Answer: (a) (602.95,705.37)
(b) 33
Step-by-step explanation:
(a) Given : Sample size : [tex]n=40[/tex]
Sample mean : [tex]\overline{x}=654.16[/tex]
Standard deviation : [tex]\sigma= 165.23[/tex]
Significance level :[tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The confidence interval for population mean is given by :-
[tex]\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=654.16\pm(1.96)\dfrac{165.23}{\sqrt{40}}\\\\\approx654.16\pm51.21\\\\=(654.16-51.21,\ 654.16+51.21)=(602.95,705.37)[/tex]
Hence, the 95% (two-sided) confidence interval for true average [tex]CO_2[/tex] level in the population of all homes from which the sample was selected.
(b) Given : Standard deviation : [tex]s= 167\text{ ppm}[/tex]
Margin of error : [tex]E=\pm57\text{ ppm}[/tex]
Significance level :[tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The formula to calculate the sample size is given by :-
[tex]n=(\dfrac{z_{\alpha/2}s}{E})^2\\\\\Rightarrow\ n=(\dfrac{(1.96)(167)}{57})^2=32.9758025239\approx33[/tex]
Hence, the minimum required sample size would be 33.
In the figure below, angle B and arc AC are congruent.
Answer:
False
Step-by-step explanation:
Correct me if I'm wrong but this suppose to be a true or false question.
The measure of angle of B is going to be half the arc measure of AC so they don't have the same measurement. If they don't have the same measurement, then they can't be congruent.
What is the coefficient of x^4y^4 in the expansion (x+y)^8?
A. 1
B. 40
C. 70
D. It does not exist
Answer:
C. 70
Step-by-step explanation:
In the expansion of (a + b)^n, the k-th term is ...
nCk·a^(n-k)b^k . . . . . k = 0 to n; nCk = n!/(k!(n-k)!)
Here, we have n=8, k=4, so the term of interest is ...
8C4·x^4y^4 = (8·7·6·5)/(4·3·2·1)x^4y^4 = 70x^4y^4
The coefficient of the term is 70.
NASA received three messages in a strange language from a distant planet. Scientists studied these messages and found that "Floos Beiling Hoomp" means "We come in peace" and "Moog Naline Floos" means "Peace, Love, and Freedom " and "Beiling Boog Vladi" means "In the last hour". What does "Hoomp" mean?
Answer:
Hoomp means "we come".
Step-by-step explanation:
"Floos Beiling Hoomp" means "We come in peace"
"Moog Naline Floos" means "Peace, Love, and Freedom "
"Beiling Boog Vladi" means "In the last hour"
Comparing 1st two statements, we get Floos means peace.
Comparing 1st and 3rd statements, we get Beiling means in
So, Hoomp is "we come".
Final answer:
"Hoomp" means "we come".
Explanation:
The question at hand involves deciphering the meaning of a word from messages in a strange language received from a distant planet.
By analyzing the given messages and their translations, we can determine the meaning of individual words through comparison and elimination.
Here's a step-by-step explanation:
"Floos Beiling Hoomp" means "We come in peace"."Moog Naline Floos" means "Peace, Love, and Freedom "."Beiling Boog Vladi" means "In the last hour".Comparing the first and second statements, we understand that "Floos" means peace. From the first and third statements, we deduce "Beiling" means in.
Therefore, given its unique presence in the first statement, "Hoomp" logically translates to "we come".
This question illustrates the process of deciphering language through pattern recognition and comparative analysis, which is a fundamental aspect of linguistics and communication studies.
What is the difference between the GCF and LCM?
Answer:
GCF -The greatest real number shared between two integers. On the other hand, the Lowest Common Multiple (or LCM) is the integer shared by two numbers that can be divided by both number.
Step-by-step explanation:
MAJORR HELP!!!!
In the graph, what are the x- and y-coordinates of the center?
Answer:
D: (-1,2)
Step-by-step explanation:
The X coordinate is between 2 and -4. There is a difference of 6, so you should do -4 + (6/2) = -1.
so the X coordinate is -1
The y coordinate is between 0 and 4. There is a difference of 4, so you should do 0 + (4/2) = 2.
so the y coordinate is 2
This results in the centre being (-1,2)
The coordinates of the center of the equation is (- 1, 2).
