Answers
Answer:
f(x) = 2·5^x . . . b = 5; a = 2f(x) = (9/2)(2/3)^x . . . b = 2/3; a = 9/2f(x) = (1/2)4^x . . . b = 4; a = 1/2Step-by-step explanation:
Actually, the lesson is giving you wrong information. The exponential function written in the example does not work for the point (4, 24).
Here's another way to look at it.
Given
two points: (x1, y1) and (x2, y2)
Solution
The exponential function can be written as ...
y = (y1)(y2/y1)^((x -x1)/(x2 -x1))
Example
For the example points, the function would be ...
y = (6)(24/6)^((x-2)/(4-2)) = 6·4^(x/2 -1) = (6/4)(4^(1/2))^x = (3/2)2^x
Check
For x=2, y=(3/2)2^2 = 6. For x=4, y = (3/2)2^4 = 24.
You will notice that we figure out "b" and "a" as a part of the process of simplifying the equation. The equation would work perfectly well without simplification.
_____
1. Given points (2, 50) and (3, 250), the equation is ...
f(x) = 50(250/50)^((x -2)/(3 -2)) = 50·5^(x -2) = (50/25)5^x
f(x) = 2·5^x . . . b = 5; a = 2
__
2. Given points (1, 3) and (2, 9/2), the equation is ...
f(x) = (3)(3/(9/2))^((x -1)/(2 -1)) = (3)(2/3)^(x -1) = (3/(2/3))(2/3)^x
f(x) = (9/2)(2/3)^x . . . b = 2/3; a = 9/2
__
3. Given points (3, 32) and (4, 128), the equation is ...
f(x) = (32)(128/32)^((x -3)/(4 -3)) = (32)4^(x -3) = (32/64)4^x
f(x) = (1/2)4^x . . . b = 4; a = 1/2
_____
Additional comments
The usual rules of exponents are useful in this:
a^(b+c) = (a^b)(a^c)
a^(bc) = (a^b)^c
a^-b = 1/a^b
Related Questions
please help me with this question (:
Answers
[tex] \frac{59 + x}{2} = 78 \\ 59 + x = 156 \\ x = 97[/tex]
Answer: VW=97
NEED HELP ASAP! Tomos is a skier he completed a ski race in 2 min 6 seconds the race was 525 m in length. tomos assumes that his average speed is the same for each race. using this assumption, work out how long tomos should take to complete an 800 m race give your answer in minutes and seconds
Answers
Answer:
3min 12sec
Step-by-step explanation:
Turn 2min 6sec into seconds
2m 6sec = 126 secs
divide 525 by 126
525/126 = 4.16666667
divide 800 by 4.16666667
800/4.16666667 = 192
192 to min secs = 3min 12sec
PLEASE HELP!! TON OF POINTS
Answers
Answer:
it is (7,-6)
Step-by-step explanation:
Solve the system of equations.
x+y+z=10
5x+3y=14
x−2y+z=2.5
PLZ HELP!!!!!!!!!!
Answers
Answer:
y=3,x=1.3,z=6.2 :)
Step-by-step explanation:
y=3,x=1.3,z=6.2 :)
So, we have:
: x+y+z=10 [equation 1]
: 5x+3y=14 [equation 2]
: x−2y+z=2.5 [equation3]
(I'm going to assume that you know how to solve equations with 2 variables)
1. eliminate a variable to get 2 variables
Let's reverse equation 2:
-x+2y-z= -2.5
and take equation 1, to try to eliminate "z"
x+y+z=10
add up the 2 equations to get:
3y=7.5
and solve to get
y=2.5
2. substitute what we already solved into another equation
Luckily, equation 2 only has 2 variables, and one is y, so we can sub it in.
5x+3y=14 --> 3x+3(7.5)=14
solve to get
x=1.3
3. Substitute both of our variables in to get the final variable: z
Let's take the first equation.
x+y+z=10 --> 1.3+2.5+z=10
solve to get
z=6.2
I hope this helps you!
What is the circumference of circle P?
Express your answer in terms of
Answers
Might be wrong
Write an inequality for: There are at most 50 people on the bus.
Answers
Answer:
>50
Step-by-step explanation:
It says there is at most 50 people so it'd be less than 50
The inequality for "There are at most 50 people on the bus." is b≤ 50.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
As, we know that the sign for atmost ≤.
Now, There are at most 50 people on the bus.
let the number of bus represented by 'b'.
Then, the inequality is
b≤ 50.
Hence, the inequality is b≤ 50.
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A blueprint for a new triangular playground shows that the sides
measure 480 ft, 140 ft, and 500 ft. Is the playground in the shape of
a right triangle? Explain.
Answers
Yes, the playgrounds shape is the right angle triangle.
Step-by-step explanation:
The sides of the triangular ground are 480 ft. 140 ft. And 500ft.
We can find if the sides given are the sides of a right triangle by using pythogoras theorem.
Here, the largest side is 500ft.
So,
√[(480x480) +(140x140) ]
= √[(230400) +(19600) ]
= √(250000)
= 500
The pythogoras theorem is proved.
So, the playground is in the shape of triangle.
Jabier places five cards that are labeled 1 to 5 faced down on the table and mixes them up. What is the likelihood that his archenemy Luke will draw an odd numbered card?
A.Impossible
B.Unlikely
C.As likely as not
D. Certain
Answers
Plz Help! ASAP!!!!
Weights of eggs laid by two chickens are recorded for a full year. Both data sets follow a normal distribution.
Chicken A: Standard deviation of A is 4.6 grams; 68% of the eggs fall between 50.9 grams and 60.1 grams.
Chicken B: Standard deviation of B is 4.9 grams; 68% of the eggs fall between 51.9 grams and 61.7 grams.
The difference between the mean weight of Chicken B’s eggs and the mean weight of Chicken A’s eggs to the nearest tenth is...?
Answers
The difference between the mean weight of Chicken B's eggs and the mean weight of Chicken A's eggs to the nearest tenth is 1.8 grams.
What is a normal distribution?A normal distribution is a probability distribution that is symmetric around the mean, with most of the data points falling close to the mean and fewer data points falling farther away from it.
The shape of a normal distribution is often referred to as a bell curve because when the distribution is graphed, the resulting curve resembles a bell
We have,
Since both data sets follow a normal distribution, we can use the empirical rule (also known as the 68-95-99.7 rule) to find the mean weight of each chicken's eggs.
For Chicken A, we know that 68% of the eggs fall between 50.9 grams and 60.1 grams. This means that the mean weight of Chicken A's eggs is the average of these two values:
Mean of A = (50.9 + 60.1) / 2 = 55.0 grams
For Chicken B, we know that 68% of the eggs fall between 51.9 grams and 61.7 grams. This means that the mean weight of Chicken B's eggs is the average of these two values:
Mean of B = (51.9 + 61.7) / 2 = 56.8 grams
The difference between the mean weight of Chicken B's eggs and the mean weight of Chicken A's eggs is:
Difference = Mean of B - Mean of A
= 56.8 - 55.0
= 1.8 grams
Therefore,
The difference between the mean weight of Chicken B's eggs and the mean weight of Chicken A's eggs to the nearest tenth is 1.8 grams.
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SIMPLIFY THIS EXPRESSION: 6p+4p+3
ILL GIVE U BRAINLIEST LIKE ALWAYS
Answers
Answer:
[tex]10p+3[/tex]
Step-by-step explanation:
To work this out you would add up all of the like terms
1) Add the like terms.
[tex]6p+4p=10p[/tex]
2)Add the 3
[tex]10p+3[/tex]
which number rational?
Answers
Answer:
A rational number is a number that can be express as the ratio of two integers.
Step-by-step explanation:
A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever).
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 15% vinegar. The chef wants to make 240 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
Answers
You want to setup an equation that will match the word problem. Let's call the amount of the first brand, F and the amount of the second brand, S.
We want the total mixture to be 310mL so: F + S = 310
Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)
Now, we can solve the system of equations using substitution.
