Suppose that two cards are dealt from a standard 52-card poker deck. let a be the event that the sum of the two cards is 8 (assume that aces have a numerical value of 1). how many outcomes are in a?

Answers

Answer 1

Case 1: You have an Ace and a seven.
There are 4 ways to pick 1 Ace out of 4. There are 4 ways to pick 1 seven out of 4. -----> 4*4 = 16
There are 16 ways to be dealt an Ace and a seven.

Case 2: You have a two and a six.
In the same way there are 4*4=16 ways to be dealt a two and a six.

Case 3: You have a three and a five.
In the same way there are 4*4=16 ways to be dealt a three and a five.

Case 4: You have 2 fours.
There are 6 ways to get 2 fours out of 4. (4 choose 2)

Total number of outcomes = 16+16+16+6 = 54

Related Questions

which of the following is a solution set to 4|x+3|

Answers

It is absolute value. We also need more info because their is no solution set.

For student spent $12 on school lunch at this rate find the amount 10 students would spend on the same school lunch?

Answers

12 / 4 = 3
3 * 10 = 30

i think $120
because 12*10=120

. Which is equivalent to a drink made with 3 ounces of 80-proof vodka?

Answers

Omg frat part y lsolldlddld

For football tryouts at the local school 12 coaches and 42 players will split into groups each group will have the same number of coaches and players what is the greatest number of groups that can play that can be formed how many coaches and players will be in each of these group

Answers

Multiply the numbers

how many gallons of 80% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 70% antifreeze? use the six step method

Answers

let's say we'll mix "x" amount of the 80% solution, how much antifreeze is in it? well is just 80% of antifreeze, and the rest is something else.... what's 80% of "x"? so is (80/100)*x, or 0.8x.

likewise, the mixture will be a 70% solution, and let's say it adds up to "y" amount, so how much antifreeze is in it? well (70/100) * y or 0.7y.

[tex]\bf \begin{array}{lccclll} &\stackrel{gallons}{amount}&\stackrel{\%}{quantity}&\stackrel{antifreeze}{quantity}\\ &------&------&------\\ \textit{80\% sol'n}&x&0.80&0.8x\\ \textit{10\% sol'n}&100&0.10&10\\ ------&------&------&------\\ mixture&y&0.70&0.7y \end{array}[/tex]

so whatever "x" is, we know that x + 100 = y.

and we know that 0.8x + 10 = 0.7y.

[tex]\bf \begin{cases} x+100=\boxed{y}\\ 0.8x+10=0.7y\\ ----------\\ 0.8x+10=0.7\left( \boxed{x+100} \right) \end{cases} \\\\\\ 0.8x+10=0.7x+70\implies 0.8x-0.7x=70-10\implies 0.1x=60 \\\\\\ x=\cfrac{60}{0.1}\implies x=600[/tex]

Final answer:

To get a mixture that is 70% antifreeze, you would need 600 gallons of 80% antifreeze solution mixed with 100 gallons of 10% antifreeze solution.

Explanation:

To solve this problem, we will use the six step method. Let's assign variables to our unknown quantities:

Let x be the number of gallons of 80% antifreeze solution.

Now we can set up the equation using the information given:

0.8x + 0.1(100) = 0.7(100 + x)

Simplifying the equation:

0.8x + 10 = 70 + 0.7x0.8x - 0.7x = 70 - 100.1x = 60x = 600

Therefore, you would need 600 gallons of the 80% antifreeze solution to mix with 100 gallons of the 10% antifreeze solution to get a mixture that is 70% antifreeze.

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The number n(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. initially, n(0) = 500, and it is observed that n(1) = 1000. solve for n(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 50,000. (round all coefficients to four decimal places.)

Answers

Rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

The logistic equation governing the number of people exposed to the advertisement in the community is given by:

[tex]\[ \frac{{dn}}{{dt}} = kn \left(1 - \frac{n}{M}\right) \][/tex]

Where:

n(t) is the number of people exposed to the advertisement at time t

k is the growth rate constant

M is the limiting number of people who will see the advertisement

Given:

[tex]$ n(0) = 500 $[/tex]

[tex]$ n(1) = 1000 $[/tex]

[tex]$ M = 50000 $[/tex]

We first need to find the growth rate constant $ k $:

[tex]\[ 1000 = 500 \times \left(1 - \frac{500}{50000}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \left(1 - \frac{1}{100}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \frac{99}{100} \times k \][/tex]

[tex]\[ k = \frac{1000 \times 100}{500 \times 99} \][/tex]