We have a ellipse in the figure.
We have to find out the coordinates of the center of ellipse (x, y).
What is an general equation of Ellipse?The general equation of an ellipse in the rectangular coordinate system is -
[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } = 1[/tex]
In the figure given to us, the center of the ellipse at the point of intersection of the lines of equation -
x + 1 = 0
and
y - 2 = 0
The coordinates of the center -
x = - 1 and y = 2.
Hence, the coordinates of the center of the ellipse is (- 1, 2).
To solve more questions on ellipse, visit the link below -
https://brainly.com/question/9448628
#SPJ2
Find the equation of the line that passes through ( 4 , 1 ) and is parallel to the line passing through ( 7 , 11 ) and ( 10 , 20 ) .
Answer:
[tex]y-1=3(x-4)[/tex] -----> equation into point slope form
[tex]y=3x-11[/tex] -----> equation into slope intercept form
[tex]3x-y=11[/tex] -----> equation in standard form
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
step 1
Find the slope of the line passing through ( 7 , 11 ) and ( 10 , 20 )
The slope m is equal to
[tex]m=(20-11)/(10-7)=3[/tex]
step 2
Find the equation of the line with m=3 that passes through (4,1)
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-1=3(x-4)[/tex] -----> equation into point slope form
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y=3x-12+1[/tex]
[tex]y=3x-11[/tex] -----> equation into slope intercept form
Convert to standard form
[tex]Ax+By=C[/tex]
[tex]3x-y=11[/tex] -----> equation in standard form
The slope of the given line passing through (7, 11) and (10, 20) is 3. Since parallel lines have equal slopes, the line passing through (4, 1) will also have a slope of 3. Plugging in the slope and point into the slope-intercept form, we find the equation of the line to be y = 3x - 11.
To find the equation of the line that passes through the point (4, 1) and is parallel to another line, we first need to determine the slope of the given line that passes through (7, 11) and (10, 20).
The slope of a line is found by taking the difference in the y-coordinates divided by the difference in the x-coordinates between two points on the line, which is often expressed as Δy/Δx or (y2-y1)/(x2-x1).
The slope of the line passing through (7, 11) and (10, 20) is calculated as follows:
Δy = 20 - 11 = 9
Δx = 10 - 7 = 3
Slope (m) = Δy/Δx = 9/3 = 3
Since parallel lines have the same slope, the line passing through (4, 1) will also have a slope of 3.
The equation of a line in slope-intercept form (y = mx + b) can then be used, where 'm' is the slope and 'b' is the y-intercept.
As we have the slope and a point on the line, we can substitute them into the equation to solve for 'b'.
The equation will look like this:
y = mx + b
1 = 3(4) + b
1 = 12 + b
b = 1 - 12
b = -11
The equation of the line that goes through (4, 1) and is parallel to the line through (7, 11) and (10, 20) is therefore y = 3x - 11.
Consider these scenarios.
1. An elephant weighs 1.5 × 104 units.
2. A mouse weighs 6.3 × 10-2 units.
3. A puppy weighs 1.2 × 102 units.
Determine the unit of measurement that best represents each scenario.
1.
2.
3.
Final answer:
The elephant is likely measured in pounds, as it fits the known weight range for adult elephants. The mouse is measured in a smaller unit such as grams due to its size. The puppy is best measured in pounds, a common unit for pet animals.
Explanation:
In mathematics, specifically in the context of measurement, it is important to choose the most appropriate unit of measurement depending on the size of the object or substance being measured. When we look at the example scenarios, we can determine the best units as follows:
An elephant weighs 1.5 × 10⁴ units. Given that the range of weight for a male African elephant is between 12,000 and 16,000 pounds, and considering that 1.5 × 104 is 15,000, which is within this range, it is most likely that the unit of measurement in this scenario is pounds.A mouse weighs 6.3 × 10⁻² units. Since a mouse is a very small creature, a larger unit like pounds would be impractical. Generally, rodents are weighed in grams, a smaller and manageable unit of measurement more appropriate for small animals.A puppy weighs 1.2 × 10² units. A puppy, larger than a mouse but much smaller than an elephant, would be best measured in pounds, as that is a common unit of weight for domestic animals like dogs.The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?
