A 5.8-ft-tall person walks away from a 9-ft lamppost at a constant rate of 3.4 ft/sec. What is the rate that the tip of the person's shadow moves away from the lamppost when the person is 11 ft away from the lampost
Answers
Answer:
9.56 ft/sec
Step-by-step explanation:
We are told that a 5.8-ft-tall person walks away from a 9-ft lamppost at a constant rate of 3.4 ft/sec.
I've attached an image showing triangle that depicts this;
Thus; dx/dt = 3.4 ft/sec
From the attached image and using principle of similar triangles, we can say that;
9/y = 5.8/(y - x)
9(y - x) = 5.8y
9y - 9x = 5.8y
9y - 5.8y = 9x
3.2y = 9x
y = 9x/3.2
dy/dx = 9/3.2
Now, to find how fast the tip of the shadow is moving away from the lamp post, it is;
dy/dt = dy/dx × dx/dt
dy/dt = (9/3.2) × 3.4
dy/dt = 9.5625 ft/s ≈ 9.56 ft/sec
Related Questions
Jillian has been updating the design of a media streaming website. She wonders if users will spend more time on the site with the new design, so she designs a study. She starts with a random sample of 1,000 users and randomly assigns half of them to the old design and half of them to the new design. After a week, she notices that users with the new design spend significantly longer on the site than the users with the old design. Can we conclude that the new design caused users to spend more time on the site? Why? Choose 1 answer: A)Yes because the sample size was large, B) Yes, because the users were randomly assigned to treatment and control groups, C) Yes, because the users were randomly selected, D) Not necessarily, because the sample size was too small, E) Not necessarily, because this wasn’t an experiment.
Answers
Answer:
Yes, because the users were randomly assigned to treatment and control groups
Step-by-step explanation:
Random assignment to treatment and control groups makes this study an experiment, so we can make causal conclusions.
Answer:
C: Yes, because the users were randomly selected
Step-by-step explanation:
Got it right on USATP.
Hope this helps!
From: Aug1e
Suppose that you are attempting to estimate the annual income of 1700 families. In order to use the infinite standard deviation formula, what sample size, n, should you use
Answers
Answer:
Sample size should be less than 85
Step-by-step explanation:
Sample size should be less than 85
Step-by-step explanation:
To use the infinite standard deviation formula, n has to be <= (0.05)(1700)
n <= 85
So the sample size has to be less than 85
In another way too,
n = sample size
N = population size
For population, we multiply correction factor to the infinite standard deviation
F is <= 0.05
[tex]n/{N} <0.05[/tex]
n<0.05x1700
n<85
Sample size should be less than 85
Help me plssss I'm confused
Answers
Answer:
The first graph .. I am most likely right.
Step-by-step explanation:
Hope i helped.
State whether the given pair of sets are equal, equivalent, both, or neither. {0,9}; {8, 1)
Answers
Answer:
Equivalent
Step-by-step explanation:
A set is a well defined collection of objects.
Two sets are said to be equal if they have the same elements.
Two sets are said to be equivalent if they have the same number of elements.
Given sets are [tex]\{0,9\}\,,\,\{8,1\}[/tex]
These sets are not equal as both the sets have different elements.
Order of both the sets is 2 (number of elements in both sets is 2)
So,
these two sets are equivalent.
Help I will award brainliest help asap! Uwu: If a man can run p miles in x minutes, how long will it take him to run q miles at the same rate?
Answers
Answer:
Speed= Dist/time= p/x miles per minute
Time to run q miles=q divided by p/x= qx/p minutes
Step-by-step explanation:
Then find MN.
LM = 5
MN = x - 4
LN = 2x– 11
equation:
MN =
Answers
Answer:
[tex]MN = 8[/tex]
Step-by-step explanation:
Given
[tex]LM = 5\\MN = x - 4\\LN = 2x - 11[/tex]
Required
Determine MN
MN is calculated as thus:
[tex]LN = LM + MN[/tex]
Make MN the subject
[tex]MN = LN - LM[/tex]
Substitute values for MN, LN and LM
[tex]x - 4 = 2x - 11 - 5[/tex]
[tex]x - 4 = 2x - 16[/tex]
Collect Like Terms
[tex]x - 2x = -16 +4[/tex]
[tex]-x = -12[/tex]
[tex]x= 12[/tex]
Substitute 12 for x [tex]MN = x - 4[/tex]
[tex]MN = 12 - 4[/tex]
[tex]MN = 8[/tex]
Rewrite the equation in standard form.
y=2x-10
Answers
Answer:
The equation in standard form:
2x-y-10=0
A line with a positive slope is perpendicular to one of the lines shown. What is its slope? Use the graph
shown below.
