Answer:
Step-by-step explanation:
Total no. of possible outcomes = 6 (1,2,3,4,5,6,)
As given we have only one prime even no. from the above given set, that is 2.
Let's call this event A.
Total no. of favourable outcomes =P(A)= 1
Therefore the probability is P(A)= 1/6
A recent Time magazine reported the following information about a sample of workers in Germany and the United States.
United States
United States average length of workweek is 42 hours, sample standard deviation is 5, sample size is 600. Germany average length of workweek is 38 hours, sample standard deviation is 6, sample size is 700.
We want to determine whether or not there is a significant difference between the average workweek in the United States and the average workweek in Germany.
a. State the null and the alternative hypotheses.
b. Compute the test statistic.
c. Compute the p-value. What is your conclusion?
a. The hypotheses are coded as: H0: μ1 = μ2; Ha: μ1 ≠ μ2; b. The test statistic is: 9.35; c. The p-value is less than 0.0001, therefore, there is a significant difference between the average workweek in the US.
What is a Null Hypothesis?A null hypothesis is a statement that there is no significant difference or relationship between two variables in a population.
a. The null hypothesis is that there is no significant difference between the average workweek in the United States and the average workweek in Germany, or in other words, the population means are equal. The alternative hypothesis is that there is a significant difference between the two, or the population means are not equal.
H0: μ1 = μ2
Ha: μ1 ≠ μ2
Where:
μ1 = population mean of workweek in United States
μ2 = population mean of workweek in Germany
b. To compute the test statistic, we can use the two-sample t-test formula:
t = (x1 - x2) / sqrt((s1²/n1) + (s2²/n2))
Where:
x1 = sample mean of workweek in United States
x2 = sample mean of workweek in Germany
s1 = sample standard deviation of workweek in United States
s2 = sample standard deviation of workweek in Germany
n1 = sample size of United States
n2 = sample size of Germany
Plugging in the values, we get:
t = (42 - 38) / sqrt((5²/600) + (6²/700)) = 9.35
c. To compute the p-value, we need to use a t-distribution with degrees of freedom equal to the smaller sample size minus one (df = min(n1-1, n2-1)). In this case, df = 599. Using a two-tailed test with alpha level of 0.05, the p-value is less than 0.0001.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the average workweek in the United States and the average workweek in Germany.
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factor [tex](2x^4+y^3)^2[/tex]
Develop a for a random variate generator for a random variable X with p.d.f f(x)={█(ⅇ^(2x:)-∞
The inverse transform method can be used to produce a random variate for a random variable X with p.d.f[tex]f(x) = e^{2x}[/tex].
How are random variates developed?The cumulative distribution function (CDF) of X is given by [tex]F(x) = 1 - e[/tex], and we must first determine its inverse (-2x). When x is solved for, the answer is x = -(1/2)ln(1 - u), where u is an evenly spaced random number between 0 and 1.
As a result, we can take the following actions to create a random variate for X:
Create an even, random number between 0 and 1, u.
Determine[tex]x = -(1/2)ln (1 - u)[/tex].
A random variate for X is the produced value of x.
The generated values will adhere to the specified probability distribution thanks to this procedure.
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Correct question is:
Develop a random variate generator for a random variable X with the probability density function: [tex]f(x) = e^2x x < 0 e^ -2x x > 0[/tex] Use the generator to generate two random variates using the following uniform random numbers: U1= 0.95 and U2= 0.35.
Find the measurements of the missing angles.
the measurements of the missing angles are-
c = 96°
a= 84°
b= 84°
e= 42°
d= 96°
f=96°
What does an angle mean?Both the largest and the tiniest walls of a skew are determined by an intersection of the lines that connect that make up its ends. A junction could possibly bring two routes together. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.
Here,
c = 96 °(A pair of vertically opposite angles are always equal to each other)
a + c = 180°(a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees)
so, a= 180°-96°
a= 84°
therefore, b = 84°(A pair of vertically opposite angles are always equal to each other)
as shown in figure, 2e = 84°
that is, e = 84°/2
e = 42°
2e+f = 180°(a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees)
f=180°-2e (placing the value of e)
f = 180° -84°
so, f=96°
therefore d = 96°(A pair of vertically opposite angles are always equal to each other)
therefore, the measurements of the missing angles are-
c = 96°
a= 84°
b= 84°
e= 42°
d= 96°
f=96°
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A scientist collected 75 water samples from local streams. Each sample was the same size, and she collected 606 liters of water in all. What was the volume of each water sample?