Answer:
95% of students are between 14 and 18 years old
Step-by-step explanation:
First we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:
[tex]\mu=16[/tex]
The standard deviation is:
[tex]\sigma=1[/tex]
The z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=14 the Z-score is:
[tex]Z_{14}=\frac{14-16}{1}=-2[/tex]
For x=18 the Z-score is:
[tex]Z_{18}=\frac{18-16}{1}=2[/tex]
Then we look for the percentage of the data that is between [tex]-2 <Z <2[/tex] deviations from the mean.
According to the empirical rule 95% of the data is less than 2 standard deviations of the mean. This means that 95% of students are between 14 and 18 years old
A sequence of numbers a1, a2, a3, . . . is defined as follows: a1 = 3, a2 = 5, and every term in the sequence after a2 is the product of all terms in the sequence preceding it, e.g., a3 = (a1)(a2) and a4 = (a1)(a2)(a3). If an = t and n > 2, what is the value of an+2 in terms of t ?
(A) 4t (B) t^2 (C) t^3 (D) t^4 (E) t^8
Answer:
(D) t^4
Step-by-step explanation:
You have defined ...
a3 = a2·a1
a4 = a3·(a2·a1) = a3²
a5 = a4·(a3·a2·a1) = a4² = (a3²)² = a3⁴
Then if a3 = t, a5 = t⁴
Let's begin by understanding the given sequence and the pattern it follows.
We are given the initial terms:
a1 = 3
a2 = 5
For n > 2, the next term is defined as the product of all preceding terms. Therefore,
a3 = a1 * a2
a4 = a1 * a2 * a3
and so on.
Now, let's generalize this for any term an where n > 2. According to the problem, an = t.
The term immediately after an would be an+1, which equals the product of all preceding terms:
an+1 = a1 * a2 * a3 * ... * an-1 * an
Since an = t, and every term before it has been multiplied to give t (by definition of the sequence), we have:
an+1 = t * t
an+1 = t^2
Now, let's find an+2. This term is the product of all preceding terms, which now includes an+1:
an+2 = a1 * a2 * a3 * ... * an-1 * an * an+1
From above, we know an = t and an+1 = t^2. Hence:
an+2 = t * t^2
an+2 = t^3
Therefore, the value of an+2 in terms of t is t^3. The correct answer is (C) t^3.
Jake wanted to measure the height of the Great Sphinx of Giza. He placed a mirror on the ground and then walked backwards until he was able to see the top of the statue in the mirror. If his eyes were 5.5 feet above the ground, how tall is the statue, to the nearest foot?
Answer:
65
Step-by-step explanation:
Jake measured the height of the Great Sphinx of Giza by using a mirror and the Law of Reflection. Doubling the height of the mirror gives us an approximation of the statue's height.
Explanation:In order to measure the height of the Great Sphinx of Giza, Jake used the concept of the Law of Reflection.
He placed a mirror on the ground and walked backwards until he could see the top of the statue in the mirror.
If his eyes were 5.5 feet above the ground, the mirror's height would be equal to half the height of the statue.
Since Jake's eyes are at a height of 5.5 feet, the distance from the ground to the top of the mirror should also be 5.5 feet.
Therefore, the height of the Great Sphinx of Giza can be calculated by doubling the height of the mirror, which gives us 11 feet.
So, the approximate height of the statue is 11 feet.
ΔABC is a right triangle in which ∠B is a right angle, AB = 1, AC = 2, and BC = sqrt(3).
cos C × sin A =
I think the answer is 3/4, because cos(c) = adj / hypot and sin(a) = opposite / hypot
cos(c) = sqrt(3) / 2
sin(a) = sqrt(3) / 2
which is 3/4 when multiplied.
