[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ t=years\\ \end{cases} \\\\\\ A=20000(1 - 0.1)^{t} \implies A=20000(0.9)^t[/tex]
how long till it's $7000?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &7000\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ t=\textit{elapsed time} \end{cases} \\\\\\ 7000=20000(1 - 0.1)^{t} \implies \cfrac{7000}{20000}=0.9^t\implies \cfrac{7}{20}=0.9^t[/tex]
[tex]\log\left( \cfrac{7}{20} \right)=\log(0.9^t)\implies \log\left( \cfrac{7}{20} \right)=t\log(0.9) \\\\\\ \cfrac{\log\left( \frac{7}{20} \right)}{\log(0.9)}=t\implies 9.96\approx t \qquad \textit{about 9 years and 11 months}[/tex]
a researcher wants to examine the relationship between fat and calories in fast food. data was analyzed using linear regression. fat grams in the food represented x (the independent variable) and total calories in the food item was represented by y. the slope was 13 and the y intercept was 143. predict how many calories would be in a sandwich containing 32 grams of fat?
The predicted number of calories in a sandwich containing 32 grams of fat is 559.
What is the slope intercept form?In algebra, the slope-intercept form of a linear equation is a typical approach to express a line on a graph. A linear equation is written as y = mx + b in standard form.
The y-intercept, or place where the line crosses the y-axis, is represented by the letters b and m, respectively. The point where the lines contacts the y-axis is known as the y-intercept, and the slope is a measurement of how steep the line is. Because it explicitly displays the slope and y-intercept, this equation's form is known as the slope-intercept form.
y = mx + b
Where m is the slope, x is the value of the independent variable, and b is the y-intercept. In this case, the slope is 13 and the y-intercept is 143. So, the equation of the line of best fit is:
y = 13x + 143
To predict the number of calories in a sandwich containing 32 grams of fat, you can plug in 32 for x in the equation:
y = 13 * 32 + 143
y = 416 + 143
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the margin of error is: a. the largest possible sampling error for a specified level of confidence; b. the critical value times the standard error of the sampling distribution; c. the difference between the point estimate and the parameter. a only b only c only a and b b and c a and c all of the above none of the above
The correct is b i.e; the critical value times the standard error of the sampling distribution
Given options are :
a. The biggest sampling error that can be made while maintaining a certain level of confidence.
b. the critical value multiplied by the sampling distribution's standard error
c. the discrepancy between the parameter and the point estimate.
Margin of error
= C * SE
Where C is critical value of on
of is the Standard error
The multiple of Critical Value and Standard error is the margin of error
Correct Option is b i. e the critical value times the Standard error of Sampling distribution
Therefore, The margin of error is the product of Critical Value and Standard Error.
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Grafica y aproxima el area bajo la curva de f(x)=x³+1 en el intervalo x€[0,2]
The total area bounded by curve f(x)=x³+1 between (0,2) will be 6 units.
What is Integration ?The summing of discrete data is indicated by the integration. To determine the given functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately and integrals are calculated. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied.
Given Graph = x³+1
Area between interval x€[0,2]
To get the desired area we have to integrate between x€[0,2]
[tex]\int\limits^2_0 {(x^3 + 1)} \, dx[/tex]
∫x³dx + ∫1dx
[tex]\frac{x^4}{4}[/tex] + x + c
We can find the area by lower limit - upper limit
Putting x = 0
we get result as c
Putting x = 2
We get result as 6+c
So desired area will be ( 6+c ) - c = 6
Hence the total area bounded by curve between (0,2) will be 6 units.
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you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding mph east and your friend riding mph north. after you have travelled mi, at what rate is the distance between you and your friend changing? after you have travelled mi, the distance between you and your friend is changing at a rate of mph.
The distance between you and your friend is changing at a rate of 20 miles per hour.
What is the Pythagorean theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we
Let the east direction is denoted by x and
the north direction is denoted by y.
dx / dt = 16 miles per hour
dy / dt = 12 miles per hour
x = 4 miles
Let the distance between both the friends be s.
Time is taken by you to travel 4 miles,
time = distance / speed = 4 / 12 = 1/4 hour
Distance traveled by your friend in time t,
y = speed x time = 12 x 1/4 = 3 miles
By Using the Pythagorean theorem,
x² + y² = s² ..... (1)
Substitute, x = 4 mile, y = 3 mile
s² = 16 + 9 = 25
s = 5 miles
Now, Differentiate equation (1) with respect to t, we get
2x dx/dt + 2y dy/dt = 2s ds/dt
4 (16) + 3 (12) = 5 ds/dt
ds/dt = 20 miles per hour
Hence, the distance between you and your friend is changing at a rate of 20 miles per hour.
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in this fulcrum, the weights are perfectly balanced. how far must the fulcrum be located from the 40 lb. weight if the bar is 9 feet long?
The distance of 40 lb will be 5ft, according to the question.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have the given information:
The fulcrum be located from the 40 lb.
The weight of bar is 9ft long.
Now, we will calculate the distance,
40x = 50(x-1)
40x = 50x - 50
40x - 50x = -50
-10x = -50
x = 5
Therefore, the required answer is 5ft.
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A persons resting heart rate is typically between 60 and 100 beats per minute. Rushing looks at the watch and counts 8 heartbeats in 10 seconds. Is his heart rate typical?
Answer: No its not normal
Step-by-step explanation: The question says 60 and 100 beats per minute is normal. Rushing looks at his watch and counts 8 beats in 10 seconds
We can solve by:
[tex]\frac{8}{10}[/tex] = [tex]\frac{x}{60}[/tex] then from that answer we can check if x, the heartbeats falls between 60 and 100.
So to get 60, we have to multiply 10 by 6. We are using proportionality, so we do the same to the numerator to get 8 x 6= 48
We get [tex]\frac{8}{10}[/tex] = [tex]\frac{48}{60}[/tex]. 48 beats do not fall between 60 and 100, thus the answer is it is not normal.
Complete the statement Round to the nearest hundredth if necessary
14 m ≈ ? ft
Answer: 45.93 ft
Step-by-step explanation:
Let the random variable x represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of x.
The best interpretation of the mean of X is in the long run, a player will lose an average of $0.15 per carnival game played.
What do you mean by Mean?
The average of the specified collection of numbers is what is referred to as mean. It indicates a data set's values are distributed equally.
Given:
Amount = $1 $1 $10
Probability = 0.80 0.15 0.05
In mathematics and statistics, the arithmetic mean is the sum of a set of integers divided by the total number of the numbers in the set. When the context is clear, it is also referred to as the mean or average. A set of experiments or survey findings are typically included in the collection.
Hence, the correct option is (A) In the long run, a player will lose an average of $0.15 per carnival game played.
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a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
If a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals, the dimensions are 90 feet and 120 feet
From the figure
4x + 3y = 720
3y = 720 - 4x
y = 240 - (4/3)x
The area = l × w
Where l is the length
w is the width
Substitute the values in the equation
A = 2x × y
= 2x (240 - (4/3)x)
Apply the distributive property
= 480x - (8/3)x^2
Differentiate the values
0 = (-16/3)x + 480
(16/3) x = 480
x = 480 / (16/3)
x = 90 feet
Then,
y = 240 - (4/3)(90)
= 120 feet
Hence, the dimensions are 90 feet and 120 feet
I have answered the question is general, as the given question is incomplete.
The complete question is
A rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
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an izod impact test was performed on 20 specimens of pvc pipe. the sample mean is 1.25 and the sample standard deviation is 0.25. test the hypothesis that H0: ????
There is sufficient evidence to conclude that the population standard deviation is different from 0.1.
What is test statistic?
A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
Given,
[tex]H_0:\sigma =0.1\\H_a:\sigma \neq 0.1[/tex]
Test statistic:
Chi square=(20-1)*0.25^2/0.1^2=118.75
df=20-1=19
p-value=CHIDIST(118.75,19)=0.0000
Reject the null hypothesis.
Hence, there is sufficient evidence to conclude that the population standard deviation is different from 0.1.
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from a group of 7 men and 6 women a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?
500 Different number of committees are possible.
Initially we have 7 men and 6 women.
We have to select 4 men and 3 women to form a committee
Number of men are possible 7C4 = 35
Number of women are possible 6C3 = 20
2 of the men are refusing to server together
so we have to subtract the possibilities when these 2 men are sitting together.
we are considering 2 men are already sitting together.
now, we have only need of 2 men from remaining 5 men.
number of ways to select 2 men from 5 men is 5C2 = 10
We have to subtract 10 from number of men possible.
Number of men possible when 2 of the men refuse to serve together =
35 - 10 = 25.
Number of possible committees are 25*20 = 500.
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A punch recipe calls for 1 1/2 quarts of sparkling water and 3/4 of a quart of grape juice. How much of each ingredient would you need to make 75 quarts of punch?
The number of each ingredient of water and grape juice you can use for 75 quarts of punch would be = 112.5 of sparkling water and 56.25 of grape juice.
What is recipe?Recipe is defined as the comprehensive list of items that includes various measurements which is used for making different food meals.
The quantity of sparkling water used for each punch quarts = 1½ = 1.5
1.5 = 1
X = 75
make X the subject of formula;
X = 75×1.5
X = 112.5
The quantity of grape juice used for each punch quarts= ¾ = 0.75
0.75 = 1
y = 75
make y the subject of formula;
y = 0.75×75
y = 56.25
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Which conclusion is appropriate at the 5% level of significance? check all that apply. Group of answer choices the differences observed in sample means do not provide strong evidence of a difference in mean course load for freshmen, sophomores, juniors and seniors at this university. There are statistically significant differences in mean course loads for freshmen, sophomores, juniors and seniors at this university. This study provides strong evidence that the mean course loads differ for freshmen, sophomores, juniors and seniors at this university. This study provides strong evidence that the mean course loads for freshmen are larger than the mean for sophomores. This study suggests that the mean course loads are the same for freshmen, sophomores, juniors and seniors at this university. We cannot draw a conclusion because conditions for the anova f-test are not met
A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.
What is Anova test?In statistics, the analysis of variance (ANOVA) method is used to compare the means of two groups.
In an experiment with a completely randomized design, samples are at random assigned to either a treatment group or a placebo group.
For instance, if 40 persons are chosen to evaluate the effects of an analgesic,
four groups—Groups A, B, C, and D—could be created. Different dosages of the medication can be administered to Groups A, B, and C, while Group D receives a placebo. Due to the random grouping of the participants
, this is an illustration of a randomized design.
We assume that the sample populations are normally distributed and have the same variances in order for an ANOVA test to display completely randomized design.
Hence, A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.
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9 2 8 7 6 5 1 4 3 show the contents of the array above each time an insertion sort changes it while sorting the array into ascending order.
The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.
A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.
Initial Pass: 2 9 8 7 6 5 1 4 3
The array's first two members are initially compared using an insertion sort.
Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.
Therefore, 2 is currently kept in a sorted sub-array.
Second Pass: Continue with the next two elements and compare them.
2 8 9 7 6 5 1 4 3
Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.
Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.
Moving on to the following two components, which are 9 & 7,
2 7 8 9 6 5 1 4 3
Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.
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What are the missing angle measures in parallelogram rstu? m∠r = 70°, m∠t = 110°, m∠u = 110° m∠r = 110°, m∠t = 110°, m∠u = 70° m∠r = 110°, m∠t = 70°, m∠u = 110° m∠r = 70°, m∠t = 110°, m∠u = 70°
∠R= 110°, ∠U= 70°, ∠T= 110° are the missing angle measures in parallelogram RSTU.
A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
Because RSTU is a parallelogram, we may use parallelogram characteristics to calculate S=U=70° ( Opposite angles of parallelogram are equal).
Using the property, sum of adjacent angles is equal to 180°, therefore,
⇒∠S+∠R= 180°
⇒70°+∠R= 180°
⇒∠R= 180°- 70°
⇒∠R=110°
Also, ∠R= ∠T= 110° (Opposite angles of parallelogram are equal).
Thus, ∠R=110°, ∠T= 110° and ∠U=70°
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help plsssssssssssssssss
Answer: A 121/324
Step-by-step explanation:
1.0489343455493443 is the result so it is irrational
the time is 11:06 in 2 hours it will be
Answer:
Step-by-step explanation:
01:06
Answer:
1:06
Step-by-step explanation:
11:06 + 2:00 = 13:06
13:06-12:00= 1:6
the population of a town increased from 3050 in 2006 to 5500 in 2009. find the absolute and relative (percent) increase. absolute increase: relative increase: % give answers accurate to at least 1 decimal place.
In the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.
What is the percentage increase?When you want to analyze how a value has evolved over time, a percentage increase is helpful.
Although percentage increase and absolute increase are fairly comparable, the former is more helpful when contrasting different data sets.
For instance, a change from 1 to 51 and a change from 50 to 100 both have an absolute change of 50, but the first change grew significantly more due to the higher percentage growth of 5000% compared to the second change of 100%.
The most popular method of assessing growth is percentage increase because of this.
So, the absolute and relative percentage increase is:
The town's population grew from 3,250 in 2008 to 4,300 in 2010.
2008: P1 = 3250
2010: P2 = 4330
Absolute variation:
Absolute difference = P2 - P1
Absolute difference = 4330 - 3250
Absolute difference = 1050
Relative increase:
Relative percentage = P2 - P1/P1 * 100
Relative percentage = 1050/3250 * 100
Relative percentage = 32.3076
Therefore, in the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.
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Correct question:
The population of the town increased from 3,250 in 2008 to 4,300 in 2010. Find the absolute and relative(percent) increase.
write a function that computes a hask key for a string. the hash key is the average of the position of each letter in the alphabet divided by the size of the table. you can use the charposition() defined in the previous exercise in your calculation, this correct implementation was provided for you in this exercises.
a function that determines a string's hask key. The average position of each letter in the alphabet divided by the size of the table yields the hash key.
def char_position(char):
alphabet = list("abcdefghijklmnopqrstuvwxyz")
return alphabet.index(char)
def hash_key(string):
total = 0
for char in string.lower():
total += char_position(char)
return total / len(string)
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which point on the unit circle corresponds to −π? responses (1, 0) begin ordered pair 1 comma 0 end ordered pair (0, −1) begin ordered pair 0 comma negative 1 end ordered pair (0, 1) begin ordered pair 0 comma 1 end ordered pair (−1, 0) begin ordered pair negative 1 comma 0 end ordered pair
(-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
Option (D) is the correct one.
Given, a unit circle
and we have to mention the point on the unit circle that corresponds to -π.
As, the equation of a unit circle is
x² + y² = 1
now -π is represented by the left side of the x-axis
therefore to represent the given point we have to take a point on x-axis that will be at the left side of the origin and at the unit distance from the origin.
So, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
Hence, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
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Your question is incomplete kindly find the complete question below.
Which point on a unit circle corresponds to -π ?
(a) (1 , 0)
(a) (0 , -1)
(c) (0 , 1)
(d) (-1 , 0)
Answer:
(-1,0)
Step-by-step explanation:
I just took the quiz :)
flipping a fair two-sided coin, the probability of getting heads is equal to the probability of getting tails. if the coin is flipped three times consecutively, what is the probability of getting heads at least twice?
The probability of getting heads at least twice is 0.5
Since we are given two-sided coin, where the probability of getting heads is equal to the probability of getting tails.NO of outcomes in this case is 2,The probability of getting a head = 1/2, similarly probability of getting a tail is =1/2 .So when a coin is flipped three times, the sample space for the event will be (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT), H stands for head and T stands for tails, here for tossing the coin the number of outcomes is 8 .So the probability of getting at least two heads is: 4/8= 1/2 =0.5
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Please help! Lots of points and brainliest!
4 bracelets and 3 Necklaces are made by the Jeweler.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us represent Bracelet as B and Necklace as N
B+N=7..(1)
7B+18N=82..(2)
From equation 1,
B=7-N
Now plug in B value in equation 2
7(7-N)+18N=82
49-7N+18N=82
49+11N=82
Subtract 49 on both sides
11N=33
N=3
Now we have to find B
B+N=7
B+3=7
Subtract 3 on both sides
B=4
Hence, 4 bracelets and 3 Necklaces are made by the Jeweler.
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a rectangular crate has length 15 in, width 4 in, and height 10 in. find its volume as surface area.
Answer:
volume: 600 cubic inchesarea: 500 square inchesStep-by-step explanation:
You want the volume and surface area of a rectangular crate that is 15 in long, 4 in wide, and 10 in high.
VolumeThe volume is given by the formula ...
V = LWH
For the given crate, the volume is ...
V = (15 in)(4 in)(10 in) = 600 in³
AreaThe area is given by the formula ...
A = 2(LW +H(L +W))
For the given dimensions, the crate has an area of ...
A = 2((15 in)(4 in) +(10 in)(15 in +4 in)) = 2(60 in² +(10 in)(19 in))
= 2(60 in² +190 in²) = 500 in²
The crate's volume is 600 cubic inches; its area is 500 square inches.
f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance. true false
True , the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
Given :
f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
at 10 % significance:
z score = 1.282
at 90 % confidence interval :
z score = 1.645
[tex]H_0 :[/tex] differences between population mean = 1.282
so true the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
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this exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 5????/11 rad is 15 m2. find the radius of the circle. (round your answer to one decimal place.) incorrect: your answer is incorrect. m
The radius of the circle will be 4.6m.
What is area of a circle?
The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value. The area of the circle will be A = [tex]\pi r^{2}[/tex].
The area of the circle given is = 15 m²
Sector of a circle with a central angle of 5π/11 rad
The area will be (1/2) * r² * Ф
15 = (1/2) * r² * (5π/11)
⇒r² = 30 * (11/5π)
⇒r² = 21.00
⇒r=4.6m
Hence, the radius of the circle will be 4.6m.
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Uppose there are three pipes filling a tank. The first pipe can fill the tank in 5 hours. The second pipe can fill the tank in 8 hours. The third pipe can fill the tank in 11 hours. How much of the tank can the first pipe fill in one hour? how much of the tank can the second pipe fill in one hour? how much of the tank can the third pipe fill in one hour?
Answer:
Step-by-step explanation:
12. A clothing store has 621 blouses.
they place these on 9 racks. About the
same number of blouses were placed on
each rack. About how many blouses are
on each rack? (equation & sentence
Answer:
you have to divide
Step-by-step explanation:
621/9=69 so there are 69 blouses on each of the 9 racks
It is more than 7+3
It is less than 8+5
Answer:
11 or 12 ....?
Step-by-step explanation:
This seems simple... so simple i feel like im overthinking it (x_x)
How do you find the distance between these two integers? Complete the following statement that answers this question. Count the units between integer and zero. There is______ unit(s) between 0 and 1. There are______ unit(s) between 0 and 1. There are0 and -3. So, the sum of these two values is______ units.
Answer: (A) There is 1 unit between 0 and 1.
(B) There are 1 units between 0 and 1
(C) There are 0 and -3 so the sum of these two values is 3 units.
Step-by-step explanation:
How to find a distance between two integers? Easy!
First find the absolute value! Its gonna help a lot!
Write a rule for g(x)=f(x+2) when f(x)=x+1.
Answer:
g(x) = x+3
Step-by-step explanation:
f(x) = x+1
g(x) = f(x+2)
so g(x) = (x+2)+1
g(x)=x+3