Answer:
The answer is " [tex]C= \frac{5}{2x^2}+ 4xy - 2y^4.[/tex]"
Step-by-step explanation:
It given that, [tex]\frac {\partial(5x + 4y)}{\partial y} = \frac{\partial(4x- 8y^3)} {\partial x} \\\\[/tex] it is the differential equation.
Solve the above equation.
[tex]\frac {\partial M (x, y)}{\partial y} = (5x+ 4y)[/tex]
So, [tex]M (x, y) = \frac{5}{2x^2}+4xy +\varphi (y).[/tex]
[tex]\frac{\partial M (x, y)}{ \partial y }= 4x- 8y^3 \ and \ \ 4x + \varphi ' (y) = 4x- 8y^3 \\\\\ so, \ \\varphi ' (y) = -8y^3[/tex]
or [tex]\varphi (y) = -2y^4+c[/tex]
To find the general solution
[tex]M(x, y )= c \\C= \frac{5}{2x^2}+ 4xy - 2y^4.[/tex]
Which of the following is equivalent to tan(x) * csc(x) when simplified?
O
O
O
sec(x)
cos(x)
sin(x)
csc(x)
O
cot(x) + 1
Answer:
Sec(x)
Step-by-step explanation:
Tan(x) = Sin(x)/Cos(x)
Csc(x) = 1/Sin(x)
Sin(x) 1
--------- . ---------
Cos(x) Sin(x)
Sin(x) cancel
1
--------- =
Cos(x)
Sec(x)
The simplified expression is,
⇒ sec x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ tan x × csc x
Now,
We can simplify as;
⇒ tan x × csc x
⇒ ( sin x/ cos x ) × (1 / sin x)
⇒ 1 / cos x
⇒ sec x
Thus, The simplified expression is,
⇒ sec x
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Which best describes the complement of spinning any number less than 3?
spinning a 4
spinning a 3 or 4
spinning a 1 or 2
spinning a 1, 2 or 3
Answer:
spinning a 1 or 2
Step-by-step explanation:
less than 3 is 1 or 2
Answer:
B
Step-by-step explanation:
taking the test too
Katrina bought a package of 500 stickers. These sheet in the package has 20 stickers. 25% of the stickers on each sheet our hearts. The remaining stickers are stars. Select all the statements that are true. A Katrina has 100 heart stickers B Katrina has 375 star stickers C the package contains 20 sheets of stickers D 75% of the stickers on each sheet our stars see the number of heart stickers is the same number I start stickers
Answer:B
Step-by-step explanation:
Given
There are total of 500 stickers
Each sheet has 20 stickers out of which 25 % is Hearts and remaining are stars
So in each sheet 5 are hearts and 15 are stars
therefore in [tex]\frac{500}{20}=25[/tex] sheet
There are [tex]25\times 5=125[/tex] heart stickers
and [tex]25\times 15=375[/tex] star stickers
So statement B is true
Please help 15 points
Answer:
D) Alternate exterior angles
Step-by-step explanation:
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Use the Venn diagram to calculate probabilities.
Which probabilities are correct? Select two options.
P(AIC) =
PCB) = 0
PLA) =
PC)
PBIA) = 3
Corrected Question
These are the given probabilities. The Venn diagram is also attached. are (A) P(A|C) = 2/3
(B) P(C|B) = 8/27
(C) P(A) = 31/59
(D) P(C) = 3/7
(E) P(B|A) = 13/27
Answer:
A and C
Step-by-step explanation:
[tex]P(A|C)=\dfrac{P(A\cap C)}{P(C)}= \dfrac{14/59}{21/59}=\dfrac{14}{21}=\dfrac{2}{3}[/tex]
[tex]P(C|B) =\dfrac{P(C\cap B)}{P(B)}= \dfrac{11/59}{27/59}=\dfrac{11}{27}\neq \dfrac{8}{27}\\\\P(A) = \dfrac{31}{59}\\\\P(C) =\dfrac{21}{59}\neq \dfrac{3}{7}\\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{13/59}{31/59}=\dfrac{13}{31}\neq\dfrac{13}{27}[/tex]
From the above, only A and C are correct.
