Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The best estimatr for the proportionis 0.5 since we don't have any other info provided. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
I’m Confused On The Question
Choose the correct way to simplify 4(5-3) using the distributive property of multiplication over subtraction.
━━━━━━━☆☆━━━━━━━
▹ Answer
20 - 12 or 8 (depending on what you need to find)
▹ Step-by-Step Explanation
4(5 - 3)
Distribute 4 * 5 and 4 * -3
This will give 20 - 12
If you are looking for the final answer, it would be 8.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2-4n/3
Answer:
(n- 2/3)²
Step-by-step explanation:
Perfect square trinomial is: a²+2ab+b²= (a+b)²We have:
n² - 4n/3It can be put as:
n² -2×n×2/3Here we consider n = a and -2/3 = b, then
b²= (-2/3)²= 4/9Now we add 4/9 to a given binomial to make it perfect square:
n² - 2×n×3/2 + 4/9= (n- 2/3)²So, added 4/9 and got a perfect square (n- 2/3)²
Round 2826 to the nearest hundred.
Answer:
2800
Step-by-step explanation:
2826 to the nearest hundred is 2800
A circle is shown. Angles 3 and 4 intersect an arc with a measure of 106 degrees. Angles 1 and 2 intersect an arc with measure 58 degrees. Is the measure of ∠1 equal to the measure of ∠2? Why?
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
3.A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly
Answer:
Probability of answering 5out of 10 correctly= 0.246
Step-by-step explanation:
Total question answered= 2
Question answered correctly= 1
Probability of answered correctly= 1/2
Probability of answered correctly= 0.5
Probability of answered incorrectly = 0.5
Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5
Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5
Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)
Probability of answering 5out of 10 correctly= 0.246
plz answer question in screen shot
Answer:
tan theta = 2 sqrt(5) /15
Step-by-step explanation:
sin theta = opp / hypotenuse
sin theta = 2/7
We can use the Pythagorean theorem to find the length of the adjacent side
a^2 + b^2 = c^2
2^2 +adj^2 = 7^2
4 + adj^2 = 49
adj ^2 = 49-4
adj^2 = 45
Taking the square root of each side
adj = sqrt(45) = sqrt(9*5) =sqrt(9) sqrt(5) = 3 sqrt(5)
The tan theta = opp/ adj
tan theta = 2 / 3 sqrt(5)
Multiply by sqrt(5) / sqrt(5)
= 2 sqrt(5) / 3 *5
= 2 sqrt(5) /15
Question
Drag each description to the correct location on the table.
Examine the equation to determine if the descriptions listed are key features of the function or not.
Answer:
Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.
Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.
Step-by-step explanation:
How do you write 416.7 in scientific notation? ___× 10^____
Answer:
4.167(10²)
Step-by-step explanation:
Step 1: Put number into proper decimal form
416.7 = 4.167
Step 2: Figure out exponent
Since we are moving the decimal places 2 places to the right, our exponent is 2
Answer:
4.167 × 10^2
Step-by-step explanation:
= 4.167 × 10^2
(scientific notation)
= 4.167e2
(scientific e notation)
= 416.7 × 10^0
(engineering notation)
(one)
= 416.7
(real number)
In how many ways can you arrange the black and white kings on an empty chess board to get an acceptable position (according to standard chess rules)
Answer:
Number of ways = 3612 ways
Step-by-step explanation:
I have attached a diagram representing two scenarios on the chess board. The scenarios are; when the first king takes away 4 squares (label A) while the second scenario is when it takes 6 squares (label B).
Now, If the white king is in a corner, it has 4 possibilities while the black king can be at any of (64 − 4 =) 60 positions.
If the white king is at the boundary, but not in a corner which is 24 possibilities, the black king can be at any of (64 − 6 =) 58 positions
Finally, in all other cases, for the white king which has 36 possibilities, the black king can be at any of (64 − 9 =) 55 positions.
So, in total, the number of ways would be;
(60 × 4) + (58 × 24) + (55 × 36) = 3612 ways
f(x) = 5x^2 + 2, find the inverse
Hey there! :)
Answer:
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]
Step-by-step explanation:
Given:
f(x) = 5x² + 2
Switch the x and y variables in the equation:
x = 5y² + 2
Subtract 2 from both sides:
x - 2 = 5y²
Divide 5 from both sides:
[tex]\frac{1}{5}(x-2) = y^{2}[/tex]
Square root both sides:
y = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]
**Make sure to add a ± sign when finding the inverse of a parabolic function.
Therefore, the inverse of this function is:
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16.
a. Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?