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
cosC = cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]
sinA = sin60° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
Hence
cosC × sinA = [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{3}{4}[/tex]
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Since,
[tex]\sin \theta=\frac{Opposite leg of }\theta}{\text{Hypotenuse}}[/tex]
[tex]\cos \theta=\frac{Adjacent leg of }\theta}{\text{Hypotenuse}}[/tex]
Given,
In triangle ABC,
AB = 1 unit, AC = 2 unit, and BC = √3 unit
Thus, by the above formule,
[tex]\cos C = \frac{\sqrt{3}}{2}[/tex]
[tex]\sin A=\frac{\sqrt{3}}{2}[/tex]
[tex]\implies \cos C\times \sin A = \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}= \frac{3}{4}[/tex]
let f(x)=3x+5 and g(x)=x^2 find f(x) + g(x)
A) x^2 +3x+5
B) x^3+5
C)3x^2+5
D)3x^3 +5x^2
Answer:
[tex]\large\boxed{A).\,x^2+3x+5}[/tex]
Step-by-step explanation:
In this question, we're trying to figure out what f(x) + g(x) equals to.
We are going to be plugging in the equations they gave to us and solve.
Equations we're going to use:
f(x)=3x+5g(x)=x^2Now, lets get to solving.
We would plug the equations in the appropriate spot. In other words, we're pretty much plugging them in to the right variable.
Your expression should look like this:
[tex]3x+5+x^2[/tex]
Now we solve.
[tex]3x+5+x^2\\\\x^2\,\text{can't combine with 3x because of the exponent, so we will eave it as is}\\\\\text{There is nothing else we can combine, so it would stay as:}\\\\x^2+3x+5[/tex]
You should end up with x²+3x+5.
This means that your final answer would be A) x^2 +3x+5
I hope this helped you out.Good luck on your academics.Have a fantastic day!Find the value for tan θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form
Find the value for sec θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form.
Answer:
Step-by-step explanation:
The point (-3, 4) is in QII. If we plot this point and drop an altitude then connect the point to the origin, we have a right triangle with side opposite measuring 4 units and side adjacent measuring |-3|. The tangent of the reference angle is the ratio side opposite/side adjacent, so
[tex]tan\theta=-\frac{4}{3}[/tex]
Since secant is the reciprocal of cosine, let's find the cosine of the reference angle and then flip it upside down. The cosine of the angle is the side adjacent (got it) over the hypotenuse (don't have it). We can find the hypotenuse using Pythagorean's Theorem:
[tex]c^2=-3^2+4^2[/tex] s0
[tex]c^2=25[/tex] and
c = 5
The cosine of the angle theta is
[tex]cos\theta=-\frac{3}{5}[/tex]; therefore,
[tex]sec\theta=-\frac{5}{3}[/tex]
Please help!! If you really love math!! 50 POINTS!!!!!!
Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated?
1/5x + 3/4y = 9
2/3x - 5/6y = 8
A: –10 times the first equation and 3 times the second equation
B: 10 times the first equation and 3 times the second equation
C: –3 times the first equation and 5 times the second equation
D: 3 times the first equation and 5 times the second equation
The multipliers of this system of equations have been determined to create opposite terms of the x-variable.
12(-1/6x - 2/3y = -5 )--------> -2x-8y=-60
5(2/5x + 1/5y = -9)----------> 2x+y=-45
What is the value of y?
A: –30
B:–15
C: 15
D: 30
Examine the system of equations. Which is an equivalent form of the first equation that when added to the second equation eliminates the y terms?
-5x + 3/4y = 12
8x + 12y = 11
A: 10x – 12y = –192
B:–10x + 12y = 192
C: 5x – 12y = 96
D: –5x + 12y = 96
Answer:
A: –10 times the first equation and 3 times the second equationC: 15none of the choices shown. Should be 80x -12y = -192Step-by-step explanation:
1. The multiplier for the first equation can be found by the ratio ...
-(second equation x-coefficient)/(first equation x-coefficient)
= (-2/3)/(1/5) = -10/3
This tells you that multiplying the first equation by -10 and the second equation by 3 will make the x-terms cancel. Matches selection A.
__
2. Adding the two equations shown gives ...
(-2x -8y) +(2x +y) = (-60) +(-45)
-7y = -105
y = -105/-7 = 15 . . . . matches selection C.
__
3. Using the rule shown in question 1, the multiplier for the first equation will be ...
-(second equation y-coefficient)/(first equation y-coefficient)
-12/(3/4) = -16
Multiplying the first equation by -16 gives ...
-16(-5x +3/4y) = -16(12)
80x -12y = -192 . . . . no matching answer choice
(Sometimes, the problems have errors in their answers. This is one of those times. Choice A will probably be graded as correct, even though it is not.)
