According to the given statement the probability that the hand contain exactly 2 face card is [tex]\frac{1}{221}[/tex].
Simple probability: What is it?Calculating a result or perhaps the probability that an event would ever occur is known as simple probability. Probability statistics are used by insurance firms to calculate the probability that they'll have to give out a claimed. By dividing one possible outcome by all other possible possibilities, one may determine a basic probability.
Briefing:A regular 52-card deck is used to deal a poker hand, which consists of 4 cards.
The total number of cards in a deck 52
Number of faces cards in a deck = 2
Number of cards not face cards = 50
The total number of combinations of drawing 4 cards out of 52 cards = [tex]={ }^{52} C_4[/tex]
Now , the combination of 4 cards such that exactly 2 of them are face cards = [tex]{ }^{2} C_2 \times{ }^{50} C_2[/tex]
That probability that perhaps the collection will comprise exactly six face cards is as follows:
= [tex]\frac{{ }^{2} C_2 \times{ }^{50} C_2}{{ }^{52} C_4}[/tex]
[tex]=\frac{\frac{2 !}{2 ! 0 !} \times \frac{50 !}{2 ! 48 !}}{\frac{52 !}{4 ! \times 48 !}}[/tex]
=[tex]\frac{1}{221}[/tex]
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ4
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 9.
The surface area of the plane is π√14 sq. units.
Given plane = x+2y+3z=1 and cylinder = x² + y² = 9
Let J be the projection on the plane x+2y+3z=1
We know that the surface area of an equation is
∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA
It is given that the plane is inside the cylinder.
We can use the coordinates of the cylinder to get
x = r cosθ and y = rsinθ
Therefore,
x² = r²cos²θ
y² = r²sin²θ
Therefore,
x² + y² = r²cos²θ + r²sin²θ
= r²(cos²θ + sin²θ)
= r² [Since cos²θ + sin²θ = 1]
Putting the value of x² + y² in the initial equation we get
r² = 9
or, r = 3
Therefore,
J = {(r,θ)/ 0 ≤ r ≤ 3, 0 ≤ θ ≤ 2π}
Now,
x +2y + 3z =1
or, z = 1/3(1 - x - 2y)
Partially differentiating z with respect to x gives us
∂z/∂x = -1/3
Partially differentiating z with respect to y gives us
∂z/∂y = -2/3
Hence,
Surface Area = ∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA
= ∫∫j √{1+ (-⅓) ² + (-⅔) ²} dA
= ∫∫j √(9+1+4)/√9 dA
= √14 /3∫∫j dA
=√14/2 [2π - 0]
= π√14 sq units
To know more about the Surface Area visit
https://brainly.com/question/14697595
#SPJ4
PLEASE HELP I NEED IT ASAP
a report of the national center for health statistics says that the height of a 20-year-old man chosen at random is a random variable h with mean 5.8 feet and standard deviation 0.24 feet. find the mean and standard deviation of the height j of a randomly selected 20-year-old man in inches. there are 12 inches in a foot.
The required mean and standard deviation of height J is 69.6 inches and 2.88 inches.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
here,
1 foot = 12 inches,
Mean = 5.8 feet
Mean = 5.8 (12 inches)
mean = 69.6 inches,
Now,
Standard deviation = 0.24 (feet)
Standard deviation = 0.24 (12 inches)
Standard deviation = 2.88 inches
Thus, the required mean and standard deviation of height J is 69.6 inches and 2.88 inches.
Learn more about mean here:
https://brainly.com/question/15397049
#SPJ1
I need help with this question
Answer:b
Step-by-step explanation:
Need help ASAP
Remember to round your answer to the nearest cent
hurry please!! - question on attached image
Answer:
the answer is y=2x+3 hope this helps
How do you get 1/2 of a number?
Answer: to get 1/2 of a number, simply divide it by 2
Step-by-step explanation: the denominator, or the second digit after the numerator, is the one you use to divide a number. for example 1/3 of 33 = 11, as you divide 33 by 3, or 1/2 of 500 = 250.