Answer: A and C
Step-by-step explanation:
Edg 2021
A graph shows the horizontal axis numbered 2 to 8 and the vertical axis numbered 10 to 50. A line increases from 0 to 4 then decreases from 4 to 9.
Which type of function best models the data shown on the scatterplot?
Answer:
Quadratic
Step-by-step explanation:
Took a test and got it right
Answer:
quadratic
Step-by-step explanation:
A country's balance of payments is divided up into three categories, the
current account, capital account and financial account. The current account
mainly measures
A) the flow of credit.
B) the flow of goods and services.
c) purchases and sales of nonfinancial assets.
D) purchases of sales of stocks and bonds and other financial assets.
Answer:
B) the flow of goods and services
Step-by-step explanation:
Balance of payments (BOP) is a statement of all transactions made between one country and the rest of the world at a particular period of time. It is also called balance of international payment. BoP is divided into current and capital account.
1. The current account: This is account of country's net trade in goods and services, net earnings on cross-border investments, and its net transfer payments. The current account measures the flow of goods and services.
2. The capital account: This is a country's imports and exports of capital and foreign aid. It can also be called financial account.
The sum of all transactions recorded in the balance of payments should be zero.
Balance of payment deficit is when a country's import is higher than its export.
Balance of payment surplus is when a country's export is greater than its import.
HURRY PLEASE
morgan poured 3/4 gallon of punch into each of 6 bottles. how many gallons of punch did she pour in all
Answer:
gallons of punch in all = 4.5 gallons
Step-by-step explanation:
Morgan poured 3/4 gallons of punch into each of 6 bottles . This means Morgan poured 3/4 gallons of punch in each of the available 6 bottle .
He pours 3/4 gallons of punch in 1 bottle . For 6 bottles the gallons of punch poured is calculated below
1 bottle = 3/4 gallons of punch
6 bottles = ? gallons of punch
cross multiply
gallons of punch in all = 3/4 × 6
gallons of punch in all = 18/4
gallons of punch in all = 9/2 gallons
gallons of punch in all = 4.5 gallons
The snack bar at the soccer field is charging $12 for 9 hamburgers. At that rate, how many hamburgers could you get for $20?
Answer:
6
Step-by-step explanation:
12 = 9 so u do 12 divided by 9
$20 to get 15 hamburgers. By dividing the price to produce one unit of your product by the number of items you have created, you can use the total variable cost.
locate total variables cost?By dividing the price to produce one unit of your product by the number of items you have created, you can determine the total variable cost.
Multiply the cost of producing one unit of your product by the total number of items you have produced to determine variable costs. Total Variable Costs = Cost Per Unit x Total Number of Units is the calculation for this cost.
For instance, if producing one unit of your product costs $12 and you produced 9 pieces, your total variable cost would be $12 x 9, or $108.
$12/9 = 1.34 then $20 to get 15 hamburgers.
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HELP!! pls pls pls
The average price of a movie ticket in 1990 was $4.22. Since then, the price has increased by approximately 3.1% each year. Write an exponential function to model this situation, then find the price of a ticket in 2016. Is this growth or decay?
Answer:
$9.33
Exponential growth.
Step-by-step explanation:
The formula for an exponential function is:
abˣ = y OR
a(1 + r)ˣ = y
a is the initial value (4.22)
r is the rate of increase (3.1% or 0.031 in dec. form) where 1 + r is b
x is the time (26 years)
y is the ending value.
If we plug those values in, the equation will turn out to be 4.22(1 + 0.031)²⁶ = y
Plug it into a calculator and you will get 9.333354216
This is exponential growth because x, the initial value, increases to get to y, the ending value.
