The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%
How to determine the probability?The given parameters are:
Cards = 52
Face card = 12
Ace = 4
The probability of selecting a face card is:
P(Face card) = 12/52
Now, there are 51 cards.
The probability of selecting an ace is:
P(Ace) = 4/51
The required probability is:
P = 12/52 * 4/51
Evaluate
P = 0.0181
Express as percentage
P = 1.81%
Approximate
P = 2%
Hence, the probability is 2%
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Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent.
The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have three linear equations in three variables:
x - y - z = 0 ..(1)
2x - y + 2z = 1 ..(2)
x - y + z = -2 ..(3)
From the equation (1):
[tex]\rm x=y+z[/tex]
Plug this value in the equation (2) and (3):
[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]
After solving we get:
z = -1
y = 5
Plug the above two values in equation (1) we get:
x = 4
Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
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8. Resuelve los siguientes problemas:
a) Cinco trabajadores de una empresa reci-
ben salarios de $1 200, $1 500, $1 600,
$1 300 y $2 500. ¿Cuál es el promedio
salarial?
see the attachment photo!
The demand function for a christmas music cd is given by q=0. 6(3800-p^2)
The expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a demand function:
q=0. 6(3800-p²)
Differentiate with respect to p:
[tex]\rm \dfrac{dq}{dp} = -1.2p[/tex]
We know the elasticity:
[tex]\rm E(p) = \dfrac{dq}{dp}\times\dfrac{p}{q}[/tex]
[tex]\rm E(p) =-1.2p \times\dfrac{p}{0.6(3800-p^2)}[/tex]
[tex]\rm E(p) = -\dfrac{2p^2}{(3800-p^2)}[/tex]
Here the data for p and q are not given, but we can find any value using the above expression by putting the known data.
Thus, the expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.
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It makes that every time we flip a fair the probability of flipping tails is
It makes that every time we flip a fair the probability of flipping tails is 50%.
What is the probability?Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. If it is equally likely and unlikely that the event would happen, it would have a probability of 0.5
Probability of flipping tails = number of tails / number of sides
1/2 = 0.5 = 50%
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Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 boxes of cookies after different football games. Which data value(s) are outliers? Select all that apply.
The data values that are outliers are 4 and 56.
What is an outlier?
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.
In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.
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Mrs. Yamaguchi's class weighed the potatoes that they grew in their garden and recorded the data on a table. Determine how many dots are above each data value in a line plot of this data.
Weights of Potatoes (in pounds)
1
4
3
8
5
8
1
2
5
8
1
2
1
2
3
4
1
4
1
8
3
4
1
2
3
8
1
2
3
4
3
8
The value
1
8
will have
Choose...
dots above it.
The value
1
4
will have
Choose...
dots above it.
The value
3
8
will have
Choose...
dots above it.
The value
1
2
will have
Choose...
dots above it.
Using a dot plot, it is found that the number of dots of each point are given as follows:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.The value [tex]\frac{1}{4}[/tex] will have two dots above it.The value [tex]\frac{3}{8}[/tex] will have three dots above it.The value [tex]\frac{1}{2}[/tex] will have five dots above it.The value [tex]\frac{5}{8}[/tex] will have two dots above it.The value [tex]\frac{3}{4}[/tex] will have three dots above it.What does a dot plot shows?The dot plot shows the number of times each measure appears in the data-set.
In this problem, one measure has a value of 1/8, hence:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.
Two measures have a value of 1/4, hence:
The value [tex]\frac{1}{4}[/tex] will have two dots above it.
Three measures have a value of 3/8, hence:
The value [tex]\frac{3}{8}[/tex] will have three dots above it.
Five measures have a value of 1/2, hence:
The value [tex]\frac{1}{2}[/tex] will have five dots above it.
Two measures have a value of 5/8, hence:
The value [tex]\frac{5}{8}[/tex] will have two dots above it.
Three measures have a value of 3/4, hence:
The value [tex]\frac{3}{4}[/tex] will have three dots above it.
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Answer:
1 2 3 5 2 3
Step-by-step explanation:
PLEASE HELPPP ITS WORTH 20 points!!!
Answer:
tanD =4/7
Step-by-step explanation:
tanD = P/B
Where P=4 and B=7
So;
tanD=4/7
Match the tan R, cos R and sin R to the correct ratios
Volume of a triangular prism with numbers 3 4 5 6
Answer:
Step-by-step explanation:
V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight
i will ask alot of questions again sorry
Answer:
7.5 m = 0.0075 km (Correct)
0.31 = 310 mm (Correct)
46 m = 4,600 cm (Correct)
457 mm =4.57 cm (Incorrect)
0.6 km = 6,000 m (Incorrect)
Step-by-step explanation:
Tell me if something is wrong.
Solve each equation.
1. x+6=4
2.x- -4 = -6
3.2(x-1)=-200
4.2x+-3=-23
Step-by-step explanation:
1) x+6 =4
x. =4-6
x. =-2
2) x-(-4) =-6
x+ 4. =-6
x. =-6-4
x. =-10
3)2(x-1)=-200
2x-2 =-200
2x. = -200+2
2x. = -198
x. = -198/2
x. = -99
4)2x+(-3) =-23
2x-3. =-23
2x. =-23+3
2x. =-20
x. =-20/2
x. = -10
ΔXYZ has angles with the following measurements:
m∠X=(10x-33)°
m∠Y=(4x-19)°
m∠Z=(100-2x)°
What are the measures of the three angles?
Answer:
Below in bold.
Step-by-step explanation:
The 3 angles add up to 180 degrees as they are in a triangle.
So 10x - 33 + 4x - 19 + 100 - 2x = 180
12x = 180 + 33 + 19 - 100
12x = 132
x = 11.
So the 3 angles are
10(11) - 33 = 110 - 33 = 77 degrees
4(11) - 19 = 25 degrees
100 - 2(11) = 78 degrees
HELP ASAP
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.
The correct true statement is the swimmer comes back up 9 seconds after the timer was started.
Maximum height of a functionThe maximum height of a function is the point where the velocity the body is zero.
Given the function that represent the height of the swimmer as h(t)=t^2−12t+27
If the velocity of the function is zero, hence;
h'(t) = 2t - 12
0 = 2t - 12
2t = 12
t = 6secs
Substitute t = 6 into the function as shown:
h(6) = 6^2−12(6)+27
h(6) = 36 - 72 + 27
h(6) = -36 + 27
h(6) = -9 feet
Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.
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please help with math
There are two pieces of wires, each of length 66 cm. One wire is bent into a square and the other wire is bent into a circle. Find (a) the area of the square, (b) the area of the circle.
Answer:
Area of Circle = 346.5 cm².
Area of square = 272.25 cm ² .
Step-by-step explanation:
So , 2πR = 66
2 × 22 / 7 × R = 66
R comes out is 21/2 cm .
Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2
= 693 / 2 = 346.5 cm².
If bent into the shape of a square ;
4 a = 66
a = 33/2 . ( Side of a square )
Area of square = a ² = 33×33/4 = 1089/4
= 272.25 cm ² .
Can anyone help me solve this?
Answer:9
Step-by-step explanation:
Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]
We know both a and c, so it becomes
[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=
16+b^2=97=
97-16=b^2=
81=b^2=
9=b
Question in the picture 1-5
how to understand next steps what will be anyone give me explains
Step-by-step explanation:
remember a few things :
a × -1 = -a
-a × -1 = a
-1 × -1 = 1
1 × a = a
therefore,
-1 × -1 × a = 1 × a = a
and finally
c × (a + b) = c×a + c×b
so, we can say
(1 - 5) = -1 × -1 × (1 - 5) =
= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =
= -1 × (5 - 1) = -(5 - 1)
3. Twelve people work together: four of them are managers and eight of them are office workers. Two people are chosen at random from the twelve members of the group. Calculate the probability that one is a manager and one is an office worker.
Answer:
2/9
Step-by-step explanation:
8/12 you pick an office worker
4/12 chance you pick a manager
8/12 multiplied by 4/12 is 32/144
We can simplify this to 16/72
We can simplify this to 8/36
We can simplify this to 4/18
We can simplify this to 2/9
use the information given to answer the question. write your answer as a decimal rounded to the nearest tenth
Answer: The value of x is 3.5
Explanation:
Equation:
y = 2x - 7
When the equation's Line intersects the x-axis, the value of y shall be always 0
Insert y = 0, to find x intercept
⇒ 0 = 2x - 7
⇒ 2x - 7 = 0
⇒ 2x = 7
⇒ x = 3.5
So coordinates: (x, y) → (3.5, 0)
What is the value of x?