F + S = 310
.06F + .11S = .08(310)
F = 310 - S [solve 1st equation for F]
.06(310 - S) + .11S = .08(310) [substitute into 2nd equation]
18.6 -.06S +.11S = 24.8
.05S = 6.2
S = 124
F + 124 = 310 [substitute answer for S back into original equation]
F = 186
Answer: to make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.
To make 240 milliliter of mixture that contain 8% vinegar, use 168 milliliter of first brand and 72 milliliter of second brand
What is Linear equation?
An equation between two variables that gives a straight line when plotted on a graph.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given,
Quantity of vinegar in first brand = 5%
Quantity of vinegar in second brand = 15%
The chef wants to make 240 milliliter of a dressing that 8% vinegar
Consider,
Quantity of first brand = x
Quantity of second brand = y
Then,
x + y = 240
x=240-y
We want total of 8% of mixture by adding first brand and second brand
0.05x + 0.15y = 0.08×240
Substitute the value of x in this equation
0.05(240-y) + 0.15y =19.2
12 - 0.05y + 0.15y = 19.2
0.1y = 7.2
y = 72
Substitute the value of y in first equation
x + y = 240
x + 72 =240
x = 168
Hence, to make 240 milliliter of mixture that contain 8% vinegar, use 168 milliliter of first brand and 72 milliliter of second brand
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About 3.9 * 10 ^ 7 people live in California. About 1.3 * 10 ^ 6 people live in Maine. About how many more people live in California than live in Maine?
Answers
Answer:
3.7*10⁷ people.
Step-by-step explanation:
Estimated population of California = 3.9*10⁷ people
Estimated population of Maine = 1.3*10⁶ people.
Let x represent the estimated number of people that live in California more than Maine.
The number of people that live in California more than Maine can be found by finding the difference between the population of California to Maine.
No. Of people living in California - no. Of people living in Maine = estimated no of people that live in California more than Maine.
X = 3.9*10⁷ - 1.3*10⁶
X = 3.7*10⁷ people
About 3.7*10⁷ people live more in California than Maine
how many more people live in California than live in Maine is 37.7 × 10⁶ people.
Since 3.9 × 10⁷ people live in California and about 1.3 × 10⁶ people live in Maine. To find how many more people live in California than live in Maine, we take the difference of the two values.
Number of people more living in CaliforniaDifference,D = N - n where
N = number of people living in California = 3.9 × 10⁷ people and n = number of people living in Maine = 1.3 × 10⁶ peopleSo, substituting the values of the variables into the equation, we have
D = N - n
D = 3.9 × 10⁷ - 1.3 × 10⁶
D = 39 × 10⁶ - 1.3 × 10⁶
D = 37.7 × 10⁶ people
So, how many more people live in California than live in Maine is 37.7 × 10⁶ people.
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A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean μ S =60 and standard deviation σ S =5. The number of miles that the extended life tires last has a mean μ E =70 and standard deviation σ E =7. If mileages for both tires follow a normal distribution, what is the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire?
Answers
Answer: .123
Step-by-step explanation: use random variable e-s which will follow a normal distribution with a mean of 70-60=10 and SD= sq root of 25+49. P(e-s<0)=.123
The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have the number of thousands of miles that the standard model tires last has a mean:
[tex]\rm \mu_S = 60[/tex]
And standard deviation:
[tex]\rm \sigma_s = 5[/tex]
The number of miles that the extended life tires last has a mean:
[tex]\rm \mu_E = 70[/tex]
And standard deviation:
[tex]\rm \sigma_E = 7[/tex]
As the mileages for both tires follow a normal distribution curve.
If we use the E-S random variables and these random variables follow the normal distribution.
Now:
[tex]\rm E =\mu_E- \mu_S[/tex]
E = 70 - 60 ⇒ 10 and
[tex]\rm S= \sqrt{\sigma_S ^2+\sigma_E^2}[/tex]
[tex]\rm S= \sqrt{5^2+7^2}[/tex]
S = √74 ⇒ 8.6023
Now from the normal distribution table the value of the probability:
=P(E - S<0)
= 0.123
Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123
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The mean and the standard deviation of the sampled population are, respectively, 77.4 and 4.0. Find the mean and standard deviation of the sampling distribution of the sample mean x overbar for samples of size n equals 225. Round your answers to one decimal place.
Answers
Answer:
See explanation below.
Step-by-step explanation:
We are looking for the mean and the standard deviation of the sampling distribution of the sample of mean x, given that the mean and standard deviation of sampled population are as follows:
Mean=μ= 77.4
Standard deviation = σ = 4.0
Sample size n = 255
so, the mean of sample mean x will be same as mean of the sampled population:
μₓ = μ = 77.4
and the standard deviation of sample mean x will be standard deviation of the sampled population divided by square root of sample size:
σₓ = σ / √ n
= 4.0 / √225
= 4.0 / 15
= 0.3
Determine the slope of the line that is perpendicular to the line y = -7x - 12.
Answers
Answer:
the slope that is perpendicular to line y=-7x-12 is 1/7
1/7 is the perpendicular slope
Step-by-step explanation:
Solve for x please help
Answers
Answer:
x = 9
Step-by-step explanation:
By remote exterior angle theorem:
[tex](12x + 14)\degree = (1 + 5x) \degree+ 76 \degree \\ 12x + 14 = 1 + 5x + 76 \\ 12x - 5x = 77 - 14 \\ 7x = 63 \\x = \frac{63}{7} \\ \huge \red{ \boxed{ x = 9}}[/tex]
“the jones family spent 12% of their family budget on clothes and 25% on food. what fractional part of the budget did they spend in each category”
Answers
Answer:
Tyey spent 3/25 on clothes and 1/4 on food
Step-by-step explanation:
12% is 12/100 which simplifies to 3/25
25% with 25/100 which simplifies to 1/4
Answer:
Clothes: 3/25
Food: 1/4
Step-by-step explanation:
Clothes: 12/100 = 3/25
Food: 25/100 = 1/4
Bobby purchases a new car for $25,000. The car's value can be modeled by the following exponential function: y = 25000(0.84)^t where y represents the car's value and t represents time in years. How much is her car worth after 3 years rounded to the nearest cent?
Answers
Answer:
Step-by-step explanation:
y=25000(0.84)^t
y=25000(0.84)^3
y=$14817.6
Write the numbers in order from greatest to least.
-4, 2 1⁄5, -2 3⁄4, 1⁄10
Answers
Answer:
2 1/5, 1/10, - 2 3/4, -4
Step-by-step explanation:
If you're ever confused about whether a number is greater than another number, think about them on a number line. If the number is further to the left than another number, it is less (for example, 0 is further to the left than 2).
Is 27/-62 and -62/-27 parallel , perpendicular or neither ? please help !
Answers
Answer:
those fractions are perpendicular
Step-by-step explanation:
-27/62
62/27
I need help with this question please!
Answers
Answer:
Can you put a better pic of it I can’t really see what it’s asking
Step-by-step explanation:
I’ll be glady to help
What is the slope of the line through (-2,-6) and (2, 2)?
Choose 1 answer:
Answers
Answer:
2
Step-by-step explanation:
The slope given two points is found by
m= (y2-y1)/(x2-x1)
= (2 - -6)/(2 - -2)
=(2+6)/(2+2)
=8/4
2
f(x) = 2x + 10 g(x) = 1(1.01)x
10 1.00
12 1.01
14 1.02
16 1.03
Which statement BEST compares the growth of the two functions as x approaches ∞?
A) The linear function will only exceed the exponential function if its initial value is greater.
B) The exponential function will only exceed the linear function if its initial value is greater.
C) The value of the linear function will eventually exceed the value of the exponential function.
D) The value of the exponential function will eventually exceed the value of the linear function.
Answers
Answer:
D
Step-by-step explanation:
I just did it on usatestprep so. its D
Answer:
d
Step-by-step explanation:
The value of the exponential function will eventually exceed the value of the linear function. A quantity increasing exponentially eventually exceeds a quantity increasing linearly.
Can anyone help me with this? I will mark you as brainliest
Answers
Answer:
2/7
then 2/14
Step-by-step explanation:
Let P(H)=p be the probability of one head. In many scenarios, this probability is assumed to be p=12 for an unbiased coin. In this instance, P(H)=3P(T) so that p=3(1−p)⟹4p=3 or p=34.
You are interested in the event that out of three coin tosses, at least 2 of them are Heads, or equivalently, at most one of them is tails. So you are interested in finding the likelihood of zero tails, or one tails.
The probability of zero tails would be the case where you only received heads. Since each coin toss is independent, you can multiply these three tosses together: P(H)P(H)P(H)=p3 or in your case, (34)3=2764.
Now we must consider the case where one of your coin flips is a tails. Since you have three flips, you have three independent opportunities for tails. The likelihood of two heads and one tails is 3(p2)(1−p). The reason for the 3 coefficient is the fact that there are three possible events which include two heads and one tails: HHT,HTH,THH. In your case (where the coin is 3 times more likely to have heads): 3(34)2(14)=2764.
Adding those events together you get p3+3(p2)(1−p)=5464. Note that the 3 coefficient
solve for x
i will give brain-liest to whoever answers
Answers
Answer:
x = 10
Step-by-step explanation:
x² = 4×25
x² = 100
x = √100
x = 10
AB² = BD×BC
What is the value of x if gx-1 -2 =25? x=1/2 x=2 x=5/2 x=4
Answers
Answer:
x=5/2
Step-by-step explanation:
The value of x in the equation is 4.
What is meant by exponent ?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Here,
The equation given is,
g⁽ˣ⁻¹⁾- 2 = 25
g⁽ˣ⁻¹⁾ = 27
g⁽ˣ⁻¹⁾ = 3³
Therefore,
x - 1 = 3
x = 4
Hence,
The value of x in the equation is 4.
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Find the average rate of change for f(x) = x - 8x + 15 from x = -3 to x = 2.
A)
-3
TM and
Submit
Answers
Answer:
Look at the picture
Step-by-step explanation:
The answer is B. -9
At a yearly basketball tournament, 84 different teams complete, after each round of the tournament, one-fourth of the team remain.
Create a function which models the above scenario and explain how you arrived at each part of the function
Answers
Answer:
84*(1/4)^x
Step-by-step explanation:
84 is the constant as it is the starting amount. However each round (x because the amount of rounds is constantly changing) divides the team by 4 or multiplies by 1/4 (Reciprocal).
So, if you wanted to see if the amount of teams after three rounds you would do:
84 * 1/4 * 1/4 * 1/4. However, any number times itself is an exponent, so we would simplify to 84³. But due to the fact we do not know how many rounds we are going to calculate we change the exponent to x.
Which equation represents a line that passes through the two points in the table
Answers
Answer:
B
Step-by-step explanation:
Slope:
[tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2}} =\frac{6-1}{6-3} =\frac{5}{3}[/tex]
This eliminates answer options C and D
If you plug either set of coordinates into equation B then you will know that it works because both sides will end up equal to each other
The line that passes through the given points in the table is represented by the equation y = 3x + 9. You can verify this by plugging the x-values into the equation and arriving at the corresponding y-values or by checking if the points lie on the line in the graph.
Explanation:To answer your question about which equation represents a line that passes through the two points given in the mentioned table, we can use the concept of linear equations and their graph. The equation of a line in slope-intercept form is given by y=mx+b where 'm' is the slope and 'b' is the y-intercept. From the information given, we can see the value of 'm' as 3 and 'b' as 9.
Therefore, the line that passes through the points provided is represented by the equation y = 3x + 9. To verify this, you can plug in the x-values from the table into this equation and you should be able to arrive at the corresponding y-values given in the table.
In the given figure, these points should lie on the line represented by the equation y = 3x + 9, verifying our solution.
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