A family is traveling in a car at a constant average speed during a road trip. The function d(t)=70t+620 models the distance d, in miles, the family is from their house t hours after starting to drive on the second day of the road trip.
A) At what average speed is the family's car traveling?
-Explain
B) What is the distance between the family's house and the point where they started driving on the second day
-Explain
Answer:
A. 70 miles per hour B. 620 miles from home
Step-by-step explanation:
This function is a linear equation, following the slope-intercept form of a line. This standard form is y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is the rate at which the steepness of the line is changing. The y-intercept is where the function is "starting".
In our case, the number in the rate of change position is 70. It is being multiplied by t. If t = 1, that means that after 1 hour, we have gone 70 miles. If t = 2, that means after 2 hours we have gone 140 miles. If t = 3, that means that after 3 hours, we have gone 210 miles; etc. That number in the slope position represents the rate at which you are traveling PER HOUR; the slope.
The "starting" position of day 2 is found in the y-intercept. Replacing x with 0, meaning NO time has gone by at all, at the beginning of the second day, we are starting 620 miles from home.
The family's car is traveling at an average speed of 70 miles per hour. The distance between the family's house and the starting point on the second day is 620 miles.
The given function d(t) = 70t + 620 models the distance in miles from the family's house t hours after starting to drive on the second day of their road trip.
A) At what average speed is the family's car traveling?
The coefficient of t in the distance function, which is 70, represents the family's car average speed. Therefore, the car is traveling at an average speed of 70 miles per hour.
B) What is the distance between the family's house and the point where they started driving on the second day?
The constant term in the distance function, which is 620, signifies the distance in miles from the family's house at t = 0 or the starting point. Thus, the distance between the family's house and the starting point on the second day is 620 miles.
The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of pgreater than>0.5, which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is >0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?
Answer:
The preferred p-value among the options offered is 0.001. The reason is because p-value represents the minimum probability of committing the type I error, that is, the probability of rejecting the null hypothesis, with the information contained in the sample, given that this hypothesis is true. The p-value of 0.001 is the lowest value proposed for this probability. Therefore, it supports more evidence that the null hypothesis is false.
Step-by-step explanation:
The preferred P-value among the options provided is 0.001.
0.001 is the preferred p-value simply because it shows the minimum probability of committing an error, it also implies that the probability of rejecting the null hypothesis based on the information presented in the sample, considering that the hypothesis is true.
Further ExplanationTherefore, the p-value 0.001 is the lowest value proposed for this probability and it also corresponds to the sample of evidence that supports the alternative hypothesis which shows the method is effective.
Hypothesis testing refers to an act in statistics in which an analyst test the assumption as regards to a population parameter.
The methodology to be used by analysts is based on the nature of the data that are used and the purpose of the analysis
An analysts test a sample to accept or reject a null hypothesis. The outcome of the tests will reveal the analysis if his primary hypothesis is true or not. If the analysis of the tests is not true, it then means the analysts will have to formulate a new hypothesis and do the analysis again.
It implies the analysts will continue to repeat the process until the analysis shows the data hypothesis is true.
LEARN MORE:
The Ericsson method is one of several methods https://brainly.com/question/12921499Ericsson method is one of several methods https://brainly.com/question/13543177KEYWORDS:
hypothesis testericsson methodanalysisproportionprobabilityGiven: ∠LKM ≅ ∠JKM
∠LMK ≅ ∠JMK
Prove: ∆LKM ≅ ∆JKM
Which method can you use to prove these triangles congruent?
the ASA Postulate
the SAS Postulate
the HL Theorem
the AAS Theorem
Answer:
ASA
Step-by-step explanation:
Answer: the ASA Postulate
Step-by-step explanation:
In the given picture , we have two triangles ∆LKM and ∆JKM , in which we have
[tex]\angle{LKM}\cong\angle{JKM}\\\\\angle{LMK}\cong\angle{JMK}[/tex]
[tex]\overline{KM}\cong\overline{KM}[/tex] [common]
By using ASA congruence postulate , we have
∆LKM and ∆JKM
ASA congruence postulate tells that if two angles and the included side of a triangle are congruent to two angles and the included side of other triangle then the triangles are congruent.
