The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.
According to the statement
we have to give the terms which explain the sin (pi/3) perfectly.
And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.
And Now we explain all terms below
So,
"Right Triangle is a triangle whose one of the angle measures 90° "
And "The hypotenuse is a longest side of the right triangle.
And"Unit Circle is a circle with radius 1."
For given question,
We have been given a unit circle.
So, We need to find the sin (pi/3)
We know, in a right triangle for any angle , θ
Sinθ = Opposite side of angle / Hypotenuse
So, for , Sin(pi/3) = Opposite side of angle / 1
Sin(pi/3) = Opposite side of angle
Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.
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3) A normal distribution has a mean of 75 and a standard deviation of 15. Determine the z-score for the data value of 85.
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (85 - 75)/15 = 10/15 = 2/3 = 0.666666... ≈ 0.67
as z-tables usually round the z-score to hundredths.
The z-score for the data value of 85 is 0.67.
How to Calculate Z-Score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.
To find the z-score, you simply need to apply the following formula:
z = (x - μ) / σ
μ=75
σ=15
x=85
z =85-75/15
z=10/15
=2/3
=0,66666....=0.67
Therefore, the z-score for the data value of 85 is 0.67.
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What is the mass percent of cashews in a 10. 0g mixed nut sample if the cashews are 0. 87g?
Answer:
0.87%
Step-by-step explanation:
→ Divide 0.87 by 10
0.87 ÷ 100 = 0.0087
→ Multiply answer by 100
0.0087 × 100 = 0.87
Which geometric solids would model the tent?
cone and sphere
cylinder and cone
pyramid and rectangular prism
triangular prism and rectangular prism
A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.
Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex] --->(1)
Given,[tex]\frac{dx}{dt}= 2feet/second[/tex] at x=3
Put x=3 in Pythagoras theorem equation (1)
[tex](3)^{2} + y^{2} = 144[/tex]
[tex]y^{2} = 144 - 9[/tex]
[tex]y^{2}[/tex] = 135
y = 11.61
Derive equation (1) w.r.t to 't'
[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex] ---->(2)
substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]
12 + 23.22 [tex]\frac{dy}{dt}[/tex] = 0
[tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]
[tex]\frac{dy}{dt} = -0.518[/tex]
Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
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James and Simon have a reading assignment to complete. James has read r
rr pages, and Simon has read 75 pages. Together they have read a total of 200 pages. Select the equation that matches this situation.
Choose 1 answer:
Answer:
Step-by-step explanation:
125 I think
State the transformations being applied to each quadratic function.
a) y = -1/2(x+2)^2+4
b) y= -(x-1)^2-2
c) y=(4x)^2
d) y= 4x^2
The function transformations are:
The function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 unitsThe function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 unitsThe function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4The function (d) y = 4x^2 is stretched vertically by a factor of 4What are transformations?Transformations involve translating, reflecting, rotating and dilating a function across the coordinate plane
How to determine the transformations?The parent function of a quadratic function is represented as:
y = x^2
When the function is stretched horizontally by a factor of k, where k is between 0 and 1, we have:
y = (x/k)^2
Assume k = 1/4. we have:
y = (4x)^2
This means that the function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4
When the function is stretched vertically by a factor of k, where k is greater than 1, we have:
y = k(x)^2
Assume k = 4. we have:
y = 4x^2
This means that the function (d) y = 4x^2 is stretched vertically by a factor of 4
Translating the function left is represented as:
y = (x + k)^2
Assume k = 2. we have:
y = (x + 2)^2
Reflecting the function across the x-axis is represented as
y = -(x + 2)^2
When the function is compressed vertically by a factor of k, where k is between 0 and 1, we have:
y = -k(x + 2)^2
Assume k = 1/2. we have:
y = -1/2(x + 2)^2
Translating the function up is represented as:
y = -1/2(x + 2)^2 + k
Assume k = 4. we have:
y = -1/2(x + 2)^2 + 4
Hence, the function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 units
Translating the function right is represented as:
y = (x - k)^2
Assume k = 1. we have:
y = (x - 1)^2
Reflecting the function across the x-axis is represented as
y = -(x - 1)^2
Translating the function down is represented as:
y = -(x - 1)^2 - k
Assume k = 2. we have:
y = -(x - 1)^2 - 2
Hence, the function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 units
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The diameter of a varicocele measures more than _____ millimeters (mm). * 5 points 5 3 4 2
Answer:
A varicocele measures more than 2 mm in diameter.
