Answer:
We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
Step-by-step explanation:
We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;
1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.
Let [tex]\mu[/tex] = true average percentage of organic matter
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 3% {means that the true average percentage of organic matter in such soil is 3%}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu \neq[/tex] 3% {means that the true average percentage of organic matter in such soil is something other than 3%}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean percentage of organic matter = 2.481%
s = sample standard deviation = 1.616%
n = sample of soil specimens = 30
So, the test statistics = [tex]\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }[/tex] ~ [tex]t_2_9[/tex]
= -1.76
The value of t-test statistics is -1.76.
(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
Step-by-step explanation:
t=V100-50/4
t=V50/4=1.76≈1.8 s
when h=0
t=V100/4=10/4=2.5 s
Answer: a) (5√2)/4 ≈ 1.77 seconds
b) 5/2 = 2.5 seconds
Step-by-step explanation:
[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]
[tex] 3 {x}^{2} - 15x = 15[/tex]
[tex]3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\[/tex]
Please answer this for me!!! 25 points to whoever answers this!!!!!!
Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?
Answer:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Step-by-step explanation:
Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:
[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]
Solving the linear system:
[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]
The price of each item is:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Graph the line y=-1/3x+2
Answer:
Graphed below.
Step-by-step explanation:
The slope of the line is -1/3.
The y-intercept is at (0, 2).
The x-intercept is at (6, 0).
What is 66 tens + 24 tens
Answer:
900.
Step-by-step explanation:
66 tens are 660.
and 24 tens are 240.
so, It is 900!
798/8×41 rounded to one significant figure
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
Find out more information about rounding off here:
https://brainly.com/question/17353491
#SPJ2
Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 360 units2 586 units2 456 units2 552 units2
Answer:
Option (4)
Step-by-step explanation:
Surface area of a prism = 2B + P×h
where B = Area of the triangular base
P = perimeter of the triangular base
h = height of the prism
B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]
Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]
(20)² = (12)² + (Leg 2)²
Leg 2 = [tex]\sqrt{400-144}[/tex]
= 16 units
Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]
= 96 units²
P = 12 + 16 + 20
P = 48 units
h = 7.5 units
Surface area of the prism = 2(96) + (48×7.5)
= 192 + 360
= 552 units²
Therefore, surface area of the given triangular prism = 552 units²
Option (4) will be the answer.
If (x) = 3x - 5 and g(x) = x + 3, find (f - g)(x).
O A. 8 - 2x
O B. 2x-2
O c. 2x-8
O D. 4x-2
Answer:
C
Step-by-step explanation:
(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8
Answer:
2x -8
Step-by-step explanation:
f (x) = 3x - 5
g(x) = x + 3,
(f - g)(x) = 3x - 5 - ( x+3)
Distribute the minus sign
= 3x-5 -x-3
Combine like terms
= 2x -8
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers 3 or odd are 1, 3, 5, and 7.
4 numbers out of 8.
4/8 = 1/2
P(3 or odd) = 1/2
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
Identify the range of the function shown in the graph.
Answer:
B
Step-by-step explanation:
The range is all values of y. Y goes from -1 to 1. Please mark brainliest.
Answer:
see below
Step-by-step explanation:
The domain of the function is the possible x values
The domain is all real values since x can be any number
The range of the function is the possible y value
The values of y go from -1 to 1 so
-1 ≤y≤1
A car is driving at 100 kilometers per hour. How far, in meters, does it travel in 3 seconds?
Answer:
The car travels 83 1/3 meters in 3 seconds.
Step-by-step explanation:
Speed of car = 100 KM/ hour
1 km= 1000m
1 hour = 3600 seconds
Lets find speed of car in Meters/second
speed of car in m/sec = 100*1000 m/3600 second
here we have taken 1000 for km and 3600 for hour
speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second
speed of car in m/sec = 250/9 m per sec
We know that
distance = speed*time
speed = 250/9 m per sec
time =3 second
distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.
Thus, car travels 83 1/3 meters in 3 seconds.
Ten different numbers are written on pieces of paper and thrown into a hat. The sum of all the numbers is 205. What is the probability of selecting four numbers that have a sum greater than 82
Answer:
The probability is 40%
Step-by-step explanation:
a) There are ten pieces of paper with ten numbers
Probability of selecting four pieces of paper = 4/10 or 40%
Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%
Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.
b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes. In other words, it is a measure of the likelihood of an event (or measure of chance).
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only one number 5 from a total of 8 parts.
1 out of 8.
1/8 = 0.125
P(5) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Spinner divided in parts = 8
Number 5 = 1
P(5) = 12.5%
Convert 100 kilometers to meters.
Answer:
100,000 meters
Step-by-step explanation:
There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.
Answer:
it is 100000 kilometers
Step-by-step explanation:
use the metric system and you get 10000 kilometers.
