Final answer:
There are 1326 different 2-card hands possible when drawing without replacement from a standard deck of 52 playing cards, using combinations to calculate it.
Explanation:
To determine how many different 2-card hands are possible from a standard deck of 52 playing cards when drawing without replacement, we need to consider combinations since the order of the cards does not matter. Using the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose, we calculate C(52, 2).
We have:
n = 52 (total number of cards)
r = 2 (number of cards to choose)
Therefore, the calculation is as follows:
C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326.
So, there are 1326 different 2-card hands possible when drawing without replacement from a standard deck of cards.
residents of a small city voted on whether to allow a developer to build a shopping center.the number of votes favor of the shopping center was 4,400.the number of votes against the shopping center was 17,600.what percent of the voters were in favor of building the shopping center?
1.) One side of a rectangle is 7 inches and the other side is x inches. What values of x will make the perimeter at most 26 inches?
2.) Use the fact that the sum of the 3 angles in a triangle is 180 degree to answer this question. One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 35 degree more than that of the smallest angle. Find the measure of the each of the angles.
I need the smallest angle, The middle angle and largest angle .
Thank you !
simplify x + 2/ x^2 - 6x - 16 divided by 1/9x
solve for x in the equation x^2 + 20x + 100 = 36
Answer:
x = -4 or x = -16
Step-by-step explanation:
We have to solve equation x^2 + 20x + 100 = 36 and find the value of x
x² + 20x + 100 = 36
x² + 20x + 100 - 36 = 36 - 36
x² + 20x + 64 = 0
(x + 4 ) ( x + 16 ) = 0
x + 4 = 0 or x + 16 = 0
x = -4 or x = -16
Answer would be x = -4 or x = -16
PLEASE HELP!! WILL GIVE BRAINLIEST!!
Question 3: The figure below shows a shaded region and a nonshaded region. Angles in the figure that appear to be right angles are right angles
Part A: What is the area, in square feet, of the shaded region?
Part B: What is the area, in square feet, of the nonshaded region?
What is the following sum? 2(^3√16x^3y)+4(^3√54x^6y^5)
Answer: the answer is a
Step-by-step explanation:
I just took the test
Mr. Jacobs is going to make a histogram of the test scores from the last math test he gave. He plans to first organize the data into a stem-and-leaf plot and then make the histogram from the stem-and-leaf plot. The test scores are listed below. 79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87, 85 What is the mode interval of the data?60-69 70-79 80-89 90-99
Answer:4
Step-by-step explanation: just mark me brainlest
Steven earns extra money babysitting. He charges $37.50 for 6 hours and $50.00 for 8 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation is y =
a taxi cost $1.65 for the 1st Mile and $0.85 for each additional mile. Which equation could be solved to find the number x of additional miles traveled in the taxi given that the total cost of the trip is $20?
Which statements are true regarding quadrilateral ABCD? Check all that apply.
ABCD has congruent diagonals.
ABCD is a rhombus.
ABCD is not a rectangle.
ABCD is not a parallelogram.
ABCD has four congruent angles.
The statements that are true regarding quadrilateral ABCD include:
ABCD has congruent diagonals.ABCD is a rhombus.ABCD has four congruent anglesBased on the information given, ABCD has congruent diagonals and can be treated as a rhombus. This is because it's a regular quadrilateral.
It should be noted that ABCD can be treated as a rectangle and a parallelogram as well.
In conclusion, the correct options are 1, 2, and 5.
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Your typical markup for merchandise is 40%. Your cost on an item is $8.00. Calculate the selling price.
What number would you add to both sides of x2 + 7x = 4 to complete the square? 22 72
neeeeeed help asp please. thx:)
Choose the correct product of (3x − 8)2.
9x2 − 64
9x2 + 64
9x2 − 48x + 64
9x2 + 48x + 64
A large tank is filled to capacity with 400 gallons of pure water. brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t. a(t) = lb
Final answer:
The student's question involves setting up and solving a differential equation for the amount of salt in a tank where brine is added and mixed solution is removed at constant rates.
