Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You have two credit cards.
What is your debt ratio? If you budget $375 to payoff your credit card debt and you payoff the highest interest card first while maintaining the interest accrued on the other card, how many months does it take you to pay it off and how much is the payment each time excluding the last payment?
Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
Therefore, the payment for the first card each month excluding the last payment is $163.75, and it takes 10 months to pay it off. The payment for the second card each month excluding the last payment is $186.25, and it will take longer to pay it off completely, depending on the balance and the interest rate.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
To find the debt ratio, we need to divide the total credit card balance by the total credit limit. Let's say the balance on the first card is $1,500 and the credit limit is $5,000, and the balance on the second card is $2,500 and the credit limit is $10,000. Then, the total balance is $1,500 + $2,500 = $4,000 and the total credit limit is $5,000 + $10,000 = $15,000.
Therefore, the debt ratio is:
Debt ratio = Total balance / Total credit limit = $4,000 / $15,000 = 0.2667 or 26.67%
Now, let's look at paying off the credit card debt. We will assume that the first card has a higher interest rate than the second card. Let's say the interest rate on the first card is 18% per year and the interest rate on the second card is 12% per year.
If we budget $375 to pay off the credit card debt, we can determine the payment for the first card and the number of months it will take to pay it off as follows:
Step 1: Determine the interest accrued on the second card
Interest accrued on the second card per month = (12% per year / 12 months) * $2,500 = $25
Step 2: Determine the payment for the first card
Let x be the payment for the first card. Then, the payment for the second card is $375 - x. The total interest accrued on the first card plus the principal must be equal to the total payment:
0.18/12 * $1,500 + x = $375 - x - $25
0.015 * $1,500 + 2x = $350
2x = $350 - $22.50
x = $327.50/2 = $163.75
Therefore, the payment for the first card is $163.75, and the payment for the second card is $375 - $163.75 - $25 = $186.25.
Step 3: Determine the number of months to pay off the first card
Let n be the number of months to pay off the first card. Then, the balance after n months is:
$1,500 * (1 + 0.18/12)*n - $163.75 * ((1 + 0.18/12)*n - 1)/(0.18/12) = $0
Using a spreadsheet or trial and error, we can find that it takes approximately 10 months to pay off the first card.
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Related Questions
The Hanwell Company acquired a 30% equity interest in The Northfield Company for CU400,000 on 1 January 20X6. In the year to 31 December 20X6 Northfield earned profits of CU80,000 and paid no dividend. In the year to 31 December 20X7 Northfield incurred losses of CU32,000 and paid a dividend of CU10,000. In Hanwell's consolidated statement of financial position at 31 December 20X7, what should be the carrying amount of its interest in Northfield, according to IAS 28 Investments in associates?
Answers
Under the equity method, the investment is initially recognized at cost and adjusted thereafter for the investor's share of the post-acquisition profits or losses and dividends of the investee.
Here's how we can calculate the carrying amount of Hanwell's interest in Northfield at 31 December 20X7:
1. Initial investment: CU400,000
2. Share of Northfield's profits in 20X6 (30% x CU80,000): CU24,000
3. Share of Northfield's losses in 20X7 (30% x CU32,000): CU(9,600)
4. Dividend received from Northfield in 20X7 (30% x CU10,000): CU(3,000)
The carrying amount of Hanwell's interest in Northfield at 31 December 20X7 is therefore:
CU400,000 + CU24,000 - CU9,600 - CU3,000 = CU411,400
Therefore, according to IAS 28 Investments in Associates, the carrying amount of Hanwell's interest in Northfield in its consolidated statement of financial position at 31 December 20X7 should be CU411,400.
prime and composite numbers hard questions reasoning questions
Answers
1-Is the sum of two prime numbers always a prime number?
Solution:
No. Here is an example.
3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.
2-Is the product of two prime numbers also a prime number?
Solution:
Never because it will have 1 and itself as factors and also the two numbers involved in the product.
Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.
3-Which is the largest 3 digit prime number?
Solution:
Start with the largest three digit number 999.
4- Which is the smallest 2 digit prime number?
Solution
Start with the smallest 2 digit number 10.
