Answer:
Step-by-step explanation:
Sure, here is the input table for f(x) and g(x) using inputs from 0 to 5:
| Input (x) | f(x) = 25x^(2) | g(x) = 3*3^(x) |
|-----------|----------------|----------------|
| 0 | 0 | 3 |
| 1 | 25 | 9 |
| 2 | 100 | 27 |
| 3 | 225 | 81 |
| 4 | 400 | 243 |
| 5 | 625 | 729 |
As x gets very large, g(x) will have greater output values than f(x). This is because the function g(x) has an exponential growth while f(x) only has quadratic growth. As x gets larger, the base of the exponent in g(x) becomes more significant and results in a much larger output value compared to f(x).
What is the angle of the 3rd order bright fringe produced by two slits that are 5.82x10-5m apart if the wavelength of the incident light is 5.04x10-7m?
A. 0.0867o
B. 4.97o
C. 0.260o
D. 15.1o
We can use the equation for the angle of the bright fringes in a double-slit experiment. The answer is D. 15.1o.
where θ is the angle of the bright fringe, m is the order of the fringe (in this case, m=3), λ is the wavelength of the incident light, and d is the distance between the slits.
Plugging in the given values, we get:
sinθ = (3)(5.04x10^-7m)/(5.82x10^-5m) = 0.260
Taking the inverse sine of both sides, we get:
θ = sin^-1(0.260) = 15.1o
Therefore, the answer is D. 15.1o.
To find the angle of the 3rd order bright fringe, we can use the formula for the double-slit interference pattern:
mλ = d * sinθ
where m is the order number (3 in this case), λ is the wavelength of the incident light (5.04x10^-7 m), d is the distance between the slits (5.82x10^-5 m), and θ is the angle we want to find.
First, rearrange the formula to solve for the angle:
sinθ = (mλ) / d
Now, plug in the given values:
sinθ = (3 * 5.04x10^-7 m) / 5.82x10^-5 m
Calculate the result:
sinθ = 0.02594
Now, find the inverse sine (arcsin) of the result to get the angle:
θ = arcsin(0.02594) ≈ 1.49°
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The segment below is dilated by a scale factor of 2 to form I'J'. What is the measure
of I'J'?
Answer:
Submit Answer
attempt 1 out of 2
The measure of I'J' is 18 units.
We have,
Scale factor= 2
length of IJ = 9
Now, If the segment IJ is dilated by a scale factor of 2, the length of I'J' will be:
I'J' = 2 x IJ
I'J' = 2 x 9
I'J' = 18
Therefore, the measure of I'J' is 18 units.
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Ivan is an artist. He creates 1 sculpture for every 6 paintings. If he has created 54 paintings, how many sculptures has he created?
A.)324
B.)9
C.)252
D.)42
Ivan has created 9 sculptures.
We know, ratio is a comparison between two quantities or numbers. It expresses how many times one quantity is contained in another or how the two quantities relate to each other.
To find the number of sculptures he has created, we need to divide the number of paintings by the ratio of paintings to sculptures.
Number of paintings: 54
Ratio of paintings to sculptures: 6 paintings : 1 sculpture
Number of sculptures
= Number of paintings / Ratio of paintings to sculptures
= 54 / (6/1)
= 54 / 6
= 9
Therefore, Ivan has created 9 sculptures.
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What are the first five terms in the recursive sequence defined by
a1=2
a2=3
an=an-2*an-1
?
The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.
First five terms of the recursive sequence defined by a1 = 2, a2 = 3, and an = an-2 * an-1.
1. First term (a1): Given as 2.
2. Second term (a2): Given as 3.
3. Third term (a3): To find a3, use the formula an = an-2 * an-1. In this case, n = 3, so a3 = a1 * a2 = 2 * 3 = 6.
4. Fourth term (a4): Similarly, to find a4, use the formula with n = 4. So a4 = a2 * a3 = 3 * 6 = 18.
5. Fifth term (a5): Finally, to find a5, use the formula with n = 5. So a5 = a3 * a4 = 6 * 18 = 108.
The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.
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in a survey, 13 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean and standard deviation of $36 and $15, respectively. construct a confidence interval at a 95% confidence level. give your answers to one decimal place. answer should be written in e format.
Answer:
Sure. Here are the steps on how to construct a confidence interval at a 95% confidence level for the mean amount spent on a child's last birthday gift:
Identify the sample size, n. In this case, n=13.
Identify the sample mean,
x
ˉ
. In this case, $\bar{x} = $36.
Identify the sample standard deviation, s. In this case, $s = $15.
Identify the t-critical value, t. The t-critical value is the value that cuts off 2.5% of the distribution in each tail, leaving 95% of the distribution in the middle. To find the t-critical value, we need to know the degrees of freedom, df. The degrees of freedom are calculated as df=n−1. In this case, df=13−1=12.
We can find the t-critical value using a t-distribution table. The t-distribution table shows the t-critical values for different degrees of freedom and different confidence levels. For a 95% confidence level and 12 degrees of freedom, the t-critical value is 2.179.
Calculate the confidence interval. The confidence interval is calculated as follows:
$\bar{x} \pm t \cdot \frac{s}{\sqrt{n}}$
In this case, the confidence interval is:
$36 \pm 2.179 \cdot \frac{15}{\sqrt{13}} = (27.28, 44.72)$
Therefore, a 95% confidence interval for the mean amount spent on a child's last birthday gift is $27.28 to $44.72.
Step-by-step explanation:
(sinθ+cosθ)
2
−(sinθ−cosθ)
2
=2sin2θ
The trigonometric equation is (sinθ+cosθ)²−(sinθ−cosθ)² is equal to 2sin2θ
We can use the identity (a+b)² = a² + 2ab + b² to simplify the left-hand side of the equation:
The trigonometric expression is (sinθ+cosθ)²−(sinθ−cosθ)²
Expand the trigonometric expression by using the identity (a+b)² = a² + 2ab + b²
(sinθ+cosθ)² will be sin²θ + 2sinθcosθ + cos²θ
(sinθ−cosθ)² is sin²θ - 2sinθcosθ + cos²θ
Now plug in these in the above trigonometric equation
= sin²θ + 2sinθcosθ + cos²θ - (sin²θ - 2sinθcosθ + cos²θ)
= sin²θ + 2sinθcosθ + cos²θ - sin²θ + 2sinθcosθ - cos²θ
= 4sinθcosθ
= 2 × 2sinθcosθ
= 2sin2θ
Hence, the trigonometric equation is (sinθ+cosθ)²−(sinθ−cosθ)² is equal to 2sin2θ
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Which could be Brooke’s sixth quiz score? Select three options. 85
90
83
86
92
The solution is: 90, 86, 92 and 89 could be Brooke’s sixth quiz score
Here, we have,
step 1
Find the mean
To do this, add all the numbers, then divide by the number of numbers there are.
so
mean = 85.60
step 2
if after taking the sixth quiz, Brooke’s mean score increased
then
the sixth score of Brooke's quiz must be higher than the mean obtained in the first 5 quizzes
case a)
85 < 85.60------> is not a solution
case b)
90 > 85.60------> is a solution
case c)
83< 85.60------> is not a solution
case d)
86 > 85.60------> is a solution
case e)
92 > 85.60------> is a solution
case f)
89 > 85.60------> is a solution
so, we get,
the answers are
90, 86, 92 and 89
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the complete question is
Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke’s mean score increased.
Which could be Brooke’s sixth quiz score? Check all that apply.
85
90
83
86
92
89
Help please DUE TONIGHT ! You have been contracted to paint the grain silo pictured below find the combined surface area of the top and sides of the sail to determine the amount of paint needed for the job note there is no need to paint the bottom of the silo as it is resting on the ground the height of the right cylinder is twice it’s diameter round ur answer to the nearest whole number
90π m² is the combined surface area of the top and sides of the sail to determine the amount of paint needed for the job note there is no need to paint the bottom of the silo
We know that t = 12m
t= 2×diameter
12=2×diameter
6=diameter
Radius = 3m
Combined surface area = 2πrt+1/2×4πr²
=2π(3)(12)+1/2×4π(9)
=72π+18π
=90π m²
Hence, 90π m² is the combined surface area of the top and sides of the sail to determine the amount of paint needed for the job note there is no need to paint the bottom of the silo
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As the project progresses, the actual finish times (AFs) of completed activities will determine
the earliest start and earliest finish times for the remaining activities in the network diagram, as well as the total slack.
As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.
The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.
By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.
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Find the value of x. Assume that lines that
appear tangent are tangent.
X
10 15
24
The value of x in the chord intersection is 16 units.
How to find the length of chord?The intersecting chord theorem states that the products of the lengths of the line segments on each chord are equal. In other words, If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.
Therefore, lets find the value of x in the intersecting chords as follows:
15 × x = 24 × 10
15x = 240
divide both sides of the equation by 15
x = 240 / 15
x = 16
Therefore,
x = 16 units
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How to Draw a table of values for the first 6 natural numbers.
To draw a table of values for the first 6 natural numbers, draw the rows and columns and input the numbers 1, 2, 3, 4, 5, and 6 against the variables being compared.
How to draw the tableA table is a visual representation that is used to compare two or more variables. To draw this sort of table for natural numbers, you need to insert 6 rows to contain all of the numbers.
The number of columns that will e drawn depends on the variable or variables that you are checking. The first 6 natural numbers are numbers 1 to 6.
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An international speculator invests 15,800 euros at 5%, compounded daily. How much will she have after 6 years? (Round your answer to the nearest hundredth of a euro.)”
Step-by-step explanation:
Decimal interset per period (day) = .05/365
# periods = 365 *6 = 2190
FV = 15800 ( 1 + .05/365)^2190 = 21327.33 Euros
A woman drives an SUV that gets 15 mi/gal (mpg). Her husband drives a hybrid that gets 65 mg. Every week, they travel the same number of miles. They want to improve their combined mpg. They
have two options on how they can improve it.
Option 1: They can tune the SUV and increase its mileage by 1 mpg and keep the hybrid as it is.
Option 2: They can buy a new hybrid that gets 80 mpg and keep the SUV as it is.
Which option will give them a better combined mpa?
Answer:
option 2
Step-by-step explanation:
They both travel x miles per week
option 1: SUV (15 + 1)mpg + hybrid (65)mpg = 81combined mpg
option 2: SUV (15)mpg + hybrid (80) mpg = 95 combined mpg
getting 95mpg is better than 81mpg.
so they should choose option 2
Help Will give BRAINLYST How many years will it take mr sanchez to have 10,568.52 in the college fund ,if mr sanchez does not make any deposits or withdrawals
Answer:
16 years
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the number of years.
In this case, P = $5000, r = 0.05 (since the annual interest rate is 5%), n = 12 (since the interest is compounded monthly), and we need to solve for t when A = $6,568.52.
Plugging in the values, we get:
$6,568.52 = $5000(1 + 0.05/12)^(12t)
Dividing both sides by $5000 and taking the natural logarithm of both sides, we get:
ln(1.313704) = ln(1 + 0.05/12)^(12t)
Using the logarithmic identity ln(a^b) = b ln(a), we can simplify the right side:
ln(1.313704) = 12t ln(1 + 0.05/12)
Dividing both sides by 12 ln(1 + 0.05/12), we get:
t = ln(1.313704) / (12 ln(1 + 0.05/12)) = 16.0
Therefore, it will take Mr. Sanchez 16 years to have $6,568.52 in the college fund, if he does not make any deposits or withdrawals. The answer is 16 years.
registered voters are classified as democrat, republican, or independent. suppose that the percentage of voters registered as democrat and republican is 35% and 40%, respectively. (a) what percent of the registered voters are independent?
We need to use the fact that the percentages of all three categories must add up to 100%. Therefore, the percentage of independent voters can be found by subtracting the percentages of democrat and republican voters from 100%.
Percentage of independent voters = 100% - 35% - 40% = 25%
So, 25% of the registered voters are independent.
In conclusion, the percentage of independent voters is 25%. This is because the percentages of democrat, republican, and independent voters must add up to 100%. The percentages of democrat and republican voters are given, so we can find the percentage of independent voters by subtracting those from 100%.
Based on the given information, 35% of registered voters are classified as Democrats, and 40% are classified as Republicans. To find the percentage of registered voters who are independent, we need to subtract the total percentage of Democrats and Republicans from 100%.
100% - (35% + 40%) = 100% - 75% = 25%
Therefore, 25% of the registered voters are classified as independent.
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answer the questions please
The probability that the number is in set B is 20 %.
The probability that the number is in the set A ∪ B is 30 %.
What is the probability of the number chosen?If a number is chosen at random from the universal set, the probability that the number is in set B is calculated as follows;
The total number of outcome = {1, 2, 3, 4, 5, 6, 7, 8, 9 , 10} = 10 numbers
The numbers in set B = { 3, 7}
The probability = 2/10 = 1/5 = 20%
The probability that the number is in the set A ∪ B is calculated as follows;
A ∪ B = { 2, 3, 7 }
The probability = 3/10 = 30%
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a sample of 800 persons showed that 120 persons do not have any health insurance. the 95% confidence interval for the population proportion of all persons who do not have any health insurance is close to: (use at least five decimal places during your computation)
Answer:
The 95% confidence interval for the population proportion of all persons who do not have any health insurance is (0.148, 0.192).
Here is the calculation:
Sample size = 800
Number of persons who do not have any health insurance = 120
Sample proportion = 120 / 800 = 0.15
Confidence level = 95%
Z-critical value for 95% confidence level = 1.96
Confidence interval = (sample proportion - Z-critical value * standard error of the sample proportion, sample proportion + Z-critical value * standard error of the sample proportion)
Standard error of the sample proportion = sqrt(sample proportion * (1 - sample proportion) / sample size)
Standard error of the sample proportion = sqrt(0.15 * (1 - 0.15) / 800) = 0.0128
Confidence interval = (0.15 - 1.96 * 0.0128, 0.15 + 1.96 * 0.0128)
Confidence interval = (0.148, 0.192)
Step-by-step explanation:
May 03, 2023
i) y = -1/2x² + 6x + 5
2
Step-by-step explanation:
To evaluate y when x = 2 in the equation y = -1/2x² + 6x + 5, we simply substitute x = 2 into the equation and solve for y:
y = -1/2(2)² + 6(2) + 5
y = -1/2(4) + 12 + 5
y = -2 + 12 + 5
y = 15
Therefore, when x = 2, y = 15 in the equation y = -1/2x² + 6x + 5.
378=63t please i need help??
Answer: 6
Step-by-step explanation:
If you divide both sides by 63 it isolates the t and leaves you with 6=t.
An online store charges for the cost in dollars of each item sold plus a 15 shipping fee. Enter an inequality that represents c the total amount in dollars of all possible costs of items sold plus shipping fees if the total order does not exceed 345$
Answer:
15 + c ≤ 345
Step-by-step explanation:
Inequality equation:Inequality is a mathematical statement that compares two algebraic expressions using the symbols < , > , ≠ ,≤ or ≥.
'c' is the total cost of all the items sold. The total order should not exceed 345. This 345 includes the total cost and the shipping fee.
15 + c ≤ 345
help help help help help help help help help help
Answer:
7, right9, upStep-by-step explanation:
Given that vector (g, h) moves a shape g squares right and h squares up, you want the description for the vector (7, 9).
SubstitutionAs with a numerical expression, you can substitute the values for the letters in the English description. When (g, h) = (7, 9), it means "g" can be replaced by "7" and "h" can be replaced by "9". The sentence with these replacements is ...
vector (7, 9) moves a shape 7 squares right and 9 squares up
__
Additional comment
It's not math. It's reading comprehension.
<95141404393>
Find the length of the third side. If necessary, write in simplest radical form.
The length of the third side is 4.
Given information:
A right-angled triangle is provided in the diagram.
So, as per the diagram,
The hypotenuse leg = √(97)
Opposite leg = 9
Let the length of the adjacent leg, which is the third side be x. By the Pythagorean theorem, we have:
x² + 9² = √(97)²
Simplifying the right side, we get:
x² + 81 = 97
Subtracting 81 from both sides, we get:
x² = 16
Apply square root property, we get,
x = +/- 4
Since the length of a side of a triangle must be positive, the length of the third side is 4.
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50 POINTSS! I NEED HELPP if the coach bases her decisions on the player Who is most consistent, whom should she choose? Justify your answer using measures of variability
If the coach was to pick the player based on the best average, the coach would choose Jessie.
If the coach is picking based on who has been the most consistent, they would pick Sam.
How the coach would decide ?The average for Jessie is :
= ( 150 + 145 + 181 + 235 + 196 + 211 + 204 + 221 + 185 ) / 9
= 192 points
The average for Sam :
= ( 186 + 187 + 192 + 195 + 194 + 157 + 157 + 162 + 200 ) / 9
= 181 points
The coach would pick Jessie based on average.
For consistency, we can use the measure of variability of range. The range for Jessie is:
= 235 - 145
= 90 points
The range for Sam would be:
= 200 - 157
= 43 points
This shows that Sam is more consistent and so would be picked based on consistency.
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Unlike the traditional IQ test, a group of researchers have designed new IQ questions
testing for the 9 different types of intelligence. The distribution of IQ scores using the new test for high
school students is normally distributed with a mean of 80 points and a standard deviation of 12 points.
Use technology to find the following. (Note: for full credit, write correct probability notation)
(a) Find the probability to 3 decimal places that a high school student chosen at random has an IQ
score between 60 to 75 points, inclusive.
(b) A student will need special attention if the student’s IQ score is below 55 (at most 54) or above
100 (at least 101). What proportion of the high school students will need special attention?
Hint: Look carefully at the bolded phrases.
(c) Mensa International is the largest and oldest high IQ society in the world. Members of this
society are individuals who score at the 98th percentile or higher on this new IQ test. Determine the
cutoff IQ score (it must be a whole number) to be a member of Mensa International.
(a) The probability of a random high school student having an IQ score between 60 and 75 points is approximately 0.186. (b) About 6.5% of high school students will require special attention based on IQ scores below 55 or above 100 points. (c) The cutoff IQ score to be a member of Mensa International is approximately 105.
To solve these problems, we will use the standard normal distribution, also known as the Z-distribution. We'll need to calculate z-scores and use the z-table or technology to find probabilities.
(a) To find the probability that a high school student chosen at random has an IQ score between 60 and 75 points, inclusive, we need to calculate the area under the normal curve between these two values.
First, we convert the IQ scores to z-scores using the formula:
z = (x - μ) / σ
where x is the value we want to convert, μ is the mean, and σ is the standard deviation.
For 60 points:
z1 = (60 - 80) / 12 = -1.6667
For 75 points:
z2 = (75 - 80) / 12 = -0.4167
Next, we use technology or a z-table to find the probabilities associated with these z-scores:
P(-1.6667 ≤ Z ≤ -0.4167)
Using technology or a z-table, the probability comes out to be approximately 0.186.
Therefore, the probability that a high school student chosen at random has an IQ score between 60 and 75 points, inclusive, is 0.186.
(b) To find the proportion of high school students who will need special attention, we need to calculate the area under the normal curve below 55 points (z ≤ (55 - 80) / 12) and above 100 points (z ≥ (100 - 80) / 12).
P(Z ≤ -2.0833) + P(Z ≥ 1.6667)
Using technology or a z-table, we find the probabilities:
P(Z ≤ -2.0833) ≈ 0.018
P(Z ≥ 1.6667) ≈ 0.047
Adding these probabilities, the proportion of high school students who will need special attention is approximately 0.018 + 0.047 = 0.065.
Therefore, about 6.5% of high school students will need special attention.
(c) To determine the cutoff IQ score to be a member of Mensa International, we need to find the value corresponding to the 98th percentile of the standard normal distribution.
We want to find the IQ score x such that P(Z ≤ z) = 0.98.
Using technology or a z-table, we find the z-score corresponding to a cumulative probability of 0.98 is approximately 2.055.
Now, we solve for x in the z-score formula:
2.055 = (x - 80) / 12
Simplifying and solving for x:
24.66 = x - 80
x = 24.66 + 80
x ≈ 104.66
Therefore, the cutoff IQ score to be a member of Mensa International would be 105 (rounded to the nearest whole number).
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what is the fomula of perimeter, area and volume
There are several formulas for finding the area, volume, and perimeter of different shapes. Some examples are: [tex]P = 2(l + w)[/tex], [tex]A = lw[/tex], and [tex]V = lwh[/tex]
What are the formulas to find the perimeter, area and volume of the different geometric figures?Perimeter:
Perimeter of a rectangle: [tex]P = 2(l + w)[/tex] where l is the length and w is the width.Perimeter of a square: [tex]P = 4s[/tex] where s is the length of a side.Perimeter of a circle: [tex]P = 2\pi r[/tex] where r is the radius.Area:
Area of a rectangle: [tex]A = lw[/tex] where l is the length and w is the width.Area of a square: [tex]A = s^2[/tex] where s is the length of a side.Area of a circle: [tex]A = \pi r^2[/tex] where r is the radius.Volume:
Volume of a rectangular prism: [tex]V = lwh[/tex] where l is the length, w is the width, and h is the height.Volume of a cube: [tex]V = s^3[/tex] where s is the length of a side.Volume of a cylinder: [tex]V = \pi r^2\pi[/tex] where r is the radius and h is the height.Note: This question is incomplete. Here is the complete question:
What is the formula of perimeter, area and volumen of rectangle, square, and circle
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On the basis of a survey of 1000 families with six ​children, the probability of a family having six girls is 0.0054.
A.Empirical method
B.Classical method
C.Subjective method
D.It is impossible to determine which method is used.
The method used to determine the probability of a family having six girls, based on a survey of 1000 families with six children, is the classical method.
The classical method involves calculating probabilities based on the assumption of equally likely outcomes and known sample spaces. In this case, the sample space consists of all possible combinations of genders for six children, and the probability of a family having six girls is calculated as the ratio of the favorable outcome (one specific combination) to the total number of outcomes (all possible combinations).
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What is the sum for the 4th and 6th square numbers
The sum of the 4th and 6th square numbers is 52.
How to find the sum of the square numbers requiredThe formula for the nth square number is as below
n²
Using this formula we can find the 4th and 6th square numbers
4th square number = 4² = 16
6th square number = 6² = 36
The sum of the 4th and 6th square numbers is solved by addition
16 + 36 = 52
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20 points for answering this
Answer: 90
Step-by-step explanation:
c(n,r) is the number of subsets of r elements each that can be formed from a set of n elements. true or false
True.
The expression c(n,r), also known as "n choose r" or the binomial coefficient, represents the number of ways that r elements can be selected from a set of n elements without regard to order. It is commonly used in combinatorics, probability, and statistics. The formula for c(n,r) is c(n,r) = n!/r!(n-r)!, which can be calculated using factorials.
For example, c(5,2) = 10, which represents the number of ways to choose 2 elements from a set of 5 elements (i.e., {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4}, {3,5}, {4,5}).
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Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately . f(x) = 3 and g(x) = x – 2 3 = x – 2 5 = x The x-value at which the two functions’ values are equal is . please
explanation
Note that the input value for which the statement f(x) = g(x) is true are
3.5 and 10/3
How is this so?In this question , we have a graph given, and we have to find the x coordinate of the intersection point .
From the graph , the input value is approximately 3.3 .
In the graph, f(x) = 3
And for g(x), we need the slope and y intercept .
Slope is the ratio of rise and run .
Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .
So the equation of g(x) = (3/2)x - 2
Since we need to factor f(x) = g(x)
Substituting the values of the two functions, we will get
3 = (3/2)x - 2
Adding 2 to both sides
5 = (3/2)x
Cross multiply and you have
10 = 3x
x = 10/3
So the input value for which the statement f(x) = g(x) is true are
3.5 and 10/3
Learn more about input values;
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