Mr. De Leon's Geometry class has 34 students. After lunch everyone returns to the classroom. Within an hour, each person produces 800 BTUs. The room is 25 feet by 32 feet by 12 feet. How many BTUs per cubic foot were produced?
Plz provide the work.
Answer:
2.833 BTUs per cubic foot were produced.
Step-by-step explanation:
BTU's produced by one person = 800
No. of students = 34
Therefore no. of BTU's produced by 34 person = 800 * 34 = 27,200 BTU
Dimension of class 25 feet by 32 feet by 12 feet
Volume of class = length * width * height = 25 * 12 * 32 = 9,600 cubic feet
________________________________________________
BTUs per cubic foot produced = Total BTU's produced by 34 person/ Volume of class
Substituting the value of Total BTU produced and volume of class
BTUs per cubic foot produced = 27,200 BTU/ 9,600 cubic feet
= 2.833 BTUs per cubic foot
2.833 BTUs per cubic foot were produced.
Which sentence is written correctly? Kino said that if play practice does not start on time, the director “will be mad.” Kino said that if play practice does not start on time, the director “Will be mad”. Kino said that if play practice does not start on time, the director “will be mad”. Kino said that if play practice does not start on time, the director “Will be mad.”
The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."
Explanation:The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."
In this sentence, the verb "will" is correctly written in lowercase, as it is not a proper noun or the start of a sentence. Additionally, the punctuation marks, such as the quotation marks and the comma, are correctly placed.
It is important to use proper capitalization and punctuation to ensure clear and effective communication in writing.
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The Cartesian coordinates of a point are given.(a) (6, −6)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) = (b) (−1, 3)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) =
To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the equations (r, θ) = (√(x² + y²), atan2(y, x)).
Explanation:To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the following equations:
(r, θ) = (√(x² + y²), atan2(y, x))
(a)(i) For the Cartesian coordinates (6, -6),
(r, θ) = (√(6² + (-6)²), atan2(-6, 6))
(r, θ) = (√(36 + 36), atan2(-6, 6))
(r, θ) = (6√2, -45°)
(a)(ii) For the Cartesian coordinates (6, -6),
(r, θ) = (-√(6² + (-6)²), atan2(-6, 6) + π)
(r, θ) = (-6√2, -45° + π)
(b)(i) For the Cartesian coordinates (-1, 3),
(r, θ) = (√((-1)² + 3²), atan2(3, -1))
(r, θ) = (√(1 + 9), atan2(3, -1))
(r, θ) = (√10, 116.57°)
(b)(ii) For the Cartesian coordinates (-1, 3),
(r, θ) = (-√((-1)² + 3²), atan2(3, -1) + π)
(r, θ) = (-√10, 116.57° + π)
It was claimed that when tossing a fair coin 4 times it is quite likely to not obtain 2 heads and 2 tails. However, when tossing a fair coin 4,000 times one should expect to obtain number of tails in the range between 1940 and 2060. Let us compare the situation for 2 versus 2,000 coins. Let X be the number of heads when tossing a fair coin 2 times and let Y be the number of heads when tossing a fair coin 2,000 times.
1. P(940 ≤ Y ≤ 1,060) is equal to:______.2. E(X) is equal to:______.3. The standard deviation of X is equal to:______.4. E(Y) is equal to:_______.
Final answer:
The expected value of flipping a coin twice (X) is 1 head, with a standard deviation of 0.7071. The expected value of flipping a coin 2,000 times (Y) is 1,000 heads, but we cannot calculate P(940 ≤ Y ≤ 1,060) from the given information.
Explanation:
The question involves the concept of probability, expected value (E), and standard deviation (SD) in the context of flipping coins. We'll address each part of the query using basic probability and statistics principles.
P(940 ≤ Y ≤ 1,060) would require the use of the Central Limit Theorem for large sample sizes; however, with the information given, we cannot calculate this probability without additional statistical tables or tools, so we must refuse to answer this part.
The expected value of X, E(X), when flipping a coin twice would be the sum of products of each outcome's value and its probability. E(X) = (0 * 0.25) + (1 * 0.5) + (2 * 0.25) = 1.
The standard deviation of X requires calculating the variance first, then the square root of the variance. σ(X) = √[((0-1)^2 * 0.25) + ((1-1)^2 * 0.5) + ((2-1)^2 * 0.25)] = √(0.5) = 0.7071.
The expected value of Y, E(Y), when flipping a coin 2,000 times is simply 0.5 * 2,000 = 1,000 because the probability of a head for each flip is 0.5.
The probability P(940 ≤ Y ≤ 1,060) is approximately 99.63%, E(X) equals to 1, and the standard deviation of X is approximately 0.707. E(Y) is 1000.
To understand the probability and expectations for tossing fair coins, we will address your questions step by step.
P(940 ≤ Y ≤ 1,060) involves using the normal approximation to the binomial distribution.
For large numbers of coin tosses, the binomial distribution can be approximated by a normal distribution.
Since we are tossing the coin 2,000 times, our mean (μ) and variance (σ²) need to be calculated.
μ = n * p = 2000 * 0.5 = 1000 σ² = n * p * (1 - p) = 2000 * 0.5 * 0.5 = 500Hence σ ≈ 22.36.
Now, we standardize the range [940, 1060].
Z-score = (940 - 1000) / 22.36 ≈ -2.68 and (1060 - 1000) / 22.36 ≈ 2.68.From the Z-table, P(-2.68 ≤ Z ≤ 2.68) is approximately 0.9963, or 99.63%.
E(X) represents the expected number of heads when tossing 2 coins. Since each coin is fair and has a probability of 0.5 for heads,
E(X) = n * p = 2 * 0.5 = 1.Standard Deviation = √(n * p * (1 - p)). Here, n = 2, p = 0.5.
= √(2 * 0.5 * 0.5) = √0.5 = 0.707.E(Y) is the expected number of heads when tossing 2,000 coins. Similarly,
E(Y) = n * p = 2000 * 0.5 = 1000.Therefore, probability P(940 ≤ Y ≤ 1,060) is 99.63%, E(X) is 1, and the standard deviation is 0.707. E(Y) is 1000.
In a random sample of 125 highway bridges around the country, 75 were in need of repair.
What is the sample proportion (point estimate) of highway bridges that need repaired? (Only type ONE decimal place)
Answer:
The sample proportion of highway bridges that need repaired is 0.6.
Step-by-step explanation:
The sample proportion of highway bridges that need repaired is the number of bridges in need of repair divided by the number of bridges around the country.
In this question:
75 bridges in need of repair, out of 125. So
75/125 = 0.6
The sample proportion of highway bridges that need repaired is 0.6.
Spanky, Alfalfa, and Buckwheat sit down to take a geography test that has 12 multiple-choice questions. Each question has three possible answers, of which only one is correct. Alfalfa, as usual, has been spending too much time daydreaming about Darla and has not properly studied for the exam. After looking it over, he discovers that he knows the answers to just five of the questions. So, he answers those questions correctly and randomly guesses on the remaining seven. Afterward, as Miss Crabtree is grading Alfalfa’s exam, she selects one question at random and finds that he answered it correctly. What is the exact probability that Alfalfa actually knew the answer to this question? Answer this question by completing the following parts:a. Carefully construct a correct tree diagram using the letters K for the event that he knows the answer to a question, N for the event that he doesn’t know the answer to a question, and C for the event that he answers a question correctly. Also, label each edge with its exact probability (as either a fraction or a whole number).b. Use the definition of conditional probability to compute the exact value of P(K|C), writing your answer as a fraction in simplified form.
A car travels at an average speed of 52 mph. Jow long does it take to travel 169 miles?