2: Angle 1 and Angle 4 are vertical angles. If the measure of angle 1 equals 3x + 14 and the
measure of angle 4 equals 5x − 52, what is the measure of Angle 1?
3: Suppose that ∠ = 3x + 8 and ∠ = 2/3x + 62
If ∠ and ∠ are supplementary
angles, what is the measure of ∠?
4:Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the
measure of angle 3 equals 9x + 59, find the value of .
Each part of the question is answered above and the angles are given below.
What are angles?In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.Given are the angles as mentioned in the question.
[1] -
Since, angle [1] and angle [4] are vertically opposite angles, we can write-
3x + 14 = 5x - 52
14 + 52 = 5x - 3x
2x = 66
x = 33
∠1 = 3x + 14 = 3 x 33 + 14 = 99 + 14 = 113°
∠1 = 113°
[2] -
Since, angle [A] and angle [B] are supplementary angles, we can write-
(3x + 8) + {(2/3)x + 62} = 180
3x + 8 + 62 + (2/3)x = 180
3x + (2/3)x = 110
x{3 + 2/3} = 110
x{(9 + 2)/3} = 110
(11/3)x = 110
x = (110 x 3)/11
x = 30
∠A = 3x + 8 = 3 x 30 + 8 = 98°
∠A = 98°
∠A = (2/3)x + 62 = 2/3 x 30 + 62 = 82°
∠B = 82°
[3] -
Since, angle [2] and angle [3] are vertically opposite angles, we can write -
13x + 27 = 9x + 59
13x - 9x = 59 - 27
4x = 32
x = 8
∠2 = 13x + 27 = 13 x 8 + 27 = 104 + 27 = 131°
∠2 = 131°
∠3 = 9x + 59 = 9 x 8 + 59 = 72 + 59 = 131°
∠3 = 131°
Therefore, each part of the question is answered above and the angles are given above.
To solve more questions on angles and triangles, visit the link below -
brainly.com/question/18584968
#SPJ1
How many inches are in 32 yards?
Answer:
1152
why cant you bing it?
A coach selects 2 of his 8 team members to gather the equipment. In how many ways can-the coach select this pair?
PLEASE Help me
There are 28 ways can-the coach select this pair.
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
A coach selects 2 of his 8 team members to gather the equipment.
Now,
Since, A coach selects 2 of his 8 team members to gather the equipment.
Hence, Number of ways = [tex]^{8} C_{2}[/tex]
= 8! / 2! 6!
= 8 × 7 / 2
= 28
Thus, Number of ways = 28
Learn more about the combination visit:
https://brainly.com/question/11732255
#SPJ1
Identify the quadratic function that is in standard form and has zeros −2 and 8.
f(x) = x2 − 6x − 16
f(x) = x2 + 10x + 16
f(x) = x2 − 6x + 16
f(x) = x2 + 10x − 16
The quadratic function is f(x) = x² -6x + 16.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Let the standard form of quadratic function polynomial is ax² + bx + c = 0
And the zeros of the equation is (x +2) and (x-8)
Now to find the polynomial,
we multiply both zeros
(x +2)(x -8)
= x² + 2x -8x + 16
= x² -6x + 16
And the function in the standard form.
Therefore, the quadratic function is f(x) = x² -6x + 16.
To learn more about the Polynomials;
brainly.com/question/11536910
#SPJ1
5. Lenore had a coupon
for 50 cents off each box
of cookies. She bought two
boxes that were $4.50
each and 4 cans of soup.
If her total bill was $16.00,
how much were the cans
of soup?
Answer: $8 for 4 cans of soup!
Step-by-step explanation:
We know that a box is $4.50 each, but Lenore had a coupon off 50 cents each, so the price of the box is $4
Lenore bought 2 box
4 times 2 = $8
16 - 8 =8
So the 4 cans of soup cost is $8 or $2 each can of soup
What does a scale factor of greater than 1 indicate?