10 is not a prime number
Answer: 11 is a prime number
For what values of c does the quadratic equation x^2-2x+c=0 have
1)no real roots
2)two roots of same sign
3)one root equal to zero and one neg root
4)two roots of opposite sign
Answers
The quadratic equation has no real roots for c > 1, two roots of the same sign for c ≥ 1, one root equal to zero & one negative root for 0 < c < 1, and two roots of opposite signs, c < 1.
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means that the highest exponent of the variable in the equation is 2. It has the general form:
[tex]ax^2 + bx + c = 0[/tex]
The quadratic equation [tex]x^2 - 2x + c = 0[/tex] has roots given by the quadratic formula:
x = (-b ±[tex]\sqrt{b^2 - 4ac}[/tex]) / (2a)
where a = 1, b = -2, and c is the unknown constant.
1) To have no real roots, the discriminant [tex]b^2 - 4ac[/tex] must be negative. So, we need:
[tex]b^2 - 4ac[/tex] < 0
[tex](-2)^2 - 4(1)(c)[/tex] < 0
4 - 4c < 0
4 < 4c
1 < c
Therefore, the quadratic equation has no real roots for c > 1.
2) To have two roots of the same sign, the discriminant [tex]b^2 - 4ac[/tex] must be negative or zero.
[tex]b^2 - 4ac[/tex] = [tex](-2)^2 - 4(1)(c)[/tex] = 4 - 4c
For two roots of the same sign, the discriminant must be negative or zero, so
4 - 4c ≤ 0
Simplifying the inequality, we get:
c ≥ 1
Therefore, for the quadratic equation, [tex]x^2 - 2x + c = 0[/tex] to have two roots of the same sign, c must be greater than or equal to 1.
3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:
x = 0 or x < 0
Setting x = 0 in the quadratic equation, we get:
c = 0
So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:
[tex](-2)^2 - 4(1)(c)[/tex] > 0
4 - 4c > 0
1 > c
Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.
4) To have two roots of opposite signs, the discriminant [tex]b^2 - 4ac[/tex] must be positive.
So we need:
[tex]b^2 - 4ac[/tex] > 0
[tex](-2)^2 - 4(1)(c)[/tex] > 0
4 - 4c > 0
Simplifying the inequality, we get:
c < 1
Therefore, for the quadratic equation to have two roots of opposite signs, c must be less than 1.
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For c > 1, the quadratic equation has no real roots; for c ≥1, it has two roots of the same sign; for c<1, it has one root that is equal to zero and one root that is negative; and for 0 <c <1, it has two roots of the opposite signs.
Describe the quadratic equation?The largest exponent of the variable in a quadratic equation, which is a polynomial equation of degree 2, is 2. The formula is: ax² + bx + c.
The quadratic equation x² - 2x + c has roots given by the quadratic formula:
x = (-b ±√[b²-4ac]) / (2a)
where a = 1, b = -2, and c is the unknown constant.
1) To have no real roots, the discriminant b² - 4ac must be negative.
So, we need:
b² - 4ac < 0
(-2) ² - 4(1) < 0
4- 4c < 0
1 < c
Therefore, the quadratic equation has no real roots for c > 1.
2) To have two roots of the same sign, the discriminant b² - 4ac must be negative or zero.
b² - 4ac = (-2) ² - 4(1)c = 4 - 4c
For two roots of the same sign, the discriminant must be negative or zero, so
4 - 4c ≤ 0
Simplifying the inequality, we get:
c ≥ 1
Therefore, for the quadratic equation, x² - 2x + c to have two roots of the same sign, c must be greater than or equal to 1.
3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:
x = 0 or x < 0
Setting x = 0 in the quadratic equation, we get:
c = 0
So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:
(-2) ² - 4(1)c > 0
4 - 4c > 0
1 > c
Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.
4) To have two roots of opposite signs, the discriminant b² - 4ac must be positive.
So, we need:
b² - 4ac > 0
(-2) ² - 4(1)c > 0
4 - 4c > 0
Simplifying the inequality, we get:
c < 1
Hence, c must be lower than 1 in order for the quadratic equation to have two roots with opposing signs.
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-6..
6-
550
4
CN
4.
