Answer:
The value of the z-test statistic is [tex]z = 0.68[/tex]
Step-by-step explanation:
An article claims that 12% of trees are infested by a bark beetle.
At the null hypothesis, we test if the proportion is of 12%, that is:
[tex]H_0: p = 0.12[/tex]
At the alternative hypothesis, we test if the proportion is different of 12%, that is:
[tex]H_1: p \neq 0.12[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.12 is tested at the null hypothesis:
This means that [tex]\mu = 0.12, \sigma = \sqrt{0.12*0.88}[/tex]
A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected.
This means that [tex]n = 1000, X = \frac{127}{1000} = 0.127[/tex]
What is the value of the z-test statistic?
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.127 - 0.12}{\frac{\sqrt{0.12*0.88}}{\sqrt{1000}}}[/tex]
[tex]z = 0.68[/tex]
The value of the z-test statistic is [tex]z = 0.68[/tex]
MP of an article is $1400. Find the SP of that article in cents if the shopkeeper adds 13% VAT after allowing 45% discount. (100 cents =$1)
Answer:
87,010 cents is the SP.
Step-by-step explanation:
MP = $1400
VAT = 13%
Discount = 45%
so,
discount amount = 45% of MP
= 45% of $1400
= 45/100 * $1400
= 9/20 * $1400
= 9* $70
= $630
so,
MP - discount amount
= $1400 - $630
= $770(SP)
so,
VAT amount = 13% of SP
= 13% of $770
= 13/100 * $770
= $100.1
so,
SP + VAT
= $770 + $100.1
= $870.1
so,
$1 = 100 cents
$870.1 = 100*870.1
= 87,010 cents
High school students across the nation compete in a national financial capability challenge exam. students who score in the top 5 percent get recognized publically for their achievement by the Dept of Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Answer:
2
Step-by-step explanation:
Follow the 68-95-99.7 rule
The answer is 2 standard deviations
Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.)
f(x) = 8|x − 6|
f(−2) =
f(0) =
f (1/2)=
f(2) =
f(x + 1) =
f(x2 + 7) =
Step-by-step explanation:
my answer is in the image above
Suppose you are asked to take a sample of men and women in order to measure their emotional IQ. The emotional IQ scale that you administer has a minimum of 0 and a maximum of 100, with higher scores indicating higher emotional intelligence (the range of the scale is not pertinent to the question -- I simply provide it so that you have some context in which to provide your answer). You sample 25 men and 25 women. The mean for men is 70 with a standard deviation of 10 and the mean for women is 82 with a standard deviation of 15.
Required:
What is the 99% confidence interval for the scores of men and women?
Answer:
The 99% confidence interval for the scores of men is (64.406,75.594).
The 99% confidence interval for the scores of women is (73.609,90.391).
Step-by-step explanation:
We have the standard deviations for the sample, which means that the t-distribution will be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797.
For men:
Standard deviation of 10.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{10}{\sqrt{25}} = 5.594[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 70 - 5.594 = 64.406
The upper end of the interval is the sample mean added to M. So it is 70 + 5.594 = 75.594
The 99% confidence interval for the scores of men is (64.406,75.594).
For women:
Standard deviation of 15.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{15}{\sqrt{25}} = 8.391[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 82 - 8.391 = 73.609
The upper end of the interval is the sample mean added to M. So it is 82 + 8.391 = 90.391
The 99% confidence interval for the scores of women is (73.609,90.391).
A group of people were asked if they had run a red light in the last year. 315 responded "yes", and 190 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
0.624
Step-by-step explanation:
Number who have run a red light = 315
Number who haven't run a red light = 190
From the data :
The total number of people sampled = total possible outcome = (315 + 190) = 505
Selecting a person at random, probability that the selected person has run a red light :
P = required outcome / Total possible outcomes
Required outcome = Number who have run a red light = 315
P(having run a red light) = 315 / 505 = 0.624
Q2 find the degree of the polynomial
x4(4x+1)
Step-by-step explanation:
x⁴(4x+1)
4x⁵+x⁴
degree is 5
Olivia can bake 95 cookies in 5 hours. At this rate, how many cookies can she bake
in 11 hours?
Answer:
Olivia will make 209 cookies on 11 hours
Step-by-step explanation:
if she makes 95 per 5 hours
we can make
5 + 5 = 10
this is the same as doing
95 + 95 = 190
now, for the 1 hour
95 : 5 = 19
now to verify it
19 x 5 = 95
now you make
95 + 95 + 15 = 209
Oops, srry my bad, i fixed the thing i did wrong
Which of the following fraction pairs are equivalent?
Answer:
8/12 and 12/18
Step-by-step explanation:
8/12 and 12/18
both equal 2/3
Find the difference quotient of f; that is, find f(x+h)-f(x) , h ≠ 0 for the following function
f (x)=6x+8
f(x+h)-f (x)/h =
For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation:
y = 3 x squared + 2 x minus 8
Answer:
Table A
Step-by-step explanation:
y = 3x^2 +2x -8
The quadratic is in the form
y = a x^2 +bx+c
a = 3 b = 2 c = -8
Since a > 0 it opens up
The y intercept is c so the y intercept is -8
what is the area of the figure below
Answer:
190 in²
Step-by-step explanation:
Cut the shape into simpler ones:
A=6 x 6= 36 in²
A=7x22= 154 in²
A=36 + 154= 190 in²
PLEASE HELP ME WILL GIVE BRAINLIEST
Answer:
Reason 5
Step-by-step explanation:
Reason 1 and 2 are Given
Reason 3 is Reflexive
Reason 4 is Side-Side-Side congruency
Answer:
Reason 5
Step-by-step explanation:
It helps to know what CPCTC means and how it's used.
