Answer:
t < [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
10t - 4 < 2t
8t - 4 < 0
8t < 4
t < [tex]\frac{1}{2}[/tex]
Construct a table of values for the following functions using the integers from -4 to 4.
a. F(x)=6/x-2
b. r(x)=6x+12/x^-4
Step-by-step explanation:
Find the table attached
a) Given
F(x) = 6/x-2
When x = -4
F(-4) = 6/-4-2
F(-4) = 6/-6
F(-4) = -1
F(x) = 6/x-2
When x = -3
F(-3) = 6/-3-2
F(-3) = 6/-5
F(-3) = -1.2
F(x) = 6/x-2
When x = -2
F(-2) = 6/-2-2
F(-2) = 6/-4
F(-2) = -1.5
F(x) = 6/x-2
When x = -1
F(-1) = 6/-1-2
F(-1) = 6/-3
F(-1) = -2.0
F(x) = 6/x-2
When x = 0
F(0) = 6/0-2
F(0) = 6/-2
F(0) = -3
F(x) = 6/x-2
When x = 1
F(1) = 6/1-2
F(1) = 6/-1
F(1) = -6
F(x) = 6/x-2
When x = 2
F(2) = 6/2-2
F(2) = 6/0
F(2) = infty
F(x) = 6/x-2
When x = 3
F(3) = 6/3-2
F(3) = 6/1
F(3) = 6
F(x) = 6/x-2
When x = 4
F(4) = 6/4-2
F(4) = 6/2
F(4) = 3
b) Given
r(x)=6x+12/x^-4
When x = -4
r(-4) = 6(-4)+12/(-4)^-4
r(-4) = -24+12/(1/256)
r(-4) = -12(256)
r(-4) = -3072
When x = -3
r(-3) = 6(-3)+12/(-3)^-4
r(-3) = -18+12/(1/81)
r(-3) = -6(81)
r(-3) = -486
When x = -2
r(-2) = 6(-2)+12/(-2)^-4
r(-2) = -12+12/(1/16)
r(-2) = -0(16)
r(-2) = 0
When x = -1
r(-1) = 6(-1)+12/(-1)^-4
r(-1) = -6+12/(1)
r(-1) = -6+12
r(-1) = 6
When x = 0
r(0) = 6(0)+12/(0)^-4
r(0) = 0+12/0
r(0) = 12/0
r(0) = infty
When x = 1
r(1) = 6(1)+12/(1)^-4
r(1) = 6+12/1
r(1) = 18(1)
r(1) = 18
When x = 2
r(2) = 6(2)+12/(2)^-4
r(2) = 12+12/1/16
r(2) = 24(16)
r(2) = 384
When x = 3
r(3) = 6(3)+12/(3)^-4
r(3) = 18+12/1/81
r(3) = 30(81)
r(3) = 2430
When x = 4
r(4) = 6(4)+12/(4)^-4
r(4) = 24+12/1/256
r(4) = 36(256)
r(4) = 9216
We want to construct tables of values for the two given functions.
The tables are:
a)
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b)
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
A table will be something like:
[tex]\left[\begin{array}{ccc}x&y\\-4&\\-3&\\-2&\\-1&\\0&\\1&\\2&\\3&\\4&\end{array}\right][/tex]
Where the values of x go from -4 to 4.
To complete the tables, we just need to evaluate the functions in each one of the x-values at the left, and the outcome will be placed at the right.
a) f(x) = 6/x - 2
Now we just need to evaluate the function in all the given points:
f(-4) = 6/(-4) - 2 = -3/2 - 4/2 = -7/2
f(-3) = 6/-3 - 2 = -4
f(-2) = 6/-2 - 2 = -5
f(-1) = 6/-1 - 2 = -8
f(0) is undefined, as we can't divide by zero, here we can write NaN (Not a number).
f(1) = 6/1 - 2 = 4
f(2) = 6/2 - 2 = 1
f(3) = 6/3 - 2 = 0
f(4) = 6/4 - 2 = -1/2
Now we put all of these in the correspondent place of the table:
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b) We do the same thing, here we have:
r(x) = 6*x + 12/x^-4 = 6*x + 12*x^4
Now we evaluate this in the given values:
r(-4) = 6*(-4) + 12*(-4)^4 = 3,048
r(3) = 6*(-3) + 12*(-3)^4 = 954
r(-2) = 6*(-2) + 12*(-2)^4 = 180
r(-1) = 6*(-1) + 12*(-1)^4 = 6
r(0) = 6*0 + 120^4 = 0
r(1) = 6*1 + 12*1^4 = 18
r(2) = 6*2 + 12*2^4 = 204
r(3) = 6*3 + 12*3^4 = 990
r(4) = 6*4 + 12*4^4 = 3,096
Now we place these values in the correspondent place on the table:
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
These are our two tables.
If you want to learn more, you can read.
https://brainly.com/question/8629807
What is a single discount rate and how does it apply to chain discounts?
Answer:
Single discount rates are one off discounts which are given by seller on certain products with certain conditions which most be met for it to apply such conditions can be for buyers who pay in cash, buyers who buy in bulks e.g buy 10 get one free, or for every 5 bought you get a 5% discount e.t.c.
This is related to chain discount because its also a series of discount which is allowed for list price of products or services.
A circle is inscribed in a square. If the perimeter of the square is 40, what is the area of the circle? Use 3.14 for pi.
Answer:
78.5
Step-by-step explanation:
We have the perimeter of the square, which is 40, and 40/4=10. In this picture, we see that the circle's diameter is the same as the length of one side of the square. Therefore, the diameter of the circle is 10. The are formula for circles is [tex]\pi r^{2}[/tex], where [tex]r[/tex] is the radius. The radius of the circle is just the diameter divided by 2, and 10/2=5. Now, [tex]5^2[/tex] is 25, and [tex]3.14\cdot25=78.5[/tex].
If m<3 =54°. find each measure.
Answer/Step-by-step explanation:
Given:
m<3 = 54°
m<2 = right angle
a. m<1 + m<2 + m<3 = 180° (angles in a straight line)
m<1 + 90° + 54° = 180° (substitution)
m<1 + 144° = 180°
m<1 = 180° - 144°
m<1 = 36°
b. m<2 = 90° (right angle)
c. m<4 = m<1 (vertical angles)
m<4 = 36° (substitution)
d. m<5 = m<2 (vertical angles)
m<5 = 90°
e. m<6 = m<3 (vertical angles)
m<6 = 54°
f. m<7 + m<6 = 180° (same side interior angles)
m<7 + 54° = 180° (substitution)
m<7 = 180 - 54
m<7 = 126°
g. m<8 = m<6 (alternate interior angles are congruent)
m<8 = 54°
h. m<9 = m<7 (vertical angles)
m<9 = 126°
i. m<10 = m<8 (vertical angles)
m<10 = 54°
j. m<11 = m<4 (alternate interior angles are congruent)
m<11 = 36° (substitution)
k. m<12 + m<11 = 180° (linear pair)
m<12 + 36° = 180° (substitution)
m<12 = 180° - 36°
m<12 = 144°
l. m<13 = m<11 (vertical angles)
m<13 = 36°
m. m<14 = m<12 (vertical angles)
m<14 = 144° (substitution)
Use inductive reasoning to predict the next three numbers in the pattern.
Home
3, 5, 8, 13, 21, 34, ...
nents
Predict the next three numbers in the pattern.
3, 5, 8, 13, 21, 34,
Answer:
The next three terms are 55,89 and 144
Step-by-step explanation:
We want to predict the next three numbers in the pattern
3, 5, 8 , 13 , 21 , 34
The difference between two successive terms is written between them.
Thus, we have
3 2 5 3 8 5 13 8 21 13 34
So the rule here is to add the next term to the previous so as to get the next coming term
Thus, we have;
34 + 21 = 55
55 + 34 = 89
89 + 55 = 144
Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours. . Let x = the time needed to fix a furnace.
Required:
a. What is the probability that it takes the repairman more than 7 hours to fix a furnace?
b. Find the probability that a randomly selected furnace repair requires less than 3 hours.
c. Find the 30th percentile of furnace repair times.
d. The longest 25% of repair furnace repairs take at least how long? (In other words: Find the minimum time for the longest 25% of repair times.) What percentile does this represent?
e. Find the mean and standard deviation
Answer:
a
[tex]P(X > 7) = 0.5[/tex]
b
[tex]P(X < 3) = -0.5[/tex]
c
[tex]x = 6.2 \ hours[/tex]
d
[tex]x_1 = 8 \ hours[/tex]
e
Mean [tex]\mu = 7[/tex]
Standard deviation [tex]s \approx 1.1547[/tex]
Step-by-step explanation:
From the question we are told that
The amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours
Generally the probability that it takes the repairman more than 7 hours to fix a furnace is mathematically represented as
[tex]P(X > 7) = \frac{9- 7}{9-5}[/tex]
=>[tex]P(X > 7) = 0.5[/tex]
Generally the probability that a randomly selected furnace repair requires less than 3 hours. is mathematically represented as
[tex]P(X < 3) = \frac{3 -5}{9-5}[/tex]
=>[tex]P(X < 3) = -0.5[/tex]
Generally the 30th percentile of furnace repair times is mathematically represented as
[tex]30^{th} \ percentile = \frac{x - 5}{9-5}[/tex]
=> [tex]0.3 = \frac{x - 5}{9-5}[/tex]
=> [tex]x = 6.2 \ hours[/tex]
Generally the time taken for the longest 25% of furnace repair is mathematically evaluated as
[tex]75^{th} \ percentile = \frac{x_1 - 5}{9-5}[/tex]
Here making use of the [tex]75^{th}[/tex] because we are considering duration that fall with the top [tex]25^{th}[/tex]
=> [tex]0.75 = \frac{x_1 - 5}{9-5}[/tex]
=> [tex]x_1 = 8 \ hours[/tex]
Generally the mean is mathematically represented as
[tex]\mu = \frac{5 + 9 }{2}[/tex]
=> [tex]\mu = 7[/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{ \frac{(9- 5)^2}{12} }[/tex]
=> [tex]s \approx 1.1547[/tex]
How much will cost to buy beef for a family of 2 if each person gets 1/2 pound of beef and the beef cost 5.99 per pound?
Answer:
it will cost 5.99
Step-by-step explanation:
because each person getting half and there are 2 peeps so add up the meet to make on pound
A scientist observes and counts 155 bacteria in a culture. Later, the scientist counts again and finds the number has increased by 40%.How many bacteria are there now?
Answer:
217
Step-by-step explanation:
155 + 40% = 217
1
bushels
A farmer has 140 bushels of wheat to sell at his roadside stand. He sells an average of 16
each day. Represent the total change in the number of bushels he has for sale after 5 days.
The total change in the number of bushels he has for sale is I.
(Type an integer, proper fraction, or mixed number.)
Answer: 60
Step-by-step explanation:
If he sells 16 each day after 5 days he would sell 80 leaving him with 60 bushels of wheat
What number must be added to 101 to produce a number equal to the product of 101 x 21
Answer:
2020
Step-by-step explanation:
101 • 21 = 2121
2121 - 101 = 2020
What property is if x=12 , then 3x=36
Answer:
3x=x+12 This is not quadratic. This is linear in x. (3x-x) = 12 (bringing x from the right to the left, change side then change sign, in other words add - x to both the sides.
Step-by-step explanation:
What is 3/100 - 1/50 equal?
Answer:
0.01?
Step-by-step explanation:
I need help with this! Right nowww I will brainliest
Answer:
2 and 7: Alternate exterior
3 and 7: Corresponding
3 and 5: Same side interior
3 and 6: Alternate interior
What's the slop of ( 2.5),(6,13)
Answer:
2
Step-by-step explanation:
m=y2-y1/x2-x1
13-5=8
6-2=4
8/4=2
hope this helps :3
if it did pls mark brainliest
The Acme Battery Company has developed a new cell phone battery. On average, the battery lasts 60 minutes on a single charge. The standard deviation is 4 minutes. Suppose the manufacturing department runs a quality control test. They randomly select 7 batteries. The standard deviation of the selected batteries is 6 minutes. a. What would be the chi-square statistic represented by this test? b. What are the degrees of freedom for the chi-square statistic? c. Suppose they repeated the test with a new random sample of 7 batteries. What is the probability that the standard deviation in the new test would be greater than 6 minutes? (Use the applet)
Answer:
X² = 13.5
Degree of freedom = 6
0.04
Step-by-step explanation:
Give the following :
Number of samples (n) = 7
Population standard deviation (σ) =.4 minutes
Sample standard deviation (s) = 6
Mean battery life = 60 minutes
A) Chisquare (X²) :
X² = ((n - 1) * s²) / σ²
X² = ((7 - 1) * 6²) / 4²
X² = (6 * 6²) / 4²
X² = (6 * 36) / 16
X² = 216 / 16
X² = 13.5
B.) The degree of freedom:
degree of freedom = n - 1
Degree of freedom = 7 - 1 = 6
C.) using a chisquare distribution calculator :
With degree of freedom (df) = 6
X² = 13.5
Hence,
P(X² > 13.5) = 0.04 ( from calculator)
Sophia earned $18 for working 2 1/4 hours. How much did she earn per hour?
Answer:
It is price between 1~100 lol
Step-by-step explanation:
The value of the 7 in 2,751 is how many times the value of the 7 in 7,433?
Answer:
Step-by-step explanation:
The value of 7 in 2,751 is 700 since 7 is in the hundred place in the value
The value of 7 in 7,433 is 7000, since 7 is in the thousand place in the value.
In order to know how many times the 7 in 2,751 is more than 7 in 7,433, we will take the ratio of 700 to 7000 as shown:
ratio = 700:7000
ratio = 700/7000
ratio = 0.1
Hence the value of the 7 in 2,751 is 0.1 times the value of the 7 in 7433
Answer:
I believe it’s 1/10 but I’m not to sure
Step-by-step explanation:
9.831 rounded to the nearest tenth
Answer:
9.8
Can i get brainliest please?
Answer:
9.8
Step-by-step explanation:
Hoped that helped :)
ANSWER ASAP PLEASE!!!!!
Amir draws two parallel lines cut by a transversal.
What is the value of y?
Answer: y = 45
Step-by-step explanation:
the two angles will be supplementary to each other
4y - 45 + y = 180
Combine like terms
5y - 45 = 180
Add 45 to both sides
5y = 225
Divide both sides by 5
y = 45
Jackie earns $172 per week at her part time job. She is saving this money to buy a used car that cost $2000. At this rate, how many weeks will it take her to earn enough money to buy the car..? Explain.
Answer:
12 weeks
Step-by-step explanation:
It will take Jackie 12 weeks to buy her car because she earns 172 per week.
If you divide 2000 buy 172 you end up with 11.6
if you multiply 11 and 172 you get 1,892 which is just a little under 2000
if you add another week = 172$ you will arrive at 2064 which is enough to buy
her car.
Hope this helps.
Can someone who knows Pre Calculus help me on these questions.
Answer:
the answer should be B:12/5
123x78=
how much it equals too?
Answer:9,594 thats tha answer
Customers at the Palace Pro Shop receive a 10% discount if they are members. All customers must pay 7% in sales tax. The function f(x)=0.9x is used to determine the price of an item after the 10% member discount, where x is the regular price of the item. The function g(x)=1.07x is used to determine the total amount customers pay for a purchase after all discounts are applied. Which function can be used to determine T(x), the total amount a member pays for an item with a regular price of x dollars?
T(x)=0.963x
T(x)=0.17x
T(x)=1.19x
T(x)=1.97x
Answer:
0.963
Step-by-step explanation:
It’s correct
find the sum of 2x ÷ x-1 and x÷x-1
Answer with step-by-step explanation:
First of all, ORDER OF OPERATIONS!! 2x/x is 2/1, which is 2. Then, subtract 1, which is 1.
2x ÷ x - 1 = 1
Same thing: x/x = 1. Subtract 1 from 1, which is 0.
x ÷ x - 1 = 0
1 + 0 = 1
Hope this helped!
3.Each day you exercise you either walk 5 miles or jog 2 miles. You exercised 19 days last month and the total distance you travelled was 74 miles. How many days did you walk?
Answer:
You walk 12 days
Step-by-step explanation:
Let's call:
W=Number of days you walk
J=Number of days you jog
Since you only do one of the exercises per day:
W + J = 19
Solving for J:
J = 19 - W
Every day you walk, you travel 5 miles, and every day you jog, you travel 2 miles, thus:
5W + 2J = 74
Replacing the expression for J:
5W + 2(19 - W) = 74
Operating:
5W + 38 - 2W = 74
Simplifying:
3W = 74 - 38 = 36
Solving:
W = 36 / 3 = 12
You walk 12 days
The normal distribution 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. Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.)
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 0.62% of its batteries free.
2) a standard deviation of 6.0843 results in a 1.07% replacement rate
3) using the revised standard deviation for battery life, 91.9% of the manufacturer's batteries don't get free replacement but qualifies for the prorated credit
Step-by-step explanation:
based on the given data;
x will represent the random variable such that the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months
so
x → N( U = 45, ∝ = 5.6)
Under the warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charges to the consumer.
if the battery fails after 31 months but within 54 months, the manufacturer provides a prostrated credit towards the purchase of anew battery
1) If the manufacturer's assumptions are correct,
p(x < 3) = p( [x-u / ∝ ] < [ 31-45 / 5.6] )
= p( z < -2.5 )
using the standard normal table,
value of z = 0.0062 ≈ 0.62%
so if the manufacturer's assumptions are correct, it would reed to replace 0.62% 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, so a standard deviation of ? results in a 1.07%
so lets say;
p ( x < 31 ) = ( 1.07%) = 0.0107
p ( [x-u / ∝ ] < [ 31-45 / ∝] ) = 0.0107
now from the standard table
-2.301 is 1.07%
so
( 31 - 45 / ∝ ) = -2.301
-14 / ∝ = -2.301
∝ = -14 / - 2.301
∝ = 6.0843
therefore a standard deviation of 6.0843 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?
p( 31 < x < 54 ) = p ( [31 - u / ∝ ] < [ x-u / ∝] < [ 54 - 45 / ∝] )
= p ( [31 - 45 / 6.0843 ] < [ x-u / ∝] < [ 54 - 45 / 6.0843] )
= p ( -2.301 < z < 1.4792 )
= p(Z < 1.5) - p(Z < -2.3)
= 0.9393 - 0.0108
= 0.919 ≈ 91.9%
therefore using the revised standard deviation for battery life, 91.9% of the manufacturer's batteries don't get free replacement but qualifies for the prorated credit
3.1 to the nearest tenth
Answer:
3.1 to the nearest tenth is 3.1.
Step-by-step explanation:
The first decimal place is the tenths place. Hope this helps!
3.1 because 1 can't be raised to the next number
please help, I can't get it
What is the length of LA?
The length of LA in the triangle will be 8.
How to calculate the triangle?From the information given, it was stated that both the triangles are similar.
In this situation, the length of LA will be:
= (12 × 4)/6
= 48/6
= 8
Therefore, the length of LA in the triangle will be 8.
Learn more about triangles on:
brainly.com/question/17335144
#SPJ6
Find the slope of the line
Answer:
0
Step-by-step explanation:
