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]
Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants.
Class Frequency
8.26 20
10.01-11.75 38
11.76 36
13.51-15.25 25
15.26-17.00 27
Sample Variance: ___________
Sample Standard Deviation: _________
Answer:
(a) The sample variance is 16.51
(a) The sample standard deviation is 4.06
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}[/tex]
Solving (a); The sample variance.
First, calculate the class midpoints.
This is the mean of the intervals.
i.e.
[tex]x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13[/tex]
[tex]x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88[/tex]
[tex]x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63[/tex]
[tex]x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38[/tex]
[tex]x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13[/tex]
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}[/tex]
Next, calculate the mean
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}[/tex]
[tex]\bar x = \frac{1845.73}{146}[/tex]
[tex]\bar x = 12.64[/tex]
Next, the sample variance is:
[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]
So, we have:
[tex]\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}[/tex]
[tex]\sigma^2 = \frac{2393.6875}{145}[/tex]
[tex]\sigma^2 = 16.51[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{16.51}[/tex]
[tex]\sigma = 4.06[/tex]
Which of the following is most likely the next step in the series?
B
Answer:
C
Step-by-step explanation:
The pattern seems to go as follows:
1. Top left portion is in blue
2. Top left portion is in blue as well as the rest of the upper half filled with red.
3. Another portion of blue is added directly underneath the red.
This leads me to believe that the colors are alternating from blue to red to blue to finally, red. This makes your answer C. Please let me know if you still need help!
What is the equation of the following line? Be sure to scroll down first to see
(-1/2, 3) (0,0)
A. y = 1/2 X
B. y = -1/2 X
C. y = 3 X
D. y= 2X
E. y= 6
F. y= -6

a p e x :(
Answer: (f)
Step-by-step explanation:
Given
Line that passes through [tex](-\frac{1}{2},3)[/tex] and [tex](0,0)[/tex]
Using two point form, equation of a line is given by
[tex]\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert the values
[tex]\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x[/tex]
Thus, option (f) is correct
247 1372 as a number
Answer:
Do you mean in words?
Step-by-step explanation:
then it is
Two million,four hundred and seventy one thousand,three hundred and seventy two.
Which function is a translation of the parent absolute value function?
f(x) = 2x1
f(x) = |x+6| f(x)=|x| f(x)=-4|x|
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Step-by-step explanation; did it on the website euphoria
The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the transformation of the function be a translation , where
The parent function is f ( x ) = | x |
And , the translated function is f ( x ) = | x + 6 |
So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
And , the function is translated 6 units to the left
Hence , the translated function is f ( x ) = | x + 6 |
To learn more about transformation of function click ;
https://brainly.com/question/26896273
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Verify that a÷(b+c)=(a÷b)+(a ÷c), a=10 , b=5 , 6=2
Answer:
a÷(b+c)≠(a÷b)+(a ÷c)
Step-by-step explanation:
To verify that a÷(b+c)=(a÷b)+(a ÷c)
Using the values ;
a=10 , b=5 , 6=2
plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;
That is, right hand side = left hand side
a÷(b+c) = 10 ÷ (5+ 2)
a÷(b+c) = 10 / 7
Also;
(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7
Given the result, it can be seen that ;
RHS ≠ LHS
10/7 ≠ 7
Find X in the triangle. Round answer to the nearest TENTH of a degree (GIVING BRAINLEST TO BEST ANSWER :D )
Answer:
x = 59,53445508
Tan(x) = 34/20
Step-by-step explanation:
Answer:
30÷20 degree x=n
Step-by-step explanation:
Mark me as brainliest
Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)
Answer:
(a) [tex]A = A_0 * e^{kt}[/tex]
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
[tex]A(t) = A_0 * e^{kt}[/tex]
Where
[tex]A_0 \to[/tex] Initial Amount
[tex]k \to[/tex] rate
[tex]t \to[/tex] time
[tex]A(t) \to[/tex] Amount at time t
Solving (b):
We have:
[tex]t = 4.6hr[/tex]
[tex]A_0 = 8[/tex]
[tex]A(4.6) = 4[/tex]
First, we calculate k using:
[tex]A(t) = A_0 * e^{kt}[/tex]
This gives:
[tex]A(4.6) = 8 * e^{k*4.6}[/tex]
Substitute: [tex]A(4.6) = 4[/tex]
[tex]4 = 8 * e^{k*4.6}[/tex]
Divide both sides by 4
[tex]0.5 = e^{k*4.6}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]
This gives:
[tex]-0.6931 = k*4.6[/tex]
Solve for k
[tex]k = \frac{-0.6931}{4.6}[/tex]
[tex]k = -0.1507[/tex]
So, we have:
[tex]A(t) = A_0 * e^{kt}[/tex]
[tex]A(t) = 8e^{-0.1507t}[/tex]
To calculate the time when 1 lb will remain, we have:
[tex]A(t) = 1[/tex]
So, the equation becomes
[tex]1= 8e^{-0.1507t}[/tex]
Divide both sides by 8
[tex]0.125= e^{-0.1507t}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]
[tex]-2.0794= -0.1507t[/tex]
Solve for t
[tex]t = \frac{-2.0794}{-0.1507}[/tex]
[tex]t = 13.7983[/tex]
[tex]t = 14[/tex] --- approximated
If 137 is subtracted from three times of square of a natural number the result is 55. Find the number
Answer:
8
Step-by-step explanation:
Let the unknown number be x.
Therefore, we can write the question as a mathematical statement and this will be:
3x^2 - 137 = 55. (Note: ^2 = to the power of 2 or "squared"
(In the question, we can break it up as being three times of a square of a natural number = (3x^2) and 137 is subtracted from = (- 137) and the result is 55 = (= 55). Therefore, this gives 3x^2 - 137 = 55
Then, we add 137 first to get rid of the (-137)
Therefore:
3x^2 = 192
Then, we divide 3 from both sides to get rid of the (3) in (3x^2).
Therefore,
x^2 = 64.
So, we square root 64. This gives
x = 8.
Therefore, the answer is 8.
what is a 36% markup to $150 dallors
Answer:
Markup amount: $54
New price with markup: $204
Step-by-step explanation:
36% markup to $150
We can find the amount of markup by finding 36% of 150.
36% of $150
Write 36% as a decimal and multiply it by the price
0.36(150) = $54
The amount of markup (36%) is equal to $54
When this is added to the original price, the new price is $150 + $54 = $204
Let me know if you have any questions!
Given that yx is a diameter of V, find mZVX if mYVZ=(15r -1)", mWVX =(8x- 2).mUVW =(7x +15).
and mYVU = 3x + 5).
A 32
B 45°
C 70
D. 134
ASAP. There are three marbles in a bag. When is red and two are black. What is the probability of picking a black marble first, putting it back in the bag and then picking a black marble? Use the following probably need to find the answer.
Answer:
Number of black balls=2
Total number of balls=3
Probability =2/3
Which of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1
Answer:
y=1/4x - 1
Step-by-step explanation:
going off of the picture, I'd say this is your answer
Find the value of y for a given value of x, if y varies directly with x. If y = 0.15 when x = 1.5, what is y when x = 6.3? a. –0.63 b. 0.63 c. 63 d. –63 Please select the best answer from the choices provided A B C D
Answer:
b
Step-by-step explanation:
I believe its b, because1.5 is 10 times 0.15
and 6.3 is 10 times 0.63
Graph the line with y-intercept-2 and slope -3/5 .
Answer:
MATH
Dior H. asked • 01/13/21
graph the line with the slope 1/2 and y-intercept -2
i need help badly i am crying because its hard
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1 Expert Answer
By:
Raymond B. answered • 01/14/21
TUTOR 5 (1)
Math, microeconomics or criminal justice
ABOUT THIS TUTOR ›
y=mx + b is the standard slope intercept form for a line
m=1/2, b =-2
y=(1/2)x -2. y-intercept is -2 or the point (0,-2)
x intercept is found by setting y=0 and solving for x
0=(1/2)x - 2
(1/2)x = 2
x = 4 = the x intercept or (4,0)
plot the 2 intercepts (0,-2) and (4,0)
(4,0) is on the x axis, 4 units to the right of the origin (0,0)
(0,-2) is on the y axis, 2 units below the origin
once you plot those two points, draw a straight line connecting them. That's the graph of the line
What's the area of the trapezoid
Answer:
i dont know just study hard bro
Step-by-step explanation:
Answer:
A =36 ft^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the lengths of the bases
A = 1/2 ( 13+5) *4
A = 1/2 ( 18)*4
A =36 ft^2
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
9514 1404 393
Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
HW HELP ASAP PLZZZZZ
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (x - 5)(x - 4) }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
[tex] {x}^{2} - 9x + 20[/tex]
[tex] = {x}^{2} - 4x - 5x + 20[/tex]
Taking "[tex]x[/tex]" as common from first two terms and "[tex]5[/tex]" from last two terms, we have
[tex] = x(x - 4) - 5(x - 4)[/tex]
Taking the factor [tex](x-4)[/tex] as common,
[tex] = (x - 5)(x - 4)[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
prove that 1 + sin a + cos 2A upon 1 + Sin A minus Cos 2A = 2 cot a prudent
Answer:
LHS×0=RHS×0
0=0
hence,proved
Use the formula v = IR for current flowing through a resistor, where V is the voltage in volts, I is current in amps, and R is resistance in ohms. Find the current through a resistor with resistance 15 ohms if the voltage across it is 3 volts.
