Answer:
7 school buses will be needed to take the children of Anderson school on a field trip
Step-by-step explanation:
number of children = 390
We are told that each bus carries 60 people
Therefore
60 people = 1 bus
1 person = (1 ÷ 60)
∴ 390 people = [tex]\frac{1}{60}[/tex] × [tex]\frac{390}{1}[/tex] = [tex]\frac{390}{60}[/tex] = 6.5 (approx. 7 buses)
Therefore, 7 school buses will be needed to take the children of Anderson school on a field trip, but the seventh bus will be half-filled with children.
Consider the differential equation y '' − 2y ' + 5y = 0; ex cos(2x), ex sin(2x), (−[infinity], [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(ex cos(2x), ex sin(2x)
Answer:
Step-by-step explanation:
Characteristic equation:
[tex]\lambda^2-2\lambda + 5 =0[/tex]
[tex]\lambda = 1\pm2i[/tex]
The solution of the ODE is
[tex]y = e^x(C_1 cos(2x) + C_2 sin(2x) )[/tex]
Now, very find by taking the first and the second derivative of y.
[tex]y' = e^x(-2 C_1 sin (2x) +2C_2 cos (2x)) +e^x (C_1 cos (2x) + C_2sin(2x))[/tex]
[tex]=-2e^xC_1 sin(2x) +2e^xC_2 cos (2x)+C_1e^xcos(2x) + C_2e^x sin(2x)[/tex]
[tex]y" = -2e^x C_1 sin(2x) -4e^x C_1cos(2x)+2e^xC_2cos(2x)-4e^xC_2sin(2x) +C_1e^x cos(2x) -2C_1e^xsin(2x)+C_2e^x sin(2x) +2C_2e^x cos(2x)[/tex]
[tex]=-4C_1e^xsin(2x) -3C_1e^x cos(2x) +4C_2e^xcos(2x) -3C_2e^xsin(2x)[/tex]
Now, put all in y" -2y'+5y and consider if it = 0 or not.
Jane has a pre-paid cell phone with NextFell. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 370 minutes and the cost was $133.00. In July she used 530 minutes and the cost was $181.00.
A) Express the monthly cost C
C
in terms of x
x
, the number of minutes of calling time she used.
Answer: c
B) If Jane used 477 minutes of calling time in August, how much was her bill?
Answer: $
Answer:
C = 0.30x +22$165.10Step-by-step explanation:
A) Let x represent minutes used, and C represent monthly charge. We are given two (x, C) pairs: (370, 133.00) and (530, 181.00)
We can use these in the 2-point form of the equation for a line.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
C = (181 -133)/(530 -370)(x -370) +133
C = 48/160(x -370) +133
C = 0.30x -111 +133
C = 0.30x +22
__
B) For x = 477 minutes, the charge will be ...
C = 0.30(477) +22 = $165.10 . . . . for 477 minutes
The monthly cost C = $22 + $0.30x
Jane's bill for August is $165.10
The total amount Jane pays is the sum of the monthly fee and the charge per minute.
Total amount = monthly fee + charge per minute
Two equations can be derived from the question
a + 370b = 133 equation 1
a + 530b = 181 equation 2
Where:
a = monthly fee
b = charge per minute
This equation would be solved using simultaneous equation
Subtract equation 1 from equation 2
160b = 48
Divide both sides of the equation by 160
b = 48 / 160
b = 0.30
Substitute for b in equation 1
a + 370(0.30) = 133
a + 111 = 133
a = 133 - 111
a = 22
Based on the above calculations, the monthly fee is $22 and the charge per minute is $0.30
Equation for monthly cost = $22 + $0.30x
If Jane used 477 minutes, total charge :
$22 + $0.30(477) =
22 + 143.10
= $165.10
A similar question was solved here: https://brainly.com/question/17911105?referrer=searchResults
what is the solution to 2.8(2+0.5n)=2.4(n+1.2)
Answer:
Step-by-step explanation:
Parker invested $7,800 in an account
paying an interest rate of 1.7%
compounded continuously. Assuming no
deposits or withdrawals are made, how
much money, to the nearest dollar, would
be in the account after 11 years?
Answer:
A=9404
Step-by-step explanation:
Answer:
9404
Step-by-step explanation:
Hypertension is when an adult is classified as having high blood pressure (above 130 systolic blood pressure is considered hypertension). Researchers want to know the proportion of adult North Americans (above age of 18) that have hypertension. Based on a study of 3532 adult North Americans, 1219 of them were classified as having hypertension.
a. Researchers want to test if more than a quarter of all North American adults have hypertension (that is to say more than 25% proportion of North American adults). State the null and alternative hypothesis in proper notation.
b. Create a 95% confidence interval for the true proportion of adult North Americans that have hypertension. Interpret this interval in context of the study.c. Say your 95% confidence interval is (0.329 , 0.361). Can you say with a high degree of confidence that more than a quarter of all North Americans have hypertension. Explain in a sentence or two.
d. If we were to decrease our level of confidence, what would we expect to happen to the confidence interval? Get wider/ get narrower/ stay the same ?
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test.
For the null hypothesis,
H0 : p ≥ 0.25
For the alternative hypothesis,
H1 : p < 0.25
b) from the given information,the sample proportion or point estimate for the population proportion is
1219/3532 = 0.35
Confidence interval = sample proportion ± margin of error
Margin of error = z × √pq/n
p = 0.35
q = 1 - 0.35 = 0.65
z score for 95% confidence level is 1.96
Margin of error = 1.96 × √(0.35 × 0.65)/3532 = 0.016
Confidence interval = 0.35 ± 0.016
c) Given that the 95% confidence interval is (0.329 , 0.361), it means that the lower limit of the confidence interval is 0.329 and the upper limit is 0.361
If more than a quarter of all North Americans have hypertension. It means that the true proportion can be within this interval. 95% confidence interval is a high degree of confidence. Therefore, we can say that with a high degree of confidence that more than a quarter of all North Americans have hypertension.
d) it would get narrower
g(x) = x-6
Domain of g:
Answer:
All real numbers
Step-by-step explanation:
The domain is just what values of x you can plug in as an input. In this case, you can plug in any number, as the graph is just a line that has no restrictions. An example of a case where the domain isnt just any number would be g(x) = 5/x, because in that case, x couldn't be 0 because you cant divide by zero.
Answer: all real numbers
Step-by-step explanation:
Daniel is packing his bags for his vacation. He has
5
55 unique socks, but only
4
44 fit in his bag
Answer:
yes
Step-by-step explanation:
Dr. Dormeur studies sleep and sleep disorders. She is curious as to whether technology exposure before bedtime causes people to fall asleep more slowly. She recruits a sample of 60 middle-aged women from a local church who reported no history of sleep problems. She creates three conditions, and randomly assigns participants to one condition. All participants come to the sleep lab for two nights in a row, the first night with no treatment, the second night with treatment. In the first condition (A), participants were asked to play an online game (Candy Crush) on an iPad for 10 minutes prior to going to bed. In the second condition (B), participants were asked to read an article using an iPad that discussed tricks and tips for improving one’s score on Candy Crush (which took about 10 minutes). In the third condition (C), participants were asked to read a newspaper article about the inventor of Candy Crush (which took about 10 minutes). With the use of an electroencephalograph (EEG), the researcher measures how long it takes participants to fall asleep. Which of the following designs is Dr. Dormeur using?
a. one-way between-subjects ANOVA.b. chi-square test.c. simple linear regression.d. repeated-measures t-test.
Answer:
Dr Domeur is using repeated measures t-test
Step-by-step explanation:
Dr Dormeur is using the repeated measures t test also known as within-subjects design because the design is between participants. Repeated Measures assesses the change in a continuous outcome across time or within-subject.
Dr Domeur makes measurements using only one group of subjects, and the tests on each subject can be repeated more than once after different treatments. From the question, the researcher Dr Domeur uses the same subjects with every condition of the research and the control. Repeated measures are collected in a longitudinal study that assesses change over time.
una persona cobra 7/4 de una cantidad, gasta 1/4 y presta 1/8 ¿Que fraccion de la cantidad cobrada le quedo?
Answer: (11/8)
Step-by-step explanation:
I will answer this in English.
a person collects 7/4 of an amount, spends 1/4 and lends 1/8. What fraction of the amount collected is left?
If the amount is A, then he collects:
C = (7/4)*A
Now, he spends 1/4 and lends 1/8 of the amount A, so the fraction left is:
Left = (7/4)*A - (1/4)*A - (1/8)*A
now i will write 7/4 as 14/8 and 1/4 as 2/8.
left = (14/8)*A - (2/8)*A - (1/8)*A = ((14 - 2 - 1)/8)*A = (11/8)*A
I need to know if the graph makes sense based on how Naoya shoots, everything is in the photo.
Answer:
Not correct
Step-by-step explanation:
Sample 8 has one free throw, sample 9 has 3 free throw success,
sample 10 has 3 free throw success
sample 11 has 5 free throw success
sample 12 has 5 free throw success
sample 13 has 2 free throw success
sample 14 has 1 free throw success;
See one sample should contain 15 free throw and the probability of success should be 0.7
Let's look at sample 8
Total no of success is 1
Total no of free throws 15
Probability is 1/15 = 1/15 * 100 =6.67%
Similarly you can do so for the others.
What is x to the nearest tenth?
Answer:
x= 13.7 (nearest tenth)
Step-by-step explanation:
Please see attached picture for full solution.
Can you divide 81 into 4 parts so that if you add 2 to the 1st part, subtract 2 from the 2nd part, multiply the 3rd part by 2, and divide the 4th part by 2, the answer in each case will be the same
Answer:
Yes I believe the answer will be the same.
Step-by-step explanation:
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 55% C: Scores below the top 45% and above the bottom 23% D: Scores below the top 77% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 76 and a standard deviation of 7.9. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 85.
Step-by-step explanation:
When the distribution is normal, we use 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 = 76, \sigma = 7.9[/tex]
Find the minimum score required for an A grade.
The top 13% of the scores are A, so the minimum is the 100-13 = 87th percentile, which is X when Z has a pvalue of 0.87. So X when Z = 1.127.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.127 = \frac{X - 76}{7.9}[/tex]
[tex]X - 76 = 7.9*1.127[/tex]
[tex]X = 84.9[/tex]
Rounding to the nearest whole number:
The minimum score required for an A grade is 85.
3. Candace drew quadrilateral ABCD with vertices A(3, 3), B(5, 3), C(7, 1), and D(1, 1). Miguel wants to dilate Candace's quadrilateral by a scale factor of 5/5. Which statement is true? *
A-Quadrilateral ABCD is smaller than quadrilateral A'B'C'D'.
B-The algebraic expression of the dilation is (x, y) -> (5x, 5y).
C-The coordinates of quadrilateral A'B'C'D' will be A'(15, 15), B'(9, 15), C'(5, 35), D'(5, 5).
D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Answer:
D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Step-by-step explanation:
The scale factor is equal to 1. Hence, the quadrilateral A'B'C'D' will be identical to quadrilateral ABCD, whose vertices are the same.
The algebraic expression of the dilation is:
[tex](x',y') = (x,y)[/tex]
Besides, the coordinates of the new quadrilateral are A'(3, 3), B'(5, 3), C'(7, 1), and D'(1, 1)
And quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Therefore, the right answer is D.
Answer: D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Step-by-step explanation: just did a test with this question and got it right. Hope this helped! thx for the points :D
Given: 1; -5; -13 ; -23 ; ...
Derive a formula for the nth term in the pattern.
Answer:
f(n) = -n^2 -3n +5
Step-by-step explanation:
Suppose the formula is ...
f(n) = an^2 +bn +c
Then we have ...
f(1) = 1 = a(1^2) +b(1) +c
f(2) = -5 = a(2^2) +b(2) +c
f(3) = -13 = a(3^2) +b(3) +c
__
Here's a way to solve these equations.
Subtract the first equation from the second:
-6 = 3a +b . . . . . 4th equation
Subtract the second equation from the third:
-8 = 5a +b . . . . . 5th equation
Subtract the fourth equation from the fifth:
-2 = 2a
a = -1
Then substituting into the 4th equation to find b, we have ...
-6 = 3(-1) +b
-3 = b
and ...
1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation
5 = c
The formula is ...
f(n) = -n^2 -3n +5
Which of these generalizations is true?
A. All rectangles are squares.
В. All parallelogram s are rectangles.
C. All squares are parallelograms.
D. All trapezoids are parallelograms.
PLEASE HELP QUICKLY !THANK YOU :)
As part of his dissertation, Joe wanted to know if math anxiety differs between males and females. He developed a new measure to assess math anxiety with a scale of 0 – 100, a higher number indicating more anxiety. He went to a large university and asked several sections of an introductory math class to participate.What is the dependent variable?
Answer:
Maths anxiety
Step-by-step explanation:
In a typical research study, there are basically 2 types of variables involved, which are the dependent and the independent variable.
The dependent variable is affected by other factors or the independent variable involved in the study. The dependent variable would change is the independent variable is manipulated, changed or varied.
The dependent variable in Joe's dissertation is MATHS ANXIETY, which is dependent on the gender of students. Gender is the independent variable as he wants to find out if there's any difference in maths anxiety between males and females.
The dependent variable is Math Anxiety which is dependent on gender of the students.
An item is regularly priced at $80. Chau bought it on sale for 15% off the regular price. How much did Chau pay?
only $68...steps.... (80*15% =12 /80-12=68
Sam and Joe are painters. Sam makes $2 an hour less than Joe. On a job that took them both 40 hours to complete they made $440. How much does Sam make an hour?
Answer:
$4.50Step-by-step explanation:
If they earned $440 in 40 hours
This means they earned 440÷40=11 in one hour
Sam makes x-2 amount of money per hour so the difference between Sam's and Joe's salary is $2
Find two numbers that add up to Ten and can subtract to make a difference of 2 (I am starting with ten as it is easier) 6+4=10 6-4=2
So to make 6 and. 4 add to make a 11 we need to add a 0.5 to each of them so 6.5+4.5=11 and 6.5-4.5= $2.
Therefore Joe makes $6.50 an hour and Sam makes £4.50
[tex]\left[\begin{array}{ccc}1&0&-2\\&&\\&&\end{array}\right] +\left[\begin{array}{ccc}1&2&3\\&&\\&&\end{array}\right][/tex]
The answer is [ 2 2 1]
look at the attached picture
Hope it helps
Good luck on your assignment
What’s the correct answer for this?
Answer:
2.5 ft
Step-by-step explanation:
As radius is perpendicular to tangent ,
LT [tex]\perp[/tex]KT
By pythagoras theorem:
LT² = LK² - KT²
LT² = (6.5)² - 6²
LT² = 42.25 - 36
LT² = 6.25
LT = 2.5 ft
LT = radius = 2.5 ft
A car is traveling 80 KM in an hour how many minutes will it take to go from Miami to key largo
84.5 minutes reeeeeee
The car will take 84 minutes to go from Miami to Key Largo.
Given that, speed=80 km/hour and distance = 70 miles.
What is the speed of a object?Speed is the rate at which an object's position changes, measured in meters per second. The equation for speed is simple: distance divided by time.
Now, convert miles to kilometres. We know that 1 mile=1.6 kilometre.
That is 70 miles =70×1.6 =112 km
Then, Time=Distance/Speed
⇒Time =112/80=1.4 hours
So, 1.4 hours=60×1.4=84 minutes
Therefore, the car will take 84 minutes to go from Miami to Key Largo.
To learn more about the speed visit:
https://brainly.com/question/7359669.
#SPJ2
Your question is incomplete, probably the complete question/missing part is:
A car is travelling 80 KM in an hour how many minutes will it take to go from Miami to key largo? (70 miles)
Use the fundamental theorem of calculus to find the area of the region between the graph of the function x^5 + 8x^4 + 2x^2 + 5x + 15 and the x-axis on the interval [-6,6]. Round off your answer to the nearest integer.
A) 25,351 units^2
B) 149,473 units^2
C) 3,758 units^2
D) 2,362 units^2
Answer:
The area of the region is 25,351 [tex]units^2[/tex].
Step-by-step explanation:
The Fundamental Theorem of Calculus: if [tex]f[/tex] is a continuous function on [tex][a,b][/tex], then
[tex]\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}[/tex]
where [tex]F[/tex] is an antiderivative of [tex]f[/tex].
A function [tex]F[/tex] is an antiderivative of the function [tex]f[/tex] if
[tex]F^{'}(x)=f(x)[/tex]
The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
To find the area of the region between the graph of the function [tex]x^5 + 8x^4 + 2x^2 + 5x + 15[/tex] and the x-axis on the interval [-6, 6] you must:
Apply the Fundamental Theorem of Calculus
[tex]\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx[/tex]
[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx[/tex]
[tex]\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2[/tex]
Mr. Corbin measures the lengths of three branches. The first branch
is 2/3 foot long. The second branch is 2/2 foot long. The third branch is 2/8
foot long. Which list orders the fractions from greatest to least? *
Answer:
2nd branch > 1st branch > 3rd branch
or
[tex]\dfrac{2}{2} > \dfrac{2}{3} > \dfrac{2}{8}[/tex]
Step-by-step explanation:
Length of First branch = [tex]\frac{2}{3}[/tex] foot
Length of second branch = [tex]\frac{2}{2}[/tex] foot
Length of third branch = [tex]\frac{2}{8}[/tex] foot
Let us convert the fractions in decimal forms:
[tex]1.\ \dfrac{2}{3} = 0.67[/tex]
[tex]2. \dfrac{2}{2} = 1[/tex]
[tex]3.\ \dfrac{2}{8} = \dfrac{1}{4}=0.25[/tex]
It can be clearly seen that 1 is the largest value among the three values.
So, 2nd branch is the largest.
Now, let us have a look at the values of first and third branches:
0.67 and 0.25.
Clearly, 0.67 is greater than 0.25.
So, the correct order is:
2nd branch > 1st branch > 3rd branch
OR
We can use other method to see it.
Here, all the 3 fractions have same numerator.
So, denominator can help us decide the which fraction has a large value.
If numerator is same, the larger denominator will have smaller fractions.
The denominators are 2, 3 and 8.
8 > 3 > 2
So, the answer is
2nd branch > 1st branch > 3rd branch
or
[tex]\dfrac{2}{2} > \dfrac{2}{3} > \dfrac{2}{8}[/tex]
An urn contains 5 are red balls and 6 blue balls. Suppose 5 are randomly selected without replacement. What is the probability that exactly 3 are red? Answer correct to four decimal places.
Answer:
27.94%
Step-by-step explanation:
The statement tells us that we have 5 red balls and 6 blue balls, that is, there are 11 in total (5 + 6)
So the probability of red balls = 5/11 and blue balls probability = 6/11
Let X be the number of red balls of those 5 selected balls.
Then X follows a binomial distribution with the following parameters:
n = 5
p = 5/11
q = 6/11
P (X) = nCx * p ^ (x) * q ^ (n -x)
required probability is P (X = 3), replacing:
P (X = 3) = 5C3 * (5/11) ^ (3) * (6/11) ^ (5 -3)
P (X = 3) = 5! / (3! (5-3)!) * 0.02794
P (X = 3) = 10 * 0.02794
P (X = 3) = 0.2794
Which means that the probability is 27.94%
lee and maya are collecting leaves for an art project. lee collects 24-100 of the total leaves needed. maya collects 4-10 of the total leaves needed. What fraction of the total number leaves did they collect altogether
Answer:
1/8 but idk im not good with math
Step-by-step explanation:
Answer:
16-25
Step-by-step explanation:
Step 1 :
2
Simplify —
5
Equation at the end of step 1 :
24 2
——— + —
100 5
Step 2 :
6
Simplify ——
25
Equation at the end of step 2 :
6 2
—— + —
25 5
A juggler perform in a telant contest. He is given 10 marks by each of the 4 judges. What’s his total score?
Answer:
40
Step-by-step explanation:
The answer is 40. There are 4 judges, and each gave him a 10. This can be shown by an equation.
1. 4 * 10 = total score
2. 40 = total score.
Hope this helps! (Please consider giving brainliest)
Answer:
40 marks
Step-by-step explanation:
Since each judge gives him 10 marks each, then we get:
10 marks × 4 judges = 40 marks
His total score is 40 marks.
A cup of coffee is cooling down such that its temperature is decreasing at a constant rate of 8% per minute. Let’s say the coffee starts at a temperature of 200 degrees Fahrenheit.
What’s its temperature after one minute by finding 8% of 200 and then subtracting?
Answer:
Temperature after 1 minute = 184 ° F
Step-by-step explanation:
starting temperature = 200 °F
rate of decrease = 8% per minute
Temperature lost = 8% of 200 = 8/100 × 200 = 0.08 × 200 = 16 °F
It therefore means that after 1 minute, the cup of coffee loses 16 °F,
∴ Temperature after 1 minute = (starting temperature) - (lost temperature)
= 200 - 16 = 184 °F
2 Points
Suppose you buy 6 buckets of apples and 4 buckets of peaches for $42. If
you bought 8 buckets of apples and 2 buckets of peaches, you would have
spent $36. How much is one bucket of apples (a), and one bucket of peaches
(p)?
A. a = $3, p = $6
B. a = $8, p = $2
C. a = $6, p = $4
D. a = $6, p = $3
SUBMIT
Answer:
A. a = $3, p = $6
Step-by-step explanation:
Let the cost of a bucket of apple=a
Let the cost of a bucket of peaches=p
6 buckets of apples and 4 buckets of peaches costs $42.
6a+4p=428 buckets of apples and 2 buckets of peaches costs $36.
8a+2p=36 (Multiply by 2 to make the coefficient of p 4)16a+4p=72We solve the two resulting equations simultaneously
6a+4p=42
16a+4p=72
Subtract
-10a=-30
Divide both sides by -10
a=$3
Next, we substitute a=$3 in any of the equation to solve for p
6a+4p=42
6(3)+4p=42
4p=42-6(3)
4p=42-18
4p=24
Divide both sides by 4
p=$6
Therefore, a bucket of apple costs $3 and a bucket of peaches costs $6.
What is a plane in mathematical terms
Answer:
Step-by-step explanation:
A plane is a flat, two-dimensional surface that extends infinitely far.