What is the possibility of choosing a red jack first and then choosing a red card without replacement
Answers
Answer:
25/1326
Explanation:
In a standard deck of cards, there are 52 cards divided into 4 suits.
• Hearts (Red)
,• Diamonds(Red)
,• Spades(Black)
,• Clubs (Black)
There are two red jacks and two black jacks.
Therefore:
[tex]P(\text{ picking a red jack\rparen}=\frac{2}{52}[/tex]Next, there are 26 red cards in a suit.
Since the selection is without replacement, the number of red cards has been reduced by 1. Therefore:
[tex]P\text{ \lparen then choosing a red card\rparen}=\frac{25}{51}[/tex]Multiply the two probabilities:
[tex]\begin{gathered} P(\text{ choosing a red jack first and then a red card\rparen}=\frac{2}{52}\times\frac{25}{51} \\ =\frac{1}{26}\times\frac{25}{51} \\ =\frac{25}{1326} \end{gathered}[/tex]The probability is 25/1326.
The third option is correct.
Related Questions
×-12=-8one step equation
Answers
As it is given that
[tex]\begin{gathered} x-12=-8 \\ x=-8+12=4 \end{gathered}[/tex]Find the volume of each cone. Use 3.14 for π and round answers to the nearest tenth. Match each answer to a letter below to help you solve the riddle.
Answers
In order to find the volume of the cone, we will use the next formula
[tex]V=\frac{1}{3}\pi r^2h[/tex]In our case
pi=3.14
r=7
h=14
We substitute
[tex]V=\frac{1}{3}(3.14)(7)^2(14)=718[/tex]ANSWER
V=718
container is shaped like a triangular prism. 3 cm 5 cm
Answers
ANSWER
[tex]A=222\operatorname{cm}[/tex]EXPLANATION
A) From the diagram, we see that the base of the triangular face is 4 cm long and the height of the triangular face is 3 cm.
B) From the diagram, we see that the length of two of the rectangular face is 15 cm and the width of the rectangular face is 5 cm.
The third rectangular face has a length of 15 cm and a width of 4 cm.
C) The surface area of the prism is the sum of the areas of the faces of the prism.
The area of a triangle is given as:
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]where b = base, h = height
The area of a rectangle is given as:
[tex]A=l\cdot w[/tex]where l = length, w = width
Therefore, the surface area of the prism is:
[tex]\begin{gathered} A=2(\frac{1}{2}\cdot4\cdot3)+2(15\cdot5)+(15\cdot4) \\ A=12+150+60 \\ A=222\operatorname{cm}^2 \end{gathered}[/tex]use number properties to simplify the following expression. -5+(5+3) show each step in simplifying the expression and explain which property you used in each step
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The expression is:
[tex]-5+(5+3)[/tex]Now we always solve the operation inside the parenthesis, and this is an addition so the expression will be:
[tex]-5+(5+3)=-5+8[/tex]Now we have a substraction so:
[tex]-5+8=3[/tex]Jim's new car has 150 miles on the odometer. He takes a trip and drives an average of m miles each day for three weeks. Which expression represents the mileage on Jim's car after his trip?A) 150m+3B) 150+3mC) 150m+21D) 150+21m
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The answer is D) 150 + 21m
The value of y varies directly with x. If y is 31.5 when x is 9, what is the value of x when y is 49?
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You have that y varies directly with x, it means tha you can write the relation between both variables as follow:
[tex]y=kx[/tex]where k is the constant of proportionality.
If y = 3.15 when x = 9, you can find the value of k, just as follow:
[tex]k=\frac{y}{x}=\frac{3.15}{9}=0.35[/tex]Then, the equation that relates y and x can be writen as follow:
[tex]y=0.35x[/tex]or
[tex]x=\frac{y}{0.35}[/tex]Now, you can find the value of x when y = 49, by replacing this value into the previous equation:
[tex]x=\frac{49}{0.35}=140[/tex]Hence, the value of x when y = 49 is x = 140
Which picture below that does not contain enough information to prove that ∆ABC=∆DEF
Answers
Answer
Picture 3 does not contain enough information to prove that ∆ABC = ∆DEF
Explanation
The rules for congruence in Mathematics include SSS, SAS, ASA
SSS
This represents two triangles with 3 similar sides. Picture 4 shows this type of congruency.
SAS
This represents two triangles with two similar sides and one similar included angle. An included angle is usually located right in between the two similar sides. Picture 2 shows this type of congruency.
ASA
This includes two similar angles and a similar side in between the angles, for the two triangles. Picture 1 shows this type of congruency.
Picture 3 shows two similar sides and a similar angle, but the angle isn't between the similar sides, that is, it isn't an included angle. So, it is the image with not enough information to prove that ∆ABC = ∆DEF.
Hope this Helps!!!
hi there ms or mr could you please help me out with this problem?
Answers
Answer:
They can all be used to prove congruency
Explanation:
SAS - which stands for
Side - Angle - Side
This means: Given two triangles with two know sides and one known angle, If the know sides and angle of both triangles are equal, then we cal conclude that the triangles are equal or congruent.
SSA - Stand for
Side - SIde - Angle
This also satisfies the congruency property
ASA - Stands for
Angle - Side - Angle
This also satisfies the congruency property
AAS - Stands for
Angle - Angle - Side
This also satisfies the congruency property
Draw a mapping diagram. Is the mapping diagram a function?For these ordered pairs: (0,1), (2,4), (3,4), (5,7)
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That is the diagram of the function.
It is a function since for each value of the first conjunct we have an image.
Calculate the next term of the sequence below to use the recursive formula.
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We will have that the sequence follows:
[tex]a_n=a_{n-1}-6[/tex]Then the next value will be:
[tex]a_3=-9-6\Rightarrow a_3=-15[/tex]Suppose that is isosceles with base .Suppose also that and .Find the degree measure of each angle in the triangle.KJL
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We know that the base angles in an isoscles triangle are the same. The sum of the angles in a triangle add to 180
< J + < L + < K = 180
Replace L with J since they are the same
< J + < J + < K = 180
2 < J +
2 ( 3x+29) + ( 2x+34) = 180
Distribute
6x+58 + 2x+34 = 180
Combine like terms
8x +92 = 180
Subtract 92 from each side
8x+92-92 = 180-92
8x =88
Divide by 8
8x/8 = 88/8
x =11
Now we can find the measure of each angle
Find a future value of the long round your answer to the nearest cent
Answers
For this problem, we are given the principal for an account, the rate at which it gets compounded, and the elapsed time. We need to calculate the future value of the loan.
Assuming that the account is compounded every year, we can use the following expression to calculate the future value:
[tex]A=8000\cdot(1.06)^7[/tex]Solving for A, we have:
[tex]\begin{gathered} A=8000\cdot1.5036\\ \\ A=12029.04 \end{gathered}[/tex]The future value of the loan is $12029.04.
the demand equation for a certain product is given by P=132-0.08x where P is the unit price (in dollars ) of the product and x is the number of units produced the total revenue obtained by producing and selling x units is given by R=xp determine prices p that would yield a revenue of 8830 dollarsLowest price=___highest price=_____
Answers
P= 132 - 0.08x
R = xP
R = x ( 132 - 0.08x)
R = 132x - 0.08x^2
8830 = 132x - 0.08 x^2
0.08x^2 - 132x + 8830 = 0 (transposing all ters to the lefthand side of the eq.)
x^2 - 1650x + 110375 = 0 (dividing all terms of the eq by 0.08)
Solve the equation using quadratic formula.
where a = 1 b = -1650 and c = 110375
Quadratic Formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-(-1650)\pm\sqrt[]{(-1650)^2-4(1)(110375)}}{2(1)}[/tex][tex]x=\frac{1650\pm\sqrt[]{2722500-441500}}{2}=\frac{1650\pm\sqrt[]{2281000}}{2}=\frac{1650\pm1510.30}{2}[/tex][tex]x=\frac{1650\pm1510.30}{2}\Rightarrow\frac{1650+1510.30}{2}\Rightarrow\frac{1650-1510.30}{2}[/tex][tex]x_1=\frac{1650+1510.30}{2}=1580.15[/tex][tex]x_2=\frac{1650-1510.30}{2}=69.85_{}[/tex]x1 and x2 are the number of units sold at the lowest and highest price respectively that yields a profit of $8830
Now, we wil solve for P= 132 - 0.08x for x1 and x2
(x1 will give us the lowest price since it has the higher number of units than x2, and it follows that x2 will give us the highest price)
Lowest Price, P = 132 - 0.08x1 = 132 - 0.08 (1580.15) = $ 5.588
Highest Price, P = 132 - 0.08x2 = 132 - 0.08 (69.85 ) = $ 126.412
Translate the following phrase to an expression: the product of a number and 2.Evaluate the expression for n = 18n + 2; 202 n; 36n ÷ 2; 918 n; 36
Answers
Solution:
Question:
Translate the following phrase to an expression: the product of a number and 2.
Let the number be
[tex]=n[/tex]The product of a number and 2.can be represented below as
[tex]\begin{gathered} =n\times2 \\ =2n \end{gathered}[/tex]Hence,
The expression is
[tex]\Rightarrow2n[/tex]When =18, we will have the evaluation be
[tex]\begin{gathered} 2n \\ =2\times18 \\ =36 \end{gathered}[/tex]Hence,
The final answer is
[tex]2n;36[/tex]Find the volume of each cylinder. Round your answers to the nearest tenth, if necessary. Do not include units (i.e. ft, in, cm, etc.). (FR)
Answers
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} volume\text{ = }\pi\times r^2\times h \\ where \\ r\Rightarrow radius\text{ of the circular ends of the circle} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylinder:
Step 1: Evaluate the radius of the circular end of the cylinder.
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ =\frac{4cm}{2} \\ \Rightarrow r=2\text{ cm} \end{gathered}[/tex]Step 2: Evaluate the volume of the cylinder.
Thus,
[tex]\begin{gathered} volume\text{ = }\pi\times r^2\times h \\ where \\ r=2\text{ cm} \\ h=\text{ 8 cm} \\ thus, \\ volume\text{ = }\pi\times2\text{ }\times2\times8 \\ =100.5309649\text{ } \\ \Rightarrow volume\approx100.5\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Hence, the volume of the cylinder, to the nearest tenth, is
[tex]100.5[/tex]which is the correct way to evaluate F (15) with a function f (x )=2 (x + 3)?
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The Solution:
The correct answer is [option 3]
Given the function:
[tex]f(x)=2(x+3)[/tex]We are required to find the value of f(15).
We shall substitute 15 for x in the given function.
[tex]f(15)=2(15+3)=2\times18=36_{}[/tex]Thus, we start by substituting 15 for x and then simplify to get f(15) =36.
Therefore, the correct answer is [option 3]
laws of exponent : multiplication and power to a power simplify
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the whole expression is a multiplication
we must group what we can multiply
[tex](4\times-3)(r^4\times r\times r)(s^{-2}\times s^{-3}\times s)[/tex]when multiply equal terms the exponents are added
so
[tex](-12)(r^{4+1+1})(s^{-2+(-3)+1})[/tex]do the sum and the final expression is
[tex]-12r^6s^{-4}[/tex]I need help solving this practice Having a tough time
Answers
The given function is:
[tex]f(x)=-19\sin(\frac{7}{3}x+\frac{1}{6})-3[/tex]This function is written in the form:
[tex]f(x)=A\sin(B(x+C))+D[/tex]Where:
A is the amplitude of the function
B is given by the period=2pi/B
C is the phase shift
D is the vertical shift
By definition, the amplitude is the measure between half the wave and the crest.
To find the range of temperatures then we need to take into account the amplitude is 19, but also the function has a vertical shift of D=-3, then we need to subtract -3 to the upper and lower range, so:
The initial range given by the amplitude is: -19°F to 19°F.
When we apply the vertical shift we obtain:
-19-3=-22°F
19-3=16°F
The answer is: the range in the average rate of change in temperature of the substance is from a low temperature of -22°F to a high of 16°F.
which one of the following statements is true. a) tan Q =15/8 B) Cos P = 8/15 C) Sin P = 8/17 D) Cos Q= 15/17
Answers
To determine which statement is true we need to remember the definition of the trigonometric functions:
[tex]\begin{gathered} \sin\theta=\frac{opp}{hyp} \\ \cos\theta=\frac{adj}{hyp} \\ \tan\theta=\frac{opp}{adj} \end{gathered}[/tex]where opp denotes the opposite leg to the angle, adj the adjecent leg to the angle and hyp the hypotenuse of the triangle.
In the triangle given the hypotenuse is 17. For angle P the adjecent leg is 8 and the opposite leg is 15, then we have:
[tex]\begin{gathered} \cos P=\frac{8}{17} \\ \sin P=\frac{15}{17} \end{gathered}[/tex]For angle Q the adjecent leg is 15 and the opposite leg is 8, then we have:
[tex]\begin{gathered} \tan Q=\frac{8}{15} \\ \cos Q=\frac{15}{17} \end{gathered}[/tex]Comparing what we found and the options given we notice that the only correct one is cosQ; therefore, the correct statement is D.
Clark Kent and Lois Lane were laying on a blanket,enjoying a relaxing picnic when Clark noticed a giantasteroid approaching Earth. Clark calculates the angleof elevation of the asteroid's approach to be 62°. Lois'penthouse apartment is also in the pathway of theasteroid's approach, 100 feet above ground. Clark'seye is 75 feet from the base of Lois' building. Will theasteroid take out Lois' penthouse apartment? Show allwork and justify your answer.
Answers
Asteroid angle approach = 62°
Louise apartment heigh H = 100 feet
Clark distance from Lois apartment D = 75 feet
NOW GOTO Drawing
NOW find Angle A
tan A =H/D= 100/75 = 1.33
Then
A= 53.13 °
Asteroid angle A'= 62°
THEN WE CAN CONCLUDE
ITS NOT gonna hit Lois apartment
Because angle A < angle A'
53.13° < 62°
What's the decay rate?A) 0.9%B) 90%C) 0.1%D) 10%(I put the answer choises and question in here since they would not fit good with a picture)
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We are given the following function which models the decline of a population.
[tex]y=6.5(\text{0}.9)^x[/tex]The standard form of such a population decay function is given by
[tex]y=a(b)^x[/tex]Where a is the initial population, b is the decay rate and x is the time period.
The decay rate is greater than 0 and less than 1
Comparing the given function with the standard form, we see that the decay rate is 0.9
In percentage, the decay rate is 90%
[tex]b=0.9\times100=90\%[/tex]Therefore, the decay rate of the function is 90%
factor completely first by factoring out the greatest common factor and then factor the remaining trinomial100x² - 1200x +2,000
Answers
Given the expression:
[tex]100x^2-1200x+2000[/tex]notice that all coefficients are divisible by 100, then, we can factor it to get the following:
[tex]100x^2-1200x+2000=100(x^2-12x+20)[/tex]now, we can factor the resulting trinomial in the following way:
[tex]x^2-12x+20=(x-10)(x-2)[/tex]therefore, the complete factorization is:
[tex]100(x-10)(x-2)[/tex]Can you please help with 44Please put it in all 3 such as: up/down, as _,_ , limits
Answers
Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]x-intercept, h(x)=0,
[tex]\begin{gathered} (x-1)^3(x+3)^2=0 \\ x=1,1,1,-3,-3 \end{gathered}[/tex]y-intercept, x=0,
[tex]\begin{gathered} h(0)=(-1)^3(3)^2 \\ h(0)=-1(9) \\ h(0)=-9 \end{gathered}[/tex][tex]\begin{gathered} \text{Multiplicity of (x-1)}^3\text{ is 3} \\ \text{Multiplicity of (x+3)}^2\text{ is 2} \end{gathered}[/tex]Find the solutions of the equation. 1/2x^2+2x+4=0
Answers
Given the equation :
[tex]undefined[/tex]The ratio of men to women is 5:8, how many men are in the dance recital
Answers
Given : the ratio of men to women = 5 : 8
And there are 56 female in the dance recital
So, let the number of men = x
[tex]x\colon56=5\colon8[/tex]Solve for x :
[tex]\begin{gathered} \frac{x}{56}=\frac{5}{8} \\ \\ x=\frac{5}{8}\cdot56=5\cdot\frac{56}{8}=5\cdot7=35 \end{gathered}[/tex]So, the answer is : the number of men = 35
23) Jalen is buying an area rug for his front hall. He wants the rug to be triple the dimensions of hiscurrent front hall rug. How will the area of the new rug compare to the area of his current rug?A. The area is increased by 3 units.B. The area is nine times larger.C. The area is three times larger.D. The area is six times larger.
Answers
Answer:
B. The area is nine times larger.
Explanation:
To answer this question, we use sample dimensions.
If the dimensions of his current front hall rug are
Width = 1 units
Length =2 units
Area = 1 x 2= 2 square units
If the dimensions are tripled, we have:
Width = 1 X 3 = 3units
Length =2 X 3 =6 units
Area = 3 x 6= 18 square units
Now, 18/2 =9
Therefore, we conclude that the area is nine times larger.
Another Approach
Scale factor = 3
Change in Area = Area of Previous Dimension X 3 X 3
=9 X Area of the Previous Dimensions
The correct choice is B.
Do you know how to solve I got 19/26 but it was wrong
Answers
We need to know the number of favourable outcomes.
The black cards are half of the deck, thus there are 26 black cards
Now there is 12 face cards in a deck. But, half of them are black, which we have already take count of them. There is 6 red face cards.
Then, the number of favourable outcomes is 26 for the black cards, plus 6 for the red face cards:
[tex]26+6=32[/tex]Now, to calculate the probabilities we need to divide the favourable outcomes by the total outcomes:
[tex]\frac{32}{52}=\frac{8}{13}[/tex]The probability of the even is 8/13
y is in direct proportion to x. If x = 25 than y = 5. Find the value of y, if x = 9.
Answers
Given
y is in direct proportion to x.
And, if x = 25 then y = 5.
To find the value of y if x=9.
Explanation:
It is given that,
y is in direct proportion to x.
Then,
[tex]\begin{gathered} y\propto x \\ y=kx\text{ \_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Since, x=25 and y=5.
Then,
[tex]\begin{gathered} 5=k(25) \\ k=\frac{5}{25} \\ k=\frac{1}{5} \end{gathered}[/tex]Therefore,
[tex]y=\frac{1}{5}x[/tex]That implies, for x=9.
[tex]\begin{gathered} y=\frac{1}{5}(9) \\ y=\frac{9}{5} \\ y=1.8 \end{gathered}[/tex]Hence,
[tex]y=1.8[/tex]Sun Valley has 15,000 people living in an area of 12.5 square miles.Pearce City has 22,500 people living in an area of 15 square miles. Which city is likely morecrowded?
Answers
We will pluck out the data from the given problem. We will express the number of people ( population) in two cities ( P1 and P2 ) and the area over which the people are spread in each city as ( A1 and A2 ).
Sun Valley:
[tex]\begin{gathered} Population(P_1\text{) = 15,000 people } \\ \text{Area of spread ( A}_{1\text{ }})=12.5miles^2 \end{gathered}[/tex]Peatce City:
[tex]\begin{gathered} \text{Population ( P}_2\text{ ) = 22,500 people} \\ \text{Area of spread ( A}_2)=15miles^2 \end{gathered}[/tex]We are to compare the two cities on the basis of "crowding". We will first interpret what is meant by crowding in the context of this question.
Crowding is termed as number of people in a unit area. This means a city with more number of people in a small area would be more crowded than a city with less number of people in large area.
Mathematically speaking, its the ratio of Population ( P ) in each city to the area coverage ( A ) over which the population is spreaded to. Statisticians represents this ratio as " Population Density ( PD )".
It is a useful parameter used in various statistical analysis at higher proects level.
We will compute the population density of each city as follows.
SunValley:
[tex]\begin{gathered} PD_1\text{ = }\frac{P_1}{A_1}\text{ = }\frac{15,000}{12.5} \\ \textcolor{#FF7968}{PD}_{\textcolor{#FF7968}{1}}\text{\textcolor{#FF7968}{ = 1,200 }}\textcolor{#FF7968}{\frac{people}{miles^2}} \end{gathered}[/tex]Pearce City:
[tex]\begin{gathered} PD_2\text{ = }\frac{P_2}{A_2}\text{ = }\frac{22,500}{15} \\ \textcolor{#FF7968}{PD_2}\text{\textcolor{#FF7968}{ = 1,500}}\textcolor{#FF7968}{\frac{people}{miles^2}} \end{gathered}[/tex]Note: The reason why we used population density as a paramter for crowding is because the population and coverage area are both different in each city. So for adequate comparison we equalize one of the two quantities ( Population or Area ) for both cities. In the parameter of " population density - PD " we equated the coverage area. We can see this from the units of poluation density ( PD1 and PD2 ) where the coverage area is equated to 1 square mile.
Now, once we have the required parameter for "crowding". We can compare the population densities of each city as follows:
[tex]\begin{gathered} PD_2>PD_1 \\ 1,500\text{ > 1,200} \end{gathered}[/tex]Therefore, we see that Pearce City has more number of people residing in a square mile than the number of people in a square mile at Sun Valley! Hence,
The city which is most likely to be crowded is the one with higher population density:
[tex]\text{\textcolor{#FF7968}{Pearce City}}[/tex]in a class experiment, Sean finds that the probability that a student plays soccer is 12/25. if the school population is 300, how many students would we expect to play soccer, based on Sean's experiment?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the requested value, so we obtain the following:
Then we will substitute in the following formula:
Students who play soccer=Number of students*(Probability that they play soccer)
Replacing:
Students who play soccer=300*(12/25)
Students who play soccer=3600/25
Students who play soccer=144
Finally we obtain that 144 students would we expect to play soccer, based on Sean's experiment.
