65% of men consider themselves knowledgeable soccer fans. If 12 men are randomly selected, find the probability that exactly 7 of them will consider themselves knowledgeable fans. Also, calculate the mean and standard deviation of this binomial distribution.
Answers
Answer
Question 1:
The probability that 7 men would consider themselves knowledgeable is 0.20392
Question 2:
The Mean and Standard Deviation of the distribution are 7.8 and 1.6523
SOLUTION
Problem Statement
We are told 65% of men consider themselves knowledgeable soccer fans. We are told that 12 men are randomly chosen.
1. We are required to find the probability that 7 of them will consider themselves knowledgeable.
2. We are also required to find the mean and standard deviation of this survey of 12 men.
Method
To solve this question, we need to know 3 things outlined below:
1. Binomial probability formula:
This formula is used to calculate the probability of a particular event occurring after multiple trials. In the case of this question, one event is asking 1 man if he considers himself knowledgeable. Thus, asking 12 men results in multiple trials and leads to Binomial probability being invoked.
The formula to calculate this probability is:
\(\begin{gathered} P=^nC_rp^rq^{n-r} \\ \text{where,} \\ p=\text{probability of success (In this case, probability of 7 men claiming to be knowledgeable)} \\ q=\text{probability of failure}=1-p \\ n=\text{ Number of possible trials (In this case, 12)} \\ r=\text{ Number of occurrence of an event (In this case, 7)} \end{gathered}\)2. Mean of a Binomial distribution:
\(\begin{gathered} \mu=np \\ \text{where,} \\ n=\text{ Number of possible trials} \\ p=\text{ }The\text{ probability of success.} \end{gathered}\)3. Standard deviation of a Binomial Distribution
\(\sigma=\sqrt[]{\text{npq}}\)Implementation
Question 1:
The probability that 7 of the men will consider themselves knowledgeable is:
\(\begin{gathered} p=65\text{ \%}=\frac{65}{100}=0.65 \\ q=1-p=1-\frac{65}{100}=0.35 \\ n=12 \\ r=7 \\ \\ \therefore P=^nC_rp^rq^{n-r} \\ P=^{12}C_7\times0.65^7\times0.35^{12-7} \\ P=792\times0.0490223\times0.0052522 \\ P=0.20392 \end{gathered}\)Therefore, the probability that 7 men would consider themselves knowledgeable is 0.20392
Question 2:
The Mean and Standard deviation are gotten as follows:
\(\begin{gathered} p=0.65 \\ n=12 \\ q=1-p,q=1-0.65\implies q=0.35 \\ \\ \therefore Mean(\mu)=np=0.65\times12=7.8 \\ \\ \text{ Standard deviation (}\sigma)=\sqrt[]{\text{npq}}=\sqrt[]{12\times0.65\times0.35} \\ \therefore\sigma=1.6523 \end{gathered}\)Final Answer
Question 1:
The probability that 7 men would consider themselves knowledgeable is 0.20392
Question 2:
The Mean and Standard Deviation of the distribution are 7.8 and 1.6523
Related Questions
HW3 Applying the Pythagorean theorem
Tony is building a dog house, and the front view of the roof is shown below. What is the height of the roof?
25 inches
41 inches
21 inches
20 inches
40 inches
29 inches
Answers
By using Pythagoras theorem we get the height of the roof of dog house is 21 inches.
What is Pythagoras theorem?The Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
This theorem is named after the Greek philosopher Pythagoras, who lived around 570 BC. born.
According to the question:
Given, Hypotenuse(h) = 29 inches
Base(b) = 40/2 = 20 inches
Using Pythagoras theorem, we get
h² = b² + p²
⇒ 29² = 20² + p²
⇒ p² = 29² - 20²
⇒ p² = 841 - 400
⇒ p² = 441
⇒ p = √441
⇒ p = 21
∴ The height of the roof of dog house is 21 inches.
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Need help with proofs, anyone know how?
Answers
Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.
Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;
MS ≅ QSNS ≅ RSMN ≅ QN ∠NMS and ∠NQSΔMNS ≅ ΔQNSRead more on perpendicular bisectors here: brainly.com/question/19154899
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Complete Question:
The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS
We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.