Jemmma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What ratio of the number of red balls to the number of balls that are either yellow or pink?
Laura has pledges of $5 for each mile she walks in the Juvenile Diabetes Walkathon fundraiser.
-Use the table below to record the miles walked and the money earned for miles 0 through 6
- Write a rule relating miles walked to money collected
Answer:
r = 5m
Step-by-step explanation:
miles walked money earned
0 0
1 1*5 5
2 2 * 5 10
3 3 * 5 15
4 4 * 5 20
5 5 * 5 25
6 6 * 5 30
We multiply 5 by each mile walked to determine how much money was raised
r = 5m where r is the money raised and m is the miles walked
Benito spent $1822 to operate his car last year. Some of these expenses are listed below. Benito's only other expense was for gasoline. If he drove 7340 miles, what was the average cost of the gasoline per mile?
Operating Expenses
Insurance $809
Registration $170
Maintenance $57
A. 61.06 cents
B. 10.71 cents
C. 1.27 cents
D. not enough information
Answer:
B. 10.71 cents
Step-by-step explanation:
Benito's other expenses total ...
$809 +170 +57 = $1036
so his gas expense is ...
$1822 -1036 = $786
Then the per-mile cost is ...
$786/(7340 mi) ≈ $0.10708/mi
Benito's gas cost averaged 10.71¢ per mile.
Answer is B) 10.71 cents.
You just add Benito's operating expenses togther, like so:
809 + 170 + 57 = $1036 so far.
Next, subtract the total amount he spent this last year (1822), with how much he spent so far (1036).
1822 - 1036 = $786
Finally, divide the final total with the 7340 miles he plans to drive.
786 ÷ 7340 = 0.10708
Answer is B) 10.71 cents.
☺☺☺☺
WANT FREE 20 POINTS + BRAINLIEST? answer this geometry question correct and i got you
Which statements are true based on the diagram? Select three options.
A. Points N and K are on plane A and plane S.
B. Points P and M are on plane B and plane S.
C. Point P is the intersection of line n and line g.
D. Points M, P, and Q are noncollinear.
E. Line d intersects plane A at point N.
Answer:
the three options i chose:
A. n and k are on plane A and s
C. p is the inteersection of n and g
D. those 3 lines are noncollinear
Answer:
The correct options are A, C and D.
Step-by-step explanation:
From the given figure it is clear that points N and K lie on the line f, and line f is the intersection line of plane A and S.
So, points N and K are on plane A and S. Option A is correct.
Points P and M lie on the line n, and line n is not the intersection line of plane B and S.
We clearly see that point M is not on the plane S.
So, option B is incorrect.
Point P is the intersection of line n and line g.
So, option C is correct.
Point M and P lie on line n and point P and Q lie on line g.
Three points are collinear if they are lie on a straight line.
Since points M, P and Q are not collinear, therefore they are noncollinear.
So, option D is correct.
Line d intersects plane A at point L.
So, option E is incorrect.
Graph the parametric equation x = 2t y = t + 5, -2 ≤ t ≤ 3
Just fun I'm going to add something above the below.
You can write an equation for this without the parameter.
You have y=t+5 and x=2t. If you multiply both sides of y=t+5 by 2 you should get 2y=2t+10 and guess what you can replace 2t with x since you have x=2t. So you can write 2y=x+10 as your equation to represent the parametric version they have here.
This is a linear equation as our graph appears to be below. Solve for y by dividing both sides by 2 gives you y=x/2 +5. The slope is 1/2 and the y-intercept is 5. If t is between -2 and 3 then x is between -4 and 6 since x is doubled t (inclusive here since we have those equal signs along with those inequalities).
So you could have just graph the line y=x/2+5 on the interval [tex]-4 \le x \le 6 [/tex]/
Anyways, I'm also going to look at this without the rewrite:
I'm going to make a table with 4 columns. The first column is t. The second is x(t), the third is y(t), and the fourth will be a list of points (x,y) our relation will go through).
t | x(t) | y(t) | (x,y)
------------------------------------------------------
-2 2(-2)=-4 -2+5=3 (-4,3)
-1 2(-1)=-2 -1+5=4 (-2,4)
0 2(0)=0 0+5=5 (0,5)
1 2(1)=2 1+5=6 (2,6)
2 2(2)=4 2+5=7 (4,7)
3 2(3)=6 3+5=8 (6,8)
Now I'm going to graph the points in the last column on a coordinate-plane.