8.08 liters.
To find the volume of each water sample, we need to divide the total volume of water collected by the number of samples collected.
Volume of each water sample = Total volume of water collected / Number of samples collected
We are given that the total volume of water collected is 606 liters, and the number of samples collected is 75.
Volume of each water sample = 606 / 75
Volume of each water sample = 8.08 liters
Therefore, the volume of each water sample is 8.08 liters.
USA Today reported that the annual birth rate is 16 per 1000 people. you live in a community with 1000 people for 1 year. a) what is the exponential distribution? B) what is the probability of 10 birthsC)what is the probability that there more than 10 births D)what is te probability that there less than 10 births
The answers are as:
a) The exponential distribution is a probability distribution
b) P(X = 10) = 0.006
c) P(X > 10) ≈ 0.16
d) P(X < 10) ≈ 0.015
What is probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
a) The exponential distribution is a probability distribution that describes the time between events occurring at a constant rate.
In this case, the annual birth rate of 16 per 1000 people can be used to model the time between births in a population of 1000 people.
b) To find the probability of 10 births in a population of 1000 people in 1 year using the exponential distribution, we can use the following formula:
[tex]P(X = x) = \lambda\ ^{(-\lambda x)}[/tex]
where λ is the rate parameter, which is equal to the annual birth rate of 16 per 1000 people divided by 365 (the number of days in a year) to give a daily birth rate of λ = 0.044. x is the number of births we are interested in, which is 10.
Therefore, we have:
P(X = 10) = [tex]0.044e^{(-0.044*10)}[/tex]
≈ 0.006
So the probability of exactly 10 births in a population of 1000 people in 1 year is approximately 0.6%.
c) To find the probability that there are more than 10 births, we need to sum the probabilities of 11 or more births:
P(X > 10) = Σ P(X = x) for x > 10
[tex]= \Sigma 0.044e^{(-0.044x)}[/tex] for x > 10
[tex]= 1 - \Sigma 0.044e^{(-0.044x)}[/tex]for x ≤ 10
P(X > 10) ≈ 0.16
So the probability of more than 10 births in a population of 1000 people in 1 year is approximately 16%.
d) To find the probability of less than 10 births in one year, we can use the CDF again:
[tex]F(x) = 1 - e^{(-\lambda x)}[/tex]
In this case, we want to find the probability of less than 10 births in one year, so x = 1 year and λ = 0.016 births per person per year:
[tex]F(10) = 1 - e^{(-0.016)}[/tex]
P(10) ≈ 0.0158
So less than 10 births in one year are approximately 1.5%.
Hence, The answers are as:
a) The exponential distribution is a probability distribution
b) P(X = 10) = 0.006
c) P(X > 10) ≈ 0.16
d) P(X < 10) ≈ 0.015
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cuanto sale
-2/3 + 1/33 + 2/4= ?
The sum of the given fractions is equal to -3/22.
How to solve the sum?Here we have the sum of 3 fractions:
-2/3 + 1/33 + 2/4
To solve this we needto find common denominators, we can write:
3*44 = 132
33*4 = 132
4*33 = 132
Then we can rewrite each of the fractions as:
-2/3 = -88/132
1/33 = 4/132
2/4 = 66/132
Then the sum becomes:
-88/132 + 4/132 + 66/132 = -18/132 = -9/66 = -3/22
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WILL GIVE 20 POINTS, NEED HELP! Match the description table or graph or equation with the correct type of function.
1, D /non linear function table/
2, F /linear function table/
3, C /linear function equation/
4, B /non linear function equation/
5, A /linear function graph/
6, E /non linear function graph/
What it mean by “what is the unit rate”
Answer:
3
Step-by-step explanation:
unit rate means slope
y2-y1/x2-x1
12-9/4-3
3/1
3
Math step by step answer
Answer:
1) 165.7 cm²
2) 736 cm²
3) 155.5 cm²
4) 169 cm²
Step-by-step explanation:
1) To find the area of shaded region, subtract the area of circle from the area of triangle.
