Answer:
See below.
Step-by-step explanation:
So, we have:
[tex]\sec(\theta)=-2/\sqrt{3}[/tex]
Recall that secant is simply the reciprocal of cosine. So we can:
[tex]\cos(\theta)=(\sec(\theta))^{-1}=(-2/\sqrt{3})^{-1}\\\cos(\theta)=-\sqrt{3}/2[/tex]
Now, recall the unit circle. Since cosine is negative, it must be in Quadrants II and/or III. The numerator is the square root of 3. The denominator is 2. The whole thing is negative. Therefore, this means that 150 or 5π/6 is a candidate. Therefore, due to reference angles, 180+30=210 or 7π/6 is also a candidate.
Therefore, the possible values for theta is
5π/6 +2nπ
and
7π/6 + 2nπ
x(x+3)(x+3)=0 Please I NEED HELP FAST! PLLLLLLLLLLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
Answer:
[tex]\boxed{x^3+6x^2+9x}[/tex]
Step-by-step explanation:
[tex]x(x+3)(x+3)[/tex]
Resolving the first parenthesis
[tex](x^2+3x) (x+3)[/tex]
Using FOIL
[tex]x^3+3x^2+3x^2+9x[/tex]
Adding like terms
[tex]x^3+6x^2+9x[/tex]
[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]
[tex]x(x+3)(x+3) =0[/tex]
[tex]\boxed{x_1 =0}[/tex]
[tex]x_2+3 =0[/tex]
[tex]\boxed{x_2 = -3}[/tex]
[tex]x_3+3 =0[/tex]
[tex]\boxed{x_3 = -3}[/tex]
Select the correct answer. Sarah wants to print copies of her artwork. At the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies. How much would it cost Sarah to make 100 copies? A. $15 B. $20 C. $25 D. $30
$1 = 5copies means
$5 = 25 copies obviously
then
$x = 100 copies
100 / 5 = $x
so she needs
$20
The cost of printing 100 copies of artwork is $20.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost $10, So the cost of 1 pen is (10/2) = $5.
From this unitary cost of pens, we can determine the cost of any no. of pens by multiplying the unit cost by the no. of pens.
Given, The cost of printing 5 artworks is $1.
∴ The cost of printing 100 copies is $(100/5),
= $20.
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The population of Oak Forest is increasing at a rate of 4% per year. If the population is 74,145 today, what will it be in three years?
Answer:
83,403
Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.
Hope this helps!
Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to four decimal places, as needed.
xbar = 8.8 sx = 1.5 sy = 1.8 ybar = 30.3
r = -0.84
Download data
Regression line equation: y = ______ + _______ x
Answer: Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Step-by-step explanation:
Equation of least-squares regression line for predicting y :
[tex]\hat{y}=b_1x+b_o[/tex]
, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] , [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]
Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]
Then,
[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]
Now,
[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]
Then, Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2
Answer:
The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
Step-by-step explanation:
GIven that :
[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]
This implies that the distance between the x-axis and the axis of the rotation = 2 units
The distance between the x-axis and the inner ring is r = (2+sec x) -2
Let R be the outer radius and r be the inner radius
By integration; the volume of the of the solid can be calculated as follows:
[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]
[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]
[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
A student is using the elimination method to solve the system of equations below. What is the best first
step?
4x - 5y = 2
2x + y = -3
Answer:
The best first step would be to multiply the second equation by -2
Step-by-step explanation:
The best first step would be to multiply the second equation by -2
then you would have the following
[tex]\ \ \ \ \ \ 4x - 5y = 2 \\-2*(2x)+ (-2)*y = (-2)*3[/tex]
and when you multiply it is easy to eliminate because you will get
[tex]4x - 5y = 2 \\-4x -2y = 6[/tex]
and if you sum the equations you get
-7y = 8
so that is a single variable equation which is easier to solve.
Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below
11.3 10.6 11.7 9.7 11.7 9.5 11.7
What is the mean score? Select the correct choice below and fill in any answer box to complete your choice
A. The mean score is Round to one decimal place as needed.)
B. There is no mean score. Does the mean represent the center of the data?
A. The mean represents the center
B. The mean does not represent the center because it is the smallest data value.
C. The mean does not represent the center because it is not a data value.
D. The mean does not represent the center because it is the largest data value.
What is the median score? Select the correct choice below and fill in any answer box to complete your choice.
A. The median score is 0
B. There is no median score.
Does the median represent the center of the data? (Round to one decimal place as needed.)
