b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.
Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.
We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.
Using this information, we can create an equation:
6b + 12p = 60
Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:
b + 2p = 10
Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":
b + 2(2) = 10
b + 4 = 10
b = 6
So if Evelyn buys two purses, she also buys six bracelets.
In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.
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Given f(x)=5x+7 and g(x)=2x+2, find g(g(1-3w))
Enter as the final value or expression without parentheses
As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).
Which of these are they known as?When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).
We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).
We must first determine g(1-3w):
Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.
g(1-3w) ≈ 2 - 6w + 2 (distribute the 2)
g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)
We can again again enter the result of g(1-3w) into g(x):
If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2
g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)
g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)
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When George Washington became president in 1789, the army he had commanded in the American Revolution had
disbanded
ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE
When George Washington became president in 1789, the army he had
commanded in the American Revolution had disbanded. This means that
the soldiers were released from service and the military units were
dissolved after the end of the war.He pursued two intertwined interests:
military arts and western expansion. At 16 he helped survey Shenandoah
lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,
he fought the first skirmishes of what grew into the French and Indian War.
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Sara cut a 2 1/2 meter rope to hang a swing for her sister. How many centimeters is the rope
Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.
To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:
2.5 meters = 2.5 x 100 centimeters
= 250 centimeters
Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.
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Please help
What is the value of x?
Enter your answer in the box.
X =
F
E
L
24
25
1
2 3 4 5
x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.
Give a brief account on Pythagoras theorem.The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².
It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.
Given,
DF = 24
DE = 25
Using Pythagoras theorem:
Hypotenuse² = Base² + Perpendicular²
25² = x² + 24²
x² = 25² - 24²
x² = 625 - 576
x² = 49
x = √49
x = 7
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help pls its too much
Answer:
24.13
Step-by-step explanation:
how many ways can you select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer?
There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.
In this case, n = 15 and r = 3.
Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
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you have been tracking how long you spend on each course subject during your homework sessions. you want to see what percentage each subject represents. which type of chart would be best for this purpose?
a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
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a laptop has a listed price of 882.99 before tax. if the sales tax rate is 6.25% , find the total cost of the laptop with sales tax included. round your answer to the nearest cent, as necessary.
The total cost of the laptop with the sales tax included is 938.18.
The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:
Total Cost = Original Price + (Original Price * Sales Tax Rate)
In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:
Total Cost = 882.99 + (882.99 * 0.0625)
Total Cost = 882.99 + 55.19
Total Cost = 938.18
Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.
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a high school baseball player has a 0.253 batting average. in one game, he gets 8 at bats. what is the probability he will get at least 6 hits in the game?
The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.
Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.
We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.
P(X≥6) = 1 - P(X<6)
P(X<6) = ∑P(X=i), i=0 to 5
We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.
P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3
≈ 0.9799
Therefore, P(X≥6) = 1 - 0.9799
= 0.0201 or approximately 2%.
Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.
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julio has $31.00 he earns half of that much mowing a lawn. How much money does he have in all?
Answer: $ 46.50
First divided 31 by 2
Which equals...
15.50
Then add 15.50 to 31.
46.50
The answer is $46.50
A triangle with side lengths 7, 6, 4 is
Acute
Right
Obtuse
Right
so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.
(a)²+(b)²=c²
(6)²+(4)²=c²
36+16=c²
(square root) 52=c²
the square root of 52 is 7
so therefore it is a right triangle.
To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtain [Cr^3+]=0.03933 M. Calculate the %Cr in the complex.
the %Cr in the complex is 26.294%.
To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtained [Cr3+]=0.03933 M. Calculate the %Cr in the complex.
To determine the % Cr in the chromium-complex synthesized by Legna, we can use the following formula:% Cr = (mass of Cr/mass of sample) x 100We have the mass of the sample, which is 1.0240 g. We need to find the mass of Cr in the sample. To do this, we need to find the number of moles of Cr in the solution, and then use the molar mass of Cr to convert this to mass.
The concentration of Cr3+ in the solution is given as 0.03933 M. We know that the complex is made up of Cr and some other ligands, and the concentration of Cr3+ is not the same as the concentration of Cr in the complex. To find the concentration of Cr in the complex, we need to use the formula:[Cr] = [Cr3+] x (1/x), where x is the number of moles of Cr3+ in the complex.