Scale factor of greater than 1 indicates the size of the shape will increases
The scale factor is defined as the ratio between the original size of the figure and the new size of the figure.
The scale factor of the figure maybe greater than 1 or the between 0 and 1
If the scale factor of the figure is between 0 and 1, then the size of the figure will decreases, the new size of the figure will be less than original figure
Similarly, if the scale factor is greater than 1, the size of the figure will increase, new figure will be larger than original figure
Therefore, if the scale factor is greater than 1 the figure will enlarge
Learn more about scale factor here
brainly.com/question/29464385
#SPJ4
Which description of a figure and its image match the transformation described by (x,y) → (-x+1,y+1)
Answer:
the figue which is translated one unit up and one unit to the right
Step-by-step explanation:
Lauren and Hazel's families provide money for their school lunch accounts. Hazel starts with $200 in her account. She spends $30 each week on lunches. Lauren starts with $50 in her account and does not spend any of it. Her family adds $20 each week to her account. Write an equation to represent how much money (y) Hazel has in her account after a number of weeks (x).
triangle ABC is being enlarged using a scale factor of 1/2 and center (1,9) to give triangle A' B' C'
Answer:
When a triangle is enlarged using a scale factor of 1/2 and center (1,9), the resulting triangle will be similar to the original triangle. This means that the angles of the new triangle will be the same as the angles of the original triangle, but the lengths of the sides will be scaled down by a factor of 1/2.
For example, if triangle ABC has vertices at (0,0), (3,0), and (3,4), then the coordinates of the vertices of triangle A'B'C' would be (1,9), (1.5, 9), and (1.5, 9.2), respectively. The side lengths of triangle A'B'C' would be half the length of the corresponding sides of triangle ABC, but the angles would be the same.
It is important to note that the center of the enlargement, (1,9), will not be a vertex of triangle A'B'C'. Instead, it will be the point at which the enlargement is centered, and the resulting triangle will be positioned relative to this point.
Step-by-step explanation:
What is the meaning of infinitives example?
Meaning of infinitive generally represents the action or some purpose of the given word. For example: They will lock the front gate to prevent the house from theft.
Explanation:
Meaning of infinitive :
Infinitive generally represents the some action or the purpose of the given word.Example of infinitive representing action is:
They will lock the front gate to prevent the house from theft.
To prevent represent the action.
As subject of the sentence.Example: To swim in the deep lake may be dangerous for a person.
As direct object :Example : i like to read in Sanskrit.
As an adverb infinitiveExample : I can't wait to eat.
Therefore, infinitive meaning generally represents the action or some purpose of the given word. For example: They will lock the front gate to prevent the house from theft.
learn more about infinitive here
brainly.com/question/11017391
#SPJ4
Edgar wants to get ice cream for dessert. He looks up the prices at The Ice Cream Factory and Main Street Scoops. The Ice Cream Factory charges $1.75 per scoop and a $0.75 fee for unlimited toppings. Main Street Scoops charges $2 per scoop and a $0.25 fee for unlimited toppings. Which inequality can be used to find when Main Street Scoops would be the cheaper option?
A. 1.75x + 0.75 < 2x + 0.25
B. 1.75x + 0.75 > 2x + 0.25
C. 1.85 + 0.75x < 2 + 0.25x
D. 1.75x + 0.75 ≥ 2x + 0.25
1.75x + 0.75 < 2x + 0.25 inequality can be used to find when Main Street Scoops would be the cheaper option.
How do you explain inequality?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different individuals, it is prone to misunderstanding in public discourse. However, certain distinctions are universal.Related ideas include lifetime inequality (the distribution of incomes over a person's lifetime), inequality of wealth (the distribution of wealth across households or individuals at a particular point in time), and inequality of opportunity (the effects on income of factors that people cannot control, like.1.75x + 0.75 < 2x + 0.25 inequality can be used to find when Main Street Scoops would be the cheaper option.