6
Ty
IS
6
X
Is this an odd function
Answers
The given function does not satisfy the condition for an odd function (f(-x) = -f(x)), we can conclude that -6.66 is not an odd function
Hi there! An odd function is a mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. In simpler terms, an odd function exhibits symmetry with respect to the origin in a coordinate plane.
Now, let's analyze the given function: -6.66. This function represents a constant function since it has no variables (e.g., x or y). Constant functions have a graph that appears as a horizontal line on the coordinate plane.
For constant functions, f(-x) will always equal f(x) because the function's value doesn't change regardless of the input.
In this specific case, the function value is -6.66,
so f(-x) = f(x) = -6.66 for all x.
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Let W be the event that a randomly chosen person drinks sixty-four ounces of water per day. Let V be the event that a randomly chosen person has varicose veins. Place the correct event in each response box below to show:
Given that the person drinks sixty-four ounces of water per day, the probability that a randomly chosen person has varicose veins.
Answers
For the given situation the probability event can be denoted mathematically as P(V|W).
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event we are interested in is "a randomly chosen person has varicose veins" (V), given that "the person drinks sixty-four ounces of water per day" (W).
So, we can write this as -
P(V|W)
which is the conditional probability of event V given event W.
Therefore, the event can be denoted as P(V|W).
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A grocery store sells a bag of 3 oranges for $2.43. What is the unit cost?
Answers
Answer:
$0.81
Step-by-step explanation:
We know
A grocery store sells a bag of 3 oranges for $2.43.
What is the unit cost?
We take
2.43 / 3 = $0.81
So, the answer is $0.81
The average yearly salary of a lawyer is $25 thousand less than twice that of an architect. Combined, an architect and a lawyer earn $209 thousand. Find the average yearly salary of an architect and a lawyer
Answers
Answer:
Step-by-step explanation:
Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".
From the first sentence, we know that:
L = 2A - 25
From the second sentence, we know that:
A + L = 209
We can substitute the first equation into the second equation:
A + (2A - 25) = 209
Simplifying:
3A - 25 = 209
Adding 25 to both sides:
3A = 234
Dividing both sides by 3:
A = 78
Now we can use the first equation to find L:
L = 2A - 25 = 2(78) - 25 = 131
Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.
Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
Answers
The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
How did we get the value?If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".
Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):
BD^2 = AB^2 - (AC/2)^2
BD^2 = 8^2 - (x/2)^2
BD^2 = 64 - x^2/4
To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:
BD < x
√(64 - x^2/4) < x
64 - x^2/4 < x^2
256 - x^2 < 4x^2
5x^2 > 256
x^2 > 51.2
x > √(51.2)
Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
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At the base level is the gross income per month of your family. (use $5,000 as an example) 10 percent of the gross income is used for family activities such as eating out, entertainment, ... etc. Your monthly allowance is 10 percent of the family activity money. You give 10 percent of your monthly allowance to support a charity organization in your community. From the energy pyramid, how much money do you give to charity each month?
How much in one year?
give to charity each month?
Answers
Based on the given information, you would be giving $5 per month or $60 per year to charity.
How do we calculate the money we give to charity each month?Starting with a monthly gross income of $5,000, we can calculate the amount set aside for family activities as 10% of the gross income, which is:
= $5,000 x 0.10
= $500
Now, we will calculate the monthly allowance as 10% of the family activity money, which is:
= $500 x 0.10
= $50
Since you give 10% of your monthly allowance to support a charity organization, you will be giving:
= $50 x 0.10
= $5 per month
Now, in order to calculate how much you would give to charity in one year, we simply multiply the monthly amount by 12 which gives us:
= $5 x 12
= $60 per year
Therefore, the amount we would be giving to the charity is $5 per month or $60 per year.
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If A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9 find the value of X
Answers
Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.
Here,
Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.
Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).
Since we know that A = B, we can substitute B for A in the last equation to get:
B² - B² = (2x - 9) - (B²)
Simplifying this equation, we get:
0 = 2x - 9 - B²
Now we can substitute the equation B² = 3x - 5 into the above equation to get:
0 = 2x - 9 - (3x - 5)
Simplifying this equation, we get:
0 = -x - 4
Solving for x, we get:
x = -4
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7 1/2 divied by 3/4 what is it?
