Answer:
1)
a) 0.9706 = 97.06% probability that x is less than 60.
b) 0.9987 = 99.87% probability that x is greater than 16.
c) 0.9693 = 96.93% probability that x is between 16 and 60.
d) 0.0294 = 2.94% probability that x is more than 60.
2)
a) 0.0668 = 6.68% probability that the thickness is less than 3.0 mm.
b) 0.0062 = 0.62% probability that the thickness is more than 7.0 mm
c) 0.9270 = 92.70% probability that the thickness is between 3.0 mm and 7.0 mm.
Step-by-step explanation:
Problems of normally distributed samples are 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.
1)
We have that [tex]\mu = 43, \sigma = 9[/tex]
a) x is less than 60
This is the pvalue of Z when X = 60.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 43}{9}[/tex]
[tex]Z = 1.89[/tex]
[tex]Z = 1.89[/tex] has a pvalue of 0.9706
0.9706 = 97.06% probability that x is less than 60.
b) x is greater than 16
This is 1 subtracted by the pvalue of Z when X = 16.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 43}{9}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3[/tex] has a pvalue of 0.0013.
1 - 0.0013 = 0.9987
0.9987 = 99.87% probability that x is greater than 16.
c) x is between 16 and 60
This is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 16.
From a), Z when X = 60 has a pvalue of 0.9706.
From b), Z when X = 16 has a pvalue of 0.0013
0.9706 - 0.0013 = 0.9693
0.9693 = 96.93% probability that x is between 16 and 60.
d) x is more than 60
This is 1 subtracted by the pvalue of Z when X = 60.
From a), Z when X = 60 has a pvalue of 0.9706.
1 - 0.9706 = 0.0294
0.0294 = 2.94% probability that x is more than 60.
2)
Now [tex]\mu = 4.5, \sigma = 1[/tex]
a) the thickness is less than 3.0 mm
This is the pvalue of Z when X = 3.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 4.5}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.0668 = 6.68% probability that the thickness is less than 3.0 mm.
b) the thickness is more than 7.0 mm
This is 1 subtracted by the pvalue of Z when X = 7.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7 - 4.5}{1}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938.
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that the thickness is more than 7.0 mm
c) the thickness is between 3.0 mm and 7.0 mm.
This is the pvalue of Z when X = 7 subtracted by the pvalue of Z when X = 3.
From b), Z when X = 7 has a pvalue of 0.9938.
From a), Z when X = 3 has a pvalue of 0.0668
0.9938 - 0.0668 = 0.9270
0.9270 = 92.70% probability that the thickness is between 3.0 mm and 7.0 mm.
10^xy=1000, where x and y are positive integers and x > y, what is one possible value of x?
Answer:
hey
Step-by-step explanation:
What is the y-intercept of the equation 3y + 2x =-21?
In slope-intercept form, we can classify the following values.
m = slope
b = y-intercept
Turn the equation into slope-intercept form (y = mx + b).
3y + 2x = -21
~Subtract 2x to both sides
3y + 2x - 2x = -21 - 2x
~Simplify
3y = -21 - 2x
~Divide 3 to both sides
3y/3 = -21/3 - 2/3x
~Simplify
y = -7 - 2/3x
~Put into correct order
y = -2/3x - 7
So, the y-intercept is -7
Best of Luck!
Answer: -7
Step-by-step explanation: To identify the y-intercept of the line, we would first convert the equation to slope-intercept form.
In slope-intercept form or y = mx + b form, the y
is by itself on the left side of the equation.
So our first task in this problem is to get y by itself on the left side of the equation and we do that by first subtracting 2x from both sides to get 3y = -2x - 21.
Notice that I put the x term first on the right side of the equation and then the number because in y = mx + b form, the x term comes first on the right side of the equation.
Continuing on, to get y by itself we would
divide both sides by 3 to get y = -2/3x - 7.
Now our equation is written in slope-intercept form and
we can identity that the y-intercept of this line is -7.
surface area of a cylinder 1m radius and 5m side
Answer:
37.7 m
Step-by-step explanation:
Use this formula:
A=2πrh+2π[tex]r^{2}[/tex]
Answer: A=12pi
Step-by-step explanation:
A= 2*pi*R*H + 2*pi*R^2
A=2*pi*1*5 + 2*pi*1^2
A=10pi + 2pi
A=12pi
a delivry truck is transporiting boxes of two sizes large and small the combined weight of a large box and a small box is 65 pounds the truck transporting 55 large boxes and 65 small boxes if the truck is carrying a totall of 3774 pounds of boxes how much does each type of box way
Answer: S = 20 lbs L = 45 lbs. Both answer have been rounded from below
Step-by-step explanation:
L+S = 65 lbs
55L + 65S = 3774 lbs
55L+55S = (65)(55) = 3,575 lbs
10S = 199 lbs
S = 19.99 (round to 20)
L + S = 65
L + 19.99 = 65
L = 45.01 (round to 45)
Someone please help!!!! I’ll give most brainliest
Answer:
252 inches squared
Step-by-step explanation:
(6 x 9) + (6 x 15) + (9 x 12) = 252
What is the domain of the given function?