Step-by-step explanation:
pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.
What is the area of parallelogram ABCD?
A. 12 units²
B. 30 units²
C. 24 units²
D. 55 units²
Answer:
C, 24 units^2
Step-by-step explanation:
The formula for area of a parallelogram is base times height.
The height of the parallelogram is 4 units
The base of the parallelogram is 6 units
4 times 6 is 24
Hope this helps:)
Answer:
C. 24 units²
Step-by-step explanation:
To calculate the area of a parallelogram we use the following formula:
A = B*h (B: base, h: height)
The base of the parallelogram is 6 units and the height is 4 units
4*6 = 24 units but, the area is presented in square units so the answer is 24 units²
15 POINTS!!!! PLS HELP LOOK AT PIC
Answer:
A
Step-by-step explanation:
The solutions of a quadratic function will always be the x intercepts. Thus, if there are two solutions, there are two x intercepts.
Solve for X in the diagram below
Step-by-step explanation:
the sum of all angles around a single point on one side of a line must be 180°.
because that line can be seen as the extension of the diameter of a circle, and the point would be the center of that circle. so, one side of the line represents a half-circle, which stands for 180°.
so we have
180 = 40 + 40 + (2x + 30) = 80 + 2x + 30 = 110 + 2x
70 = 2x
x = 35
Points A and B are 200 miles apart. A cyclist starting at point A and a motorcyclist starting at point B move toward each other. The speed of the cyclist is 17 mph and the speed of the motorcyclist is 83 mph. what distance from point A will they meet.
Answer:
34 miles from A
Step-by-step explanation:
Find time to cover 200 miles at ( 17 + 83 mph) = 200/100 = 2hours
cyclist will be at 2 * 17 = 34 miles from A
The graph of the function f(x)=x2+12 is shown which stamen te describe the graph Check all that apply
65. Find the perimeter & area:
13 cm
5 cm
12 cm
66.
Given, that the sides of a triangle are [tex]$5 \mathrm{~cm}, 12 \mathrm{~cm}$[/tex] and [tex]$13 \mathrm{~cm}$[/tex] semi-perimeter [tex]$=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$[/tex]
[tex]$$\begin{aligned}&\mathrm{s}=\frac{(5+12+13)}{2} \\&\mathrm{~s}=\frac{30}{2} \\&\mathrm{~s}=15 \mathrm{~cm}\end{aligned}$$[/tex]
Area of the triangle (according to Heron's Formula)
[tex]$$\begin{aligned}&=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{15(15-5)(15-12)(15-13)} \\&=\sqrt{15(10)(3)(2)} \\&=\sqrt{900} \\&=30 \mathrm{~cm}^{2}\end{aligned}$$[/tex]
What is Heron's Formula?
Heron's formula was first given by Heron of Alexandria. It is used to calculate the area of various triangles such as equilateral, isosceles, and scalene triangles or quadrilaterals. When we know the sides of a triangle, we can use Heron's formula to find its area. Using Heron's formula, we find the area of a triangle by taking its semi-perimeter and side lengths.Heron's formula is used to calculate the area of triangles given the lengths of all their sides, as well as the area of quadrilaterals. It's also known as Hero's formula. This formula for calculating the area does not rely on the angles of a triangle. It is solely determined by the lengths of all triangle sides. It contains the term "s," which stands for semi-perimeter, which is obtained by halving a triangle's perimeter. Similarly, the concept of determining the area is extended to determine the area of quadrilaterals.To learn more about Hero's formula visit:
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URGENT WILL GIVE BRAINLIEST
Answer:
626.7 [tex]cm^{2}[/tex]
Step-by-step explanation:
Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.
