Answer:
a. the values are the same.
Step-by-step explanation:
The sine = y-coordinate / hypotenuse. The unit circle has hypotenuse = 1, so
the sine = y /1 = y.
Final answer:
The value of the sine of an angle on the unit circle is the same as the y-coordinate of the corresponding point on the circle, as the sine function is defined as the ratio of the opposite side to the hypotenuse in a right triangle.
Explanation:
When looking at the unit circle, we can observe that the value of the sine of an angle is indeed the same as the y-coordinate of the point on the unit circle at that angle. In other words, if we take a point on the unit circle at an angle θ from the positive x-axis, its coordinates can be expressed as (cos(θ), sin(θ)). Therefore, the sine of the angle gives us the y-coordinate of the point on the circle. This relationship is a direct consequence of how the trigonometric functions are defined in the context of a right triangle, where the sine of an angle is the length of the side opposite to the angle (y) divided by the hypotenuse (which is 1 for the unit circle).
If three unbiased coins are tossed, then what is the probability of getting one or more heads is
The odds would be 7/8 that at least one would be a heads.
Step-by-step explanation:To find your answer, see each coin flip as unrelated to the last one.
For the first coin flip, you can either get heads or tails. So, there's only 2 possible outcomes.
Flip 1 (Outcome 1): H or T
Flip 1 (Outcome 2): H or T
But when it comes to the second flip, now each outcome has two possible "sub-outcomes" of their own. So there's now four total outcomes.
Flip 2 (Outcome 1) : H, H
Flip 2 (Outcome 2) : H, T
Flip 2 (Outcome 3) : T, H
Flip 2 (Outcome 4) : T, T
On the third flip, there would now be 8 outcomes. As each "sub-outcome" has own of their own.
Flip 3 (Outcome 1) : H, H, H
Flip 3 (Outcome 2) : H, H, T
Flip 3 (Outcome 3) : H, T, H
Flip 3 (Outcome 4 : H, T, T
Flip 3 (Outcome 5) : T, H, H
Flip 3 (Outcome 6) : T, H, T
Flip 3 (Outcome 7) : T, T, H
Flip 3 (Outcome 8): T, T, T
So all but one of the eight outcomes have at least one heads drawn. Due to this, the odds of an heads happening would be 7/8 within all of the possible outcomes.
Select the expression equal to square root of 24
look at the attached picture⤴
Hope it will help u...
Final answer:
To express the square root of 24 in simplest radical form, we break down 24 into 4 and 6, and since 4 is a perfect square, the simplified expression is 2√6.
Explanation:
To find the expression equal to the square root of 24, we can simplify the square root by looking for perfect square factors within 24. The number 24 can be factored into 4 and 6, where 4 is a perfect square. Therefore, we have:
√24 = √(4 × 6)√24 = √4 × √6√24 = 2√6As a result, the simplified expression equal to the square root of 24 is 2√6.
Find the focus and directrix of the parabola y = 1/2(x+1)2 + 4.
C A) Focus: (1,41/2); Directrix: y = 31/2
C B) Focus: (-1,41/2); Directrix: y= 31/2
C C) Focus: (1,31/2); Directrix: y = 41/2
CD) Focus: (-1,31/2); Directrix: y = 41/2
Answer is B! Correct on exam!
Step-by-step explanation:
1. Identify the values for a, h, and k: a= 1/2 h= -1 k= 4. (Remember that the sign of h changes!)
2. Determine vertex: (-1,4)
3. Determine x and y for focus: X= -1 (same as vertex) y= K + 1/4(a)
Substitute what we know into that formula: y= 4 + 1/4(1/2)
y= 4 + 1/2 so y= 4 1/2.
4. Determine directrix: y= k - 1/4(a) ]
Substitute in what we know: y= 4 - 1/4(1/2)
y= 4-1/2 so y= 3 1/2
The focus and directrix of the parabola are (-1, 9/2) and y=7/2 respectively.
The given function is y = 1/2(x+1)² + 4.
We need to find the focus and directrix of the parabola.
What are focus and directrix?A parabola is a set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix. The focus lies on the axis of symmetry of the parabola.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Directrix: Use the vertex form to find the directrix
y=7/2
Focus: Use the vertex form to find the focus.
(-1, 9/2)
Axis of symmetry: x=-1
The coordinates to plot the graph are as follows:
(-3, 6), (-2, 9/2), (-1, 4), (0, 9/2) and (1, 6).
Therefore, the focus and directrix of the parabola are (-1, 9/2) and y=7/2 respectively.
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The sum of -4 and 5 times a number is multiplied by 3. The result is 212 less than 7 times the number. What is the number?
Answer:
-25
Step-by-step explanation:
(-4 + 5n) × 3= 7n - 212
-12 + 15n = 7n - 212
8n = -200
n = -25
Answer:
The number is -25
Step-by-step explanation:
(-4 +5n)*3 = 7n-212
Distribute
-12 +15n = 7n -212
Subtract 7n from each side
-12 +15n-7n = 7n-7n -212
-12 +8n = -212
Add 12 to each side
-12+12 +8n = -212+12
8n = -200
Divide each side by 8
8n/8 = -200 /8
n =-25
A pair of designer sneakers were purchased for $150. Since they were purchased, their price has increased by 20%. After the increase what would the new ammount for the sneakers?
Answer:
the new price is... i think 180
Step-by-step explanation:
The function f(x)f(x) is a quartic function and the zeros of f(x)f(x) are -6−6, -5−5, -2−2 and 11. Assume the leading coefficient of f(x)f(x) is 11. Write the equation of the quartic polynomial in standard form.
[tex]\boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}[/tex]
Explanation:A quartic function is a function given by the the following equation in standard form:
[tex]f(x)=a_{4}x^4+a_{3}x^3+a_{2}x^2+a_{1}x+a_{0} \\ \\ \\ Where: \\ \\ a_{4},a_{3},a_{2},a_{1},a_{0} \ \text{are constant} \\ \\ \text{and} \ a_{4} \ \text{is the leading coefficient}[/tex]
From the statement we must assume the leading coefficient of f(x) is 11, so:
[tex]a_{4}=11[/tex]
The zeros are:
[tex]x=-6 \\ \\ x=-5 \\ \\ x=-2 \\ \\ x=11[/tex]
So, we can write:
[tex]f(x)=11(x-(-6))(x-(-5))(x-(-2))(x-11) \\ \\ \\ So: \\ \\ \mathrm{Rule}:-\left(-a\right)=a \\ \\ \\ Then: \\ \\ f(x)=11\left(x+6\right)\left(x+5\right)\left(x+2\right)\left(x-11\right)[/tex]
[tex]Expand:\left(x+6\right)\left(x+5\right):\ x^2+11x+30: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^2+11x+30\right)\left(x+2\right)\left(x-11\right) \\ \\ \\ Expand:\left(x^2+11x+30\right)\left(x+2\right):\ x^3+13x^2+52x+60: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^3+13x^2+52x+60\right)\left(x-11\right)[/tex]
[tex]Expand: \left(x^3+13x^2+52x+60\right)\left(x-11\right):\ x^4+2x^3-91x^2-512x-660 \\ (Distributive \ property)[/tex]
Finally:
[tex]f(x) = 11(x^4 + 2x^3 - 91x^2 - 512x - 660) \\ \\ \boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}[/tex]
Rita wants to know the average weight of each apple in
an 8-pound bag of apples. She purchased 5 bags and
found the average apple weight. Using her results, an
apple from an 8-pound bag of apples should weigh
between:
O
O lbs and 0.9 lb.
1.0 lb and 1.2 lbs.
0.8 lb and 1.2 lbs.
O 0.8 lb and 0.9 lb.
Answer:
c
Step-by-step explanation:
because all your doing is picking the smallest and the biggest number and i just got it right .
Answer:C
Step-by-step explanation: 0.8 lb and 1.2 lb
How many Starbucks do you think there were in the US in 20152 Make a quick estimate and write it in the box below
Answer:
0
Step-by-step explanation:
Some president will make Russia mad enough to start a nuclear war and the entire planet will be destroyed, let alone Starbucks.
How much grain can this container hold? Express your
answer in terms of it. It’s a cylinder
4 in.
11 in.
176pie in.3
88pie in.3
44pie in.3
484pie in.3
Answer:
[tex]176\pi in.^3[/tex]
Step-by-step explanation:
The figure of the problem is missing: find it in attachment.
In this problem, the container has a shape of a cylinder.
The volume of a cylinder is given by the formula:
[tex]V=\pi r^2 h[/tex]
where
V is the volume
r is the radius of the base of the cylinder
h is its height
For the container in this problem, we have:
r = 4 in. is the radius of the base
h = 11 in. is the height of the container
Substituting into the formula, we can find the volume of the container, and so the volume of grain that it can contain:
[tex]V=\pi (4)^2 (11)=176\pi in.^3[/tex]
The given cylinder container can hold 44π cubic inches of grain. This is calculated using the formula for the volume of a cylinder which is πr²h.
Explanation:To compute the amount of grain a cylindrical container can hold, you would have to calculate the cylinder's volume. The formula for the volume of a cylinder is πr²h, where r represents the radius, and h represents the height.
In this case, the diameter is 4 inches, so the radius (r) would be 2 inches. The height (h) of the cylinder is 11 inches. So, substituting these values into the formula gives us:
Volume = π(2²) x 11 = 44π cubic inches
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you have a bag containing five purple marbles three yellow marbles to red marbles and four blue marbles you pull one more wall what is the probability that you will pull a yellow marble give your answer in a fraction.
Answer:
3/14
Step-by-step explanation:
5+3+2+4=14....
3 yellow
inverse cosine is used to find to find a given angle measure when we know the ________ and the ______.
Answer: adjacent and hypotenuse
Step-by-step explanation: Cos theta is adjacent/Hypotenuse
Final answer:
Inverse cosine is used to find an angle measure when we know the length of the adjacent side and the hypotenuse in a right triangle.
Explanation:
The inverse cosine function, also known as arccosine, is used to find a given angle measure when we know the length of the side adjacent to the angle and the length of the hypotenuse of a right triangle. The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. By using the inverse cosine function, we can find the angle whose cosine is the given ratio. This is particularly useful in trigonometry for solving right triangles or when dealing with any scenario where angle and side lengths are related through the cosine ratio.
In mathematical terms, if we have a right triangle with an angle labeled as θ (theta), and we know the lengths of the side adjacent to θ (adjacent) and the hypotenuse (hypotenuse), the cosine of θ is given by-
cos(θ) = adjacent / hypotenuse
To find the angle measure θ based on the ratio of these two sides, we would compute-
θ = arc cos(adjacent / hypotenuse).
What is the correct answer to the equation
Answer:
right answer is 8cm
Step-by-step explanation:
if QM=x
so. Om=32+x
ON=64+16=80
(32+x)/x=80/16
32+x=5x
4x=32
x=8
Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15. n an 1 5 2 −10 3 20
Answer:
The answer to this would be 662.
Step-by-step explanation:
Sigma notation calls for the sum of the terms in the sequence.
Answer:
15
∑ 5(-2)^n-1
n =4
Step-by-step explanation:
15 and n = 4 should be on top (15) and below (n = 4) of the ∑
hope this helps :]
?/6=1/2 Will get Brainliest
Answer:
3/6
Step-by-step explanation:
Answer:
3/6=1/2
Step-by-step explanation:
Cross multiply
x/6=1/2
2x=6
Divide by 2 on both sides
x=3
So, 3/6=1/2
Hope this helps! :)
A sprinkler head is equidistant from flower garden A and a small shrub B. The sprinkler waters in a
circular pattern. If the length of minor arc AB is 12 feet and the radius of the circle is 10 feet, find the
measure of the central angle subtended by minor arc AB, to the nearest degree.
Answer:
[tex]69^{\circ}[/tex]
Step-by-step explanation:
We are given that
Length of minor arc AB=12 feet
Radius of circle=r=10 feet
Let x be the measure of central angle subtended by minor arc AB.
We know that
Length of an arc=[tex]\frac{Central\;angle}{360}\times 2\pi r[/tex]
Where [tex]\pi=3.14[/tex]
Using the formula
[tex]12=\frac{x}{360}\times 2\times 3.14\times 10[/tex]
[tex]x=\frac{12\times 360}{2\times 3.14\times 10}[/tex]
[tex]x=69^{\circ}[/tex]
If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?
100 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)
95 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)
(100 minus 5) (StartFraction 1 Over 500 EndFraction) = E (X)
(100) (StartFraction 1 Over 500 EndFraction) = E (X)
Answer:
B
Step-by-step explanation:
It's the right answer
The expected value of the given scenario is -$4.80
What is probability?The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.
The expected value refers to the value for a person who decides to purchase one ticket.
And that value is the sum of the values of the different possible scenarios.
There are two scenarios, wining and losing.
Note that we need to subtract the cost of the ticket (i.e. $5) from the return.
Winning :-
Probability 1 out of 500 chances
Return expected: ($100 - $5) *1/500 = $95 * 1/500 = $0.19
Losing :-
Probability 499 out of 500 chances
Return expected: (0 - $5)*499/500 = -$4.99
The expected value is the sum of the two returns: $0.19 - $4.99 = -$4.80 (it is negative).
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The calculator shows the result that Luiza got after
evaluating the expression 9 (52+ 18) + 42. She checked
her work by rounding all of the values to the nearest ten and
comparing it to the calculator result. Which is true regarding
her estimate and the accuracy of her calculator result?
1.) The estimated result is 560, which suggests the
calculator is correct.
2.)The estimated result is 740, which suggests the
calculator is incorrect.
3.) The estimated result is 840, which suggests the
calculator is incorrect.
4.) The estimated result is 1,100, which suggests the
calculator is incorrect.
Answer:
Answer 2 is correct, 740
Step-by-step explanation:
The rounded equation would be 10 (50+20) + 40. So if you do the equation then it would be 740
Which is the reflection line for the transformation
shown?
x-axis
y-axis
x = -2
y = -2
Answer:
y= -2
Step-by-step explanation:
Answer:
y = -2
Step-by-step explanation:
Khan academy use Pythagorean theorem to find isosceles triangle size length
Answer:
I know
Step-by-step explanation:
The length of each equal side of the isosceles triangle Pythagorean theorem is equal to the square root of half the square of the length of the base.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
To find the length of an isosceles triangle, we need to consider the two equal sides as the legs of a right-angled triangle, and the remaining side as the hypotenuse.
Let's denote the length of the equal sides as "a" and the length of the remaining side (the base) as "b".
According to the Pythagorean theorem, we have:
[tex]a^2 + a^2 = b^2[/tex]
Simplifying this equation, we get:
[tex]2a^2 = b^2[/tex]
To find the length of the equal sides, we can solve for "a" by taking the square root of both sides:
[tex]a = \sqrt{b^2 / 2}[/tex]
Therefore, the length of each equal side of the isosceles triangle Pythagorean theorem is equal to the square root of half the square of the length of the base.
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The radius of the base of a metallic rod is 2 centimeters, and its height is 15 centimeters. What is the volume of this cylinder?
A) 60π cm³
B) 50π cm³
C) 27π cm³
D) 36π cm³
Answer:
A) 60π cm³
Step-by-step explanation:
Given:
The radius of the base of a metallic rod is 2 centimetres, and its height is 15 centimetres.
Question asked:
What is the volume of this cylinder?
Solution:
As we know''
[tex]Volume\ of\ cylinder=\pi r^{2} h[/tex]
[tex]=\pi \times2\times2\times15\\ \\ =60\pi[/tex]
Therefore, the volume of this cylinder will be [tex]60\pi\ cm^{3}[/tex]
Answer:
The correct option is option (A)
The volume of the metallic rod is 60π cm³.
Step-by-step explanation:
Cylinder:
It is three dimension shape.The lateral surface area is 2πrh, r= radius, h= heightTotal surface area = 2πrh+2πr²,Volume = πr²h.The radius of the base of metallic rod is 2 cm and its height is 15 cm.
Here r= 2 cm, h= 15 cm, [tex]\pi =\frac{22}7[/tex]
The volume of metallic rod is
=πr²h
=π(2 cm)² (15 cm)
=π(4)(15) cm³
=60π cm³
tommy likes to run up and down and "up" escalator. Going up, he can cover 30 steps in 6 seconds. Going down, it takes him 15 seconds to cover 30 steps. Find Tommy's rate (in steps per second) if the escalator stopped moving.
Answer:
3 steps per second.
Step-by-step explanation:
Find the Unit Rates of each going up and down:
--> 30/6 unit rate is 5 steps per second.
