Answer:
75°Step-by-step explanation:
We know that:
sin 30° = 1/2, therefore arcsin (1/2) = 30°tan 45° = 1, therefore arctan (1) = 45°So the value of the expression is:
arcsin (1/2) + arctan (1) = 30° + 45° = 75°Answer:
75°
Step-by-step explanation:
Recall the common trigonometric angles:
[tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]
[tex]\tan 45^{\circ}=1[/tex]
Arcsin is the inverse of sin.
Arctan is the inverse of tan.
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)=30^{\circ}[/tex]
[tex]\implies \arctan (1) = 45^{\circ}[/tex]
Therefore:
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)+\arctan (1) = 30^{\circ}+ 45^{\circ}=75^{\circ}[/tex]
A cone has a height of 12 centimeters and a diameter of 10 centimeters. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
please help i really need like 6 more questions
Answer:
314 cm³
Step-by-step explanation:
Given ::
Cone height, h = 12 cm
Diameter of cone, d = 10 cm
Hence, radius, r = diameter / 2 = 10/2 = 5cm
The volume of a cone = 1/3 πr²h
V = 1/3 * 3.14 * 5² * 12
V = 3.14 * 25 * 4
V = 314cm³
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
y
p(x, y) 0 1 2
x 0 0.10 0.03 0.01
1 0.08 0.20 0.06
2 0.05 0.14 0.33
(a) Given that X = 1, determine the conditional pmf of Yi.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.)
y 0 1 2
pY|X(y|1)
(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.)
y 0 1 2
pY|X(y|2)
Answer:
(a)
[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}[/tex]
(b)
[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {0} &{0.1}&{0.03} & {0.01} & {0.14} & {1} &{0.08}&{0.20} & {0.06} &{0.34}& {2} &{0.05}&{0.14} & {0.33} &{0.52 } \ \end{array}[/tex]
Solving (a): Find PMF of y if x = 1
This implies that, we consider the dataset of the row where x = 1 i.e.
[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {1} &{0.08}&{0.20} & {0.06} &{0.34} \ \end{array}[/tex]
The PMF of y given x is calculated using:
[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{P(x)}[/tex]
When x = 1
[tex]P(x) = 0.34[/tex] --- the sum of the rows
So, we have:
[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.34}[/tex]
For i = 0 to 2, we have:
[tex]i = 0[/tex]
[tex]P(y=0|x)=\frac{P(y=0\ \&\ x = 1)}{0.34}[/tex]
[tex]P(y=0|x)=\frac{0.08}{0.34}[/tex]
[tex]P(y=0|x)=0.2353[/tex]
[tex]i =1[/tex]
[tex]P(y=1|x)=\frac{P(y=1\ \&\ x = 1)}{0.34}[/tex]
[tex]P(y=1|x)=\frac{0.20}{0.34}[/tex]
[tex]P(y=1|x)=0.5882[/tex]
[tex]i = 2[/tex]
[tex]P(y=2|x)=\frac{P(y=2\ \&\ x = 1)}{0.34}[/tex]
[tex]P(y=2|x)=\frac{0.06}{0.34}[/tex]
[tex]P(y=2|x)=0.1765[/tex]
So, the PMF of y given that x = 1 is:
[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}[/tex]
Solving (b): The interpretation of (b) is to find the PMF of y if x = 2
This implies that, we consider the dataset of the row where x = 2 i.e.
[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {2} &{0.05}&{0.14} & {0.33} &{0.52 }\ \end{array}[/tex]
When [tex]x = 2[/tex]
[tex]P(x) = 0.52[/tex]
So, we have:
[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.52}[/tex]
For i = 0 to 2, we have:
[tex]i = 0[/tex]
[tex]P(y=0|x)=\frac{P(y=0\ \&\ x = 2)}{0.52}[/tex]
[tex]P(y=0|x)=\frac{0.05}{0.52}[/tex]
[tex]P(y=0|x)=0.0962\\[/tex]
[tex]i =1[/tex]
[tex]P(y=1|x)=\frac{P(y=1\ \&\ x = 2)}{0.52}[/tex]
[tex]P(y=1|x)=\frac{0.14}{0.52}[/tex]
[tex]P(y=1|x)=0.2692[/tex]
[tex]i = 2[/tex]
[tex]P(y=2|x)=\frac{P(y=2\ \&\ x = 2)}{0.52}[/tex]
[tex]P(y=2|x)=\frac{0.33}{0.52}[/tex]
[tex]P(y=2|x)=0.6346[/tex]
[tex]P(y=0|x)=0.0962\\[/tex]
[tex]P(y=1|x)=0.2692[/tex]
[tex]P(y=2|x)=0.6346[/tex]
So, the PMF of y given that x = 1 is:
[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}[/tex]
when a fraction has a small numerator and a bigger denominator what you notice about the percent
when a fraction has a small numerator and a bigger denominator, the percent would be a proper fraction.
What is percent?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.
As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol “%” represents it.
Therefore, When a fraction has a small numerator and a large denominator, it is a proper fraction.
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An ice cream store offers waffle cones or sugar cones. Each is equally likely to be chosen.
Which of the following models could be used to simulate this situation?
(HINT: Choose the model with the same number of possible outcomes as cone choices.)
Group of answer choices
A rolling a 6-sided number cube
B spinning a spinner with 3 equal sections
C flipping a coin
D using a random number generator that generates numbers 1 through 9
Answer:
C
Step-by-step explanation:
hopes it helps you!
Answer:
Flipping a coin
Step-by-step explanation:
It is the best answer, because the other choices do not represent a 50% chance. Rolling a 6-sided number cube would be good if you had 6 things, spinning a spinner would be ideal for 3, and using a number generator would be good for 9 things.
Given that f(x)=x+9 and g(x)=4x
Evaluate:
a) fg(2)
b) gf(2)
Answer:
f(x)=11
g(x)=8
Step-by-step explanation:
f(x)=(2)+9=11
g(x)=4(2)=8
BRAINLIEST PLEASE
Help!! Like what even is this
The new transformation coordinates are B""(6, 15), C""(-3, 12), and Dilate k=3 by multiplying both x and y by 3.
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
For point B,
B(1,2) → B'(1 , -2) → B"( 2, -5) → B""( 6 ,-15)
For point C,
C(-2,1) → C'( -2 , -1) → C"( -1 , -4 )→ C"" ( -3 , -12)
In order to reflect a point across the x-axis, keep the x coordinate constant while changing the y coordinate to its opposite.
<1, -3> the following translations: Add 1 to x, take 3 away from y.
Add 3 to both x and y to dilate k=3.
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Please help (the value are 50 and 45
Answer:
85 degrees
Step-by-step explanation:
Angle DEC = 50 degrees (vertically opposite angles are equal).
So angle CDE= 180-45-50=85 degrees (angles in triangle sum to 180).
Because they are similar x = 85 degrees
Select the correct answer from each drop-down menu. Graph of a four-sided polygon on a coordinate plane at A (minus 1, minus 1), B (0, 1), C (2, 2), and D (2, minus 1). In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′ is at (-2, -2) , and point D′ is at (4, -2) .
The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The vertices of the original polygon for this problem are given as follows:
A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).
The scale factor for the dilation in this problem is given as follows:
k = 2.
Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
(as each coordinate of each vertex was multiplied by the scale factor of 2).
Missing InformationThe problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.
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BRAINLIEST FOR ANSWER UNDER 10 MINUTES The table shown represents a linear relationship.
x 0 1
3
4
y-8-6-20
Based on the table, what is the equation of the linear relationship in slope-intercept form?
Oy=2x-8
Oy = 2x+8
Oy = -2x + 4
Oy=-2x - 4
Answer: y = 2x-8
Step-by-step explanation:
Let's try to determine by substitution method. Starting from the first equation:
y = 2x-8
2·0-8 = -8
2·1-8 = -6
2·3-8 = -2
2·4-8 = 0
The first equation satisfies the conditions of the table.
2(-2b)+2b=-8 what does b equal
Answer:
b = 4
Step-by-step explanation:
[tex]2(-2b) + 2b = -8[/tex]
Open the brackets & simplify the terms (which were in brackets).[tex]=> -4b + 2b = -8[/tex]
[tex]=> -2b = -8[/tex]
Divide both the sides by -2[tex]=> \frac{-2b}{-2} = \frac{-8}{-2}[/tex]
[tex]=> b = 4[/tex]
2 1/12 - 1 5/12
How many are left?
Answer:
is it 21 or 2 whole?
Step-by-step explanation:
plz clarify the question first i am discombobulated
) For comparison with other years and with other countries, we prefer a histogram of the percentages in each age class rather than the countries. Explain why.
Therefore , the solution of the given question of percentage comes out to be It's because Different years and countries may have different overall numbers of newborns,.
What is percentage?A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Here,
Given : we prefer a histogram of the percentages in each age class rather than the countries
It's because Different years and countries may have different overall numbers of newborns, making a comparison based on the absolute numbers difficult
If we insist on using the absolute numbers,
The group with the most population would definitely result in higher results, and make it impossible for us to see the changes in weight that happen to average inborns.
Therefore , the solution of the given question of percentage comes out to be It's because Different years and countries may have different overall numbers of newborns.
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A jar contains 6 blue gumballs, 4 yellow gumballs, and 8 red gumballs. What is the probability of choosing a yellow gumball and then a red gumball if the first gumball is placed back into the jar before the second is chosen?
Answer:
2/9 or 22.22% and 4/9 or 44.44%
Step-by-step explanation:
6+4+8=18 4/18=2/9 8/18=4/9
Every month $50 is withdrawn from Tom’s savings account to pay for his gym membership he has enough savings to withdraw no more than $200 for how many months can Tom pay for his gym membership.
Answer:
4 months.
Step-by-step explanation:
Ques below: please answer that
please answer this question right now
Answer:
6) c
7) d
Step-by-step explanation:
6) 25 + 15= 40
40+35=75
Php. 75
7) 29•3=87
150-87=63
Php. 63
Hope this helps!
Which equation is equivalent 2^4x=8^x-3
can someone help me please i really have to do this right now
Answer: Angles 2 and 4 = 38, Angle 1 = 142
Step-by-step explanation:
Given that angle 3 is equal to 142, the angle between 2 and 3 has to add up to 180. 142 + 38 = 180. The same applies for angle 4 and 3. So, angle 1 + angle 2 has to add up to 180. We already know angle 2, so now we just have to subtract that from 180 to find angle 1.
A roller coaster begins at ground level, rises 63 feet, then falls 71 feet. What is the
elevation of the roller coaster, relative to the ground? *
134 feet
8 feet
- 8 feet
- 134 feet
Answer:
-8 feet
Step-by-step explanation:
63 - 71 = -8
Swimming Pool B is also rectangular and has a perimeter of 90m. Its length is 25m. What is the width?
By using the formula for the perimeter, we will get that the width of the pool is 20 meters.
What is the width of the swimming pool?
Remember that for a rectangle of length L and width W, the perimeter is given by the formula:
P = 2*(L + W)
In this case, we know that the perimeter is 90m, and the length is 25m, then we know that:
P = 90m
L = 25m
Replacing that in the formula above we will get:
90m = 2*(25m + W)
now we can solve this for W.
90m/2 = 25m + W
45m - 25m = W
20m = W
The width of the pool is 20 meters.
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Find the missing fraction worksheet 5 1/2 + ? = 7
Answer:
1 1/2
Step-by-step explanation:
7-5 1/2 is 1 1/2 so 1 1/2+5 1/2 -7
Consider two stocks. Stock 1 always sells for $10 or $20. If stock 1 is selling for $10 today, there is a .80 chance that it will sell for $10 tomorrow. If it is selling for $20 today, there is a .90 chance that it will sell for $20 tomorrow. Stock 2 always sells for $10 or $25. If stock 2 sells today for $10, there is a .90 chance that it will sell tomorrow for $10. If it sells today for $25, there is a .85 chance that it will sell tomorrow for $25. On the average, which stock will sell for a higher price? Find and interpret all mean first passage times.
Answer:
On stock 2 will be has an average sell of $50 for higher price.
Step-by-step explanation:
stock 1 of $10 (today)+ $10 (80% chance tommorow)=$20 stock sell price and for $20(today)+$20(90% chance tommorow)= $40 this two final of price for stock 1.
Stock 2 of $10 (today)+$10(90% chance tommorow)= $20 and of $25(today)+$25(85% chance tomorrow)= $50 this two for final of it's price for stock 2.So as for Stock 2 has the average sell higher price.
Hope this helps you
00:00
Which is greater: 10 centimeters or 103 millimeters? How much greater?
Answer:
103 is greater by .3
Step-by-step explanation:
103 mm equals 10.3 cm so it is greater by .3
Captain Crunch costs $3.50, while a pack of gourmet oatmeal costs $2.50. If $25 of
breakfast food was purchased and 8 total items were purchased, how many oatmeal
packets must have been bought?
Answer:
I believe the answer is 3
Step-by-step explanation:
1) 3.50 * 5 = 17.50
2) 2.50 * 3 = 7.50
3) 17.50 + 7.50 = 25
Answer:
Step-by-step explanation:
given:
25 = 3.5x + 2.5y
8 = x +y
use substitution to solve
8-x = y
25 = 3.5x + 2.5(8-x)
25 = 3.5x + 20-2.5x
5 = 1x
x = 5
they bought 5 Captain Crunch :P yes, Captain Crunch is sooooo good
and 3 yucky oatmeal packets :P
so 3 packets of oatmeal :)
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
The spaceship will meet in how many hours?
The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.The intercept b represents the initial position.The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?
Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.
The intercept b represents the initial position.
The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.
x2(t) = 600 - 90t. (negative as they travel in opposite direction).
They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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Which expression results in a rational number?
Answer:
3
Step-by-step explanation:
It equal .4, which is rational because it doesn't repeat.
Answer:
3
Step-by-step explanation:
How are they equivalent?
Answer:
A
Step-by-step explanation:
When you distribute what is in the parentheses you get 2.5m + 7m=9.5m, and then you add that to m aka 1m, which is 10.5m and they both end with -2.
100 POINTS TO WHOEVER ANSWERS CORRECT
if you could ask any 2 questions about a 5th degree polynomial function what would they be and why. HURRY
Answer:
Why is there no general symmetry?
Does it always take six points or six pieces of information to describe a quintic function?
Why are the roots not solvable by radicals?
I really don't know the "why", I just steer away from them when I can.
14. Find ST, 5 points plz
Answer:
7 Can I have brainliest
Step-by-step explanation:
a biking track has a length of 2376 feet. how long is this in miles
Answer:0.45 miles
Step-by-step explanation:
Conversion