Part A: The stated values is; x = 31π/6
A circle has 360 degrees. We must decrease the present angle to an angle between 0° and 360° in order to determine the reference angle.
As, 360° = 2π radians, subtract 2π = 12π/6 radians for each iteration.
Iteration 1 => 31π/6 - 12π/6 = 19π/6
Iteration 2 => 19π/6 - 12π/6 = 7π/6
0 ≤ 7π/6 ≤ 12π/6
Thus, reference angle is found as 7π/6 radians
Part B) The value for the sin x, tan x, and sec x.
sin (7π/6) = -1/2
tan (7π/6) = 1/√3
sec (7π/6) = 1/cos(7π/6) = -1/(√3)/2
sec (7π/6) = -2/√3
Thus, the simplest values of sin x, tan x, and sec x are found.
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Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches. If 500 men want to enlist in the U.S. Marine Corps, how many would you not expect to meet the height requirements?
Answer:
19
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 69.0 inchesStandard deviation σ = 2.8 inchesTherefore, if the heights of men are normally distributed:
[tex]\boxed{X \sim\text{N} \left(69.0, 2.8^2 \right)}[/tex]
where X is height in inches.
Given:
The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches.Find the probability that the heights of men is between 64 and 78 inches by calculating P(64 ≤ X ≤ 78).
Calculator input for "normal cumulative distribution function (cdf)":
Lower bound: x = 64Upper bound: x = 78μ = 69.0σ = 2.8⇒ P(64 ≤ X ≤ 78) = 0.9622733869...
To calculate how many men who want to enlist in the U.S. Marine Corps would not expect to meet the height requirements from a group of 500, multiply 500 by 1 less than the probability found above:
⇒ 500 × [1 - P(64 ≤ X ≤ 78)]
⇒ 500 × [1 - 0.9622733869...]
⇒ 500 × 0.03772661307...
⇒ 18.86330654...
Therefore, we would expect for 19 men to not meet the height requirements.
The heights of the starting 5 players (not including the libero) on a volleyball team like karasuno high school are 60 inches, 67 inches, 64 inches, and 65 inches. If the balance point of the players is 65, what is the height of the 5th player?.
The height of the 5th player would be 69 inches
To find the Height, first, we have to calculate the mean value.
No. of players=5
The height of 4 players is 60 inches, 67 inches, and 64 inches, 65 inches.
Mean =Sum of observations/No of observations
Mean of the 5th players=65
To find, Height of 5th player
As we know,
Assuming the height of the 5th player is x
Mean =Sum of observations/No of observations
65=(60+67+64+65+x)/5
65*5=60+67+64+65+x
325=256+x
x=69
Thus, the height of the 5th player is 69 inches.
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5350 divided by Equals 5.35
Answer:
1000
Step-by-step explanation:
you could write this as 5350 divided by x = 5.35
multiply both sides by x you get 5.35x = 5350
divide both by 5.35
x =1000
or you could just do 5350/5.35 which is 1000
therefore 5350 divided by 1000 would be 5.35
Precalc wohoo help would rlly appreciate it
Answer:
1. Apply a Pythagorean Identitie
2. Seperate the quotient into two terms.
3. Divide the common factor
4. Apply a reprical identity.
Step-by-step explanation:
The steps below in the image I just wrote.
I am not sure if your teacher would let you have a cheat sheet on the test or quiz. Remember your reciprocal identities and Pythagorean identities.
Is the data set approximately periodic?
If so, what are its period and amplitude?
Hour
Number of bikes
O
O
not periodic
1 2 3 4 5 6
7
5 19 14 4 19 15 6
8 9 10 11 12
5 20 16
22 15
periodic with period of 3 and amplitude of about 7.5
periodic with period of 4 and amplitude of about 7.5
periodic with period of 4 and amplitude of about 5
The data is A. periodic with period of 3 and amplitude of about 7.5
How to illustrate the data?From the information, we are given the number of hours as well as the number of bikes. It should be noted that we can see that ty values are periodic as it repeats every third value.
Also, the amplitude will be the:
= Larger value - Smallest value / 3
For the first set it is 7.
