Step-by-step explanation:
Assuming c is the hypotenuse:
c = √(a² + b²)
c = 22.1
tan A = a/b
A = 36.7°
tan B = b/a
B = 53.3°
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.
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]
FOR BRAINLIEST ANSWER IF CORRECT Find an equation of the line passing through the pair of points. Write the equation in the form Ax + By = C. (-7,9) and (-8,-8)
Answer:
-17x + y = 128
Step-by-step explanation:
First, find the slope.
[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{9-(-8) }{-7-(-8)}\\m=\frac{9+8 }{-7+8}\\m=\frac{17}{1} \\m=17[/tex]
Now, use point-slope form to find the equation.
y - y = m(x - x)
y - 9 = 17(x - (-7))
y - 9 = 17(x + 7)
y - 9 = 17x + 119
y = 17x + 128
Since your equation needs to be in Ax + By = C form, rearrange the equation so that the x and y values are on the left side of the equation.
y = 17x + 128
-17x + y = 128
Use the upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.)
y = 1 − x2
upper sum __________
lower sum ___________
Answer:
upper sum= 0.859
lower sum = 0.659
Step-by-step explanation:
y = √(1 − x²)
if n= 5
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.
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.
Line A has equation 3x-4y=5
Line B goes through the points (4, 7) and (–1, 3)
Are lines A and B parallel?
(4 marks)
Gradient of Line A (as a decimal):
Gradient of Line B (as a decimal):
Therefore the lines parallel
Step-by-step explanation:
line A can be written as y1= 3/4.x -5/4
line B is a linear function : y2= ax +b
4a+b=7 and -a +b =3 so a=4/5 and b=19/5
so y2=4/5x +19/5
so they are not parallel
Line A goes through (0,-5/4) and (1,-1/2)
Gradient of line A = G1= (-1/2 - (-5/4))/(1-0) =3/4=0.75
Gradient of line B= G2= (7/3)/(4-(-1))=4/5=0.8
The Line A and Line B are not parallel to each other.
Equation of line :The equation of line A is,
[tex]3x-4y=5[/tex]
Now write in slope intercept form,
[tex]3x-4y=5\\\\4y=3x-5\\\\y=\frac{3}{4} x-\frac{5}{4}[/tex]
Slope of line A is [tex]\frac{3}{4}[/tex].
Equation of line B is,
[tex]y-7=\frac{3-7}{-1-4}(x-4) \\\\y-7=\frac{4}{5} x-\frac{16}{5}\\ \\y=\frac{4}{5} x+\frac{19}{5}[/tex]
Slope of line B is [tex]\frac{4}{5}[/tex]
Since, the slope of both line A and B are different. therefore, Line A and Line B are not parallel to each other.
Learn more about the parallel lines here:
https://brainly.com/question/24607467
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
2) Find the diameter.
4) If the diameter is equal to 3 inches ,d=
Answer:
d = 3 in
Step-by-step explanation:
Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.
I’m Confused On The Question
If you average your costs over your total production, you get the average cost, written C: C(x, y) = C(x, y) x + y . Find the average cost for the cost function C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−0.01(x + y).
Answer:
Average cost
= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)
Step-by-step explanation:
Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.
If total cost = C(x, y)
Average cost = C(x, y) ÷ (x+y)
For this question, total cost function is
C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾
The average cost is simply this total cost function divided by the total number of units produced.
Average cost
= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)
If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.
Hope this Helps!!!
Which of the following is not a congruence theorem or postulate? A. SSS B. SAS C. SSA D. AAS
Answer:
SSA the only other right one missing is ASA
the lines given by the equations y=2x and y=4x+1 are
Answer:
A
Step-by-step explanation:
For lines to be parallel, their slopes need to be the same.
For lines to be perpendicular, the product of their slopes needs to be -1.
None of these conditions are met since the slopes are 2 and 4 respectively.
Sooo.... The answer must be A! :)
Answer:
The lines given are neither perpendicular nor are they parallel.
Step-by-step explanation:
In order for two lines to be be parallel, they must have the same slope but different y-intercepts. In order for two lines to be perpendicular, one line has to have a slope that is the negative reciprocal of the other line.
We are given two line equations.
y = 2x
y = 4x + 1
These lines do not represent a perpendicular situation nor do they represent a parallel situation.
Shrinivas deposited $1300 in an account which pays 8% annual interest, compounded continuously. How long will it take to reach $3500?
Select one:
O a. 12.4 years
O b. 9.2 years
O c. 176 years
O d. 1.2 years
Answer: a. 12.4 years
Step-by-step explanation:
Function to represent exponential growth continuously:
[tex]A=A_0e^{rt}[/tex] ...(i)
, where [tex]A_0[/tex] = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.
As per given , we have
[tex]A_0=\$1300\\\\r=8\%=0.08\\\\ A=\$3500[/tex]
To find : t
Put all values in (i) ,
[tex]3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}[/tex]
Taking natural log on both sides
[tex]\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4[/tex]
Hence, it would take 12.4 years.
so, the correct option is a. 12.4 years .
Which equation describes the same line as y- 6 = -4(x + 1)?
A. y=-4x- 4
B. y= -4x+ 2
C. y = -4x+3
O D. y=-4x+7
SUBMI
Answer:
B. y=-4x+2
Step-by-step explanation:
y-6=-4x-4
y=-4x-4+6
y=-4x+2
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)
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
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.
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:
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
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
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
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!
What is the value of X in equation? 1/3 X - 2/3 = - 18
Answer:
x=-52
Step-by-step explanation:
1/3x=-17 1/3
x=-52
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:
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
Want Brainliest? Get this correct Which of the following is the product of the rational expressions shown below?
Answer:
[tex]\frac{12}{x^2 +7x}[/tex]
Step-by-step explanation:
Simply multiply straight across which you get
12/X X × ( X +7 )
Then just multiply X into the parenthesis
Hope this helps :)
nikki grows 12 tomato plants. she measures their heights to the nearest centimetre, and writes them down. Complete the frequency table.
Answer:
Nikki grows 20 tomato plants and she measures their heights.
We want to complete the frequency table.
All we have to do is count the number of values that fall between each range.
The values are:
5 10 12 16 14
17 20 15 10 7
13 11 6 18 15
6 12 17 8 12
Height Frequency
-> 5 ≤ h < 10 5
10 ≤ h < 15 8
15 ≤ h < 20 6
20 ≤ h < 25 1
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]