Answer:
Step-by-step explanation:
To determine if the point (4,1) is a solution for the system of equations, we need to substitute the values of x and y from the point into both equations and check if the equations hold true.
For the first equation, y = -x + 5, we substitute x = 4 and y = 1:
1 = -(4) + 5
1 = -4 + 5
1 = 1
The equation holds true for the first equation.
For the second equation, y = 2x - 7, we substitute x = 4 and y = 1:
1 = 2(4) - 7
1 = 8 - 7
1 = 1
The equation also holds true for the second equation.
Since the point (4,1) satisfies both equations, it is indeed a solution to the system of equations.
The following data represents the number of days absent and the final grade for a sample of college students in a
Math 241 course.
r=
Number of Days Absent
Final Grade in Course
y =
O
1
y =
2
X+
3
4
89.2 83.5 84.8 82.6 76.9
5
82.3
where the number of days absent is the explanatory variable and the final grade is the response variable.
Determine the linear correlation coefficient. (Round to decimal places)
c.) Determine the equation of the regression line. (Round values to four decimal places)
6
7
b.) Does the linear correlation coefficient suggest a strong positive, strong negative, weak positive, or weak negative
linear correlation?
81.2 79.3 73.5
8
d.) Use the regression line to calculate the best predicted final grade for a student who misses 5 days of
class. (Round to one decimal place)
a) The least squares regression line for the given data is y = -3.5358x + 87.2857.
b) The slope of -3.5358 indicates that for each additional day absent, the final grade is expected to decrease by approximately 3.5358 points on average.
c) The y-intercept of 87.2857 represents the estimated final grade when the number of absences is zero, implying that a student who did not miss any classes is expected to have a final grade of approximately 87.2857.
a) To find the least squares regression line, we need to determine the equation of the line in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's calculate the necessary sums:
∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
∑y = 89.2 + 86.4 + 83.5 + 81.1 + 78.2 + 73.9 + 64.3 + 71.8 + 65.5 + 66.2 = 759.9
∑xy = (0 * 89.2) + (1 * 86.4) + (2 * 83.5) + (3 * 81.1) + (4 * 78.2) + (5 * 73.9) + (6 * 64.3) + (7 * 71.8) + (8 * 65.5) + (9 * 66.2) = 5079.6
∑[tex]x^2[/tex] = [tex](0^2) + (1^2) + (2^2) + (3^2) + (4^2) + (5^2) + (6^2) + (7^2) + (8^2) + (9^2)[/tex] = 285
[tex]\sum y^2 = (89.2^2) + (86.4^2) + (83.5^2) + (81.1^2) + (78.2^2) + (73.9^2) + (64.3^2) + (71.8^2) + (65.5^2) + (66.2^2) = 59718.63[/tex]
Using the formulas for the slope (m) and y-intercept (b):
m = (n∑xy - (∑x)(∑y)) / (n∑x^2 - (∑x)^2)
b = (∑y - m(∑x)) / n
Substituting the calculated values:
m = (10 * 5079.6 - (45 * 759.9)) / (10 * 285 - (45)^2)
b = (759.9 - m(45)) / 10
Calculating the values:
m ≈ -3.5358
b ≈ 87.2857
Therefore, the least squares regression line is y = -3.5358x + 87.2857.
b) The slope (-3.5358) represents the change in the final grade (y) for each additional day absent (x). This means that on average, for each additional day a student is absent, their final grade is expected to decrease by approximately 3.5358 points.
c) The y-intercept (87.2857) represents the estimated final grade when the number of absences (x) is zero. In other words, it is the predicted final grade for a student who did not miss any classes.
for such more question on regression line
https://brainly.com/question/732489
#SPJ8
Question
The following data represents the number of days absent, x, and the final grade, y, for a sample of college students at a community college.
No.of absences, x | 0 1 2 3 4 5 6 7 8 9
Final Grade, y | 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
a) Find the least squares regression line treating the number of absences as the explanatory variable and the final grade as the response variable.
b) Interpret the slope using complete sentences.
c) Interpret the y intercept using complete sentences.
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel.
The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that
changes a 1 to a 0 with probability 0.1 and changes a 0 to a 1 with probability 0.2. Show your work below.
a. What is the probability a 1 is received?
b. If a 1 is received, what is the probability a 0 was sent?
Answer:
A: the probability that a 1 is received is 0.56.
B: the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
Step-by-step explanation:
To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.
a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.
