890700
Probabilty= 0.037
A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the
number of shoppers is 10o more than the number of shoppers the day before.
What is the total number of shoppers that visited the mall in the first 7 days?
Round your final answer to the nearest integer.
shoppers
Show Calculator
Report e problem
Answer:
The total number of shoppers that visited the mall in the first 7 days is 234.
Step-by-step explanation:
The number of customers at the new shopping mall on their first day of business was, X = 120.
It is provided that each day the number of shoppers is 10% more than the number of shoppers the day before.
This implies that the number of shoppers on the second day of the opening is:
Number of shoppers on the 2nd day = (120 × 1.10)
Then the number of shoppers on the third day of the opening will be:
Number of shoppers on the 3rd day = (120 × 1.10) × 1.10
And so on.
Compute the total number of shoppers that visited the mall in the first 7 days as follows:
[tex]\text{Number of shoppers on the first 7 days} = 120 \times (1.10)^{7}[/tex]
[tex]=120\times 1.9487171\\=233.846052\\\approx 234[/tex]
Thus, the total number of shoppers that visited the mall in the first 7 days is 234.
Answer:
1138 shoppers
Step-by-step explanation:
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 +7. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer:
Step-by-step explanation:
The function f(x) = x^2 has only one x-intercept which means only {0} is the only number that makes y zero.
The second function g(x) = (x-2)^2 -3 has also one x-intercept, {3.732} which will make the value of y, zero.
Answer:
The function started facing up with a vertex at (0, 0). Since 7 was added before squaring, the graph shifts 7 units up so the vertex at (7, 0). Also, the function is negative so the graph is pointing down
This means that there are two x-intercepts in g(x) and there was one x-intercept in f(x).
Step-by-step explanation:
used this and it was right.
What is -4 = -3 + x 8
Answer:
x=-1/8
Step-by-step explanation:
You solve this like an regular equation
Hope this Helps
Stay Safe:)
what are the factors of x^2+4x+3x?
Answer:
x(x+7)
Step-by-step explanation:
x^2+4x+3x
Combine like terms
x^2+7x
Factor out an x
x(x+7)
Answer:
[tex]x(x + 7)[/tex]
Step-by-step explanation:
[tex] {x}^{2} + 4x + 3x[/tex]
Combine like terms
[tex] {x}^{2} + 7x[/tex]
Factoring
[tex]x(x + 7)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
It is known that 25% of inhabitants of a community favour a political party A.
A random sample of 20 inhabitants was selected from the community and each person was asked he/she will vote for party A in an impending election. This follows a Binomial distribution, what is the probability that:
(i) exactly two persons will vote for party A?
(ii) at least three persons will vote for party A?
(iii) fewer than two persons will vote for party A?
Answer:
i) [tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
ii) [tex]P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317[/tex]
[tex]P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211[/tex]
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883[/tex]
iii) [tex]P(X <2)= 0.00317+ 0.0211= 0.02427[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:
[tex]X \sim Binom(n=20, p=0.25)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part i
We want this probability:
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
Part ii
We want this probability:
[tex]P(X\geq 3)[/tex]
And we can use the complement rule and we have:
[tex]P(X\geq 3) = 1-P(X<3)= 1-P(X \leq 2) =1- [P(X=0) +P(X=1) +P(X=2)][/tex]
And if we find the individual probabilites we got:
[tex]P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317[/tex]
[tex]P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211[/tex]
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883[/tex]
Part iii
We want this probability:
[tex] P(X <2)= P(X=0) +P(X=1)[/tex]
And replacing we got:
[tex]P(X <2)= 0.00317+ 0.0211= 0.02427[/tex]
5) Horatio Reyes earns 3.625% interest on his account. If his principal is
$6000 and he deposits $150 into the account every 6 days, how much total
interest will Horatio earn after 30 days? *
Answer:
$20.11
Step-by-step explanation:
Solution:-
- We will define the interest rate ( R ) earned on his deposits in the account per annum ( 365 days ).
- He deposits a principal amount of ( P ) = $6,000 once at the start of the accounting period.
- After the principal amount is deposited he deposits $ 150 in the account after every 6 days.
- We will first determine the amount in his account at the end of 30 days.
- We need to see how many additional deposits of $150 were made in these 30 days.
- The ( n ) number of additional deposits can be determined from the ratio of time-span of each deposition and the total accounting period:
[tex]n = \frac{30}{6} = 5[/tex]
- Horatio Reyes makes ( n = 5 ) additional deposits after the principal amount till the end of 30th day.
