The percent P of defective parts produced by a new employee t days after the employee starts work can be modeled by
P = t + 1810/50(t + 2).
Find the rates of change of P at t = 1 and t = 10. (Round your answers to two decimal places.)
Answer:
[tex]\frac{dP}{dt} (1) = -4.02\,\frac{\%}{day}[/tex], [tex]\frac{dP}{dt} (10) = -0.25\,\frac{\%}{day}[/tex]
Step-by-step explanation:
The complete statement is:
The percent [tex]p[/tex] of defective parts produced by a new employee [tex]t[/tex] days after the employee starts work can be modeled by:
[tex]p(t) = \frac{t+1810}{50\cdot (t+2)}[/tex]
Find the rates of change of [tex]p[/tex] at [tex]t = 1[/tex] and [tex]t = 10[/tex] (Round your answer to two decimal places.)
The rate of change of the function is the first derivative of the function in time. By rules of differentiation, we obtain the expression of the rate of change of the percent of defective parts:
[tex]\frac{dP}{dt} = \frac{50\cdot (t+2)-50\cdot (t+1810)}{50^{2}\cdot (t+2)^{2}}[/tex]
[tex]\frac{dP}{dt} = \frac{1}{50\cdot (t+2)}-\frac{t+1810}{50\cdot (t+2)^{2}}[/tex] (1)
The rates of change of P at [tex]t = 1[/tex] and [tex]t = 10[/tex] are, respectively:
[tex]\frac{dP}{dt} (1) = -4.02\,\frac{\%}{day}[/tex]
[tex]\frac{dP}{dt} (10) = -0.25\,\frac{\%}{day}[/tex]
If a video game cost $60 and it's on sale for 10% off, how much is the discount?
Answer:
$6
Step-by-step explanation:
Percentages have a cool little trick where they can be reversed :) 10% of 60 is a little tough, but we can switch it to 60% of 10, which is much easier. 60% of 10 is 6, so the discount is $6
Helppp please I'm stuck
Which is a pair of dependent events?
Answer:
Two events are dependent if the outcome of the first event affects the outcome of the second event, so that the probability is changed.
Step-by-step explanation:
Answer:
A.
You get a head and a tail in two coin tosses with two different coins.
Step-by-step explanation:
I took the test and got it right!
Marvin solved the equation 4(x+5)=88 fill in the blanks
Answer:
x=17
Step-by-step explanation:
4(x+5) = 88
4x + 20 = 88
4x = 88-20
4x = 68
x = 68/4
x = 17
Answer:
17
Step-by-step explanation:
4(x+5)=88
4x+20=88
4x=88-20
4x=68
4x÷4=68÷4
x=17
Help nnananannanannanananannannanansnnsnsnnsnsnsnsnnsns
Answer:
2
Step-by-step explanation:
The two x's end up being -4 and 6, so added together that's 2
Post Test:Transformation answer key?
Answer:
ur gay
Step-by-step explanation:
LOL
What is the CONSTANT in the expression 3k + 12?
Answer: 12
Step-by-step explanation:
The constant of the expression is 12.
What is a constant?'A constant is a value or number that never changes in expression that is it's constantly the same.'
According to the given problem,
In the expression 3k + 12 , k is a variable. A variable is a quantity that may change with respect to the mathematical criteria.
If k = 1, the value of the expression is (3 × 1) + 12 = 15
k =2, the value is (3 × 2) + 12 = 18
But we can see that no matter the value of k is, the expression has to be added with 12.
Hence, we can conclude that since the value of 12 does not change irrespective of the changing values k, the constant of this expression is 12.
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Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 43 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 43 births.
The value of the mean is__ (Type an integer or a decimal. Do not round.)
The value of the standard deviation is __. (Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ girls or fewer are significantly low. (Round to one decimal place as needed.)
Values of ___ girls or greater are significantly high. (Round to one decimal place as needed.)
c. Is the result of 32 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
The result is/is not significantly high, because 32 girls is greater than/equal to/less than ___ girls. A result of 32 girls would suggest that the method is not effective/is effective.(Round to one decimal place as needed.)
Answer:
A) Mean = 21.5
Standard deviation = 3.3
B) - Values of 14.9 girls or fewer are significantly low.
- Values of 28.1 girls or higher are significantly high
C) - The result is significantly high, because 32 girls is greater than 28.1 girls
-A result of 32 girls would suggest that the method is effective.
Step-by-step explanation:
A) We are given;
Number of couples; n = 43
Probability it is a girl; p = 0.5
Formula for mean is;
Mean; x¯ = np
x¯ = 43 × 0.5
x¯ = 21.5
Formula for standard deviation is;
SD = √(np(1 - p))
SD = √(43 × 0.5 × (1 - 0.5))
SD = √(43 × 0.5²)
SD ≈ 3.3
B) range rule of thumb is that the values are usually within 2 standard deviations from the mean.
Thus, we have;
x¯ ± 2SD
This gives;
21.5 ± 2(3.3)
That is;
21.5 + 6.6 and 21.5 - 6.6
To get; 28.1 and 14.9
This means that;
- Values of 14.9 girls or fewer are significantly low.
