Which of the following exponential functions is represented by the graph? Question 15 options: A) ƒ(x) = (1∕2)x B) ƒ(x) = 2x C) ƒ(x) = −2x D) ƒ(x) = (1∕2)−x
Answers
Answer:
Option (A)Step-by-step explanation:
Let the equation of the exponential function is f(x) = a(b)ˣ
Two points (-2, 4) and (-1, 2) lie on the graph,
For (-2, 4),
By substituting the values in the given function,
[tex]4=a(b)^{(-2)}[/tex]
[tex]4=\frac{a}{b^{2} }[/tex] ------(1)
For second point (-1, 2),
[tex]2=a(b)^{-1}[/tex]
[tex]2=\frac{a}{b}[/tex] -----(2)
Dividing equation (1) by equation (2),
[tex]\frac{4}{2}=\frac{\frac{a}{b^2}}{\frac{a}{b} }[/tex]
[tex]2=\frac{a}{b^{2}}\times \frac{b}{a}[/tex]
[tex]2=\frac{1}{b}[/tex]
b = [tex]\frac{1}{2}[/tex]
From equation (1),
[tex]4=\frac{a}{(\frac{1}{2} )^2}[/tex]
4 = 4a
a = 1
Therefore, equation of the exponential function will be,
f(x) = [tex]1.(\frac{1}{2})^{x}[/tex]
[tex]f(x)=(\frac{1}{2})^x[/tex]
Option (A) will be the answer.
Answer:Answer:
Option (A)
Step-by-step explanation:
Let the equation of the exponential function is f(x) = a(b)ˣ
Two points (-2, 4) and (-1, 2) lie on the graph,
For (-2, 4),
By substituting the values in the given function,
------(1)
For second point (-1, 2),
-----(2)
Dividing equation (1) by equation (2),
b =
From equation (1),
4 = 4a
a = 1
Therefore, equation of the exponential function will be,
f(x) =
Option (A) will be the answer.
Step-by-step explanation:
Related Questions
What is the domain and range of each relation?
Drag the answer into the box to match each relation.
A relation mapping diagram. Element x contains negative 2, 0, 2, and 4. Element y contains negative 3, negative 1, and 0. Negative 2 maps to negative 3 and negative 1. Zero maps to 0. Two maps to 0. Four maps to negative 3.
Points plotted on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. Five points are plotted. Begin ordered pair negative 3 comma 1 end ordered pair. Begin ordered pair negative 1 comma negative 1 end ordered pair. Begin ordered pair 0 comma 0 end ordered pair. Begin ordered pair 3 comma 2 end ordered pair. Begin ordered pair 3 comma 3 end ordered pair.
Answers
Answer:
[tex]\text{Domain of}R_1=\{-2,0,2,4\}[/tex] and [tex]\text{Range of}R_1=\{-3,-1,0\}[/tex]
[tex]\text{Domain of}R_2=\{-3,-1,0,3\}[/tex] and [tex]\text{Range of}R_2=\{-1,0,1,2,3\}[/tex]
Step-by-step explanation:
Domain is the set of input values or x-values.
Range is the set of output values or y-values.
According to the relation mapping diagram, the relation is
[tex]R_1=\{(-2,-3),(-2,-1),(0,0),(2,0),(4,-3)\}[/tex]
So,
[tex]\text{Domain of}R_1=\{-2,0,2,4\}[/tex]
[tex]\text{Range of}R_1=\{-3,-1,0\}[/tex]
In the graph 5 points are plotted. So, the relation is
[tex]R_2=\{(-3,1),(-1,-1),(0,0),(3,2),(3,3)\}[/tex]
So,
[tex]\text{Domain of}R_2=\{-3,-1,0,3\}[/tex]
[tex]\text{Range of}R_2=\{-1,0,1,2,3\}[/tex]
A school trip requires students to score at least a total of 335 points on four tests. Each test is worth 100 points. If a student's scores on the first three tests
were 77, 95, and 82, what score would the student need on the last test to have no less than 335 points ?
O A. 79
OB. 75
O C. 93
O D. 81
Answers
Answer:
D. 81
Step-by-step explanation:
You need to first add 77, 95 and 82 to get 254, Then you do 335 - 254 which is 81.
Answer:
D. 81
Step-by-step explanation:
To get the answer all you need to do is add all of the scores of the first three tests and then subtract that from 335.
24 ÷ [ 33- (1+2)^2] = ?
21 + 3 (2-2^2) = ?
[(14+[tex]\sqrt 4[/tex])÷2^3] - 14 = ?
20 + [18÷(4+1)] - (3^2 + 2) = ?
please simplify the expressions using the proper order of operations.
Answers
Answer:
Below in bold.
Step-by-step explanation:
24 ÷ [ 33- (1+2)^2]
= 24 / ( 33 - 3^2)
= 24 / 24 = 1.
21 + 3 (2-2^2)
= 21 + 3(2 - 4)
= 21 + 3 * -2
= 21 - 6
= 15.
[(14+√4)÷2^3] - 14
= [ (14 + 2) / 8] - 14
= 16/8 - 14
= 2 - 14
= -12.
20 + [18÷(4+1)] - (3^2 + 2)
= 20 + [18÷ 5] - (9 + 2)
= 20 + 3.6 - 11
= 23.6 - 11
= 12.6.
solve by factoring x^2+5x-14=0
Answers
Answer: {-7, 2}
Step-by-step explanation: This type of equation is called a polynomial equation and in order to solve for x, we would first factor the left side.
Notice that the left side of the equation is a trinomial in a special
form that can be factored as he product of two binomials.
As our first term for each binomial, we have the factors of x², x · x
and as the second term, we have the factors of -14 that add to 5.
In this case, the factors are +7 and -2.
So we have (x + 7)(x - 2) = 0.
If (x + 7)(x - 2) = 0, that means that either x + 7 = 0 or x - 2 = 0.
Solving for x in each equation, we have x = -7 or x = 2.
We can write our answer as the solution set {-7, 2}.
The solution of quadratic equation is,
⇒ x = - 7, 2
We have to given that,
An equation is,
⇒ x² + 5x - 14 = 0
We can factorized the above quadratic equation as,
⇒ x² + 5x - 14 = 0
⇒ x² + (7 - 2)x - 14 = 0
⇒ x² + 7x - 2x - 14 = 0
⇒ x (x + 7) - 2 (x + 7) = 0
⇒ (x + 7) (x - 2) = 0
This gives,
x + 7 = 0
x = - 7
x - 2 = 0
x = 2
Therefore, The solution of quadratic equation is,
⇒ x = - 7, 2
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A rancher has 5,000 feet of fencing available to enclose a rectangular area bordering a river. He wants to separate his cows and horses by dividing the enclosure into two equal areas. If no fencing is required along the river, find the length of the center partition that will yield the maximum area.
Answers
Answer:
1,000 feet
Step-by-step explanation:
The closer to a square a rectangle is, the greater the area. So the 5,000 feet should be divided into 5 equal sections to create 2 squares with the river making one side. (Like the letter "E").
5,000/5=1,000
84"
7'
A
B
Given the conversion factor 12 in, which line segment is longer?
O A. Line segment A
O B. Line segment B
O C. They are the same size.
Answers
Michelle is changing her health care insurance and deciding between two different plans that charge the
same premium. Plan A has a $1,700 deductible with 20% coinsurance. Plan B has a $1,450 with 30%
coinsurance. Michelle had a total of $8,450 in medical bills last year. Under which plan would Michelle's
share have been less? Support your answer with mathematical calculations. Answer in complete
sentence.
Answers
plan B would share less
because, 20% of 1700 is 340 and 30% of 1450 is 435
I hope this helps!!
Answer:
plan A
Step-by-step explanation:
Plan A
1700-8450=6750*.20=1350+1700=3050
Plan B
1450-8450=7000*.30=2100+1450=3550
Answer=Plan A
NEED ANWSER ASAP! WILL GIVE BRAINLIEST! An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?
Answers
Answer:
any way since the sides are the same leangth
Step-by-step explanation:
(20 POINTS!!!) Richie and his brother have a paper route. Together they can deliver all of the papers in 40 minutes, and Richie can do it alone in 90 minutes. Richie’s brother slept in one day, leaving Richie to deliver alone for 30 minutes. How long must the two of them work together to finish delivering the newspapers?
Answers
Simplify equation: 14 - 7y + 5 = 1 + 3y + 24
simplify again: 19 - 7y = 25 + 3y
add -25 and 7y to both sides: -6 = 10y
y = -6/10 or -0.6
2. After 30 minutes, richie has delivered 1/3 of the papers, so they have to deliver the remaining 2/3. Since they can deliver them all in 40 minutes, would the answer be 2/3 of 40? I'm not sure about this.
50 points, show your work. This table shows the battery life of 4 different mobile phones: Phone A: 20 hours Phone B: 25 hours Phone C: 10 Hours Phone D: 18 hours. If 8.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 0.8 hour of battery life used in a day? Phone A Phone B Phone C Phone D
Answers
Answer:
phone c :)
Step-by-step explanation:
Which number is an irrational numbe?
Answers
Answer:
Option D
Step-by-step explanation:
=> [tex]\sqrt[3]{16}[/tex] is an irrational number because it cannot be written in the form of [tex]\frac{p}{q}[/tex] which is one of the most important characteristics of rational number.
=> The simplified form of [tex]\sqrt[3]{16}[/tex] is [tex]16 ^{1/3[/tex].
Answer:
[tex]\boxed{\sqrt[3]{16}}[/tex]
Step-by-step explanation:
Irrational numbers cannot be expressed as a fraction in the form [tex]\frac{p}{q}[/tex], where [tex]p[/tex] and [tex]q[/tex] are whole integers.
[tex]\sqrt{100} =10[/tex]
[tex]\frac{1}{8} = \frac{1}{8}[/tex]
[tex]-2.2675=\frac{-907}{400}[/tex]
[tex]\sqrt[3]{16} = 2.51984209979...[/tex]
For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7
Answers
Answer:
a) 6
Step-by-step explanation:
Expanding the polynomial using the formula:
[tex]$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $[/tex]
Also
[tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]
I think you mean [tex]210x^6y^4[/tex]
We can deduce that this term will be located somewhere in the middle. So I will calculate [tex]k= 5; k=6 \text{ and } k =7[/tex].
For [tex]k=5[/tex]
[tex]$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$[/tex]
Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just [tex]x^{n-k} y^k[/tex]
For [tex]k=6[/tex]
[tex]$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$[/tex]
if the standard deviation of a variable is 8, what is the variance?
Answers
Answer:
r]
Step-by-step explanation:
From the set {20, 30, 35}, use substitution to determine which value of x makes the inequality true. x - 5 > 25 A. 30 B. 20 C. none of these D. 35
Answers
Answer:
D. 35
Step-by-step explanation:
20-5>25 = 20>25 incorrect
30-5>25 = 25>25 incorrect
35-5>25 = 20>25 correct
A computer tallied the time to work for 200 days and found it reasonable to normal curve. The main Thomas 35 minutes, and the standard deviation with six minutes. For the 200 workday experiment, find the percent of tonic me to work more than 41 minutes.
Answers
Answer:
The probability that computers work more than 41 minutes is 0.15866 or 15.87%.
Step-by-step explanation:
We are given that a computer tallied the time to work for 200 days and found it reasonable to the normal curve. The mean is 35 minutes, and the standard deviation with six minutes.
Let X = the time taken by computer to work for 200 days.
So, X ~ Normal([tex]\mu=35, \sigma^{2} =6^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 35 minutes
[tex]\sigma[/tex] = standard deviation = 6 minutes
Now, the probability that computers work more than 41 minutes is given by = P(X > 41 minutes)
P(X > 41 minutes) = P( [tex]\frac{X-\mu}{\sigma }[/tex] > [tex]\frac{41-35}{6 }[/tex] ) = P(Z > 1) = 1 - P(Z [tex]\leq[/tex] 1)
= 1 - 0.84134 = 0.15866
The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.84134.
(20 POINTS!!!) Bob can paint a room in 3 hours, and Suzie can paint one in 2 hours. How long will it take them together to paint a room?
Answers
Answer:
1 hour 12 minutes or 1.2 hours
Step-by-step explanation:
You add fractions to get this.
1 room/3 hours + 1 room / 2 hours = 1 room / x
0.33333333+0.5 = 1 room / x
0.83333333 = 1 / x Multiply both sides by x
0.83333333x = 1 Divide by 0.8333333
x = 1/0.833333
x = 1.2 hours or
x = 1 hour and 12 minutes
HELPPPP FIRST GET BRAINLLEST Measure the difference between the lower quartile of Data Set A and the lower quartile of Data Set B. Round to the nearest tenth when performing all operations.
Answers
Answer:
26
Step-by-step explanation:
Let's find first the lower quartile in both A and B
steps:
look for the smallest sum of two consecutive numbers divide by 2 to get the lower quartile A73 and 75 are the smallest consecutive numbers
73+75 = 148 148/2 =74The lower quartile in A is 74
B47 and 49 are the smallest consecutive numbers
47+49 = 9696/2 = 48The lower quartile in B is 48
74-48 = 26Answer:
29
Step-by-step explanation:
To find the lower quartile of each you need to find the median to split them into 2 groups (upper and lower quartile).
Lower quartile of Set A: 73, 75, 79, 81, 84, 85
Lower quartile of Set B: 47, 49, 51, 51, 55, 56
Now you find the median of the 2
Set A: 80
Set B: 51
Lastly you subtract A & B and get 29
How many houses have an area less than 100^2m?
Answers
Answer:
4
Step-by-step explanation:
Each bar represents a range in area. The first bar represents the number of houses with an area of more than 50 but less than 100. It's height is 4, so there are 4 of those houses.
WILL MARK BRAINLIEST! Which of the following is a discrete random variable? a) length of time you play in a baseball game b) length of a car c) volume of water in a tank d) number of candies in a box
Answers
Answer:
d.which is number of candle's in a box
Answer:
number of candies in a box
Step-by-step explanation:
i really need this can someone help solve asap!!!
Answers
Answer: to find this answer .we need to do pegothogs property
Step-by-step explanation:
30° + 90° = 90 (because it is right angle )
120° - 90° = 30°
Plz mark me as brainlist
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1. What solid is represented by this net? (Image 1). A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid 2. Choose all the solids from the list below. A. Rectangle B. Circle C. Cone D. Pyramid E. Prism F. Cylinder 3. The volume of the following figure = ___________ cm3. (Image 2) A. 288 B. 72 C. 216 D. 144
Answers
Answer:
1) TRIANGULAR PRISM
3) d. 144 cm3
Step-by-step explanation:
1) When figuring out what shape a net is, look at the two shapes that are different. In this case, its the triangles. Then take a look at the other shapes. If it has a rectangle base then you know its a prism. If it has a different shpes base then you know its pyramid. Now just combine the two key words you found. Triangle + Prism = Triangular Prism
2) A solid is something that is firm and stable. So it is not a liquid or solid. Pretty much everything that you listed is a solid.
3) The formula for finding the volume of a triangular prism is bxhxl divided by 2. So it would be 8x3x12= 288 divided by 2= 144 cm3
Answer:
Triangular prism.
Step-by-step explanation:
What is the solution for x. 4/3x-1/3=9
Answers
Answer:
x=7
Step-by-step explanation:
4/3x-1/3=9
Add 1/3 on both sides
4/3x=28/3
Multiply the reciprocal
(3/4)(4/3)x=28/3(3/4)
x=7
Hope this helps !!
please hurry! I'll mark brainliest if you're fast!
To find the quotient 5/7 ÷ 1/3
multiply 7/5 by 1/3
multiply 7/5 by 3.
multiply 5/7 by 3.
multiply 5/7 by 1/3
Answers
Answer:
multiply 5/7 by 3
Step-by-step explanation:
FIRST GETS BRAINLLEST If you spin the spinner below 240 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 131 times B) Lands on yellow 95 times C) Lands on red 95 times D) Lands on blue 210 times
Answers
Answer:
it is d
Step-by-step explanation:
it is because d has more parts so it would land on it more then yellow and have a higher chance to land on blue
hope this helps
Answer:
C is the most reasonable.
Step-by-step explanation:
So we can put it in a ratio of 4:3:1. Then add all those up and do 240/8 which is 30. So each number in the ratio is 30. Then we do 4*30=120. 3*30=90. 1*30=30. Both red and blue are close to there answers but red is closer.
The initial count of a certain type of bacteria in a culture is 350. If the bacteria grows at the rate of 20% per hour, which
function models the number of bacteria after t hours?
Answers
Answer:
70
Step-by-step explanation:
[tex]\frac{20}{100}*350=70[/tex]
f(x) = 28 + 10x²; solve for f(1) and f(27)
Answers
Answer:
f(x) = 28 + 10x²
For f(1) substitute 1 into f(x)
That's
f(1) = 28 + 10(1)²
= 28 + 10
= 38f(27) = 28 + 10(27)²
= 28 + 7290
= 7318Hope this helps you
If the variance of a variable is 16, what is the standard deviation?
Answers
Answer:
Standard deviation=4
Step-by-step explanation:
Standard deviation = square root of variance
Standard deviation=√variance
Variance=standard deviation square
Variance=standard deviation^2
From the question
Variance=16
Standard deviation=?
Standard deviation=√variance
=√16
=4
Standard deviation=4
check:
If standard deviation=4
Variance=standard deviation^2
=4^2
=16
Therefore,
Standard deviation=√variance
[tex]4[/tex]
VarianceThe variance is a measure of how much each point deviates from the mean on average.The standard deviation of a set of numbers is the distance between them and the mean. (The mean is the arithmetic average of a given group of integers.)To compute the standard deviation, take the square root of the variance.Variance of the variable [tex]=16[/tex]
Standard deviation [tex]=\sqrt{16}[/tex]
[tex]=\boldsymbol{4}[/tex]
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posts does Tom need and what are the
dimensions of the fence?
I postdyards Therefore, Dimensions are
A bag of marbles can be shared equally among 3,
or 6 students with none left over. What's the least
amount of marbles that can be in the bag?
If there are 150 people born in the world every
minute; how many are bom every Hour? Day?
Year?
Answers
Answer:
1) 3 marbles
2) The number of people born every hour is 9000 people
The number of people born every day is 216,000 people
The number of people born every year = 78,840,000 people
Step-by-step explanation:
1) The given information are;
The number of students = 3 or 6
Amount of marbles remaining after sharing = None
Least amount of marbles that can be shared equally among the students = Condition each student gets one marble = 1 × 3 = 3 marbles
The least amount of marbles that can be shared equally among the students = 3 marbles
2) The number of people born int eh world every minute = 150 people
The number of minute in one hour = 60 minutes
∴ The number of people born every hour = 150 × 60 = 9000 people
Given that the number of hours in one day = 24 hours
∴ The number of people born every day = 9000 × 24= 216,000 people
Given that the number of days in one year = 365 days
∴ The number of people born every year = 216,000 × 365= 78,840,000 people
Suppose a poll of 700 voters says that 45% of the voters will vote for Candidate A for president. Compute the 99% confidence interval
Answers
Answer: (0.4016, 0.4984).
Step-by-step explanation:
Let p be the proportion of voters will vote for Candidate A for president.
Formula for confidence interval for proportion:
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
, here [tex]\hat{p}[/tex]= sample proportion
n= sample size.
z* =two-tailed critical z- value.
As per given, we have
n= 700
[tex]\hat{p}[/tex] = 0.45
Critical two-tailed z-value for 99% confidence interval = 2.576
Then, the required 99% confidence interval for p would be:
[tex]0.45\pm (2.576)\sqrt{\dfrac{0.45(1-0.45)}{700}}\\\\=0.45\pm(2.576)\sqrt{0.000353571428}\\\\=0.45\pm (2.576)(0.0188035)\\\\=0.45\pm0.04844\\\\=(0.45-0.048437,\ 0.45+0.048437)\\\\=(0.401563,\ 0.498437)\approx(0.4016,\ 0.4984)[/tex]
Hence, the required confidence interval (0.4016, 0.4984).
Find the measure of b.
Answers
The lines around the angle is saying that they are corresponding. so the angle of b is 25
Answer:
[tex]\boxed{<b = 25}[/tex]
Step-by-step explanation:
Two angles in the same sector/segment have congruent measures.
So, <b = 25 (These are the two angles in the same segment).