- Now we can calculate the total amount accumulated ( A ) in his account at the end of 30 days time period. It comprises of the initial principal amount and the 5 series of $150 deposits:
[tex]A = P + $150*n[/tex]
- Plug in the respective amounts ( P and n ):
[tex]A = 6000 + 150*5\\\\A = 6000 + 750\\\\A = 6750[/tex]
- At the end of 30th day Horatio Reyes has $6,750 in his account.
- The interest rate ( r ) applied at the end of the 30-day time period is sub-part of the total interest rate ( R ) applied per annum.
- So the interest rate applied at the end of 30-day tim period is determined from simple proportional ratios of time-period:
Rate(%) Time(days)
R: 3.625 365
r: x 30
========================================
x = 30*3.625 / 365 = 0.29795%
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- Now we will apply the rate ( r ) on the accumulated amount ( A ) by the end of 30-day time period in the account to determine the interest earned ( I ):
[tex]I= \frac{r*A}{100} \\\\I = \frac{0.29795*6750}{100} \\\\I = 20.111[/tex]
- The amount of interest earned ( I ) is $20.11 after 30 days.
Given AC=LN and BA=ML, which statement must be true?
Answer: BC<MN
Step-by-step explanation:
Answer: BC <MN
Step-by-step explanation: i just took the test on eginuity
What is the range of the function
Y = 2eX-1?
Answer:
-4293272 (y|y>-1)(y|y>-1)
If a(x) = 2x - 4 and b(x) = x + 2, which of the following expressions produces a quadratic function?
(ab)(x)
Ol
(x)
(a - b)(x)
(a + b)(x)
Answer:
(ab)(x)
Step-by-step explanation:
The sum or difference of two linear functions will be a linear function. The product of two linear functions will be a quadratic function.
which expression is equivalent to -f-5(2f-3)
[tex]\text{One of the expressions can be the simplified version}\\\\\text{Simplify:}\\\\-f-5(2f-3)\\\\\text{Use the distributive property}\\\\-f-10f+15\\\\\text{Combine like terms}\\\\\boxed{-11f+15}\\\\\text{That expression is equivalent to the expression listed in the question}[/tex]
Answer:
11f+5
Step-by-step explanation:
khan
Determine whether the equation is exact. If it is, then solve it. e Superscript t Baseline (7 y minus 3 t )dt plus (2 plus 7 e Superscript t Baseline )dy equals 0et(7y−3t)dy2+7et dy=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
[tex]F(t,y)=(2+7e^t)y+3(1-t)e^t +C[/tex]
Step-by-step explanation:
You have the following differential equation:
[tex]e^t(7y-3t)dt+(2+7e^t)dy=0[/tex]
This equation can be written as:
[tex]Mdt+Ndy=0[/tex]
where
[tex]M=e^t(7y-3t)\\\\N=(2+7e^t)[/tex]
If the differential equation is exact, it is necessary the following:
[tex]\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}[/tex]
Then, you evaluate the partial derivatives:
[tex]\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}[/tex]
The partial derivatives are equal, then, the differential equation is exact.
In order to obtain the solution of the equation you first integrate M or N:
[tex]F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)[/tex] (1)
Next, you derive the last equation respect to t:
[tex]\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)[/tex]
however, the last derivative must be equal to M. From there you can calculate g(t):
[tex]\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t][/tex]
Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:
[tex]F(t,y)=(2+7e^t)y+3(1-t)e^t +C[/tex]
where C is the constant of integration
A group of 570 students were surveyed about the courses they were taking at their college with the following results:
257 students said they were taking Math.
282 students said they were taking English.
323 students said they were taking History.
154 students said they were taking Math and English.
171 students said they were taking Math and History.
143 students said they were taking English and History.
80 students said they were taking all three courses.
How many students took English and History, but not Math
Answer:
The number of students who took English and History, but not Math is 143.
Step-by-step explanation:
Denote the subject choices as follows:
M = a students was taking Math
E = a students was taking English
H = a students was taking History
The data provided is as follows:
N (M) = 257
N (E) = 282
N (H) = 323
n (M ∩ E) = 154
n (M ∩ H) = 171
n (E ∩ H) = 143
n (M ∩ E ∩ H) = 80
Consider the Venn diagram below.
From the provided data and the Venn diagram the value of the set E and H minus M is 143.
Thus, the number of students who took English and History, but not Math is 143.
