Step-by-step explanation:
to get a we use cos and for b we use sin
so
cos(45°) =a/5√2....... when u criss cross it
a = cos(45°) × 5√2
a = √2/2 × 5√2
a= 5
sin(45) = b/5√2
b= sin(45) × 5√2
b = 5
In other way if u find the 1st side you r indirectly find the 2nd one which they are equal .
Max is going to the carnival. He has $20 to spend. The entrance fee is $6. if each ride costs $1.50 per ride, how many rides can he ride? Write and solve a inequality to show how many rides he can ride.
Let's use r to represent the number of rides that Max can go on.
The entrance fee is $6, which means that Max will have $20 - $6 = $14 left to spend on rides.
Each ride costs $1.50, so the total cost of r rides would be 1.5r.
To find out how many rides Max can afford, we can write an inequality:
1.5r ≤ 14
This inequality means that the total cost of the rides Max goes on (1.5r) cannot be more than the amount of money he has left after paying the entrance fee ($14).
To solve for r, we can divide both sides of the inequality by 1.5:
r ≤ 14/1.5
r ≤ 9.333
Since Max can't go on a fractional number of rides, he can go on at most 9 rides.
Therefore, Max can ride at most 9 rides.
if the level of significance of a hypothesis test is raised from .01 to .05, the probability of a type ii error will group of answer choices also increase from .01 to .05. not change. decrease. increase.
if the level of significance of a hypothesis test is raised from .01 to .05, then the probability of a Type II error will decrease when the level of significance of a hypothesis test is raised from .01 to .05. (option a)
This change in the level of significance does not directly affect the probability of a Type II error. A Type II error occurs when we fail to reject the null hypothesis, even though it is false. This means that we have concluded that there is no relationship between the variables, even though there actually is one.
The probability of a Type II error depends on several factors, such as the sample size, the effect size, and the level of significance. In general, as the level of significance increases, the probability of a Type II error decreases.
This is because when we are more lenient in rejecting the null hypothesis, we are more likely to detect any real relationship that exists between the variables.
Therefore, the correct answer to your question is (a)
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Planet plan will need to do outreach to at least 294 people to get volunteers. Now we need to see if this is enough outreach to get the number of needed options
If the result of (294 * y%) is greater than or equivalent to x, then the quantity of approaches taken is satisfactory; however, if the sum is less than x, more efforts must be made in order to meet the specified scope.
How to solveIn order to answer the question of whether it is enough to reach out to 294 people and acquire the desired number of volunteers, two critical things must be recognized:
the specified amount of volunteers for the project, as well as the predicted rate of conversion (the percentage of those contacted that will volunteer).
Assume a necessity for 'x' volunteers, and a ratio of 'y%'.
The following formula can be used to calculate how many volunteers can be obtained from reaching out to 294 people:
Number of Volunteers = (Number of People Reached) * (Conversion Rate). In this particular case: Number of Volunteers = 294 * (y%).
Finally, so as to determine if the outreach is sufficient in regards to achieving the target number of volunteers ('x'), one must compare the attained number with the given goal.
If the result of (294 * y%) is greater than or equivalent to x, then the quantity of approaches taken is satisfactory; however, if the sum is less than x, more efforts must be made in order to meet the specified scope.
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There are 4 squares and 20 triangles. What is the simplest ratio of squares to triangles?
unit 12 probability homework 4 compound probability
The probability of rolling a 3 on the first roll and a 5 on the second roll is 1/36.
We have,
Compound probability is the probability of multiple events occurring together.
It is calculated by multiplying the probabilities of each individual event.
For example:
Suppose you are rolling a fair six-sided die, and you want to know the probability of rolling a 3 on the first roll and a 5 on the second roll.
The probability of rolling a 3 on the first roll is 1/6.
The probability of rolling a 5 on the second roll is also 1/6.
The compound probability of rolling a 3 on the first roll and a 5 on the second roll is:
1/6 x 1/6 = 1/36
Thus,
The probability of rolling a 3 on the first roll and a 5 on the second roll is 1/36.
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Yesterday, a parking lot had 10 cars parked in it. Of the cars parked in the parking lot, 40% were silver, 3 were red, and the rest were blue. How many of the cars were blue?
HELP GIVING BRAINLIST
PLEASE SHOW WORK
30 percent of the 10 cars in the parking lot, or 3 cars, were blue.
If 40% of the cars were silver, then the remaining percentage of cars must be split between red and blue cars. Since there were 10 cars in total, we can set up the following equation:
40% + R% + B% = 100%
where R% and B% represent the percentage of red and blue cars, respectively.
Simplifying this equation, we get:
60% = R% + B%
Since we know that there were 3 red cars, we can use this information to find the percentage of red cars:
3 cars = R% of 10 cars
R% = (3/10) x 100% = 30%
Substituting this into our equation, we get:
60% = 30% + B%
B% = 30%
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Ann compró cuatro pares de aretes por 25. 00 cada uno al comprar 4 pares. Recibió un par gratis. ¿Cuál fue el precio promedio de cada par de aretes?
For bought four pairs of earrings by annu and price of each being $25.00, then the average price of each pair of earrings is equals to the $20.00.
The average of a group of numbers is also known as mean of numbers. It is calculated by summing up all the numbers together and then dividing the resultant by the total number of numbers in the group. Annu bought four pairs of earrings. The price of one pair of earrings = $25.00
Also, she will get one pair free at buying four pairs of earrings. We have to determine the average price each pair of earrings. Number of pairs of earrings = 5
Total price paid by annu for earings = 4 × $25.00 = $ 100.00
That sum of prices of earings pairs = $100.00
Using the average formula, the average price = ( sum of each pair of earings prices )/total pairs of earrings she bought
[tex]= \frac{100}{5}[/tex]
= 20
Hence required value is $20.
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Complete question:
Ann bought four pairs of earrings for 25.00 each by buying 4 pairs. Received a free pair. What was the average price of each pair of earrings?
How do you undo an algebra equation?
Answer: You work backwards from the way it was set up. For example if you want to find the are of a triangle you would multiple the side lengths and then divide it by two, which gives you the area. To undo the equation you would work backwards. So lets say you only know one side, you would take the area of the triangle, multiply it by two( because we divided it the first time) and then divide the new number by one of the side lengths you know, this will leave you will the other side length. This is the principle you can go off of when trying to undo an algebra equation... Just work backwards.
Step-by-step explanation:
The Candle Factory is producing a new candle. It has a radius of 3 inches and a height of 5 inches. How much wax is needed to make a candle? Use 3.14 for pie. Round to the nearest whole cubic inch.
Answer: 141 cubic inches
Step-by-step explanation:
Volume of cylinder = r^2 x h (area of circle x height)
= 3.14
3.14 x 3^2 = 28.26
28.26 x 5 = 141.3
Help Please
Answer Part A and Part B clearly to win brainly
Show your work (I want to see more numbers than words)
Answer:
Part A:
[tex]2 {x}^{3} y = 2(x)(x)(x)(y)[/tex]
[tex]18xy = 2(3)(3)(x)(y)[/tex]
[tex]10 {x}^{2} y = 2(5)(x)(x)(y)[/tex]
[tex]90y = 2(3)(3)(5)(y)[/tex]
So the greatest common factor is 2y.
Part B:
[tex]2 {x}^{3} y - 18xy - 10 {x}^{2}y + 90y [/tex]
[tex]2xy( {x}^{2} - 9) - 10y( {x}^{2} - 9)[/tex]
[tex]2y(x - 5)( {x}^{2} - 9)[/tex]
[tex]2y(x - 5)(x - 3)(x + 3)[/tex]
Julie has accumulated $1,000 in a bank savings account, which pays 2.7 percent interest. She investigates several options and finds that she can invest her money in a 1-year Treasury note paying 4.4 percent interest, a
1-vear CD paying 3.9 percent interest, or a money market mutual fund with an average yield of 3.7 percent. What are the pros and cons of each of these investment options?
Julie has $1,000 and wants to invest it. She has three options: 1-year Treasury note paying 4.4% interest, 1-year CD paying 3.9% interest, or money market mutual fund with an average yield of 3.7%. Pros of Treasury note are high interest rate but con is lack of flexibility. Pros of CD are lower risk and predictable return but con is lower interest rate. Pros of money market fund are liquidity and flexibility but con is lower interest rate.
The investment options available to Julie are 1-year Treasury note paying 4.4 percent interest This option offers the highest interest rate among the three options and is a low-risk investment as it is backed by the government. However, the money is locked in for one year, and there may be penalties for early withdrawal.
1-year CD paying 3.9 percent interest This option is also a low-risk investment, but the interest rate is slightly lower than the Treasury note. The money is also locked in for one year, and there may be penalties for early withdrawal.
Money market mutual fund with an average yield of 3.7 percent This option offers a slightly higher return than a savings account, but the risk level is slightly higher. The money can be withdrawn at any time without penalty, making it a more flexible option.
The pros of the Treasury note and CD options are higher interest rates and low-risk investments, while the cons are that the money is locked in for one year, and there may be penalties for early withdrawal.
The pros of the money market mutual fund are flexibility and slightly higher returns, while the cons are slightly higher risk and lower returns compared to the other two options. Julie should weigh the pros and cons of each option based on her personal financial goals and risk tolerance.
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David borrows $1400 from the bank at an 8.5% simple interest rate per year. How
much will he have to pay back in total in 2 years?
A.$1638
B.$1625
C.$238
D.$225
Answer:
Figure out your monthly interest due by dividing your interest rate by 12. For example, an 8% interest rate loan would be . 007 (. 08 divided by 12).
Principle amount is $600 (P), rate of interest is 8\% per annum (R), and the number of years is 5 (N). Hence, here, the interest the man would be paying is $240 and the total money he'd be collecting at the end of 5-year tenure is $840.
Help needed quick please!
Torrin rode his bike to school at
13.5 km/h. He returned home using
the same route at 10.5 km/h. Torrin
took a total of 36 min to ride to school
and back. Express your answer to the
nearest hundredth.
a) How many minutes did Torrin take
to ride to school?
b) How far is it from Torrin’s house to
school?
Answer:
a) 15.75 minutes
b) 3.54 km
Step-by-step explanation:
Given speeds to school and back of 13.5 km/h and 10.5 km/h, respectively, and a total travel time of 36 minutes, you want to know the time to ride to school, and the distance.
RatioThe ratio of times is the inverse of the ratio of speeds over the same distance. The ratio of times is ...
time to school : time to home = 10.5 : 13.5 = 7 : 9
a) TimeThen the fraction of total time it takes to get to school is ...
(7/(7+9))·(36 min) = 15.75 min = 0.2625 hour . . . . . . . 1 min = 1/60 hour
b) DistanceThe distance can be found from the relation ...
distance = speed · time
distance = (13.5 km/h)(0.2625 h) = 3.54375 km ≈ 3.54 km
It takes Torrin 15.75 minutes to ride the 3.54 km to school.
in how many ways can $4$ balls be placed in $3$ boxes if the balls are distinguishable, and the boxes are indistinguishable?
The number of ways to place 4 distinguishable balls in 3 indistinguishable boxes can be found using the technique of "stars and bars" and is equal to 15.
We can use the stars and bars technique to represent each of the four identifiable balls as a star and the three indistinguishable boxes as two bars (|).
Using this strategy, we can consider the challenge as arranging four stars and two bars in a row. The row has a total of six spots, and we must choose two of them to place the bars. As a result, the binomial coefficient gives the number of ways to arrange the stars and bars:
C(6,2) = 6! / (2! * 4!) = 15
So there are 15 different ways to arrange four identifiable balls in three indistinguishable compartments.
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A temperature of -12°F is lower than a temperature of -7°F. A temperature of -7°F is higher than a temperature of -9°F. Which set of inequalities expresses these relationships? Explain your choice.
Answer: The answer is A.
a new surgical procedure has promising results to alleviate hip pain, but a portion of patients who receive the procedure report an audible squeaking noise coming from the hip within six months. data from a follow-up study of 143 patients revealed that 10 of them could hear squeaking. if you were to construct a 99% confidence interval around the follow-up study point estimate, what would be e, the margin of error, or half-width of the confidence interval? since the sample size is so large, you can reference the z distribution to determine a critical
The margin of error of the 99% confidence interval is given as follows:
0.0549 = 5.49%.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The parameters for this problem are given as follows:
[tex]n = 143, \pi = \frac{10}{143} = 0.0699[/tex]
Hence the margin of error is of:
M = 2.575 x sqrt(0.0699 x 0.9301/143)
M = 0.0549 = 5.49%.
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he movement of
Which does not represent a way to show 6 + 6 + 6 + 6 with multiplication?
O 6.4
○ 6(4)
O 6x4
O 6÷4
The method that does not represent 6 + 6 + 6 + 6 using multiplication is 6 ÷ 4 since it represents division, not multiplication or repeated addition.
Explanation:The question is asking which method does not represent 6 + 6 + 6 + 6 in terms of multiplication. The equivalent multiplication expression for 6 + 6 + 6 + 6 is 6 x 4 which is also represented as 6(4). This is because multiplication is repeated addition. The expression 6.4 is a decimal multiplication, not an integer multiplication. Therefore, it is not a correct representation of 6 + 6 + 6 + 6. However, the method that clearly does not represent 6 + 6 + 6 + 6 in terms of multiplication is 6 ÷ 4 as it expresses division, not multiplication or repeated addition as requested.
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In circle N with m/MNP = 34° and MN = 7, find the area of sector MNP.
Round to the nearest hundredth.
N
M
P
Answer: 35.90
Step-by-step explanation:
Question 2
For which distribution shape is it usually appropriate to use the median when summarizing the data?
Multiple choice question. A)
bell-shaped
B)
skewed
C)
symmetric
D)
uniform
The distribution shape that is usually appropriate to use the median when summarizing the data is B) skewed.
What is median?The median is the value that divides the higher half of a population, a probability distribution, or a sample of data from the lower half.
The median is usually appropriate when summarizing data with a skewed distribution, where the data is not evenly distributed around the center. In a skewed distribution, the mean can be affected by extreme values, and may not be a good representation of the typical value.
The median, on the other hand, is the middle value of the data when arranged in order, and is less affected by extreme values. Therefore, it provides a better summary measure for skewed data. In contrast, for a bell-shaped or symmetric distribution, the mean and median are usually similar and either one can be used to summarize the data.
Therefore, the distribution shape that is usually appropriate to use the median when summarizing the data is B) skewed.
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A basketball has a diameter of 9 inches. About how many cubic inches(volume) of air do you need to fill up the basketball?
Responses
381.51 cubic inches
381.51 cubic inches
286.16 cubic inches
286.16 cubic inches
84.78 cubic inches
84.78 cubic inches
21.19 cubic inches
You would need approximately 381.51 cubic inches of air to fill up the basketball. The correct option is 381.51.
To calculate the volume of a sphere (which a basketball is approximately shaped like), you use the formula V = (4/3)πr³, where r is the radius (half the diameter) of the sphere.
So, the radius of the basketball would be 4.5 inches (half of 9 inches), and plugging that into the formula we get:
V = (4/3)π(4.5)³
V = (4/3)π(91.125)
V = 381.51 cubic inches
Therefore, the correct option is 381.51.
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suppose you have a small holiday party and invite 7 guests asking each to bring a gift to exchange. then you and your guests exchange gifts. how many ways can you exchange so that no one gets their own gift?
The number of ways for the 7 guests to exchange gifts at a small holiday party so that no one gets their own gift is 1854
This problem involves finding the number of derangements, which is the number of permutations of n elements such that no element appears in its original position. In this case, n=7, since there are 7 guests.
The formula for the number of derangements of n elements is
D(n) = n! × (1/0! - 1/1! + 1/2! - 1/3! + ... + [tex](-1)^{n/n!}[/tex])
Using this formula, we can find the number of derangements of 7 elements:
D(7) = 7! × (1/0! - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!)
Do the arithmetic operations
= 1854
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Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.
What is the most appropriate conclusion?
The Child Health and Development Studies data support the conclusion that there is a difference in weight gain during the second trimester for expectant mothers in the 2015 sample compared to the historical average.
Based on the results of the one-sided T-test with a significance level of 5%, we can conclude that there is statistically significant evidence to suggest that the mean weight increase in the second trimester of expectant mothers in 2015 is greater than 14 pounds. This is supported by the p-value of 0.021, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis that the mean weight increase is equal to 14 pounds and accept the alternative hypothesis that the mean weight increase is greater than 14 pounds.
The most appropriate conclusion is that there is significant evidence to suggest that the mean weight increase in the second trimester for the 2015 sample of expectant mothers is greater than 14 pounds. Since the p - value (0.021) is less than the 5% significance level, we reject the null hypothesis and accept the alternative hypothesis, which states that the mean weight increase is greater than 14 pounds. The Child Health and Development Studies data support the conclusion that there is a difference in weight gain during the second trimester for expectant mothers in the 2015 sample compared to the historical average.
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What is stapel scale (Type of interval scale)
The Stapel scale is a type of interval scale used in survey research to measure attitudes and opinions. It is a unipolar scale with a range of numerical values, typically from -5 to +5 or -10 to +10, with a neutral point of zero in the center.
The Stapel scale is a type of interval scale that is commonly used in market research. It is a unipolar rating scale that measures attitudes and opinions towards a particular object or concept.
The scale consists of a single horizontal line, with a numerical scale ranging from -5 to +5, and a single adjective or phrase representing the concept being measured placed at one end of the line.
Respondents are asked to rate the concept by placing a mark on the line, with higher values indicating more positive attitudes or opinions and lower values indicating more negative attitudes or opinions.
The Stapel scale is often used in situations where a traditional bipolar scale (such as the Likert scale) may not be appropriate.By using the Stapel scale, researchers can gather precise and nuanced data about people's attitudes and opinions, making it a valuable tool in survey research.
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Which of the points plotted is farther away from (4, 4), and what is the distance?
A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at negative 7, 4, at 4, 4 and at 4, negative 5.
Point (4, −5), and it is 9 units away
Point (4, −5), and it is 11 units away
Point (−7, 4), and it is 9 units away
Point (−7, 4), and it is 11 units away
The point (-7,4) is the farthest from the point and the distance is 11 units away, the correct option is (d).
We have to find that which point is the farthest from the point (4,4),
The distance(d) between two points (x₁, y₁) and (x₂, y₂) can be calculated by the distance formula : √((x₂-x₁)² + (y₂-y₁)²);
Using this formula, we can find the distance between each of the points and (4, 4):
⇒ For point (-7, 4):
d = √((4 - (-7))² + (4 - 4)²)
d = √(11²)
d = 11 units
⇒ For point (4, 4):
d = √((4 - 4)² + (4 - 4)²)
d = 0 units
⇒ For point (4, -5):
d = √((4 - 4)² + (-5 - 4)²)
d = √(9²)
d = 9 units,
Therefore, the point farthest away from (4, 4) is (d) Point (-7, 4), and the distance is 11 units.
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The given question is incomplete, the complete question is
A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10. A point is plotted at (-7, 4), at (4, 4) and at (4, -5).
Which of the points plotted is farther away from (4, 4), and what is the distance?
(a) Point (4, -5), and it is 9 units away
(b) Point (4, -5), and it is 11 units away
(c) Point (-7, 4), and it is 9 units away
(d) Point (-7, 4), and it is 11 units away
please answer both questions
The vertical intercept of the graph is (0, 4).
The slope of the graph is -2/3.
The equation of the line graph is y = -2x/3 + 4.
The vertical intercept of the table is (0, -1).
The slope of the table is 4.
The equation of the table is y = 4x - 1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of the graph;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 4)/(6 - 0)
Slope (m) = -4/6
Slope (m) = -2/3
At point (0, 4) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -2/3(x - 0)
y = -2x/3 + 4
For the table, we have:
Slope (m) = (7 - 3)/(2 - 1)
Slope (m) = 4/1
Slope (m) = 4
At point (1, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 4(x - 1)
y = 4x - 1
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myra wants to buy flowers for her mom. roses cost $5 each and carnations cost $1.75 each. if myra has $35, how many roses and how many carnations can she buy?
The correct option stating number of roses and carnation to be bought are 4 roses and 7 carnations.
The equation to be formed here is -
Cost of each Rose × number of roses + cost of each carnation × number of carnations = total amount.
We will keep each option in the formula to find the correct choice.
Option 1
5×4 + 1.75×7
20 + 12.25
32.25 which is less than $35
Option 2
5×8 + 1.75×4
40 + 7
47 which is greater than total amount
Option 3
5×6 + 1.75×6
30 + 10.5
40.5 which is greater than total amount
Option 4
5×7 + 1.75×4
35 + 7
42 which is greater than total amount
Since only option 1 is less than total amount, it is the feasible and correct option.
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The complete question is -
Myra wants to buy flowers for her mom. Roses cost $5 each and carnations cost $1.75 each. If Myra has $35, how many roses and how many carnations can she buy?
4 roses and 7 carnations
8 roses and 4 carnations
6 roses and 6 carnations
7 roses and 4 carnations
hafiz poured 7/9 of the water in a tank into a basin and the rest into a pail. He then poured 1/2 liters of water from basin into the pail. Both the basin and the pail had an equal amount of water in the end. How much water was poured into the basin at first?
the rear windshield wiper blade on a car has a length of 11 inches. the blade is mounted on a 19 inch arm, 8 inches from the pivot point. if the wiper turns through an angle of 105 degrees, how much area is swept clean?
The area swept clean by the wiper blade is 221.128 square inches.
To find the area swept clean by the wiper blade, we can calculate the area of the sector of a circle that the blade moves through.
The radius of the circle that the blade moves through is the length of the arm, which is 19 inches.
The angle that the blade moves through is 105 degrees.
To calculate the area of the sector, we need to convert the angle to radians:
105 degrees * (π/180) = 1.8326 radians (rounded to 4 decimal places)
The area of the sector is then:
(1/2) * r^2 * θ = (1/2) * (19^2) * 1.8326 = 325.628 square inches (rounded to 3 decimal places)
However, the area swept clean by the wiper blade is not the full area of the sector, as the blade itself has a width of 11 inches. Therefore, we need to subtract the area of the triangle formed by the blade and the two radii of the sector that intersect at the blade's pivot point.
The length of one of the radii is the length of the arm, which is 19 inches. The length of the other radius is 19 - 8 = 11 inches since the blade is mounted 8 inches from the pivot point.
Using the formula for the area of a triangle:
(1/2) * base * height = (1/2) * 11 * 19 = 104.5 square inches
Therefore, the area swept clean by the wiper blade is:
325.628 - 104.5 = 221.128 square inches (rounded to 3 decimal places)
So the area swept clean by the wiper blade is approximately 221.128 square inches.
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Emma invested $90,000 in an account paying an interest rate of 3 3 8 3 8 3 % compounded daily. Juan invested $90,000 in an account paying an interest rate of 3 1 4 3 4 1 % compounded annually. After 17 years, how much more money would Emma have in her account than Juan, to the nearest dollar?
Emma would have approximately $4,723 more than Juan.
To solve given problem, we will use the formula for compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A = amount
P = principal investment
r = interest rate
t = number of years.
For Emma's account, we have:
P = $90,000
r = 3.375% = 0.03375 (since 3 (3/8) % is equivalent to 0.03375 as a decimal)
n = 365
t = 17 years
So, we can calculate the amount of money in Emma's account after 17 years as:
A = $90,000(1 + 0.03375/365)⁽³⁶⁵⁾⁽¹⁷⁾
A = $ 159,737.70
For Juan's account, we have:
P = $90,000
r = 3.25% = 0.0325 (since 3 (1/4) % is equivalent to 0.0325 as a decimal)
n = 1
t = 17 years
So, we can calculate the amount of money in Juan's account after 17 years as:
A = $90,000(1 + 0.0325)¹⁷
A = $155,014.93
Therefore, Emma would have more money in her account than Juan after 17 years by:
$ 159,737.70 - $155,014.93 = $4,722.77
Rounding to the nearest dollar, Emma would have approximately $4,723 more than Juan.
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g in estimation of the population variance of a variable, what statistic is used? z student's t chi squared thompson's tau
The statistic typically used in the estimation of the population variance of a variable is the sample variance, denoted by s².
The sample variance is a measure of the spread or dispersion of a set of data around its mean. It is calculated by taking the sum of the squared differences between each data point and the sample mean, and then dividing by the sample size minus one.
The sample variance is an unbiased estimator of the population variance, which means that its expected value is equal to the true population variance. However, the sample variance is not the only statistic used in the estimation of the population variance. Other statistics, such as the z-score, Student's t-test, chi-squared test, and Thompson's tau, may also be used in certain contexts depending on the specific research question and data characteristics.
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