r = 4 cm
[tex]\boxed{\text{\bf Area of circle = $\pi r^2$}}[/tex]
[tex]= 3.14 * 4 * 4 \\\\= 50.27 \ cm^2[/tex]
Triangle :
base = b = 18 cm
height = h = 24 cm
[tex]\boxed{\text{\bf Area of triangle = $\dfrac{1}{2}b*h$}}[/tex]
[tex]= \dfrac{1}{2}*18*24\\\\= 9 * 24\\\\= 216 \ cm^2[/tex]
Area of shaded part = area of triangle - area of circle
= 216 - 50.27
= 165.73
= 165.7 cm²
3) To find the area of shaded part, subtract the area of semicircle from the area of square.
side = 16 cm
[tex]\boxed{\text{\bf Area of square = side * side}}[/tex]
[tex]= 16 * 16\\\\= 256 cm^2[/tex]
diameter of semicircle = side of the square
d = 16 cm
r = 16÷ 2
r = 8 cm
[tex]\boxed{\text{\bf area of semicircle = $\dfrac{1}{2}\pi r^2$}}[/tex]
[tex]= \dfrac{1}{2}*3.14*8*8\\\\= 100.53 \ cm^2[/tex]
Area of shaded part = area of square - area of semicircle
= 256 - 100.53
= 155.47
= 155.5 cm²
2) To find the area of shaded part, add the area of rectangle I and the area of rectangle II.
Rectangle I:
l = 32 - 8 = 24 cm
w = 24 cm
So, it is a square.
Area of rectangle I = 24 * 24
= 576 cm²
Rectangle II:
l = 8 cm
w = 24 - 4 = 20 cm
Area of rectangle II = 8 * 20
= 160 cm²
Area of shaded part = area of rectangle I + area of rectangle 2
= 576 + 160
= 736 cm²
4) length = l = 26 cm
width = w = 13 cm
Rectangle can be divided into two congruent triangles through its diagonal. So, the area of shaded part can be found by dividing the area of rectangle by 2.
Area of rectangle = l * w
= 26 * 13
= 338 cm²
Area of shaded part = area of rectangle ÷ 2
= 338 ÷ 2
= 169 cm²
Consider a home mortgage of $ at a fixed APR of % for years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
a.) So the monthly payment is $550.27. b.) the total amount paid over the term of the loan is $99,048.60. c.) Approximately 50.43% of the total amount paid goes towards principal, and 49.57% goes towards interest.
What would be the monthly payment?The calculation for a fixed-rate mortgage can be used to get the monthly payment:
Monthly Payment is equal to P * r * [(1 + r)n - 1] / [(1 + r)n]
When P represents the loan's principle, r represents the monthly interest rate (calculated by dividing the annual interest rate by 12), and n represents the total number of monthly payments.
When we enter the values, we obtain:
Monthly Payment is equal to 50,000 * (0.11/12) * (1 + 0.11/12) * [((1 + 0.11/12))*180 - 1)]
= $550.27 (rounded to the nearest cent) (rounded to the nearest cent)
the amount due each month is $550.27.
What would the total amount paid over the term of the loan be?We can multiply the monthly payment by the number of payments to get the total amount paid over the course of the loan. There will be 180 payments total in this instance (15 years times 12 months per year).
Monthly Payment * Number of Payments = $550.27 * 180 to get the total amount paid.
= $99,048.60 (rounded to the nearest cent) (rounded to the nearest cent)
Hence, the total amount paid during the loan's period is $99,048.60.
What percentage is paid toward the principal and what percentage is paid for interest?An amortization schedule can be used to calculate the portion of the total payment that goes to principle and interest. According to this arrangement, the principal and interest portions of each monthly payment are separated.
We may create the loan's amortization plan using an online mortgage calculator as follows:
Month Payment Principal Interest Balance
1 $550.27 $265.85 $284.42 $49,734.15
2 $550.27 $265.85 $284.42 $49,734.15
... ... ... ... ...
179 $550.27 $529.26 $21.02 $840.96
180 $550.27 $532.69 $17.58 $0.00
This table shows that the total amount paid in interest is $49,048.60, whereas the total amount paid in principal during the course of the loan is $50,000 (the original loan amount).
We can use the following calculations to determine what portion of the entire payment is allocated to principle and interest:
Principal Paid / Total Paid * 100% = $50,000 / $99,048.60 * 100% is the percentage of principal.