Let's assume that there is one mole of Cr3+ in the complex, then x = 1. If there are n moles of Cr3+ in the complex, then x = n. We can find x by using the formula:x = (mass of sample/Mr of Cr3+) x [Cr3+]/volume of solutionWe know that the mass of the sample is 1.0240 g, and the volume of the solution is 100.0 mL = 0.1000 L. The molar mass of Cr3+ is 52.00 g/mol. Substituting these values into the formula, we get:x = (1.0240/52.00) x 0.03933/0.1000x = 0.000761 moles of Cr3+ in the complex
Now we can use the formula [Cr] = [Cr3+] x (1/x) to find the concentration of Cr in the complex:[Cr] = 0.03933/0.000761[Cr] = 51.69 M
Finally, we can use the formula:% Cr = (mass of Cr/mass of sample) x 100The molar mass of Cr is 52.00 g/mol. The mass of Cr in the complex is 51.69 x 52.00 = 2689.88 g/mol. Substituting this value and the mass of the sample (1.0240 g) into the formula, we get:% Cr = (2689.88/1.0240) x 100% Cr = 262944.53% Cr = 26.294%
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What is the simplest form of 8(5k+7)−10(6k−7)
The simplest form of the given expression is -20k + 126.
To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
(40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
-20k + 126
The simplest form of the given expression is -20k + 126.
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which property is shown 16x5x2=2x5x16
Answer:
Commutative property
The Commutative property is most simply shown with: a x b = b x a. In multiplication, the values can shift or "commute" in any order
What is the endpoint of a line segment with these points? Endpoint: Z(–21, 15) Midpoint: M(–13, 29) (–5, 43) (–17, 22) (–27, 21) (–29, 1)
Answer: A - (-5, 43)
Step-by-step explanation:
PLEASE HURRY !! I NEED HELP!!!
Answer:$10
Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?
He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.
A rectangular tank measures 15 cm by 7 cm by 10 cm. How many milliliters of water are in the tank when it is full? How many liters?
The tank contains 1050 milliliters of water when full or 1.05 liters.
To calculate the volume of the tank in milliliters, we multiply the length (15 cm), width (7 cm), and height (10 cm) together:
15 cm x 7 cm x 10 cm = 1050 cm³
Since 1 milliliter equals 1 cubic centimeter (cm^3), we know that the tank can hold 1050 milliliters of water.
To convert milliliters to liters, we can divide the volume in milliliters by 1000:
1050 mL ÷ 1000 = 1.05 L
Therefore, when full, the tank can hold 1050 milliliters of water or 1.05 liters.
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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?
There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
What is experimental probability?Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability
According to question:The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.
Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:
Experimental probability = Number of bassists / Total number of musicians
Experimental probability = 15 / 89
Experimental probability = 0.1685 or approximately 16.85%
As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
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What is the value of k?
127.3°
a cable tv receiving dish is in the shape of a paraboloid of revolution. find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.
the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).To find the location of the receiver, we first need to determine the equation of the paraboloid.
The standard equation for a paraboloid of revolution with a vertical axis is:
z = [tex](x^2 + y^2)[/tex]/(4f)
Where:
z is the height at any point (x, y) on the paraboloid.
x and y are the horizontal coordinates of the point.
f is the focal length of the paraboloid, which is half the depth of the dish.
In this case, the dish is 6 feet across at its opening, so the diameter is 6 feet and the radius is 3 feet. Therefore, the maximum value of x and y is 3 feet. The depth of the dish is given as 2 feet.
Using these values, we can solve for the focal length:
2 = [tex](3^2 + 3^2)[/tex]/(4f)
2 = 18/(4f)
f = 18/8 = 9/4 = 2.25 feet
Now that we have the value of f, we can find the location of the receiver, which is placed at the focus of the paraboloid. The focus is located at (0, 0, f).
Therefore, the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).
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if one flag pole is y feet tall and casts a shadow x feet long, then how tall is another nearby flag pole that casts a shadow p feet long at the same time of day?
If one flag pole is y feet tall and casts a shadow x feet long, and another nearby flag pole casts a shadow p feet long at the same time of day, we can use similar triangles to determine the shadow of the second flag pole.
In this scenario, the two flag poles and the ground form two similar right triangles. The height of the first flag pole (y) corresponds to one leg of the first triangle, and the length of its shadow (x) corresponds to the other leg.
Similarly, the height of the second flag pole (h) corresponds to one leg of the second triangle, and the length of its shadow (p) corresponds to the other leg.
Therefore, the height of the second flag pole is equal to the product of the height of the first flag pole and the length of the shadow of the second flag pole, divided by the length of the shadow of the first flag pole.
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A house plan has concrete stairs leading down into the garage. How much concrete is needed to make the stairs? 3 ft 2 ft 8 ft 5 ft [? ] ft ³ 2 ft 8 ft 1 ft
The amount of concrete needed to make the stairs that leads to the garage is 64 cubic feet
Calculating the amount of concrete needed to make the stairs?The missing information is added as an attachment
The concrete needed to make the stairs is the volume of the stairs and this is calculated using
Volume = Base area * Height
Where
Base area = 3 * 2 + 2 * 1
Base area = 8
And
Height = 8
So, we have
Volume = 8 * 8
Evaluate
Volume = 64
Hence, the amount needed is 64 cubic feet
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Five interior angles of a hexagon measure 119°, 129°, 104°, 139°, and 95°. What is the measure of the sixth angle?
Answer:
A
Step-by-step explanation:
the volume of a cube decreases at a rate of 6 m 3 / s . find the rate at which the side of the cube changes when the side of the cube is 4 m . answer exactly or round to 2 decimal places.
The rate at which the side of the cube changes when the side of the cube is 4 m is -1/8 m/s (or approximately -0.125 m/s).
Let's use the formula for the volume of a cube:
V = s³
where V is the volume and s is the length of one side of the cube. To find the rate of change of the side length, we need to differentiate this formula with respect to time t:
dV/dt = d/dt (s³) = 3s² ds/dt
We know that dV/dt = -6 m³/s (the negative sign indicates that the volume is decreasing), and when s = 4 m, we have:
-6 = 3(4²) ds/dt
Simplifying this equation gives us:
ds/dt = -6 / (3*4²) = -1/8 m/s
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suppose you roll a pair of fair dice repeatedly. what is the probability that by the time the sum has been even three times, the sum has already been 7 twice?
The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.
This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.
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Casper has a balloon with a diameter of
6 inches that is seven times the volume of
his brother's balloon. What is the
volume of Casper brother's
approximate
balloon?
Answer:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:
V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)
We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:
V1 = 7V2
Substituting the value of V1, we get:
113.1 cubic inches = 7V2
Dividing both sides by 7, we get:
V2 = 16.2 cubic inches (approx.)
Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.
John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Enter the four constraints into the graphing calculator.
What are the vertices of the feasible region?
Hint: input your answers from questions 3, 4, and 5 into Desmos to find the vertices.
Answers from questions 3, 4, and 5
[tex]4x+2y≤16\\3x+3y≤15\\x≥0\\y≤0[/tex]
Answer:huh,
Step-by-step explanation:I don’t understand you’re saying
Find Sum to infinity of the given series: a. 1 + 2x + 3x² + 4x³+... to ∞ (|x| <1)
The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.
How do we calculate?The formula for the sum of an infinite geometric series when |x| < 1 is given as:
S = a/(1-r)
We have a = 1 and r = x/1.
S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...
we multiply both sides of this equation by (1-x)²,
S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...
S(1-x)² = 1 + x + x² + x³ + ... eqn (1)
Using the formula for the sum of an infinite geometric series when |x| < 1, we have:
1/(1-x) = 1 + x + x² + x³ + ...
Substituting this into equation (1), we get:
S(1-x)² = 1/(1-x)
S = 1/[(1-x)²]
In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1
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an 8-person committee is to be formed from a group of 15 women and 12 men. in how many ways can the committee be formed if the committee must contain four men and four women? if there must be at least two men? if there must be more women than men?
The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of Permutation and Combination.
If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.
To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.
To get the total number of ways, we can multiply these numbers:
495 x 1,365 = 7,425.
To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.
To get the total number of ways, we can add these numbers:
495 x 5,005 + 2,190 x 3,003 = 58,275.
To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.
To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.
Adding these numbers gives us the total number of committees with more women than men:
15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700
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A business owner applies for a credit card to cover $14,000 in emergency expenses. The credit card charges 16.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
Credit card charges $19665.33 will the balance on the card be, rounded to the nearest penny.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The interest rate for the loan is denoted by this proportion.
Interest is the cost of borrowing money and is typically stated as a percentage, such an annual percentage rate (APR). Lenders may charge interest to borrowers for the use of their funds, or borrowers may charge interest to lenders for the use of their funds.
amount applied for = $14,000
interest rate = 16.99%
the balance after 2 years
P₀ = $1400
r = 16.99% = 0.1699
t = 2
[tex]P_{0} = P_{0}e^{rt}[/tex]
[tex]P_{2} = 1400e^{0.1699 * 2}[/tex]
≈ $19665.33
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