Given that angle B is in standard position, the terminal side is in quadrant III and sin B=-5/13, evaluate the following functions:
csc B = b) cot B = c) cos B = d) sec B = e) tan B =
Answers
Given that sin B = -5/13 and angle B is in quadrant III, we can use the Pythagorean identity to find the value of cos B:cos² B + sin² B = 1
cos² B + (-5/13)² = 1
cos² B = 1 - 25/169
cos² B = 144/169
cos B = -12/13 (since cos B is negative in quadrant III)a) To find csc B, we can use the reciprocal identity:
csc B = 1/sin B
csc B = 1/(-5/13)
csc B = -13/5b) To find cot B, we can use the quotient identity:
cot B = cos B/sin B
cot B = (-12/13)/(-5/13)
cot B = 12/5c) To find cos B, we have already calculated it above:
cos B = -12/13d) To find sec B, we can use the reciprocal identity:
sec B = 1/cos B
sec B = 1/(-12/13)
sec B = -13/12e) To find tan B, we can use the ratio identity:
tan B = sin B/cos B
tan B = (-5/13)/(-12/13)
tan B = 5/12Therefore, the values of the trigonometric functions for angle B in standard position with terminal side in quadrant III and sin B = -5/13 are:
a) csc B = -13/5
b) cot B = 12/5
c) cos B = -12/13
d) sec B = -13/12
e) tan B = 5/12
Step-by-step explanation:
Related Questions
Leila worked for 13 hours each day for 6 days. Then the next day she worked 7 hours. How many hours did Leila work in all?
Answers
Answer:
85
Step-by-step explanation:
13(6)+7=85
:)
Answer:
85
Step-by-step explanation:
Let's calculate the working hours of the first 6 days:
[tex]13 * 6 = 78[/tex] hours
Now let's add that to the last 7 hours she worked:
[tex]78 + 7 = \fbox{85}[/tex] hours
determine the best method to solve each system of equations. then solve the system 3x-5y=7 2x+5y=13
Answers
Answer:
(4, 1 )
Step-by-step explanation:
3x - 5y = 7 → (1)
2x + 5y = 13 → (2)
the 'best' or 'simplest' way to solve this system is the elimination method
since the signs of 5y are opposites then adding will eliminate the y term
add (1) and (2) term by term to eliminate y
(3x + 2x) + (- 5y + 5y) = 7 + 13 , that is
5x + 0 = 20
5x = 20 ( divide both sides by 5 )
x = 4
substitute x = 4 into either of the 2 equations and solve for y
substituting into (2)
2(4) + 5y = 13
8 + 5y = 13 ( subtract 8 from both sides )
5y = 5 ( divide both sides by 5 )
y = 1
solution is (4, 1 )
40% of the group are athletes. There are 20 athletes. What is the total number of people in the group
Answers
Answer:
the number of athletes is 8
SOMEONE, PLEASE HELP ME!
Answers
Answer:
Find the heigh if a=550cm and r=7cm
C) 92.65%
To find the percent decrease in customers, we first need to find the difference in the number of customers between the two given hours.
Number of customers on Saturday from 6:00 p.m. to 7:00 p.m. = 68
Number of customers on Wednesday from 5:00 p.m. to 6:00 p.m. = 5
Difference in number of customers = 68 - 5 = 63
Next, we need to find the percent decrease in customers, which is given by:
(percent decrease) = (difference / original) x 100%
where "original" refers to the number of customers on Saturday from 6:00 p.m. to 7:00 p.m.
Plugging in the values, we get:
(percent decrease) = (63 / 68) x 100% ≈ 92.65%
Therefore, the percent decrease in customers from the given hour on Saturday to the given hour on Wednesday is approximately 92.65%.
What is the properties of rhombus and rectangle and square?
Answers
There are some traits that rectangles, squares, and rhombuses have in common. These are also some differences between them. Rectangles, squares, and rhombuses all have 4 sides. If a shape is a rectangle the diagonal sides will be congruent. If a shape is a square all the sides will be congruent, the shape will also have a right angle. The diaganles of a rombus are perpendicular.