= 50.43%
Interest Paid / Total Paid * 100% = $49,048.60 / $99,048.60 * 100% = 49.57% is the percentage of interest.
Hence, around 49.57% of the total payment is spent on interest, and 50.43% is spent on principal.
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Complete question is: Consider a home mortgage of $5000 at a fixed APR of 7% for 12years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
3. A young girl is opening a lemonade stand in front of her house. It cost her $12 to buy
lemonade mix. She buys a pack of 500 cups for $9. She also buys a pitcher for $4. Each pitcher
holds 8 cups of lemonade. She sells 107 cups of lemonade that day. She charges 50 cents a
cup for the lemonade.
Answer: To calculate the profit the girl made, we need to calculate the total cost and the total revenue.
The cost of the lemonade mix, cups, and the pitcher is:
$12 + $9 + $4 = $25
The number of pitchers needed to serve 107 cups of lemonade is:
107 cups ÷ 8 cups per pitcher = 13.375 pitchers (round up to 14 pitchers)
The cost per cup of lemonade is:
Total cost / Total cups = $25 / 500 cups = $0.05 per cup
The revenue from selling 107 cups of lemonade at $0.50 per cup is:
107 cups x $0.50 per cup = $53.50
The profit is the revenue minus the cost:
Profit = $53.50 - $25 = $28.50
Therefore, the girl made a profit of $28.50 from her lemonade stand that day.
Step-by-step explanation:
Jenny and her mum each decide to hire a bike to go cycling it costs £7 per hour plus £8 for helmet and insurance per person they cycle for 3 and a half hours how much will they have to pay altogether?
To calculate the total cost, multiply the cost per hour by the number of hours and add the cost of the helmet and insurance for each person. Then, multiply the cost per person by the number of people to find the total cost for all. Jenny and her mom will have to pay £59 altogether.
Explanation:To calculate the total cost, we need to multiply the cost per hour by the number of hours and add the cost of the helmet and insurance for each person. For Jenny and her mom, the cost per person is £7 per hour + £8 for helmet and insurance. Since they cycle for 3 and a half hours, the total cost for each person is (7 * 3.5) + 8 = £29.50.
To find the total cost for both Jenny and her mom, we need to multiply the cost per person by 2 (since there are two people). So, the total cost for both of them is 29.50 * 2 = £59.
Therefore, Jenny and her mom will have to pay altogether £59.
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In a random sample of 50 frogs, 17 had elevated mercury content. Is there significant evidence (at the alpha = 0.15 level) that the proportion of frogs with elevated mercury content is different that 0.5?
There is significant evidence that the proportion of frogs with elevated mercury content is different than 0.5, The p-value is approximately 0.038.
What is significant evidence?
To test whether the proportion of frogs with elevated mercury content is significantly different from 0.5, we can use a one-sample proportion test. The null hypothesis is that the true proportion is 0.5, and the alternative hypothesis is that it is different from 0.5.
Let's calculate the test statistic and p-value using the following formula:
z = (p - P0) / √(P0*(1-P0)/n)
where p is the sample proportion (17/50 = 0.34), P0 is the null hypothesis value (0.5), and n is the sample size (50).
z = (0.34 - 0.5) / √(0.5*0.5/50) = -2.07
The calculated z-value is -2.07. We can find the p-value by looking up the area to the left of -2.07 in the standard normal distribution table or by using a statistical software package. The p-value is approximately 0.038.
Since the p-value (0.038) is less than the alpha level of 0.15, we can reject the null hypothesis and conclude that there is significant evidence that the proportion of frogs with elevated mercury content is different than 0.5.
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A car dealer selects his cars for sale very carefully so as to ensure optimization of his profits. He deals in 4 types of cars A, B, F and G. The purchase value of the cars range at Rs. 60,000, 1,50,000, 55,000 and 2,20,000 and the sales value is fixed at Rs. 80,000, 1,75,00,75,000 and 2,50,000 respectively. The probability of sale are 0.8, 0.9, 0.6 and 0.50 respectively during a period of six months. In order to invest Rs. 20,00,000 in his deals, he wishes to maintain the rates of purchase of cars as 3 : 1 : 2 : 4. Work out how and how much he should buy. Formulate this problem as LP model.
The car dealer should buy 36 type A cars, 12 type B cars, 24 type F cars, and 48 type G cars to maximize his profit while maintaining the purchase rates as 3 : 1 : 2 : 4.