- Values of 28.1 girls or higher are significantly high
C) If the result is 32,it doesn't fall in between 14.9 and 28.1. As a matter of fact it is higher than 28.1, therefore we can say it is significantly high
- A result of 32 girls would suggest that the method is effective.
choose all answers that apply
Answer:
none of the above
Step-by-step explanation:
An isosceles trapezoid cannot be rotated to create the same image therefore it has no angle of rotational symmetry.
PLEASE HELP!
Please help me I don’t understand how to do this and it has to be done by tonight!!!
Answer:
these are notes i wrote in geometry I'm not sure if this will help. it's been a few months since i did this
A local television news station includes a viewer survey question about a current issue at the beginning of every evening news broadcast. Viewers are invited to use social media to respond to the question. The results of the survey are shared with the audience at the end of each broadcast. In relation to the opinions of the population of the region, which of the following is a possible reason why the results of such surveys could be biased?
I. Viewers with strong opinions about the current issue are more likely to respond than are viewers without strong opinions.
II. The opinions of viewers of one television station are not necessarily representative of the population of a region.
III. Viewers with access to social media are not necessarily representative of the population of a region.
a. I only
b. II only
c. III only
d. II and III only
e. I, II, and III
Answer:
ll
Step-by-step explanation:
ll is the msot resanable
PLEASE HELP
WILL MARK BRAINLIEST (not if you get it wrong)
Just with the median question :)
Answer:
Group one has the larger median
Step-by-step explanation:
Group One:
By taking off 8 on both ends we see that the median is 53 for group one.
33, 35, 40, 41, 43, 46, 48, 49, 53, 54, 55, 58, 58, 58, 62, 62, 67
Group two:
By taking off 8 on each end as well we get 47 and 49.
35, 38, 40, 41, 42, 43, 47, 47, 47, 49, 50, 50, 53, 54, 57, 61, 66, 69
we then take the average of the two numbers
47 + 49 = 96
96 / 2 = 48
Help out thankssssssssss !!!!!!
Answer:
x =20?
Step-by-step explanation:
I set them equal to each other
Answer:
it says the answer s t u v
Today only a table is being sold at a 15% discount. The sale price is $629
Answer:
740
Step-by-step explanation:
Answer:
The answer is $566.73.
Step-by-step explanation:
The way that you find the answer is dividing .15 to the price
Suppose that you reach into a bag and randomly select one piece of candy from 4 chocolates, 8 caramels and 19
peppermints. Find the probability of selecting a chocolate.
Answer:
Step-by-step explanation:
4 : 31
4/31
or .129
or 12.9%
Answer:
4/31
Step-by-step explanation:
4 chocolates out of a total of 31 pieces of candy
what is 6x1/3? in math ok.
HELPPP plssss pls pls
Answer:
∠C = 75°
Step-by-step explanation:
using the formula for the sum of interior mangles for a polygon:
total interior angles = (180° x 5 angles) - 360° = 540°
113° + 4x + 113° + 2x + 9° + 3x + 8° = 540°
combine like terms:
9x + 243° = 540°
9x = 297°
x = 33°
∠C = 2(33) + 9 = 75°
-3(-2-3x6)-5{4+2(-1)}
Answer:
The answer is 50
Step-by-step explanation:
= -3(-2-3×6)-5{4+2(-1)}
= -3(-2-18)-5{4-2}
= -3(-20)-5{2}
= 60-10
= 50
Answer:
-3(-2-18)-5(6-1)
-3(20)-5(5)
-60--25
=35
=====
8. Determine the area of a sector
with a central angle of 42° in a
circle with radius 3 inches.
NEED IT ASAP
Answer:
[tex]\boxed {\boxed {\sf A \approx 3.3 \ in^2}}[/tex]
Step-by-step explanation:
Since we are given the central angle in degrees, we should use the following formula for sector area.
[tex]A= \frac {\theta}{360}* \pi r^2[/tex]
The angle is 42 degrees and the radius is 3 inches. Therefore,
[tex]\theta= 42 \\r=3 \ in[/tex]
[tex]A=\frac {42}{360} * \pi (3 \ in)^2[/tex]
Solve the exponent.
(3 in)²= 3 in*3in = 9 in²[tex]A=\frac {42}{360} * \pi (9 \ in^2)[/tex]
Multiply all three numbers together.
[tex]A= 0.116666666667* 3.14159265359 * 9 \ in^2[/tex]
[tex]A=3.29867228627 \ in^2[/tex]
Let's round to the tenth place. The 9 in the hundredth place tells us to round the 2 up to a 3.
[tex]A \approx 3.3 \ in^2[/tex]
The area of the sector is approximately 3.3 square inches.
A path 2 m wide surrounds a large flowerbed.
Answer:
what are we supposed to do here
Which equations represent exponential growth functions? Select all that apply.
Question 6 options:
f(x)=(2.6)x
g(x)=(52)x
h(x)=(0.4)x
m(x)=(13)x
A 200g packet of oreos costs $3, calculate how much would a 50g packet cost?
Answer:
75c
Step-by-step explanation:
(50/200)×3=3/4=0.75
In a 24-hour period, Grace spends 8 hours sleeping, 8 hours at school, 2 hours at dance class, and the rest of the time with her family. What percentage of her day is used for family time?
Consider the following food chain:
Plants are eaten by grasshoppers, which are eaten by mice, which are eaten by snakes.
What will happen to the other members of the food chain if the grasshoppers are removed?
a.
the number of plants will increase, the number of mice will decrease, the number of snakes will decrease
b.
the number of plants will decrease, the number of mice will increase, the number of snakes will increase
c.
the number of plants will decrease, the number of mice will increase, the number of snakes will decrease
d.
the number of plants will increase, the number of mice will increase, the number of snakes will increase
Answer:
A
Step-by-step explanation:
the plant will increase because no grasshopper will be present to eat them without the grasshopper the mice cannot eat so the mice population will decrease....
If the grasshoppers are removed then the number of plants will increase, the number of mice will decrease, the number of snakes will decrease.
The correct answer is option a.
For the given Food chain:
If the grasshoppers are removed from the food chain, it will lead to a increase in the number of plants, as there will be no herbivores (grasshoppers) to consume them. This is because grasshoppers help control plant populations by feeding on them.
With the removal of grasshoppers, the mouse population is likely to decrease since their primary food source (grasshoppers) is no longer available.
As a consequence of the decreased mouse population, the snake population may also decrease because their primary food source (mice) has been affected.
Thus, the number of plants will increase, the number of mice will decrease, the number of snakes will decrease.
Thus, option a is correct.
Learn more about Food chain here:
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Find the equation of a line parallel to y - 5 = 6x – 10 that passes through the
point (4,10). (answer in slope-intercept form)
Answer:
y=6x-14
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
add 5 on both sides to make y on the left side and the other part on the right side.
y=6x-5
IMPORTANT: Parallel lines have the same slope
if the line passes through the point (4,10) we can substitute values for x and y into y=mx+b
10=4m+b
Now since we know that this line is parallel to y=6x-5 they have the same slope which means m is 6
10=4(6)+b
now solve for b
-14=b
so we know that m is 6 and b =14 now we substitute it back into y=mx+b for m and b
y=6x-14
Hope that helps :)
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
bottom half
bottom- 3 x 12.5 = 37.5
front side- 3 x 4 = 12
back side- 12
left side- 4 x 12.5 = 50
right side- 50
total: 161.5
top half
front triangle- (3x4)/2 = 6
back triangle- 6
left side- 4 x 12.5 = 50
right side- 50
total: 112
161.5 + 112 = 273.5
siny dy/dx= cosy(1-xcosy)
pls i need it fast
Answer:
sec y = x+1 + ce x ; c is constant
Hope it helps....
I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS
Answer:
54.85 un²
Step-by-step explanation:
Calculate the square and the circle and add them together.
[tex]2\pi[/tex]r
radius = 3
[tex]2\pi[/tex]3
Circumference = [tex]2\pi[/tex]r = 2 × [tex]\pi[/tex] × 3 = 18.84956
18.84956 rounds to 18.85
The circle's area is 18.85 un².
The square is 6 by 6.
6 × 6 = 36
The square's area is 36 un².
18.85 un² + 36 un² = 54.85 un²
Three landmarks of baseballachievement are Ty Cobb’s batting average of 0.420 in 1911,Ted Williams’s 0.406 in 1941, and George Brett’s 0.390in 1980. These batting averages cannot be compared directly becausethe distribution of major league batting averages has changed overthe years. The distributions are quite symmetric and (except foroutliers such as Cobb, Williams, and Brett) reasonably normal.While the mean batting average has been held roughly constant byrule changes and the balance between hitting and pitching, thestandard deviation has dropped over time. Here are the facts:
Decade
Mean
Standard Deviation
1910s
0.266
0.0371
1940s
0.267
0.0326
1970s
0.261
0.0317
Compute the standard units for the batting averages of Cobb,Williams, and Brett to compare how far each stood above his peers.Who is the better player of the three?
Answer:
Ted Williams has the highest standardized score, hence Williams is the best of the three
Cobb is the second highest and hence, the better player
George Brett is third
Step-by-step explanation:
Given the data:
Decade : 1910 __ 1940 ____ 1970
Mean, μ: 0.266 __0.267 ___ 0.261
S/dev, σ : 0.0371 _ 0.0326 __ 0.0317
To compute the standard unit for batting averages, we obtain the standardized score for each of Cobb,Williams, and Brett.
Standardized score (Zscore) : (x - μ) / σ
Cobb, x = 0.420
Ted Williams, x = 0.406
George Brett, x = 0.390
COBB:
Zscore = (0.420 - 0.266) / 0.0371 = 4.1509
Ted Williams :
Zscore = (0.406 - 0.267) / 0.0326 = 4.2638
George, Brett = (0.390 - 0.261) / 0.0317 = 4.0694
Ted Williams has the highest standardized score, hence Williams is the best of the three
Cobb is the second highest and hence, the better player
George Brett is third