3:
Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.
List 1 List 2 List 3 List 4
O O, O O, O O, O
G O, G O, G O, G
B O, B O, B O, B
G, O G, O G, O
G, B G, B G, B
G, G G, G G, G
B, B B, B B, B
B, G B, G B, G
B, O B, O
G, O
O, B
G, B
Which list gives the sample space for pulling 2 marbles from the bag with replacement?
List 1
List 2
List 3
List 4
Answers
List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
What is sample?In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.
According to question:List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.
The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").
Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.
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Answer:
List 4
Step-by-step explanation:
List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
What is sample?
In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.
According to question:
List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.
The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").
Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.
Question 1C Answer to (a) is alpha-theta answer to (b) C=90-alpha will give brainliest
Answers
Please mark answer as brainliest
Answer:
(c) AE = x·cos(α)/sin(θ)
(d) BD = x·cos(α)cos(α-θ)/cos(θ)
Step-by-step explanation:
In the given diagram, you want expressions for (c) AE and (d) BD in terms of x, α, and θ.
C. AEThe law of sines can be used in ∆ACE to give the measure of AE.
[tex]\dfrac{AE}{\sin(C)}=\dfrac{CE}{\sin(\theta)}\\\\\boxed{AE=\dfrac{x\,\cos(\alpha)}{\sin(\theta)}}\qquad\text{where $\sin(C)=\cos(\alpha)$ and $CE=x$}[/tex]
D. BDThe length BD can be found in terms of AD and θ:
BD = AD·tan(θ)
The length AD can be found in terms of AE and (α-θ):
AD = AE·cos(α-θ)
Using the value of AE from part (c), we have ...
BD = AE·cos(α-θ)·tan(θ) = x·cos(α)cos(α-θ)·tan(θ)/sin(θ)
BD = x·cos(α)cos(α-θ)/cos(θ) . . . . . . . using tan/sin = 1/cos
__
Additional comment
We assume angle EAC is θ throughout, as it is in part (a).
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The cylinder has height of 31mm and a volume of 4700mm³ what is the radius? (give ans to 2 d.p.) giving away 5 stars and a thanks
Answers
The radius of the cylinder is approximately 9.02 mm.
What is cylinder?
A cylinder is a three-dimensional shape that consists of two parallel and congruent circular bases that are connected by a curved lateral surface. It can be thought of as a stack of circular discs or coins of equal size, with a constant distance between them. The axis that passes through the center of the circular bases is called the axis of the cylinder.
The formula for the volume of a cylinder is:
[tex]$$ V = \pi r^2 h $$[/tex]
where [tex]$V$[/tex] is the volume, [tex]$r$[/tex] is the radius, and [tex]$h$[/tex] is the height.
We can rearrange this formula to solve for the radius:
[tex]$$ r = \sqrt{\frac{V}{\pi h}} $$[/tex]
Substituting the given values, we get:
[tex]$$ r = \sqrt{\frac{4700}{\pi \cdot 31}} $$[/tex]
Simplifying this expression, we get:
[tex]$$ r \approx 9.02\ \text{mm} $$[/tex]
Therefore, the radius of the cylinder is approximately 9.02 mm.
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answers
According to the given information, the correct answer is Bus 18, with a median of 13.
What is median?
The median is a measure of central tendency in statistics. It is the value that separates the dataset into two equal halves, with half the values being greater than the median and half being less than the median.
To compare the travel times of the two buses and determine which typically has the faster travel time, we need to look at the measures of central tendency.
The two common measures of central tendency are mean and median.
For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school and half take more than 13 minutes. The mean can be calculated by finding the sum of all travel times and dividing by the number of students, but this information is not provided in the given line plot.
For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school and half take more than 16 minutes. The mean can be estimated by calculating the average of all the travel times, which is:
(4+6+10+10+12+12+14+14+18+18+22+22+28+28+28)/15 = 16
Therefore, the mean travel time for Bus 47 is also 16.
Comparing the median travel times, we can see that Bus 47 has a higher median of 16 compared to Bus 18's median of 13. This suggests that the travel times for Bus 47 are typically longer than those for Bus 18, and therefore Bus 18 typically has the faster travel time.
Therefore, the correct answer is Bus 18, with a median of 13.
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the origin of playing cards is debatable but what is definitely known is different countries had different suits. what comprised the suits in spanish cards?
Answers
Spanish playing cards have four suits: coins, cups, swords, and clubs, with each suit representing a different aspect of life, and consisting of ten numbered cards and three court cards.
Spanish playing cards traditionally have four suits: coins, cups, swords, and clubs. These suits are similar to the suits found in Italian and Latin American playing cards, but different from the suits found in French and German playing cards. The coins suit represents wealth and commerce, the cups suit represents love and pleasure, the swords suit represents warfare and justice, and the clubs suit represents agriculture and prosperity. Each suit typically contains ten numbered cards and three court cards: the knight, the queen, and the king.
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forty-four percent of us adults have little confidence in their cars. you randomly select twelve us adults. find the probability that the number of us adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7.
Answers
The proportion of adults who have little faith in their automobiles, or the chance of success (p), is 44%.
How does probability work?The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.
At the point when this happens, we broadcast that there is plausible that the occasion will happen.
In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence. By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.
Given that "p" stands for probability—that is, the fact that 45 percent of adults in the United States have little faith in their automobiles—p = 0.45, the likelihood of failure is q = 1-p = 1 - 0.45.
The chance of success (p), or the percentage of adults who have little faith in their automobiles, is therefore 44%, with q =0.55.
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Find the surface area of a sphere with radius, r = 10 in.
Answers
Answer: ~1256.64
Step-by-step explanation:
The equation for the surface area of a sphere is 4πr². So you would substitute 10 in for r which would then be 4π10². That will get you 1256.63706 but rounded it would be approximately 1256.64.
Answer: [tex]\text{400}\pi \ \text{square inches}[/tex]
Step-by-step explanation:
Given: The radius of the sphere = 10 in.
The formula to calculate the surface area of the sphere is given by:
[tex]\text{Surface Area}=4\pi r^2[/tex], where r is the radius of the sphere.
For r = 10 in. we have
[tex]\text{Surface Area of the sphere}=4\pi (10)^2[/tex]
[tex]\implies \text{Surface Area of sphere}=4\pi (100)[/tex]
[tex]\implies \text{Surface Area of the sphere}=\text{400}\pi \ \text{square inches}[/tex]
[tex]400\pi =1256.64 \ \text{square inches}[/tex]PROOFS please fill in blanks need help badly !! would gratefully appreciate it
9. Given: U is the midpoint of ST, SVTW, VU =WU
Prove: SVU = ZTWU
Answers
For the given congruence triangle:
ΔSUV ≅ ΔTUW By Side Side Side (SSS) congruence ∠SVU ≅ ∠TWU BY CPCT Explain about the congruence triangle:Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides plus three angles of another triangle, two triangles are said to be congruent.
For the given data:
U is the midpoint of ST, SV ≅ TW, VU ≅ WU.Statement Reasons
U is the midpoint of ST Given
SV ≅ TW Given
VU ≅ WU Given
SU = UT U is the midpoint of ST
ΔSUV ≅ ΔTUW By Side Side Side (SSS) congruence
∠SVU ≅ ∠TWU BY CPCT
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What is the area of the shaded region?
Answers
Answer: 7[tex]x^{2}[/tex]+13x-7
Step-by-step explanation: (3x + 7)(3x - 1) = 9[tex]x^{2} \\[/tex] + 18x - 7. (2x + 5)x = 2[tex]x^{2}[/tex]+5x. 9[tex]x^{2} \\[/tex] + 18x - 7 - (2[tex]x^{2}[/tex]+5x) = 7[tex]x^{2}[/tex]+13x-7
There is a right triangle with one side that says(x+42) and the other which says 3x I need to find the x help em out please
Answers
If the sides of a right triangle are x, 3x+3, and 4x-3, the value of x is 7
In a right triangle, the Pythagorean theorem states that the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). Using this theorem, we can set up an equation as follows
x^2 + (3x+3)^2 = (4x-3)^2
Expanding the squares, we get
x^2 + 9x^2 + 18x + 9 = 16x^2 - 24x + 9
Simplifying and rearranging terms, we get
6x^2 - 42x = 0
Factorizing out x, we get
x(6x - 42) = 0
Therefore, x = 0 or x = 7. However, since the sides of the triangle cannot be zero, we must choose x = 7 as the solution.
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I have solved the question in general as the given question is incomplete:
The complete question is:
If the sides of a right triangle are x, 3x+3, and 4x-3, then what is the value of x?
The International Committee on the Taxonomy of Viruses estimates that 8.3% of the US population has COVID 19. The Center for Disease Control and Prevention has developed a diagnostic test for COVID 19 that is 98% accurate for people who have COVID 19 and 95% accurate for people who don't have it. The Center gives the test to a randomly selected person. What is the probability that diagnosis is correct? Round your answer to hundredth percent.
Answers
Let's first define some events:
A: The person has COVID-19.
B: The test result is positive.
Using the information provided, we can calculate the probability of a correct diagnosis using Bayes' theorem:
P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|not A) * P(not A)]
where P(B|A) is the probability of a positive test result given that the person has COVID-19, P(A) is the prevalence of COVID-19 in the population (0.083 or 8.3%), P(B|not A) is the probability of a positive test result given that the person does not have COVID-19 (false positive rate, 0.05 or 5%), and P(not A) is the complement of P(A) (0.917 or 91.7%).
Plugging in the values, we get:
P(A|B) = (0.98 * 0.083) / [(0.98 * 0.083) + (0.05 * 0.917)]
= 0.6037 or 60.37%
Therefore, the probability that the diagnosis is correct is 60.37%, rounded to the nearest hundredth percent.
ANSWER THIS PLSSSS WHAT R THE NUMBERS IN THE MIDDLE!!
Answers
Answer:
Step-by-step explanation:
in the middle is 0 in the first one is -5 and last one is 5
[tex]\frac{(8^{3} -9^{0})}{7}[/tex]
Answers
Answer:
exact form-512/7
decimal form-73.1
Mixed number form-73 1/7
Step-by-step explanation:
The drama club at Lee Middle School is deciding on their spring production. There are 25 students who want to do a musical and 5 students who want to do a play. What is the probability that a randomly selected student would want to do a musical?
Answers
Answer:
20 percent
Step-by-step explanation:
5/25=0.2
Answer:
25/30 which reduces to 5/6
Step-by-step explanation:
There is a net total of 30 students (25 for musical and 5 for play)
It's asking for the probability of someone who wants to do a musical getting selected, which would be 25 kids out of 30. Which reduces to 5/6
Hey guys I need help with 3 math problems the image is below please no is answering and I only need one homework to pass this year image is below giving brainliest
Answers
Answer:
I did the first image. I'm sorry but I don't remember fully how to do the other two, and I don't want to give you the wrong answer. GL
Step-by-step explanation:
Okay, for the first image if the perimeter is 48 you can divide that by 3 getting you 16. M=16.
