Answer:
11.45 lumens
Step-by-step explanation:
We are given that
[tex]log(I/12)=-0.00235x[/tex]
Where x=Depth
I=Intensity of light
We have to find the intensity of the light at a depth of 20 feet.
Substitute the value of x
[tex]log(I/12)=-0.00235\times 20[/tex]
[tex]log(I/12)=-0.047[/tex]
[tex]\frac{I}{12}=e^{-0.047}[/tex]
[tex]I=12e^{-0.047}[/tex]
[tex]I=11.45 Lumens[/tex]
Hence, the intensity of the light (in lumens) at a depth of 20 feet=11.45 lumens
Question
Elvira and Aletheia live 3.2 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira 1/2 hour and Aletheia 2/3 hour to walk to the coffee shop. Find both women's walking speeds.
Missing from the question
Aletheia's speed is 0.6 miles per hour slower than Elvira's speed.
Answer:
[tex]s_E = 3.0[/tex]
[tex]s_A = 2.4[/tex]
Step-by-step explanation:
Given
[tex]d = 3.2m[/tex] -- distance
[tex]t_E = 1/2[/tex] --- Elvira time
[tex]t_A = 2/3[/tex] --- Aletheia time
[tex]s_E - s_A = 0.6[/tex] --- the relationship between their speeds
Required
Their walking speed
Distance (d) is calculated as:
[tex]d = speed * time[/tex]
For Elvira, we have:
[tex]d_E = s_E * 1/2[/tex]
For Aletheia, we have:
[tex]d_A = s_A * 2/3[/tex]
So, we have:
[tex]d_E + d_A = d[/tex] --- total distance
This gives:
[tex]s_E * 1/2 + s_A * 2/3 = 3.2[/tex]
Recall that:
[tex]s_E - s_A = 0.6[/tex]
Make sE the subject
[tex]s_E = 0.6+s_A[/tex]
Substitute [tex]s_E = 0.6+s_A[/tex] in [tex]s_E * 1/2 + s_A * 2/3 = 3.2[/tex]
[tex](0.6+s_A)* 1/2 + s_A * 2/3 = 3.2[/tex]
[tex]0.3+1/2s_A + 2/3s_A = 3.2[/tex]
Collect like terms
[tex]1/2s_A + 2/3s_A = 3.2-0.3[/tex]
[tex]1/2s_A + 2/3s_A = 2.9[/tex]
Express all as decimal
[tex]0.5s_A + 0.7s_A= 2.9[/tex]
[tex]1.2s_A= 2.9[/tex]
Divide both sides by 1.2
[tex]s_A = 2.4[/tex]
Recall that:
[tex]s_E = 0.6+s_A[/tex]
So, we have:
[tex]s_E = 0.6+2.4[/tex]
[tex]s_E = 3.0[/tex]
Simplify. (x+y)/(x^2y)-(x-2y)/(xy^2)
Answer:
[tex]{ \tt{ = \frac{(x + y)}{ {x}^{2}y } - \frac{(x - 2y)}{ {xy}^{2} } }} [/tex]
Find the LCM of denominators: x²y²
[tex]{ \tt{ = \frac{y(x + y) - x(x - 2y)}{ {x}^{2} {y}^{2} } }} \\ \\ = { \tt{ \frac{xy + {y}^{2} - {x}^{2} +2xy }{ {x}^{2} {y}^{2} } }}[/tex]
Simplify further:
[tex] = { \tt{ \frac{(y - x)(y + x) +3xy}{ {(xy)}^{2} } }} \\ \\ = { \tt{ \frac{(y - x)(y + x)}{ {(xy)}^{2} } - \frac{3}{xy} }}[/tex]
During spring, young moose, unfamiliar with roads and traffic, are wandering around at night in a province, causing risk and road accidents. Suppose that the average number of road accidents involving moose was per day. The government increased the number of hunting licenses and cleared brush to improve drivers' visibility. On one day after these measures were implemented, there were road accidents involving moose.
Required:
a. What would be the chance of such accidents or fewer, assuming the government's measures were ineffective?
b. Do you think the government's measures were effective? State your reasons clearly.