[tex]\[ k = \frac{2000}{99} \][/tex]

Now, we integrate to find [tex]$ n(t) $[/tex]:

[tex]\[ \int \frac{{dn}}{{n(1 - \frac{n}{50000})}} = \int \frac{{2000}}{{99}} dt \][/tex]

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t + C \][/tex]

Using the initial condition [tex]$ n(0) = 500 $[/tex], we find[tex]$ C $[/tex]:

[tex]\[ -\ln|1 - \frac{500}{50000}| = 0 + C \][/tex]

[tex]\[ -\ln\left(\frac{99}{100}\right) = C \][/tex]

So, the equation becomes:

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t - \ln\left(\frac{99}{100}\right) \][/tex]

Solving for n(t) :

[tex]\[ |1 - \frac{n}{50000}| = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ 1 - \frac{n}{50000} = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ \frac{n}{50000} = 1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ n(t) = 50000 \times \left(1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)}\right) \][/tex]

This is the solution for [tex]$ n(t) $[/tex]. Now, rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

How would you write the name of a segment differently than the name of a line

Answers

A line segment is represented (written) using letters for the start point and the end point, as in QR: QR is the line segment connecting Q to R. This is the most common case.

Expecially when we're not talking about points on a given line, a line can be refered to by any arbitrary name, such as "line f."

Final answer:

Segments and lines can be named using the letters that represent the points on them, such as AB or line AB.

Explanation:

In geometry, segments and lines are fundamental elements. A line is an infinite set of points extending in opposite directions, while a segment is a finite portion of a line with two distinct endpoints. These concepts are essential for understanding geometric shapes, angles, and spatial relationships in mathematics.

In mathematics, the name of a segment and the name of a line can be written differently by using the letters that represent the points on the segment or the line. For example, a segment between points A and B can be written as AB, while a line passing through points A and B can be written as line AB or simply AB. It is important to note that in both cases, the order of the points does not matter, as AB is the same as BA.

The graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units a)up b)down c)left D) right

Answers

Correct ansver: a) translated 3 units up

Answer:

A)up

Step-by-step explanation:

Given : f(x)=log x +3

g(x)= log x

To Find :

The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units

a)up

b)down

c)left

d) right

Solution:

Rule: f(x)→f(x)+b

So, the graph f(x) is translated up by b units

So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units

Thus option A is correct.

Hence The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units up

if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?

Answers

Sent a picture of the solution.

Final answer:

To find (g-f)(3), evaluate g(3) and f(3), then subtract f(3) from g(3).

Explanation:

To find (g-f)(3), we need to subtract the function f(x) from g(x) and then evaluate the result at x = 3. Let's first simplify the expressions for f(x) and g(x):

f(x) = 4 - x^2

g(x) = 6x

Now substitute these into (g-f)(3) and simplify:

(g-f)(3) = g(3) - f(3)

= 6(3) - (4 - 3^2)

= 18 - (4 - 9)

= 18 - (-5)

= 23

Therefore, (g-f)(3) is equivalent to 23.

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is -8 a solution of -9f=64-f

Answers

-9f = 64 - f...add f to both sides
-9f + f = 64
-8f = 64 ...divide both sides by -8
f = -64/8
f = -8 <=== yes, -8 is a solution

describe a situation in which a formula could be used more easily if it were rearranged. Include the formula in your description.

Answers

I need to find the length of something when I am given the volume, width, and height.

v=lwh
l = v/wh

Hope this helps!

distance,speed, time formula

d = s * t

if ur looking for time, re-arrange the formula so it reads t = d / s
if ur looking for speed, re-arrange the formula so it reads s = d / t

A homeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long

Answers

You didn't type rest of answer but here
Draw a diagram to illustrate the problem.
Let n = number of strips required.

Note that 10 feet = 10*12 = 120 inches.
Because each strip is 20 inches wide, therefore
20n = 120
n = 120/20 = 6

Answer: 6 strips

If decking cost $5.75 per square feet, how much would it cost to build a deck that is 22 feet by 18.5 feet

Answers

Sent a picture of the solution to the problem (s).

It would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.

To calculate the cost of building a deck, we need to find the total area of the deck and then multiply it by the cost per square foot.

The area of a rectangle (deck) is given by the formula:

Area = length * width

Given that the deck has a length of 22 feet and a width of 18.5 feet, we can calculate the total area:

Area = 22 feet * 18.5 feet

Area = 407 square feet

Now, to find the total cost of building the deck, we multiply the area by the cost per square foot:

Total cost = Area * Cost per square foot

Total cost = 407 square feet * $5.75/square foot

Total cost = $2338.75

So, it would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.