(Round your answer to
the nearest tenth.)
Answer:
x ≈ 8.7
Step-by-step explanation:
given 2 secants from an external point to the circle, then
the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is
6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides
36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )
6x = 52 (divide both sides by 6 )
x ≈ 8.7 ( to the nearest tenth )
Do ∠ABE and ∠DBC share a ray
Answer:
yes they do
Step-by-step explanation:
they share a ray
Sheryl makes $7 per pair of
earrings, e, and $13 per necklace,
n, she sells. What expression
represents her total income?
The expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
Sheryl makes $7 per a pair of earrings, e, and $13 per necklace, n, she sells.
Let's suppose the total income of Sherly is T:
Then,
T = 7e + 13n
Here e is the number of earrings she sells and n is the number of necklace she sells.
T is the total income and the expression T = 7e + 13n represents the total income of Sherly.
Thus, the expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.
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Which set of values could be the side lengths of a 30-60-90 triangle?
OA. (6,6 2,12}
OB. (6,6√3, 12)
OC. (6, 12, 12√√3}
D. (6, 12, 12 √2)
The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
What is the right-angled triangle?A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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Factor 6x¹ − 5x² + 12x² − 10 by grouping. What is the resulting expression?
(6x + 5)(x²-2)
(6x - 5)(x²+2)
(6x² + 5)(x-2)
(6x²-5)(x+2)
Answer:
[tex](6x-5)(x^2+2)[/tex]
Step-by-step explanation:
[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]
Which equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17)?
Answer: y - 17 = -2(x-7)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= 9+17/-6-7
= 26/-13
= -2
y1 = -17
x1 = 7
y - 17 = -2(x-7)
The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
What is the general equation of a straight line?The general equation of a straight line is-
y = mx + c
where, m is the gradient and is given by y₂ - y₁/x₂ - x₁
and, c is the value where the line cuts y-axis.
Now it is given that the line passes through points (−6,9) and (7,−17)
Therefore we have,
x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17
So, the slope m of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
Put the values,
m = (-17 - 9)/(7 - (-6))
m = -26/7+6
m = -26/13
m = -2
Thus, the equation parallel to the line will be given as:
y - y₁ = m(x - x₁)
y - 9 = -2{x - (-6)}
y - 9 = -2(x + 6)
y = -2x - 12 + 9
y = -2x - 3
Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
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Hailey's laundry basket contains 777 socks. These 777 socks account for approximately 21\!!, percent of Hailey's socks. How many socks does Hailey have in total
The number of socks for Hailey will be 163.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Hailey's laundry basket contains 777 socks. These 777 socks account for approximately 21, per cent of Hailey's socks.The number of Haley's socks will be calculated as=
Socks = 777 x 21/100
Socks = 777 x 0.21
Socks = 163
Therefore the number of socks for Hailey will be 163.
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Question 1 of 10
The slope of the line below is - Write a point-slope equation of the line -1/7
using the coordinates of the labeled point.
10
610
(3, 3)
10
610
Step-by-step explanation:
A triangle cannot have one obutse angle and one right angle. True or flase?
Answer:
No
Step-by-step explanation:
Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.
Answer:
false
Step-by-step explanation:
(x + 8/3)^2 + y^2 = 1 What is the center of the circle? what is the radius?
(x+8/3)²+y²=1
(x+8/3)²+y²+0²+2×0y=1
(x+8/3)²+(y+0)²=(V1)²
->center: C(8/3,0)
-> radius: V1
To identify the most efficient model for a windmill, Gandalf Engineering Company designs the windmill shown. The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF¯¯¯¯¯ and DH¯¯¯¯¯¯.
Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.
What is the proof that ∠A ≅ ∠E?Looing at ΔOAB and ΔOEF
It is clear that
OB = OF (O is the midpoint)
∠OBA = ∠OFE = 90°
Therefore
∠AOB = ∠EOF (Vertically Opposite Angles)
⇒ ΔOAB ≅ ΔOEF and
∠ A ≅ ∠E.
QED
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