CIRCLE
A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7
RECTANGLE
A = l*w = 15*30 = 450
176.7 + 450 = 626.7 [tex]cm^{2}[/tex]
Answer: 626.7cm^2
Step-by-step explanation:
30 * 15 = 450
area of circle = πr^2
r = 15/2 = 7.5
[tex]7.5^2=56.25*pi=176.7[/tex]
450+176.7 = 626.7
The volume, V, of a cylinder is V=r²h, where r is the
radius of the cylinder and h is the height. Using rounding
to the nearest whole number, which of the following is an
estimate of the volume of a cylinder with a radius of
3.75 inches and height of 6.21 inches?
Answer:
~87.33 in³
Step-by-step explanation:
All you have to to is pkug the numbers in the formula. You start by doing 3.75 as the r² and you get around 14.06. Then you multiply that by the height (6.21) which gets you around 87.33. I hope this helps!
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the
Answer:
10 points
Step-by-step explanation:
From the passage, we know:
1. Jay earned 15 points after spending $60
2. We want to know the number of points he can earn if he spends $40
We can set this up into proportions.
60:15 = 40:x
The x is the number of points he will get after spending $40.
15(40) = 60x
600 = 60x
x = 10
Jay will earn 10 points if he uses $40.
I need help on this please!
Answer:
Step-by-step explanation:
Part A:
CIRCLE A : Circumference is (pi)(diameter) so if they give you the circumference (21.98), divide it by 7 which gives you 3.14.
CIRCLE B: 18.84/6 = 3.14
Part B:
CIRCLE A: Area is (pi)(radius^2) so if they give you the area (38.465), divide it by radius^2 (7/2 = 3.5^2 = 12.25) = 3.14
CIRCLE B: 28.26/(3^2) = 3.14
Part C:
The value of pi stays the same for circle A and B.
Hope this helps :)
The interior angles of a polygon are; (3x + 30), x, 2x, (x + 20) and 3x. find the value of x
Answer: 49
Step-by-step explanation:
This polygon has 5 sides, meaning its interior angles add to [tex]180(5-2)=540^{\circ}[/tex].
[tex]3x+30+x+2x+x+20+3x=540\\\\10x+50=540\\\\10x=490\\\\x=49[/tex]
The likelihood that a patient with a heart attack dies of the attack is 0.04 (i.e., 4 of 100 die of the attack). Suppose we have 50 patients who suffer a heart attack. What is the probability that all will survive
The probability solved by binomial distribution that all will survive is 0.8154.
What is Binomial distribution?When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
Computation of probability of all survived people from heart attack;
A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).
What is the likelihood that each of the five patients who experience a heart attack will survive?
We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).
Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.
Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.
By binomial distribution,
[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]
Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).
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The combination for opening a safe is a four-digit number made up of different digits. How many different comninations can you make, using only add digits?
There are 625 different 4-digit codes only made with odd numbers.
How many different combinations can you make?To find the total number of combinations, we need to find the number of options for each one of the digits.
There are 4 digits, such that each digit can only be an odd number.
For the first digit, there are 5 options {1, 3, 5, 7, 9}For the second digit, there are 5 options {1, 3, 5, 7, 9}For the third digit, there are 5 options {1, 3, 5, 7, 9}For the fourth digit, there are 5 options {1, 3, 5, 7, 9}The total number of different combinations is given by the product between the numbers of options, so we have:
C = 5*5*5*5 = 625.
There are 625 different 4-digit codes only made with odd numbers.
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A pattern has 77 yellow triangles to every 33 green triangles. What is the ratios of green triangles to yellow triangles?
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answer:
y is equal to 24
Step-by-step explanation:
If y is directly proportional to x when x is equal to 5 and y is 12, then when you multiply 5 by 2 which is 10, y will be proportional to that when you multiply 12 by 2 which is 24
Answer:
b: 25
Step-by-step explanation:
The previous answer wowwubbzy13 uploaded is absolutely correct!
I'll set up a proportion.
If y = 12, then x = 5
--> 12:5
We want to find the y when x is 10
--> y:10
12:5 = y:10
5y = 120
y = 25
So B: 25 is the correct answer!
which whole number is equal to the fraction 42/6
Answer:
7.
Step-by-step explanation:
Think of 42/6 as a division question.
42 ÷ 6.
The answer to this equation is 7.
What is the parameter of interest to compare the proportions from two populations?.
Answer:
also known as the population parameter of interest the parameter of interest is a practical value that gives you more information about the research sample or population being studied in other words these parameter define the describe the search population
what is parameter answer is given above
A bookstore sells books for $2, $3, $5, and $10. Let random variable X = "amount of
money for one book."
Look at the relative-frequency table below representing the amount of money spent on
one item and the relative frequencies with which customers purchase them
If the expected amount of money spent by a customer is $3.23 what is the standard deviation?
The value of the standard deviation is σ = 2.20. Using probability distribution, the required standard deviation is calculated.
How to calculate the standard deviation?The formula for the standard deviation of the given probability distribution is
σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²
Where the mean μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]
Calculation:It is given that,
x: $2, $3, $5, $10
P(X=x): 0.55, 0.26, 0.11, 0.08
Step 1: Calculating the mean:
we have μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]
⇒ μₓ = 2 × 0.55 + 3 × 0.26 + 5 × 0.11 + 10 × 0.08
∴ μₓ = 3.23
Step 2: Calculating the standard deviation:
x: 2, 3, 5, 10
x²: 4, 9, 25, 100
P(X=x): 0.55, 0.26, 0.11, 0.08
([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]: 4 × 0.55 = 2.2; 9 × 0.26 = 2.34; 25 × 0.11 = 2.75; 100 × 0.08 =8
∑[([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]]: 2.2 + 2.34 + 2.75 + 8 = 15.29
Therefore,
The standard deviation, σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²
⇒ σ = [tex]\sqrt{15.29-(3.23)^2}[/tex]
= [tex]\sqrt{15.29-10.43}[/tex]
∴ σ = 2.20
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Which type of function describes f(x)?
Exponential
Logarithmic
Rational
Polynomial
11. What is the y-intercept of a line that passes through the point (5,17)
and has a slope of 4?
1. 17
2. 11
3. -3
4. 46
5. 2
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
y - intercept = -3[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Equation of straight line in point - slope form :
[tex]\qquad❖ \: \sf \:y - y1 = m(x - x1)[/tex]
( m = slope = 4, point (5 , 17) )
[tex] \qquad◈ \: \: \sf \: y - 17 = 4(x - 5)[/tex]
[tex] \qquad◈ \: \: \sf \: y - 17= 4x - 20[/tex]
[tex] \qquad◈ \: \: \sf \: y = 4x - 20 + 17[/tex]
[tex] \qquad◈ \: \: \sf \: y = 4x - 3[/tex]
Now, it's the form of line in slope - intercept form, ( slope = coefficient of x = 4 and y - intercept = -3 )
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex] \qquad◈ \: \: \sf \: y \: \: int = - 3[/tex]
uan recently hired a roofer to do some necessary work. On the final bill, Juan was charged a total of $1131.5. $450 was listed for parts and the rest for labor. If the hourly rate for labor was $47, how many hours of labor was needed to complete the job?
Based on the total cost that Juan incurred to hire the roofer including the charge for parts and labor, the number of hours that was needed to complete the job was 14.50 hours.
How many hours did the roofer use?The first thing to do is to find out the amount that went to labor:
= Final bill - cost of materials
= 1,131.5 - 450
= $681.50
Now that you have the cost of labor, you can find out the number of labor hours that were used based on the hourly rate:
= Cost of labor / Hourly rate
Solving gives:
= 681.50 / 47
= 14.5 hours
In conclusion, the number of labor hours that the roofer used to complete the work, based on the total amount charged to Juan is 14.50 hours.
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Find the distance between the pair of points: (-3,-6) and (1,2).
d² = (y2 - y1)² + (x2 - x1)²
..............
[tex] \color{red} \sf Solve \: for \: x : \\ \sf \: \: 4x + 2 = -8?[/tex]
Thank uh !
Answer:
x = -5/2
Step-by-step explanation:
4x+2 = -8
We are solving for x
The first step in isolating x is to subtract 2 from each side
4x+2-2 = -8-2
4x = -10
Divide each side by 4
4x/4 = -10/4
x = -10/4
Simplify the fraction
x = -5/2
Answer:
x= -5/2Step-by-step explanation:
4x+2 = -8
4x = -10
4x/4 = -10/4
x = -5/2