To calculate the time it takes for the car to travel 169 miles at an average speed of 52 mph, divide the distance by the speed. The car would take approximately 3.25 hours.
Explanation:To calculate the time it takes for the car to travel 169 miles, we can divide the distance by the average speed. The formula for speed is:
Speed = Distance / Time
Rearranging the formula to solve for time, we get:
Time = Distance / Speed
Plugging in the values, we have:
Time = 169 miles / 52 mph
Calculating this, the car would take approximately 3.25 hours to travel 169 miles.
Plot the point (3 comma StartFraction 7 pi Over 4 EndFraction ), given in polar coordinates, and find other polar coordinates (r comma theta )of the point for which the following are true. (a) r greater than 0 comma negative 2 pi less than or equals theta less than 0 (b) r less than 0 comma 0 less than or equals theta less than 2 pi (c) r greater than 0 comma 2 pi less than or equals theta less than 4 pi
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for the step by step solution of the given problem.
The attached file have the solved problem.
Answer: B
Step-by-step explanation:
just did it
n is an integer and -2
Answer:
-1, 0,1
Step-by-step explanation:
Hope this helps.
A manager at a shipping company will purchase boxes in the shape of right rectangular prisms. He wants the volume of each box to be exactly 98 cubic feet. Which figure shows a box with the dimensions, in feet, that the manager will purchase?
The manager needs to select dimensions for a right rectangular prism that when multiplied together equal 98 to achieve a volume of 98 cubic feet. Possible dimensions could be 7 feet by 7 feet by 2 feet, or 14 feet by 7 feet by 1 foot.
The question pertains to calculating the volume of right rectangular prisms (boxes) and understanding the relationship between their dimensions and volume. To find a box with a volume of 98 cubic feet, one can use the formula for the volume of a right rectangular prism, which is Volume = length * width * height. The manager needs to identify the dimensions that, when multiplied together, equal 98. For instance, if a box has dimensions of 7 feet, 7 feet, and 2 feet, the volume would be 7 * 7 * 2 = 98 cubic feet, as required. Other possible dimensions could be 14 feet by 7 feet by 1 foot, as 14 * 7 * 1 also gives 98 cubic feet.
The mayor of a large city claims that the average net worth of families living in this city is at most $300,000. A random sample of 25 families selected from this city produced a mean net worth $288,000. Assume that the net worth of all families in this city have a normal distribution with the population standard deviation of $80,000. What is the parameter of interest?
Answer:
Check the explanation
Step-by-step explanation:
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 300000
Alternative Hypothesis, Ha: μ < 300000
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (288000 - 300000)/(80000/sqrt(25))
z = -0.75
P-value Approach
P-value = 0.2266
As P-value >= 0.05, fail to reject null hypothesis.
The parameter of interest is the average net worth of families living in the city. Hypothesis testing can be used to evaluate the mayor's claim using a random sample of households. The test statistic can be calculated using the sample mean, sample standard deviation, and sample size.
Explanation:The parameter of interest in this question is the average net worth of families living in the city. The mayor claims that the average net worth is at most $300,000. To determine if this claim is true, a random sample of 25 families is selected. The mean net worth of this sample is $288,000. This mean is an estimate of the population mean net worth.
Based on the information given, the population standard deviation of net worth for all families in the city is $80,000. This information allows us to perform hypothesis testing to evaluate the claim made by the mayor.
Null Hypothesis (H0): The average net worth of families living in the city is $300,000.Alternative Hypothesis (Ha): The average net worth of families living in the city is less than $300,000.Using the sample mean of $288,000, the sample standard deviation ($80,000), and the sample size (25), we can calculate the test statistic.The test statistic is calculated as follows:Test Statistic = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(Sample Size))
Plugging in the values:
Test Statistic = (288,000 - 300,000) / (80,000 / √25)
After calculating the test statistic, we can compare it to the critical value of the test (based on the desired significance level) to determine if we reject or fail to reject the null hypothesis. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the average net worth of families living in the city is less than $300,000.