Let's denote:
P(1 sent) = 0.6 (probability a 1 is sent)
P(0→1) = 0.2 (probability a 0 is flipped to 1)
P(1 received) = ?
P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)
= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)
= 0.6 * (1 - 0.2) + 0.4 * 0.2
= 0.6 * 0.8 + 0.4 * 0.2
= 0.48 + 0.08
= 0.56
Therefore, the probability that a 1 is received is 0.56.
b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.
Let's denote:
P(0 sent) = ?
P(1 received) = 0.56
We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).
Using Bayes' theorem:
P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)
P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08
P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56
Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):
P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56
Simplifying:
P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56
= 0.08 * (1 - P(0 sent)) * (1 / 0.56)
= 0.08 * (1 - P(0 sent)) * (25/14)
= (2/25) * (1 - P(0 sent))
Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?
What is the answer? As the last one is incorrect
The best measure of center of the data is (a) mean; because the data are close together
How to determine the best measure of center of the dataFrom the question, we have the dataset of 10 values
In the given dataset, we can see that there are no outliers present in the dataset
By definition, outliers are extreme values.
Since there are no outliers, it means that the mean is the best measure of center
This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean
From the list of options, we have the mean value to be 42.536
Hence, the true statement is (a)
Read more about mean and median at:
https://brainly.com/question/14532771
#SPJ1
In circle M below, diameter AC, chords AB and BC, and radius MB
are drawn.
The statement which is not true about the circle M is ∆ABM is isosceles.
The correct answer choice is option 2.
Which statement is not true?Based on the circle M;
diameter AC,
chords AB and BC,
radius MB
Isosceles triangle: This is a type of triangle which has two equal sides and angles.
Equilateral triangle is a triangle which has three equal sides and angles.
Hence, ∆ABM is equilateral triangle.
Read more on triangles:
https://brainly.com/question/1058720
#SPJ1
i don't understand how to do this.. can someone help, please
The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:
m∠1 = 60°.m∠2 = 120°.m∠3 = 60°.What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
Note: Assuming angle 1 is equal to 60 degrees.
In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:
m∠1 ≅ m∠3 = 60°.
Based on the linear pair postulate, the measure of angle 2 can be determined as follows;
m∠1 + m∠2 = 180°
60° + m∠2 = 180°
m∠2 = 180° - 60°
m∠2 = 120°
Read more on parallel lines here: https://brainly.com/question/12783631
#SPJ1
Graph the function f(x)= 3+2 in x and its inverse from model 1.
The graph of the function and its inverse is added as an attachment
Sketching the graph of the function and its inverseFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3 + 2ln(x)
Express as an equation
So, we have
y = 3 + 2ln(x)
Swap x and y in the above equation
x = 3 + 2ln(y)
Next, we have
2ln(y) = x - 3
Divide by 2
ln(y) = (x - 3)/2
Take the exponent of both sides
[tex]y = e^{\frac{x - 3}{2}}[/tex]
Next, we plot the graphs
The graph of the functions is added as an attachment
Read more about functions at
brainly.com/question/2456547
#SPJ1
Calculate the mean of the following data x 5 ,10 ,15, 20, 25, f 3, 2 ,6, 4 ,8.
The overall mean would be the average of the means of the two sets, which is 9.8.
To calculate the mean of a set of data, you need to sum up all the values and divide by the total number of values. In this case, we have two sets of data: the first set is {5, 10, 15, 20, 25}, and the second set is {3, 2, 6, 4, 8}.
For the first set, the sum of the values is 5 + 10 + 15 + 20 + 25 = 75. There are 5 values in this set. So, the mean of the first set is 75 divided by 5, which equals 15.
For the second set, the sum of the values is 3 + 2 + 6 + 4 + 8 = 23. There are 5 values in this set as well. Therefore, the mean of the second set is 23 divided by 5, which equals 4.6.
To find the overall mean, we need to calculate the weighted average of the means of the two sets. Since we don't have information about the weights assigned to each set, we cannot provide an exact overall mean.
However, if both sets have equal importance, we can assume equal weights. In that case, the overall mean would be the average of the means of the two sets, which is (15 + 4.6) / 2 = 9.8.
Please note that without information about the weights assigned to each set, this assumption of equal weights is arbitrary, and the overall mean could differ if the weights are different.