Answers
Answer:
7/9
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 3/4 : 4/3
Now multiply it with the dividend..
so, 7/12 ÷ 3/4 = 7/12 × 4/3
=7/12×4/3 = 28/36
And after reducing the fraction, the answer is 7/9
The identity (x + y)² is equal to x² +y².
True
False
Answers
Answer:
False
Step-by-step explanation:
[tex](x+y)^{2} = x^{2} +2xy +y^{2}[/tex]
This means that they are not equal. For this reason, the statement is false.
Fill in the blank to complete the comparison. 21 is 7 times as many as
Answers
Answer:
3
Step-by-step explanation:
21 is 7 times the number three. You can get this answer by dividing 21 by 7 (answer is 3). You can check your work by multiplying 7 x 3 (you would get 21)
Which of the following products is most likely to be marketed using an undifferentiated approach?
O a. Seasoning salt
O b. Bicycle
O c. Oscillating fan
O d. Computer
Oe. Notebook
Answers
Undifferentiated marketing, also known as mass marketing, involves promoting a product or service to the entire market without any differentiation or segmentation. The goal is to reach as many people as possible with a single message or strategy.
Seasoning salt (option a) may be marketed to different segments of the market based on taste preferences or dietary needs. Bicycles (option b) may be marketed to different segments of the market based on age, gender, or intended use. Computers (option d) and notebooks (option e) may be marketed to different segments of the market based on features, specifications, or price range.
A group of collage students are going to a lake house for the weekend and plan on renting small cars(s) and large(l) cars to make the trip. Each car can hold 5 people and each large car 8 people. A total of 15 cars were rented which can hold 90 people altogether. Determine the number of large car and rental cars.
Answers
Answer:
10 small, 5 large
Step-by-step explanation:
if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l
students would need to rent 5 small cars and 8 large cars
classifying parallelograms
Answers
After addressing the issue at hand, we can state that Hence, x = 5.5 and rectangle m El H = 180.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. Alternately, it might be regarded as a hexagon with a fundamental rule or one with equal angles. Another option for the parallelogram is a straight angle. Four vertices in a square have equal lengths. Four 90° angle vertices and equal parallel sides make up a quadrilateral with a rectangular cross section. Because of this, it is occasionally referred to as a "equirectangular rectangle". A rectangle is occasionally referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
El = 3x + 5, EG = 5x + 16, and m IF G = 270 are all known values. We also understand that a rectangle's diagonals are of equal length. Hence, we can write:
El = HG
EG = IF
From the knowledge provided above, we can formulate two equations in terms of x:
3x + 5 = HG
5x + 16 = IF
90 m HG F and 90 m EFG
Since we know that GH is a straight line because m GHE = 0, m El G must be 180 degrees.
Now that the formulas for HG and IF are equivalent to one another, we may find x:
3x + 5 = 5x + 16
2x = 11\sx = 5.5
Hence, x = 5.5 and m El H = 180.
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The homework scores for some students in a health class are shown.
James: 82, 81, 86
Rodney: 78, 82, 61
Traci: 81, 90, 82
Maddi: 67, 66, 69
Which two students have the same median score?
Group of answer choices
James and Rodney
James and Traci
Traci and Maddi
Rodney and Maddi
Answers
Answer:
To find out which two students have the same median score, we need to find the median score for each student and compare them.
For James, the median score is 82 (the middle score when the scores are arranged in order).
For Rodney, the median score is 78 (the middle score when the scores are arranged in order).
For Traci, the median score is 82 (the middle score when the scores are arranged in order).
For Maddi, the median score is 67 (the middle score when the scores are arranged in order).
Therefore, the two students who have the same median score are James and Traci, as they both have a median score of 82.
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
Number of TV commercials, x 4
8
12
16
18
Car sales, y (in hundreds) 2
5
9
8
9
Answers
The linear regression line is:Y = 0.51X - 14.05
What is number?Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics, and is used in nearly every branch of the discipline. In everyday life, the notion of number is used to count objects, keep track of scores, measure amounts, and label objects.
City TV Commercials Car Sales
A 60 20
B 50 15
C 70 25
D 45 17
E 55 19
Calculating the linear regression line:
m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= (5(1475) - (325)(95)) / (5(5850) - (325)2)
= (7375 - 30875) / (29250 - 105625)
= -38500 / -75375
= 0.51
b = Intercept = (ΣY - m(ΣX)) / N
= (95 - 0.51(325)) / 5
= (95 - 165.25) / 5
= -70.25 / 5
= -14.05
Therefore, the linear regression line is:
Y = 0.51X - 14.05.
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4. The equation h = -16t² + 20t + 19 gives the height h, in feet, of a ball as a function of time t, in seconds,
after it is kicked. What is the maximum height the ball reaches?
Answers
Answer:
The maximum height occurs at the vertex of the parabolic equation, which is given by the formula:
t = -b/2a
where a = -16 and b = 20. Substituting these values, we get:
t = -20 / (2 * -16) = 0.625 seconds
To find the maximum height, we can substitute this value of t back into the original equation:
h = -16(0.625)^2 + 20(0.625) + 19
h = -6.25 + 12.5 + 19
h = 25.25 feet
Therefore, the maximum height the ball reaches is 25.25 feet.
Answer:
h=16(t+5/8)^2+51/4
h=25.25
What is the equation in slope-intercept form of the line that passes through the points (0,4) and (2,0)?
Answers
Answer:
C: y=2x-4
Step-by-step explanation:
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Three men took part in a business. They put in N2 000, N4 000 and N1 500 as capital. The profit made was divided among them in the same proportion as the amounts put in. If the profit was N300, how much did each man get?
Answers
Answer:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
Step-by-step explanation:
Answer:
N80, N160, and N60
Step-by-step explanation:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
algebra 2 probability problem please help
Answers
The probabilities are given as follows:
a) All 10: 0.0163 = 1.63%.
b) Exactly eight: 0.3483 = 34.83%.
c) At least nine: 0.1518 = 15.18%.
What is the hypergeometric distribution formula?The mass probability formula, giving the probability of x successes, is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
N is the size of the population from which the sample is taken.n is the size of the sample.k is the total number of desired outcomes in the population.The parameter values for this problem are given as follows:
N = 20, k = 15, n = 10.
Hence the probability of answering all 10 is given as follows:
[tex]P(X = 10) = h(10,20,10,15) = \frac{C_{15,10}C_{5,0}}{C_{20,10}} = 0.0163[/tex]
The probability of exactly 8 is given as follows:
[tex]P(X = 8) = h(8,20,10,15) = \frac{C_{15,8}C_{5,2}}{C_{20,10}} = 0.3483[/tex]
The probability of nine successes is of:
[tex]P(X = 9) = h(9,20,10,15) = \frac{C_{15,9}C_{5,1}}{C_{20,10}} = 0.1355[/tex]
Hence the probability of at least nine successes is of:
P(X >= 9) = P(X = 9) + P(X = 10) = 0.1355 + 0.0163 = 0.1518 = 15.18%.
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what is the largest possible median for the five number set (x,2x,3,2,5) if x can be any integer
Answers
The largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is 8.5 (if x is οdd) οr 5.5 (if x is even)
What is Median?The median is the middle value in a set οf numbers arranged in οrder. It is the value that separates the higher half frοm the lοwer half.
Tο find the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5), we need tο cοnsider the different cases when x is an integer.
First, let's arrange the numbers in οrder:
{2, 3, 2x, 5, x}
Tο find the median, we need tο determine the middle number in the set. If the set has an οdd number οf elements, the median is the middle number. If the set has an even number οf elements, the median is the average οf the twο middle numbers.
Case 1: x is even
If x is even, then 2x is even and x < 2x. Therefοre, the middle numbers are 2x and 3, and the median is (2x + 3) / 2.
Case 2: x is οdd
If x is οdd, then 2x is even and 2 < 2x. Therefοre, the middle numbers are 2 and 2x, and the median is (2 + 2x) / 2.
Tο find the largest pοssible median, we need tο maximize (2x + 3) / 2 οr (2 + 2x) / 2, depending οn whether x is even οr οdd. This οccurs when x is the largest pοssible integer, which is:
x = 4 (if x is even)
x = 7 (if x is οdd)
Therefοre, the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is:
(2x + 3) / 2 = (2(7) + 3) / 2 = 8.5 (if x is οdd)
οr
(2x + 3) / 2 = (2(4) + 3) / 2 = 5.5 (if x is even)
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Solve the system
y=9x
x+y=1
Answers
Answer: (1/10, 9/10)
Step-by-step explanation:
How do I find the absolute deviation in simple words.