The horizontal axis is your x-axis and the vertical axis is your y-axis. I did the x-axis going up or down by two's while the y-axis is going up and down only by one's.
Huixian needs to pack 171 pens, 63 pencil, and 27 erasers into identical bags so that each item is equally distributed among the gift bags. Find the largest number of gift bags that can be packed, and the number of each item in a gift bag
Answer:
87 gift bags
Step-by-step explanation:
Answer:
6 pens
2 pencils
1 eraser in each gift bag
Most number of Gift Bags = 27.
Step-by-step explanation:
There will be some bags left over. The limiting factor is the erasers. At most, you can have 27 erasers and therefore 27 gift bags.
171 pens: 171/27 = 6 (you have to round down). The number of pens left over is 9.
(27*6 = 162)
171 - 162 = 9
63 Pencils: 63/27 = 2 pencils per gift bag. There will be
63 - 2*27
63 - 54
9 pencils will be left over.
What is the end behavior of the graph of the polynomial function f(x)=-x^5+9x-4
Answer:
Because it's an odd function, the "tails" go off in different directions. Also, because it's a negative function, the left starts from the upper left and the right goes down into negative infinity. If it was a positive, the tails would be going in the other directions, meaning that the left would come up from negative infinity and the right would go up into positive infinity.
Step-by-step explanation:
Answer:
C on Edge: As x--> -∞, y-->+∞ and as x-->+∞, y-->-∞
:) Have a good day / night Everyone and stay safe!
Darren teaches a class of 25 students. He assigns homework 3 times a week, and each assignment consists of 12 problems. How many problems must Darren correct each week?
A.
225 problems
B.
890 problems
C.
900 problems
D.
1,000 problems
Answer:
Option C is correct.
Step-by-step explanation:
Homework is assigned: 3 times a week
Each assignment consists problems = 12
Total questions in 1 week = 12*3 = 36
Total no of students = 25
So, Problems Darren must correct each week = Total no of students * Total questions in 1 week
Problems Darren must correct each week = 25*36
Problems Darren must correct each week = 900
So, Option C is correct.
For this case we have that each week assign 3 tasks, each of 12 problems, then multiply:
[tex]3 * 12 = 36[/tex]
Thus, assign 36 weekly problems to each student. Darren has 25 students, so, multiplying, we have:
[tex]36 * 25 = 900[/tex]
Thus, Darren must correct 900 weekly problems.
Answer:
Option C
The percent body fat in a random sample of 36 men aged 20 to 29 has a sample mean of 14.42. Find a 99% confidence interval for the mean percent body fat in all men aged 20 to 29. Assume that percent body fat follows a Normal distribution, with a standard deviation of 6.95.
A) (0.8, 28.04)B) (12.15, 16.69)C) (12.51, 16.33)D) (12.07, 16.77)
Answer: [tex](11.44,\ 17.4)[/tex]
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Given : Sample size : [tex]n=36[/tex]
Sample mean : [tex]\ovreline{x}=14.42[/tex]
Standard deviation : [tex]\sigma=6.95[/tex]
Significance level : [tex]\alpha=1-0.99=0.01[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.005}=2.576[/tex]
Now, the 99% confidence interval for the mean percent body fat in all men aged 20 to 29 will be :-
[tex]14.42\pm (2.576)\dfrac{6.95}{\sqrt{36}}\\\\\approx14.42\pm2.98\\\\=(14.42-2.98,\ 14.42+2.98)=(11.44,\ 17.4)[/tex]
Can u guys PLEASE do this question 30 a
Answer:
1/2 units (I'm not sure what units the scale is using).
Step-by-step explanation:
We could setup a proportion. The trick to doing this is lining up corresponding parts.
The scale of a plan is 1 to 200.
We want to know the scale distance that represents the distance 100 m.