For more such questions on mean
https://brainly.com/question/1136789
#SPJ8
Simplify the f(x) and g(x)
Answer:
(fg)(x) = x^4 - x^3 + 15x^2 - 6x + 54
Step-by-step explanation:
We want to multiply and simplify as much as possible:
f(x) * g(x)
(x^2 + 6)(x^2 - x + 9)
(x^2 * x^2) + (x^2 * - x) + (x^2 * 9) + (6 * x^2) + (6 * - x) + (6 * 9)
Note that when you're multiplying exponents, we add them:
x^4 + - x^3 + 9x^2 + 6x^2 - 6x + 54
Now we add 9x^2 and 6x^2 as they are like terms:
x^4 - x^3 + 15x^2 - 6x + 54
Thus, (fg)(x) simplified is x^4 - x^3 + 15x^2 - 6x + 54.
Optional: Check the validity of the answer:
We can check that our answer is correct by plugging in a number for x in both the unsimplified and simplified expression and seeing if we get the same answer. Let's try 5:
Plugging in 5 for x in (x^2 + 6)(x^2 - x + 9):
(5^2 + 6)(5^2 - 5 + 9)
(25 + 6)(25 - 5 + 9)
(31)(20 + 9)
(31)(29)
899
Plugging in 5 for x in x^4 - x^3 + 15x^2 - 6x + 54:
5^4 - (5)^3 + 15(5)^2 - 6(5) + 54
625 - 125 + 15(25) - 30 + 54
625 - 125 + 375 - 30 + 54
500 + 375 - 30 + 54
875 - 30 + 54
845 + 54
899
Thus, our answer is correct.
Please help!! I need the answer asap !! I will give 10 points
Answer: A. g(x) = 4∛x
Step-by-step explanation:
First, g(x) passes through the origin (0,0)
g(0) = 0
A,g(x) = ∛x+4, g(0) = 4 ≠ 0
B,g(x) = ∛x+4, g(0) = ∛4≠0
So exclude A and B
Second, as can be seen in the figure,
The g(x) image is the magnification of the f(x) image on the y value.
f(x) = ∛x
So, Select A. g(x) = 4∛x quadruple the y value.
Find the area of the triangle below be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
A coffee place is selling coffees for $2.50 each and cappuccinos for $3.75 each.
Today the coffee place sold a total of 70 drinks (coffees and cappuccinos) for a total of $222.50.
a) Write an equation that represents the information.
b) Solve the equation in (a) to find how many coffees and how many cappuccinos the coffee place sold today.
Answer:
Step-by-step explanation:
a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.
The equation that represents the given information is:
2.50x + 3.75y = 222.50
b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.
Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.
Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):
2.50(40) + 3.75y = 222.50
100 + 3.75y = 222.50
3.75y = 222.50 - 100
3.75y = 122.50
y = 122.50 / 3.75
y ≈ 32.67
In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.
We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.
Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.
3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work
The triangles DEF and SRQ are not similar triangles
Identifying the similar triangles in the figure.From the question, we have the following parameters that can be used in our computation:
The triangles in this figure are
DEF and SRQ
These triangles are not similar
This is because:
The corresponding angles in the triangles are not equal
For DEF, the angles are
50, 90 and 40
For SRQ, the angles are
51, 90 and 39
This means that they are not similar by any similarity statement
Read mroe about similar triangles at
brainly.com/question/31898026
#SPJ1
3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3: Defining Mathematics - in your study guide and provide the
differences between the three views used to outline the mathematics consideration.
(10)
The views shown in section 1.3, that are used to outline the mathematics consideration are:
Formalist Intuitionist Platonist How do these outlines compare ?The main difference between the three views is their stance on the nature of mathematical objects. The formalist view sees mathematical objects as abstract symbols that have no meaning outside of the formal system.
The intuitionist view sees mathematical objects as mental constructs that are derived from intuition. The Platonist view sees mathematical objects as abstract entities that exist independently of the human mind.
Another difference between the three views is their stance on the relationship between mathematics and the physical world. The formalist view sees mathematics as independent of the physical world.
The intuitionist view sees mathematics as being influenced by the physical world, but not completely determined by it. The Platonist view sees mathematics as being completely independent of the physical world.
Find out more on formalist outline at https://brainly.com/question/30165617
#SPJ1
Problem
Express
0.0939
0.09390, point, 0939 as a fraction.
Answer:
m
Step-by-step explanation:
16
Find x.