H0:
-mu is greater than or equal to $108.50
mu is greater than $108.50
mu is less than $108.50mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50
Ha: -
-mu is greater than or equal to $108.50
mu is greater than $108.50mu is less than $108.50
mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50
b. Test to determine if whether or not the average room price is significantly different from $108.50, using an alpha level of .05.
Reject H0
or
Fail to reject H0
Answer:
Step-by-step explanation:
H0: mu is equal to $108.50
Ha: mu is not equal to $108.50
This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.
z = x-u / sd/√n
Where x is $112, u is $108.50 sd is $16 and n is 64
z = 112-108.50 / 16/√64
z = 3.5/(16/8)
z = 3.5/2
z = 1.75
To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50
evaluate 25.1 * 2.51 in two decimal places
Answer:
63.00
Step-by-step explanation:
25.1 × 2.51
Multiply.
= 63.001
Round to two decimal places.
63.00
Answer:
63.00
Step-by-step explanation:
when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00
A fair coin is flipped 1000 times. What is the approximate probability that heads comes up at most 600 times?
0%
100%
50%
60%
Answer:
50%
Step-by-step explanation:
Answer:
60%
Step-by-step explanation:
Heads coming up at most 600 times when a fair coin is flipped 1000 times.
600/1000
= 0.6
0.6 × 100
= 60
A particular fruit's weights are normally distributed, with a mean of 212 grams and a standard deviation of 20 grams.
If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
Answer:
220 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 212, \sigma = 20, n = 22, s = \frac{20}{\sqrt{22}} = 4.264[/tex]
If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.88 = \frac{X - 212}{4.264}[/tex]
[tex]X - 212 = 1.88*4.264[/tex]
[tex]X = 220[/tex]
The answer is 220 grams.
A simple random sample of 44 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.31 and the sample standard deviation is 0.51 . Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4 comma which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?
Answer:
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean is significantly less than 5.4.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]
The significance level is 0.05.
The sample has a size n=44.
The sample mean is M=5.31.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=44-1=43[/tex]
This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]
As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
help with this I don't know how to solve please and thank you !!!
Answer:
tan∅ = 3√29/10
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
cos∅ = adjacent/hypotenuse
Since we are given cos∅ = 10/19, we know that one leg is 10 and the hypotenuse is 19. We need to find the missing leg length:
10² + b² = 19²
b² = 19² - 10²
b = √261
b = 3√29
We know that tan∅ equals opposite over adjacent. Our adjacent is given to us by cos∅, so we simply plug in our values:
tan∅ = opposite/adjacent
tan∅ = 3√29/10
Need Help
*Show Work*
The correct answer is $216
Explanation:
The chart shows the price users need to pay for visiting the museum or riding on the train. This includes a difference in price between adults and students. However, as the club includes only students (27 students) the price that should be considered are $3 for visiting the museum and $5 for the train ride. Additionally, you can know the total the student spend if you multiply the prices by the total number of students.
27 (number of students) x $3 (price for visiting the museum) = $81 (total for visiting the museum)
27 (number of students) x $5 (price for the train ride) = $135 (total for the train ride)
Additionally, you will need to add both results to know the total: $81 + $135 = $216
You can also get the same result if you consider each student will spend $8 (price for visiting the museum and for the train ride) and then multiply this by the number of students ($8 x 27 = $216)
A geometric series has second term
375 and fifth term 81. The nth term
of the series is Un. Find the value of
un
n = 6
Answer: 243/5 = 48.6
Step-by-step explanation:
a₁, 375, a₃, a₄, 81 , a₆
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₆ which is one multiple from 81.
[tex]a_6=81\bigg(\dfrac{3}{5}\bigg)^1\\\\\\.\quad =\large\boxed{\dfrac{243}{5}}[/tex]
A veteran treated 7 dogs this morning. The list gives the weights in pounds of each dog 41,36,20,36,62,5,6 find the range of the data set
Answer:
57
Step-by-step explanation:
The range of a data set is
Largest data value - Smallest data value
62 - 5
= 57
The range of the data set is 57 pounds.
Answer:
[tex]\boxed{\red{57}}[/tex]
Step-by-step explanation:
[tex]\blue {range \: \: of \: \: a \: \: data \: \: set \: \: means}[/tex]
you have to subtract the smallest value from the largest value in the data set.
[tex]\boxed{\green{largest \: \: value - smallest \: \: value}} \\ \boxed{\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 62 - 5}} \\ \: \: \: \: \: \: \: \: \boxed{\pink{ =57}}[/tex]
Need help asap please!!!!!!
