Your classmates Sarah, Gene and Paul are proposing plans for a class fundraiser. Each presents his or her proposal for the amount of money raised, y, for x number of hours worked, in different ways. Part A: Are each of the proposals represented by linear functions? Explain. Refer to lesson 7. 4 Comparing Linear and Non-Linear Functions. Part B: Does the class have any money in the account now? How can you tell? Calculate the y-intercept in order to find your answer. Part C: Which fundraising proposal raises money at the fastest rate? Explain. Refer to lesson 7. 2 Representations of Functions Part D: If Sarah and her classmates are hoping to raise $200, which proposal do you recommend that Sarah and her classmates choose? Analyze your answers to explain why you recommend that proposal. Note that there are different ways to analyze and display your thinking
Answers
All the plans proposed by classmates Sarah, Gene and Paul represents linear function.
Total money in the account at (0 ,0 ) is $24.
Fundraising proposal showing fastest rate is of Sarah proposal plan.
To raise $200 recommended plan is of Sarah.
Standard linear function is y = mx + c
'm' is the slope and 'c' is the y-intercept.
For attached question
Let y represents the amount of money
And x represents the number of hours worked.
Proposing plan of Sarah represents the straight line
From graph consider two points
( x₁ , y₁ ) = ( 1, 20 )
(x₂ , y₂ ) = ( 2 , 30 )
Slope 'm' = ( y₂ - y₁ ) / ( x₂ - x₁ )
= (30 -20 ) / ( 2 - 1 )
= 10 /1
y = mx + c
⇒ 20 = 10(1) + c
⇒ c = 10
Linear function for Sarah is y = 10x + 10
Gene proposal ,
( x₁ , y₁ ) = ( 5, 42 )
(x₂ , y₂ ) = ( 10 , 77 )
Slope 'm' = ( y₂ - y₁ ) / ( x₂ - x₁ )
= (77 -42 ) / ( 10 - 5 )
= 35 /5
= 7
y = mx + c
⇒ 112 = 7(15) + c
⇒ c = 7
Linear equation for Sarah is y = 7x + 7
Paul proposal is,
y = 10x + 7
Linear function.
This implies all proposal plans represents linear function .
As they are in form y = mx + c.
Yes class has money in the account.
Sarah has 10 , Gene has 7 and Paul has 7 in his account.
Total money in account = 24
If we put x = 5 in all the plans
Sarah raised
y = 10(5) + 10
= 60
Gene raised
y = 7x + 7
= 7(5) + 7
= 42
Paul raised
y = 10x + 7
= 10(5) + 7
= 57
This implies Sarah plan raised the money at fastest rate.
Sarah and her classmates are hoping to raise $200
Sarah plan,
200 = 10x + 10
⇒ x = 19 hours
Gene plan
200 = 7x + 7
⇒ x = 27.6 hours
Paul plan
y = 10x + 7
⇒ 200 = 10x + 7
⇒x = 19.3hours
Recommended plan is of Sarah.
Therefore, all the proposal plans represents linear function.
Class has $24 in the account.
Sarah plan raises at the fastest rate.
Recommended plan is Sarah proposal plan.
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The above question is incomplete, the complete question is:
Attached question.
Related Questions
The weight of an object on the moon is
1/6 of its weight on Earth. If a moon rock
weighs 20.5 lb on Earth, how much did
the moon rock weigh on the moon?
Answers
Answer:
1/6 = 0.16 = 16%
restate the question: 16% of 20.5 is what? multiply: 20.5*.16 = 3.28 now, to find the weight of the object on the moon, subtract 16% from 20.5. 16% of 20.5 is 3.28 20.5-3.28 = 17.22 = 17 22/100 = 17 11/50
the weight of the object is 17 11/50 pounds on the moon.
the mayor of a town believes that under 46% of the residents favor construction of an adjoining bridge. is there sufficient evidence at the 0.05 level to support the mayor's claim? after information is gathered from 190 voters and a hypothesis test is completed, the mayor fails to reject the null hypothesis at the 0.05 level. what is the conclusion regarding the mayor's claim?
Answers
Since the null hypothesis was not rejected, there is not enough evidence to conclude that under 46% of the residents favor construction of an adjoining bridge.
What is the relation between the decision and the conclusion?There are two decisions possible regarding the null hypothesis, as follows;
Reject the null hypothesis.Do not reject the null hypothesis.The hypothesis are given as follows:
Null hypothesis: proportion is not under 46%.Alternative hypothesis: proportion is under 46%.The null hypothesis was not rejected, meaning that the conclusion regarding the mayor's claim is that there is not enough evidence from the sample of 190 voters to conclude that the percentage is below 46%.
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LESSON 18 SESSION 4
7 Tell whether each statement is True or False.
a. 80% of 90 is the same as of 90.
b. 45% of 60 is 27.
c. 20% of 90 is the same as
as
d. 25 is 35% of 80.
of 90.
of
True False
о
O
о
O
L
Answers
a. 80% of 90 is the same as of 90 - False
b. 45% of 60 is 27 - True
c. 20% of 90 is the same as as of 90- True
d. 25 is 35% of 80 -False
What are the statement about?a. 80% of 90 is not the same as 90. To find 80% of 90, we multiply 90 by 0.8, which gives us 72. Therefore, the statement is false.
b. To find 45% of 60, we multiply 60 by 0.45, which gives us 27. Therefore, the statement is true.
c. 20% of 90 is the same as of 90. To find 20% of 90, we multiply 90 by 0.2, which gives us 18. Therefore, the statement is true.
Lastly, for question d. 25 is not 35% of 80. To find 35% of 80, we multiply 80 by 0.35, which gives us 28. Therefore, the statement is false.
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What is the volume of the right rectangular prism shown?
A)
96 cm3
B) 128 cm3
C) 512 cm3
D) 1,536 cm3
Answers
Help plz
I will mark brainliest
Answers
Answer:
Angle 2= 127
Angle 3= 23
The measure of angle 4 is 90° because the 90° is marked
Find the smallest number which when divided by 12,15,18&27 leaves as remainder 8,11,14,23 respectively.
Answers
Answer:
\( \boxed{ \bold{ \huge{ \boxed{ \sf{536}}}}}\)
Step-by-step explanation:
Solution :
Here, 12 - 8 = 4
15 - 11 = 4
18 - 14 = 4
27 - 23 = 4
Thus, every divisor is greater than its remainder by 4. So, the required smallest number is the difference of the L.C.M of the given number and 4
Finding the L.C.M
First of find the prime factors of each numbers
12 = 2 × 2 × 3
15 = 3 × 5
18 = 3 × 3 × 3
27 = 3 × 3 × 3
Take out the common prime factors : 3 , 3 and 3
Also take out the other remaining prime factors : 2 , 2 and 5
Now, Multiply those all prime factors and obtain L.C.M
L.C.M = Common factors × Remaining factors
= 3 × 3 × 3 × 2 × 2 × 5
= 540
L.C.M of 12 , 15 , 18 and 27 = 540
So, The required smallest number = 540 - 4
= 536
Hope I helped!
Best regards!!
A satellite travels 12 miles in 15 minutes at a constant speed. What is the satellite’s speed in mile per hour?
Answers
Answer: 46 mph
Step-by-step explanation: 15*4=60 so 12*4=46
I hope this helps!
The average age of 6 men is 35 years and the average age of four of them is 32 year.
Find the ages of the remaining two ment one is 3 years older than the other.
Answers
Let's denote the ages of the two remaining men as x and x + 3 (since one is 3 years older than the other).
We know that the average age of 6 men is 35 years. So, the sum of their ages is 6 * 35 = 210 years.
We also know that the average age of four of them is 32 years. So, the sum of their ages is 4 * 32 = 128 years.
To find the sum of the ages of the two remaining men, we subtract the sum of the ages of the four men from the sum of the ages of all six men:
210 - 128 = 82 years.
Now, we can set up an equation to solve for the ages of the remaining two men:
x + (x + 3) = 82.
Combining like terms, we get:
2x + 3 = 82.
Subtracting 3 from both sides:
2x = 79.
Dividing both sides by 2:
x = 39.5.
So, one of the remaining men is 39.5 years old, and the other is 39.5 + 3 = 42.5 years old.
A water bottle costs $9.45. Sales tax is 7%. What is the total cost?
Answers
Answer:
$10.11
Step-by-step explanation:
Before Tax Price: $9.45
Sale Tax: 7.00% or $0.66
After Tax Price: $10.11
Answer:
9.46
Step-by-step explanation:
divide 9.45 by .07 then add that to 9.45 and round
To stay within your budget,the area of the house and the garage combined is at most 3000 square feet.The area of the garage is 528 square feet.Write and slove an inequality that represents the area of the house. write the inequality, do not simplify. Let h=area of the house simplify the inequality
Answers
Answer:
h ≤ 3000 ft² - 528 ft²
h ≤ 2472 ft²
Step-by-step explanation:
Area of house and garage is at most 3000 ft²
Area of garage = 528 ft²
Area of house (h) =?
Area of garage + Area of house ≤ 3000 ft²
528 ft² + h ≤ 3000 ft²
h ≤ 3000 ft² - 528 ft²
h ≤ 2472 ft²
What is x² − 4x + 7 factored?
Answers
Answer:
The expression is not factorable with rational numbers.
x² − 4x + 7
help somebody please , i’ll cash app you .
Answers
Answer:
Yes
Step-by-step explanation:
When you substitute
y: 11
x: -2
Substitute:
y=x+13
11=-2+13
11=11
This is always true.
What is the range of f/x )= sin x the set of all real numbers?
Answers
On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = \(-1 < y < 1\)
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
The Range of the given function, f(x) = sin(x)
\(-1 < y < 1\)
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Create a proportion using the form = to represent the following word problem. 78% of what number is 42?.
Answers
Therefore the solution to this question of proportion, 78% of what number is 42 is 53.84.
What is proportion?In general, the word "proportion" is used to describe a part, share, or amount that is compared to an entire. Two ratios are in proportion, according to the definition of proportion, when they are equal. Two ratios or fractions being equal is expressed by an equation or a statement.
Here,
If 78% of x (any number) equals 42, then we need to set this up as an equation in order to figure it out.
1) Writing down 78% as a fraction. Taking into account that we refer to a product when we say 78% of some amount (x).
78%=78/100 \s=>78x/100=42
2) Afterward, we can continue:
100*78x/100=42*100
78x=4200
x=4200/78
x=53.84
Therefore the solution of 78% of what number is 42 is 53.84.
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Composite Figures Question 4.
A. 42 cm
B. 35 cm
C. 26 cm
D. 14 cm
Answers
Answer:
42 cm A
Step-by-step explanation:
Use indicator random variables to compute the expected value of the sum of n dice.
Answers
The expected value of the sum of n dice is E[X] = 3.5n.
Indicator random variables are a probability theory tool. They are used to help evaluate probabilities for a given random variable.
Let X be the total number that results from n throws of a fair six-sided die.
By linearity of expectation,E[X] = E[X1 + X2 + ... + Xn] = E[X1] + E[X2] + ... + E[Xn]
Where Xj is the number obtained on the jth die roll.
Each Xi is a discrete random variable with a uniform distribution on the set {1, 2, 3, 4, 5, 6}.
To evaluate E[Xi], we define an indicator random variable Yi as follows: Yi = 1 if Xi = i and Yi = 0 otherwise.
Then, Xi = 1Y1 + 2Y2 + 3Y3 + 4Y4 + 5Y5 + 6Y6.
Thus,E[Xi] = E[1Y1 + 2Y2 + 3Y3 + 4Y4 + 5Y5 + 6Y6] = E[1Y1] + E[2Y2] + ... + E[6Y6] = 1P(Xi = 1) + 2P(Xi = 2) + ... + 6P(Xi = 6) = (1 + 2 + ... + 6) / 6 = 3.5.
Therefore, E[X] = E[X1] + E[X2] + ... + E[Xn] = 3.5n.
Thus, we have computed the expected value of the sum of n dice using indicator random variables. The expected value of the sum of n dice is E[X] = 3.5n.
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in a one-sample chi-square test, if your respondents are distributed very unequally across the levels of your variable, your chi-square value will be: a. high b. low c. 0 d. 1
Answers
The correct answer is a. high. In a one-sample chi-square test, the observed frequencies of the variable being studied are compared to the expected frequencies assuming a particular distribution or hypothesis.
The chi-square test statistic measures the difference between the observed and expected frequencies and determines whether this difference is statistically significant.
If the respondents are distributed very unequally across the levels of the variable being studied, the observed frequencies will be very different from the expected frequencies. This will result in a large difference between the observed and expected frequencies, leading to a high value for the chi-square test statistic.
The chi-square value is calculated by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies. If the respondents are distributed very unequally across the levels of the variable being studied, the expected frequencies will be very different from the observed frequencies, resulting in a high value for the chi-square test statistic.
Therefore, in a one-sample chi-square test, if your respondents are distributed very unequally across the levels of your variable, your chi-square value will be high.
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Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Answers
We are given two plots of normal distributions A and B.
The mean of a normal distribution is located at the center of the plot.
Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.
The standard deviation basically determines the shape of the distribution.
As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.
Therefore, the two correct options are
• The means of A and B are equal.
,• A has larger standard deviation.
dtermine the linerar velocity and acceleration of a point on the surface of the earth at the equator
Answers
The linear velocity of a point on the surface of the Earth at the equator is approximately 1670 kilometers per hour, and the acceleration is negligible.
The linear velocity of a point on the Earth's surface can be calculated using the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the distance from the axis of rotation. The Earth completes one rotation in approximately 24 hours, which corresponds to an angular velocity of 2π radians per 24 hours or approximately 0.0000727 radians per second.
At the equator, the distance from the axis of rotation is equal to the Earth's radius, which is approximately 6,371 kilometers. Plugging these values into the formula, we find that the linear velocity at the equator is approximately 1670 kilometers per hour. The acceleration of a point on the Earth's surface due to its rotation is given by the formula a = ω²r.
However, the acceleration at the equator is negligible because the distance from the axis of rotation remains constant, and the angular velocity is relatively small. Therefore, the acceleration of a point at the equator is considered negligible in practical calculations.
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In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student who has a brother also has a
sister?
Answers
The probability that a student with a brother also has a sister is 15/21.
From the data, it is clear that the total number of students in the class is
15+6+2+2=25
Therefore there are 25 total students in the class.
According to conditional probability the probability of having a sister given that the person has a brother can be given by
\(\frac{Probability of having a brother and sister}{Total Probability of having a brother}\)
Therefore it can also be stated as
P(s|b)= P(s∩b)/P(b)
Thus from the data given
P(s|b)= (15/25)/(21/25)
Therefore,
P(s|b)= 15/21
Thus the probability of having a sister for a student with a brother is 15/21.
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You borrow $30,000 to buy a car. The loan is to be paid off in 10 equal quarterly payments at 6% interest annual interest rate. The first payment is due one quarter from today. What is the amount of each quarterly payment (rounded)? A. $1,777. B. $2,803. C. $3,253. D. None of the above.
Answers
The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).
To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.
Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.
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In 10 and 11, find the area in square units of each polygon.
Answers
Answer:
10: 12 units^2 11: 33 units^2
Step-by-step explanation:
10:
Divide into square and 2 triangles (for simplicity)
square=9
one triangle=3/2
both triangles combined=3
9+3=12
11:
divide into 2 triangles
top triangle: height= 4, base=6
bottom triangle: height= 7, base=6
top=12
bottom=21
Add, 33.
The heights (in inches) of 10 adult males are listed below. Find the sample standard deviation of the data set.
70 72 71 70 69 73 69 68 70 71
Answers
The sample standard deviation of the heights (in inches) of 10 adult males is approximately 1.464 inches.
To find the sample standard deviation of the heights of the 10 adult males, follow these steps:
1. Calculate the mean (average) height:
(70+72+71+70+69+73+69+68+70+71) / 10 = 703 / 10 = 70.3 inches.
2. Subtract the mean from each height and square the result:
\([(70-70.3)^2, (72-70.3)^2, ... (71-70.3)^2].\)
3. Calculate the sum of these squared differences:
0.09+2.89+0.49+0.09+1.69+7.29+1.69+5.29+0.09+0.49 = 19.31.
4. Divide the sum by (n-1), where n is the sample size: \(19.31 / (10-1) = 19.31 / 9 = 2.145.\)
5. Take the square root of the result: √2.145 = 1.464 (rounded to 3 decimal places).
The sample standard deviation of the heights of the 10 adult males is approximately 1.464 inches.
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evaluate for f(6), show all work
Answers
Answer:
32
Step-by-step explanation:
f(6)=6^2-4
f(6)=36-4
f(6)=32
Answer:
f(6)=32
Step-by-step explanation:f(6)=6^2 -4
f(6)=36-4
f(6)=32
What is the approximate circumference of a circle that has a diameter of 15 inches? A) 14 ft
B) 21.98 ft
C) 28 ft
D) 7 ft
Answers
Answer:
47 ft
Step-by-step explanation:
3.14 x 15
In a 2-sample z-test for two proportions, you find the following: X1 = 24 n1 = 200 X2 = 17 my = 150 You decide
to run a test for which the alternative hypothesis is Hj: p1 > p2- Find the appropriate test statistic for the
test. Enter the test statistic - round to 4 decimal places. Z =
Answers
The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).
To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:
SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]
Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
In this case, we have the following values:
X1 = 24 (number of successes in sample 1)
n1 = 200 (sample size 1)
X2 = 17 (number of successes in sample 2)
n2 = 150 (sample size 2)
To calculate the sample proportions, we divide the number of successes by the respective sample sizes:
p1 = X1 / n1 = 24 / 200 = 0.12
p2 = X2 / n2 = 17 / 150 = 0.1133
Now, we can plug these values into the formula to calculate the standard error:
SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]
SE ≈ 0.0319
Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:
Z = (p1 - p2) / SE
Z = (0.12 - 0.1133) / 0.0319
Z ≈ 0.2103
Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).
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Help! Also even though it looks blurry, just zoom in to see the full question
Answers
The matrix transformation of triangle XYZ with coordinates
\(\begin{gathered} X=(-2,-2) \\ Y=(4,1) \\ Z=(0,6) \end{gathered}\)When dilated by a factor of 2.5 now becomes;
\(\begin{gathered} 2.5\begin{bmatrix}{-2} & 4{} & 0{} \\ {-2} & {1} & {6}{}\end{bmatrix}=\begin{bmatrix}{2.5(-2)} & {2.5(4)} & {2.5(0)} \\ {2.5(-2)} & {2.5(1)} & {2.5(6)} \\ & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{-5} & {10} & {0} \\ {-5} & {2.5} & {15} \\ {} & {} & {}\end{bmatrix} \end{gathered}\)ANSWER:
The correct vertices of the image now becomes;
\(\begin{gathered} X^{\prime}=(-5,-5) \\ Y^{\prime}=(10,2.5) \\ Z^{\prime}=(0,15) \end{gathered}\)A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. Stores benefit by gleaning information about shopping habits and hope to encourage shoppers to spend more. A typical Saturday morning shopper who does not participate in this program spends $150 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $165 on average during a recent Saturday, with standard deviation, s= $40. A test of whether shoppers participating in the loyalty program spend more on average than typical shoppers was then conducted. If the population mean spending amount for shoppers in the loyalty program is $165 (with σ= $40), then what is the probability that the test procedure used in this question will fail to reject H0 if α= 0.05?
Answers
The probability of failing to reject H0 in this test procedure is 1 - 0.008 = 0.992, or 99.2%.
To determine the probability of failing to reject the null hypothesis (H0) given an alpha level of 0.05, we need to perform a hypothesis test using the sample data provided.
H0: μ = $150 (population mean spending for typical shoppers)
Ha: μ > $150 (population mean spending for loyalty program shoppers)
The test statistic for this situation is a one-sample t-test, given that the population standard deviation (σ) is not known and we have a sample size of 80.
The test statistic (t) can be calculated as:
t = (sample mean - population mean) / (sample standard deviation / √sample size)
Using the given information, we can plug in the values:
t = ($165 - $150) / ($40 / √80)
Calculating this expression gives us t ≈ 2.5.
Now, we need to find the probability of observing a t-value greater than 2.5 (or equally extreme) under the null hypothesis. This probability is the p-value associated with the test.
Consulting a t-table or using statistical software, we find that the p-value for t > 2.5 with 79 degrees of freedom is approximately 0.008.
Since the p-value (0.008) is less than the given significance level (α = 0.05), we reject the null hypothesis.
Therefore, the probability of failing to reject H0 in this test procedure is 1 - 0.008 = 0.992, or 99.2%.
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we took a sample of 6 students from the classroom. the mean height of the 6 students is 70 inches, and the standard deviation of height of 6 students in the classroom is 2. what is the standard error of the mean?
Answers
If the standard deviation is 2 then the standard error of the mean is 0.8165 .
In the question ,
it is given that ,
the sample size of students taken from the classroom is(n) = 6 students ;
the mean height of students is = 70 inches ;
the standard deviation(S.D.) height of students is = 2 inches ;
the standard error of mean can be calculated using formula ;
S.E. = (S.D.)/√n
substituting the value of S.D. and sample size ,
we get ,
S.E. = 2/√6
= 0.816496
≈ 0.8165
Therefore , the Standard Error of the mean is 0.8165 .
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3) Main Idea: You can write the equation of an exponential function given the graph. This is the graph of an equation in the form f(x) = a bx.
What is the equation shown in this graph?
The y-intercept is _______. The a-value of the function is _______.
The point when x = 1 is _______. The b-value of the function is _______.
What is the equation of the function? ___________
Answers
Blank 1: The y-intercept is 3
Blank 2: The a-value is 3
Blank 3: The point is (1,6)
Blank 4: The b-value is 2
The function equation: \(f(x) = 3(2^x)\)
Step-by-step explanation:What you have here is an exponential function of the form: \(f(x)=a(b^x)\) or \(y = a(b^x)\).
Finding the y-interceptTo find the y-intercept, you have to find the y-value of the point on the equation where x = 0 or where the line crosses the y-axis. So, on the graph, this point is (0, 3).
Finding the a-valueIn an exponential equation, the a-value is the same as the y-intercept. This because, if x = 0 in the equation \(f(x)=a(b^x)\) then we have the following:
\(f(x)=a(b^x)\\\\f(x)=a(b^{0}) \mbox{ -any number to the power of 0 is 1}\\\\f(x)=a(1)\\\\f(x)=a \mbox{ or } y = a\)
Finding the point when x = 1We look at the graph and find the point where x = 1, this will be (1,6).
Finding the b-valueSince we want to find the b-value, we will use the point (1,6), because we want a value of x that will give us b. So, when x = 1 then \(b^1=b\).
We know that x = 1, y = 6, a = 3 then;
\(f(x)=a(b^x)\\\\y=a(b^x)\\\\6=3(b^1)\\\\6=3b\\\\3b=6\\\\b=\frac{6}{3} \\\\b=2\)
Therefore , the solution of the given problem of function comes out to be the equation shown in the curve is f(x) = 5 * 3ˣ .
What precisely does function mean?The math lesson covers a variety of subjects, including math, integers, as well as one's subdivisions, architecture, architecture, and both real and mostly fictitious geographic locations. A work covers the connections between different variable that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinct results for each input.
Here,
The spot where x = 1 is the point on the graph with x-coordinate 1. We can see from the graph that this spot is (1, 15). the location where x = 1 is therefore (1, 15).
We can use the exponential growth or decline formula to determine the function's b-value:
=> f(x) = a + bˣ
where b is the growth or decay factor and an is the starting value.
We can use the coordinates (0, 5) and (1, 15) to find b:
=> 15 = 5 * b¹
=> b = 3
Consequently, the function's b-value is 3.
Ultimately, the function's equation can be expressed as follows:
=> f(x) = 5 * 3ˣ
Therefore, the equation shown in the curve is f(x) = 5 * 3ˣ
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