By providing a random sample from the population, we can use hypothesis testing to evaluate the mayor's claim and determine if there is evidence to support it.
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The radial spokes of a bicycle tire are 13 inches long. What is the diameter of the tire?
Answer:
the answer is 5
Step-by-step explanation:
the
HELP ASAP timed question. A table is 4 ft high. A model of the table is 6 in high. What is the ratio of the height of the actual table to the helght of the model table? 3/2 8/1 2.3 1/8
Answer:
The ratio of the height of the actual table to the height of the model table is .
Step-by-step explanation:
As given
A table is 4 ft high. A model of the table is 6 in. high.
As
1 foot = 12 inch
Now convert 4 ft into inches .
4 ft = 4 × 12
= 48 inches
Height of the actual table = 48 inches
Now the ratio of the height of the actual table to the height of the model
table .
Therefore the ratio of the height of the actual table to the height of the model table is .
Do political science classes require less writing than history classes? The 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages. The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages. What can be concluded at the α = 0.01 level of significance?
Answer:
We conclude that political science classes require less writing time than history classes at 0.01 level of significance.
Step-by-step explanation:
We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.
The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.
Let [tex]\mu_1[/tex] = average writing time required by political science classes.
[tex]\mu_2[/tex] = average writing time required by history classes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1\geq\mu_2[/tex] {means that political science classes require more or equal writing time than history classes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex] {means that political science classes require less writing time than history classes}
The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_-_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample average pages of essay writing for political science classes = 16.3 pages
[tex]\bar X_2[/tex] = sample average pages of essay writing for history classes = 18.9 pages
[tex]s_1[/tex] = sample standard deviation for political science classes = 4.8 pages
[tex]s_2[/tex] = sample standard deviation for history classes = 5 pages
[tex]n_1[/tex] = sample of political science classes = 55
[tex]n_2[/tex] = sample of history classes = 54
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }[/tex] = 4.90
So, test statistics = [tex]\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }[/tex] ~ [tex]t_1_0_7[/tex]
= -2.77
The value of t test statistics is -2.77.
Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.
Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that political science classes require less writing time than history classes.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
Answer:
We need a sample size of at least 383.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
85% confidence level
So [tex]\alpha = 0.15[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.15}{2} = 0.925[/tex], so [tex]Z = 1.44[/tex].
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
We need a sample size of at least n.
n is found with [tex]M = 0.03, \pi = 0.21[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.44\sqrt{\frac{0.21*0.79}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.44\sqrt{0.21*0.79}[/tex]
[tex]\sqrt{n} = \frac{1.44\sqrt{0.21*0.79}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.44\sqrt{0.21*0.79}}{0.03})^{2}[/tex]
[tex]n = 382.23[/tex]
Rounding up
We need a sample size of at least 383.
To estimate the proportion of tenth graders reading at or below the eighth grade level with an 85% confidence level and a 0.03 margin of error, a sample size of 550 students is needed.
To estimate the fraction of tenth grade students with reading skills at or below the eighth grade level with an 85% confidence interval and a margin of error of at most 0.03, we use the following formula for sample size:
⇒ n = (Z² × p × (1 - p)) ÷ E²
Where:
Z is the z-value corresponding to the desired confidence level.p is the estimated population proportion (0.21).E is the desired margin of error (0.03).For an 85% confidence level, the z-value is approximately 1.44. Plugging in the values:
Calculate the numerator:⇒ Z² × p × (1 - p) = 1.44² × 0.21 × (1 - 0.21)
≈ 0.494668.
Calculate the denominator:⇒ E² = 0.03²
= 0.0009.
Divide the numerator by the denominator:⇒ 0.494668 ÷ 0.0009 ≈ 549.63.
