Answers
Answer:
B.
C.
E.
F.
Step-by-step explanation:
A. no. any log(x) function is increasing. it says to what power I have to put the base to get x. and the bigger x, the bigger also that power number has to be. a log(x) increases much slower than x itself, but it increases.
B. any log(x) can only be calculated for positive x (and not 0).
C. of course. there are no gaps or breaks in a log(x) function. over time, with a growing x, we have to cover every possible y.
D. no. since (0,4) means x=0, this can't be true. as log(0) is power definition undefined (representing minus infinity).
E. yes. see A.
F. yes. for x=1 any log(x) function has to deliver 0 as functional value (to what power do I have to put my base to get 1 ? only base⁰ delivers 1. also 0.725⁰ = 1. therefore, (1,0) is a valid point on the graph.
Related Questions
What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator
Answers
Answer:
4033
Step-by-step explanation:
An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 - b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:
a^2 = 2017^4
a = 2017^2
b^2 = 2016^4
b = 2016^2
Now, the special product a^2 - b^2 factors to (a + b)(a - b), so we can substitute that for the numerator:
[tex]\frac{(2017^2+2016^2)(2017^2 - 2016^2)}{2017^2+2016^2}[/tex]We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by [tex]\frac{2017^2+2016^2}{2017^2+2016^2}[/tex] which is just one, and will simplify the fraction to just:
2017^2 - 2016^2
This again is just the special product a^2 - b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:
(2017 + 2016)(2017 - 2016)
And, without using a calculator, this is easy to simplify:
(4033)(1)
4033
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 14 cups of coffee, using 204 ounces of coffee, while collecting a total of $16.70. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answers
Answer:
Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Step-by-step explanation:
Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.
Since a total of 14 cups of coffee was served:
[tex]a+b+c=14[/tex]
A total of 204 ounces of coffee was served. Therefore:
[tex]10a+14b+20c=204[/tex]
A total of $16.70 was collected. Hence:
[tex]0.95a+1.15b+1.5c=16.7[/tex]
This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.
From the first equation, let's subtract a and b from both sides:
[tex]c=14-a-b[/tex]
Substitute this into both the second and third equations:
[tex]10a+14b+20(14-a-b)=204[/tex]
And:
[tex]0.95a+1.15b+1.5(14-a-b)=16.7[/tex]
In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:
For the Second Equation:
[tex]\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}[/tex]
And for the Third:
[tex]\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}[/tex]
We can solve this using substitution. From the second equation, isolate a:
[tex]\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b[/tex]
Substitute into the third:
[tex]-0.55(7.6-0.6b)-0.35b=-4.3[/tex]
Distribute and simplify:
[tex]-4.18+0.33b-0.35b=-4.3[/tex]
Therefore:
[tex]-0.02b=-0.12\Rightarrow b=6[/tex]
Using the equation for a:
[tex]a=7.6-0.6(6)=4[/tex]
And using the equation for c:
[tex]c=14-(4)-(6)=14-10=4[/tex]
Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 6 minutes and a population standard deviation of 2 minutes.
Find the probability that it took less than one minute to find a parking space. Round answer to four decimal places.
Answers
Answer:
56
Step-by-step explanation:
Answer: 0.0062
Step-by-step explanation:
An isosceles triangle has legs of length 12 and base angles that measure 28°. What is the measure of its base to the nearest tenth? Be careful on this one.
Answers
Answer:
base = 21.2
Step-by-step explanation:
Let the base be 2x
Drawing a perpendicular bisector divides the bases into 2 equal parts.
Then using trigonometric ratio :
[tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex] , [tex][ \ where \ \theta = 28^{ \circ} , \ adjacent = x,\ hypotenuse = 12 \ ][/tex]
The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the base of the isosceles triangle is 21.19 units.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
In order to solve the problem, we will draw a line between the triangle such that it will bisect the angle at the top(∠A) and the base(BC). As shown in the image below.
Now, as we know that the line(AD) is perpendicular to the base(BC) of the isosceles triangle, therefore, using the function of trigonometry in the Δ ABD we can write,
[tex]Cos \theta=\dfrac{BD}{AB}\\\\\\Cos (\angle B)=\dfrac{BD}{12}\\\\\\Cos 28^o \times 12={BD}\\\\BD = 10.5953[/tex]
Now, we know that the line BD divides the base BC into two equal parts, therefore, BD=BC.
BC = BD + DC
BC = 10.5953 +10.5953
BC = 21.19 units
Hence, the length of the base of the isosceles triangle is21.19 units.
Learn more about Trigonometric functions:
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Q.1 You are Nu.9 in debt. You borrowed Nu. 15 more. What is the total amount of your debt?
Answers
Answer:
total of it is Nu.24
Step-by-step explanation:
just add all up into
9 + 15 = 24
Use the drawing tools to form the correct answer on the graph. Graph this function. - 2 + 8 = Reset ® Delet Undo Drawing Tools Click on a tool to begin drawing. Select Point 10 Line 8 3 6- 4 2 2 4 6 -2 8 10 -4 -10 -8 -6 -2 7071 Frmentum. All rights reserved.
Answers
Answer:
we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm
The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
The function is given as:
[tex]f(x) = -2x + 8[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]y =mx + c[/tex]
Where:
m represents the slope, and c represents the y-intercept.
So, by comparison;
[tex]m =-2[/tex]
[tex]c = 8[/tex]
This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
See attachment for the graph of the function
Read more about linear functions at:
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length 21cm area 315cm2 find the breath
Answers
Answer:
Breadth = 15 cm
Step-by-step explanation:
Area = length x breadth
315 = 21 x breadth
[tex]\frac{315}{21} = \frac{21}{21} \times breadth[/tex] [ dividing both sides by 21 ]
[tex]15 = 1 \times breadth\\\\breadth = 15 \ cm[/tex]
___________________________________
Symbols of:[tex]\quad\quad\quad\quad\tt{A = A rea}[/tex]
[tex]\quad\quad\quad\quad\tt{ l = length} [/tex]
[tex]\quad\quad\quad\quad\tt{ b \: = breadth} [/tex]
Given that:[tex]\quad\quad\quad\quad\tt{A = 315 {cm}^{2} }[/tex]
[tex]\quad\quad\quad\quad\tt{l = 21cm}[/tex]
[tex]\quad\quad\quad\quad\tt{b = \: ? }[/tex]
Formula for breadth (b):[tex]\quad\quad\quad\quad\tt{breadth = \frac{Area}{length} }[/tex]
Solution:[tex]\quad\quad\quad\quad\tt{b = \frac{315 {cm}^{2} }{21cm} }[/tex]
[tex]\quad\quad\quad\tt{\:\:b = {15cm}}[/tex]So, the breadth (b) is:[tex]\quad\quad\quad\quad\tt \boxed{ \boxed{ \color{magenta}{b = 15cm }}}[/tex]
___________________________________
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✍︎ C.Rose❀
The following data represent the weights in pounds of a sample of 25 police officers:
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
Required:
a. Determine the location and value of the lower quartile of the weights
b. Determine the location and value of the upper quartile of the weights.
c. Find the interquartile range of the weights.
Answers
Given:
The data values are:
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
To find;
a. Lower quartile.
b. Upper quartile.
c. Interquartile range.
Solution:
We have,
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, 171.
Arrange the data values in ascending order.
134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157, 162, 163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177.
Divide the data values in two equal parts.
(134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177)
Divide each parentheses in two equal parts.
(134, 137, 140, 145, 146, 148), (151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169), (171, 172, 173, 174, 174, 177)
a. Location of lower quartile is:
[tex]Q_1=\dfrac{1}{4}(n+1)\text{th term}[/tex]
[tex]Q_1=\dfrac{1}{4}(25+1)\text{th term}[/tex]
[tex]Q_1=\dfrac{26}{4}\text{th term}[/tex]
[tex]Q_1=6.5\text{th term}[/tex]
The lower quartile of the weights is:
[tex]Q_1=\dfrac{148+151}{2}[/tex]
[tex]Q_1=\dfrac{299}{2}[/tex]
[tex]Q_1=149.5[/tex]
Therefore, the location of the lower quartile of the weights is between 6th term and the 7th term. The value of the lower quartile is 149.5.
b. Location of upper quartile is:
[tex]Q_3=\dfrac{3}{4}(n+1)\text{th term}[/tex]
[tex]Q_3=\dfrac{3}{4}(25+1)\text{th term}[/tex]
[tex]Q_3=\dfrac{3\cdot 26}{4}\text{th term}[/tex]
[tex]Q_3=19.5\text{th term}[/tex]
The upper quartile of the weights is:
[tex]Q_3=\dfrac{169+171}{2}[/tex]
[tex]Q_3=\dfrac{340}{2}[/tex]
[tex]Q_3=170[/tex]
Therefore, the location of the upper quartile of the weights is between 19th term and the 20th term. The value of the upper quartile is 170.
c. The interquartile range of the given data set is:
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=170-149.5[/tex]
[tex]IQR=20.5[/tex]
Therefore, the interquartile range of the weights is 20.5.
The club will use the plurality criterion without elimination method to determine the final winner. Parker wins the contest by receiving 56 votes. However, while finalizing the votes, a member of the club discovers that Myers did not meet the original criteria to be considered for the tickets, so Myers is eliminated from the votes. Who actually will win the tickets? Is the irrelevant alternative criterion violated in this case?
Answers
Answer:
No
Explanation:
The independent irrelevant alternative criterion is not violated here. The law of irrelevant alternative criterion holds that if candidate A is liked more than candidate B then a new candidate C who is liked less than candidate A should not spoil the victory of Candidate A, so that candidate B wins.
In the example in the question, candidate Parker was the preferred candidate before the elimination of candidate Myers and so will still be the winner of the election, therefore the irrelevant alternative criterion has not been violated.
These are two similar triangles. What is the measure of X?
Answers
Answer:
18
Step-by-step explanation:
just type the thing in the calculator
The measure of x for the given similar triangle will be 18 units.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
The triangle is a highly common shape that we deal with on a daily basis. For instance, the right-angle triangle is frequently used to estimate the height of towers.
By similar triangle rule ;
If two triangles are similar then the ratio of the corresponding side will be the same.
So,
x/12 = 24/(12+4)
x/12 = 1.5
x = 18 units.
Hence the measure of x will be 18 units.
For more information about triangle
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What is the area of the grey matting in this 8” by 10” picture frame if the picture to be framed is 4” x 6”? picture frame 64 square inches 56 square inches 24 square inches 80 square inches
Answers
Answer:
so if 8x10 is 80 and 4x6 is 24 then take 24 of 80 you get 56
Write .125 as a fraction reduced to lowest terms.
Answers
Answer:
125 as a fraction is 1/8.
0.125 = 125/1000. We can reduce this to lowest terms by dividing the numerator and denominator by 125 to get the equivalent fraction 1/8.
Step-by-step explanation:
hey mate hope it cleared your problem!!
In a school there are totally 108 students in the third, fourth, and fifth grades. The third grade has 11 fewer students than the fourth grade, and the fourth grade has 16 more students than the fifth grade. How many students are there in each grade?
Answers
Answer:
there are about 36 students in each grade.
Step-by-step explanation:
divide the total amount of students by the amount of grades. 108/3 = 36
đường cầu về tiền có hướng nghiêng dốc xuống thể hiện?
Answers
whats the probabily of drawing one blue marbel from a bag that contains 4 red marbels 6 green marbles and 1 white marbel and 3 blue marble
Answers
Answer: 3/14
Step-by-step explanation:
Number of red marbles = 4
Number of green marbles = 6
Number of white marbles = 1
Number of blue marbles = 3
Total number of marbles = 14
Therefore, the probability of drawing one blue marble will be:
= Number of blue marbles / Total number of marbles
= 3/14
Which mathematical operation changes 2amd 1/3 to 2
Answers
the addition sign thus 2+1÷3=2
jos3ph has 16 meters of rope he wants to cut pieces of rope that are 0.2meters long how many prices can be cut
A 3.2
B8
C32
D80
Answers
Answer:
D.80
Step-by-step explanation:
You need to divide thus
16m/0.2m=80m
Question 5(Multiple Choice Worth 1 points)
(02.04 LC)
What is the equation of a line that contains the points (2,-2) and (0, -2)?
O y = 0
Ox= -2
O y = -2
Ox=0
Answers
Mckenna kept track of the number of miles she rode her horse each day for 2 weeks 3.2.8, 8, 2,8, 8, 10, 4, 0, 0, 0, 0, 0, 0, 0 Part A Find the measures of center and variability that best summarize Mckenna's data. Use the dropdown menus to explain your reasoning, Choose The Choose is the best measure hours, is the best measure of center, so the Chooso... of variability LIVE Part 1 Mckenna says that she typically rides her horse for about 6 hours because the mode is 6. Is Mokenna's conclusion appropriate? Use the dropdown menus to explain your reasoning, Mckenna's conclusion Choose... accurate. The mode of her data Choose... 6 hours. However, Choose... than half of the time, she spends Choose.... than 6 hours riding her horse.
Answers
Answer: 110
Step-by-step explanation:
I did it it’s correct :)
What is the slope of the line?
Answers
Answer:
3/1
Step-by-step explanation:
Answer:
[tex]-3[/tex]
Step-by-step explanation:
The slope of the line is -3 because to get to one point from another point, you would need to go down 3 and right 1 which is -3/1, and that is also just -3
Hope this helps
By mistakenly using π as 3, the area of a circle was found to be 147cm2. Taking π to be 22/7 the true area, in cm2, is
Answers
Answer:
pie times radius square is equal to 147
when pie is 3, radius square is 49
radius is equal to 7
actual pie r square is 22/7 times 7 times 7 is 154
Step-by-step explanation:
ans is 154
((X + 2) + (y - 5) =1
Answers
Answer:
on like term
Step-by-step explanation:
x+2)=(y-5)=2+5=7
x-y{x-y]=7x-y
by Emmanuel okorie
REIVIAINING
29:07
LS
Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50. If she plans to
tip at 20%, what should she pay if she doesn't want to leave pennies on the table?
O $0.55
Answers
Answer:
$5.30 :DDD
Step-by-step explanation:
SO WHAT YOU DO IS 26.50 X 0.20 AND YOU WILL GET 5.30 SO BAM
Given a line passes through point (5,8) and the origin, find the equation of the line.
y=
Answers
Answer:
y = 8/5x
Step-by-step explanation:
I'm assuming that they're asking for the equation in point-slope form.
The formula is y=mx+b where:
m = slope
b = y intercept
However, the y intercept is just (0,0) so b = 0
To find the slope we already have 2 given points: (0,0) and (5,8)
To find slope you do rise/run and you get 8/5
Substitute the slope & y intercept in the formula:
y = 8/5x
Let me know if I'm wrong!!
Answer:
y=8/5x
Step-by-step explanation:
Hi there!
We need to find the equation of the line that passes through (5,8) and the origin (the point (0,0)).
There are 3 ways to write the equation of the line, although the most common way is slope-intercept form, or y=mx+b where m is the slope and b is the y intercept
first, let's find m (slope)
The formula for the slope calculated from two points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points
we have two points, but let's label their values to avoid any confusion
[tex]x_{1}[/tex]=5
[tex]y_{1}[/tex]=8
[tex]x_{2}[/tex]=0
[tex]y_{2}[/tex]=0
now substitute into the formula
m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m=[tex]\frac{0-8}{0-5}[/tex]
multiply
m=[tex]\frac{-8}{-5}[/tex]
divide
m=8/5
The slope of the line is 8/5
here's the equation so far
y=8/5x+b
now we need to find b
as the point will pass through both (5,8) and (0,0) we can use either one of them to solve for b
let's take (0,0) as an example
substitute 0 as x and 0 as y
0=8/5(0)+b
multiply
0=0+b
add
0=b
substitute 0 as b into the equation
Therefore the equation of the line is:
y=8/5x (the 0 is not necessary)
Hope this helps! :)
What is the highest common factor of 60 and 70.
Answers
Consider the function
f(x) = 327
=
As x + -00, then f(x) approaches what?
O A O
OB) 7
C) –00
C
D) 3
Ouestion 3 (1 point)
Answers
The survey of a group of students showed that 50 like tea,40 liked coffee,35 liked milk,20 liked coffee as well as tea,18 liked tea as well as milk,12 liked coffee as well as milk and 7 liked all three. If every students liked at least one drink, how many students were asked this question ? Solve it by drawing a Venn- diagram.
Answers
Answer:
82
Step-by-step explanation:
The storage center sells rectangular storage spaces that are each 200 cubic feet. Each space is 5 feet long and 5 feet wide. What is the height of each storage space?
Answers
Answer:
h=8ft
Step-by-step explanation:
[tex]v = l \times w \times h[/tex]
[tex]h = \frac{v}{l \times v} = \frac{200}{5 \times 5} = 8[/tex]
Owen is driving to a concert and needs to pay for parking. There is an automatic fee of $11 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $4 for every hour he had his car in the lot. How much total money would Owen have to pay for parking if he left his car in the lot for 5 hours? How much would Owen have to pay if he left his car in the lot for t hours?
Cost for 5 hours:
Cost for t hours:
Answers
Answer:
Cost = 11 + 4*t
Step-by-step explanation:
Cost = 11 + 4*t
Part A
t = 5 hours.
Cost = 11 + 4*5
Cost = 11 + 20
Cost = 31
Part B
time = t hours.
Cost = 11 + 4*t
for 5h he would need to pay $20 ( +$11 ) $31
i dont know what T is so ya :/
A bag contains 10 red marbles, 8
blue marbles and 2 yellow
marbles. What is the probability of
getting a blue marble?