CPCTC means "corresponding parts of congruent triangles are congruent."
To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.
Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.
In step 4, the triangles are proven congruent by SSS.
Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.
The expression w^4 - 36 is equivalent to
Answer:
(w² + 6)(w² - 6)
Step-by-step explanation:
difference of squares
w⁴ - 36 = (w² + 6)(w² - 6)
Which is the graph of the parent function f(x) = x2?
Answer:
it should look like a U shape. Its called a parabola
(0,0) is the bottom center.
Step-by-step explanation:
I need help pleaseee
Answer:
7
Step-by-step explanation:
refer to solution in picture
What is the sum of the series 18 E n=4 (n+1) ^2? 1,239 2,415 2,440 2,469
9514 1404 393
Answer:
(c) 2440
Step-by-step explanation:
The sum of the squares of numbers 1 .. n is ...
s(n) = n(n +1)(2n +1)/6
You want the sum of squares from 5 to 19. We can compute that from ...
s(19) -s(4) = (19(20)(39) -4(5)(9))/6 = (14820 -180)/6 = 2440
Answer:
C. 2440Step-by-step explanation:
hope it helps u too
What is the standard form polynomial that represents this product?
(-2m3+3m2-m) (4m2+m-5)
Environmental researchers have collected rain acidity data for several decades. They want to see if there is any evidence that attempts to reduce industrial pollution have produced a trend toward less acidic rainfall. They should display their data in a(n)... a. Bar graph b. Time plot c. Histogram d. Box plot
Answer:
Time plot
Step-by-step explanation:
The data from which a plot or graph is to be generated will have only one variable, which is the rain acidity, that is acidity level of Rainfall over a certain period. However, the data gbwre is time dependent, hence, it is a time series plot. Hence, this is a two dimensional univariate plot, with the acidity label of Rainfall on one axis and time on the other. Therefore, the graph which is best to display such information is the time series plot.
no spam pls
for which x is f(x)=-3
1. -7
2.-4
3. 4
4. 5
9514 1404 393
Answer:
(a) -7
Step-by-step explanation:
You are given f(x) = -3. Look for -3 in the f(x) column. (You will find it in the first row.)
You want the corresponding value of x. It will be in the first row of the x column. The value there is -7.
The value of x for f(x) = -3 is -7.
Round 51,939 to the nearest thousands
Answer:
50,000
Step-by-step explanation:
in my opinion I would think this would be the answer because you are rounding to the nearest 10,000
What is the slope of the line passing through (-3, 5) and (5, -3)?
Answer:
The line has a slope of -1.
Step-by-step explanation:
To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2 }-y_{1} }{x_{2} -x_{1} }[/tex].
For finding the slope of this line with the points (-3,5) and (5,-3), start by writing down the information given from the question.
[tex]y_{2}=-3[/tex]
[tex]y_{1}= 5[/tex]
[tex]x_{2}=5[/tex]
[tex]x_{1} =-3[/tex]
Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(5)}{5-(-3)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-8}{8}=-1[/tex]. The final answer will be -1.
Pls I’ve been stuck on this
Area of a circle is pi x radius^2
Area = pi x 22 ^2
Area = pi x 484
Area = 1,519.8 mm^2
Answer:
1520.5mm²
Step-by-step explanation:
Area of a circle=πr²
π(22mm)²
π484mm²
1520.5308443374599mm²
to one decimal place
1520.5mm²
Darla decides to buy books and magazines with her money. Books cost $16 each and magazines cost $8 each. Write a function that shows the function of the total money that she spends.
Answer:
m=16x+8y
Step-by-step explanation:
let the amount of money she spend be 'm'
m=16x+8y
Answer:
a=16x+8y
Step-by-step explanation:
Let the amt of money she spends be a.
hope it helps!!!
Which is the graph of the function y = 3x?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The graph that includes the point (1, 3) will be the one that is a graph of ...
y = 3^x
What translation maps ABC to A'B'C'?
Need help ASAP!! Giving brainliest!
Which of the following is not an example of a parent function?
y=x
y=2x^3
y=1/2
y=2^x
9514 1404 393
Answer:
(b) y=2x^3
Step-by-step explanation:
The function y=2x^3 is an example of the parent function y=x^3 being vertically scaled by a factor of 2. As such, it is not the parent function.
_____
Additional comment
A parent function is one that has not been translated or scaled in any way. One could argue that the parent function of the form y=constant is y=1, so that the function y=1/2 has been scaled by a factor of 1/2. In this problem, we recognize the parent function y=x^3 has clearly been scaled to get y=2x^3, so the latter is not an example of a parent function.
If this is a "check all that apply" question, then y=1/2 is another reasonable answer.
Answer:(b) y=2x^3
Step-by-step explanation:
Find the 22nd term of the arithmetic sequence whose common difference is d =3 and whose first term is a_1=-20
A cosmetics salesman earns a basic wage of $2000 per month plus 10% commission on all sales he makes. Calculate his total wage for the month when he sold $89,000 worth of cosmetics.
The table shows the displacement-time data for a ship relative to a shore.
t(hours) 2.95 3.15 3.75 3.95 3.99 4.00
s(0 (miles) 14.95 17.61 27.23 31.01 31.80 32.00
Estimate the instantaneous velocity of the ship at t = 4 hours.
A.
20.00 mi./h.
B.
20.15 mi./h.
C.
20.25 mi./h.
OD.
20.50 mi./h.
Answer:
Step-by-step explanation: