Answer:
[tex]\frac{28}{n}[/tex]
Step-by-step explanation:
-moves "The string of a kite is perfectly taut" and always makes an angle of 35 degrees above horizontal. (a) If the kite flyer has let out 500 feet of string, how high is the kite? (b) If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?
Answer:
a) [tex]h=286.8ft[/tex]
b) [tex]\frac{dh}{dt}=5.7ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Angle [tex]\theta=35[/tex]
a)
Slant height [tex]h_s=500ft[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=h_ssin\theta[/tex]
[tex]h=500sin35[/tex]
[tex]h=286.8ft[/tex]
b)
Rate of release
[tex]\frac{dl}{dt}=10ft/sec[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=lsin35[/tex]
Differentiate
[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]
[tex]\frac{dh}{dt}=10sin35[/tex]
[tex]\frac{dh}{dt}=5.7ft/s[/tex]
In a pool of water filled to a depth of 10 ft, calculate the fluid force on one side of a 3 ft by 4 ft rectangular plate if it rests vertically on its 4 ft edge at the bottom of the pool. Remember that water weighs 62.4 lb/ft3
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Answer:
6,364.8 lb
Step-by-step explanation:
The centroid of the plate is its center, so is 1.5 ft above the bottom of the pool, or 8.5 ft below the surface. The area of the plate is (3 ft)(4 ft) = 12 ft². Then the fluid force is ...
(62.4 lb/ft³)(8.5 ft)(12 ft²) = 6,364.8 lb
A wheelchair ramp with a length of 61 inches has a horizontal distance of 60 inches. What is the ramp’s vertical distance
Answer:
Step-by-step explanation:
The solution triangle attached below :
Since we have a right angled triangle, we can make use of Pythagoras rule to obtain the vertical distance, x
Recall :
Hypotenus² = opposite² + adjacent²
Hence,
x² = 61² - 60²
x² = 3721 - 3600
x² = 121
x = √121
x = 11
Vertical distance equals 11 inches
1,620 to the nearest ten ? Please don't answer if you know your wrong !
Answer:
I will say 2,000 yes so that is what I am putting
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 57% C: Scores below the top 43% and above the bottom 19% D: Scores below the top 81% and above the bottom 5% F: Bottom 5% of scores Scores on the test are normally distributed with a mean of 66.5 and a standard deviation of 9.9. 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 80.
Step-by-step explanation:
According to the Question,
Given That, A philosophy professor assigns letter grades on a test according to the following scheme.A: Top 12% of scores
B: Scores below the top 12% and above the bottom 57%
C: Scores below the top 43% and above the bottom 19%
D: Scores below the top 81% and above the bottom 5%
F: Bottom 5% of scores Scores on the test
And The normally distributed with a mean of 66.5 and a standard deviation of 9.9.
Now,
In a set with mean and standard deviation, the Z score of a measure X is given by Z = (X-μ)/σwe have μ=66.5 , σ=9.9
Find the minimum score required for an A grade.Top 12%, so at least the 100-12 = 88th percentile, which is the value of X when Z has a p-value of 0.88. So it is X when Z = 1.175.
⇒ Z = (X-μ)/σ
⇒ 1.175×9.9 = X-66.5
⇒ X=78.132
Rounding to the nearest whole number, the answer is 80.
The minimum score required for an A grade is 80.
Which choice is equivalent to(√6)( √8). How do you solve
A. 4√6
B. 4√3
C. 16√3
D. 3√16
Answer:
B
Step-by-step explanation:
(6)^1/2 × (8)^1/2
6^1/2 × 2 (2)^1/2
4 (3)^1/2
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected (without replacement).
Answer:
The probability of getting two good coils is 77.33%.
Step-by-step explanation:
Since a batch consists of 12 defective coils and 88 good ones, to determine the probability of getting two good coils when two coils are randomly selected (without replacement), the following calculation must be performed:
88/100 x 87/99 = X
0.88 x 0.878787 = X
0.77333 = X
Therefore, the probability of getting two good coils is 77.33%.
Can you please help me with this question
A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.
Answer:
(a) 3178
(b) 14231
(c) 33152
Step-by-step explanation:
Given
[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]
Solving (a): Year = 1998
1998 means t = 8 i.e. 1998 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]
[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]
[tex]y = \frac{269573}{1+985*0.08509}[/tex]
[tex]y = \frac{269573}{84.81365}[/tex]
[tex]y = 3178[/tex] --- approximated
Solving (b): Year = 2003
2003 means t = 13 i.e. 2003 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]
[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]
[tex]y = \frac{269573}{1+985*0.01824}[/tex]
[tex]y = \frac{269573}{18.9664}[/tex]
[tex]y = 14213[/tex] --- approximated
Solving (c): Year = 2006
2006 means t = 16 i.e. 2006 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]
[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]
[tex]y = \frac{269573}{1+985*0.00724}[/tex]
[tex]y = \frac{269573}{8.1314}[/tex]
[tex]y = 33152[/tex] --- approximated
A town recently dismissed 5 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50
Answer:
0.7513 = 75.13% probability that no more than 1 employee was over 50
Step-by-step explanation:
The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
4 + 16 = 20 employees, which means that [tex]N = 20[/tex]
4 over 50, which means that [tex]k = 4[/tex]
5 were dismissed, which means that [tex]n = 5[/tex]
What is the probability that no more than 1 employee was over 50?
Probability of at most one over 50, which is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]
[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]
0.7513 = 75.13% probability that no more than 1 employee was over 50
Factor 2x^2+15x+25. Rewrite the trinomial with the x-term expanded,using the two factors. Then, group the first two and last two terms together and find the GCF of each.
Answer:
[tex][x + 5][2x+ 5][/tex]
Step-by-step explanation:
Given
[tex]2x^2 + 15x + 25[/tex]
Required
Factorize
Expand the x term
[tex]2x^2 + 5x + 10x+ 25[/tex]
Group into 2
[tex][2x^2 + 5x] + [10x+ 25][/tex]
Take the GCF of each group
[tex]x[2x + 5] + 5[2x+ 5][/tex]
Factor out 2x + 5
[tex][x + 5][2x+ 5][/tex]
A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
2498x2364
explaine how to solve
Answer:
5 905 272
Step-by-step explanation:
you can refer to this lattice multiplication or u can search you tube for the examples of lattice multiplication
Which point is part of the solution of the inequality y ≤ |x + 4| − 3?
Answer:
Step-by-step explanation:
would someone mind looking over my answers to geometry!!
Answer:
Question 1: x = 6
Question 2: Correct!
Question 3: x = 11
Question 4: Correct!
Step-by-step explanation:
Question 1:
Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.
Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:
First, subtract 50 from 180 to find what angle 22x - 2 will equal:
180 - 50 = 130
130 = 22x - 2
Now use basic algebra to solve for x:
130 = 22x - 2
(add 2 to both sides)
132 = 22x
(divide both sides by 22)
x = 6
Question 3:
Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.
With that in mind, to solve for x, add the two equations and set it equal to 180:
5x + 15 + (9x + 11) = 180
Now use basic algebra to solve for x:
5x + 15 + 9x + 11 = 180
(add like terms)
14x + 26 = 180
(subtract 26 from both sides)
14x = 154
(divide 14 from both sides)
x = 11
Hope it helps (●'◡'●)
Simplify the ratio.
2.25 to 0.5
Answer:
9:2
Step-by-step explanation:
Which of the following situations WOULD NOT represent a binomial application? A. Choosing a card randomly from a standard deck and noting its color (remember color has only two outcomes black or red) B. Choosing a card randomly from a standard deck and noting whether its a face card C. Choosing a card randomly from a standard deck and noting its suit D. Choosing a card randomly from a standard deck and noting whether or not it's an ace
Answer:
Choosing a card randomly and noting its suit
Step-by-step explanation:
Choosing a card randomly and noting its suit
This is because binomial distributions only work for bernoulli trials (a trail in which there are only two outcomes)
what is 221st number out of 5,6,7,8,9
Answer:
221
Step-by-step explanation:
Given sequence is ,
> 5 , 6 , 7 , 8 , 9.
The common difference is 6-5 = 1 .
Therefore , the 221st number will be
> 221 st term = 221 × 1 = 221 .
Hence the 221 st term is 221 .
Answer:
225
Step-by-step explanation:
d = 6 - 5 = 1 (common differences)
a = 5 (first term)
221st term
a+(n-1)d
5 +(221 - 1) 1
5 + 220 =225
Therefore the answer is 225
Use the values in 9 = 2.2 and In 200 – 5.3 to find the approximate value of log, 200.
Answer:
2.409
Step-by-step explanation:
㏑ 9 = 2.2
ln 200 = 5.3
[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]
[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]
= [tex]\frac{ln 200}{ln 9}[/tex]= [tex]\frac{5.3}{2.2}[/tex]
= 2.409
The approximate value of log 200 would be; 2.409
What is a logarithm?When we raise a number with an exponent, there comes a result.
Let's say you get a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
We have given the values in 9 = 2.2 and 200 – 5.3
We need to find the approximate value of log, 200.
Therefore,
㏑ 9 = 2.2
ln 200 = 5.3
[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]
Using the logarithm property;
[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]
= 2.409
Hence, the approximate value of log, 200 would be; 2.409
Learn more about logarithm here:
https://brainly.com/question/20835449
#SPJ2
..................................................................
Answer:
Hello?
Step-by-step explanation:
a, b, c are prime numbers and 5≤a
Answer:
a=5
Step-by-step explanation:
Solve the equation for x.
2/3x-1/9x+5=20
Answer:
x = 27
Step-by-step explanation:
I'm assuming the equation looks like this:
[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]
Here's how to solve for x:
[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]
(subtract 5 from both sides)
[tex]\frac{2}{3}x-\frac{1}{9}x=15[/tex]
(Find the GCF of 3 and 9, which is 3. Multiply 2/3 by 3/3. You get 6/9)
[tex]\frac{6}{9}x-\frac{1}{9}x=15[/tex]
(add like terms)
[tex]\frac{5}{9}x=15[/tex]
(multiply 9/5 to both sides, which is the same as dividing both sides by 5/9)
x = 27
Hope it helps (●'◡'●)
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
Answer:
0.96784
Step-by-step explanation:
17-13.3/2
=1.85
p(x<1.85)
=0.96784
The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
Mean [tex]\mu[/tex]=13.3 minutes
Standard deviation[tex]\sigma[/tex]=2 minutes
What is a z-score?The value of the z-score tells you how many standard deviations you are away from the mean.
So, the z-score of the above data
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{17-13.3}{2}[/tex]
[tex]z=1.85[/tex]
From the standard normal table, the p-value corresponding to z=1.85
Or, p(x<1.85)=0.9678 or 96.78%
Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
To get more about the z-score visit:
https://brainly.com/question/25638875
r=4+7x-sx
I need help so any one can help with this
How would I simplify the expressions on the picture?
Answer:
7. [tex]x^{11}[/tex] 8. [tex]y^{2}\\[/tex] 9. [tex]p^{12}[/tex] 10.[tex]a^{3} b^{2}[/tex] 11.[tex]g^{16}[/tex] 12.[tex]r^{9} h^{3}[/tex] 13.[tex]m^{15} p^{6}[/tex] 14.[tex]k^{6} y[/tex] 15.[tex]x^6 z^4[/tex]
Step-by-step explanation:
7. [tex]x^3[/tex] × [tex]x^8[/tex] = [tex]x^{11}[/tex] when multiplying with exponents you add
8. [tex]\frac{y^{6} }{y^{4} }[/tex] = [tex]y^{2}[/tex] when dividing with exponents you subtract
9. [tex](p^{3})^4[/tex] = [tex]p^{12}\\[/tex] when it's power to power, you multiply
10. [tex]\frac{a^{9} b^{4}}{a^{6} b^{2}}[/tex] = [tex]a^{3} b^{2}[/tex] (subtract exponents)
11. [tex](g^{8})^2[/tex] = [tex]g^{16}[/tex] (multiply exponents)
12. [tex]r^{4} h^{2} r^{5} h[/tex] = [tex]r^{9} h^{3}[/tex] (add exponents [tex]r^4 + r^5\\[/tex] and [tex]h^2 +h^1\\[/tex] )
13. [tex](m^{5} p^{2})^3[/tex] = [tex]m^{15} p^{6}[/tex] (multiply exponents)
14. [tex]\frac{k^{7} y^{4}}{y^{3}k}[/tex] = [tex]k^{6} y[/tex] (subtract exponents [tex]k^7-k^1[/tex] and [tex]y^4-y^3\\[/tex] )
15. [tex]x^3 z^2 x^3 z^2[/tex] = [tex]x^6 z^4[/tex] (add exponents same as #12)
Simplify the given expression below:
(4 + 21) – (1 – 71)
Hey there!
(4 + 21) - (1 - 71)
4 + 21 = 25
= 25 - (1 - 71)
1 - 71 = -70
= 25 - (-70)
= 25 + 70
= 95
Answer: 95
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
help me plz----------------------------
9514 1404 393
Answer:
A. 5 should have been subtracted in step 4
Step-by-step explanation:
No question is stated, so there is no "answer."
__
If we assume the question is, "What error did Keith make?" then choice A properly describes it.
Step 4 should look like ...
x -5 = 7y . . . . . . . 5 should be subtracted from both sides
and the final result should be ...
g(x) = (x -5)/7
Find the value of x.
Answer:
the value of x is 29°
hope it helps
have a nice day
Last year, Manuel deposited $7000 into an account that paid 11% interest per year and $1000 into an account that paid 5% interest per year. No withdrawals were made from the accounts. Answer the questions below. Do not do any rounding. (a) What was the total interest earned at the end of year? (b) What was the percent interest for the total deposited?
Answer:
The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.
Step-by-step explanation:
Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:
7000 x 0.11 + 1000 x 0.05 = X
770 + 50 = X
820 = X
8000 = 100
820 = X
820 x 100/8000 = X
82,000 / 8,000 = X
10.25 = X
Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.
A senior class of 420 students will rent buses and vans for a class trip. Each bus can transport 50 students and 3 chaperones and costs $1200 to rent. Each van can transport 10 students and 1 chaperone and costs $100 to rent. There are 36 chaperones available (so they can't all go in vans). How many vehicles of each type should be rented in order to minimize the cost
Answer:
37 buses and 1 van.
Step-by-step explanation:
The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .
The cost of renting buses for 50 students is $500
What we do is rent 37 buses and 1 van
37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.
Then rent 1 van to take in 50 students and 1 chaperone.
The total cost here will be
$3700 + $1200 = $ 4900
This will help to safe cost.
