By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
How to prove this point lies on the unit circle?In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
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SOMEONE PLEASE HELP!!! Find the area of the sector. Round your answer to the nearest tenth.
Answer:
398.2 cm^2
Step-by-step explanation:
[tex]\frac{270}{360}[/tex] * [tex]169\pi[/tex] ≈398.2 cm^2
A supermarket increases the prices of some grocery items by 10%.
(a) What will be the new price of a loaf of bread marked at $1.80.
(b) What will the price of a packet of cereal that has a price tag of $4.20, but already discounted by 50%
Answer:
(a) $1.98
(b) $6.30
Step-by-step explanation:
(a)
The new value =
1.80 + The value of the percentage increase =
1.80 + (10% × 1.80) =
1.80 + 10% × 1.80 =
(1 + 10%) × 1.80 =
(100% + 10%) × 1.80 =
110% × 1.80 =
110 ÷ 100 × 1.80 =
110 × 1.80 ÷ 100 =
198 ÷ 100 =
1.98
Calculate the actual change (the absolute difference) between the two values
The actual change =
The new value - 1.80 =
1.98 - 1.80 =
0.18
Proof of calculation.
Calculate the percentage increased value...
... and see if we get as a result...
... the actual change (the absolute difference).
Calculate the percentage increased value:
The value of the percentage increase =
10% × 1.80 =
10 ÷ 100 × 1.80 =
10 × 1.80 ÷ 100 =
18 ÷ 100 =
0.18
So we have proven that the calculations are correct.
For positive numbers
The actual change =
The value of the percentage increase
The answer:
1.80 increased by 10% = 1.98
The actual change:
1.98 - 1.80 = 0.18
(b)
Calculate the New value
The new value =
42.0 + The value of the percentage increase =
4.20 + (50% × 4.20) =
4.20 + 50% × 4.20 =
(1 + 50%) × 4.20 =
(100% + 50%) × 4.20 =
150% × 4.20 =
150 ÷ 100 × 4.20 =
150 × 4.20 ÷ 100 =
63,000 ÷ 100 =
630
(but its as a dollar so its 6.30)
Calculate the actual change (the absolute difference) between the two values
The actual change =
The new value - 4.20 =
6.30 - 4.20 =
2.10
Proof of calculation.
Calculate the percentage increased value...
... and see if we get as a result...
... the actual change (the absolute difference).
Calculate the percentage increased value:
The value of the percentage increase =
50% × 4.20 =
50 ÷ 100 × 4.20 =
50 × 4.20 ÷ 100 =
21,000 ÷ 100 =
210
(but its as a dollar so its 2.10)
So we have proven that the calculations are correct.
For positive numbers
The actual change =
The value of the percentage increase
The answer:
4.20 increased by 50% = 6.30
The actual change:
6.30 - 4.20 = 2.10
The probability of an outcome being more than three standard deviations away from the mean in a normal distribution is approximately ___ percent.
The probability in a normal distribution is approximately 90% percent.
According to the statement
we have given that the
Probability of the more three standard deviations and we have to find the percentage in a normal distribution.
We know that the
A normal distribution is a type of continuous probability distribution for a real-valued random variable.
So, In the presence of a more than three standard deviations the normal distribution is about 95%.
Because in the normal distribution is 95% due to the empirical rule.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So, The probability in a normal distribution is approximately 90% percent.
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Circle O is shown. Line segments B O and O C are radii. Point A is on the circle and is not within angle B O C.
The measure of Arc B A C is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?
3:1
1:3
2:1
1:2
The ratio of major to minor arc = 2 : 1
What is a Circle?
A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
Calculation
The length of an arc (L) with center angle θ is given by:
L = (θ/360) * 2πr
where r is the radius.
Putting the values in the above formula.
For the major arc:
L = (240/360) * 2πr
For the major arc:
l = ((360-240)/360) * 2πr
l = (120/360) * 2πr
The ratio of major to minor arc = [(240/360) * 2πr] / [(120/360) *2πr] = 2 : 1
The ratio of major to minor arc = 2 : 1.
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Answer:c
Step-by-step explanation:
The points (-3,2) (5,2) and (5,1) are three vertices of a rectangle what is the fourth vortex?
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
show all work
insert picture of the tree diagram pls
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)
Using the law of sines, it is found that 1 triangle can be formed with the given conditions.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, for this problem, we have that the relation is:
[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]
[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]
[tex]\sin{G} = 0.8089[/tex]
[tex]G = \arcsin{0.8089}[/tex]
G = 54º
A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.
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Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?
Answer:
Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?
Step-by-step explanation:
determine which two of the three given triangles are similar. Find the scale factor for the pair.
On a coordinate plane, square P Q R S is shown. It has points (0, 4), (4, 4), (0, 0), and (4, 0).
Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other.
Step 1: Calculate the slope of the diagonals.
The slope of diagonal PS is
.
The slope of diagonal QR is
.
Step 2: Calculate the midpoint of the diagonals.
The midpoint of PS is
.
The midpoint of QR is
.
The diagonals of the square are perpendicular bisectors because the diagonals are
.
The slope of diagonal PS is -1 and the slope of diagonal QR is 1 based on the information about the coordinate plane.
How to illustrate the information?Step 1: Calculate the slope of the diagonals.
The slope of diagonal PS is -1
The slope of diagonal QR is 1
Step 2: Calculate the midpoint of the diagonals.
The midpoint of PS is (2,2)
The midpoint of QR is (2,2)
The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint
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Answer:
1. The slope of diagonal PS is -1.
2. The slope of diagonal QR is 1.
3. The midpoint of PS is (2,2).
4. The midpoint of QR is (2,2).
5. The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint.
Step-by-step explanation: I just did it on edge 2023. Hope this helps!
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite
direction. The number b varies directly with the number a. For example b = 22 when a = -22. Which
equation represents this direct variation between a and b?
b=-a
-b=-a
b-a=0
b(-a) = 0
Answer:
b = -a
Step-by-step explanation:
Since a and b are equally distant to zero but in opposite directions, a and b are opposites, or additive inverses.
The sum of additive inverses is zero.
a + b = 0
b = -a
Check all that apply
X^2+7x-8
Answer:
x = -8, 1.
Step-by-step explanation:
x^2 + 7x - 8 = 0
(x + 8)(x - 1) = 0
x = -8, 1.
Answer:
-8 and 1
Step-by-step explanation:
Quadratic expression.
A quadratic expression is an expression with 2 as the highest power of the unknown.
Solving the question:
[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]
Copy DEF to the line so that S is the
vertex.
This task will be complete when you have
constructed an angle with vertex S that is
congruent to ZDEF.
Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.
How to construct an angle with vertex?
To copy an angle we observe the subsequent steps,
1). Mark a working line with the help of a straightedge.
2). Now we set a point S as the vertex of the angle.
3). Create an arc with a radius 'r' (any length ) from vertex S which bisects the working line V.
4). With the exact radius we mark an arc from point E which bisects the line ED and EF at G and H respectively.
5). Mark an arc from point G which bisects line EF at I.
6). Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.
7). Now join the points S and U.
Therefore we copy any angle.
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Which expression is equivalent to -7(y - 2)
The expression equivalent to -7(y - 2) is -7y + 14
Which expression is equivalent to -7(y - 2)?
Given the expression; -7(y - 2)
We expand the expression by multiplying each element inside the parentheses the element out i.e -7
-7(y - 2)
[ -7 × y and -7 × -2 ]
-7y + 14
Therefore, the expression equivalent to -7(y - 2) is -7y + 14.
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A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700
26.8% of examinees will score between 600 and 700.
This question is based on z score concept.
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
[tex]z={x-\mu \over \sigma }[/tex]
where:
μ is the mean
σ is the standard deviation of the population
Given:
μ = 560
σ = 90
For
600≤ X≤700
for x = 700
Z score =x - μ/σ
=(700 - 560)/90
= 1.55556
P-value from Z-Table:
P(560<x<700) = P(x<700) - 0.5 = 0.44009
for x = 600
Z score =x - μ/σ
=(600 - 560)/90
= 0.44444
P-value from Z-Table:
P(560<x<600) = P(x<600) - 0.5 = 0.17164
∴ P(600<x<700) = P(560<x<700) - P(560<x<600)
= 0.44009 - 0.17164
=0.26845
∴26.8% percentage of examinees will score between 600 and 700.
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For how many positive integers $n$ less than or equal to $24$ is $n!$ evenly divisible by $1 2 \dots n$
The value of positive integers in the set are 16.
According to the statement
we have given that the there is a set of numbers from 1 to n and we have to find that the how many integers in this set. and there is one condition that the numbers in the set are less than or equal to 24.
So, For this purpose,
Since [tex]$1 + 2 + \cdots + n = \frac{n(n+1)}{2}$[/tex]
the condition is equivalent to having an integer value for [tex]$\frac{n!} {\frac{n(n+1)}{2}}$.[/tex]
This reduces, when [tex]$n\ge 1$[/tex], to having an integer value for [tex]$\frac{2(n-1)!}{n+1}$[/tex]
This fraction is an integer unless n+1 is an odd prime. There are 8 odd primes less than or equal to 24,
so there are 24-8 = 16.
So, The value of positive integers in the set are 16.
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Someone pls pls PLS, help, its urgent!!! ASAP!!
“Complete the proof (geometry)”
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ACB[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABC[/tex] and [tex]\triangle BED[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\therefore \triangle ACB \cong \triangle DEB[/tex] (HL)
5) [tex]\therefore \angle ACB \cong \angle DEB[/tex] (CPCTC)
can you help me with this
A waste management survey collected data about the types of materials that were recycled by three different states in
2008
20082008. The table at left shows the approximate amount of each material recycled measured in thousands of tons. Based on the information in the table at left, as a percentage, approximately what is the relative frequency of plastics recycled in New Mexico in plastics recycled in all three states combined?
As a percentage, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.
What is relative frequency?A relative frequency measures the proportion of events that occur within a class out of the total number of observations.
When using relative frequency, the results are usually displayed in percentages, proportions, and fractions.
Data and Calculations:Year State Recycled Plastics Relative
(thousands of tons) Frequency
2008 New Mexico 500 0.111 (500/4,500)
2008 New York 1,500 0.333 (1,500/4,500)
2008 Texas 2,500 0.566 (2,500/4,500)
Total 4,500 1
Thus, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.
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Answer: 9%
Step-by-step explanation:
just did the question
Theo earns a base salary plus commission. At the end of September, he was paid $3,835.25 based on his monthly sales of $12,850. At the end of October, he earned $3,641 based on $9,875 in sales. What was Theo’s base salary?
Theo's base salary using a simultaneous equation approach is $2,996.22 .
In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary
Bear in mind that total earnings are determined as base salary plus commission
Let X be the base salary
Let R be the rate of commission
commission =sales*rate of commission
When earnings were $3,835.25 and sales is $12,850, we have the below equation:
X+(12,850*R)=3,835.25
X+12850R=3,835.25 .................... equation (1)
When earnings were $3,641 and sales is $9,875, we have the below equation:
X+(9,875*R)=3641
X+9875R=3641 ......................... equation (2)
subtract equation 2 from 1
2975R=194.25
R=194.25/2975
R=commission rate=6.52941176470588%
substitute for R in equation 1 to arrive at X(base salary)
X+(12850*6.52941176470588%)=3,835.25
X=3,835.25-(12850*6.52941176470588%)
X=base salary=$2,996.22
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Could someone help me with the first two parts of this geometry question? I can do the third and fourth myself.
Answer:
see image
Step-by-step explanation:
see image. We can use the given info and definition of isosceles (congruent sides) and reflexive property (something is congruent to itself) to prove (i) by SSS.
The using "Corresponding Parts of Congruent Triangles are Conguent" (CPCTC) to get more info to prove (ii) by SAS
If you live in Miami, then you live in
Florida.
Choose the equivalent statement.
A. If you live in Florida, then you live in Miami.
B. If you don't live in Miami, then you don't live in
Florida.
C. If you don't live in Florida, then you don't live in
Miami.
Answer: the answer is c.
Step-by-step explanation:
I’ve tried everything and yet don’t understand this
Snow reaches at a 15 inches after 16 hours. and 8 inches melt in next 6 hours.
According to the statement
we have a given that there was 1 inch snow on the ground before the snowstorm starts.
then snow fell at constant rate of 3 inches every 2 hours until the snow level reaches at 12 inch had fallen
It means after that there was 13 inch snow on the ground.
and in 1 hour only 1.5 inches snow increases
and if snow takes 2 hours to increase at 3 inches then
it takes 10 hours to reach at 12 inches.
So, snow falls for 10 hours to increase at 12 inches.
And then the snow falls at constant rate of 1 inch per hour for 2 hours.
It means now snow reaches at a 15 inches after 16 hours.
Then sun melt the snow at a 4 inches per 3 hours and sun came for 6 hours then
it means now the level of snow reduced and came at the 7 inches.
because sun reduced 8 inches snow in 6 hours.
So, this is the data collected by a person.
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Three less than a number x is more than 15. an inequality that represents this word sentence is
Answer:
x - 3 > 15
Step-by-step explanation:
Find the maximum or minimum value of the product of two numbers whose difference is 14.
The maximum value of the product of two number whose difference is 14 is 49.
What is the maximum or minimum value of a function?The maximum or minimum value of a function is the highest or lowest value of that function.
How to determine the maximum or minimum of the product of two numbers?Let the numbers be x and y
Their product f(x,y) = xy
Since their difference is 14, x - y = 14
So, x = 14 - y
Substituting x into f(x,y), we have
f(x,y) = xy
= (14 - y)y
= 14y - y²
To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.
So, f(x,y) = f(y) = 14y - y²
df(y)/dy = d(14y - y²)/dy
df(y)/dy = d(14y)/dy - dy²/dy
df(y)/dy = 14 - 2y
Equating to zero, we have
df(y)/dy = 0
14 - 2y = 0
14 = 2y
y = 14/2
y = 7
To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again
So, df'(y)/dy = d(14 - 2y)/dy
= d14/dy + d(-2y)/dy
= 0 - 2
= -2 < 0.
Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)
So, since y = 7,
x = 14 - y = 14 - 7 = 7
So, f(x,y) is maximum at x = 7 and y = 7
So, f(7,7) = 7 × 7
= 49
So, the maximum value of the product of two number whose difference is 14 is 49.
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Can someone help me please?
A.0.36
B.0.55
C.0.18
D.0.45
Answer:
B
Step-by-step explanation:
44/77
=0.55
The ratio of butter:flour:sugar in a recipe is 1:9:6. When using 8 cups of sugar in this recipe, how many total cups of ingredients will be used
Answer:
21 and a third cups bxisjsbdn
Shannon wants to make snack bags that contain an equal amount of three different types of nuts. If she has 26
almonds, 78 pecans, and 52 peanuts, what will be the most number of bags she can have?
I'm having a hard time with this question so someone help please
Answer:
7.7 km
Step-by-step explanation:
This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.
Law of SinesThe Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...
t/sin(T) = p/sin(P) = j/sin(J)
We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.
SetupWe know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:
7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j
SolutionThis can be solved in two steps. First, we find angle P, then we use that to find length j.
sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847
P = arcsin(0.642847) ≈ 40.0045°
Now, we can find j:
j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km
The distance from the tower to the plane is about 7.7 km.
__
Additional comment
We have used T, P, and J to refer to the vertices at the tower, plane, and jet.
The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.
Select all the correct systems of equations. Which systems of equations have infinite solutions? 2x + 5y = 31 6x - y = 13 y = 14 - 2x 6x + 3y = 42 2x + y = 14 x = 13-2y Reset 2x + y = 10 -6x = 3y + 7 y = 13-2x 4x - 3y = -19 2x + y = 17 Next -6x = 3y - 51
Answer:
The system of equations y=14-2x and 6x+3y=42.
Step-by-step explanation:
Please see attachment to see the answer as a graph.
Hope this helps!