Please help out would really appreciate it
Answer:
Step-by-step explanation:
1. Apply the Pythagoras theorem to determine the value of x, we have;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]x^{2}[/tex] = [tex]15^{2}[/tex] + [tex]8^{2}[/tex]
= 289
x = [tex]\sqrt{289}[/tex]
x = 17
2. Trigonometric ratios of <D.
i. Sin <D = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{8}{17}[/tex]
ii. Cos <D = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
= [tex]\frac{15}{17}[/tex]
iii. Tan <D = [tex]\frac{Opposite}{Adjacent}[/tex]
= [tex]\frac{8}{15}[/tex]
3. Trigonometric ratios of <F.
i. Sin <F = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{15}{17}[/tex]
ii. Cos <F = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
= [tex]\frac{8}{17}[/tex]
iii. Tan <F = [tex]\frac{Opposite}{Adjacent}[/tex]
= [tex]\frac{15}{8}[/tex]
Remember the dataset of alligators which was about the length and weight of several aligators in Florida. The variable X is the length of aligator and the Y variable is the weight of them. A researcher decided to use decision tree and designed two steps: X<4, X>4. What is the name of this method of splitting?A. Multi-way splitting.B. Entropy classification.C. Binary splitting.D. Gini index.
Answer:
A. multi-way split.
Step-by-step explanation:
Multi way split consists of internal at decision tree branches. Gini index measures probability of impurity in the random variables chosen. Entropy is measure of uncertainty in the sample selected. Binary splitting is used to speed up numerical evaluation.
The price of a certain item is P dollars. The sales tax on the item is 7%. Which expressions represent the total cost of the item, in dollars, after the tax has been applied? Select EACH correct anwser
0.07P 1.07P P+0.07P 1+0.07P (1+0.07)P
Step-by-step explanation:
P = $ Dollars
Item = 7%
Answer
item 7/100 = 0.07/1 item
(1+0.07) P
(A) Over 1000 students organized to celebrate running water and electricity. To count the exact number of students protesting, the chief organizer lined the students up in columns of different length. If the students are arranged in columns of 3, 5, and 7, then 2, 3, and 4 people are left out, respectively. What is the minimum number of students present? Solve it with Chinese Remainder Theorem. (B) Prove that for n> 1, if 935 = 5 x 11 x 17 divides n80 – 1, then 5, 11, and 17 do not divide n.
Solution :
A). x = 2 (mod 3) [tex]$\mu = 3\times 5 \times 7 = 105$[/tex]
x = 3 (mod 5) [tex]$y_1=35^{-1} (\mod 3)$[/tex]
x = 4 (mod 7) [tex]y_1=2[/tex]
[tex]$y_2=21^{-1}(\mod5) = 1$[/tex]
[tex]$y_3=15^{-1}(\mod7) = 1$[/tex]
[tex]$x=2 \times 35 \times 2 + 3\times 21\times 1+4\times 15\times 1$[/tex]
[tex]=140+63+60[/tex]
[tex]=263[/tex]
≡ 53(mod 105)
Hence the solution is 105 k + 53 > 1000 for k = 10
Therefore, the minimum number of students = 1103
B). [tex]$\phi (935) = 640$[/tex]
By Eulu's theory
[tex]$935 | a^{640}_n -1$[/tex] if n and 935 are coprime.
Now, [tex]$935|n^{80}-1$[/tex] and 80 x 8 = 640
[tex]$935|n^{640}-1$[/tex] ⇒ g(n,935) = 1
⇒ 5, 11, 17 do not divide n
There are two 5s in the number 855,309. Rico
says that the 5 in the ten-thousinds place is 1000
times greater than the 5 to its right. Is she correct?
Explain how
you know
Answer:
no it is 10 times greater because we use the base 10 system where each number to the left is 10 times greater
Step-by-step explanation:
he following chart reports the number of cell phones sold at a big-box retail store for the last 26 days. a. What are the maximum and the minimum numbers of cell phones sold in a day? b. Using the median, what is the typical number of cell phones sold?
Answer:
Maximum = 19
Minimum = 4
Median = 12
Step-by-step explanation:
The maximum number of phone sold per day is the value to the right of the horizontal axis as the values are arranged in ascending order ; Hence, the maximum number of phones sold per day is 19
Also, the minimum number of phones sold per day is the value to the left of the plot, Hence, minimum number of phones sold per day is 14.
The Median value : 4, 9, 14, 19
The median = 1/2(n+1)th term
1/2(5)th term = 2.5 th term
Median (9 + 14) /2 = 13 /2 = 11.5 = 12 phones
Which of the following is the vertical asymptote for the graph below?
Answer:
C
Step-by-step explanation:
Vertical asymptotes are always in the form x = ?
If you look at the dotted line, it lands on 2. Because it's a vertical line, the asymptote is going to be x = 2
Consider the probability that no more than 76 out of 504 computers will crash in a day. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 75.5
b. Area to the right of 76.5
c. Area to the left of 75.5
d. Area to the left of 76.5
e. Area between 75.5 and 76.5
Answer:
e
Step-by-step explanation:
can you help me with these high rated questions
I wish you will help me with his highlighted questions
Answer:
52 is (a)
55 is.( d)
56. is (d)
Choose the function whose graph is given by:
OA.y= cos(2x)
OB.y= cos(1/2x)
OC.y= cos(4x)
D. y = cos(1/4x)
Using translation concepts, it is found that the function whose graph is given is:
A. y= cos(2x)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The original cosine function has period of [tex]2\pi[/tex], and in this problem, the function has a period of [tex]\pi[/tex], hence the domain was multiplied by 2, which means that option A is correct.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
An ecologist finds 220 yellow-flowered plants and 180 white-flowered plants. Use the normal distribution to find the Lower boundary of a 95% confidence interval for the proportion of yellow-flowered plants. Which of the following answers is correct to 2 decimal places?
a. Lower boundary = 0.30
b. Lower boundary = 0.60
c. Lower boundary = 0.50
d. Lower boundary = 0.40
Answer:
c. Lower boundary = 0.50
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
An ecologist finds 220 yellow-flowered plants and 180 white-flowered plants.
220 out of 220 + 180 = 400. So
[tex]n = 400, \pi = \frac{220}{400} = 0.55[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.96\sqrt{\frac{0.55*0.45}{400}} = 0.5[/tex]
Thus the correct answer is given by option c.
Evaluate each expression.
helppp .....................
Answer:
D represents a proportional relationship
Step-by-step explanation:
Proportional graphs always intersect with zero
please help me!!!!!!!!!!!!
Step-by-step explanation:
24. = 249030/30
=8,301 rs
Answer:
24. 8301, divide 249030 by 30
25. 9989001, but i dont know the property
Step-by-step explanation:
A psychology professor assigns letter grades on a test according to the following scheme. A: Top 14% of scores B: Scores below the top 14% and above the bottom 65% C: Scores below the top 35% and above the bottom 16% D: Scores below the top 84% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 68.4 and a standard deviation of 9.7. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a B grade are 72 and 79, that is, a score between 72 and 79 results in a B grade.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 68.4 and a standard deviation of 9.7.
This means that [tex]\mu = 68.4, \sigma = 9.7[/tex]
Find the numerical limits for a B grade.
Below the 100 - 14 = 86th percentile and above the 65th percentile.
65th percentile:
X when Z has a p-value of 0.65, so X when Z = 0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.385 = \frac{X - 68.4}{9.7}[/tex]
[tex]X - 68.4 = 0.385*9.7[/tex]
[tex]X = 72[/tex]
86th percentile:
X when Z has a p-value of 0.86, so X when Z = 1.08.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.08 = \frac{X - 68.4}{9.7}[/tex]
[tex]X - 68.4 = 1.08*9.7[/tex]
[tex]X = 79[/tex]
The numerical limits for a B grade are 72 and 79, that is, a score between 72 and 79 results in a B grade.
Initial amount problem help
Answer:
3000
growth
2.2%
Step-by-step explanation:
If you apply the changes below to the cube root parent function, F(x) = 3/x
what is the equation of the new function?
• Translate 1 unit right.
• Translate 1 unit up.
A. G(x) = 3/x-1+1
B. G(x) = 3/x +1-1
C. G(x) =3/ x - 1-1
D. G(x) = 3/x+1+1
9514 1404 393
Answer:
A. G(x) = ∛(x -1) +1
Step-by-step explanation:
The transformation f(x-h) +k represents a translation (right, up) by (h, k) of the parent function f(x).
Your translation of f(x) = ∛x by (1, 1) will give you the function ...
G(x) = ∛(x -1) +1
Find the intercepts of the function y = 3x + 9
Step-by-step explanation:
To solve for the x-intercept, set y=0 then solve for x.
y=−3x−9. 0=−3x−9. 3x=−9.
x=−3 when y=0.
To solve for the y-intercept, set x=0 then solve for y.
y=−3x−9. y=−3(0)−9. y=−9 when x=0.
Hi there!
Y-intercept:
Set the x value to 0:
y = 3(0) + 9
y = 9 --> (0, 9)
X-intercept:
Set the y value to 0:
0 = 3x + 9
Solve for x:
-9 = 3x
x = -3 --> (-3, 0)
if ABCD is a parallelogram,find m>D and angle C=(9×-1) and angle A=(13×-25)
9514 1404 393
Answer:
∠C = ∠A = 53°
∠D = 127°
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so ...
∠A = ∠C
13x -25 = 9x -1
4x = 24
x = 6
∠C = ∠A = 9(6) -1
∠C = ∠A = 53°
Adjacent angles of a parallelogram are supplementary.
∠D = 180 -∠C
∠D = 180 -(9(6) -1) = 180 -53
∠D = 127°
Drag each tile to the correct box.