Explanation:
The problem is related to a differential equation modeling the amount of salt in a tank of water where the concentration changes over time. We are given a tank with an initial volume of 400 gallons of pure water. Brine with 3 pounds of salt per gallon is added at a rate of 4 gallons per minute, and the well-mixed solution leaves the tank at the same rate.
To find the number of pounds of salt a(t) in the tank at any time t, we can set up a differential equation based on the rates of salt entering and leaving the tank:
[tex]\(\frac{dA}{dt} = rate_{in} - rate_{out}\)[/tex]
Where A represents the amount of salt in the tank, \(rate_{in}\) is the rate at which salt enters the tank, and \(rate_{out}\) is the rate at which salt leaves the tank.
[tex]\(rate_{in} = 3 pounds/gallon \times 4 gallons/minute = 12 pounds/minute\)[/tex]
[tex]\(rate_{out} = \frac{A(t)}{400} \times 4 gallons/minute = \frac{A(t)}{100} pounds/minute\),[/tex] since the concentration of salt leaving is[tex]\(\frac{A(t)}{400}\) pounds/gallon.[/tex]
The differential equation becomes:
[tex]\(\frac{dA}{dt} = 12 - \frac{A}{100}\)[/tex]
This equation can be solved using the separation of variables or an integrating factor method, depending on the student's level of mathematical knowledge.
Choose the correct simplification of the expression the quantity a to the 4th power over b to the 2nd power all raised to the 3rd power.
a to the 7th power over b to the 5th power
a to the 12th power over b to the 6th power
ab9
a12b6
If a translation maps point (3, 2) to (4, 5); or T: (3, 2) (4, 5), then what is the image of the point (0, 0)?
Answer:
(1,3)
Step-by-step explanation:
Mr. Fry is building a fence around his pool. •Length of the fence is 60 feet. •Width of the fence is 30 feet. How many yards of fence will Mr. Fry build? A) 30 yards B) 60 yards C) 90 yards D) 540 yards i need help!!!!!!!!!
Mr. Fry will need 60 yards of fencing to encircle his pool, as the perimeter of the rectangular pool area is 180 feet and there are 3 feet in a yard.
To determine the total amount of fencing Mr. Fry will need, we calculate the perimeter of the rectangular area around the pool. The perimeter can be found by doubling the length then adding this to double the width. Therefore:
Perimeter = 2× Length + 2× Wid
= 2 × 60 feet + 2 × 30 feet
= 120 feet + 60 feet
= 180 feet
Now, knowing that 1 yard equals 3 feet, we can convert feet into yards:
Yards = Feet ÷ 3
= 180 feet ÷ 3
= 60 yards
Hence, Mr. Fry will need 60 yards of fence for his pool.
To determine the number of yards of fence Mr. Fry will build, we calculate the perimeter of the rectangular area (2 x (60 + 30) feet = 180 feet) and then convert it to yards (180 feet / 3 = 60 yards).
Mr. Fry is building a fence around his pool and wants to know how many yards of fence he will need. The fence has a length of 60 feet and a width of 30 feet. To find the total length of the fence in yards, we first calculate the perimeter of the rectangular fence which is 2 x (length + width). So, the perimeter in feet is 2 x (60 + 30) = 180 feet. Since 1 yard is equal to 3 feet, we divide the total number of feet by 3 to get the measurement in yards: 180 feet / 3 = 60 yards. Therefore, Mr. Fry will build 60 yards of fence.
Your promotional budget for this year is $200 for personal selling, $400 for sales promotion, $1000 for advertising, and $700 for image promotion. What is your total promotion budget for this year?