Answer:
C.
Step-by-step explanation:
Area of a Sector Formula: A = x/360πr²
Since we are given x and r, simply plug it in:
A = 40/360π(4)²
A = 1/9π(16)
A = 16π/9
Answer:
[tex] \frac{16\pi}{9} {cm}^{2} [/tex]Option C is the correct optionStep-by-step explanation:
[tex]angle \: theta = 40 \: degree \\ theta = 40 \times \frac{\pi}{180 } \\ theta = \frac{2\pi}{9} [/tex]
Radius= 4 cm
[tex]area = \frac{1}{2} \times theta \: \times {r}^{2} \\ \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times \frac{2\pi}{9} \times {4}^{2} \\ \: \: \: \: \: \: \: \: = \frac{1}{2} \times \frac{2\pi}{9} \times 16 \\ \: \: \: \: \: \: \: = \frac{16\pi}{9 \: {cm}^{2} } [/tex]
Hope this helps....
Good luck on your assignment...
Determine the best answer
6 points
MULTIPLE CHOICE Find the length of BC. (Lesson 10-2)
B
21 cm
C
168°
A 18°
C 168°
B 2.20 cm
D 30.79 cm
A
Answer:
angle of bc= 180-168= 12°
length of bc= 12/360 × π × diameter
= 12/360 × 22/7 × 21
= 12/360 × 66
= 2,20 cm (b)
Find the value of Z such that 0.11 of the area lies to the right of Z.
Round your answer to 2 decimal places.
Answer:
1.23
Step-by-step explanation:
"Appropriate technology" makes short work of this.
how do you solve this problem
Answer:
more info is needed
Step-by-step explanation:
What is the height, X, of the equilateral triangle ? (Help)
Answer:
A. 7√3 in
Step-by-step explanation:
We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:
tan60° = x/7
x = 7tan60°
x = 7√3
Answer:
It's A
Step-by-step explanation:
Which of the following is the missing side length that completes the
Pythagorean triple below?
5, 12,
Answer:
13
Step-by-step explanation:
We can find the missing side length by using the pythagorean theorem
a² + b² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
So, 13 is the missing side length.
The reciprocal function of sine is: A. cosine B. cosecant C. secant D. tangent
Answer:
The reciprocal is cosecant that is option B
The reciprocal function of sine is cosecant.
What is a reciprocal function?It is the opposite of a function meaning by if a function is f(x) then the reciprocal function will be 1/f(x).
What is a trigonometric function?They are real function which relates with the angle of a right angle triangle to ratios of two sides.
How to find the reciprocal function?We have to find the reciprocal function of sine.
f=sine
Reciprocal of f=1/sine
=cosecant
Hence the reciprocal of sine is cosecant.
Learn more about trigonometry at https://brainly.com/question/24349828
#SPJ2
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→[infinity] x4e−x3
Here the l'Hospital's Rule is appropriate, as the limit is in the form [tex]\infty / \infty[/tex]. Take a look at the procedure below -
[tex]\lim_{x \to \infty} x^4e^{-x^3} = \lim_{x \to \infty} \frac{x^4}{e^{x^3}}[/tex],
At this point, one can conclude that the solution should " boil down " to the expression [tex]4 / \infty[/tex], and thus the solution is 0.
Hope that helps!
TIME REMAINING
53:46
What is the value of c?
O 4 units
5 units
6 units
0 7 units
Mark this and retum
Save and Exit
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Submit
WY = a = 4
ZY = b = 3
As WYZ is forming a right angle triangle, therefore, we can use pythagorean theorem to find the value of c
a2+b2=c2 (4)2+(3)2=C2 16+9=C2 C2=25
Taking square root on both sides
√c2= √25 c=5
The value of c is 5 units.
The value of c is 5 units
The complete question is an illustration of a right-triangle, where the equation to calculate the value of c is:
c^2 = a^2 + b^2
The equation becomes
c^2 = 3^2 + 4^2
Evaluate the exponents
c^2 = 9 + 16
Evaluate the sum
c^2 = 25
Take the square root of both sides
c =5
Hence, the value of c is 5 units
Read more about right-triangles at:
https://brainly.com/question/2437195
In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies.
Answer:
A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
Step-by-step explanation:
We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.
Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 94.3
n = sample of car drivers = 16
[tex]\mu[/tex] = population mean number of chips in a bag
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95 {As the critical value of t at 15 degrees of
freedom are -2.131 & 2.131 with P = 2.5%}
P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95
P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]
= [1187.96, 1288.44]
Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].