Help!!!! It’s due at 9:30 tomorrow
Answers
The two-column proofs of the segments are shown below
Proving that AG ≅ EDThe proof is as follows
Statement Reason
ABCD and BCDE are parallelogram Given
AG = BC Opposite sides of
parallelogram
ED = BC Opposite sides of
parallelogram
AG ≅ ED Substitution property (proved)
Proving that KLMN is a parallelogram
The proof is as follows
Statement Reason
KL || NM and ∠L ≅ ∠N Given
KN ≅ LM CPCTC
KL ≅ NM CPCTC
We've proved that the opposites sides are equal and parallel
So, KLMN is a parallelogram
Proving that STUV is a parallelogram
The proof is as follows
Statement Reason
ST || VU and W is midpoint of SU Given
SW = UW Definition of midpoint
VW = TW Definition of midpoint
VU = ST CPCTC
VS = UT CPCTC
We've proved that the opposites sides are equal and parallel
So, STUV is a parallelogram
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What is the missing value for x on the diagram below?
Answers
For the given cyclic quadrilateral the missing values of x is 82°, y is 130° and z = 118°
Define the term Circle identities?In trigonometry, a set of fundamental identities is referred to as the "Circle identities" and connects the six trigonometric functions of an angle in a right-angled triangle.
Here given a quadrilateral inside the circle, we know that,
Sum of opposite angle of cyclic quadrilateral is 180 degree;
Then, x + 98° = 180°
x = 82°
Opposite angle of 76° will be; 180° - 76° = 104°
Radius are same in ΔAOB, (See the below figure)
Then, a + a + 34° = 180°
a = 73°
then, ∠OBC = 98° - a = 25°
and in ΔCOB, 25° + 25° + y° = 180°
Then, y = 130°
and in ΔDOA,
∠OAD = 104° - 73° = 31°
Then, z = 118°
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Simplify figure for understanding-
Simplify (2x3y2 − 8x2y + 4y) − (5x3y2 − 4x2y − 4y).
−3x3y2 − 4x2y
−3x3y2 + 12x2y
( −3x3y2 − 4x2y + 8y)
−3x3y2 − 12x2y + 8y
Answers
Answer:
-3x^3y^2 - 4x^2y + 8y.
Step-by-step explanation:
When we distribute the negative sign to the terms inside the parentheses, we get:
(2x^3y^2 − 8x^2y + 4y) − (5x^3y^2 − 4x^2y − 4y) = 2x^3y^2 − 8x^2y + 4y - 5x^3y^2 + 4x^2y + 4y
Now, we can combine like terms. The terms with x^3y^2 are 2x^3y^2 and -5x^3y^2, which combine to give -3x^3y^2. The terms with x^2y are -8x^2y and 4x^2y, which combine to give -4x^2y. The terms with y are 4y and 4y, which combine to give 8y. Therefore, we have:
(2x^3y^2 − 8x^2y + 4y) − (5x^3y^2 − 4x^2y − 4y) = -3x^3y^2 - 4x^2y + 8y
Therefore, the simplified expression is -3x^3y^2 - 4x^2y + 8y.
The expression can be simplified by subtracting the coefficients of matching terms from the first and second parentheses. The simplified expression is -3x3y2 - 4x2y + 8y.
Explanation:To simplify the expression (2x3y2 − 8x2y + 4y) − (5x3y2 − 4x2y − 4y), you must subtract each term in the second parentheses from the corresponding term in the first. In this case, it works as follows:
First, subtract the coefficients of the matching terms in both brackets. The term x3y2 is present in both, so subtract 5 (the coefficient from the second bracket) from 2 (the coefficient from the first). This results in -3x3y2.Then, do the same for the x2y term. Subtract -4 (the coefficient from the second bracket) from -8 (from the first). Because you're subtracting a negative, that's like adding, so we get -4x2y.Finally, subtract -4 (the coefficient for y in the second bracket) from 4 (from the first). Again, subtracting a negative is like adding, so this results in 8y.So, the simplified expression becomes −3x3y2 − 4x2y + 8y.
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Katie, Toby and Molly sold a total of 72 games at a car boot sale. The ratio of the numbers of games that they each sold is 5: 3: 1. How many more games did Toby sell than Molly?
Answers
Toby sold 16 more games than Molly.
What is ratio?A ratio is a comparison of two or more quantities of the same kind. It is often expressed as a fraction or with a colon (:). For example, the ratio of the number of boys to the number of girls in a class of 30 students could be 2:3, which means that for every two boys, there are three girls.
Let's start by finding the total number of parts in the ratio: 5 + 3 + 1 = 9.
Next, we can use the ratio to find out how many parts of the total each person sold:
Katie: 5/9 of 72 games = 40 games
Toby: 3/9 of 72 games = 24 games
Molly: 1/9 of 72 games = 8 games
To find out how many more games Toby sold than Molly, we can subtract Molly's sales from Toby's sales: 24 - 8 = 16.
Therefore, Toby sold 16 more games than Molly.
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Answer:
Toby sold 16 more games than Molly.
Step-by-step explanation:
Let's start by finding the total number of parts in the ratio: 5 + 3 + 1 = 9.
Next, we can use the ratio to find out how many parts of the total each person sold:
Katie: 5/9 of 72 games = 40 games
Toby: 3/9 of 72 games = 24 games
Molly: 1/9 of 72 games = 8 games
Then we subtract Toby's number of games by Molly's. (24-8)
Therefore, Toby sold 16 more games than Molly.
Select the correct answer from each drop-down menu.
Given: ST bisects
Prove: SU = SV
Answers
Check the picture below.
so since ST is bisecting at the vertex T, that means that T will end up with twin angles and thus both triangles the yellow and green one since both are sharing the hypotenuse ST, both triangles are congruent by the HA theorem, and thus CPCTC.
iq scores in a certain population are normally distributed. it is given that: (1) 13% of people have iq that does not exceed 80. (2) mensa is an organization whose members have iqs in the top 3% of the population. the minimum iq score required for admission to mensa is 128. 9(a) find the mean and the standard deviation of iq scores. round your answers to the nearest whole numbers. hint. find z-scores.
Answers
The mean IQ score in the population is approximately 98, and the standard deviation is approximately 16.
Let μ = mean and σ = standard deviation of IQ scores in population.
Then we can write the two equations as :
⇒ P(X ≤ 80) = 0.13 ...equation(1)
⇒ P(X ≥ 128) = 0.03 ...equation(2)
we standardize the data by using the formula:
⇒ Z = (X - μ)/σ,
Where Z = standard normal variable.
Using the standard normal distribution, we know that P(Z ≤ -1.126) = 0.13,
So, -1.126 = (80 - μ)/σ .....equation(3),
and we know that P(Z ≥ 1.881) = 0.03.
So, 1.88 = (128 - μ)/σ ...equation(4),
⇒ μ = 128 - 1.881σ,
Solving equation(3) and equation(4),
We get,
⇒ σ ≈ 16.
Substituting σ = 16 into the equation(4),
We get,
⇒ μ = 128 - 1.881×16,
⇒ μ = 98.
Therefore, the mean IQ score = 98, and standard deviation is = 16.
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PLEASE HELP ON TIME LIMIT
What is the correct mathematical description for the expression 25 ÷ 5 + (6 x 2) − 4.5?
25 divided by 5 plus 6 times 2 minus 4 and 5 tenths
25 divided by the sum of 5 and 6 times 2 minus 4 and 5 tenths
25 divided by 5 plus 6 times the difference of 2 and 4 and 5 tenths
25 divided by 5 plus the product of 6 and 2 minus 4 and 5 tenths
Answers
Answer: 25 divided by 5 plus 6 times 2 minus 4 and 5 tenths
Step-by-step explanation: order of operations, PE(MD)(AS)
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Explain how to graph a polynomial function in factored form. What do the factors
mean in terms of the polynomial? What other ways have we learned to write a
polynomial function? Graph f(x) = (x - 2)²(x + 1)(x − 4). You may
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handwrite your explanation if you would like. You can also attach a snip of the graph
to help explain your thinking.
Some terms to think about:
Factors, Zeros, x-intercepts, multiplicity, end behavior, degree of function
Answers
The x-intercepts (zeros), end behaviors, degree and multiplicity of the function f(x) = (x - 2)²·(x + 1)·(x - 4), can be used to graph the polynomial in factored form. Please find attached the graph of the polynomial created with MS Excel.
What is the difference between a zero and a root of a function?A zero is an input variable value that makes the value of the output to be zero. A root is a value that satisfies the equation.
The steps to graph the polynomial in factored form are;
1. Find the x-intercepts; The x-intercepts are obtained by setting each factor as being equivalent to zero and solve for x. The values obtained are the x-intercepts or the zeros of the function.
The specified function, f(x) = (x - 2)²·(x + 1)·(x - 4), the zeros are; x = 2, (with a multiplicity of 2), x = -1, and x = 4.
2. Determine the end behavior of the function: The degree and leading coefficient of a polynomial determines the end behavior of the polynomial.
The degree of a function is the highest exponent of the function. The highest exponent of x in the function f(x) is 4, therefore, the degree of f(x) is 4.
The leading coefficient is the coefficient of the term with the highest exponent of x. The leading coefficient of f(x) is therefore, the coefficient of the term with the highest exponent of x, which is 1
The even degree of f(x), (4), and the positive leading coefficient, (1), indicates that the end behavior is upwards on both ends.3. Determine the multiplicity of the zeros: The number of times a factor appears in the factored form determines the multiplicity of the zero of the factor.
The zero of x = 2 in the function has a multiplicity of 2 indicating that the graph touch and bounces upwards on the x-axis at x = 2.
The multiplicities of 1 of the of the zeros x = -1, and x = 4 indicates that the graph crosses the x-axis at the points x = -1, and x = 44. Determine the behaviour at the x-intercepts: The multiplicity of the zero determines the behavior of the graph at the x-intercept, such that an odd multiplicity indicates that the graph crosses the x-axis and an even multiplicity indicates that the graph touches the x-axis and bounces upwards or downwards at the point.
The information in the steps 1 – 4 can then be used to sketch the graph of the polynomial.
Please find attached the graph of the polynomial created with MS Excel, using the function, f(x) = (x - 2)²·(x + 1)·(x - 4)
Learn more on the zeros of a function here: https://brainly.com/question/1626261
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Find the greatest common factor of 40 and 16, then use the GCF to factory 40 + 16.
Answers
Answer:
The GCF of 16 and 40 is 8. To calculate the greatest common factor of 16 and 40, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 16 and 40, i.e., 8.
Answer:
The GCF is 8 ; factored is 8(5+2)
Step-by-step explanation:
The gcf of 40 and 16 is 8.
Since 8*5 = 40 and 8*2 = 16:
40+16 = 8(5+2).
Help with this equation pls.
Answers
To create the figure with the new scale of 1 unit = 3 yd. The steps are mentioned below.
Describe Scale?Scale refers to the proportional relationship between the measurements of an object or a system and the corresponding measurements on a representation or a model of that object or system. It is commonly used in many fields, including mathematics, engineering, architecture, art, and geography.
In mathematics, scale can be expressed as a ratio or a fraction, which indicates how much the measurements on the representation or model have been reduced or enlarged relative to the actual measurements of the object or system. For example, a scale of 1:100 means that every measurement on the representation or model is 100 times smaller than the corresponding measurement on the actual object or system.
In art and architecture, scale is used to create a sense of proportion and perspective in a work. For example, an artist might use a smaller scale for a background object to make it appear farther away, while using a larger scale for a foreground object to make it appear closer.
To create the figure with the new scale of 1 unit = 3 yd. Here are the steps:
Determine the dimensions of the rectangle in yards using the original scale of 1 unit = 6 yd.
Divide the dimensions by 2 to get the new dimensions using the new scale of 1 unit = 3 yd.
Draw a rectangle on a new grid using the new dimensions.
If you want to place the rectangle in a specific location on the grid, you can use the coordinates on the grid to position it.
To know more about dimensions visit:
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