The slope is
Answers
Answer:
¾
Step-by-step explanation:
The line that slants upward from left to right is a positive slope, while the line that slants downwards from left to right is a negative slope.
Therefore, the blue line would have a positive slope. Since the blue line with a positive slope is perpendicular to the red line with a negative slope, therefore, the slope of the line with a positive slope that we are looking for and that is perpendicular to one of the lines (red line) would be the same with the slope of the blue line.
The slope of the blue line is calculated as shown below:
Use the coordinates of these two points on the blue line to find the slope, (0, 1) and (4, 4)
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} [/tex]
[tex] slope(m) = \frac{3}{4} [/tex]
The slope of the line we are looking for is ¾.
Answer:
3/4
Step-by-step explanation:
How can I prove to my teacher I’m smart when I’m a kinda low-key student to her. Especially in mathematics.
Answers
Answer:
Do your work? Especially if you do it fast, it amazes them lol
(1 point) Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the following data: Assume that the suburb has a population of 320000 and is growing at a rate of 5000 per year. Assume that the city has a population of 624000 and is declining at a rate of 14000 per year. In how many years will the populations of the suburb and the city be equal
Answers
Answer:
16 years
Step-by-step explanation:
Let x represent the number of years. The suburb population is growing at a rate of 5000 per year after x years, it can be represented by the equation:
320000 + 5000x
The city population is declining at a rate of 14000 per year after x years, it can be represented by the equation:
624000 - 14000x
The number of years for the city and suburb population to be equal can be gotten from:
320000 + 5000x = 624000 - 14000x
14000x + 5000x = 624000 - 320000
19000x = 304000
x = 304000 / 19000
x = 16
In 16 years the populations of the suburb and the city be equal
Whats the circumference of a circle object that's 2 meters ?
Answers
NEED HELP PLEASE ANSWER
Answers
Answer:
I think its 1430 miles
Step-by-step explanation:
A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below. Age (in years) Height (inches) 7 47.3 8 48.8 5 41.3 8 50.4 8 51 7 47.1 7 46.9 7 48 9 51.2 8 51.2 5 40.3 8 48.9 6 45.2 5 41.9 8 49.6 How much of the variation in the sample values of height does the model estimate
Answers
Answer:
0.940
Step-by-step explanation:
Given the data:
Age in years(X) _____Height(Y)
7 _________ 47.3
8 _________48.8
5 __________41.3
8 _________ 50.4
8 ___________51
7 __________47.1
7 __________46.9
7 ___________48
9 __________51.2
8 __________51.2
5 __________40.3
8 __________48.9
6 __________45.2
5 __________41.9
8 __________49.6
The proportion of Variation explained by the line of best fit in a regression model can be determined by calculating the Coefficient of determination (R²) of the model.
Using the online R² calculator, the variation in the sample values of height which is estimated by the model is 0.9696² = 0.94012416.
Hence about 0.94 or 94% variation in sample values of height is estimated by the model while (1 - 0.94 = 0.06 or 6%) is explained by other factors.
A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest hundredth foot.) PLEASE HELP!!
Answers
Answer:
A = a^2.....the Area (A) of a square = a^2...where a = one side
79 = a^2...now take the sqrt of both sides, this eliminates the ^2
sqrt 79 = a
8.888 rounded = 8.89 = a......so one side = 8.89 ft
Step-by-step explanation:
If you roll a die once, what is the probability of rolling a 3?
Answers
Answer:
1/6
Step-by-step explanation:
there are 6 sides, and 3 is one of the 6 sides. thus, the answer is 1/6
Answer:
1/6
Step-by-step explanation: there are 6 incomes and 1 number 3 in a die
RS¯¯¯¯¯¯ bisects ∠QRT. If m∠QRT = 116°, what is m∠QRS?
A. 26°
B. 232°
C. 64°
D. 58°
Answers
Answer:
D. 58
Step-by-step explanation:
pretty easy clap
bisecting is midpoint which makes the two angles congruent
HURRYYYY PLSSSSS IM TIMED
Which equation represents the number of books (b) a student reads each week (w) if the student reads 3 books each week? How many books will the student read in 18 weeks?