Match each equation with its solution.
n =
= -1
n = -25
n = 1
Equation
Solution
12 + 15 = -10
>
-511 = 1
- 13 = -12
Answer:
n = 1
n = - 1
n = - 1/5
n = - 25
Step-by-step explanation:
We are to obtain the value if n in the given equations :
1.)
n - 13 = - 12
To find, n ;
Add 13 to both sides
n - 13 + 13 = - 12 + 13
n = 1
2.)
n/5 = - 1/5
Multiply both sides by 5
n/5 * 5 = - 1/5 * 5
n = - 1
3.)
-5n = 1
Divide both sides by - 5
-5n/-5 = 1/-5
n = - 1/5
4.)
n + 15 = - 10
Subtract 15 from both sides :
n + 15 - 15 = - 10 - 15
n = - 25
2) If licorice cost $6.59 a pound, how much would it cost to buy a quarter pound of licoric
(Hint: Convert the mixed fraction to an improper fraction or decimal and multiply by th
quantity required)
Answer:
$1.65
Step-by-step explanation:
[tex]6.59*.25=1.65[/tex]or
[tex]6.59*\frac{1}{4} =1.65[/tex]Estimate the square root between two consecutive whole numbers of sqrt [55]
9514 1404 393
Answer:
7.4 . . . . between 7 and 8
Step-by-step explanation:
55 is between the perfect squares 49 = 7² and 64 = 8². Using linear interpolation, the square root is approximately 7 +(55-49)/(64-49) = 7 6/15 = 7.4
√55 ≈ 7.4 . . . . approximate root by linear interpolation
_____
Additional comment
A way to improve the estimate of the root is to use the "Babylonian method" of iterating the root. Divide the original number (55) by the estimate of the root, and average that result with the estimate:
next best guess = (55/7.4 +7.4)/2 = 7 77/185 ≈ 7.4162_162(repeating)
This matches the actual root when rounded to 4 decimal places. The number of accurate decimal places approximately doubles with each iteration.
__
Another way to improve the estimate is to modify the fractional portion. (The above method converges on a root more quickly.) For this, the iteration of the fractional part of the root is ...
next fractional part = 6/(14 +(fractional part))
where 6/14 is the linear estimate fractional value with 1 subtracted from its denominator.
For one iteration, the new estimate of the fractional part is 6/(14 +6/15) = 5/12, so the root estimate is about 7.4167 compared to the above 7.4162.
Complete the table for the function y = x−−√3 + 7.
Answer:
option D (5 6 8 9) is the answer
Answer:
X [tex]\Longrightarrow -8\Longrightarrow -1\Longrightarrow 1\Longrightarrow 8[/tex]
Y[tex]\Longrightarrow 5\Longrightarrow 6\Longrightarrow 8\Longrightarrow 9[/tex]
[tex]Answer\hookrightarrow D)[/tex]
-------------------------
Hope it helps...
Have a great day!!
The Tres Difficult race helps raise money for charity. According to the website, of the proceeds from ticket sales go directly to charity.
2/5
Last year they made $8000 from ticket sales. How much was given to charity?
Answer:
3200
Step-by-step explanation:
We need to find 2/5 of the tickets sales
2/5 * 8000
3200
Answer:
3200
Step-by-step explanation:
you need to find what 2/5 is and the you take that away from 8000 and then you have your answer of 3200
Find the exact values of the six trigonometric functions at “a” given cos(2a) = - 4/5 and a is
in the 2nd quadrant.
If a is in the second quadrant, then cos(a) < 0 and sin(a) > 0.
Recall the double angle identity for cosine:
cos(2a) = 2 cos²(a) - 1 = 1 - 2 sin²(a)
It follows that
2 cos²(a) - 1 = -4/5 ==> cos²(a) = 1/10 ==> cos(a) = -1/√10
1 - 2 sin²(a) = -4/5 ==> sin²(a) = 9/10 ==> sin(a) = 3/√10
Then we find
1/cos(a) = sec(a) = -√10
1/sin(a) = csc(a) = √10/3
sin(a)/cos(a) = tan(a) = -3
1/tan(a) = cot(a) = -1/3
y – 1 = 2(x – 2), solve for y
Answer:
y = 2x-3
Step-by-step explanation:
y – 1 = 2(x – 2)
Distribute
y-1 =2x-4
Add 1 to each side
y-1+1 = 2x-4+1
y = 2x-3
HELP PLEASE, Function problem
Answer:
-2
-1
-2
Step-by-step explanation:
please forgive me, but again, this is the simplest of the simplest things. how is that a problem ?
this costs so much more time to just put it in here and then copy answers than just doing it. this is literally a matter of seconds.
the functional value is -2 for all x that are not equal to 2.
and the functional value is -1, when x = 2
so, what is the problem ?
please see my other answer for more details on the solution.