Budget for personal selling =$200
Budget for sales promotion = $400
Budget for advertising =$1000
Budget for image promotion =$700
Total Budget =Adding all the values = 200 +400+1000 +700 = 2300
So total promotion budget for this year is $2300
A) A pack of 8 batteries cost £3.99 how much dose each battry cost? ( give your answer in penny ?) ________________________________B) A pack of 6 batteries of the same type costs 2.79. By calculating the price of the battery determine if this is a better value. You must show your working out?
(A) cost of each battery is [tex]49 \;\rm{penny}\\[/tex].
(B) cost of each battery is [tex]\£\;0.465[/tex].
Given: Cost of a pack of [tex]8[/tex] batteries is [tex]\£\; 3.99[/tex].
According to question,
(A) Cost of each battery can be calculated as [tex]\£\;\frac{3.99}{8}=\£\;0.49875[/tex].
As we know that,
[tex]\£\;1=100 \;\rm{penny}\\\£\;0.49=49 \;\rm{penny}\\[/tex]
(B) costs of a pack of [tex]6[/tex] batteries is [tex]\£\; 2.79[/tex].
Cost of each battery can be calculated as [tex]\£\;\frac{2.79}{6}=\£\;0.465[/tex].
Therefore, (A) cost of each battery is [tex]49 \;\rm{penny}\\[/tex].
(B) cost of each battery is [tex]\£\;0.465[/tex].
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what is the value of log3^81
Answer:
Third option is correct. The value of given expression is 4.
Step-by-step explanation:
The given expression is
[tex]log_381[/tex]
The given expression can be written as
[tex]log_3(3\times 3\times 3\times 3)[/tex]
[tex]log_3(3^4)[/tex]
According to the property of logarithm expression,
[tex]log_a(a^b)=b[/tex]
Using this property of logarithm expression, we get
[tex]log_3(3^4)=4[/tex]
Therefore the value of given expression is 4 and option third is correct.
The value of the expression log₃(81) is 4.
We have,
The value of log base 3 of 81 can be found by asking the question: "To what power must 3 be raised to obtain 81?"
In this case, the answer is 4, because 3 raised to the power of 4 equals 81.
i.e
[tex]3^4[/tex] = 81
Therefore,
The value of the expression log₃(81) is 4.
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BRAINLIEST to the one who can asnwer my question and show me the work step by step so that I can understand. I want to understand.
Approximate the arc length of one-quarter of the unit circle (which is π /2) by computing the length of the polygonal approximation with n=4 segments. (As seen in picture)
The length of the line segment on the interval 0≤x≤0.25
The length of the line segment on the interval 0.25≤x≤0.5
The length of the line segment on the interval 0.5≤x≤0.75
The length of the line segment on the interval 0.75≤x≤1
Hello,
Please, see the attached files.
Thanks.
y varies directly as x. If y = -2 when x = 4, find x when y = 5.
for a stem competition julienne constructed a model rocket the rocket can reach an average height of 545 ft. Find the differences between the average height and the actual Heights reached. Then write them as a positive and negative rational numbers. order the differences from least to greatest
paleontologists have put together bones to make a t-rex skull that has a mass of 600 pounds.They just found a new tooth fossil to add to the skull that has a mass of 40 ounces.how many pounds in the t-rex skull with the new tooth
Answer:
40/16 = 2.5 . 600 lbs +2.5 lbs = 602.5 lbs skull
Step-by-step explanation:
convert 40 oz lbs and then make it 40/16
The area of a trapezoid is 20 square units. The sum of the base lengths is 10 units. What is the height of the trapezoid
someone please show me to how to find x, thank you.
Rosa is thinking of a number between 9.04 and 9.15 that has a six in the hundreds place what is the number explain
PLEASE HELP!!! LAST QUESTION
Which of the following is the equation of a line that passes through the points (2,5) and (4,3)
A. y= -2x+5
B. y= 2x+5
C. y= -x+7
D. y= x+7
Simplify
(343) 1/3
a)21
b)19
c)49
d)7