--> 30/15 unit rate is 2 steps per second.
Now subtract them to get the amount if the elevator wasn't moving:
--> 5-2= 3.
Final answer:
To find Tommy's rate (in steps per second) if the escalator stopped moving, calculate his speed going up and going down, then subtract the speed going down from the speed going up.
Explanation:
To find Tommy's rate (in steps per second) if the escalator stopped moving, we need to calculate his speed when going up and when going down.
When going up, Tommy covers 30 steps in 6 seconds. So his speed going up is 30 steps / 6 seconds = 5 steps per second.
When going down, Tommy covers 30 steps in 15 seconds. So his speed going down is 30 steps / 15 seconds = 2 steps per second.
If the escalator stopped moving, Tommy's rate would be the difference between his speed going up and his speed going down. So his rate would be 5 steps per second - 2 steps per second = 3 steps per second.
the length of AB ( the minor arc) is 20cm. what is the circumference of C? 10
A)200 cm
B)56 cm
C)720 cm
D)72 cm
E)360 cm
F)12 cm
Answer:
c. 720 cm
Step-by-step explanation:
Paula designed a three-dimensional scale model of a department store. The volume of the scale model was 35 cubic feet. The ratio of the dimensions of the model to the dimensions of the store was 1:20. Determine the volume of the actual department store that Paula planned to build
Answer:
700 cubic feet
Step-by-step explanation:
Volume of scale model = 35 cubic feet
ratio of the dimensions of the model to the dimensions of the store was 1:20
Therefore
dimensions of the model/ dimensions of the store = 1/20
we know that in scaling
dimensions of the model/ dimensions of the store = Volume of scale model / volume of the actual department store
Now substituting the value of scale model in the above ratio equation we have
1/20 = 35/volume of the actual department store
=> volume of the actual department store = 35*20 = 700
Therefore volume of the actual department store is 700 cubic feet
brad put 10 crickets in his pet lizards cage.after one day brad's lizard had eaten 20% of the crickets.how many crickets were left in the of the second day? cage at the end
Answer:
8 crickets
Step-by-step explanation:
since 20% is in percent form, if you convert it to a whole number, it is 2. That means that Brad's lizard ate 2 crickets and there are 8 left.
Suppose integers a and b are even. Which expression MUST be even?
A) ab + 1
B) a + b + 1
C) 3(ab + 1)
D) 2(ab + 1)
E) a2 + b2 + 1
Answer:
D
Step-by-step explanation:
2 multiplying by any number even or odd=even number
Final answer:
The correct answer is D) 2(ab + 1), because multiplying an odd number (ab + 1) by 2 results in an even number.
Explanation:
The question asks which expression must be even if integers a and b are even. We know that the product of two even numbers is always even. Therefore, ab is even.
When we add 1 to an even number, the result is odd, so ab + 1 is odd. Multiplying by 3, as in option C, won't change the oddness, so 3(ab + 1) is also odd. The expression in option E, a2 + b2 + 1, will be odd for the same reason - the sum of even squares is even, and adding 1 makes it odd.
However, option D multiplies the odd number ab + 1 by 2, guaranteeing that the result is even regardless of the values of a and b since any number multiplied by 2 is even. Thus, the correct answer is D) 2(ab + 1).
Three friends ate lunch at a restaurant. Their friend Reggie arrived late
and only ordered a glass of juice. The total bill was $39.50 before taxes.
Reggie paid $2 for his juice, and the others divided the remaining
amount equally. How much did each of Reggie's three friends pay?
what unit of measurement do you measure the length of a living room?
Answer:
ft
Step-by-step explanation:
just the most common
area
i would say feet, so it could be like ''the room is 45 feet long'' or something
Help quick thanks plz tanks
Answer:
3 meters must be drained off so that the water levels falls to 5 meters.
Step-by-step explanation:
Look at all the measurements given and try to find one that matches the amount of room needed to be drained out.
Compute the following: Subscript 325 Baseline C Subscript 1 a. 325 b. 324 c. 1 d. 326
Answer:
325
Step-by-step explanation:
What is the range of the data represented in the box plot below?
Group of answer choices
10
20
30
15
Answer:
30
Step-by-step explanation:
40- 10 equals 30
the range is the maximum divided by the minimum.