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How do I solve this equation? I need a refresher on Algebra.

Answers

These equations seem tricky, but aren't as hard as you think. Just solve it like you are regularly adding fractions.

Your common denominator is 9x + 9, so

1/(9x+9) = 36/(9x + 9) - (5x + 5)/9

1 - 36 + 5x + 5 / 9x - 9
30x - 30/9x - 9
10x-10/3x - 3
10(x-1)/3(x-1)
10/3

Hope this helped!

A baker uses 3/4 cup of honey in one of his cakes. There are 60 calories in 1/8 cup of honey. How many cups of honey will the baker use for 15 cakes.

Answers

The answer is 11 1/4 cups.

I hope this helps.

One part of the question doesn't matter, which is "There are 60 calories in 1/8 cup of honey" because he is asking how much cups of honey will be used in 15 cakes.
If 1 cake uses 3/4 cups of honey, we should multiply 3/4 by 15, in order to get 11 1/4 (Which is 45/4 as a fraction, or 11.25 as a decimal.0

I hope this helps! :>

in a mayoral election Jane received 213 more votes than Jack. If Jack received N votes how many votes did Jane receive?

Answers

jane=213 more than jacj
jane=213+jack
if jack=n

jane=213+N

jane reciefed 213+N votes

highest common factor of 92 and 42

Answers

To get the Greates Common Factor (GCF) of 92 and 42 we need to factor each value first and then we choose all the copies of factors and multiply them:

92: 22 2342: 2 37 GCF: 2

The Greates Common Factor (GCF) is: 2

You can always share this solution

The correct answer is going to be 2

glad to help anytime

Object a has less thermal energy than object b but heat flows from object a to object begat conditions make this possible

Answers

Object B must contain many more particles than object A. This way object B still has a greater thermal energy

how many more kilometers in 4320 than 7200

Answers

2880 more kilometers

The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 2007-03-04-00-00_files/i0120000.jpg% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount. a. The Changs family paid $0.33 too much for their purchases. b. The Changs family paid $0.99 too much for their purchases. c. The Changs family paid $5.94 too much for their purchases. d. The Changs family paid the correct amount for their purchases

Answers

In order to determine the correct answer, we need to confirm it first by making the solution below:
Costs: $89.95 = New Lamp
$239.99 = Comforter
6 3/5% = Sales Tax (convert this to decimal and we get 6.6%)
$351.72 = Total amount the Chang's paid
Let's get the total costs first which is $329.94
6.6% of 329.94 is $21.78
The total cost with the tax would be $351.72.
Therefore, the Chang's paid the correct amount. The correct answer would be option D. The Chang's family paid the correct amount for their purchases.

In this exercise we will use the knowledge of finance to calculate the total value of the purchase, we have:

Letter D

First, let's organize the information given in the statement as:

$89.95 = New Lamp $239.99 = Comforter 6.6% = Sales Tax $351.72 = Total amount the Chang's paid

Taking the percentage over the total amount, we find:

[tex]6.6\% \ of \ 329.94\ is\ \$21.78\\Total= \$351.72[/tex]

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what is the answer to 72-(-58)-62

Answers

72-(-58)-62
72+58-62= 68
the answer is 68

The answer to [tex]72 - (-58) - 62[/tex] is 68.

Understanding Double Negatives: When we subtract a negative number, it is equivalent to adding that number. Therefore, [tex]-(-58)[/tex] becomes [tex]+58[/tex].

So, the expression can be rewritten as:

[tex]72 + 58 - 62[/tex]

Performing the Addition: Now we add [tex]72[/tex] and [tex]58[/tex]:

[tex]72 + 58 = 130[/tex]

Performing the Final Subtraction: Next, we subtract [tex]62[/tex] from [tex]130[/tex]:

[tex]130 - 62 = 68[/tex]

Therefore, the final answer is [tex]68[/tex].

1.5x - 3y = 6 (solve for y)

Answers

hello :
1.5x - 3y = 6
3y = 1.5x - 6
y = (1.5x - 6)/3

An equation is formed of two equal expressions. The value of y for the given equation is (1.5x - 6)/3.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1.5x - 3y = 6

Subtract 1.5x from both the sides of the equation,

1.5x - 3y - 1.5x = 6 - 1.5x

-3y = 6 - 1.5x

Divide both the sides of the equation by -3,

-3y/(-3) = (6 - 1.5x)/(-3)

y = (1.5x - 6)/3

Hence, the value of y for the given equation is (1.5x - 6)/3.

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Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. Using the tables in the Business Math Handbook that accompanies the course textbook, determine which one of the following is the best deal.
A. Four Rivers
B. Mystic
C. Mystic for last two years
D. Four Rivers for first two years

Answers

The answer to this question would be B. Mystic

Since the rate should be constant, option C and D wouldn't be true.
If the Four Rivers bank gives 12% per year and Mystic Bank gives 14% per year, it will be 3% per quarter year for Four Rivers Bank and 7% semiannually for Mystic Bank.
The total rate would become:
Four rivers 103%^4= 1.125
Mystic : 107%^2= 1.145

How do you rewrite 4x24 using the distributive property

Answers

Hey! Hope that I can help.

To do this, we have to remove the multiplication sign and replace it with 2 parentheses on both sides of the number we're multiplying (24).

Answer: 4(24)

The expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.

An expression 4x24 is given.

We have to write it using distributive property.

What is the distributive property of multiplication ?

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

As per the question ;

Expression is 4x24.

Let's rewrite it in form of distributive property ;

4 × 24

= 4 × ( 20 + 4 )

So ,

It is now in form A ( B + C ) , where ; A = 4 , B = 20 and C = 4

⇒ 4 × ( 20 + 4 )

= 80 + 16

= 96

Thus , the expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.

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some hot dogs come in packages of 8.Why would a baker of hot dog buns packages 7 hot dog buns to a package

Answers

The reason as to why the baker had package hotdogs of seven and not eight because they are making consumers buy another package because other people will likely buy eight and if it is only comprise with seven, they will likely buy another package, to have eight hotdogs and not just seven.

Find the distance between the points on a number line -7, -54

Answers

the answer to the question is 47

since they are both negative numbers just subtract 7 from 54

54-7 = 47

Is the line y = 3x – 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer. Intro Done Go Left Go Right Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 10 of 10

Answers

line y = 3x – 7 has slope = 3

3x + 9y = 9
9y = -3x+ 9
y = -1/3x + 1
so this 3x + 9y = 9 has slope = -1/3

Parallel lines , slope is the same
Perpendicular lines, slope is opposite and reciprocal

Answer
Line y = 3x – 7 is perpendicular to 3x + 9y = 9

Answer:

the answer is 6.

Step-by-step explanation:

on edge i got my question wrong and the answer was 6 <33.

what is -2/3 - (1 1/3)

Answers

-2/3 - (1 1/3)

-2/3 - ( 4/3)

-6/3

hope this helps

om class we learned that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million. Use this information to compute the federal debt per capita in 2010.

Answers

$13,561,623/ 309

So the debt per capita = $43,889

Answer:

$43888.75

Step-by-step explanation:

We have been given that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million.

[tex]\text{The federal debt per capita}=\frac{\text{Total debt}}{\text{Total population}}[/tex]

[tex]\text{The federal debt per capita}=\frac{\$13,561,623}{309}[/tex]

[tex]\text{The federal debt per capita}=\$43888.74757[/tex]

[tex]\text{The federal debt per capita}\approx \$43888.75[/tex]

Therefore, the federal debt per capita in 2010 was $43888.75.

The figure illustrates the apparatus for a tightrope walker. Two poles are set y = 50 feet apart, but the point of attachment P for the rope is yet to be determined. (a) Express the length L of the rope as a function of the distance x from P to the ground.

Answers

Since L is to the second pole, not x, we can't simply say that x^2+y^2=l^2 using the Pythagorean Theorem. We can, however, say that (x-2)^2+y^2=L^2 due to that we simply increase the original height by 2, decreasing x by 2. Plugging 50 as y in, we get (x-2)^2+50^2 =L^2. Square rooting both sides, we get L=sqrt((x-2)^2+50^) and therefore a function of x

Equation for the length L of the rope as a function of the distance x from P to the ground is,

⇒ L = √((x-2)²+50²)

Since L is to the second pole, not x, we can't simply say that;

⇒ x² + y²= L² using the Pythagorean Theorem.

Since, due to that we simply increase the original height by 2, decreasing x by 2.

We can, however, say that ;

⇒ (x-2)² + y² = L²

Plugging 50 as y in, we get ;

⇒ (x-2)² + 50² = L².

Square rooting both sides, we get;

⇒ L = √((x-2)²+50²)

Thus, Equation for the length L of the rope as a function of the distance x from P to the ground is,

⇒ L = √((x-2)²+50²)

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