Answer:
(x,y)=(-1.-2)
Step-by-step explanation:
Using the elimination method:
-27x+45y=-63
-35x-45y=125
---------------------
-62x=62-->x=-1
-3*(-1)+5*6=-7-->y=-2
11. Albert has 12 more 10 cent coins than 20-cent
coins. The total value of all his coins is $5.40. Find
the total number of coins he has.
Step-by-step explanation:
Let x be the number of 10 cent coins
Let y be the number of 20 cent coins
given
[tex]x = y + 12 \\ x - y = 12[/tex]
as equation 1
and
[tex]0.1x + 0.2y = 5.4[/tex]
as equation 2.
Now we will use elimination method to solve simultaneous equations.
Now we multiply equation 1 by 0.2 to eliminate y and solve for x first.
[tex]0.2 \times x - 0.2 \times y = 12 \times 0.2 \\ 0.2x - 0.2y = 2.4[/tex]
Let this new equation be equation 3.
Now use equation 2 + equation 3.
[tex]0.1x + 0.2x + (0.2y + ( - 0.2y)) = 5.4 + 2.4 \\ 0.3x = 7.8 \\ x = 7.8 \div 0.3 \\ = 26[/tex]
Substitute x into equation 1,
[tex]x = y + 12 \\ y + 12 = x \\ y = x - 12 \\ = 26 - 12 \\ = 14[/tex]
Therefore total number of coins = x + y = 26 + 14 = 40
Answer:
in total he has 62 cents
Step-by-step explanation:
I hope it's the correct answer if I'm wrong tell me right away.
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.
a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
c. What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
d. What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) By the Central Limit Theorem, it is approximately normal.
b) The standard error of the distribution of the sample mean is 1.8333.
c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours
e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 36 hours and a standard deviation of 5.5 hours.
This means that [tex]\mu = 36, \sigma = 5.5[/tex]
a. What can you say about the shape of the distribution of the sample mean?
By the Central Limit Theorem, it is approximately normal.
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Sample of 9 means that [tex]n = 9[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]
The standard error of the distribution of the sample mean is 1.8333.
c. What proportion of the samples will have a mean useful life of more than 38 hours?
This is 1 subtracted by the pvalue of Z when X = 38. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{38 - 36}{1.8333}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
1 - 0.8621 = 0.1379
0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
This is 1 subtracted by the pvalue of Z when X = 34.5. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061.
1 - 0.2061 = 0.7939
0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?
pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So
0.8621 - 0.2061 = 0.656
0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
simplify
[tex] {a}^{3} - {b}^{3} [/tex]
Answer:
[tex] {a}^{3} - {b}^{3} [/tex]
[tex] = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Hence, simplified.
If f(x)=3x^2+2x=1 find f(x+2)
Answer:
f(x+2) = 3(x+2)^2 + 2(x+2) + 1
Step-by-step explanation:
Replace x with x+2 and you get the solution above. Hope this helps!
helpp will get brainliest
(the figure is not drawn to scale)
which one?
154 cm2
217 cm2
308 cm2
5488 cm2
The Lazy River has a current of 5 miles per hour. A motorboat can travel 20 miles
down the river in and back in 3 hours. What is the speed of the boat in still water?
Please show your work and use table to relate time, speed, distance.
Answer:
5 mph
Step-by-step explanation:
Answer:
15 mph = rate of boat in still water
Step-by-step explanation:
D = RT
Let R = rate of boat in still water
Rate down stream = R + 5
Time down stream = 20/(R + 5)
Rate upstream = R - 5
Time upstream = 20/(R - 5)
Total time = 20/(R + 5) + 20/(R - 5) = 3
20(R - 5) + 20(R + 5) = 3(R + 5)(R - 5)
20R - 100 + 20R + 100 = 3R^2 - 75
3R^2 + 40R - 75 = 0
(3R + 5)(R - 15) = 0
R = -5/3 or 15
Rate cannot be negative, so R = 15 mph = rate of boat in still water
Each day, the number of births in the world is 92 thousand less than three times the number of deaths. If the
population increase in a single day is 214 thousand, determine the number deaths per day.
Answer:
two points in the xy plane has cartesian coordinate (2,-4) and (-3,3) where the units are in m determine.
a) the distance between these points and
b) their polar coordinates.
Please answer the question in the picture
Answer:
Step-by-step explanation:
use the distance formula
dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]
where point one ,P1, is A and point 2, P2, is C, so
P1 = (x1,y1) = (-7,3)
P2 =(x2,y2) = (0,6)
then
dist = sqrt[ (0 - (-7))^2 + (6-3)^2 ]
dist = sqrt [ 7^2 + 3^2 ]
dist = sqrt [49 +9 ]
dist = sqrt [58]
dist = 7.6157....
AC = 7.6 ( rounded to nearest tenth)
13. Which fraction is halfway between 3/5 and
5/7?
Answer:
18/35....
....
YESTERDAY
Solve for x. Sin x =3/8
Answer:
<x=22.02431284 degrees
Step-by-step explanation:
sin(x)=3/8
sin^-1(3/8)=<x
<x=22.02431284 degrees
According to the Insurance Institute for Highway Safety, the national rate for 16-year-old males was 210 accidents for every 1000 drivers (21%) during the year 2000. In a large city in the Midwest, a random sample of 150 16-year-old male drivers found that 25 of them had been in an accident during the year 2000. Does this city have a lower proportion of accidents by 16-year-old male drivers than the national proportion?
Answer:
Yes. The city has a lower proportion of accidents by 16-year-old male drivers than the national proportion (16.7% compared to 21%).
Step-by-step explanation:
a) Data and Calculations:
Number of 16-year-old males involved in driver accident during year 2000 = 210
Sample number of drivers = 1,000
National rate of accidents for 16-year-old males for every 1,000 drivers = 21% (210/1,000 * 100)
Random sample of 16-year-old male drivers in a Midwest city = 150
Number of them involved in driver-accidents = 25
Proportion of 16-year-old males involved in driver-accidents = 25/150 * 100 = 16.7%
The city's 16.7% proportion is lower than the national proportion of 21%.
so, this is in math and, I NEED HELP!!!!!. could you first multiply the width by the height? Explain.
Answer:
Explain what?? May I ask
Taiga’s teacher asked him to draw a polygon with vertices (–4, –5), (–5, 2), (–5, 3), (–4, 5), (2, 3), and (–3, 0) and to identify the polygon. Taiga drew the polygon below and identified it as a heptagon.
Which explains whether Taiga is correct?
Taiga is correct because the polygon has six sides.
Taiga is correct because the sides have different lengths.
Taiga is not correct because the polygon is a hexagon.
Taiga is not correct because he drew the polygon incorrectly.
What is the equation of the line that is parallel to the line y = 3x - 4 and passes
through the point (4, -2)?
A. Y= 3x + 2
B. y= 3x - 14
O C. --}x
D. y = 3x + 14
Answer:
B. y = 3x - 14
Step-by-step explanation:
Since the line is parallel, your slope will be 3. You're given a point, so you can use point-slope form to find the equation. Point-slope form is:
y - y1 = m(x - x1) where (x1, y1) is the point that they gave you and m is the slope. So:
y - (-2) = 3(x - 4) --> Start to simplify this by changing - (-2) to +2 and distributing the 3 to (x - 4).
y + 2 = 3x - 12 --> Subtract 2 from both sides.
y = 3x - 14
Photo Attached
Please Help ASAP
Answer:
C
Step-by-step explanation:
A is just the opposite value of the second integral.
B is just 3 times the first.
D-you can write a sum of integrals over the same intervals as one integral of the sum of the integrands of those integrals over that same interval. The answer would be 3(8)+-2.
For choice C, we would need more information.
Find the measure of angle R ((look at pic pls help)
A- 45
B- 60
C- 90
D- 30
Answer:
B
Step-by-step explanation:
Two planes, which are 2920 miles apart, fly toward each other. Their speeds differ by 80mph. If they pass each other in 4 hours, what is the speed of each?
9514 1404 393
Answer:
405 mph; 325 mph
Step-by-step explanation:
The total of their speeds is ...
2920 mi/(4 h) = 730 mi/h
If s represents the speed of the slower plane, then we have ...
s + (s+80) = 730
2s = 650 . . . . . . . subtract 80
s = 325 . . . . . . . divide by 2
s+80 = 405 . . . find the faster speed
The speeds of the planes are 405 mi/h and 325 mi/h.
Find the domain of the following functions?
Answer:
d. D: (-∞ , ∞) , R: (-10 , ∞)
Step-by-step explanation:
If logarithm of 5832 be 6, Find thw base?
Answer:
3sqrt(2) ................
4.2.6. A newly formed life insurance company has under- written term policies on 120 women between the ages of forty and forty-four. Suppose that each woman has a 1/150 probability of dying during the next calendar year, and that each death requires the company to pay out $50,000 in benefits. Approximate the probability that the company will have to pay at least $150,000 in benefits next year.
Answer:
0.047
Step-by-step explanation:
The computation of the probability is shown below:
P(dying) = 1 ÷ 150
So,
P(living) = 149 ÷ 150
As There are 120 women.
Now
P(x>=3) = 1 - [P(x=0) + P(x=1) + P(x=2)]
= 1 -[(120 = 0)((1 ÷ 150)^0)((149 ÷ 150)^120) + (120 = 1)((1 ÷ 150)^1)((149 ÷ 150)^119) + (120 = 2)((1 ÷ 150)^2)((149 ÷150)^118)]
P(x>=3)
=0.047
The Alpha company takes a survey of the age for all employees. The average age is 35 with a standard deviation of 3.2 years. The results form a normal distribution curve. If the company has 985 workers, how many are over 44 years old? (Round your answer to the nearest whole person)
Answer:
I would say to look on alpha calculator to get any help if anyone dosent answer this!!
Step-by-step explanation:
Help ASAP!!!!!! Plzzzzzz
Answer:
2nd option
Step-by-step explanation:
Need help with this if possible
Answer:
hope it helps...
Step-by-step explanation:
1/7+7/12+something =1
I'm. not the best at finding angles sadly
Answer:
obtuse it is more than 90 so not a right and a straight angles is 180 degrees so it obtuse
What is the intermediate step in the form (x+a)^2 = b as a result of x^2-16x= -68
Answer:
The intermediate step is determining what a is, knowing also that (x+a)²=x²+(2a)x+a².
Also, x²-16x= -68 (in the form (x+a)²=b) is (x-8)²=-4
Step-by-step explanation:
x²-16x=-68
x²-16x+68=0
I suppose the intermediate step is finding (x+a)².
Remember that (x+a)²=x²+(2a)x+a², so 'a' will be half the coefficient of x (number beside x, not x²). The coefficient of x here is -16, so a is -8.
(x-8)²=x²-16x+64
So, if we can create 'x²-16x+64' out of 'x²-16x+68', we'll be on our way:
x²-16x+68=0
(x²-16x+64)+4=0
(x-8)²+4=0
(x-8)²=-4
One angle of a triangle measures 110°. The other two angles are in a ratio of 3:4. What are the measures of those two angles?
Answer: 30 & 40
Step-by-step explanation:
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are Normally distributed with a mean of 5.9 inches and a standard deviation of 0.8 inches.
According to the 68-95-99.7 rule, we expect 95% of head breadths to be
between blank and blank inches.
Answer:
We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 5.9 inches, standard deviation = 0.8 inches.
We expect 95% of head breadths to be between
Within 2 standard deviations of the mean, so:
5.9 - 2*0.8 = 5.9 - 1.6 = 4.3 inches
5.9 + 2*0.8 = 5.9 + 1.6 = 7.5 inches
We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.
which of the following is written as a rational function
Answer:
f(x)=x-5/3x
Step-by-step explanation:
Solve for x.
7x - = 6x -
O x = 1/4
Ox=1
Ox= -1
O x = -1/4
Answer:
D. - 1/4
Step-by-step explanation:
