Answer:
a = 3/2
Step-by-step explanation:
Solve for a over the real numbers:
8 a^3 - 27 = 0
Hint: | Isolate terms with a to the left hand side.
Add 27 to both sides:
8 a^3 = 27
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides by 8:
a^3 = 27/8
Hint: | Elminate the power on the left hand side.
Take cube roots of both sides:
Answer: a = 3/2
Which expressions are equivalent to x + 2y + x + 2?
Choose all answers that apply:
A 2(x+y+1)
B 2x + 4y +4
C None of the above
Answer:
2x + 2y + 2
Step-by-step explanation:
A is right
Find surface area of the prism.
5 m
18 m
4 m
Answer: 27m
Step-by-step explanation:
A complex shape with measurements 4 feet, 10 feet, 4 feet, 2 feet, 4 feet, 6 feet, 4 feet, 2 feet.
The perimeter of the shape is
feet.
Answer: Add each side to get perimeter so your total is 38ft
Step-by-step explanation:
Answer: 36
Step-by-step explanation:
How many thirds are in 12?
The lifetime of battery of a device (in one charge) is normally distributed with mean µ = 18 hours and standard deviation σ = 2 hours. (a) What is the probability that a battery will last more than 20 hours? (b) Find the 10th percentile of the lifetimes. (c) A particular battery lasts 16 hours. What percentile is its lifetime on? (d) What is the probability that the lifetime of a battery is between 17.5 and 18.5? (e) Ten batteries are chosen at random, what is the probability that the mean lifetime is between 17.5 and 18.5?
Answer:
a) 0.1587 = 15.87% probability that a battery will last more than 20 hours.
b) 15.44 hours.
c) Approximately the 16th percentile.
d) 0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.
e) 0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5
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 zscore 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 pvalue, 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].
In this question, we have that:
[tex]\mu = 18, \sigma = 2[/tex]
(a) What is the probability that a battery will last more than 20 hours?
This is 1 subtracted by the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 18}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that a battery will last more than 20 hours.
(b) Find the 10th percentile of the lifetimes.
This is X when Z has a pvalue of 0.1. So X when Z = -1.28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 18}{2}[/tex]
[tex]X - 18 = -1.28*2[/tex]
[tex]X = 15.44[/tex]
So 15.44 hours.
(c) A particular battery lasts 16 hours. What percentile is its lifetime on?
We have to find the pvalue of Z when X = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 18}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
Approximately the 16th percentile.
(d) What is the probability that the lifetime of a battery is between 17.5 and 18.5?
This is the pvalue of Z when X = 18.5 subtracted by the pvalue of Z when X = 17.5. So
X = 18.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18.5 - 18}{2}[/tex]
[tex]Z = 0.25[/tex]
[tex]Z = 0.25[/tex] has a pvalue of 0.5987
X = 17.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
0.5987 - 0.4013 = 0.1974
0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.
(e) Ten batteries are chosen at random, what is the probability that the mean lifetime is between 17.5 and 18.5?
Sample of 10 means that, by the Central Limit Theorem, [tex]n = 10, s = \frac{2}{\sqrt{10}} = 0.6325[/tex]
X = 18.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18.5 - 18}{0.6325}[/tex]
[tex]Z = 0.79[/tex]
[tex]Z = 0.79[/tex] has a pvalue of 0.7852
X = 17.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.5 - 18}{0.6325}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a pvalue of 0.2148
0.7852 - 0.2148 = 0.5704
0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5
20a + 158 +6c = 20 (6) + 15 (4) + 6(8)
+
?
+
?
Step-by-step explanation:
20a + 158+6c=you will expand the brackets
= so it is 120+60+48
20a+158+6c=120+60+48
20a+ 6c=120+60+48-158
20a+6c=70
20a divide by 20+6c divide by 6 on both side
a + c = 0.58
how did you get 24/10?
Step-by-step explanation:
[tex] \tt{} \frac{24}{10} [/tex]
[tex] \tt{} \frac{24 \div 2}{10 \div 2} [/tex]
[tex]\tt{} \frac{12}{5} [/tex]
[tex]\tt{}2 \frac{2}{5} \: \: \: \: \: = 2.4[/tex]
A body starts from rest and
accelerates uniform at 5 ms2.
calculate the time taken
by the body to cover a
distance of
1km
Find the length of the third side. If necessary, round to the nearest tenth?
Answer:
3
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
6. How many of the integers between 20 and 40 are
odd?
b)11
d)12
c12
Answer: 10
Step-by-step explanation:
List out the numbers:
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
There are 10 odd numbers
Otherwise a faster method:
Odd numbers occur every other number
There are 40 - 20 = 20 numbers between 20 and 40
20/2 = 10
10 odd numbers
write an expression that mean "eight less than product of seven and X".
Answer:
7x - 8
Step-by-step explanation:
eight less than product of seven and X
seven and x = 7x
eight less than = - 8
put it all together = 7x - 8
Answer:
7x - 8
Step-by-step explanation:
product of seven and X
7 X x = 7x
8 less than it
7X - 8
This is because we're looking for something that is smaller than 7X by 8
If f(x)=(x+1)(x-2)(x-3) represents a student's displacement from school in
kilometers, where x is measured in minutes, which of the following is an
accurate interpretation of the student's trip?
a) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, continues walking to the playground, turns around, walks
back to the school and arrives after 3 minutes.
b) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, waits there for 1 minute, then returns home.
c) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, turns back to their house to the playground, turns around,
walks back to the school and arrives after 3 minutes.
d) The student starts 6 km from school, walks to school and arrives 1 minute
later, sits by the school, returns home, arrives after 2 minutes, and then turns
around and arrives back at school for a second time at 3 minutes.
e) None of the above are correct
It
Displacement means the distance traveled on a straight line to get to a certain destination. The interpretation of the given equation is option (a):
Given that:
[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]
First, we calculate how far the student traveled to arrive at the school.
This means that we calculate f(0).
So, we have:
[tex]f(0) = (0 + 1)(0 - 2)(0 - 3)[/tex]
[tex]f(0) = ( 1)( - 2)( - 3)[/tex]
[tex]f(0) = 6[/tex]
The student walked 6km to school
When x = 2, it means:
[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]
[tex]f(2) = (2 + 1)(2-2)(2 -3) = 0[/tex]
This means that the student got to school after 2 minutes
When x = 3, it means
[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]
[tex]f(3) = (3 + 1)(3-2)(3 -3) = 0[/tex]
This means that the student walked away, turned back and got to school after 3 minutes.
From the given options, option (a) fits the above description.
Read more about speed, displacement and time at:
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3.366 rounded to the nearest tenth of a ounce
Answer:
The answer is 3.4
Step-by-step explanation:
5 or more, round up
4 or less, round down
rounding 6
round up
so...
3.4
(-2, -7) and (-4, -9)
Answer:
3.4Oz
Step-by-step explanation:
write 18 1/4 as a decimal
Answer: 18.25
Step-by-step explanation: Lets start off with this: 1/4 is the same as 25 (like if you use quarters, you know 4 quarters makes a dollar, and one quarter is 25)
So, since we have 18 and 25, converting it to a decimal is easy. Put the numbers together (18 and 25) Then just add decimal in the middle.
OR
18 x 4 (which is 72) then add 72 to the numerator (1) which will give you 73 (72 + 1) Finally, divide 73 by 4, (4 is denominator) which will then give you 18.25 :D
The mixed number [tex]18\frac{1}{4}[/tex] written as a decimal is 18.25.
To write [tex]18\frac{1}{4}[/tex] as a decimal, we can convert the mixed number into an improper fraction and then divide the numerator by the denominator.
The mixed number to an improper fraction.
[tex]18\frac{1}{4}[/tex] = (18 × 4 + 1)/4
= 73/4
Divide the numerator by the denominator.
73 ÷ 4
= 18.25
Therefore, [tex]18\frac{1}{4}[/tex] written as a decimal is 18.25.
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Find the sum of the first six terms of the Geometric Progression (G.P.):
2
1, 2, 4, ....
Step-by-step explanation:
Heueueirjrjkwugoystsitso5wpysoydlusktzlhskgdlysyldj
I’ll give as many points as possible please help
xy^2 (x^2y^3+5xy-4)
Answer:
x^3y^5 + 5x^2y^3 - 4xy^2
Step-by-step explanation:
xy^2 (x^2y^3+5xy-4)
xy^2x^2y^3 + xy^2 x 5xy - 4xy^2
xy^2x^2y^3 = yx^2y^5
xy^2 x 5xy = 5x^2y^3
x^3y^5 + 5x^2y^3 - 4xy^2
Is that what you want? Let me know.
Find the volume.please :>
Answer:
The volume of the cube is 77 inches.
a. 1 third of 3 over 4 = ____ fourth(s)?
Answer:
0.25
Step-by-step explanation:
1/3 of 3/4 means
(1/3) x 3/4
3/12
0.25
Which function's graph has the same y Intercept as the line shown?
Оу в x +1
Oy -5x + 5
O y .5x-5
O y: 5x - 1
The graph has the same y Intercept as the line shown is y = 5x - 5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We take two points from the graph as (-5, 0) and (0, -5)
So, the slope of line
slope = (-5 - 0)/ (0- (-5))
slope= -5 / 5
slope= -1
Using slope intercept form
y= mx+ b
y= -x+ b
Now, put x= -5 and y= 0 then
0 = -(-5)+ b
b= -5
So, the equation of line is
y= -x - 5
Here, the y intercept is -5.
So, the equation with same y intercept is
y = 5x - 5
Learn more about slope here:
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Type in a value that represents as likely as not in a decimal form.
Answer:
I Need Numbers Somthing....... Its Imposable to answer this
Step-by-step explanation:
Reggie is making a double layer cake the recipe for the first layer calls for 2 1/4 cups sugar. the recipe for the second layer calls for 1 1/4 cups of sugar. Reggie has 5 cups of sugar. How much will he have left after making both recipes?
Answer:
Step-by-step explanation:
Meg, add the fractions
2_1/4 + 1_1/4
or 2 + 1 + _1/4 + _1/4
3 + _2/4
3 + _1/2
3_1/2
then what's left is
5 - 3_1/3 = 1_1/2
got it?
Help
Select all that apply
Answer:
A, D
Step-by-step explanation:
It's basic math, height times length = Area.
Answer:
A and D are the only ones that i can see that would be correct
Step-by-step explanation:
Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:
Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out a purple tile? (5 points)
fraction 6 over 50
fraction 44 over 50
fraction 6 over 44
fraction 18 over 44
Answer:
Step-by-step explanation:
i am not sure do they give you a number of tiles
Answer:
A: 6/50
Step-by-step explanation:
i think
Need help for 2 and 3 fast
Answer:
[tex]2^{-4}[/tex] = 1/16
[tex]6^{-5}[/tex] × [tex]6^{5}[/tex] = 1
Step-by-step explanation:
[tex]2^{-4}[/tex] = 0.0625
0.0625 = 1/16
[tex]6^{-5}[/tex] × [tex]6^{5}[/tex] = 1
irections: Find the area of each figure round to the nearest tenth where necessary.
2
Answer:
21 x 33 = 693
16 x 7 divided by 2 = 216
17.6 x 17.6 divided by 2 = 154.9
19 x 7.8 = 148.2
7 + 2 x 5.5 divided by 2 = 24.8
10 x 12 = 120
Please wait for more responses if needed!
HELP ASAP!!! THANK YOU!!!
Answer:
Additional information required is
<DBA = 90°
Step-by-step explanation:
<DBA + <DBC = 180° [Linear pair]
=> <DBA = 180° - <DBC
=> <DBA = 180 - 90
=> <DBA = 90
Hence, both the angles <DBA = <DBC = 90°
As we know that when a perpendicular bisector bisects a straight line both the angles should be,
180° ÷ 2 = 90°
And above conditions also prove that
<DBA = <DBC = 90°
Hence, DE is a perpendicular bisector of AC
PLEASE HELP I WILL GIVE BRAINLY
During the 6th grade dance, the ratio of the number of girls to the number of boys was 6:1. Create a ratio table of the number of girls to the number of boys that attended the dance. Show how many girls were there if 9 boys were counted.
Answer:
9:6
Step-by-step explanation:
Lmk ASAP please you’re the
9514 1404 393
Answer:
a ≈ 4.68
Step-by-step explanation:
The law of cosines tells you ...
a² = b² +c² -2bc·cos(A)
a = √(b² +c² -2bc·cos(A))
a = √(5² +8² -2·5·8·cos(33°)) = √(25 +64 -80·0.83867) ≈ √21.906
a ≈ 4.68
Answer:
a≈4.68
Step-by-step explanation:
have a good one!!!
The revenue from selling x bracelets is f(x) = 8x.
The cost of buying x bracelets is c(x) = 3x + 12.
The profit from selling x bracelets is p(x) = (x) - c(x).
Write a function for p(x), the profit from selling x bracelets.
O A. p(x) = 11x - 12
B. p(x) = 11x + 12
C. p(x) = 5x - 12
O D. p(x) = 5x + 12
We are given r(x) and c(x).
p(x) = 8x - (3x + 12)
p(x) = 8x - 3x - 12
p(x) = 5x - 12
Done.
ill mark brainlist plss help
Answer:
it's the3rd one
Step-by-step explanation:
it's is 182 feet