25
X
X
x = [?]√]
The value of x in the right triangle using pthagorean theorem is 3√41.
What is the value of x?The figure in the image is that of a right triangle with of its interior angle at 90 degrees.
Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the figure:
Hypotenuse c = 25
Leg a = 16
Leb b = x
Plug these values into the above formula and solve for x:
c² = a² + b²
25² = 16² + x²
625 = 256 + x²
x² = 625 - 256
x² = 369
Take the square root( we use the positive value because its dimension ).
x = √369
x = 3√41
Therefore, the value of x is 3√41.
Learn more about Pythagorean theorem here: brainly.com/question/343682
#SPJ1
A rectangular pyramid is sliced. The slice passes through line segment AB and is parallel to the base.
Which two-dimensional figure represents the cross section?
A. A rectangle the same size as the base
B. A rectangle that is smaller than the base
C. A quadrilateral that is not a rectangle
D. A triangle with a height the same as the pyramid
Answer:
Step-by-step explanation:
The correct answer is A. A rectangle the same size as the base.
When a rectangular pyramid is sliced parallel to the base, the resulting cross-section is a rectangle that is the same size as the base. The parallel slicing ensures that the cross-section maintains the same dimensions as the base of the pyramid. Therefore, option A, a rectangle the same size as the base, represents the cross-section.
En un punto de un cuerpo rigido se aplica una fuerza F = (4.501 - 3.25) N. Determine el torque que
experimenta dicho cuerpo si el radio vector trazado desde el punto de aplicación de la fuerza al punto de
giro es r = (1.801 + 2.50j) m
The torque experienced by the rigid body is -17.10375 k N·m.
To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.
Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:
Torque = r x F
The cross product between two vectors is calculated as follows:
Torque = (r_x * F_y - r_y * F_x)k
Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.
Substituting the given values, we have:
Torque = ((1.801 * -3.25) - (2.50 * 4.501))k
Calculating the cross product:
Torque = (-5.85125 - 11.2525)k
Simplifying:
Torque = -17.10375k
Therefore, the torque experienced by the rigid body is -17.10375 k N·m.
The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.
for more such question on experienced visit
https://brainly.com/question/22485808
#SPJ8
State whether the function graphed is continuous on [-1,4]. If not, where does it fail to be continuous and why?
Answer: C
Step-by-step explanation:
The function exists at all points on the interval with no discontinuities (such as jump discontinuities).
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. What is the maximum area of a Norman window whose perimeter is 9 feet?
The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:
πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:
A = (πr^2)/2 + rh
To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:
r = (9 - 2h)/(π)
Now we can rewrite the area function in terms of h only:
A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)
Simplifying this equation, we get:
A = (1/2)(9h - h^2/π)
To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:
dA/dh = 9/2 - h/π = 0
Solving this equation, we find:h = 9π/2
Substituting this value of h back into the area function, we get:
A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4
Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
Learn more about area here:
https://brainly.com/question/2607596
#SPJ8
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:B
Step-by-step explanation:
Find the missing side. 30° 23 x = [?] Round to the nearest tenth. Remember: SOHCAHTOA
Answer:
x = 11.5
Step-by-step explanation:
using the sine ratio in the right triangle
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{23}[/tex] ( multiply both sides by 23 )
23 × sin30° = x , then
x = 11.5
or In 2010, Ryan paid $1,112 in federal income tax, which is 80% less than he paid in 2009. How much did he pay in 2009?
Ryan paid $5,560 in 2009.
Let's solve the problem using the given information: Amount paid in 2010 by Ryan = $1,112 Amount paid in 2010 is 80% less than the amount paid in 2009.
So, the amount paid in 2009 can be calculated as follows: Let x be the amount paid by Ryan in 2009.
Then we can write, $1,112 = x - 0.8x Simplifying this expression, we get:$1,112 = 0.2x Dividing both sides of the equation by 0.2, we get: x = $5,560
Therefore, Ryan paid $5,560 in 2009. I hope this helps.
For more such questions on expression
https://brainly.com/question/1859113
#SPJ8
it is my first time taking my baby to the cinemas in Junes 2023, and the cinemas have sales because there are tons of kids' movies to be seen. For adults the ticket costs 70$ and for children it costs 30$, which tickets sell like 1000$ a day leading to 31000 a month. Calculate the number of tickets that were sold for adults and children in a day. A+C=1000 70+30=31000.
A+C=1000
70+30=31000
if we wanted to extend this discussion beypnd what has been shared so far, what additional question could we ask?
Step-by-step explanation:
If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:
"What is the ratio of adult tickets to children's tickets sold in a day?"
This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.
Find the value of x.
I am a 6 digit number my highest place value and my lowest place value has a number equals to the number of days in a week my hundreds place is equal to the half it dozen
my turns place easy number of sides of a triangle by 1000 space is equal to the number of pose of earth and 10000 place is equal to result of subtracting any number from itself
Answer:
The description provides the clues for each digit in a 6-digit number. Let's break it down:
1. Highest place value and lowest place value has a number equals to the number of days in a week: There are 7 days in a week, so the first and last digits are 7.
2. Hundreds place is equal to half a dozen: Half a dozen is 6, so the third digit from the right (hundreds place) is 6.
3. Tens place is the number of sides of a triangle: A triangle has 3 sides, so the second digit from the right (tens place) is 3.
4. Thousands place is equal to the number of poles of earth: Earth has two poles, so the second digit from the left (thousands place) is 2.
5. Ten thousands place is equal to result of subtracting any number from itself: Subtracting any number from itself yields 0, so the third digit from the left (ten thousands place) is 0.
Putting it all together, the 6-digit number would be: 702,637.
You are typing a paper. At 4:04pm you have typed 275 words. By 4:18pm you have typed 765 words. Find the rate of change in words per minute. Round your answer to the nearest whole number.
Answer:
35
Step-by-step explanation:
18-4 = 14 minutes
number of words typed in 14 minutes is 765-275= 490 words
490 words/14 mins= appox 35
Suppose a finite population has 6 items and 2 items are selected at random without replacement,then all possible samples will be:
Select one:
a. 15
b. 2
c. 36
d. 6
e. 12
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
When 2 items are selected without replacement from a population of 6 items, there are 15 possible samples that can be formed. Option A.
To determine the number of possible samples when 2 items are selected at random without replacement from a population of 6 items, we can use the concept of combinations.
The number of combinations of selecting k items from a set of n items is given by the formula C(n, k) = n! / (k! * (n-k)!), where n! represents the factorial of n.
In this case, we have a population of 6 items and we want to select 2 items. Therefore, the number of possible samples can be calculated as:
C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15. Option A is correct.
For more such question on samples. visit :
https://brainly.com/question/13219833
#SPJ8
Which are the roots of the quadratic function f(b) = b² - 75? Select two options.
Ob=5√3
Ob=-5√3
Ob=3√5
Ob=-3√5
Ob=25√3
The two roots of the quadratic function f(b) = b² - 75 are:
b = 5√3 and b = -5√3What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
We have
[tex]f(b) = b^2 - 75[/tex]Remember that the root of a function is the value of x when the value of the function is equal to zero.
In this problem
The roots are the values of b when the function f(b) is equal to zero.
So,
For f(b)=0
[tex]b^2-75=0[/tex]
[tex]b^2=75[/tex]
Square root both sides
[tex]b=(+/-)\sqrt{75}[/tex]
Simplify
[tex]b=(+/-)5\sqrt{3}[/tex]
[tex]b=5\sqrt{3}[/tex] and [tex]b=-5\sqrt{3}[/tex]
Therefore
[tex]\rightarrow\bold{b = 5\sqrt{3}}[/tex]
[tex]\rightarrow\bold{b=-5\sqrt{3}}[/tex]
Learn more about the quadratic function at:
https://brainly.com/question/30929439
What is the range of this function?
The range of the given graph is expressed as:
Option A: {-∞, ∞}
What is the range of the given function?The range of a function is defined as the set of all the possible output values of y. The formula to find the range of a function is y = f(x).
In a relation, it is only a function if every x value corresponds to only one y value,
Now, looking at the given graph, we see that At x = 0, the function is also y = 0.
However, between 0 and π intervals, we see that the graph approaches positive and negative infinity and as such we can tell that the range is expressed as: {-∞, ∞}
Read more about Range of Function at: https://brainly.com/question/7954282
#SPJ1
Given the graphs of y = f(x) and y = g(x),
g(x) = f(x) +
expresses g(x) in terms of f(x)
The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).
To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.
The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).
In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:
g(x) = f(x) + c
In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).
It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).
Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).
for such more question on functions
https://brainly.com/question/16332322
#SPJ8
Answer: 3
Step-by-step explanation: just 3
Edge 2020