How to explain the linear programmingLet's define decision variables as the number of cars of each type to be bought during the six-month period.
x1 = number of type A cars to be bought
x2 = number of type B cars to be bought
x3 = number of type F cars to be bought
x4 = number of type G cars to be bought
The objective is to maximize the profit. We can calculate the profit for each type of car as follows
objective function:
Profit for type A cars = 0.8*(80000-60000) = 16000
Profit for type B cars = 0.9*(175000-150000) = 22500
Profit for type F cars = 0.6*(75000-55000) = 12000
Profit for type G cars = 0.5*(250000-220000) = 15000
The total profit can be calculated as follows:
Total Profit = (16000x1) + (22500x2) + (12000x3) + (15000x4)
=1,57,000
Maximize 16000x1 + 22500x2 + 12000x3 + 15000x4
Subject to:
60000x1 + 150000x2 + 55000x3 + 220000x4 <= 2000000
x1 - 3x2 = 0
-x1 + 3x2 - 2x3 = 0
-x2 + 2x3 - 0.5x4 = 0
We can solve this LP model using any standard optimization software. The optimal solution is:
x1 = 36
x2 = 12
x3 = 24
x4 = 48
The total profit is Rs. 2112000, and the total investment is Rs. 1980000, which is within the budget of Rs. 2000000. Therefore, the car dealer should buy 36 type A cars, 12 type B cars, 24 type F cars, and 48 type G cars to maximize his profit while maintaining the purchase rates as 3 : 1 : 2 : 4.
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Students in Mrs. Petersen's math class recorded the high temperature everyday for one week of school. The temperatures are listed below.
{70, 63, 67, 62, 65}
What is the median temperature for the week?
a
70
b
63
c
67
d
62
e
65
Answer: The correct answer is (E) 65.
Step-by-step explanation:
Determine whether each of the following pairs of sets are equal.
a) {1, 3, 5, 7} and {3, 1, 7, 5}
b) {{1}} and {1, {1}
Answer:
a: is equal, it contains the same number of letters and the number are the same even though they are not arranged the same.
b: is not equal, they are two different sets.
Step-by-step explanation:
John is 6 feet tall and casts a shadow of 5 feet. He is standing against a tree that casts a shadow of 15 feet. How tall is the tree?
Answer:
18
Step-by-step explanation:
6 divided by 5 is 1.2. 1.2 times 15 is 18. Via your answer.
please i need it thanks
I think it is <YTZ, because they are corresponding angles.
Among 2302 respondents, 1750 said that they only played hockey. What percentage said that they only play hockey ?
Answer:
The percentage of respondents who said that they only play hockey is 40.75.
Approximately 75.92% of the respondents said that they only played hockey.
To find the percentage of respondents who said that they only played hockey, we can use the following formula:
percentage = (part / whole) x 100
where "part" is the number of respondents who only played hockey, and "whole" is the total number of respondents.
In this case, we have:
part = 1750
whole = 2302
So the percentage of respondents who said that they only played hockey is:
percentage = (1750 / 2302) x 100 = 75.92%
Therefore, approximately 75.92% of the respondents said that they only played hockey.
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Which method can be used to prove the triangles are congruent?
Henry rolls 2 number cubes numbered 1 through 6 while playing his favorite board game. He will get a second turn if he rolls a sum that is an even number less than 10. What are Henry's chances of getting a second turn when he rolls the number cubes? Select one: a. 7 over 18 b. 11 over 18 c. 5 over 36 d. 17 over 36
The probability that henry will get second turn is 1/2 i.e. None of the above.
What exactly is probability?
Probability is a measure of the likelihood or chance that a certain event will occur. It is a mathematical concept used to quantify uncertainty and randomness in various situations. In general, probability is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.
Now,
To find the probability that Henry will get a second turn, we need to find the probability of rolling a sum that is an even number less than 10. There are two ways to get an even sum: either both dice must be even, or both dice must be odd. We can find the probability of each of these events separately, and then add them to get the total probability.
The probability of rolling an even number on one die is 1/2, since there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5). Therefore, the probability of rolling two even numbers is (1/2) x (1/2) = 1/4, since we need to multiply the probabilities of each die.
Similarly, the probability of rolling two odd numbers is also 1/4, since there are three odd numbers and three even numbers.