A. The median represents the center.
B. The median does not represent the center because it is not a data value. °
C. The median does not represent the center because it is the largest data value.
D. The median does not represent the center because it is the smallest data value.
What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice
A. The mode(s) of the scores is (are)
B. There is no mode. Does (Do) the mode(s) represent the center of the data?
(Use a comma to separate answers as needed.)
A. The mode(s) represent(s) the center
B. The mode(s) can't represent the center because it (they) is (are) not a data value.
C. The mode(s) does (do) not represent the center because it (one) is the largest data value.
D. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Answer:
Step-by-step explanation:
Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.
Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7
Mean = 76.2/7
Mean = 10.9
The mean score is 10.9 to 1 decimal place.
Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.
b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;
9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7
After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.
The median represents the center
c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.
The mode(s) does (do) not represent the center because it (one) is the largest data value.
22,403 Check:
- 8,675
how i do this
Answer:
Hello!! :) The answer to your question is 13,728
Steps will be below.
Step-by-step explanation:
So we will subtract 22,403 and 8,675.
When we do that we will get 13,728
To check your answer we have to do the opposite of subtracting which will be adding.
This is how we check our work: the answer we got was 13,728...we have to take that answer and add it to 8,675 which will give us 22,403
(Both of the numbers are from the question)
At the bottom I attached a picture of how I did the subtracting and how I checked my work.
Sorry for my handwriting......if you can’t understand my handwriting, I attached another picture which is more clearer.
ANSWER TO YOUR QUESTION: 13,728
Brainliest would be appreciated! Thank you :3
Hope this helps! :)
Answer:
The answer is 13,728
Step-by-step explanation:
Check your work with addition.
Line j is a straight line. Which equation represents the relationship between the measures of Angle w and Angle z? A) Measure of angle w = measure of angle z b) Measure of angle w + measure of angle z = 90 degrees c) Measure of angle w + measure of angle z = 100 degrees d) Measure of angle w + measure of angle z = 180 degrees
Answer:
Measure of angle W + measure of angle Z = 180°
Step-by-step explanation:
The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)
Answer:
D is your answer
Step-by-step explanation:
I have no explanation
Determine which of the following statements is true. A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V. B: If there exists a set that spans V, then dim V = 3. C: If H is a subspace of a finite-dimensional vector space V, then dim H ≤ dim V
Answer:
A. This statement A is false.
B. This statement A is false.
C. This statement is true .
Step-by-step explanation:
Determine which of the following statements is true.
From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.
SO;
A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V
This statement A is false.
This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V
B. If there exists a set that spans V, then dim V = 3
The statement B is false.
If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V) spans V. ∴ dim V < 3
C. If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
This statement is true .
We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.
SO,
If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
You have $50,000 in savings for retirement in an investment earning 5% annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal?
Answer: It will take you about 61 years for you to reach your goal.
Step-by-step explanation:
We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.
We could represent the whole situation by the equation.
y= [tex]50,000(1.05)^{x}[/tex] where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.
1,000,000 = 50,000(1.05)^x divide both sides by 50,000
20 = (1.05)^x
x= 61.40
What is the value of x in the diagram below?
A.
6
B.
4
C.
5
D.
3
Answer:
[tex]\boxed{3}[/tex]
Step-by-step explanation:
We can use ratios to solve since the sides are proportional.
[tex]\frac{18}{x} =\frac{48}{8}[/tex]
Cross multiply.
[tex]48x=18 \times 8[/tex]
Divide both sides by 48.
[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]
[tex]x=3[/tex]
The value of x in the given triangle is 3.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given are two similar triangles,
Therefore, they have the same ratio of corresponding sides
18/48 = x/8
x = 3
Hence, The value of x in the given triangle is 3.
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a box contains 20 blue marbes, 16 green marbles, and 14 red marbles. two marbles are selected at random. let 3 be the event that first marbke selected is green. find p(fe) g
Answer:
Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.
Step-by-step explanation:
Example 2: The GPAs of 20 students are listed.
Make a stem-and-leaf plot for this data.
1.8 2.9 0.9 4.0 3.3
2.4 2.3 1.6 1.6 4.0
1.7 0.5 3.6 3.4 1.9
4.0 2.1 1.9 1.1 0.5
How do I make a stem and leaf plot for these numbers?
Answer/Step-by-step Explanation:
To create a stem-and-leaf plot for the GPAs of the 20 students that were listed in the above question, take the following steps:
Step 1: for easy plotting, write down the GPAs in an ordered manner, that is, from the smallest value to the largest.
