Answer:
g(x) = 4x - 1
Step-by-step explanation:
Linear function in the format: g(x) = ax + b
g(2t) is a*(2t)+b
g(2t) = 8t - 1 means that:
when x = 2t, g = 8t - 1.
So
Equaling both sides
8t - 1 = a*2t + b
So
b = -1,
and
2a = 8, a = 8/2, a = 4
So
g(x) = 4x - 1
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!!!!
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:
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.
The radius of a soccer ball is 4 inches. Approximately what volume of air can it hold? Use 3.14 for Pi. Round to the nearest tenth of a cubic inch.
Recall the formula V = four-thirds pi r cubed
Answer:
The volume of air that can be hold is 267.9 inches³.
Step-by-step explanation:
Given that the volume of sphere formula is V = 4/3×π×r³ where r represents radius of sphere. Then substitute the values :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
Let π = 3.14,
Let r = 4,
[tex]v = \frac{4}{3} \times 3.14 \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times 200.96[/tex]
[tex]v = 267.9 \: {inches}^{3} (near.tenth)[/tex]
The soccer can hold air up to the volume of 267.9 cubic inches.
What is volume?
The measure of the capacity that an object holds is called volume.
Formula for the volume of sphere[tex]v = \frac{4}{3} \pi r^{3}[/tex]
Where, v is the volume of sphere
r is the radius of sphere
π = 3.14
According to the given question
The radius of soccer is 4 inches.
Therefore,
The volume of the soccer = [tex]\frac{4}{3}\pi (4)^{3}[/tex] (shape of soccer is spherical)
Volume of soccer = [tex]\frac{4}{3} (3.14)(64)[/tex] [tex]= 267.946 cubic inches[/tex]
Hence, the soccer can hold air up to the volume of 267.9 cubic inches.
Learn more about the volume of sphere here:
https://brainly.com/question/9994313
#SPJ2
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)
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
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
Factor COMPLETELY the expression 2x^3 - 250
Answer:
2 (x - 5) (x^2 + 5 x + 25)
Step-by-step explanation:
Factor the following:
2 x^3 - 250
Factor 2 out of 2 x^3 - 250:
2 (x^3 - 125)
x^3 - 125 = x^3 - 5^3:
2 (x^3 - 5^3)
Factor the difference of two cubes. x^3 - 5^3 = (x - 5) (x^2 + x 5 + 5^2):
2 (x - 5) (x^2 + 5 x + 5^2)
5^2 = 25:
Answer: 2 (x - 5) (x^2 + 5 x + 25)
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.
analyze the diagram below and complete instructions that follow find the value of x in the value of y
Answer:
The values are [tex]x=2\sqrt{2}[/tex] and [tex]y=2\sqrt{6}[/tex].
Step-by-step explanation:
A right triangle is a type of triangle that has one angle that measures 90°.
In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
[tex]\sin(\theta)=\frac{opposite \:site}{hypotenuse}[/tex]
To find the value of x we use the above definition. From the diagram we can see that the angle is 30º and the hypotenuse is [tex]4\sqrt{2}[/tex]. Therefore,
[tex]\sin(30)=\frac{x}{4\sqrt{2} }\\\\\frac{x}{4\sqrt{2}}=\sin \left(30^{\circ \:}\right)\\\\\frac{8x}{4\sqrt{2}}=8\sin \left(30^{\circ \:}\right)\\\\\sqrt{2}x=4\\\\\frac{\sqrt{2}x}{\sqrt{2}}=\frac{4}{\sqrt{2}}\\\\x=2\sqrt{2}[/tex]
To find the value of y we use the above definition. From the diagram we can see that the angle is 60º and the hypotenuse is [tex]4\sqrt{2}[/tex]. Therefore,
[tex]\sin(60)=\frac{y}{4\sqrt{2} }\\\\\frac{y}{4\sqrt{2}}=\sin \left(60^{\circ \:}\right)\\\\\frac{8y}{4\sqrt{2}}=8\sin \left(60^{\circ \:}\right)\\\\\sqrt{2}y=4\sqrt{3}\\\\\frac{\sqrt{2}y}{\sqrt{2}}=\frac{4\sqrt{3}}{\sqrt{2}}\\\\y=2\sqrt{6}[/tex]
Answer:
C.
Step-by-step explanation:
trust me its correct on EDGE2021
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
What is 656 divided by 78
Answer:
8.4102
Step-by-step explanation:
656÷78=8.4102
Answer
8.41025641026
When you do long division that comes out to be your answer.
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
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
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.
What is the domain of the given function?
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
90-(18+-2)(3)
90-(16)(3)
Answer:
1: 42
2: 42
Step-by-step explanation:
1: Subtract and plus the first equation using a calculator
2: Now subtract and plus the second equation using a calculator
Answers:
1: 42
2: 42
Hope this helps.
Answer:
hmmmmmm
Step-by-step explanation:
42 easyyyyyyyyyyyyyyyyyyyyyy tyyyyyb y u y y y y y y
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
Learn more about dice problem here :
https://brainly.com/question/12727360
#SPJ2
What is 2+2=
Double tap to add text
Answer:
2+2= 4
Step-by-step explanation:
1+1+1+1= 4
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.
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 :]
Multiply (y + 4)(y - 3)
Answer: y2 + y - 12
Step-by-step explanation:
(y + 4)(y - 3)
y2 -3y + 4y -12
y2 +y -12
A recently published article included data from a survey of 2186 hiring managers and human resource professionals. The article noted that many employers are using social networks to screen job applicants and that this practice is becoming more common. Of the 2186 people who participated in the survey, 1312 indicated that they use social networking site to research job applicants. Based on the survey data, is there convincing evidence that fewer than two-thirds of hiring managers and HR professionals use social networking sites in this way? Use a significance level of = 0.01 to make your conclusion.
Calculate the test statistic.
Answer:
Step-by-step explanation:
two-thirds = 2/3 = 0.67
We would set up the hypothesis test.
For the null hypothesis,
p = 0.67
For the alternative hypothesis,
p < 0.67
This is a left tailed test.
Considering the population proportion, probability of success, p = 0.67
q = probability of failure = 1 - p
q = 1 - 0.67 = 0.33
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 1312
n = number of samples = 2186
P = 1312/2186 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.67)/√(0.67 × 0.33)/2186 = - 6.96
From the normal distribution table, the probability value corresponding to the z score is < 0.00001
Since alpha, 0.01 > than the p value, then we would reject the null hypothesis. Therefore, at 1% significance level, there is convincing evidence that fewer than two-thirds of hiring managers and HR professionals use social networking sites in this way.
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.
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
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.
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
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:
Predict what will happen to the coordinates of a point (x, y) as the point reflects across a line to produce point (x', y'). Choose the x-axis, y-axis, y = x and y = -x for the lines of reflection. Express your answers in terms of x and y. (Be sure to watch your signs
Answer:
Check the table.
Step-by-step explanation:
For edmentum.
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