So we have:
1 to 200
x to 100
Setting up a proportion:
[tex]\frac{1}{x}=\frac{200}{100}[/tex]
Cross multiply:
[tex]100(1)=200(x)[/tex]
Divide both sides by 200:
[tex]\frac{100(1)}{200}=x[/tex]
[tex]\frac{100}{200}=x[/tex]
[tex]\frac{1}{2}=x[/tex]
[tex]x=\frac{1}{2}[/tex]
So a 1/2 units in length on the scale represents 100 m.
Kate and Stella both worked at the coffee shop today. Kate's total cups of coffee made is represented by f(x); and Stella's total cups of coffee made is represented by g(x). Use the functions below to write a function that represents the total cups of coffee they made today.
f(x) = 6x − 8
g(x) = 3x + 1
Answer:
The function that represents the total cups of coffee they made today is [tex]h(x)=9x-7[/tex].
Step-by-step explanation:
The given function are
[tex]f(x)=6x-8[/tex]
[tex]g(x)=3x+1[/tex]
Where, Kate's total cups of coffee made is represented by f(x) and Stella's total cups of coffee made is represented by g(x).
The total cups of coffee they made today is represented by the function
[tex]h(x)=f(x)+g(x)[/tex]
Substitute the value of functions.
[tex]h(x)=6x-8+3x+1[/tex]
Combine like terms.
[tex]h(x)=(6x+3x)+(-8+1)[/tex]
[tex]h(x)=9x-7[/tex]
Therefore the function that represents the total cups of coffee they made today is h(x)=9x-7.
Answer:
its 9x-7
Step-by-step explanation:
Write the equation of the line that is perpendicular to the line 5y=x−5 through the point (-1,0).
A. y= 1/5x+5
B. y= 1/5x−5
C. y= −5x−5
D. y= −5x+5
Steps:
---> Re arrange equation to get the format: y = mx + c
---> Work out the perpendicular gradient from the first equation
----> Substitute the x and y coordinates of point (-1, 0) and the perpendicular gradient into y = mx + c and work out c
---> Finally, substitute the perpendicular gradient and the value for c into y =mx + c to get the gradient of the perpendicular line:
__________________________________________
Rearranging equation into the format: y = mx + c:
[tex]5y = x - 5[/tex] (Just divide both sides by y)
[tex]y = \frac{1}{5}x -1[/tex]
___________________________________________
Working out the perpendicular gradient:
To work out the perpendicular gradient, we just take the negative reciprocal of the gradient of [tex]y = \frac{1}{5}x -1[/tex]
Note: negative reciprocal means we just flip the fraction and put a minus sign.
The regular gradient is: [tex]\frac{1}{5}[/tex]
So the perpendicular gradient is the negative reciprocal of [tex]\frac{1}{5}[/tex]
which is -5 (note: [tex]\frac{-5}{1}[/tex] is just 5-)
___________________________________________
Now lets substitute in the values for the gradient (m), the y coord (0) and x coord (-1) of the point (-1, 0) into y = mx + c, and solve for c:
y = mx + c (substitute in all known values)
0 = -5(-1) + c (the -1 times -5 will make + 5)
0 = 5 + c (subtract 5 from both sides to cancel out the + 5)
-5 = c
so c = -5
____________________________________________
Finally, just substitute in the perpendicular gradient and the value for c into y = mx + c to get the equation of the perpendicular line:
y = mx + c (substitute in the perp. gradient and c)
y = -5x - 5
____________________________________________________
Answer:The equation to the line perpendicular to 5y = x - 5 through point (-1, 0) is :
C. y = -5x - 5
_______________________________________________
A quicker way to get equation of the perpendicular line once you know the perp. gradient is to use the equation:
y - y1 = m (x - x1)
y1 is the y coordinate of (-1, 0)
x1 is the x coordinate of (-1, 0)
m is the perpendicular gradient.
y - y1 = m (x - x1) (Substitute in values)
y - 0 = -5 ( x - - 1) (simplify)
y = -5 (x + 1) (expand the brackets)
y = -5x - 5
Help plz system of inequalities
Answer:
c. 1 ≤ y ≤ 3; y ≥ -2x +2
Step-by-step explanation:
The shading between the solid lines y=1 and y=3 tells you that one of the inequalities is 1 ≤ y ≤ 3 (including the "or equal to" case). The shading above the solid diagonal line tells you that inequality will be y ≥ (something).
Choice C matches these observations.