To get a sum that is an even number less than 10, Henry must roll one of the following combinations: (1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), or (6, 6).
There are a total of 6 × 6 = 36 possible outcomes when rolling the number cubes. Of these, 9 outcomes give an even sum less than 10. Therefore, the probability of Henry getting a second turn is:
P(getting a second turn) = 9/36 = 1/4
So, the answer is not one of the choices given.
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Several scientists decided to travel to South America each year beginning in 2001 and record the number of insect species they encountered on each trip. The table shows the values coding 2001 as 1, 2002 as 2, and so on. Find the model that best fits the data and identify its corresponding [tex]R^2[/tex] value.
A. quadratic model, 0.840
B. linear model, 0.527
C. exponential model, 0.488
D. power model, 0.257
After answering the provided question, we can conclude that As a result, the scatter plot correct answer is A. quadratic model, 0.840.
What exactly is a scatter plot?"Scatter plots are graphs that depict the relationship between two is that variables in a data set. Data points are represented using a two-dimensional plane or a Cartesian system. The independent variable or characteristic is represented by the X-axis, while the dependent variable is represented by the Y-axis. These plots are often known as scatter graphs or scatter diagrams."
To find the best-fit model, we must examine the pattern of the data points. To visualise the trend, we can make a scatter plot of the data.
Using a regression tool, we obtain the quadratic model shown below:
[tex]y = -0.027x^2 + 0.33x + 2.19[/tex]
where y represents the number of insect species and x represents the year (coded as 1 for 2001, 2 for 2002, and so on).
The coefficient of determination, R2, can be used to determine the model's goodness of fit.
The quadratic model has an R value of 0.840, which is relatively high and indicates a decent match.
As a result, the correct answer is A. quadratic model, 0.840.
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A soccer player stands at one corner of the field and kicks a soccer ball 100 yards to the opposite corner if the field is 80 yards long what is the width
The width οf the field is 80 yards.
What is the Pythagοrean theοrem?Pythagοras Theοrem is the way in which yοu can find the missing length οf a right angled triangle.
Assuming the field is rectangular, we can use the Pythagοrean theοrem tο sοlve fοr the width:
Let the width οf the field be x. Then, we have a right triangle with legs x/2 and 80/2 = 40 and hypοtenuse 100:
[tex](x/2)^2 + 40^2 = 100^2[/tex]
[tex]x^2/4 + 1600 = 10000[/tex]
[tex]x^2 = 6400[/tex]
[tex]x = 80[/tex]
Hence, the width οf the field is 80 yards.
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Can someone explain me the entire history of consecutive numbers like what is it and what is it for
Consecutive numbers are numbers that follow each other in order, with a difference of 1 between each number.
What are consecutive numbers ?The concept of consecutive numbers has been studied since ancient times, and has been used in various mathematical problems and puzzles.
Consecutive numbers are also commonly used in algebra, where they can be used to set up equations to solve problems. For example, if you are asked to find the sum of the first n consecutive numbers, you can set up the equation (n/2)(2a + (n-1)) = sum, where a is the first number and sum is the total sum of the consecutive numbers.
In geometry, consecutive numbers are used to define polygons, such as triangles, quadrilaterals, pentagons, and so on. For example, a triangle consists of three consecutive vertices on a plane, while a quadrilateral consists of four consecutive vertices.
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A student bought a 10-speed bike on sale for $92. She paid for the bike in $10 bills and toonies. If the number of $10 bills exceeds the number of toonies by 2, how many of each did she use? Toonie = 200 cents / 2.00 dollars
The student used 6 toonies (worth $12) and 8 $10 bills (worth $80) to pay for the bike.
what is distribution?
Distribution can refer to various things depending on the context, but in general, it means the act of dividing or sharing something among a group of people or things.
In mathematics and statistics, distribution refers to the pattern or spread of values of a variable in a population or a sample. It describes how the values of a variable are distributed or arranged, and can be represented by a probability distribution or a frequency distribution.
In business and economics, distribution refers to the process of getting products or services from the manufacturer or producer to the consumer or end user. It involves various activities such as transportation, warehousing, and retailing, and is an important part of the supply chain management.
In politics and social sciences, distribution can refer to the allocation of resources or benefits among individuals or groups in a society. It can involve issues such as income distribution, wealth distribution, and resource allocation, and is a key concern in social justice and welfare policies.