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
Lisa is packing a set of cubic inch blocks into the box shown below How many blocks will fit in the box8 in.5 in.3 in.A.16B. 32C. 120D. 180
Answer:
120 Blocks or letter C
Step-by-step explanation:
I did 8x5x3, because lxwxh so i got 120
An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that X, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months.
1. If the manufacturer's assumptions are correct, it would reed to replace _______ of its batteries free.2. The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of ____ results in a 1.07% replacement rate.3. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
Answer:
1) If the manufacturer's assumptions are correct, it would reed to replace 0.621% of its batteries free
2) The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of 6.084 results in a 1.07% replacement rate
3) Using the revised standard deviation for battery life, the percentage of the manufacturer's batteries that don't qualify for free replacement but do qualify for the prorated credit = 92%
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 45 months
Standard deviation = σ = 5.6 months.
Batteries that fail within the first 31 months get a free replacement and batteries that fail after 31 months but within 54 months get a prorated credit toward the purchase of a new battery.
1) Percentage of batteries that'll qualify for a replacement are the batteries that fail within 31 months. That is, P(X ≤ 31)
To obtain this, we first normalize or standardize 31 months.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (31 - 45)/5.6 = - 2.50
The required probability
P(X ≤ 31) = P(z ≤ -2.50)
We'll use data from the normal probability table for these probabilities
P(X ≤ 31) = P(z ≤ -2.50) = 0.00621 = 0.621%
2) The company finds that the percentage of free batteries replaced is actually 1.07%
P(X ≤ 31) = 1.07% = 0.0107
Let the z value of 31 months under this new normal distribution be z'
P(X ≤ 31) = P(z ≤ z') = 0.0107
From the normal distribution table,
z' = -2.301
z' = (x - μ)/σ
-2.301 = (31 - 45)/σ
σ = (-14) ÷ (-2.301) = 6.084 months
3) Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
That is, P(31 < X ≤ 54)
We first normalize 31 and 54 using the revised standard deviation
For 31
z = (x - μ)/σ = (31 - 45)/6.084 = - 2.30
For 54
z = (x - μ)/σ = (54 - 45)/6.084 = 1.48
The required probability = P(31 < X ≤ 54)
= P(-2.30 < z ≤ 1.48)
Using the normal distribution tables
P(31 < X ≤ 54) = P(-2.30 < z ≤ 1.48)
= P(z ≤ 1.48) - P(z < -2.30)
= 0.93056 - 0.0107
= 0.91986 = 91.986% = 92% to nearest whole number.
Hope this Helps!!!!
9. For the following vectors, x and y, calculate the indicated similarity or distance measures. a. (a) x : (0,0,1,1), y : (2,2,2,2) cosine, correlation, Euclidean b. (b) x : (0,1,0,1), y : (0,1,0,1) cosine, correlation, Euclidean, Jaccard c. (c) x : (1,1,0,1), y : (-1,0,-1,0) cosine, correlation, Euclidean d. (d) x : (1,0,0,1,0,1), y : (0,1,1,0,0,1) cosine, correlation, Jaccard e. (e) x : (2,1,0,2,0,3), y : (1,1,1,0,0,1) cosine, correlation
Answer:
The answer to this question can be defined as follows:
a)
cosine: 0.707
correlation: 0
Euclidean: 3.16
b)
cosine: 1
correlation: 1
Euclidean: 0
Jaccard: 1
c)
cosine: -0.4082
correlation: 0.5774
Euclidean: 2.64
d)
cosine: -0.333
correlation: -0.3333
Jaccard: 0.5
e)
cosine: -0.7075
correlation: 0.2132
Step-by-step explanation:
a) cosine:
[tex]x \times y( 0 \times 2+ 0 \times 2 +1 \times 2+1 \times 2) = 4\\\\ x= \sqrt{2} = 1.414\\\\y= \sqrt(16)=4\\\\\cos (x\times y) = \frac{x\times y}{x\times y}\\\\\cos (x\times y) = \frac{4}{1.414\times 4}\\\\= 0.707[/tex]
correlation:
[tex]\ corr(x,y) =[\frac{covariance (x,y)}{standec(x) \times standdev(y)}]\\X \ mean = 0.5\\Y \ mean = 2\\covariance (x,y) = 0\\standdev(x) = 0.5774\\standdev(y) = 0\\corr(x,y) = 0[/tex]
Euclidean:
[tex]d(x,y) = \sqrt((0-2)^2+(0-2)^2+(1-2)^2+(1-2)^2)\\d(x,y) = 4+4+1+1\\d(x,y)= \sqrt(10)\\d(x,y)= 3.16\\[/tex]
by applying above formula we get all the values.
b)
cosine: 1
correlation: 1
Euclidean: 0
Jaccard: 1
c)
cosine: -0.4082
correlation: 0.5774
Euclidean: 2.64
d)
cosine: -0.333
correlation: -0.3333
Jaccard: 0.5
e)
cosine: -0.7075
correlation: 0.2132
Use angles shown to make other angles
Answer:
angle ABC and angle KLM
Step-by-step explanation:
Angle ABC equals to 35 degrees and KLM equals to 95 degrees. Their sum equals 135 degrees.
Answer:
The answer is B and C.
Step-by-step explanation:
When these 2 angles are added together, they form 130° :
∠ABC + ∠KLM = 35° + 95°
= 130°
The volume of the prism shown is 84 cubic yards. What is the Height of the prism
Answer:
4 yd
Step-by-step explanation:
If l×w×h=v, then v÷l÷w=h
84÷7÷4=h
12÷3=h
h=4
The height of the prism is 4 yards.
una mulita está atada a un aranjo la mulita aburrida ha dado vueltas y vueltas alrededor del árbol manteniendo estirada la cuerda sin que ésta Se enrolle si la distancia que hay de la mulita al centro del árbol es de 5 metros qué distancia habrá recorrido después de dar 150 vueltas
Answer:
[tex]\Delta s_{T} = 4712.4\,m[/tex]
Step-by-step explanation:
(This exercise is written in Spanish and for this reason the response will be presented in such language).
La distancia recorrida por la mulita tras una vuelta es:
[tex]\Delta s = 2\pi\cdot (5\,m)[/tex]
[tex]\Delta s \approx 31.416\,m[/tex]
Ahora, la distancia recorrida total es directamente proporcional a la cantidad de vueltas invertidas. Este indicador se determina por regla de tres simple:
[tex]\Delta s_{T} = \frac{150}{1}\times (31.416\,m)[/tex]
[tex]\Delta s_{T} = 4712.4\,m[/tex]
put this on order from greatest to least pls
Answer:
0.497 < 1/2 < 0.55 < 3/5 < 6/7
Step-by-step explanation:
Order from Least to Greatest
1: Using the given inputs
2: Rewriting these inputs as decimals
3: Sorting this table by decimal values in order from least to greatest
4: Therefore, the sorted inputs in order from least to greatest is
Answer: 0.497 < 1/2 < 0.55 < 3/5 < 6/7
Hope this helps.
slope of the line with points (4,-2) and (24,-17)
Answer:
-3/4
Step-by-step explanation:
y2-y1/x2-x1
-17+2 divided by 24-4
-15/20
-3/4
Answer:
-3/4
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (-17- -2)/(24-4)
= (-17+2)/(20)
= -15/20
=-3/4
What does it mean to solve an equation or inequality
Answer:
x is less than or equal to y. An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.
please mark brainliest :]
Tess rolls 2 fair dice. What is the probability of obtaining two 4's?
Probability of getting two 4's is 1/36
What is required probability ?
Tess rolls 2 fair dice.
The possibilities of first die are 1, 2, 3, 4, 5 or 6.
Also the possibilities of second die are 1, 2, 3, 4, 5 or 6.
So, the number of possibilities is 36, when tess rolls 2 dice together.
Here, possibility of getting two 4's is 1 out of 36
∴ The probability of getting two 4's = 1/36
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Brian takes out a $1,600 discounted loan calculated using a simple interest rate of 12% for a period of 15 months. How much money does Brian receive from the bank when the loan is drawn down? Give your answer in dollars to the nearest dollar.
Answer:1360
Step-by-step explanation:
Which is the best estimate of -3/5
Answer:
-0.6
Step-by-step explanation:
3/5 is 0.6 and the negative makes it -0.6.
Answer:
-0.6
Step-by-step explanation:
James invests $100 at the beginning of each quarter in stock ABC. According to the table below, how many shares of ABC will James own at the end of the year?
A.
44 shares
B.
37 shares
C.
38 shares
D.
41 shares
Answer:
ABC | Stock price
Q1 | $10.50
Q2 | $11.50
Q3 | $9.00
Q4 | $10.50
Step-by-step explanation:
Answer is 37 shares on AP3X
find the value of this expression if x=-2. x-4/x
Step-by-step explanation:
Simple.
Putting value of x
2 - 4/2
2 - 2
= 0
Wich is a factor of x^2+ 5x-24?
Answer:
(x−3)(x+8)
Step-by-step explanation:
Let's factor x2+5x−24
x2+5x−24
The middle number is 5 and the last number is -24.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 5
Multiply together to get -24
Can you think of the two numbers?
Try -3 and 8:
-3+8 = 5
-3*8 = -24
Fill in the blanks in
(x+_)(x+_)
with -3 and 8 to get...
(x-3)(x+8)
Answer:
(x−3)(x+8)
Hope this helps.
similarity statements between triangles
Answer:
Two triangles are said to be similar if any two corresponding sets of angles are equal and the corresponding sides are in the same ratio.
If f(x) = 3x² + 1 and g(x) = 1 - X, what is the value of (f -9)(2)?
Answer:
(f -g)(2) = 14
Step-by-step explanation:
You can write the expression for the composite function as ...
(f -g)(x) = f(x) -g(x) = (3x² +1) -(1 -x)
(f -g)(x) = 3x² +x
Then for x = 2 ...
(f -g)(2) = 3(2²) +2
(f -g)(2) = 14
Sort each characteristic into the category where it fits best.
will require maintenance costs
will not allow me to build equity
will cost less up front
will have fairly constant payments
will allow me to build equity
will result in increasing payments
Answer: Buying: fairly constant payment, will build equity, require maintenance cost.
Renting: not build equit, cost less, increasing payments
Step-by-step explanation:
The categories in which these buying and renting characteristics belong are:
Buying:
Will require maintenance costs.Will have fairly constant payments.Will allow me to build equity.Renting:
Will not allow me to build equity.Will cost less up front.Will result in increasing payments.What are the characteristics of buying and renting property?When you buy property, you will have to pay for maintenance because you will own the property. You will however, build equity even though you will have to make fairly constant mortgage payments.
When you rent a house, the upfront cost will be less but you won't be able to build equity and there will be increasing payments as rent increases.
Find out more on renting property at https://brainly.com/question/26855888.
A shop has the following offers. Fig rolls (125g packet) Normal price £1.08. Buy one, get 2nd half price
Step-by-step explanation:
Fig rolls = 1.08
Half price = 1.08 ÷ 2 = 0.54
Total price = 1.08 + 0.54 = 1.62
Answer:
£8.52
Step-by-step explanation:
Fig rolls: £1.08+£1.08=£2.16
Crisps: £1.59+£1.59=£3.18 £3.18x2=£6.36
Total price= £2.16+£6.36=£8.52
show work 1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
1/4 ÷ 3/8 = 1/4 x 8/3 = 8/12 = 2/3
Answer:
2/3
Step-by-step explanation:
to divide make sure to use the reciprocal of the 3/8 which is
1/4*8/3
reduce the numbers with the greatest common factor divisor of 4
8/4=2 then 1*3 equals 3 which is 2/3
so it is 2/3
Craig Milton needs to order for his company int the catalog a 20% traidor discount is offered for a price of $481.60 what is the net price
Answer:
Net price = $385.28
Step-by-step explanation:
Trade Discount - It is the discount given by buyer to seller, as a reduction in list price, when huge (bulk) orders transactions are made.
List price = 481.60
Trade Discount = 20%
So, Trade Discount = 20 / 100 (481.60) = 96.32
Net price = List price - Trade Discount = 481.60 - 96.32 = 385.28
there are 7 row of 9 people how many people in all
Answer:
63
Step-by-step explanation:
You simply just multiply the 7 and 9.
Find an equation of the tangent line to the graph of
y = g(x) at x = 4 if g(4) = −3 and g'(4) = 2.
(Enter your answer as an equation in terms of y and x.)
Answer:
[tex] y- y_o = m(x-x_o) [/tex]
For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:
[tex] y -(-3) = 2 (x-4)[/tex]
And if we reorganize the terms we have:
[tex] y+3 = 2x -8[/tex]
And subtracting 3 in both sides we got:
[tex] y = 2x -11[/tex]
Step-by-step explanation:
For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions: [tex] g(4) =-3, g'(4)=2[/tex]
So we need a function like this one:
[tex] y- y_o = m(x-x_o) [/tex]
For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:
[tex] y -(-3)=2(x-4)[/tex]
And if we reorganize the terms we have:
[tex] y+3 = 2x -8[/tex]
And subtracting 3 in both sides we got:
[tex] y = 2x -11[/tex]
In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
9/23
Step-by-step explanation:
Of the 23 students, 9 play both baseball and basketball. The probability of choosing one of those is 9/23.
___
Let A represent basketball, and B represent baseball. Then ...
P(A or B) = P(A) +P(B) -P(A and B)
Since 8 students play neither sport, we have ...
1 -8/23 = 11/23 +13/23 -P(A and B)
15/23 = 24/23 -P(A and B)
P(A and B) = (24 -15)/23
P(A and B) = 9/23