Answer:
0.2 amps
Step-by-step explanation:
Given data
The formula V=IR is the formula for ohms law
Which state that the voltage is directly proportional to the current and the resistance in an electric circuit
Now
R= 15 ohms
V= 3volts
V= IR
3= I*15
I= 3/15
I= 0.2 amps
Hence he current flowing is 0.2 amps
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)
a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Solution :
a). P(X = x)
= [tex]$p(1-p)^x$[/tex] for x = 0, 1, 2, ....
P(x ≤ 3) = 0.837
b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]
= 1.7397
Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]
= 4.7663726
Standard deviation = 2.1832
Therefore, mean + standard deviation
= 1.7397 + 2.1832
= 3.9229
[tex]$P(x > 3.9229) = 0.1626$[/tex]
So the required P = 2 x 0.1626
= 0.325
If f(x) = 6x + 2 and g(x) = 4x - 5, find f(x) - g(x).
A. 2x - 7
B. 2x + 7
C. 10x - 3
D. 10x + 7
Answer: D
Step-by-step explanation:
set the functions to subtract
Payment types vary at the grocery store. Here are the proportions of the leading three payment methods: Payment Method Cash Credit Cards Debit Cards Proportion 0.11 0.43 0.21 If a transaction is selected at random, the probability that the customer did not pay with a Debit Card is .
Answer:
0.79
Step-by-step explanation:
Given the probability distribution :
Payment Methd: Cash Credit Cards Debit Cards Proportion : ____0.11 ____ 0.43 _____0.21
The probability that a customer did not pay with debit card can be obtained as :
If customer did not pay with debit card, then he would have paid with any of the other payment methods
This Can best be obtained using the complement method
P(not debit card) = 1 - P(debit card)
P(debit card) = 0.21
P(not debit card) = 1 - 0.21
P(not debit card) = 0.79
Express the following repeating decimal as a fraction in simplest form.
Answer:
[tex]0.\overline{369} = \frac{41}{111}[/tex]
Step-by-step explanation:
x = 0.369369369...
10x = 3.69369369...
100x = 36.9369369...
1000x = 369.369369...
1000x - x = 369
999x = 369
[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]
2
3
4
9
10
-1
NS
-6
-7
-8
-9
Which three statements correctly describe key features of the function graphed here?
did u add the attachment of the the statements? cuz i dont see it.
the cost price of an articles was 4000 find the marked price of the article so that there will be profit of 20%after allowing a discount of 20%
Answer:
The marked price of the article was $ 6000.
Step-by-step explanation:
Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:
4000 x X x 0.8 = 4000 x 1.2
4000 x X x 0.8 = 4800
4000 x X = 4800 / 0.8
4000 x X = 6000
X = 6000/4000
X = 1.5
4000 x 1.5 = 6000
Therefore, the marked price of the article was $ 6000.
Phân biệt chi phí sản xuất và giá thành sản phẩm?
Answer:
* Giống nhau: đều là biểu hiện bằng tiền về lao động sống và lao động hóa trong quá trình sản xuất
* Khác nhau:
+ Về thời gian: chi phí sản xuất gắn liền với từng thời kỳ, còn giá thành sản phẩm gắn với thời hạn hoàn thành sản phẩm. ...
+ Có những chi phí được tính vào giá thành nhưng không được tính vào chi phí kỳ này.
+ Mối quan hệ chi phí và tính giá thành sản phẩm: Chi phí là cơ sở để tính giá thành, giá thành là thước đo chi phí sản xuất mà doanh nghiệp bỏ ra để có được khối lượng hoàn thành.
+ Có nhiều chi phí phát sinh trong kỳ nhưng chưa có sản phẩm hoàn thành do đó chưa có giá thành.
Step-by-step explanation:
Help me calculate Lim for this lesson
Answer:
I'm acutally not too sure on this but give me a moment to solve this
Step-by-step explanation:
Factor each trinomial completely.
A. 2x^2 + 17x + 21
B. 3x^2 - 17x + 10
Answer:
A) (2x+3)(x+7) B) (3x-2)(x-5)
Step-by-step explanation:
A) 2x^2+17x+21=(2x+3)(x+7)
B) 3x^2-17x+10=(3x-2)(x-5)
A die is rolled twice. What is the probability of showing a 3 on the first roll and an even number on the second roll?
Answer:
1/6 * 1/2 = 1/12
Step-by-step explanation:
1 number on a 6 sided die is 1 out of 6 (1/6) and an even number (2,4,6) on a 6 sided die is 3/6 or 1/2 (always simplify when multiplying fractions)
so 1 times 1 = 1 and 6 times 2 = 12 making it 1/12
