Answer:
P = 8000
t = 2
I = p × r × t
400 = 8000 × r/100 × 2
r = 400/160 per year
r = 40/16 = 2.5 %
A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 890 ft out in the plain from the base of the mountain. Find the shortest length of cable needed.
Answer:
about 3878 ft
Step-by-step explanation:
Assuming that the cable is not doubled, we need to find the length of the base of the mountain i.e
3400/tan(74) = about 975 ft
Therefore, the length of the cable =
√[ 3400² + (975 + 890)²] = about 3878 ft
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 4 students' scores on the exam after completing the course: 12,7,13,11 Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The 80% confidence interval for the average net change is (8.596, 12.904).
Critical value t=1.638.
Step-by-step explanation:
First, we calculate the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{4}(12+7+13+11)\\\\\\M=\dfrac{43}{4}\\\\\\M=10.75\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{3}((12-10.75)^2+(7-10.75)^2+(13-10.75)^2+(11-10.75)^2)\\\\\\s=\dfrac{20.75}{3}\\\\\\s=6.92\\\\\\[/tex]
We have to calculate a 80% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=10.75.
The sample size is N=4.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.63}{\sqrt{4}}=\dfrac{2.63}{2}=1.315[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
The t-value for a 80% confidence interval and 3 degrees of freedom is t=1.638.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.638 \cdot 1.315=2.154[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 10.75-2.154=8.596\\\\UL=M+t \cdot s_M = 10.75+2.154=12.904[/tex]
The 80% confidence interval for the average net change is (8.596, 12.904).
1.solve for x 3x - 2 = 3 - 4x
Answer:
[tex]x=\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]3x - 2 = 3 - 4x[/tex]
Add [tex]2[/tex] and [tex]4x[/tex] on both sides of the equation.
[tex]3x - 2 +2+4x= 3 - 4x+2+4x[/tex]
[tex]3x+4x=-4x+5+4x[/tex]
[tex]7x=5[/tex]
Divide [tex]7[/tex] on both sides of the equation.
[tex]\frac{7x}{7}=\frac{5}{7}[/tex]
[tex]x=\frac{5}{7}[/tex]
16. Model with Math What must be the sum of
the two remaining numbers, x and y? Write an
equation to show how to find this sum.
Answer:
The sum of the two remaining numbers, x and y = 60
Question:
The question isn't clear enough as some information have been omitted. Let's consider the following:
Model with Math. The average of six numbers is 18. If the average of four numbers is 12. What must be the sum of the two remaining numbers, x and y?
Write an equation to show how to find this sum.
Step-by-step explanation:
Mathematical models are applied to represent things in the real world in order to solve problems.
The formula we would use to solve this problem is an example of a mathematical model.
Types of mathematical model we can use include equations and graphs.
Using equations:
Average of six numbers = 18
Average of four of the numbers = 12
Total sum of the four numbers = 4×12 = 48
the two unknown numbers are x and y
Average of six numbers = (Sum of all 6 numbers)/6
=(Total sum of four numbers + x + y)/6
(48 + x + y)/6 = 18
The equation that shows how to find the sum:
(1/6)(48 + x + y) = 18
48 + x + y = 18×6
48 + x + y = 108
x + y = 108-48
x+y = 60
The sum of the two remaining numbers, x and y = 60
If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).
Answer:
Step-by-step explanation:
If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).
a)
[tex]L = \lim_{n \to \infty} b_n \\\\\\L= \lim_{n \to \infty} n^{\frac{5.6}{n} }[/tex]
Log on both sides
[tex]In (L) = \lim_{n \to \infty} In (n)^{\frac{5.6}{n} }\\\\= \lim_{n \to \infty} \frac{5.6}{n} In(n)[/tex]
[tex]=5.6 \lim_{n \to \infty} \frac{d}{dn} In(n)/\frac{d}{dn} (n)\\\\=5.6 \lim_{n \to \infty} \frac{1}{n} /1 \\\\=5.6 \lim_{n \to \infty} \frac{1}{n} \\\\=5.6 \times 0\\\\In(L) =0\\\\L=e^0\\\\L=1[/tex]
[tex]\therefore \lim_{n \to \infty} (n)^{\frac{5.6}{n} =1[/tex]
The limit value of given sequece is 1.
To understand more, check below explanation.
Limit of function:The given sequence is,
[tex]b_{n}=n^{5.6/n}[/tex]
We have to find limit of above sequence.
[tex]L=\lim_{n \to \infty} b_n \\\\L=\lim_{n \to \infty}n^{5.6/n} \\\\ln(L)=\lim_{n \to \infty}\frac{5.6}{n}ln(n) \\\\ln(L)=5.6\lim_{n \to \infty}\frac{ln(n)}{n} \\\\ln(L)=5.6\lim_{n \to \infty}\frac{1/n}{1} \\\\ln(L)=5.6*0=0\\\\L=e^{0}=1[/tex]
Therefore, the limit value of given sequece is 1.
Learn more about the limit of function here:
https://brainly.com/question/2166212
For a particular diamond mine, 78% of the diamonds fail to qualify as "gemstone grade". A random sample of 106 diamonds is analyzed. Find the mean μ.
Answer:
Mean of the binomial distribution μ = 82.68
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 106 diamonds
The probability that the diamonds fail to qualify as "gemstone grade
p = 78% =0.78
We will use binomial distribution
Mean of the binomial distribution
μ = n p
μ = 106 × 0.78
μ = 82.68
conclusion:-
Mean of the binomial distribution μ = 82.68
6th grade math help me. :D.....
Answer:
(1) 4x + 28 (2) 18x- 27
Step-by-step explanation:
the first question 4(x + 7) can be simplified by multiplying the number outside the parenthesis (4) by both of the values inside:
4x + 28 or the last answer choice
in the second question you can use the same method:
9 (2x) = 18x
9 ( -3) = -27
therefore the correct answer choice is 18x - 27
hope this helps :)
Please answer this correctly
Answer:
416
Step-by-step explanation:
plz mark brainliest!
Answer:
385
Step-by-step explanation:
use l x w
14x19
16x3
7x10
385
If your answer is in decimal form, round to 2 decimal places. For example, if your answer is .412, enter it into the fill-in-the-blank as .41, or if your answer is 1.415, enter it into the fill-in-the-blank as 1.42. If there are no decimals in your answer, you will simply enter the number; so if your answer is 2, enter 2 with no decimals. Do not enter any extra spaces, do not enter commas or $ or % symbols.
Answer:
If there is no decimal just put number and if the number is higher than 5 you round up example 1.46 you would put 1.5
Step-by-step explanation:
HOPE IT HELPS
Plz help me ASAP it’s important
Answer:
D. 6.3
Step-by-step explanation:
Well you can make a triangle with the line PQ with it's height as 2 and base as 6.
Then you can use the Pythagorean Theorem to find the length of PQ.
a²+b²=c²
2²+6²=c²
4+36=c²
40=c²
c²=40
Square root both sides
c=[tex]\sqrt{40}[/tex]
c≈6.3
Our answer is D. 6.3
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives: y = x – 5
Answer:
x =6y =13Step-by-step explanation:
This is the method I am familiar with.
I Hope It helps :)
[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]
[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]
Answer:
Correct answers is
Step-by-step explanation:
1. 3
2. B
3. 6
4. (6,13)
A $210 suit is marked down by 10%. Find the sale price.
Answer:
sale prices = $252
Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252
Answer:
$189
Step-by-step explanation:
10% of 210 = 21
210 - 21 = 189
What is the part to part ratio for gender in a daycare of children in which 16 of them are male
Answer:
16:0
Step-by-step explanation:
The students in Mrs. Willow's reading class are all reading the same novel independently. Four students create a graph of their reading rates, in words per minute, as shown below. Which student reads the fastest? A. Mason B. RIley C. Sarah D. Charlie
Answer:
Mason reads the fastest
Answer:
c
Step-by-step explanation:
try to see how much every person reads every one or two minutes.
Charlie: 350 in two min
Mason :400 in two min
Sarah: 450 in two min (the middle of 300-600 is 450)
so between the three Sarah wins.
now Reilly is a bit more difficult but you can see that she read 4000 in 20 min. so if we divide it by 10 we can see she reads 400 in 2 min. and therefore Sarah os the winner.
1.82 /6 pls answer with rounding to the nearest cent plzzzz I'll mark the 1st answer brainlist
Answer:
.30
Step-by-step explanation:
the answer is .30333 (with the 3 repeating) and since 3 is less than 5 you leave the second number as is.
For problems 3 and 4, find the missing side of the triangle. Leave answers in simplest radical form.
Answer: 3. 4[tex]\sqrt{13}[/tex] 4. [tex]\sqrt{225}[/tex]
Step-by-step explanation:
8^2 + 12^3 = c^2
64 + 144 = c^2
208 = c^2
√208
[tex]4\sqrt{13}[/tex]
The final answer is the square root of 208
8^2 + b^2 = 17^2
64 + b^2 = 289
-64 64
b^2 = 225
[tex]\sqrt{225}[/tex]
Suppose that y = 5 x plus 4 and it is required that y be within 0.005 units of 8. For what values of x will this be true?
Answer:
so we have an inequality for y -
7.995<y<8.005
Then now we need in inequality for x
(y-4)/5 = x
so that means that so if we have (7.995-4)/5 we get 3.995/5 = 7.99
so we have our first 7.99<x<b
Now we solve for b
So that means that 5.005/5 = 1.001
since we are changing it we switch our signs
from 7.99<x<1.001
we do 7.99>x>1.001
therefore
1.001<x<7.99
Answer:
0.795 [tex]\leq[/tex] y [tex]\leq[/tex] 0.805
Step-by-step explanation:
8 = 5x + 4
5x = 4
x = 4/5 or 0.800
therefore 0.800 + .005 and 0.800 - .005 =
0.795 [tex]\leq[/tex] y [tex]\leq[/tex] 0.805
Indicate in standard form equation of the line passing through the given 
Answer:
x + y = 6
Step-by-step explanation:
slope is rise/run so -6/6 = -1
y = -x+b
solve for b by plugging in any point
6 = 0 + b -> b = 6
y = -x+6
x + y = 6
which expression is equivalent to (5x^3)(4x)^3?
A. 20x^6
B. 320x^6
C. 500x^6
D. 8,000x^6
Answer:
320 x^6
Step-by-step explanation:
(5x^3)(4x)^3
5 x^3 * 4^3 * x*3
5x^3 *64x^3
320 x^6
Answer:
B
Step-by-step explanation:
= 5x^3 * 4^3 * x^3
= 5x^3 *64x^3
= 320x^6
Hope this helps!
Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence.
Answer:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
Step-by-step explanation:
Information given
[tex]\bar X= 28.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =4.7[/tex] represent the population standard deviation
n=40 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
2x + 3=-7?what is this even mean
Answer:
2 times some thing and plus 3 equals -7
Step-by-step explanation:
x = -5
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
1 European euro = 1.3687 US dollars
44.70 US dollars
73.06 US dollars
136.87 US dollars
140.41 US dollars
Answer:
Step-by-step explanation:
€150 ($1.3687 / €1) = $205.30
$250 − $205.30 = $44.70
Answer:
A: 44.70 US dollars
Step-by-step explanation:
Captain Gabriela has a ship, the H.M.S. Khan. The ship is two furlongs from dead pirate Daniel and his merciless band of thieves.
The captain has the probability of 1/2 of hitting the pirate ship. the pirate only has one good eye, so he hits the captains ship with probability 1/5 .
If both fire cannons at the same time, what is the probability that both the pirate and the captain hit each other's chip
Answer:
[tex]\dfrac{1}{10}[/tex]
Step-by-step explanation:
Probability of the captain hitting the pirate ship [tex]=\dfrac{1}{2}[/tex]
Probability of the pirate hitting the captain's ship [tex]=\dfrac{1}{5}[/tex]
If both fire cannons at the same time, the probability that both the pirate and the captain hit each other's ship
=P(Captain Hits AND Pirate Hits)
=P(Captain Hits) X P(Pirate Hits)
[tex]=\dfrac{1}{2} X \dfrac{1}{5}\\\\=\dfrac{1}{10}[/tex]
I need help with this one
Answer:
I think 4^0 is the answer
Jana ran 7 days last week. She ran the same number of miles every day, and she ran 28 miles in all. What is Janas rate?
Answer:
Janas rate is of 4 miles per day.
Step-by-step explanation:
Her rate is the number of miles she ran per day.
We can solve this using a rule of three.
In 7 days, she ran 28 miles. How many miles she ran a day, that is, in one day?
1 day - x miles
7 days - 28 miles
[tex]7x = 28[/tex]
[tex]x = \frac{28}{7}[/tex]
[tex]x = 4[/tex]
Janas rate is of 4 miles per day.
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
a. 3
b. 5
c. 4
d. 4
e. 10
Step-by-step explanation:
Answer:
read below
Step-by-step explanation:
a.3
b.5
c.2
d.2
6. 8p
When writing expressions for complex numbers, what does i represent?
Answer: See below
Step-by-step explanation:
[tex]i[/tex] is an imaginary number.
[tex]i=\sqrt{-1}[/tex]
[tex]i^2=-1[/tex]
Of the mathematics degrees awarded in recent years, 76% were bachelor’s degrees, 21% were master’s degrees and the remaining 3% were doctorates. Moreover, women earned 52% of bachelors, 40% of masters and 22% of doctorates. What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman? Give your answer to 4 decimal places.
Answer:
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Given to a woman.
Event B: Masters degree.
21% were master’s degrees
This means that [tex]P(B) = 0.21[/tex]
Women earned 40% of masters
This means that [tex]P(A|B) = 0.4[/tex]
Probability of the degree being given to a women:
52% of 76%, 40% of 21% and 22% of 3%. So
[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]
What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?
[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
Please answer this correctly
Answer:
[tex]h=\sqrt{1.44}\\h = 1.2[/tex]
Step-by-step explanation:
Base of the triangle on the left = 0.5
Use pythagorean theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
Substitute
[tex]0.5^{2} + b^{2} = 1.3^{2}[/tex]
[tex]b^{2} = 1.3^2 - 0.5^2[/tex]
[tex]b^2 = 1.44[/tex]
[tex]b = \sqrt{1.44} \\[/tex]
[tex]b = 1.2[/tex]
in this case b is the height
so
[tex]h=\sqrt{1.44}\\h = 1.2[/tex]
HURRY! WILL GIVE BRAINLIEST! HURRY
[tex]answer \\ = - 0.5 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
Step-by-step explanation: