Sam entered three functions into a graphing calculator, y1 = x + 2, y2 = x2 + 2, and y3 = 2x. A portion of the table created by those functions is shown below.
Answers
y1 = x + 2
y2 = x ^ 2 + 2
y3 = 2 ^ x
For x = 0:
y1 = 0 + 2 = 2
y2 = 0 ^ 2 + 2 = 0 + 2 = 2
y1 = y2
For x = 5
y2 = 5 ^ 2 + 2 = 25 + 2 = 27
y3 = 2 ^ 5 = 32
y3> y2
For x = -1:
y1 = -1 + 2 = 1
y2 = (-1) ^ 2 + 2 = 1 + 2 = 3
y3 = 2 ^ (- 1) = 1/2 = 0.5
y3 <y1 <y2
Answer:
y1 = y2
y3> y2
y3 <y1 <y2
Related Questions
Jamie has applied for a credit card. The APR of the card is 20%. What will be the monthly interest rate?
Answers
20/12 = 1.67%
Answer:
1.67%
Step-by-step explanation:
The APR of a card is the Annual Percentage Rate. This is the yearly rate of interest that a person has to pay on the money he or she borrowed. Interest is a price that is paid for borrowing money. In this case, if the APR is 20%, we would need to divide this number by the number of months in a year in order to get the monthly interest rate:
20 / 12 = 1.67 %
Find the measure of the missing angle of a triangle, if two of its angles are 75 degree and 65 degree respectively. please show work
Answers
75° +65° +(missing angle) = 180°
(missing angle) = 180° -75° -65°
(missing angle) = 40°
Show that the curvex = 2 cos t, y = 3 sin t cos t has two tangents at (0, 0) and find their equations.
Answers
The first derivative implies that:
[tex] \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } [/tex]
So we need to find both derivatives as functions of the variable t, then:
[tex]\frac{dy}{dt} = 3[cos(t)cos(t)+sin(t)(-sin(t))][/tex]
[tex]\frac{dy}{dt} = 3[cos^{2} (t)-sin^{2} (t)][/tex]
[tex]\frac{dx}{dt} = -2sin(t)[/tex]
Thus:
[tex]\frac{dy}{dx} = \frac{-3[cos^{2} (t)-sin^{2} (t)]}{2sin(t)}[/tex]
At (0,0) [tex]x=0[/tex] and [tex]y=0[/tex], so:
[tex] \left \{ {{0=2cos(t)} \atop {0=3sin(t)cos(t)}} \right.[/tex]
∴[tex] \left \{ {{cos(t)=0} \atop {sin(t)cos(t)=0}} \right.[/tex]
There are two values between -π and π which satisfy these equations simultaneously, namely:
[tex]t =[/tex] π/2
[tex]t =[/tex] -π/2
The equation of a straight line given a point and its slope is
[tex]y - y_{0} = m(x- x_{0} )[/tex]
Given that the point is (0,0), then the equation can be written as:
[tex]y = mx [/tex]
So we will find two straight lines:
[tex] \left \{ {{y= m_{1}x } \atop {y= m_{2}x }} \right. [/tex]
For [tex]t = \pi /2[/tex]:
[tex] m_{1}= \frac{dy}{dx} = \frac{-3[cos^{2} ( \pi /2)-sin^{2} ( \pi /2)]}{2sin( \pi /2)} = \frac{3}{2} [/tex]
For [tex]t = -\pi /2[/tex]:
[tex]m_{2}= \frac{dy}{dx} = \frac{-3[cos^{2} ( -\pi /2)-sin^{2} ( -\pi /2)]}{2sin(- \pi /2)} = -\frac{3}{2} [/tex]
Lastly:
[tex]\left \{ {{y= \frac{3}{2} x } \atop {y= -\frac{3}{2} x }} \right. [/tex]
which transformations are needed to change the parent some function to the sine function below?
Answers
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Solution:the function y = sin x, which would have range from -1 to 1 and period of 2pi:
So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2
If a function is always positive, then what must be true about its derivative? (a) the derivative is increasing (b) the derivative is decreasing (c) the derivative is always positive (d) the derivative is never negative (e) you can't conclude anything about the derivative
Answers
[tex]f'(x)=2x[/tex]
which is negative for [tex]x<0[/tex] and positive for [tex]x>0[/tex]. This example alone tells you that you can't generally describe the sign of the derivative of a strictly positive function, so the answer is E.
Though a function is always positive, it doesn't provide specific information about its derivative. The derivative can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant. Hence, we can't definitively conclude anything about the derivative if we only know the function is always positive.
Explanation:If a function is always positive, it means that its graph lies entirely above the x-axis. However, this fact provides no definitive information about the derivative of the function.
The derivative of a function tells us the rate at which the function is changing. It can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant, respectively. However, for a function to be always positive, does not necessarily dictate whether it is constantly increasing, decreasing, or constant.
For instance, consider the function y = x2. This function is always positive for x ≥ 0, but its derivative, which is 2x, is not always positive. It is zero when x = 0 and positive for x > 0. Similarly, think of an undulating curve-like sine function which stays above the x-axis. Its derivative oscillates between positive and negative as the function goes through its crest and trough points.
Therefore, the answer to your question is (e) you can't conclude anything about the derivative just because the function is positive.
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Use the spinner shown. it is equally probable that the pointer will land on any one of the six regions. if the pointer lands on a borderline, spin again. if the pointer is spun twice, find the probability that it will land on grey and then purple
Answers
The probability of a spinner with six equally probable outcomes landing on specific colors in sequence (grey then purple) is 1/36 since the events are independent. Their individual probabilities (each 1/6) are multiplied to find the combined probability.
Explanation:The question involves a topic in probability called independent events. In this case, the spinner landing on grey in the first spin and purple in the second spin are independent events. That means, the outcome of the first event does not affect the outcome of the second event and vice versa.
Since the spinner has six regions, and landing on any one of them is equally probable, the probability of landing on grey (or any specific color) in one spin is 1/6. Similarly, the probability of landing on purple in one spin is also 1/6.
Since these events are independent, the probability of both these events happening in sequence can be found by multiplying the probabilities of each individual event happening. So, the probability of the spinner landing on grey in the first spin and then on purple in the second is (1/6)*(1/6) = 1/36.
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The probability of landing on the grey region first and then the purple region is 1/18.
Explanation:The question asks for the probability of landing on the grey region first, and then the purple region on a spinner. To find the probability, we first need to determine the total number of possible outcomes. Since the spinner has six regions, we have six possible outcomes on the first spin. If the spinner lands on a borderline, we spin again. So, on the second spin, we also have six possible outcomes. Since each spin is equally likely, the total number of possible outcomes is 6 x 6 = 36.
Next, we need to determine the number of favorable outcomes, which is the number of ways we can land on the grey region first and then the purple region. From the spinner, we can see that there are two grey regions and one purple region. So, the number of favourable outcomes is 2 x 1 = 2.
Finally, we can calculate the probability by dividing the number of favourable outcomes by the total number of outcomes: 2/36 = 1/18. Therefore, the probability of landing on the grey region first and then the purple region is 1/18.
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which best describes the meaning of the term theroem?
Answers
What is the letter ƒ in mathematics?
Answers
Example: f(x) = x + 1
It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).
OR
It could just be a regular ole variable
Example: f + 1 = 7, solve for f
The letter f usually indicates that the equation is a function in the notation f(x).
Example: f(x) = x + 1
It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).
OR
It could just be a regular ole variable
Example: f + 1 = 7, solve for f
it took a ball 1 minute to roll 90 feet. what was ths balls average rate of speed in feet per second
Answers
Divide the 90 by 60.
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. the 50 paired ratings yield x overbarxequals=6.46.4, y overbaryequals=6.06.0, requals=negative 0.281−0.281, p-valueequals=0.0480.048, and modifyingabove y with caretyequals=8.128.12negative 0.323−0.323x. find the best predicted value of modifyingabove y with carety (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is xequals=55. use a 0.100.10 significance level.
Answers
To find the best predicted value of female attractiveness rating for a male rating of 5, substitute '5' for 'x' in the given regression equation, then calculate the result.
Explanation:In your given problem you have mentioned a linear regression equation, modifyingabove y with caretyequals=8.128.12negative 0.323−0.323x, that was derived from paired attractiveness ratings of males and females from 50 speed dates. The male attractiveness rating is your independent variable x and the female attractiveness rating is your dependent variable y.
You are asked to calculate the predicted female attractiveness rating if a male rates a female as 5 (x equals 5). To do this, you need to substitute x with 5 in the regression equation, which leads to the following calculation:
modifyingabove y with caret = 8.12 - 0.323 * 5.
By calculating this equation, you get the best predicted value of modifyingabove y with caret (attractiveness rating by female of male).
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How would the expression x^3+8 be written using Sum of Cubes?
Answers
x³ + 8
8 is the cube of 2, so we can write the above expression as sum of two cubes as:
x³ + 2³
Using the formula of sum of cubes, we can write:
x³ + 2³ = (x + 2)(x² - 2x + 4)
Thus, option B gives the correct answer
if there are 16 ounces in a pound how manyh are in 24 ounces
Answers
1 ounce = 1/16 pound
24 ounces = 1/6 x 24 = 4 pounds
Answer: 4 pounds
24 ounces equals 1.5 pounds, based on the conversion factor of 1 pound equals 16 ounces.
Explanation:Your question is related to unit conversion. If we know that one pound equals 16 ounces, then to convert 24 ounces to pounds, we must divide 24 ounces by the number of ounces in a pound. Here's how we can do it:
Set up the conversion: 24 oz / 16 oz/lb. Dividing these amounts gives the result: 24 / 16 = 1.5 lbs.S, this means that 24 ounces is equal to 1.5 pounds.
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For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
Answers
Combine volumes up (1ft times 3.14) + (2ft times 3.14) + (3ft times 3.14)
18.8 >. rounded to the nearest cubic foot of 19
Use ratio to convert the measurement. 3 d = _____h
Answers
Here is your answer:
They proper answer to this question is "72 hours".
Reason:
By using the ratio:
[tex] \frac{3days}{hours} [/tex]
You can see that one day = 24 hours
[tex] \frac{1day}{24hours} [/tex]
Then multiply 24×3=72
[tex] \frac{3days}{72hours} [/tex]
Therefore the ratio is [tex] \frac{3days}{72hours} [/tex]!
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Looking at the ping-pong ball toss board below, whats the probability of landing on a gray square? (Note the board contains 5 rows of 5 squares.)
Answers
answer
D. 1/5
Answer:
Option D. [tex]\frac{1}{5}[/tex] is the correct option.
Step-by-step explanation:
Total number of solution sets n(S) (sample space) = 5×5 = 25
(Since a ping-pong ball can land on any block of the toss board so total number of events which can occur will be = 25)
Now preferred events n(E) = 5
(Since number of grey squares where ping-pong ball can land are = 5)
Therefore probability of landing of ping pong ball on a grey square P(E) = [tex]\frac{n(E)}{n(S)}[/tex]
P(E) = [tex]\frac{5}{25}[/tex]
P(E) = [tex]\frac{1}{5}[/tex]
Therefore, Option D. [tex]\frac{1}{5}[/tex] will be the answer.
The radius of the circle is 7 inches what is the approximate length of AB (AB is 135 degrees
Answers
circumference=2*pi*r
for r=7 in
circumference=2*pi*7------> 14*pi in
if 360° (full circle) has a length of------------ 14*pi in
135°-----------------------------> x
x=135*14*pi/360----------> x=5.25*pi in--------> 16.49 in
the answer is
5.25*pi in or 16.49 in
8+5 (15-5) X 2
please help i know its 33 but i can't prove my work i did it in my head.
Answers
Answer:
108
Step-by-step explanation:
8 + 5·(15-5)·2
= 8 + 5·10·2
= 8 + 50·2
= 8 + 100
= 108
_____
Comment on the supposed answer
33 is the result of 8 + 5(15 -10). The contents of parentheses must be evaluated first. Then the multiplication. In any event, factors outside parentheses multiply every term inside parentheses, not just the one(s) you might pick or choose.
hello can you please help me posted picture of question
Answers
Total number of numerals to be used = 6
We are to find the number of different codes that can be formed and those can be found by permutations.
We have to find the permutations of 10 numerals taken 6 at a time. So we are to find 10P6.
10P6 = 151200
So, 151200 different codes can be formed.
So the answer to this question is option A
what is 4.1363636... as a fraction?
Answers
Answer:
x = [tex]\frac{91}{22}[/tex].
Step-by-step explanation:
Given : 4.1363636...
To find : Write as fraction .
Solution : We have given that
Let x = 4.1363636...
We can see number 36 ( 2 digit repeating ) so we will multiply it by 100
On multiplying both sides by 100
100x = 100 * 4.1363636...
100 x = 413 .63636 .....
We can write it in term of x
100 x = x + 409 .5
On subtracting both sides by x
100 - x = 409 .5
99 x = 409 .5
On dividing both sides by 99
x = [tex]\frac{409.5}{99}[/tex].
x = [tex]\frac{4095}{990}[/tex].
x = [tex]\frac{819}{198}[/tex].
On dividing both number by 9
x = [tex]\frac{91}{22}[/tex].
Therefore, x = [tex]\frac{91}{22}[/tex].
We have that the the Representation of 4.1363636 as fraction is
[tex]4.1363636=\frac{517}{125}[/tex]
From the question we are told that:
4.1363636. is in decimal form
Fraction
This is the representation of a number in the format of a numerator and a denominator
Generally, the Representation of 4.1363636 as fraction is mathematically given by
Having defined fractions we have that
[tex]4.1363636 \approx 4.136[/tex]
Therefore
The 4.1363636 as fraction is mathematically given by
[tex]4.1363636=\frac{517}{125}[/tex]
in conclusion
The the Representation of 4.1363636 as fraction is
[tex]4.1363636=\frac{517}{125}[/tex]
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Dan is calculating the volume of two cylinders. Cylinder A has a radius of 2 feet and a height of 4 feet. Cylinder B also has a height of 4 feet, but the radius has been doubled. Which statement best describes the relationship between the volumes of the two cylinders? A) When the radius is doubled, the resulting volume is half the original volume. B) When the radius is doubled, the resulting volume is 2 times the original volume. C) When the radius is doubled, the resulting volume is 4 times the original volume. D) When the radius is doubled, the resulting volume is 8 times the original volume.
Answers
Cylinder A has a radius of 2 feet and a height of 4 feet
so
volume of the cylinder A=pi*r²*h-----> pi*2²*4-----> 16*pi ft³
Cylinder B also has a height of 4 feet, but the radius has been doubled
h=4 ft
r=2*2---> 4 ft
so
volume of the cylinder B=pi*r²*h-----> pi*4²*4-----> 64*pi ft³
volume cylinder B/volume cylinder A=64*pi/(16*pi)----> 4
therefore
the answer is the option
C) When the radius is doubled, the resulting volume is 4 times the original volume.
Suppose that e and f are events in a sample space and p(e) = 2/3, p(f) = 3/4, and p(f |
e.= 5/8. find p(e | f).
Answers
[tex]\mathbb P(E\mid F)=\dfrac{\mathbb P(E\cap F)}{\mathbb P(F)}=\dfrac{\mathbb P(F\mid E)\cdot\mathbb P(E)}{\mathbb P(F)}[/tex]
so the probability we want is
[tex]\dfrac{\dfrac58\cdot\dfrac23}{\dfrac34}=\dfrac59[/tex]
What’s the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21 e. 7⁄11 and 9⁄121 f. 1⁄2, 3⁄18, and 4⁄9
Answers
Now divide each piece in 2 halves; each one is ¼ of the cake. Witch is largest? 1:2=0,5; 1:4=0,25. 0,5>0,25.
5:6=0,83333
29:36=0,80555
0,83>0,80 so 5/6 is the largest.
Do this for each group.
a.5/6
b.5/8
c.19/45
d.13/14
e.7/11
f.1/2
Answer:
a. [tex]\frac{5}{6}[/tex],
b. [tex]\frac{5}{12}[/tex],
c. [tex]\frac{19}{45}[/tex],
d. [tex]\frac{13}{14}[/tex],
e. [tex]\frac{7}{11}[/tex],
f. [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
(a)
[tex]\frac{5}{6}\text{ and }\frac{29}{36}[/tex]
Making denominator common.
[tex]\frac{5\times 6}{6\times 6}\text{ and }\frac{29}{36}[/tex]
[tex]\frac{30}{36}\text{ and }\frac{29}{36}[/tex]
Now compare the numerators.
[tex]30>29[/tex]
[tex]\frac{30}{36}>\frac{29}{36}[/tex]
[tex]\frac{5}{6}>\frac{29}{36}[/tex]
Therefore [tex]\frac{5}{6}[/tex] is largest fraction.
(b)
[tex]\frac{5}{12}\text{ and }\frac{3}{8}[/tex]
Making denominator common.
[tex]\frac{5\times 2}{12\times 2}\text{ and }\frac{3\times 3}{8\times 3}[/tex]
[tex]\frac{10}{24}\text{ and }\frac{9}{24}[/tex]
Now compare the numerators.
[tex]10>9[/tex]
[tex]\frac{10}{24}>\frac{9}{24}[/tex]
[tex]\frac{5}{12}>\frac{3}{8}[/tex]
Therefore [tex]\frac{5}{12}[/tex] is largest fraction.
(c)
[tex]\frac{2}{5}\text{ and }\frac{19}{45}[/tex]
Making denominator common.
[tex]\frac{2\times 9}{5\times 9}\text{ and }\frac{19}{45}[/tex]
[tex]\frac{18}{45}\text{ and }\frac{19}{45}[/tex]
Now compare the numerators.
[tex]18<19[/tex]
[tex]\frac{18}{45}<\frac{19}{45}[/tex]
[tex]\frac{2}{5}<\frac{19}{45}[/tex]
Therefore [tex]\frac{19}{45}[/tex] is largest fraction.
Similarly,
(d)
[tex]\frac{5}{7}\text{ and }\frac{13}{14}\text{ and }\frac{19}{21}[/tex]
By making denominator common, we get
[tex]\frac{30}{42}\text{ and }\frac{39}{42}\text{ and }\frac{38}{42}[/tex]
By comparing the numerators, we get 39 is greatest therefore [tex]\frac{13}{14}[/tex] is largest fraction.
(e)
[tex]\frac{7}{11}\text{ and }\frac{9}{121}[/tex]
By making denominator common, we get
[tex]\frac{77}{121}\text{ and }\frac{9}{121}[/tex]
By comparing the numerators, we get 77 is greatest therefore [tex]\frac{7}{11}[/tex] is largest fraction.
(d)
[tex]\frac{1}{2}\text{ and }\frac{3}{18}\text{ and }\frac{4}{9}[/tex]
By making denominator common, we get
[tex]\frac{9}{18}\text{ and }\frac{3}{18}\text{ and }\frac{8}{18}[/tex]
By comparing the numerators, we get 9 is greatest therefore [tex]\frac{1}{2}[/tex] is largest fraction.
Billy is making a juice that contains 3 quarts of water, 1 quart of grape juice, 1 quart of orange juice, and 2 quarts of strawberry juice. He is putting his homemade juice into a jug that can hold 2 1⁄2 gallons. How many more quarts of juice can Billy still make before filling the jug?
Answers
Billy is making a juice that contains
3 quarts of water
1 quart of grape juice
1 quart of orange juice
2 quarts of strawberry juice
total=3+1+1+2----> 7 quarts
a jug can hold 2 1⁄2 gallons-----> 2.5 gallons
we know that
1 gallon is equal to 4 quarts
2.5 gallons------> x
x=2.5*4----> x=10 quarts
so
quarts of juice can Billy still make before filling the jug=10-7---> 3 quarts
the answer is
3 quarts
Ben runs around the track at a pace of 1 lap every 80 seconds. Sally runs on the track in the opposite direction. The two meet every 30 seconds. How long does it take Sally to run each lap around the track?
Answers
plz help ill give u brainlist plz some one help fast it is esy in just dume
Answers
If there are 5 questions and you want to pick the right one the probability is 1/5. If you don't know how to find that, let your calculator walk you to the answer.
1
÷
5
=
And it will tell you that it is 0.2.
So if you blindly (not brainly) fill in the multiple choice answer sheet, the number you will get right is
(P(0.2) * The total number of questions or
0.2 * 70 = 14
Just pure dumb luck will give you 14 correct answers.
jose bought 8 bags of oranges.each bag weighed 12 ounces. there are 16 ounces in a pound.how many pounds of oranges did jose buy
Answers
First you have to find the amount of ounces the oranges weigh
To find this you multiply the amount of oranges by the how much they weigh
12 * 8 = 96
Divide this by the amount of ounces is in a pound
96 / 16 = 6
The answer is 6 pounds
Hope this helps!
Olivia and ray walk to school. olivia walks 1\4 of a mile to school. her walks is 2\3 of the distance that ray walks to school. waht is the total distance, in miles that ray walks to school? answer
Answers
Olivia walks ---------> 1\4 of a mile to school
2/3 correspond to ------> 0.6666------> 66.67 %
3/3 correspond to--------> 1--------> 100%
so
if (2/3)-----------> 1/4 mile
(3/3)-------------> x
x=(1/4)/(2/3)-----> x=(1/4)*3/2-----> x=3/8------> x-0.375 miles
the answer is
Ray walks to school 3/8 miles (0.375 miles)
A company makes three purchases on July 5, one for $550, another for $250 and a third for $75. It returns merchandise costing $35. If the Company is given a discount 2/10 and pays the total amount due on July 20, how much was due?
Answers
8/10 ($550 + $250 + $75 - $35) = $672.
The amount due is $672.
A video posted on the internet is becoming very popular,and the total number of views is increasing by 40% every hour if the video currently has 38,000 views how many views will it have in 2 hours
Answers
Final answer:
The video with an initial 38,000 views will have approximately 74,480 views in 2 hours when it is increasing by 40% every hour.
Explanation:
To calculate the number of views a video will have in 2 hours if it is increasing by 40% every hour, we will use the formula for percentage growth. Initially, the video has 38,000 views. After one hour, the views will be increased by 40%, and after two hours, this new amount will again be increased by 40%. The formula for calculating the number of views after each hour is:
Views after n hours = Initial views × [tex](1 + growth rate)^n[/tex]
Where:
Initial views = 38,000
Growth rate = 40% = 0.40 (as a decimal)
n = number of hours
After 1 hour:
Views after 1 hour = 38,000 × (1 + 0.40)^1
Views after 1 hour = 38,000 × 1.40 = 53,200
After the second hour, we will use the number of views from the first hour to calculate the increase:
Views after 2 hours = 53,200 × [tex](1 + 0.40)^1[/tex]
Views after 2 hours = 53,200 × 1.40 = 74,480
Therefore, the video will have approximately 74,480 views in 2 hours.
please help me answer these!!!
Answers
1. Checking selection "a",
265 =? 35 +20*7 = 35 +140 = 175
a (7, 265) is NOT a solution
2. Checking selection "a",
18 =? 5*4 -2 = 20 -2 = 18
a (4, 18) IS a solution