Round up to the next integer: 550.Therefore, the required sample size is 550 students.
Complete question:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03? Round your answer up to the next integer.
Jean-Patrick found an old unopened bag of lawn fertilizer in his shed. The bag weighs 36 pounds, and the instructions claim it can cover 10,000 ft^2. If his lawn is 7,000 ft^2, how many pounds will he need? Round to the nearest tenth if needed.
Answer:
25.2
Step-by-step explanation:
Weight of one bag of lawn fertilizer = 36
area one bag of lawn fertilizer can cover = 10,000 ft^2
Total area of lawn in the given problem = 7,000 ft^2
no. of bags of lawn fertilizer needed to cover the lawn = total area of lawn in the given problem / area, one bag of lawn fertilizer can cover
= 7,000/10,000 = 7/10 = 0.7 bags
Weight of full bags has 36 pounds of lawn fertilizer.
therefore,
Pounds of lawn fertilizer in 0.7 part of bag = 36 * 0.7 = 25.2 pounds (Answer)
Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 735 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion?
Answer:
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1255, \pi = \frac{735}{1255} = 0.5857[/tex]
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 - 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.5584[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 + 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.6130[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Answer:
The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
Step-by-step explanation:
The interest is the real proportion of Americans who feel that the environment is a major issue with them. The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
Confidence interval
The confidence interval for the true proportion of interest is given by this:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
We want an interval at 95% of confidence, so then the significance level is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value for this case are:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
Replacing into the confidence interval formula we got:
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
Translate the triangle left 1 units and up 5 units. What are the coordinates of point C after the translation?
Answer:
b++nfr
Step-by-step explanation:
jjkiki
After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 48 times, recording the number of times each face appears. Do these results cast doubt on the die is fairness
Answer:
The results are
Face Count Face Count
1 6 4 9
2 12 5 5
3 8 6 20
These results are not fair, because they clearly shows that the dice was tricked. We deduct this by observing that he obtained the face 6, 20 times out of 48, which represents 42% of chances to get that result.
Now, a fair dice must have equal probabilities per side, or an approximation to that at least. In this case, we don't have such equality.
So, next time your little brother roll the dice, we probably will get 6.
To check the fairness of a die, use statistical testing. Expect each face to appear equally in a fair die. Discrepancies suggest possible bias, but randomness can make results vary. Conduct a hypothesis test, like Chi-square, for a more statistically sound conclusion.
Explanation:To verify the fairness of the die, we need to conduct a hypothesis test. With a fair six-sided die, each face (numbered 1 to 6) should have an equal probability of appearing on any given roll. That means, if you roll the die 48 times, each face should theoretically appear about 8 times (48 rolls divided by 6 faces).
If the observed frequency of each face being rolled significantly varied from 8, it would suggest that the die might be biased. However, keep in mind that random chance can also result in each face not appearing exactly 8 times. Therefore, a hypothesis test would have more statistical power if more repetitions were performed.
Conduct the hypothesis testing by comparing your observed frequencies to the expected frequencies using a Chi-square test. This would provide a more quantitative and concrete conclusion about whether the die is biased or fair.
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14/10 divided by blank equals seven
Answer:
14/10=1.4
7/1.4=5
1.4x5=7
Step-by-step explanation:
In the given equation 14/10 divided by a certain number equals seven, the missing number is 0.2
Explanation:The subject of this question is Mathematics and it appears to be suitable for a Middle School grade level. You're asking for a number that, when 14/10 or 1.4 is divided by it, the result is seven.
To solve it, one can set it up as an equation in the form of 1.4 / x = 7. To find 'x', multiply both sides by 'x' to get rid of 'x' on the denominator of the left side, so the equation becomes 1.4 = 7x. The next step is to isolate 'x' by dividing both sides of the equation by 7. Solving this equation gives x = 1.4/7 = 0.2.So, 14/10 divided by 0.2 equals seven.
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