NS and NS
NS and RS
MS and RS
MS and QS
What is the period of y = sin(3x)?
Answers
Answer:
The new period is 23π
Answer:
2pi/3
Edge 2023
Which similarity statement and postulate or theorem correctly identifies the relationship?
B
D
12
E
86°
860
15
14
5
A
C
ОА
AABC - AFED by SSS Similarity Theorem
OB
AABC - ADEF by SAS Similarity Theorem
OC
AABC - AFED by AÁS Similarity Theorem.
OD
AABC - ADEF by AA Similarity Theorem
Answers
Answer:
It is side angle side
Step-by-step explanation:
The two sides of the triangle are around the angle
The similarity theorem that identifies the given relationship correctly would be:
B). AABC - ADEF by SAS Similarity Theorem
What is SAS Similarity?The SAS similarity Theorem state that in the situation where the ratio shared by the sides of two triangles remains the same and one of their angles stays equal, both the triangles would be similar.
In the given two triangles,
ΔABC and ΔDEF
The ratio of the sides are:
\(\frac{BC}{AB} = \frac{EF}{DE}\)
so,
\(\frac{5}{15} = \frac{4}{12} = \frac{1}{3}\)
and,
∠B = ∠E = 86°
Since the ratios shared by the two sides are equal in both the given triangles and one angle is equal, the triangles are the same.
Thus,
ΔABC ~ ΔDEF
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Let f(k) = 7k6 + 6k - 10 and g(k) = -366 - 7k + 1. Find the difference (f - g)(k).
Answers
Correct question is;
Let f(k) = 7k^(6) + 6k - 10 and g(k) = -3k^(6) - 7k + 1. Find the difference (f - g)(k).
Answer:
(f - g)(k) = 10k^(6) + 13k - 9
Step-by-step explanation:
We are given;
f(k) = 7k^(6) + 6k - 10
g(k) = -3k^(6) - 7k + 1
Thus;
(f - g)(k) = 7k^(6) + 6k - 10 - ( -3k^(6) - 7k + 1)
(f - g)(k) = 7k^(6) + 6k - 10 + 3k^(6) + 7k - 1)
(f - g)(k) = 10k^(6) + 13k - 9
You draw a rectangle with vertices at (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).
What is the perimeter and area of the rectangle?
Answers
The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).
The length of the rectangle is:
l = 3.5 - (-3.5)
l = 3.5 + 3.5
l = 7
The width of the rectangle is:
w = 3-(-3)
w = 3 + 3
w = 6
The perimeter of the rectangle is given by:
P = 2 (l +w)
P = 2(7 + 6)
P = 26
The area of the rectangle is:
A = l × w
A = 7 × 6
A = 42
Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.
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A marble is selected from a bag containing eight marbles numbered 1 to 8. The number of the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event A.
Answers
Even numbers: 2, 4, 6, 8
Numbers from 3 to 6: 3, 4, 5, 6
Combining these sets and removing duplicates, we have the following outcomes: 2, 3, 4, 5, 6, 8. So, event "A or B" includes these outcomes.
b) Event "A and B" refers to the marble selected having both an even number and a number from 3 to 6. To determine the outcomes that satisfy this event, we need to find the numbers that meet both conditions.
Numbers that are both even and from 3 to 6: 4, 6
Therefore, event "A and B" includes the outcome of either 4 or 6.
c) The complement of event A refers to outcomes that are not part of event A. Since event A represents the marble selected having an even number, the complement of event A would be the marble selected having an odd number.
Odd numbers: 1, 3, 5, 7
Therefore, the complement of event A includes these outcomes.
A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
Step-by-step explanation:MAKE A PLAN:
List The OUTCOMES for EACH EVENT and their COMBINATIONS:
SOLVE THE PROBLEM:a) - EVENT "A": {2, 4, 6, 8}
EVENT "B": {3, 4, 5, 6}
EVENT "A" or "B": {2, 3, 4, 5, 6, 8}
b) - EVENT "A" or "B": {4, 6}
c) - The COMPLEMENT of the EVENT "A": {1, 3, 5, 7}
Draw the conclusion:A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
I hope this helps!
Translate the following sentence to an inequality.A number is no less than seven.On<7Ons7On27On>7
Answers
Here, we want to translate the sentence into an inequality
The sentence is that a number n is no less than 7
What this mean is that although the number can be equal to 7, it is not less than 7
The inequality is thus;
\(n\text{ }\ge\text{ 7 or 7 }\leq\text{ n}\) ASAP please!! What is the best approximation for one of the relative minimums of the
polynomial function graphed below?
Answers
Answer: C
Step-by-step explanation: Brainliest please
Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
Answers
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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Assuming that heights of professional male tennis players follow a bell-shaped distribution, arrange in ascending order.
I. A height with a z-score of 1
II. A height with a percentile rank of 80 percent
III. A height at the third quartile Q₃
(A) I,II,III
(B) I,III,II
(C) II,I,III,
(D) III,I,II
(E) III,II,I
Answers
A height with a z-score of 1 is the lowest, a height with a percentile rank of 80 percent is in the middle, and a height at the third quartile Q₃ is the highest.
A bell-shaped distribution is also known as a normal distribution. It is a symmetrical distribution where the mean, median, and mode are all equal. The distribution has two tails that extend out from the mean in either direction. A height with a z-score of 1 is the lowest because a z-score of 1 is one standard deviation below the mean. A height with a percentile rank of 80 percent is in the middle because it is the 80th percentile, meaning that 80 percent of the data is lower than it. A height at the third quartile Q₃ is the highest because it is the 75th percentile, meaning that 75 percent of the data is lower than it. In ascending order, the heights arranged are III, II, and I.
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PLEASE HELP !!
Use the information given in the figure to find the length VT.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
Answers
The value of the length of VT is 101 units
How to determine the length
Using the Pythagorean theorem, we have that the square of the hypotenuse side is equal to the sum of the squares of the other two sides, we have;
For triangle RVS
85² - 77² = Line RV²
Find the squares
7225 - 5929 = RV²
RV = √1296
36
For RUV
39² - 36² = UV²
Find the squares
1521- 1296 = UV²
Find square root
UV = 15
For UVT
102² - 15² = VT²
VT = √10179
VT = 101 units
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The slope of MN¯¯¯¯¯¯¯ is −3.
Which segments are parallel to MN¯¯¯¯¯¯¯?
Select each correct answer.
Responses
WX¯¯¯¯¯¯, where W is at (2, 6) and X is at (4, 0)
segment W X, , where , W, is at , begin ordered pair 2 comma 6 end ordered pair, and , X, is at , begin ordered pair 4 comma 0 end ordered pair
RS¯¯¯¯¯, where R is at (1, 3) and S is at (4, 2)
segment R S, , where , R, is at , begin ordered pair 1 comma 3 end ordered pair, and , S, is at , begin ordered pair 4 comma 2 end ordered pair
TU¯¯¯¯¯, where T is at (8, 1) and U is at (5, 10)
segment T U, , where , T , is at , begin ordered pair 8 comma 1 end ordered pair, and, U, is at , begin ordered pair 5 comma 10 end ordered pair
PQ¯¯¯¯¯, where P is at (5, 6) and Q is at (8, 7)
Answers
TU is parallel to MN.
Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.
Therefore,
Considering the line TU, find the slope = y₂-y₁ / x₂-x₁
= 10-1 / 5-8 = -9/3 = -3
Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.
Hence TU is parallel to MN.
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M=q+3p solve for q.
Answers
Answer:
q = M - 3p
Step-by-step explanation:
M = q+3p
to isolate q on one side, we need to remove 3p with subtraction, since it is the opposite of addition.
M-3p = q
Answer:
q=m-3p
Step-by-step explanation:
m=q+3p
-3p. -3p
-3p+m=q
Write the ratio as a ratio of whole numbers in lowest terms
$1.00 to $1.50
Answers
Answer:
50
Step-by-step explanation:
:)
detrmine if 7, 5, 84, 48 are in proportion or not
Answers
Answer:
No, the numbers are not in proportionStep-by-step explanation:
The proportion between the first two and the second two numbers are:
7/5 and 84/48Simplifying the second fraction:
84/48 = 7*12/4*12 = 7/4Comparing the fractions:
7/5 ≠ 7/4The answer is no
Sand is deposited into a pile with a circular base. The volume V of the pile is given by V = r^3/3, where r is the radius of the base, in feet. The circumference of the base is increasing at a constant rate of 5 pi feet per hour. When the circumference of the base is 8 pi feet, what is the rate of change of the volume of the pile, in cubic feet per hour?
i. 8/pi
ii. 16
iii. 40
iv. 40 pi
v. 90 pi
Answers
so the sand pile looks more or less like the one in the image below.
let's check its circumference first. We know that dC/dt = 5π
\(C=2\pi r\implies \cfrac{dC}{dt}=2\pi \cfrac{dr}{dt}\implies 5\pi =2\pi \cfrac{dr}{dt}\implies \cfrac{5\pi }{2\pi }=\cfrac{dr}{dt}\implies \boxed{\cfrac{5}{2}=\cfrac{dr}{dt}}\)
hmmm when the circumference C = 8π, what's the radius "r"?
\(8\pi =2\pi r\implies \cfrac{8\pi }{2\pi }=r\implies 4=r\)
now let's take the derivative to the volume equation, and check what dV/dt is
\(V=\cfrac{r^3}{3}\implies V=\cfrac{1}{3}r^3\implies \cfrac{dV}{dt}=\stackrel{\textit{chain rule}}{\cfrac{3}{3}r^2\cdot \cfrac{dr}{dt}}\implies \cfrac{dV}{dt}=r^2\cdot \cfrac{5}{2}\implies \cfrac{dV}{dt}=\cfrac{5r^2}{2} \\\\\\ \stackrel{\textit{when }C=8\pi \textit{ we know that }r=4}{\cfrac{dV}{dt}=\left. \cfrac{5r^2}{2}\right|_{r=4}} \implies \cfrac{dV}{dt}=\cfrac{5(4)^2}{2}\implies \cfrac{dV}{dt}=40\)
The rate of change of the volume is mathematically given as
dV/dt=40
What is the rate of change in the volume of the pile, in cubic feet per hour?Question Parameter(s):
The volume V of the pile is given by V = r^3/3,
at a constant rate of 5 pi feet per hour
Generally, the equation for the Circumference is mathematically given as
\(C=2\pi r\\\\\ \frac{5}{2}=\frac{dr}{dt}}\)
Therefore
8π=2πr
r=8π/2π
r=4
In conclusion
\(V=\cfrac{r^3}{3}\)
Hence
\(\frac{dV}{dt}=\cfrac{5r^2}{2} \\\\\\ \frac{dV}{dt}=\cfrac{5(4)^2}{2} \frac{dV}{dt}\)
dV/dt=40
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Which summation formula is equivalent to the one below?
^3Σn=0 (-1/5)^n (25)
Answers
Answer:
It's A
Step-by-step explanation:
Because it's A
Answer:
A
Step-by-step explanation:
3 ∑ n=0 (-1/5)^n x 25 = 104/5
option A also = that so A
y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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Cherise deposits $450 into a bank account that earns 3% simple interest per year.
What is the total amount in the account after four years?
PLZ ANSWER ASAP
Answers
Answer:
$504
Step-by-step explanation:
The total amount in the account after four years 504
What is simple interest ?
The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.
Simple interest formula is given as:
SI = \(\frac{PRT}{100}\)
Where SI = simple interest
P = principal
R = interest rate (in percentage)
T = time duration (in years)
In order to calculate the total amount, the following formula is used:
Amount (A) = Principal (P) + Interest (I)
Where,
Amount (A) is the total money paid back at the end of the time period for which it was borrowed.
The total amount formula in case of simple interest can also be written as:
A = P(1 + RT)
Here,
A = Total amount after the given time period
P = Principal amount or the initial loan amount
R = Rate of interest (per annum)
T = Time (in years)
Given,
P = 450
R = 3%
T = 4
Formulate and substitute: 450+ 450RT
Calculate the product or quotient: 450 X (1+0.12)
Calculate the sum or difference: 450 X 1.12
Calculate the product or quotient: 504
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can u slove ASAP please
Answers
Answer:
B) 352
Step-by-step explanation:
45% = 0.45
640 x 0.45= 288
288 is how many students walked to school
So to find how many took the bus to school
640- 288= 352
11 of 3011 of 30 Questions
Question
A baker makes peanut butter cookies and chocolate chip cookies.
She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?
Answers
The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.
Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."
From the given information, we can set up the following system of equations:
For the flour:
2x + 3y = 26
For the butter:
34x + y = 9
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply the first equation by 17 (to make the coefficients of x in both equations the same):
34x + 51y = 442
Now we have the system of equations:
34x + y = 9
34x + 51y = 442
Subtract the first equation from the second equation:
34x + 51y - (34x + y) = 442 - 9
50y = 433
Divide both sides by 50:
y = 433/50
Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.
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Which expression represents twice the sum of a number and six
Answers
Answer:
2(x + 6)
Step-by-step explanation:
If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:
2(x + 6)
Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)
The area of a circle is 65.71cm2.
Find the length of the radius rounded to 2 DP.
Answers
Answer:
5 cm
Step-by-step explanation:
Area of a circle: \(\pi r^{2}\) {r=radius}
\(\pi r^2=65.71cm2\)
\(r^2=65.71/3.14\) \((\pi =3.14)\)
\(r^2=20.92\)
\(r=\sqrt{20.92} =4.57cm\)
\(r=4.57=5cm\)
\(r=5cm\)
[RevyBreeze]
write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answers
Answer:
x = 2
Step-by-step explanation:
8 = 6x + -2x
8 = 4x
8 = 4x
4 4
2 = x
The circumference of a circle is 15pi centimeters what is the area of the circle in terms of pi?
Answers
\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)
the ratio 60 miles per hour is an example of a because it has two measurements having different units of measure
Answers
Answer:
180
Step-by-step explanation:
Answer: ejejejwjfmfmdnc
Step-by-step explanation:
How many solutions does this system of linear equations have? Explain.
1= 2
=1+3 2
Answers
Answer: There are no real solutions.
Step-by-step explanation:
We have the equation:
x = y^2
y = x + 3/2
To solve this, we can start by noticing that x is already isolated in the first equation, then we can replace it in the second equation to get:
y = y^2 + 3/2
And now we can rewrite this as:
y^2 - y + 3/2 = 0
This is a quadratic equation, and the solutions can be calculated with Bhaskara's equation, the solutions are:
\(y = \frac{-(-1) +- \sqrt{(-1)^2 - 4*3/2*1} }{2*1} = \frac{1 + \sqrt{-5} }{2}\)
We have a negative number inside the square root, this means that the solutions are complex numbers.
Then we can conclude that the system of equations has no real solutions.
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Answers
Answer: A,B,E,F
Step-by-step explanation:
Answer:
The answer is A, B, E, F
Step-by-step explanation:
Consider the following statements about the effect of different values of a on the function y = ab^x. Which one of the statements, if any, is incorrect?
A. Values of a such that |a| > 1 will vertically stretch the graph of y = b^x.
B. Values of a such that 0 < |a| < 1 will vertically compress the graph of y = b^x.
C. Negative values of a will reflect y = b^x across the y-axis.
D. All of the above statements are correct.
Answers
No, There is no any sentences are incorrect.
Hence, All sentences are correct.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Consider the following statements about the effect of different values of a on the function,
⇒ y = a bˣ
Now, We know that;
For the value of a such that |a| > 1
The graph of y = bˣ is vertically stretch.
And, For the values of a such that 0 < |a| < 1;
The graph of y = bˣ is vertically compress.
And, When we take negative value of a.
Then, Function reflect y = bˣ across the y-axis.
Thus, There is no any sentences are incorrect.
Hence, All sentences are correct.
Learn more about the function visit:
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