For the second set it is 7.5
For the third set it is 8
For the fourth set it is:
= (20 - 5)/2
= 7.5
Therefore, the amplitude is 7.5
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Please Help!! I'm super confused!
(2x ⋅ -3/y)^-3 ⋅ (-5x/y)^2
Answer: -25y/216x
Step-by-step explanation: - 25y / 216x
Answer:
(-30x^2/y^2)^5
Step-by-step explanation:
First, we can simplify the exponent in the first term by using the property that (a^m)^n = a^(m⋅n). This property tells us that we can calculate the exponent of the first term by multiplying the exponent of the base by the exponent of the power, which gives us (-3)⋅(-3) = 9. This means that the first term can be rewritten as (2x ⋅ -3/y)^9.
Next, we can simplify the second term by calculating its exponent in the same way, which gives us (-2)⋅(2) = -4. This means that the second term can be rewritten as (-5x/y)^-4.
We can then combine the two terms by using the property that (a^m)⋅(b^n) = (a⋅b)^(m+n). This property tells us that we can calculate the exponent of the combined terms by adding the exponents of the individual terms, which gives us 9 + (-4) = 5. This means that the entire expression can be rewritten as (2x ⋅ -3/y)^9 ⋅ (-5x/y)^-4 = (2x⋅-3/y⋅-5x/y)^5.
Finally, we can simplify the base of the combined terms by multiplying the factors together, which gives us (2x⋅-3/y⋅-5x/y) = -30x^2/y^2. This means that the entire expression can be rewritten as (-30x^2/y^2)^5.
a researcher wishes to test whether the mean of a normally distributed population is greater than 1.06 at the 5% significance level. based upon 22 independent observations, she observes a sample mean of 1.77 and a sample standard deviation of 0.84 . determine the observed value of student's t statistic rounded to the nearest hundredth. (rounding counts!)
The observed value of student's t statistic rounded to the nearest hundredth is 1.72.
Explain the term significance level?The likelihood that an event (like a statistical test) may have happened by chance is the significance level of the occurrence. When the level, or the possibility of the occurrence occurring by chance, is quite low, the event is considered noteworthy.The stated data is-
Sample size n = 22Significance level = 5%Thus,
Degree of freedom = n -1
Df = 22-1
Df = 21
As, the significance level is 5% then test is right tailed.
So,
Alpha value = 0.05
Now,
For alpha value = 0.05 and degree of freedom = 21.
t- critical value = 1.721 (from the t-statiscts table).
Thus, the observed value of student's t statistic rounded to the nearest hundredth is 1.72.
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List all of the integer values that could take that would satisfy the inequality shown on the number line below.
List all of the integer values that could take that would satisfy the inequality shown on the number line below.
(-2 , 1.5)
Please answer this Geometry - Conditional Forms question.
The statement “If I do not get a uniform, then I do not make the team” is the contrapositive of which of the following conditional statements?
A) If I do not get a uniform, then I do not make the team.
B) If I do not make the team, then I do not get a uniform.
C) If I get a uniform, then I make the team.
D) If I make the team, then I get a uniform.
Answer:
B) If I do not make the team, then I do not get a uniform.
Step-by-step explanation:
The contrapositive of a conditional statement is formed by negating both the antecedent and the consequent of the statement and then swapping their order. In the case of the statement "If I do not get a uniform, then I do not make the team," the contrapositive is "If I do not make the team, then I do not get a uniform."
Determine the value for x in the given diagram, with a || b.
35°
55°
125°
None of these choices are correct.
Answer:
125°
Step-by-step explanation:
the given problem is related to co-interior angle
so.
the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model. t or f
True. the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
what is slope in statistics?The slope and intercept of a line reveal the steepness of the line and the location in which it intersects an axis. The slope and intercept of the logistic relationship of the two variables can be utilized to get the average change rate. The ratio of a change in the variable y to the rise in the x component is known as the the line's slope.
Briefing:Y = a + bX, where X seems to be the mediating variable and Y is the response variable, is the equation of a linear regression line. A is the intersection (the result of y for x = 0), and b is the line's slope.
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Two cell phone plans offer differing text packages. The two plans are outlined below: Plan A: $9.25 per month charge along with a charge of $0.06 per text. Plan B: $2.50per month charge, but a charge of $0.20 per text. Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.
Answer:
48
Step-by-step explanation:
Let T be the number of texts sent on each plan.
The cost of Plan A can be represented as $9.25 + $0.06T.
The cost of Plan B can be represented as $2.50 + $0.20T.
We want to find the number of texts T at which the two plans cost the same amount. Therefore, we can set the two equations equal to each other and solve for T:
$9.25 + $0.06T = $2.50 + $0.20T
Subtracting $2.50 from both sides, we get:
$6.75 + $0.06T = $0.20T
Subtracting $0.06T from both sides, we get:
$6.75 = $0.14T
Dividing both sides by $0.14, we get:
T = 48.21
Therefore, the number of texts at which the two plans cost the same amount is approximately 48 texts. This means that if you send fewer than 48 texts per month, Plan A will be cheaper, and if you send more than 48 texts per month, Plan B will be cheaper.
a liner function contains the following points. what are the slope and y-intercept of this function (0,2) (-3,4)
The function is actually (0,-3)(2,4)
Slope:
slope = y2-y1 = 4-(-3) = 7/2
x2-x1 2-0
y intercept: (0,-3)
Find the sales tax
Selling Price 70.00
Rate of Sales Tax 7%
Sales tax ?
The sales tax is [aswer]
at a 95% level of confidence we want to estimate the population mean for a quantitative varible that is normally distributed in the population there a 10 individuals in the random sample what is the value of
As per the given confidence interval, the value of the mean is 1.96
The term confidence interval means a range of numbers constructed around a point estimate such as a sample mean or sample proportion.
Here we need to find at a 95% level of confidence we want to estimate the population mean for a quantitative variable that is normally distributed in the population there a 10 individuals in the random sample what is the value of mean.
While In the large-sample case, a 95% confidence interval estimate for the population mean is given by
=> x ± 1.96σ/√n.
Where the population standard deviation is denoted as σ, is unknown, And the the sample standard deviation is used to estimate σ in the confidence interval formula.
Here by the quantity 1.96σ/√n is often called the margin of error for the estimate.
Then the quantity σ/√n is the standard error, and 1.96 is the number of standard errors from the mean necessary to include 95% of the values in a normal distribution.
Therefore, the interpretation of a 95% confidence interval is that 95% of the intervals constructed in this manner will contain the population mean.
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Jason was riding his bicycle, making deliveries on his newspaper route. He had no less than 12 newspapers left to deliver.
Which number line represents this scenario?
number line with closed circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the right
number line with closed circle at point 12, shaded to the right
The number line to represent the given scenario is number line with close circle at point 12 and shaded to the right. The correct option is (D).
What is a number line?A number line is the pictorial representation of numbers on a graph. The reference point on the number line is known as origin and all the numbers right to the origin are taken as positive and those left to it are negative numbers.
The number of newspapers to be delivered is not less than 20.
Suppose the number of newspaper left at any time be x.
Then, the inequality for the given situation can be written as,
x ≥ 12
This implies all the whole numbers greater than and including 12 on the number line.
Hence, the solution can be represented as all numbers greater than and equal to 12.
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If a rectangle and a quare have the ame perimeter then which one will have a larger area
The area of the square is bigger than the Area of the rectangle.
Suppose the sum of all the sides in a square is this: 4 x A and the same is true of a rectangle, too.
Then, first, the area of the square is A^2.
And next, assuming that we have this: 0 < X < A and that one side in the rectangle is this: (A - X)
we can say that the side next to (A - X) is this: (A + X) because the sum of all the four sides in the rectangle has to be this: (4 x A), which equals the sum of all the sides in the square.
So now, the area of the square is this: A^2, whereas the area of the rectangle is this: (A^2 - X^2), which equals this: (A + X)(A - X).
You know thus now, which of the two areas is bigger, and it’s the area of the square. And the difference between the two areas is this: X^2.
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Write an equation in slope-intercept form of the line that passes through (-4, 3) and (-3, 1) .
An equation is
Answer: Y=-2x-5
Step-by-step explanation:
Points: (-4, 3) & (-3, 1)
To find the slope, we use m= (y₂-y₁)/(x₂-x₁)
With these points, m= (1-3)/(-3--4)
This gives us m= -2/1, or -2
Slope-intercept form is y=mx+b
We can plug in the slope now, so y=-2x+b
B is the y-intercept, which is -5, in this case
This gives us y=-2x-5
Find the measure of each angle indicated.
A. 70 degrees
B. 110 degrees
Help!!!
Answer:
110 degrees
Step-by-step explanation:
This is because they are alternate exterior angles
So they are the same angle
There were 794 fih at 9:00 A. M. The dolphin were fed at 5:00 P. M. There were 209 fih left etimate how many fih the dolphin ate
the number of fih at 9:00 A.M. (794), which yields 209 fih, the number of fih left at 5:00 P.M. is 585 fih
Subtract the number of fih at 9:00 A.M. (794) from the number of fih left at 5:00 P.M. (209).
794 - 209 = 585
Therefore, the dolphin ate 585 fih.
To estimate how many fih the dolphin ate, we must first subtract the number of fih at 9:00 A.M. (794) from the number of fih left at 5:00 P.M. (209). This gives us 585 fih, which is the estimated number of fih that the dolphin ate. This calculation can be verified by subtracting the number of fih the dolphin ate (585) from the number of fih at 9:00 A.M. (794), which yields 209 fih, the number of fih left at 5:00 P.M.
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Yaqub ha a bag of green and yellow pin. 3/7 of the pin are green
He pick out a green pin from hi bag and give it to hi iter
2/5 of the remaining pin in hi bag are green
how many of the remaining pin in hi bag are green and how many are yellow?
The number of remaining green and yellow pins is 14 pins and 21 pins.
A proportion is a mathematical calculation that compares two numbers. According to proportion, two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
The fraction of green pins present in the bag is 3/7. Then, the fraction of yellow pins present in the bag is 4/7.
When Yaqub picks up the green pin and gives it to his sister, the new fraction of green and yellow pins are 2/5 and 3/5.
Let x be the number of pins remaining in the bag after 1 pin less. This is written as,
[tex]\begin{aligned}\frac{3}{7}x-1 &= \frac{2}{5}x\\\frac{3}{7}x-\frac{2}{5}x&=1\\x&=35\end{aligned}[/tex]
There are about 35 pins remaining in the bag.
Then, the number of green pins remaining is (2/5) × 35 = 14 pins.
The number of yellow pins remaining is (3/5) × 35 = 21 pins.
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Which of the following terms represents the situation shown in the graphic below?
a glide a reflection a glide reflection
None of these choices are correct.
The term that represents the situation shown in the graphic below is B. a reflection
What is a a reflection?A glide reflection or transflection is a symmetry operation in two-dimensional geometry that combines a reflection over a line with a translation along that line into a single operation.
An exchange of points from one side of a line with points on the other side of the mirror at the same distance from the mirror occurs when a mirror line is fixed in the plane. There is a mirror line in every reflection. A mirror reflection is followed by a translation that is parallel to the mirror to create a glide reflection.
Here, the shape is mirrored in the reflection. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
In conclusion, based on the information given, it should be noted that the correct option is B.
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A teacher recorded unit 4 test scores from her class.
58, 64, 66, 70, 71, 75, 77, 80,
84, 85, 87, 90, 93, 95, 96.
Find the percentile rank of a score of 71 on this street -
Victor is in the 60th percentile, what was his score?
The percentage score for a 71 on the test is 27, and the winning score is 71.
What is Statistics?The science of statistics focuses on creating and researching strategies for gathering, evaluating, interpreting, and reporting empirical data.
As per the given information in the question,
The given scores are:
5, 4, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, and 96.
A percentage is a number in a range of one to 100 that represents the percentage of a range that falls inside or above it.
Formula for calculating percentile rank on a test score of 71,
R₁₀₀ = [100(N <) + 1/2]/N
=100 × 4 + 1/2(1)/15
=400 + 0.5/15
=400.5/15
=26.7=27th
Now we need to find the score of victor who has 60th percentile.
60 = Score/15
Score = 71
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the edwards's theater chain has studied its movie customers to determine how much money they spend on concessions. the study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. what spending amount corresponds to the top 87th percentile?
The study revealed that 87% of movie customers spend an average of $6.39 or less on concessions.
