The probability of drawing three queens from a standard deck of cards is 0.000162.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Total cards = 54
No. queens in a deck = 4
Probability of drawing a queen card = 4/54
Now that 1 queen has been taken, the no. of cards becomes = 53
and
no. of queens = 3
Probability of getting a queen again = (3/53)(4/54)
Two queens have already been removed.
No. of cards in the deck = 52
No. of queens in the deck = 2
Probability of drawing three queens
= (2/52)(3/53)(4/54)
= 0.000162 approximately
The probability of drawing three queens from a standard deck of cards is 0.000162.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
Find k.
10 mi
60⁰
K
30⁰
please help the subject is exterior angles(triangles)
PLEASE HELP!! ITS URGENT!!
Find all solutions to the equation 3 cos (5t) + 3 = 2 in the interval
ㅠ
0≤t≤ radians.
a) 0.3821, 0.2462, 0.8745
b) 0.654
c) 0.3821, 0.8745
d) No solutions in the interval.
All solutions to the equation 3 cos (5t) + 3 = 2 in the interval from 0 to π will be 0.3821, 0.2462, and 0.8745. Then the correct option is A.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The equation is given below.
3 cos (5t) + 3 = 2
By simplifying the equation, then we have
3 cos 5t = -1
cos 5t = -1/3
Then the value of t will be
5t = 1.91063, 1.12096, 4.3725
t = 0.3821, 0.2462, 0.8745
Then the correct option is A.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ1
100 POINTS!!! REPOST!!! NEED HELP!!! NO SPAMMING!!!
(Refer to the attached image)
============================================================
Explanation:
I'm going to relabel the figure as triangle ABC.
As the instructions mention, we'll use the law of cosines to find the missing side.
side a = 147side b = 166angle C = 50 degreesUse these facts to find side c
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 147^2 + 166^2 - 2*147*166*cos(50)
c^2 = 17794.393497
c = sqrt(17794.393497)
c = 133.395628
c = 133
If sin A = 3/8, find the value of cosec A - sec A.
Answer:
[tex]\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\~~~~~~\sin A = \dfrac 38 \\\\\implies \sin^2 A = \dfrac 9{64}\\\\\implies 1 - \cos^2 A = \dfrac{9}{64}\\\\\implies \cos ^2 A = 1 - \dfrac 9{64}\\\\\implies \cos^2 A = \dfrac{55}{64}\\\\\implies \cos A =\pm\sqrt{\dfrac{55}{64}}\\ \\\implies \cos A = \pm\dfrac{\sqrt{55}}8\\\\[/tex]
[tex]\implies \dfrac 1{\cos A} = \pm\dfrac{8}{\sqrt{55}}[/tex]
[tex]\text{Now,}\\\\\csc A - \sec A\\\\=\dfrac{1}{\sin A}- \dfrac{1}{\cos A}\\\\=\dfrac 83 -\left(\pm \dfrac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}[/tex]
Solve for height using the tangent method. Show your work.
Answer:
b = 17.318 height = 23.318 ft
Step-by-step explanation:
This IS very similar to the other one, Emily..... Have you tried to solve it the same way?
b = 152 tan 6.5 = 17.318 ft (using a calculator)
add the height of the victim's head (6 ft)
17.318 + 6 = 23.318 ft
y inversely proportional to x
when y=,x=9
work out an equation connecting y and x
What does y equal to? I think you had a typo
Question 7(Multiple Choice Worth 1 points)
(02.05 LC)
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points 0, 4 and negative 4, 0. Line g of x passes through points negative 9, 0 and negative 4, 5.
−4
−5
4
5
The value of k based on the information given will be k = 2.
How to calculate the value?It should be noted that the line of f(x) passes through the point (-4, 0) and (0, 4). The line of g(x) goes through (-2, 0) and (0, 4).
The slope of x will be:
= (4 - 0)/(0 + 4)
= 4/4
= 1
By using slope point form, y = kx + 4.
Substitute x = 2.
g(-2) = -2k + 4 = 0
2k = 4
k = 4/2 = 2
Learn more about slope on:
brainly.com/question/13657991
#SPJ1
Which system of equations has a solution of (-2,-2,-2)?
OA
s+y=0
3-==-2
s+y=z=-4
OB. 31 - y = -8
y - 3z = -8
2 + y + z = -8
OC.
1 + 2y = -6
y + 2z = -6
I-y-z = 2
OD. 1-2y + z = 0
2y +9z = -20
I= y + z = 0
The system of equations that have a solution of (-2,-2,-2) is (b) x + 2y = -6, y + 2z = -6 and x - y - z = 2
How to determine the system of equations?The attached figure represents the proper format of the equations.