1.75x + 0.75 < 2x + 0.25
1.75x + 0.75 -0.75 < 2x + 0.25 -0.75.
x< - 0.0068
To learn more about inequality refer to:
https://brainly.com/question/24372553
#SPJ1
Lyme disease is an infection caused by bacteria. A test for Lyme disease may be affected by other medications and medical conditions. The testing results are summarized in the table.
Tested positive Tested negative Row Totals
Has Lyme disease 53% 17% 70%
Does not have Lyme disease12% 18% 30%
Column Totals 65% 35% 100%
What percentage of all patients who took the test had a true negative result?
35%
30%
18%
12%
Answer:
its 12%
Step-by-step explanation:
i took the test and got it right
Answer: 17%
Step-by-step explanation:
908 × 65 please help me with this question
Answer:
Step-by-step explanation:
59,020
What would it mean to make a scale drawing with a scale of 1 1?
To make a scale drawing with scale of 1:1 means a full size image .
Scale drawings are images that depict objects at a scale different from their actual size.
Depending on the size of the object being represented and how the drawing will be used, they can depict objects at either a bigger or smaller scale than full size.
The scale gives the proportion of a distance at full size to the distance that, at the scale in use, would have the same length.
The notation " : " is used to denote the scale of drawings as a ratio.
So, According to the question,
In full size drawings, the ratio is 1:1 (or occasionally 1/1 or "one to one").
Hence , a full size drawing is made by scale 1:1
To know more about Scale drawing here
https://brainly.com/question/17388747
#SPJ4
What additional information could you use to show that δstu ≅ δvtu using sas? check all that apply. uv = 14 ft and m∠tuv = 45° tu = 26 ft m∠stu = 37° and m∠vtu = 37° st = 20 ft, uv = 14 ft, and m∠ust = 98° m∠ust = 98° and m ∠tuv = 45°
Options A and D are both correct. UV = 14 feet and mTUV = 45 degrees D. ST = 20 feet, UV = 14 feet, and mUST = 98 degrees by using congruence of triangles.
What is congruence triangle?Two triangles are congruent if their corresponding sides are the same length and their corresponding angles are the same size.
What exactly is SAS congruence?According to the SAS criterion for triangle congruence, two triangles are congruent if they have two pairs of congruent sides and the included angle (the one between the congruent sides) in one triangle is congruent to the included angle in the other triangle.
Given
See the attachment for the triangle.
What evidence do you have?
SAS is used by STU and VTU.
To demonstrate their resemblance, we must examine the corresponding sides and angles of both triangles.
To begin, UST must equal UVT.
As a result, UST=UVT=98⁰.
Then, UV must equal US.
So:
UV = US = 14⁰
Furthermore, ST must equal VT.
So:
Furthermore, ST must equal VT.
As a result, ST = VT = 200.
Finally, TUV must be equal to TUS.
So: TUV = TUS = 450
Options A and D are both correct. UV = 14 feet and mTUV = 45 degrees D. ST = 20 feet, UV = 14 feet, and mUST = 98 degrees.
To know more about the congruence of triangles visit :
https://brainly.com/question/20521780
#SPJ4
1. The line parallel to y=2/3x+1
that passes through the point (3, 6)
The equation of the line is y = (2/3)x + 4
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line.
y = m(1)x + c
The line is parallel to y = (2/3)x + 1
It is in the form of y = m(2)x + c
This means,
m(1) = m(2)
m(1) = 2/3
Now,
The line passes through the point (3, 6).
(3, 6) = (x, y)
y = mx + c
6 = (2/3)3 + c
6 = 2 + c
c = 6 - 2
c = 4
The equation of the line.
y = (2/3)x + 4
Thus,
The equation of the line is y = (2/3)x + 4
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ1
twice a number is equal to negative for. which equation could be used to find the number? 2 n - 4 2 n
The equation which can be used to find the number is 2n = -4, and the number is -2.
What do you mean by equation?
A mathematical statement which is known as an equation makes two expressions' values equal to each other. It is mathematical statement which says "this is equivalent to that," in different words. It appears to have an equal sign in the centre, with a mathematical expression on the right side, and a mathematical expression on the left side.