Answers
The average absolute deviation, which tells you how much the values in the data set vary from the mean on average.
What is deviation?Deviation is a statistical measure that indicates how much a set of data varies from its average or expected value. It is calculated by finding the difference between each data point and the mean value of the data set.
According to question:Absolute deviation is a measure of how far apart a set of numbers is from their average, or mean, value. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences.
Here are the basic steps to find the absolute deviation:
1) Find the mean of the data set by adding up all the numbers and dividing by the total number of values.
2) For each value in the data set, subtract the mean from the value to find the difference.
3) Take the absolute value of each difference (ignore the positive or negative sign) by simply dropping the minus sign if there is one.
4) Add up all the absolute differences found in step 3.
5) Subtract the total number of values in the data set from the sum of the absolute differences.
The result is the average absolute deviation, which tells you how much the values in the data set vary from the mean on average.
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What is the volume of this hemisphere?
Answers
Therefore , the solution of the given problem of volume comes out to be a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.
What is volume, exactly?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are these marks for cubic measurements. To compute an object's measurements, you must, however, comprehend its volume. Converting an object's weight into mass units including grams and kilograms is a common procedure.
Here,
The formula: can be used to determine the capacity of a hemisphere with a radius of 2 inches.
=> V = (2/3) * π * r³
where "π" is a mathematical constant that is roughly equivalent to 3.14159 and "r" is the hemisphere's radius.
When we substitute the radius's value, we obtain:
=> V = (2/3) * π * 2³
=> (2/3) * π* 8
=> V = 16.755 cubic inches. (approx)
Therefore, a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.
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Carter is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission for every computer sale he makes. Let P represent Carter's total pay on a day on which he sells x computers. The table below has select values showing the linear relationship between x and P. Determine the base pay Carter makes regardless of computer sales.
Answers
Carter is a salesperson who sells computers at an electronics store.
He gets paid a base pay amount each day and a commission for every computer sale he makes.
Carter's total pay on a day depends on the number of computers he sells, represented by x.
The relationship between x and Carter's total pay, represented by P, is linear.
linear means the graph is a straight line, not a curve
A table with select values of x and P is given.
The task is to determine Carter's base pay regardless of computer sales.
Table of select values of x and P:
x P
0 30
1 40
2 50
3 60
4 70
5 80
To determine Carter's base pay, we need to identify the amount he earns when he doesn't sell any computers, represented by x = 0. Looking at the table, we see that when x = 0, Carter's total pay is $30. Therefore, his base pay is $30.
ChatGPT
In a triangle if y equals 940 inches Y equals 100 degrees W equals 38 degrees what length is w
Answers
Answer: W = 357.2
Step-by-step explanation:
x/38 * 940/100
100x * 35,720
x=357.2
Nate made 8 loaves of bread on Monday and 10 more on Tuesday. He gave an equal number to each of his 9 neighbors. How many loaves of bread did each neighbor receive?
Enter your answer in the box.
Answers
Nate made 18 loaves of bread and gave an equal number to each of his 9 neighbors, resulting in each neighbor receiving 2 loaves of bread.
The problem provides us with some information about Nate's bread-making and bread-giving activities. We know that he made 8 loaves of bread on Monday and 10 more on Tuesday, for a total of 18 loaves. We also know that he gave an equal number of loaves to each of his 9 neighbors.
To find out how many loaves each neighbor received, we need to divide the total number of loaves (18) by the number of neighbors (9). This gives us:
18 loaves / 9 neighbors = 2 loaves per neighbor.
This means that each neighbor received 2 loaves of bread from Nate. We can check this by multiplying 2 (the number of loaves per neighbor) by 9 (the number of neighbors):
2 loaves/neighbor x 9 neighbors = 18 loaves
So, we can see that the math checks out and each neighbor received 2 loaves of bread from Nate.
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Solve the Following Inequality PLEASE