To calculate the spending amount that corresponds to the top 87th percentile, we must first calculate the z-score. To do this, subtract the mean of $4.11 from the desired percentile of $6.39, resulting in a difference of $2.28. Next, divide the difference of $2.28 by the standard deviation of $1.37, resulting in a z-score of 1.67. Finally, use a z-score table to find the corresponding percentile of 87%. This means that 87% of movie customers spend an average of $6.39 or less on concessions.
z-score = (6.39 - 4.11) / 1.37 = 1.67
percentile = 87%
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Tell which property you used. 50x (20 x 1.3)
Answer:100x * 65
Step-by-step explanation:
distribute the 50 into 20 and 1.3 then set it up
DISTANCE The graph represents the distance y in miles Roland is from home as a function of time x in hours. Which could very likely be true?
WHAT IS DISTANCE?
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria
You need to write complete questions in order to get good and exact answers. Here you haven't provided any graph so I could help you giving you my own graph. The relationship between speed, time and distance is as follows:
Where:
[tex]d=v t[/tex]
[tex]Where :[/tex]
[tex]d: Distance[/tex]
[tex]v:speed[/tex]
[tex]t : time[/tex]
So [tex]v[/tex] represents slope of a line that passes through the origin. In this case:
d matches the y-axis
t matches the x-axis.
So:
[tex]y=m x \rightarrow d=v t[/tex]
[tex]Where:[/tex]
[tex]\begin{aligned}& y \rightarrow d \\& m v \rightarrow v\end{aligned}[/tex]
[tex]x \rightarrow t[/tex]
The graph below (Car A) comes from the following equation:
[tex]y=\frac{5}{3} x[/tex]
And the equation for car B is:
[tex]y=\frac{5}{6} x[/tex]
By comparing them, car A moves faster than car B because:
[tex]\frac{5}{3} > \frac{5}{6}[/tex]
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help me with this math question
Answer:
Step-by-step explanation:
y = -5 (x² + 1 - 2x) + 5
y = -5x² + 10x - 5 + 5
y = -5x² + 10x
maximum height = y coordinate of the vertex of the parabola
x = -10/-10
x = 1
y = -5 (1)² + 10 (1)
y = -5 + 10
y = 5
5 meters
b) the x coordinate of the vertex is 1
1 meter
c) since the term without x is 0, the ball was kicked from the ground
0 meters
d) we have to find the x-intercept
-5x² + 10x = 0
-5/-5 x² + 10/-5 x = 0/-5
x² - 2x = 0
x(x-2) = 0
x = 0
x = 2
2 meters
2(x+1.25) =3.5 without distributive property
Answer:
x = 0.5
Step-by-step explanation:
2 (x+1.25) = 3.5
Divide by 2 on both sides.
x + 1.25 = 1.75
Subtract 1.25 on both sides.
x = 0.5
Answer:
x = 0.5
Step-by-step explanation:
2(x+1.25) =3.5
Divide both sides by 2.
x+1.25 = 3.5/2
x + 1.25 = 1.75
Subtract 1.25 from both sides.
x = 0.5
19a - 6 = 4a please help me solve this! this is due in two days and the entire paper has 50 questions, this is only question 27!!
Answer:
a=6/15
Step-by-step explanation:
19a-6=4a
(19-4)a=6
a=6/15
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Answer:
a= 2/5 =0.4
Step-by-step explanation:
19a−6=4a
Subtract 4a from both sides.
19a−6−4a=0
Combine 19a and −4a to get 15a.
15a−6=0
Add 6 to both sides. Anything plus zero gives itself.
15a=6
Divide both sides by 15.
a= 6/15
Reduce the fraction 6/15 to lowest terms by extracting and canceling out 3.
a=2/5
please show your work
d) [tex]\frac{48y^{10} }{x^{9} }[/tex] is the answer to your question
Exponents:
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64.In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.The symbol used for representing the exponent is ^. This symbol (^) is called a carrot. For example, 4 raised to 2 can be written as 4^2 or 42. Thus, 4^2 = 4 × 4 = 16Adding exponents while maintaining the same base is the rule for multiplying like bases.exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.To know more about Exponents:
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