0.5, 0.5, 0.9, 1.1, 1.6, 1.6, 1.7, 1.8, 1.9, 1.9, 2.1, 2.3, 2.4, 2.9, 3.3, 3.4, 3.6, 4.0, 4.0, 4.0
Step 2: divide each set of data into a stem and a leaf. For example, for a GPA, 0.5, 0 would be the stem, while 5 would be the leaf.
For a GPA listed, 2.9, 2 is the stem, 9 is the leaf. Same applies to all the other GPAs.
Step 3: All stems should be written in ascending order, vertically, from the smallest to the largest. From the listed GPAs, you would observe that the highest stem value would be 4, while the lowest would be 0.
Therefore, write down your stems vertically, in ascending order as shown below:
0 |
1 |
2 |
3 |
4 |
Step 4: All leaves should be written also in ascending order to their corresponding stem, from the smallest to the largest, as shown below:
Stem | Leaf
0 | 5 5 9
1 | 1 6 6 7 8 9 9
2 | 1 3 4 9
3 | 3 4 6
4 | 0 0 0
Thus,
0 | 5 5 9 represents => 0.5, 0.5, 0.9
*See attachment below for the stem-and-leaf plot.
The sides of a number cube have the numbers 9, 3, 5, 3, 7, and 9. If the cube is thrown once, what is the probability of rolling a number less than 10?
Fraction:
Decimal:
Percentage:
Likelihood of the event happening:
URGENT!!!!!! A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame? REPLY IN COMMENTS PLEASE IM GLITCHING AND CANT SEE ANSWERS
Answer:
the perimeter of the square is just "(5+2x)(2)+(7+2x)(2)
Step-by-step explanation:
Answer:
2 × 10 + 2 × 14
Step-by-step explanation:
The frame is given to have measurements 2 times that of the photograph's measurements. We also know that the photograph is given by dimensions being 5 inch by 7 inch. Therefore the measurements of the frame should be 5 [tex]*[/tex] 2, which = 10 inches, by 7 [tex]*[/tex] 2 = 14 inches.
So the dimensions of the frame are 10 inch × 14 inch. As the frame is present as a rectangle, the perimeter is given by two times both dimensions together. That would be represented by the expression " 2 × 10 inch + 2 × 14 inch. " In other words you can say that the expression is 2 × 10 + 2 × 14 - the expression that represents the perimeter of the frame.
please answer this for me. i have no idea :( please please please, i am desperate.
================================================
Explanation:
Whenever the angle theta is between 0 and 90, the reference angle is exactly that value.
It's only when you get to other quadrants is when things get a bit tricky. Right now we're in quadrant 1, often written as Q1.
-------------------
Extra info:
If theta is between 90 and 180, then the reference angle is 180-theta. This region is Q2If theta is in quadrant 3, between 180 and 270, then the reference angle is theta-180. The order of subtraction is important since x-y is the not the same as y-x.Lastly, if theta is between 270 and 360 (in Q4), then the reference angle is 360-theta.As you can see, we have four quadrants starting with Q1 in the upper right corner. Then we move counterclockwise to get Q2,Q3 and Q4.Answer:
60 degrees
Step-by-step explanation:
In Quadrant 1, the reference angle is the same as theta.
So,
Reference Angle = 60 degrees
Find the probability of each of the following, if Z~N(μ = 0,σ = 1).
(please round any numerical answers to 4 decimal places)
a) P(Z > -1.13) =
b) P(Z < 0.18) =
c) P(Z > 8) =
d) P(| Z | < 0.5) =
Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830
Step-by-step explanation:
(a)
To find P(Z>-1.13):
Since Z is negative, it lies on left hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.3708
So,
P(Z>-1.13) = 0.5 + 0.3708 = 0.8708
(b)
To find P(Z<0.18):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.0714
So,
P(Z<0.18) = 0.5 + 0.0714 = 0.5714
(c)
To find P(Z>8):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.5 nearly
So,
P(Z>8) = 0.5 - 0.5 nearly = 0.0000
(d)
To find P(| Z | < 0.5)
that is
To find P(-0.5 < Z < 0.5):
Case 1: For Z from - 0.5 to mid value:
Table of Area Under the Standard Normal Curve gives area = 0.1915
Case 2: For Z from mid value to 0.5:
Table of Area Under the Standard Normal Curve gives area = 0.1915
So,
P(| Z | < 0.5) = 2 * 0.1915 = 0.3830
The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.