Let the number be n,
we have given that the number is being twice.
So, the number becomes 2n
And, it is also given that the this twice of the number is equal to -4.
So the equation becomes as:
2n = -4
on solving this equation, we get n = -2
Therefore, the equation is 2n = -4 and the number is -2.
To know more about equation, go to link
https://brainly.com/question/22688504
#SPJ4
Find the vector v with the given magnitude and the same direction as u. Magnitude ||v|| = 51 Direction u = ⟨-8,15
The vector [v] whose direction is same as that of vector [u] is given as -
[v] = -24i + 45j.
What is an expression? What is a expression? What is a mathematical equation? What is vector?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A vector quantity is a quantity that has both magnitude and direction.
We have the a vector [v] with the given magnitude and the same direction as u.
We can write vector [u] as -
[u] = - 8i + 15j
Unit vector {u} along vector [u] -
{u} = [u] / |u|
{u} = (- 8i + 15j)/17
We can write vector [v] as -
[v] = 51 x (- 8i + 15j)/17
[v] = 3(- 8i + 15j)
[v] = -24i + 45j
Therefore, the vector [v] is given by [v] = - 24i + 45j.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ1
The functions f(x) = x and h(x) = f(x + 7) are graphed on the same coordinate grid. Which
statement below is true? (select one)
a. The graph of f is steeper than the graph of h.
b. The graph of h is steeper than the graph of f.
C. To create h, f is translated 7 units to the right.
d. To create h, f is translated 7 units to the left.
Answer: d.
Step-by-step explanation:
To create h, f is translated seven units to the left.
f(x)=x^2. What is g(x)?
Answer:
g(x) = (1/2x)^2
Step-by-step explanation:
The function of g(x) is stretched in the graph, so the value is going to be less than 1, which eliminates choice A.
Because the graph g(x) lands on the point (2,1), input this in each of the expressions and see which one is true. C is the only one that truly works.
Help with question 13
The amount of stock that is wasted is given as follows:
1 - 21/64 inches.
How to obtain the amount of stock wasted?The total amount of stock is given as follows:
9 - 7/16 inches long = 144/16 - 7/16 = 137/16 inches long.
The total amount of stock used for the two punches is given by the sum of the two amounts, as follows:
4 - 1/64 + 4 - 3/32 = 8 - 7/64 = 505/64
Then the amount wasted is given by the subtraction of the total amount by the amount used, as follows:
137/16 - 505/64 = 548/64 - 505/64 = 43/64.
The decimal of this is of:
43/64 = 0.671875.
Hence the amount wasted is of:
1 - 43/64 = 64/64 - 43/64 = 21/64
Meaning that the third option is correct.
More can be learned about operations with fractions at https://brainly.com/question/1682776
#SPJ1
in last 20 years, 238 couples have divorced out of a random sample of 500 couples in a certain city. find a 95% confidence interval for the rate of couples who divorced in that city. find the upper bound of the confidence interval (round off to second decimal place).
The upper bound of the confidence interval is 0.52
What is confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
Out of 500 couples in a given city, 238 couples had divorced in the past 20 years. As a result, the sample proportion is calculated as follows:
[tex]P=238/500 = 0.476[/tex]
As a result, the following 95% confidence interval is calculated for the city's divorce rate: [tex]P +(Z_{a}*(\sqrt{\frac{P(1-P)}{y} } )[/tex]
[tex]Z_{a}= 1.96[/tex]
the upper bound of confidence interval = 0.0438 + 0.476
= 0.52
To know more about confidence interval checkout https://brainly.com/question/24131141
#SPJ1
The school is having a fundraiser where each rose sold makes $1.25 in profit.
The school has to pay a flat shipping
cost of 50. How many roses must be
sold to earn a profit of $1000?
Answer: 800
Step-by-step explanation: 1.25$ x 800 is 1000
Answer:
840
Step-by-step explanation:
$1000+$50=$1050
$1050/$1.25=840
Answer=840