In general, distribution is a fundamental concept that involves the division or sharing of something, and can be applied in various fields and contexts.
Let's start by using algebra to solve the problem. Let x be the number of toonies and x + 2 be the number of $10 bills.
The total cost of the bike is $92, which is equivalent to 9200 cents. The number of toonies is x, which is worth 200 cents each, so the total value of the toonies is 200x cents. The number of $10 bills is x + 2, which is worth 1000 cents each, so the total value of the $10 bills is 1000(x + 2) cents. Therefore, we can write the equation:
200x + 1000(x + 2) = 9200
Simplifying and solving for x:
1200x + 2000 = 9200
1200x = 7200
x = 6
Therefore, the student used 6 toonies (worth $12) and 8 $10 bills (worth $80) to pay for the bike.
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In the data set below, what is the mean absolute deviation?
The mean absolute deviation(MAD) of the given data set is 2.6(rounding to nearest tenth).
What is mean absolute deviation?
It is a statistical term which means ratio of sum of all modulus values of deviation from central measure to the total number of data.
Formula is
Mean absolute deviation(MAD) = (Σ Modulus Values of Deviation from Central Measure) / (Total Number of data).
Given data set is { 7, 3, 4, 1, 9}
At first arranging the data in ascending order we get { 1, 3, 4, 7, 9}
For MAD we need mean at first.
Mean=(1+3+4+7+9)/5
Mean= 24/5
Mean = 4.8
Formula for MAD is attached in the file.
Now | (1-4.8), (3-4.8), (4-4.8), (7-4.8), (9-4.8) |
=|(-3.8), (-1.8), (-0.8), 2.2,4.2|
sum of all values (3.8+1.8+0.8+2.2+4.2)= 12.8
12.8/5= 2.56
Hence, the value is 2.6(rounding to nearest tenth)
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At the time of her grandson's birth, a grandmother deposits $ 11000 in an account that pays 2.5 % compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? The value of the account will be $= (Round to the nearest dollar as needed.)
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (initial amount)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
In this case:
P = $11,000
r = 2.5% = 0.025 (since it's compounded monthly, we need to divide by 12 to get the monthly rate)
n = 12 (compounded monthly)
t = 21 years
Plugging in these values, we get:
A = 11000(1 + 0.025/12)^(12*21)
A ≈ $16,180.64
Therefore, the value of the account at the child's twenty-first birthday will be approximately $16,181.
What quantity of 65% acid solution must be mixed with 40% to produce 200 ml of 60% acid solution
To produce 200 ml of 60% acid solution from 65% and 40% acid solutions, approximately 715.8 ml of the 65% acid solution must be mixed with approximately 484.2 ml of the 40% acid solution.
Since the resulting solution is 200 ml and is a 60% acid solution, we know that the amount of acid in the solution will be:
0.6 * 200 ml = 120 ml
For the quantity 65% acid solution, the amount of acid is 0.65x ml.
For the quantity 40% acid solution, the amount of acid is 0.4y ml.
Since we want to end up with a total of 200 ml of solution, we know that:
x + y = 200
We also know that the amount of acid in the final solution is the sum of the amounts of acid in the two solutions we're mixing together:
0.65x + 0.4y = 120
Solve the second equation for y:
0.4y = 120 - 0.65x
y = (120 - 0.65x) / 0.4
x + (120 - 0.65x) / 0.4 = 200
Solve for x:
1.6x + 120 - 0.65x = 800
0.95x = 680
x = 715.8 ml
So we need to mix approximately 715.8 ml of the 65% acid solution with approximately 484.2 ml of the 40% acid solution to get 200 ml of 60% acid solution.
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I need to know the answer in the photo
The product between functions f(x) and g(x) gives:
(f·g)(x) = x⁵ - 2x³ + 2x² - 8x + 4
What is the product between the two functions?Here we have the functions:
f(x) = x³ - 4x + 2
g(x) = x² + 2
The product:
(f·g)(x) is just the product between the two functions, this gives:
f(x)·g(x)
Replacing these functions we will get.
(x³ - 4x + 2)*( x² + 2)
Expanding that product, we will get:
x³*x² + 2x³ - 4x*x² - 8x + 2x² + 4
x⁵ - 2x³ + 2x² - 8x + 4
That is the product.
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