(a) The value of [tex]P(z>-1.13)=0.8708[/tex].
(b) The value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c) The value of [tex]P(Z > 8) = 0.0000[/tex].
(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].
Given:
The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]
(a)
Find the value for [tex]P(Z > -1.13)[/tex].
Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.3708[/tex].
Now,
[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]
Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].
(b)
Find the value for [tex]P(Z < 0.18)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.0714[/tex].
Now,
[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]
Thus, the value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c)
Find the value for [tex]P(Z >8)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area \approx 0.5[/tex].
Now,
[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]
Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].
(d)
Find the value for [tex]P(|Z| <0.05)[/tex].
Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Consider the positive value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Now,
[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]
Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].
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Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30
Answer:
x = 30
Step-by-step explanation:
1/2(x+6) = 18
Expand brackets or use distributive law.
1/2(x) + 1/2(6) = 18
1/2x + 6/2 = 18
1/2x + 3 = 18
Subtract 3 on both sides.
1/2x + 3 - 3 = 18 - 3
1/2x = 15
Multiply both sides by 2.
(2)1/2x = (2)15
x = 30
Answer:
30
Step-by-step explanation:
One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole class is a population). A random sample of 16 students yielded an average of a 75 on the first exam (s=16). What is the z-score of the sample mean? Is this sample significantly different from the population? (Hint: Use the z-score formula for locating a sample mean)
Answer:
(A) What is the z- score of the sample mean?
The z- score of the sample mean is 0.0959
(B) Is this sample significantly different from the population?
No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.
Step -by- step explanation:
(A) To find the z- score of the sample mean,
X = 75 which is the raw score
¶ = 74 which is the population mean
S. D. = 10.43 which is the population standard deviation of/from the mean
Z = [X-¶] ÷ S. D.
Z = [75-74] ÷ 10.43 = 0.0959
Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].
(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.
The estimated standard error of the mean is s/√n
S. E. = 16/√80 = 16/8.94 = 1.789
The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559
Setting up the hypotheses,
Null hypothesis: Sample is not significantly different from population
Alternative hypothesis: Sample is significantly different from population
Having gotten T- cal, T- tab is found thus:
The Critical (Table) t value is found using
- a specific alpha or confidence level
- (n - 1) degrees of freedom; where n is the total number of observations or items in the population
- the standard t- distribution table
Alpha level = 0.05
1 - (0.05 ÷ 2) = 0.975
Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;
The critical t value is 1.990
Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.
Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.
what is the length of bc in the right triangle below?
Answer: A) 15
Step-by-step explanation:
Because of Pythagorean Theorem, 9^2+12^2=BC^2. Thus, 81+144=BC^2. Thus, 225=BC^2. Thus, 15=BC.
Hope it helps, and ask if you want further clarification <3
A company manufacturing oil seals wants to establish X and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows:
sigma^25_i = 1 X_t = 1, 253.75, sigma^25_i = 1 R_i = 14.08
(a) Find the control limits that should be used on the X and R control charts. For n = 5, A2 = 0.577, D4 = 2.114, D3 = 0
(b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.
Answer:
A ) i) X control chart : upper limit = 50.475, lower limit = 49.825
ii) R control chart : upper limit = 1.191, lower limit = 0
Step-by-step explanation:
A) Finding the control limits
grand sample mean = 1253.75 / 25 = 50.15
mean range = 14.08 / 25 = 0.5632
Based on X control CHART
The upper control limit ( UCL ) =
grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475
The lower control limit (LCL)=
grand sample mean - A2 * mean range = 50.15 - 0.577(0.5632) = 49.825
Based on R control charts
The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191
The lower control limit = D3 * mean range = 0 * 0.5632 = 0
B) estimate the process mean and standard deviation
estimated process mean = 50.15 = grand sample mean
standard deviation = mean range / d2 = 0.5632 / 2.326 = 0.2421
note d2 is obtained from control table
Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of medication. At this rate of decay, how many bacteria would there have been at 24 hours? Round to the nearest whole number
Answer:
We can assume that the decline in the population is an exponential decay.
An exponential decay can be written as:
P(t) = A*b^t
Where A is the initial population, b is the base and t is the variable, in this case, number of hours.
We know that: A = 800,000.
P(t) = 800,000*b^t
And we know that after 6 hours, the popuation was 500,000:
p(6h) = 500,000 = 800,000*b^6
then we have that:
b^6 = 500,000/800,000 = 5/8
b = (5/8)^(1/6) = 0.925
Then our equation is:
P(t) = 800,000*0.925^t
Now, the population after 24 hours will be:
P(24) = 800,000*0.925^24 = 123,166
Answer:
122,070 bacteria.
Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt
Substitute the values in the formula.
500,000=800,000ek⋅6
Solve for k. Divide each side by 800,000.
58=e6k
Take the natural log of each side.
ln58=lne6k
Use the power property.
ln58=6klne
Simplify.
ln58=6k
Divide each side by 6.
ln586=k
Approximate the answer.
k≈−0.078
We use this rate of growth to predict the number of bacteria there will be in 24 hours.
AA0ktA=?=800,000=ln586=24hours=A0ekt
Substitute in the values.
A=800,000eln586⋅24
Evaluate.
A≈122,070.31
At this rate of decay, researchers can expect 122,070 bacteria.
In triangle abc what is the value of cos b A 5/13 B 12/13 C 5/12 D 13/12
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
In the triangle,
Hypotenuse = 13
Opposite = Perpendicular = 5
Adjacent = Base = 12
Now,
Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos B = 12/13
If the triangle is just like in the attached file!
Answer:
B) 12/13
Step-by-step explanation:
The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard. Discuss the practical consequences of making a Type I and a Type II error. (continue #5) A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4. Find the p-value of the test. Do you think that H0 should be rejected? Explain. To what type of error are you now subject?
Answer:
Step-by-step explanation:
From the summary of the given statistics;
The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:
Null hypothesis:
[tex]H_0: \mu = 0.60[/tex]
Alternative hypothesis:
[tex]H_a: \mu < 0.60[/tex]
Type I error: Here, the null hypothesis which is the new engine has a mean level equal to .6g/ml is rejected when it is true.
Type II error: Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.
Similarly;
From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.
Sample size n = 64
sample mean [tex]\overline x[/tex] = .5 g/ml
standard deviation σ = .4
From above, the normal standard test statistics can be determined by using the formula:
[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]
[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]
z = -2.00
The p-value = P(Z ≤ -2.00)
From the normal z distribution table
P -value = 0.0228
Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.
Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.
celine is drake’s granddaughter. Her age is 4 years greater than 1/3 of drake’s age . if celine is 28 years old , how old is drake ?
Which equation represents this situation?
1) 4d - 1/3 = 28
2)1/3d - 4= 28
3) 1/3 + 4= 28
4) 4d + 1/3 = 28
Answer:
It should be 1/3d+4=28, but i dont see that option
Step-by-step explanation:
All the other ones are wrong. Its plus 4 because it states that its 4 years greater not lesser. Greater in the context means that its addition of 4.
idk if theres a typo or something but yeah.
solve for inequality
ᶜ⁄₋₃ ≥ 3
Answer:
c ≤ -9
Step-by-step explanation:
c / -3 ≥ 3
c ≤ -9
Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.
Answer:
c ≤ -9
Step-by-step explanation:
c / -3 ≥ 3
c ≤ -9
Using Pascal’s Theorem, expand the expression 〖(2x-y)〗^3
Answer:
(2x - y)³ = 8x³ - 12x²y + 6xy² - y³
Step-by-step explanation:
Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.
For the expansion of
(a + b)ⁿ
As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.
The coefficient of terms are obtained starting from 1 for n = 0.
- For the next coefficients of terms are 1, 1 for n = 1.
- For n = 2, it is 1, 2, 1
- For n = 3, it is 1, 3, 3, 1
The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.
So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.
The Pascal's triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ
So, for n = 3, the coefficients are 1, 3, 3, 1
Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n
So,
(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]
= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)
= 8x³ - 12x²y + 6xy² - y³
Hope this Helps!!!
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capita consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed
Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is [tex]n = 1537 \ gallons[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]MOE = 0.5[/tex]
The confidence level is [tex]C = 95[/tex]%
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is [tex]Z_{\frac{\alpha }{2} } = 1. 96[/tex]
The reason we are obtaining critical values of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the sample size
Now the sample size is mathematically represented as
[tex]n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}[/tex]
substituting values
[tex]n = \frac{1.96^2 * 10 ^2}{0.5^2}[/tex]
[tex]n = 1537 \ gallons[/tex]
Set up a rational equation and then solve the following problems. A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18. Find the two integers.
Answer:
9 and 18
Step-by-step explanation:
2x and x are the numbers
1/x-1/2x=1/18
2/2x-1/2x=1/18
1/2x=1/18
2x=18X=9,
2x=18
The two integers are 9 and 18