The solution is given as:
(x,y,z) = (-2,-2,-2)
To determine the system of equation, we simply substitute the values of x, y and z in the equations in the options.
So, we have:
Option 1:
x + y = 0
y - z = -2
x + y - z = -4
Evaluate
x + y = 0
-2 - 2 = 0 --- False
This means that this system of equations do not have a solution of (-2,-2,-2)
Option 2:
x + 2y = -6
y + 2z = -6
x - y - z = 2
Evaluate
x + 2y = -6
-2 + 2 * -2 = -6 --- True
y + 2z = -6
-2 + 2 * -2 = -6 ---- True
x - y - z = -2
-2 + 2 + 2 = 2
This means that this system of equations have a solution of (-2,-2,-2)
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ1
The pendulum of an antique clock has been damaged and needs to be
replaced. If the original pendulum completed one swing every 1.5 seconds,
how long should the new pendulum be? Use the formula:
T= 2.
1980
OA. 351 centimeters
OB. 0.25 centimeters
O C. 55.9 centimeters
O D. 234.8 centimeters
If the original pendulum completed one swing every 1.5 seconds. How long should the new pendulum be is: C. 55.9 centimeters.
How long should the new pendulum be
Using this formula
T=2π√I/g
Where:
T=1.5 seconds
l =length of pendulum
g= acceleration of gravity=9.8m/s²
Let plug in the formula
1.5 seconds=2π√I/9.8
l/9.8=0.05699
l=0.05699×9.8
l=0.5585
l=55.9 centimeters (Approximately)
Therefore How long should the new pendulum be is: C. 55.9 centimeters.
Learn more about How long should the new pendulum be here:https://brainly.com/question/11616656
#SPJ1
If sin A = 4/5 find the value of cot A + tan A.
Answer:
2.08
Step-by-step explanation:
[tex]sin^{-1} 4/5 = 53.13\\tan 53.13 = 1.33\\cot 53.13 = 0.75\\1.33 + 0.775 = 2.08[/tex]
Answer:
The answer is 2
Step-by-step explanation:
[tex]Cot(x)=\frac{1}{tan(x)} =\frac{Cos(x)}{Sin(x)}[/tex]
[tex]Tan(x) = \frac{Sin(x)}{Cos(x)}[/tex]
[tex]Cos(\frac{\pi }{2} -x)=sin(x)[/tex]
This means that
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}[/tex]
This will be a long one to solve
-> apply cos identity to right side
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}[/tex]
-> simplify according to unit circle
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]
->apply cos identity again
[tex]\frac{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]
If you apply for unit circle numbers,
you will get 2
I do not recommend using a calculator for these questions, but instead, turn the form into [tex]sin\frac{\pi }{2}[/tex] other base unit circle locations, and most likely this is the method that your teacher counts as "right."
when using a calculator, it tends to "round" the number, which result in a inaccurate answer
A jazz concert brought in $153,500 on the sale of 7,500 tickets. If the tickets sold for $15 and $25 each, how many of each type of ticket were sold?
The number of $15 tickets is
Answer:
the answr is 87 jistg ebcaujse
Step-by-step explanation:
3,500 tickets were sold for $15 each and 4,600 tickets were sold for $25 each.
Let x be the number of $15 tickets and y be the number of $25 tickets.
We know that:
x + y = 7,500 (the total number of tickets sold)
15x + 25y = 153,500 (the total amount of money made from ticket sales)
We can use the first equation to express y in terms of x:
y = 7,500 - x
We can substitute this expression of y into the second equation:
15x + 25(7,500 - x) = 153,500
Solving for x:
15x + 25(7,500) - 25x = 153,500
15x + 187500 - 25x = 153,500
-10x = -34,000
x = 3400
Therefore, 3,400 tickets were sold for $15 each and 7,500 - 3,500 = 4000 tickets were sold for $25 each.
Learn more about Arithmetic Operations here:
brainly.com/question/20595275
#SPJ2
If the dimensions of the following cylinder are doubled, what will be the surface area of the new cylinder? 1,406.72 in. 2 2,813.44 in. 2 1,607.68 in. 2 5,626.88 in. 2
Based on the calculations, the surface area (SA) of a cylinder is equal to: B. 2,813.44 in.²
How to calculate surface area of a cylinder?Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:
SA = 2πrh + 2πr²
Where:
h is the height.r is the radius.The dimensions of this new cylinder would be equal to:
Radius = 8 × 2 = 16 in.
Height = 6 × 2 = 12 in.
Substituting the given parameters into the formula, we have;
SA = (2 × 3.14 × 16 × 12) + 2 × 3.14 × 16²
SA = 1,205.76 + 1,607.68
SA = 2,813.44 square inches.
Read more on surface area here: https://brainly.com/question/26396269
#SPJ1
Complete Question:
If the dimensions of the following cylinder are doubled, what will be the surface area of the new cylinder? Radius: 8 in and Height: 6 in.
Group of answer choices.
A. 1,406.72 in.²
B. 2,813.44 in.²
C. 1,607.68 in.²
D. 5,626.88 in.²
Which pair of angles are vertical angles? 6 and 5 2 and 3 1 and 3 5 and 8
Answer:
1 and 3
Step-by-step explanation:
1 and 3 are vertical angles
Find the range of the following equation for the domain {-4, 0, 3} f (x) = -2x^2 -3
The range of the function is {-34, -2, -20}
How to determine the range?The function is given as:
f(x) = -2x^2 - 2
The domain is {-4, 0, 3}
Substitute the domain values in the function.
f(-4) = -2(-4)^2 - 2 = -34
f(0) = -2(0)^2 - 2 = -2
f(3) = -2(3)^2 - 2 = -20
This means that the range of the function is {-34, -2, -20}
Read more about range at:
https://brainly.com/question/10197594
#SPJ1
On a popular television game show, a contestant must choose one of the five envelopes. One envelope contains the grand prize, a car. Find the probability of not choosing a car. Show your solution.
Urgent! Please answer immediately. The answers that are nonsense will be reported.
Answer:
4/5
Step-by-step explanation:
First, we know that we have 5 envelopes. So the denominator of the probability is going to be x/5. We then realize that only one envelope has the car, so the probability of that is 1/5. If we subtract 1/5 from the probability of choosing an envelope (5/5), we get 5/5-1/5=4/5.
If you walk 6 blocks east, 2 blocks north, 3 blocks west and 4 blocks south, then what is the total distance you travel?
Answer:
6 + 2 + 3 + 4 = 15
so 15 blocks
a block is about 0.05 miles
so 15 blocks in miles is 0.75 miles
f(4)=
V
If g(x) = 2, x =
V
By looking at the given graph, we can see that:
f(4) = -10g(x) = 2 if x = 0.How to identify the value of the function?
First, we want to find the value f(4). To get that, we need to look at the graph and see the y-value of the function f(x) when x = -4.
By looking at the graph, we can see that f(4) = -10.
Now we know that g(x) = 2, and we want to find the value of x.
Then we need to see the x-value such that g(x) = 2, by looking at the graph of g(x), we can see that it is equal to 2 in the vertex, which is at x = 0.
Then g(x) = 2 when x = 0.
If you want to learn more about graphs:
https://brainly.com/question/4025726
#SPJ1
Math!! finding volume of prisms
The volume of the rectangular prism will be 16.2 cubic ft.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,
then its volume is given as:
V = a x b x c unit^3
The dimensions of the given rectangular prism;
Length = 2.7ft
Width = 3 ft
Height = 2 ft
The volume of the rectangular prism
V = a x b x c unit^3
V = 2.7 x 3 x 2
V = 16.2 cubic ft
Hence, the volume of the rectangular prism will be 16.2 cubic ft.
Learn more about volume of a right rectangular prism here:
https://brainly.com/question/21308574
#SPJ1
The performance of a cyclist in a race is affected by whether it rains or not that day. The probability the cyclist crashes is 5/8 when it rains and 1/8 when it's dry. On a given day the probability of rain is 1/3 . What is the probability that the cyclist doesn't crash on any given day? please help me
To solve this problem, we have to consider the fact that if the probability that the cyclist may crash due to some circumstance. The probability the cyclist doesn't crash at any given day is 3/8
ProbabilityThe probability the cyclist crash when it's wet or dry will be the
[tex]P = P_w_e_t * P_d_r_y[/tex]
P(wet) = 5/8P(dry = 1/8The probability the cyclist crash on any given day is
[tex]P = \frac{5}{8}*\frac{1}{8} =\frac{5}{64}[/tex]
we can subtract 1 from the value above to find the probability the cyclist doesn't crash at any given day
[tex]P = 1 - \frac{5}{64} \\P=\frac{3}{8}[/tex]
The probability the cyclist doesn't crash at any given day is 3/8
Learn more on probability here;
https://brainly.com/question/24756209
#SPJ1
a lateral edge of a right prism ïs 6cm and the perimeter of its base is 20cm find area of its lateral surface
The area of a 2D form is the amount of space within its perimeter. The lateral area of the right prism is 120 cm².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given the perimeter of the base of the right prism is 20 cm, while the lateral height is 6 cm. Therefore, the lateral area of the right prism is,
Lateral Area of Right Prism = 6cm × 20cm = 120cm²
Hence, the lateral area of the right prism is 120 cm².
Learn more about the Area:
https://brainly.com/question/1631786
#SPJ1
Which function has the same domain as y= 2√x?
Y = √2x
Oy=2³√x
Oy=√x-2
O y = ³√x-2
The function that has the same domain as y= 2√x is (a) y = √2x
How to determine the function?The function is given as:
y= 2√x
The above function is a square root function.
All square root functions have the same domain when they are not translated.
This means that
y = √2x has the same domain as y= 2√x because it is not translated
Read more about domain at:
https://brainly.com/question/1770447
#SPJ1
Expand: In (4a)^3
help please
Answer: 3ln4 + 3lna
Step-by-step explanation:
[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]
Answer:
C and second one is A
In Question 1 and Question 2, what is the distance from the center if the circle to a point on the circle? Take this idea a step further: what is the
relationship between the center of any circle and the points that lle on the circle?
Step-by-step explanation:
I don't see question 1 and 2.
but it did be way for you : the distance from the verge of a circle to a point on the circle is always the radius.
that is the whole concept of a circle : it is the line (or curve) of all points that have the same, constant distance r from a single point.
triangle png Find the value of x
Answer:
x+3x+2x=180(sum of triangle)
6x=180
x=180/6
x=30
again
3x=3×30=90
2x=2×30=60
Libby built a fence that was 56ft for over 4 days, she built the same length each day. how many inches of fence did libby build each day?
27-(2c+3) = 2(c + 7) + c
Answer:
c=2
Step-by-step explanation:
We can first take out the parenthesis: 27-2c-3=2c+14+c. We can combine: -2c+24=3c+14. Then, we can subtract 14 from both sides: -2c+10=3c. Then, we can add 2c on both sides: 10=5c. To find c, we can do 10/5=2.
TIMED HURRY!! What is the sum of the series
possible answers
1,830
2,010
5,400
5,490
[tex]\\ \rm\Rrightarrow \sum^{60}_{n=1}3n[/tex]
It will form a arithmetic sequence as
[tex]\\ \rm\Rrightarrow 3(1)+3(2)+3(3)\dots 3(60)[/tex]
First term=a=3Last term=3(60)=180n=60So
Summation
[tex]\\ \rm\Rrightarrow \dfrac{n}{2}(a+\ell)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{60}{2}(3+180)[/tex]
[tex]\\ \rm\Rrightarrow 30(183)[/tex]
[tex]\\ \rm\Rrightarrow 5490[/tex]
Option D
Answer:
[tex]\mathsf {5,490}[/tex]
Step-by-step explanation:
[tex]\textsf {Given :}[/tex]
[tex]\lim_{1 \to \660} \sum3n[/tex]
[tex]\textsf {Finding the necessary :}[/tex]
[tex]\textsf {1. first term (a)}[/tex]
[tex]\implies \mathsf {a = 3(1) = 3}[/tex]
[tex]\textsf {2. final term}[/tex] [tex]\mathsf {(a_n)}[/tex]
[tex]\implies \mathsf {a_n = 3(60) = 180}[/tex]
[tex]\textsf {3. common difference (d)}[/tex]
[tex]\implies \mathsf {a_2 = 3(2) = 6}[/tex]
[tex]\implies \mathsf {d = a_2 - a_1 = 6 - 3 = 3}[/tex]
[tex]\textsf {Finding the sum of the series :}[/tex]
[tex]\implies \mathsf {S_n =\frac{n}{2}(a + a_n) }[/tex]
[tex]\implies \mathsf {S_6_0 = \frac{60}{2} (3 + 180)}[/tex]
[tex]\implies \mathsf {S_6_0 = 30 \times 183}[/tex]
[tex]\implies \mathsf {S_6_0 = 5,490}[/tex]
What additional piece of information is needed to show that DEF andPQR are congruent by ASA?
Answer:
B) Angle D is congruent to Angle P
Step-by-step explanation:
In order for the triangles to be congurent due to ASA, we need to know two pairs of congruent angles and one pair of congruent sides. We have one pair of sides and angles, so we only need another angle pair, therefore eliminating C and D, which are giving sides. If we chose option A we would get SAA property since it's supposed to be read clockwise. The only option left is option B.
Have a nice day!
This net folds into the cube shown beside it. On the cube, which letter will be on the side opposite D?
B
A
E
C
The letter that will be on the side opposite D is letter B
How to determine the letter?The attached image represents the missing piece in the question
The opposite sides of a cube always have a face in between them, when represented as a net.
From the attached image, the adjacent sides are:
A B C D
F C E
The opposite sides as represented above are;
A and C
B and D
F and E
Hence, the letter that will be on the side opposite D is letter B
Read more about cubes at:
https://brainly.com/question/1972490
#SPJ1