Answer:
1. 1/2
2. .5
3. 50%
Step-by-step explanation:
2 of the types of cards out of 4 is 2/4 which is half
Answer:
1/2 or unsimplified: 26/52
.5
50%
Step-by-step explanation:
half of the cards are a diamond or club so the probability is one out of 2 which is one half
1/2 equals .5
then a 50% chance because 50% is half of 100%
Check out this right triangular prism: Find the surface area of the right triangular prism (above) using its net (below). units2^22squared
Answer:
96 squared units
Step-by-step explanation:
Please find attached the diagram used in answering this question
The surface area is equal to the area of each shape
Area of a triangle = Area of a triangle = 1/2 x ( base x height)
1/2 x 2 x 3= 3
there are 4 triangles, area of both triangles = 3x4 = 12
Area of rectangle = length x width
Area of middle rectangle = 6 x 7 = 42
Area of two side rectangles = (3 +3) x 7 = 42
surface area = 42 + 42 + 12 = 96
Solve the trigonometric equation on the interval of [0,2π) below:
[tex] \large{cos(2 \theta + \frac{ \pi}{3} ) = \frac{ \sqrt{3} }{2} }[/tex]
Show your work, thanks!
Answer:
[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]
Step-by-step explanation:
we would like to solve the following trigonometric equation on interval of [0,2π)
[tex] \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} [/tex]
remember that,
[tex] \displaystyle \cos(t) = \cos(2\pi - t) [/tex]
so the equation has two solutions
[tex] \begin{cases} \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} \\ \cos \left(2\pi - (2 \theta + \frac{\pi}{3} )\right ) = \frac{ \sqrt{3} }{2} \end{cases}[/tex]
take inverse trig both sides which yields:
[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ 2\pi - 2 \theta - \frac{\pi}{3} = \frac{\pi}{6} \end{cases}[/tex]
simplify the second equation:
[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} \end{cases}[/tex]
add period of 2kπ:
[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} + 2k\pi \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} + 2k\pi\end{cases} [/tex]
By making theta subject of the equation we acquire:
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} - k\pi\end{cases} [/tex]
since [tex]k\in\mathbb{Z}[/tex] we get:
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} + k\pi\end{cases} [/tex]
as we want to Solve the trigonometric equation on the interval of [0,2π) we get
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + \pi \\ \theta = \frac{3\pi}{4} + \pi\end{cases} [/tex]
by simplifying we acquire:
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{23\pi}{12} \\ \theta = \frac{7\pi}{4} \end{cases} [/tex]
and we are done!
hence,
[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]
Please help me fast!!!
Answer:
y=25x+150
Step-by-step explanation:
The slope is 25 and the y-intercept is 150.
Hope this helps.
Alex is saving up to buy the newest version of Playstation. Alex earns $84 after 3 weeks of mowing lawns. How much money does Alex earn per week mowing lawns?
Answer:
84/3=28
Alex earns $28 a week mowing lawns.
Answer:
He earns 28 dollars per week mowing lawns
Step-by-step explanation:
Wow Alex should get a higher paying job lol
What is the y-intercept of the line shown below? Enter your answer as a
coordinate pair. Help!!!!!
Answer:
(0, 3)
Step-by-step explanation:
y= 3 when x=0
Each day, the seals at an aquarium are fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 400 pounds.
Answer:
32 just multiply by four
A sum of money is divided between A, B and C in the ratio 10:6:4. If B receives 515 more
than C , how much will A get and what is the total sum of money?
Answer:
Amount A get = 2,575
Total amount = 5,150
Step-by-step explanation:
Given:
Ratio between A,B and C = 10:6:4
Assume;
Common ration is 'a'
So,
Amount A get = 10a
Amount B get = 6a
Amount C get = 4a
So,
Amount B get - Amount C get = 515
6a - 4a = 515
2a = 515
a = 257.5
Total amount = 10a + 6a + 4a
Total amount = 20a
Total amount = 20(257.5)
Total amount = 5,150
Amount A get = 10a
Amount A get = 10(257.5)
Amount A get = 2,575
40 POINTS
Pleaseee help, I need to turn this in soon.
Answer:
The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.
Therefore, we have the following equation:
[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]
The Pythagorean identity comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
, where is the hypotenuse of the triangle and and are two legs of the triangle.
Therefore, we have the following equation:
Kiara gets to spin the big prize wheel, which has a radius of 2 meters. What is the prize wheel's area? PLZ HELP me
Answer:
4pi or 12.57
Step-by-step explanation:
Area = pi * radius^2
Area = pi * 2^2
Area = pi * 4
Area = 4pi or 12.57
I NEED HELP RIGHT NOW PLEASE!!!!!
NO LINKS
Answer:
48
Step-by-step explanation:
The blank would be 48 because 3 times 4 is 12. 12 times 4 is 48. And 48 times 4 would be 192
What us the range of the data below?
Need help!! Please/ Thank you!!
Answer:
d= 8.3 units
➴➵➶➴➵➶➴➵➶
[tex]Given:[/tex]
[tex]L=7[/tex]
[tex]B=4[/tex]
[tex]H=2[/tex]
[tex]d=\sqrt{L^2+B^2+H^2}[/tex]
[tex]d=\sqrt{7^2+4^2+2^2}[/tex]
[tex]d=\sqrt{49+16+4}[/tex]
[tex]d=\sqrt{69}[/tex]
[tex]d=8.3~units[/tex] ✔︎
•❅────✧❅✦❅✧────❅•
hope it helps...
have a great day!!!
Mr. Olen is looking at the drawings of two proportional city lots. One of the dimensions of Lot B is not readable. How many square feet are in Lot B?
325,000 square feet
75,000 square feet
135,000 square feet
202,000 square feet
NO LINKS
Answer:
nfdsBFS>BFBms?FBsbn
Step-by-step explanation:vkhgv
SFsASFWWFmreweebwfjfeWBEfeb
Plot the following points: A (-2, 2) B (-4,-4) C(1,-4) D (3, 2) Connect the points. What is the name of the polygon? How long is line segment AD? What is the area of the shape?
Answe545r:
45454
Step-by-step explanation:
Carleigh makes $10 more than sheryl (s) does per hour. Carleigh makes $22 an hour. which equation can be used to figure out how much sheryl makes
s+10=22 or 10+22=s
1. to a survey teens about their music preferences. you would question several teens:
a: attending a classical choir recital
b: as they enter a music store
choose the sample that is more likely to be representative of the population.
Answer:
B: as they enter a music store
Step-by-step explanation:
b is in a music store where you find people who enjoy music, but have diverse tastes.
in a classical choir recital, your results will be biased because a majority of the people there enjoy classical choir music the most.
(04.06 LC)
The first four terms of a sequence are shown below:
8, 5, 2, -1
Which of the following functions best defines this sequence? (5 points)
f(n) = - 3(n-1) +8; for n 2 1
O f(n) = 3(n-1) +8; for n 2 1
O f(n) = - 5(n-1) +8; for n 2 1
f(n) = 5(n-1) +8; for n 2 1
Given:
The first four terms of a sequence are:
8, 5, 2, -1
To find:
The function that defines the given sequence.
Solution:
We have,
8, 5, 2, -1
The differences between two consecutive terms are:
[tex]5-8=-3[/tex]
[tex]2-5=-3[/tex]
[tex]-1-2=-3[/tex]
The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.
The nth terms of an arithmetic sequence is:
[tex]f(n)=a+(n-1)d[/tex], for [tex]n\geq 1[/tex]
Where, a is the first term and d is the common difference.
Putting [tex]a=8,d=-3[/tex], we get
[tex]f(n)=8+(n-1)(-3)[/tex]
[tex]f(n)=8-3(n-1)[/tex]
[tex]f(n)=-3(n-1)+8[/tex], for [tex]n\geq 1[/tex]
Therefore, the correct option is A.
help!!!!!!! me plzzzz!!!!
Answer:
1.0
2.undefined
Step-by-step explanation:
Answer:1) 0, 2) is undefined
Step-by-step explanation:
given the figure below find the value of x and z
Answer: X is do it yourself and y is do it yourself X is do it yourself and y is do it yourself
Step-by-step explanation:
Lolol
The cost to rent a bicycle is $20.00 plus $2.65 per hour that the bicycle is checked out. What is the minimum number of hours a bicycle can be rented if a tourist can spend more than $37.00 but less than $65.00 on the rental? Round your answer to the nearest whole hour that satisfies the inequality.
Answer:
7 hours
Step-by-step explanation:
Rental cost :
Fixed pay = $20
Hourly cost = 2.65
To obtain the minimum rental hour, we work with the least amount that can be spent ;
For tourist that can spend more than $37 but less than $65
Total cost of rental :
20 + 2.65h ; h = number of hours
When total cost > 37
20 + 2.65h > 37
2.65h > 37 - 20
2.65h > 17
h > 6.415
Hence, the minimum whole hour of bicycke rental is 7 hours
I need help please I dont get this
Answer:
Step-by-step explanation:
Since this is a 30-60-90 triangle, we need the Pythagorean triple for such a triangle. the side length across from the 30 degree angle is labeled as x, the side across from the 60 degree angle is x√3, and the hypotenuse is 2x. Since we know the side length of the side across from the 60 degree angle, we use that identity and solve for x:
[tex]x\sqrt{3}=18[/tex] and
[tex]x=\frac{18}{\sqrt{3} }[/tex] and rationalizing the denominator,
[tex]x=\frac{18}{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }=\frac{18\sqrt{3} }{3}=6\sqrt{3}[/tex]
This is the side length of the side across from the 30 degree angle. In order to find the hypotenuse, we have to multiply this value by 2 to get
12√3, the third choice down.
What is the value of x when y has a value of -9 ? -3x = y + 51
A) -20
B) -14
C) 14
D) 20
i need the answer to this question
Answer:
NO = 10
Step-by-step explanation:
Given a segment joining the midpoints of 2 sides of a triangle, then it is half the length of the third side, that is
18 - 2x = [tex]\frac{1}{2}[/tex] (9x - 16) ( multiply both sides by 2 to clear the fraction )
36 - 4x = 9x - 16 ( add 4x to both sides )
36 = 13x - 16 ( add 16 to both sides )
52 = 13x ( divide both sides by 13 )
4 = x
Then
NO = 18 - 2x = 18 - 2(4) = 18 - 8 = 10
Tell whether the angles are complementary, supplementary, or neither.
Answer:they are supplementary
Step-by-step explanation:
What is the area of the white border?
Answer:
you have 48
Step-by-step explanation:
15x2=30
9x2=18
18+30=48
✰ ☆
(Only if you are right obviously)
Which beliefs do most Christians hold
A. there are many different gods
B. non-jews cannot become Christians
C. Jesus was the son of God
D. Christians should not perform rituals
Gavin needs to fill the fish tank below with water. The directions state that the water level should be 2 inches below the top of the tank. Write an expression to show the volume of water Gavin needs to fill the tank according to the directions.
Answer:
See explanation
Step-by-step explanation:
The question is incomplete; So, I will solve the question generally.
Assume the following;
[tex]l \to length[/tex]
[tex]w \to width[/tex]
[tex]h \to height[/tex]
Since the water level must be 2 inches below the tank height, the water height is:
[tex]H \to h - 2[/tex]
So, the water volume is:
[tex]Volume = l * w * H[/tex]
[tex]Volume = l * w * (h - 2)[/tex]
Hence, the expression is:
[tex]Volume = l * w * (h - 2)[/tex]
Assume that:
[tex]l = 5; w = 10; h = 8[/tex]
The volume becomes:
[tex]Volume = 5 * 10 * (8 - 2)[/tex]
[tex]Volume = 5 * 10 * 6[/tex]
[tex]Volume = 300[/tex] cubic units
i put 10 points please help me with this
Answer: X=6 Y=4
x+y= 10
6+4=10
x-y=2
6-4=2
Answer:
x=6
y=4
Step-by-step explanation:
Use an elimination method:
add equation 1 and 2 together.
2x = 12
divide both side by 2
x = 12/2
x = 6
use equal 1,
x + y = 10
y = 10 - x
y = 10 - 6
y = 4
The length of a rectangle is represented by (2x2−5x+5)cm and the width is represented by (x2+4x−3)cm. What is the representation of the perimeter
Answer: [tex]6x^2-2x+4[/tex]
Step-by-step explanation:
Given
The length of a rectangle is given by
[tex]l=2x^2-5x+5[/tex]
and the breadth is given by
[tex]w=x^2+4x-3[/tex]
Perimeter is the sum of the sides of rectangle
[tex]\therefore \text{Perimeter P= }2(2x^2-5x+5+x^2+4x-3)\\\Rightarrow P=2(3x^2-5x+4x+5-3)\\\Rightarrow P=2(3x^2-x+2)\\\Rightarrow P=6x^2-2x+4[/tex]
Thus, the perimeter is given by [tex]6x^2-2x+4[/tex].
Leroy draws a rectangle that has a length of 11.9 centimeters and a width of 7.6 centimeters. How much longer is the length than the width of Leroy's rectangle?
Answer: 4.3 cm
Step-by-step explanation:
Leroy's rectangle's width is 7.6 cm in length and the length of the triangle is 11.9 cm.
The length is therefore longer than the width and the difference is:
= Length - Width
= 11.9 - 7.6
= 4.3 cm