Question 3 options:
A)
w = 3b; 18
B)
b = 3w; 18
C)
w = 3b; 54
D)
b = 3w; 54
Answers
in order to solve the following sye of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them? 4x-2y=7. 3x-3y=15
Answers
Answer:
dnhyfnvnvghdkd
Step-by-step explanation:
duhfgjfvnhfuvejfgkejiu
PLEASE HELP ASAP
Use the discriminant to determine how many real number solutions exist for the quadratic equation −4x2 + 3x –28 = 0.
Question 2 options:
A)
0
B)
3
C)
2
D)
1
Answers
The mean useful life of car batteries is 48 months. They have a standard deviation of 3. Assume the useful life of batteries is normally distributed. a. Calculate the percent of batteries with a useful life of less than 45 months. (Round your answer to the nearest tenth percent.) b. Calculate the percent of batteries that will last longer than 54 months. (Round your answer to the nearest tenth percent.)
Answers
Answer:
a) 15.9%
b) 2.3%
Step-by-step explanation:
We solving using z score formula. This formula is given as:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Calculate the percent of batteries with a useful life of less than 45 months. (Round your answer to the nearest tenth percent.)
x = 45, μ = 48, σ = 3
z = 45 - 48/3
= -1
Probability value from Z-Table:
The probability of batteries with a useful life of less than 45 months so
P(x<45) = 0.15866
Converting to percentage
0.15866 × 100 = 15.866
Approximately to the nearest tenth of a percent = 15.9%
b. Calculate the percent of batteries that will last longer than 54 months. (Round your answer to the nearest tenth percent.)
x = 58, μ = 48, σ = 3
z = 58 - 48/3
= 2
Probability value from Z-Table:
P(x<54) = 0.97725
P(x>54) = 1 - P(x<54)
= 0.02275
The probability of batteries that will last longer than 54 months is 0.02275
Converting to percentage
0.02275 × 100
= 2.275%
Approximately to the nearest tenth of a percentage = 2.3%
Lines I and M are parallel.
What is the measure of angle 3?
Answers
Answer:
25
Step-by-step explanation:
By the vertical angle theorem, we can find that:
m∠1 = 85
By the corresponding angle theorem, we can find that:
m∠2 = 2x
By the alternate interior angle theorem, we can find that:
m∠3 = x - 10
We also know that angles 1, 2, and 3 are the measures of the angles of a triangle. So:
85 + 2x + (x - 10) = 180
Lets solve for x. Combine like terms.
75 + 3x = 180
Subtract 75 from both sides.
3x = 105
Divide both sides by 3.
x = 35
So now we know that x + 35. Knowing this, we can find the measure of angle 3 by plugging 35 for x in x - 10
m∠3 = 35 - 10 = 25
So the measure of angle 3 is 25.
I hope this helps. Happy studying.
Please help me on this problem
Answers
Answer:
the y intercept is 3 and the x intercept is 6
Step-by-step explanation:
show your work
answer:v/7= 8
Answers
Answer:
V=56
Step-by-step explanation:
7x8=56
56/7=8
Answer:
v=56
Step-by-step explanation:
1 Multiply both sides by 77.
v=8\times 7v=8×7
2 Simplify 8\times 78×7 to 5656.
v=56
You have two chances to draw from a normal pack of 52 playing cards. What is the probability of drawing an ace on the second attempt if the first card (which you did NOT put back in the pack) was not an ace
Answers
Answer:
The probability is [tex]P(k) =0.07843[/tex]
Step-by-step explanation:
From the question we are told that
The total number of cards is n = 52
Generally the number of ace in a standard deck of cards is k = 4
Generally the the first card drawn is not an ace so the remaining number of ace after the first card is drawn is k = 4
also the remaining total number of cards after the first card is drawn is
N = n- 1
=> N = 52 - 1
=> N = 51
Generally the probability of drawing an ace on the second attempt if the first card (which you did NOT put back in the pack) was not an ace is mathematically represented as
[tex]P(k) =\frac{k}{N}[/tex]
=> [tex]P(k) =\frac{4}{51}[/tex]
=> [tex]P(k) =0.07843[/tex]
Janisa researched fast-growing industries and occupations, while Rylan researched industries and occupations that have the highest employment. Which most likely describes Janisa and Rylan’s findings? Janisa found that home health care is the fastest growing occupation and services for the elderly is the fastest growing industry, while Rylan found that elementary and secondary school teaching are the occupations with the highest employment and retail sales is the industry with the highest employment. Janisa found that services for the elderly is the fastest growing occupation and home health care is the fastest growing industry, while Rylan found that retail sales is the occupation with the highest employment and elementary and secondary school teaching is the industry with the highest employment. Janisa found that home health care is the fastest growing occupation and services for the elderly is the fastest growing industry, while Rylan found that retail sales is the occupation with
Answers
Answer:
Janisa found that home health care is the fastest-growing occupation and services for the elderly is the fastest growing industry, while Rylan found that elementary and secondary school teaching are the occupations with the highest employment and retail sales is the industry with the highest employment.