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
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, which is also called standard error, [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, we have that:
[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
A teacher based in California calculated a particular date in the calendar and named it Square Root Day. Try and find out why the day was named so. Can you find more such days? When was last square root day and when is next square root day
Answer:
may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025
During a football game, a team lost 12 yards on the first play and then gained 5 yards on each of the next 3 plays. Which method finds the total yards at the end of the first four plays?
A) add –12 to 3 times 5
B) add 12 to 3 times 5
C) add –12, 5, and 3
D) add 12, 5, and 3
They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value. The answer is A.
Answer:
A
Step-by-step explanation:
m−4+m−5 how do i solve this?
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
=m+m-4-5
=2m-9
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
take the like terms
= 2m-4-5
= 2m-9
Sorry if that didn't help
The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.
Answer:
Domain stays the same while the range changes
Step-by-step explanation:
While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.
=> x- coordinate = Domain
=> y-coordinate = Range
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
What is the domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.
When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.
The Domain represent as x-coordinate and the range as y-coordinate
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
Hence, option C is correct.
Learn more about appropriate domain here:
https://brainly.com/question/20073127
#SPJ2
In a basketball shooting competition there are ten balls from 1-10. The number of points earned is based on the number on the ball (I.e shoots a 7 gets 7 points), if a person misses 2 shots what number is not possible
52
44
41
38
35
The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part
n a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. There are 450 total flying insects. (a) Create a table for how many butterflies there are for 1, 50, and 100 flying insects. Show your work. (b) How many butterflies are in the conservatory? Show your work.
Answer:
There are 172 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 172
Thus, there are 172 butterflies in the conservatory.
Answer:
There are 162 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 162
Thus, there are 162 butterflies in the conservatory.
in triangle ABC shown below, Segment DE is parallel to Segment AC:
Answer:
Selected option is correct
Step-by-step explanation:
Triangle BDE and BAC are similar because of the two pairs of equal angles (AA)
1. angle B
2. angle BDE = angle BAC
15 liters of water flow
through a water pipe
and enter a tank
within 4.5 minutes
How much time does
it take to pump 727.5
liters of water into a
water tank using 2
similar water pipes?
Answer:
Step-by-step explanation:
Since 15 liters of water flow through a water pipe and enter a tank within 4.5 minutes, the same amount of water would flow through a similar pipe at the same time. Therefore, if two similar water pipes are used, the volume of water that would flow into the tank in 4.5 minutes is 15 × 2 = 30 liters
Therefore, the time it will take to pump 727.5 liters of water into a water tank using 2 similar water pipes is
(727.5 × 4.5)/30 = 109.125 minutes
Please answer this correctly
Assume that cans are filled so that the actual amounts have a mean of 17.00 ounces. A random sample of 36 cans has a mean amount of 17.79 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 17.00 ounces and a standard deviation of 0.08 ounce.
Required:
How many standard deviations is the sample mean from the mean of the distribution of sample?
Answer:
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{s}[/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.
In this question:
[tex]X = 17.79, \mu = 17, s = 0.08[/tex]
How many standard deviations is the sample mean from the mean of the distribution of sample?
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.79 - 17}{0.08}[/tex]
[tex]Z = 9.875[/tex]
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
Select the action you would use to solve 4x = 16. Then select the property
that justifies that action.
A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Action: Multiply both sides by 4.
D. Property: Division property of equality.
E. Property: Addition property of equality.
O F. Action: Add 4 to both sides.
Answer:
A.
Step-by-step explanation:
Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.
What is the area of the figure below 13 in length, 11 in width, 29 in and 13 in?
Answer:
B. 533in²
Step-by-step explanation:
Step 1: Find the area of the rectangle
A = lw
A = (29)13
A = 377
Step 2: Find the leg of the triangle
13 + 11 = 24
Step 3: Find the area of the triangle
A = 1/2bh
A = 1/2(24)(13)
A = 12(13)
A = 156
Step 3: Add the areas of the 2 figures together
377 + 156 = 533
What is the product of (2p + 7)(3p2 + 4p – 3)?
6p3 + 29p2 – 34p + 21
6p3 + 29p2 – 22p + 21
6p3 + 29p2 + 22p – 21
6p3 + 29p2 + 34p – 21'
Answer: 6p^3+29p^2+22p-21
Which product will result in a sum or difference of cubes?
A (x + 7)(x2 – 7x + 14)
B (x + 8)(x2 + 8x + 64)
C (x – 9)(x2 + 9x + 81)
D (x – 10)(x2 – 10x + 100)
Answer:
C. (x - 9)(x^2 + 9x + 81).
Step-by-step explanation:
The cube identities are
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Checking against the list the one that fits is the difference formula:
x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).
a=1, b = 9, ab = 1 *9 = 9.