Answer:x = 8 Step-by-step explanation:4x + 112 = 9x + 72-112 -1124x = 9x - 40-9x -9x-5x = -40----- -------- -5 -5x = 8
Explanation;
the answer is 5x=8
How many license plate numbers consisting of three letters followed by
two numbers are possible when repetition is not allowed?
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78.
(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85. (Round your answers to two decimal places.)
(b) Compute a 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)
(c) How large a sample size is necessary if the width of the 95% interval is to be 0.46? (Round your answer up to the nearest whole number.)
(d) What sample size is necessary to estimate true average porosity to within 0.18 with 99% confidence? (Round your answer up to the nearest whole number.)
Answer:
a) The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).
b) The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).
c) A sample size of 12 is needed.
d) A sample size of 125 is needed.
Step-by-step explanation:
(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.78}{\sqrt{15}} = 0.39[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.39 = 4.46
The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.39 = 5.24
The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).
(b) Compute a 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{0.78}{\sqrt{11}} = 0.55[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.56 - 0.55 = 4.01
The upper end of the interval is the sample mean added to M. So it is 4.56 + 0.55 = 5.11
The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).
(c) How large a sample size is necessary if the width of the 95% interval is to be 0.46?
95% CI means that [tex]z = 1.96[/tex]
A sample of n is needed, and n is found when M = 0.46. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.46 = 1.96\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.46\sqrt{n} = 1.96*0.78[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.78}{0.46})^2[/tex]
[tex]n = 11.05[/tex]
Rounding up
A sample size of 12 is needed.
(d) What sample size is necessary to estimate true average porosity to within 0.18 with 99% confidence?
99% CI means that [tex]z = 2.575[/tex]
A sample of n is needed, and n is found when M = 0.18. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.18 = 2.575\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.18\sqrt{n} = 2.575*0.78[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.78}{0.18})^2[/tex]
[tex]n = 124.5[/tex]
Rounding up
A sample size of 125 is needed.
Please send help. I really need this asap
Answer:
Part a) The area of the figure is [tex]\frac{9}{2} (4+\pi ) cm^{2}[/tex]
Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2} +\pi )cm[/tex]
Which of these are expressions?
Check all that are true.
a/9
2 + 5
7
8 × 9 - 5 = 72 - 5
0 + 0
Answer:
a/9
2+5
0+0
maybe 7
an expression is any problem that does NOT have an equal sign
Answer:=7
Step-by-step explanation:
2+5
0+0
maybe 7
an expression is any problem that does NOT have an equal sign
Find the radius or diameter of the circle with the given dimentions.
r = 21 ft
Answer Choices:
a. 50 ft
b. 42 ft
c. 131.9 ft
d. 10.5 ft
Answer:
b. 42
Step-by-step explanation:
Your trying to find the diameter since radius is r
diameter is always double of radius
In ΔMNO, the measure of ∠O=90°, the measure of ∠N=38°, and OM = 87 feet. Find the length of NO to the nearest tenth of a foot.
Answer:
111.4
Step-by-step explanation:
trust
A state university locks in costs for a student once a student starts attending the university. The total cost is $23,500. A student has
the following help in covering the costs of school.
• An academic scholarship of $8,200.
• Other scholarships and grants of $7.400.
Grandparents pay $1,000
.
What is the amount that the student will need to save every month in order to pay off the remaining costs in 10 months ?
$690
S820
S1 660
$2 350
Answer:
720
Step-by-step explanation:
24500 (total) subtracted by (10,700 + 5000 + 1600) =7200. 7200 divide by 10 mo=720
If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690
Amount and interestGiven the following information from the question
The total cost of fee = $23,500
Amount got as help;
An academic scholarship of $8,200.
Other scholarships and grants of $7.400.
Grandparents pay $1,000
Amunt she had = 8200 + 7400 + 1000
Amount she had = $16600
Amount remaining = 23500 - 16600
Amount remaining = $6900
If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690
Learn more on the amount here:
https://brainly.com/question/25109150
Need help with this question please !!!
Answer: 27
Step-by-step explanation:
I need help on this..... FAST. Think you can help me?
Answer:
.si sey el senocar 18
Step-by-step explanation:.basflone ne ombla
struggle helpppppppp
Answer:
49
Step-by-step explanation:
|-7|=7, and 7*7 = 49
NEED HELP I SUCK AT GEOMETRY (OFFERING 100POINTS)!!! best answer get brainlest
Find the measure of angle C
show work and explain!
Answer:
Angle C = 45°
Step-by-step explanation:
Hello There!
If you didn't know opposite angles are congruent in parallelograms
So ∠A≅∠C and ∠B≅∠D
So if ∠A = 45° then ∠C also equals 45°
As it is a parallelogram
[tex]\\ \sf\longmapsto <B\cong <D[/tex]
[tex]\\ \sf\longmapsto <A\cong <C[/tex]
<A=45°[/tex][tex]\\ \sf\longmapsto <C=<A=45°[/tex]
Helppppp meeeee!!!!!!!!!!!
Answer and Step-by-step explanation:
When it says (f + g)(x), it means that it wants you to add the functions together.
So, let's add them.
[tex](2x^2 + 6x - 4) + (5x^3 -6x^2-3)\\\\\\5x^3 - 4x^2 + 6x - 7\\\\\\\\\\\\\\5x^3 - 4x^2 + 6x - 7[/tex]is the answer. (Answer choice B.)
#teamtrees #PAW (Plant And Water)
Please answer right! Thank you I will give brainalist
Answer:
C [tex]\leq 34[/tex]
Step-by-step explanation:
Answer:
34is the answer gor the question
Which regular polygon would have each of its interior angles measure 140°?
octagon
nonagon
decagon
heptagon
9514 1404 393
Answer:
nonagon
Step-by-step explanation:
The adjacent exterior angle is 180° -140° = 40°. There are 360°/40° = 9 of those angles around the regular polygon, so it is 9-sided.
The polygon is a nonagon.
Answer:
nonagon
Step-by-step explanation:
i got 100%
A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answer:
the work done in pulling the bucket to the top of the well is 2125 ft-lb
Step-by-step explanation:
Given that;
Weight of the bucket is 3 lb
weight of water which can be filled in the bucket is 42 lb
Total weight of bucket and water = 3 + 42 = 45 lb
distance, the bucket filled with water is to be pulled 50 ft
now, let at any time t be the bucket at distance x ft from the bottom of the well
then, t = x/2 × S
where S is the rate at which water is leaking from the bucket
so at this time t, the amount pf water which leaked from the bucket is;
⇒ x ft / 2.5 ft/s × 0.25 lb/s
= 0.25 lb.s⁻¹ / 2.5 ft.s⁻¹ × x ft
= 0.1 lb/ft × x ft
= 0.1x lb
now, as x represent the distance that the bucket has been raised, we the force F applied to the bucket x to be;
F = ( 45 - 0.1x ) lb
so, the required worked by Riemann sum as;
[tex]\lim_{n \to \infty}[/tex]ⁿ∑_[tex]_{i=1}[/tex] ( 45 - 0.1x[tex]_i[/tex]* ) Δx
so, the work done, pulling the bucket up will be;
[tex]\lim_{n \to \infty}[/tex]ⁿ∑_[tex]_{i=1}[/tex] ( 45 - 0.1x[tex]_i[/tex]* ) Δx = [tex]\int\limits^{50}_0 {(45-0.1x)} \, dx[/tex]
= [ 45x - 0.1[tex]\frac{x^2}2}[/tex] ]⁵⁰₀
= 45 × 50 - 0.1/2 × (50)²
= 2250 - 125
= 2125 ft-lb
Therefore, the work done in pulling the bucket to the top of the well is 2125 ft-lb
find each measurement indicated. Round your answers to the nearest tenth. Please show work. Part 1
9514 1404 393
Answer:
33.0 m26.1 mi28.0 mi33.0 miStep-by-step explanation:
In each of these Law of Sines problems, you are given side a and angles B and C and asked for side c (problems 1, 3, 4) or side b (problem 2). The solution is basically the same for each:
Find the missing angle. Find the side from ...
c = a·sin(C)/sin(A)
__
1. angle A = 180°-89°-58° = 33°
c = (18 m)sin(89°)/sin(33°) ≈ 33.0 m
__
2. angle C = 180°-13°-17° = 150°
b = (58 mi)sin(13°)/sin(150°) ≈ 26.1 mi
__
3. angle A = 180°-61°-89° = 30°
c = (16 mi)sin(61°)/sin(30°) = 28.0 mi
__
4. angle A = 180°-39°-127° = 14°
c = (10 mi)sin(127°)/sin(14°) ≈ 33.0 mi
The total service time of a multistep manufacturing operation has a gamma distribution with mean 18 minutes and standard deviation 6 minutes.
(a) Determine the parameters alpha and lambda of the distribution. (solving these two parameters using the mean and the standard deviation)
(b) Assume that each step has the same exponential distribution for service time. What distribution for each step and how many steps produce this gamma distribution of total service time?
Answer:
The answer is "[tex]\bold{r=9, \lambda=\frac{1}{2}\ and \ \ \text{exponential, 9 steps}}[/tex]"
Step-by-step explanation:
In point a:
We are aware of the random gamma variable X:
[tex]\to \mathbb{E} =\frac{r}{\lambda}\\\\\to Std(X) =\frac{\sqrt{r}}{\lambda}\\\\[/tex]
It is given:
[tex]\to \mathbb{E} = 18 \\\\\to std(X)=6[/tex]
[tex]\to 18=\frac{r}{\lambda}\\\\ \to 6=\frac{\sqrt{r}}{\lambda}\\\\[/tex]
Substituting the value:
[tex]\to \frac{\sqrt{r}}{6}=\frac{r}{18}\\\\\to r=9\\\\\to \lambda=\frac{1}{2}\\\\[/tex]
In point b:
When building the Erlang/Gammas distribution, these could reasonably be assumed to become an exponential distribution only with \lambda = 1/2 parameter with one step but to be r = 9 for one step.
Question 2 of 10
What is the slope-intercept equation of the line below?
O A. y = -2x-3
O B. y = -2x + 3
O C. y = 2x-3
O D. y = 2x + 3
Answer:
y=2x-3
Step-by-step explanation:
First we find the y-intercept of this graph whic in this case is -3. Then we plot two pints on the graph and caculate the rise over run which is 2/1=2. Finally, we get the equation- y=2x-3.
What is the slope of a line that is perpendicular to the line y = 1/6+ 4
+4?
Answer:
y = 6x + 8?
Step-by-step explanation:
The starting equation was unclear but if its perpindecular, flip the given slope. For example, if the slope was 3/4, its perpindecular slope would be 4/3.
If 26 feet 10 inches is cut from a wire that is 44 feet 8 inches long what is the length of wire that is left ?
Answer:
17 feet 10 inches
Step-by-step explanation:
26 feet 10 inches is cut from a wire that is 44 feet 8 inches
Therefore the length of wire that is left can be calculated as follows
44 feet 8 inches - 26 feet 10 inches
= 17 feet 10 inches
patrick walks at 6/8 kilometer per 8 hour. how far will he in 5 hours?
Answer:
In 5 hours, he will go 3 ¾ kilometers far.
Step-by-step explanation:
A holiday store is having a sale on bows and rolls of wrapping paper. One sign in the store states, “Buy 1 bow and 1 roll of wrapping paper for only $6.00.” A second sign in the store states, “5 bows and 1 roll of wrapping paper will only cost $10.00.”
In dollars and cents, the cost of a single roll of wrapping paper costs $
.
Answer:
3.00
Step-by-step explanation:
One bow and and 1 roll of wrapping paper cost 6.00$
so the roll by itself would cost 6.00$
I WILL GIVE MAX POINTS IF YOU WRITE STEPS AND SOLVE PLZZZZZZ
Answer:
Step-by-step explanation:
so we need two even intergeters that add to 70 when we multiply the bigger by 2 and add the smaller to that soooo
70= 2*y + x
but we can express x in terms of y b/c it's a consecutive even integer soo
(b/c x+2 = y, then x = y -2)
70= 2*y + (y-2)
70 = 2y + y - 2
72 = 3y
24 = y :) nice the bigger is 24 so the smaller is 22
70 = 2*24 + 22
70 = 48 + 22
70 = 70 nice !
bigger = 24
smaller = 22
:)
Answer:
bigger = 24
smaller = 22
Step-by-step explanation:
3. Mateus recebe a visita do seu avô Pedro a cada 15 dias. João, o tio dele, o visita a cada 100
e, devido a escalas de trabalho, a cada 12 dias Mateus vai à praia com seus pais. Um belo dia Mans
recebeu a visita do seu avô, do seu tio e foi à praia com seus pais (com o avô e o tio que o visitavam nese
dia). Quantos dias depois este acontecimento se repetirà?
Answer:
Este acontecimento se repetirá 300 dias depois.
Step-by-step explanation:
Quando os eventos se repetirão no mesmo dia?
Cada evento tem uma frequência.
Eles ocorrem simultaneamente a cada x dias, e x é dado pelo MMC(Mínimo Múltiplico Comum) entre as frequência.
Neste problema:
A cada 15 dias o avô visita.
A cada 100 dias o tio visita.
A cada 12 dias vai à praia.
Quantos dias depois este acontecimento se repetirá?
Os três no mesmo dia vão se repetir após x dias, em que x é dado pelo MMC de 15, 100 e 12
MMC de 15, 100 e 12
Fatorando simultâneamente estes valores:
15 - 100 - 12|2
15 - 50 - 6|2
15 - 25 - 3|3
5 - 25 - 1|5
1 - 5 - 1|5
1 - 1 - 1
Então:
mmc(15,100,12) = 2*2*3*5*5 = 300
Este acontecimento se repetirá 300 dias depois.
Fill in the blank so that the ordered pair is a solution of y = 6x +7: 4,25)
a) 13
b) 1
c) 18
d) 3
Answer:
it is either A OR B
Step-by-step explanation:
please. help me
thank you
Answer:
-30,10
Step-by-step explanation:
How to get 60 to -30 : 60 divided by -30 is -2
How to get -20 to 10: -20 divided by 10 is -2
24, 3, 29, 24, 8, 38, 62
Find the range of the data set
Answer:
Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 62−3=59 62 - 3 = 59 .
Step-by-step explanation:
Answer:
The answer is 59
Step-by-step explanation:
Scott is saving coins in a jar. Last week, the jar was 1/4 full. This week, he added more coins, and the jar is now 1/2 full. How much of the jar did Scott fill this week?
Answer:
Scott filled (1/2 - 1/4) of the jar, or 1/4 of the jar this week.
Let me know if this helps!
Answer:
He filled his jar 1/4 more this week.
Step-by-step explanation:
The explanation is very simple, you know that he added 1/4 coins last week and this week he added more coins that filled the jar half way:
1/2 - 1/4 = 1/4
or you can also use:
1/4 + 1/4 = 1/2
Can you please help I am getting graded:) show work too please
Answer: A - 33/100
Step-by-step explanation:
You have to multiply the first fraction by 10 to make 100 the least common denominator - 3/10(10) = 30/100
Add 30/100+3/100 = 33/100
Brainliest will be given ASAP question below!
Answer:
3/32
Step-by-step explanation:
9/16 × 3/4=27/144=3/16×1/2=3/32