Explanation:
We make this conclusion because when we look at all the other options none matches the definition of occupations and industries. However, if Janisa found that home health care is the fastest-growing occupation, and then services for the elderly are the fastest growing industry, it matches what we know an industry and occupation mean.
While, if Rylan found that elementary and secondary school teaching are the occupations with the highest employment, it matches an example of occupation also, and if he discovers that retail sales is the industry with the highest employment it also falls under industry types.
However, the other options mismatched industry examples for occupations.
Answer:I think the answer is C the third option
Step-by-step explanation:
Two pools are being filled with water. To start, the first pool had 1850 liters of water and the second pool had 1334 liters of water. Water is being added to the first pool at a rate of 27 liters per minute. Water is being added to the second pool at a rate of 39 liters per minute. (a) For each pool, write an expression for the amount of water in each pool after x months. (b) Write an equation to show when the two pools would have the same amount of water.
Answers
Answer:
a)Total amount of water in pool 1 after x minutes = 1850+27x
Total amount of water in pool 2 after x minutes = 1334+39x
b) an equation to show when the two pools would have the same amount of water is 1850+27x= 1334+39x
Step-by-step explanation:
First Pool :
Initial amount of water in Pool = 1850 liters
Water is being added to the first pool at a rate of 27 liters per minute.
Amount of water added after x minutes = 27x
So, Total amount of water after x minutes = 1850+27x
Second Pool:
Initial amount of water in Pool = 1334 liters
Water is being added to the first pool at a rate of 39 liters per minute.
Amount of water added after x minutes = 39x
So, Total amount of water after x minutes = 1334+39x
Now to find an equation to show when the two pools would have the same amount of water.
1850+27x= 1334+39x
1850-1334=39x-27x
516=12x
[tex]\frac{516}{12}=x[/tex]
43 =x
Hence
a)Total amount of water in pool 1 after x minutes = 1850+27x
Total amount of water in pool 2 after x minutes = 1334+39x
b) an equation to show when the two pools would have the same amount of water is 1850+27x= 1334+39x
Use the substitution method to determine the solution type of the following system.
3y – 6x = 3
y = 2x + 1
Question 7 options:
Infinitely many solutions
(3, –1)
(2, 0)
No solutions
Answers
Answer:
Step-by-step explanation:
3y – 6x = 3 -----------------------------------(I)
y = 2x + 1 ----------------------------------(II)
Substitute y = 2x + 1 in equation (I)
3*(2x+ 1) - 6x = 3
3*2x + 3*1 -6x = 3
6x + 3 - 6x = 3
3 = 3
So, no solutions
Answer:
Use the substitution method to determine the solution type of the following system.
3y – 6x = 3
y = 2x + 1
Correct Answer
Infinitely many solutions
No solutions
(3, –1)
(2, 0)
Step-by-step explanation:
Televisions are on sale for 40% OFF the original price of $600. After tax (8.5%) is applied, what is the final price?
Answers
First, determine what is 40% of $600. Multiple 40 (as a decimal) by 600.
0.4 x 600 = 240
Therefore, the discount is $240 off $600.
Subtract the two values to find price (before tax): 600 - 240 = 360
So the TV will cost $360 before tax.
The tax is 8.5%. Multiply 8.5 as a decimal by 360 to find the amount of tax added.
0.085 x 360 = 30.6
Add 30.6 and the price before tax to find the final price.
30.6 + 360 = 390.60
Therefore, the final price of the TV is $390.60
an earthquake with a magnitude of about 2.0 or less is called a micro earthquake it is not usually fell to the intensity of an earthquake with a magnitude of 2 is how many times greater than the intensity of a standard earthquake? M=log I/S
-Answer choice-
2 times greater
10 times greater
100 times greater
1,000 times greater
Answers
Answer: 100 times greater
Step-by-step explanation:
Second question answer is: 1000 times a standard earthquake
What is the solution to the system shown here?
x + y 25
x + y = 5
Answers
Answer:
no solution (parallel lines )=1/1=1/1=5/1
Step-by-step explanation:
