The survey question 'Do you eat at least five servings a day of fruits and vegetables?' is designed to collect categorical data, as it classifies respondents into groups based on their affirmative or negative answer, rather than providing a numerical value.
Explanation:The question "Do you eat at least five servings a day of fruits and vegetables?" is designed to collect categorical data. This is because the answers to the question will classify respondents into different categories, specifically those who do eat at least five servings of fruits and vegetables per day and those who do not. As such, the data obtained will be qualitative in nature, allowing us to compare and organize individuals based on their dietary habits.
For a more comprehensive understanding, let's compare data types. In contrast to categorical data, a quantitative variable is numeric and can be measured or counted. It can further be subdivided into discrete or continuous data. Quantitative discrete data involve counts of items or occurrences (e.g., the number of classes you take per school year), while quantitative continuous data involve measurements that can take on any value within a given range (e.g., the weights of soups measured in ounces).
Returning to the student's survey question about fruit and vegetable consumption, it is evident that the data collected does not involve counting or measuring numerical values, but rather involves placing respondents into categories based on their dietary habits. Therefore, the variable in question is indeed categorical.
The scores of 12th-grade students on the national assessment of educational progress year 2000 mathematics test have a distribution that is approximately normal with mean of 300 and standard deviation of 35.
Answer:
a)[tex]P(X>300)=P(\frac{X-\mu}{\sigma}>\frac{300-\mu}{\sigma})=P(Z>\frac{300-300}{25})=P(z>0)= 0.5[/tex]
[tex]P(X>335)=P(\frac{X-\mu}{\sigma}>\frac{335-\mu}{\sigma})=P(Z>\frac{335-300}{25})=P(z>1.4)=0.0808[/tex]
b)[tex]P(\bar X>300)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{300-\mu}{\sigma_{\bar x}})=P(Z>\frac{300-300}{17.5})=P(z>0)= 0.5[/tex]
[tex]P(\bar X>335)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{335-\mu}{\sigma_{\bar x}})=P(Z>\frac{335-300}{17.5})=P(z>2)=0.0228[/tex]
Step-by-step explanation:
Assuming the following questions:
a) Choose one twelfth-grader at random. What is the probability that his or her score is higher than 300? Higher than 335?
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(300,35)[/tex]
Where [tex]\mu=300[/tex] and [tex]\sigma=35[/tex]
We are interested on this probability
[tex]P(X>300)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>300)=P(\frac{X-\mu}{\sigma}>\frac{300-\mu}{\sigma})=P(Z>\frac{300-300}{25})=P(z>0)= 0.5[/tex]
We find the probabilities with the normal standard table or with excel.
And for the other case:
[tex]P(X>335)=P(\frac{X-\mu}{\sigma}>\frac{335-\mu}{\sigma})=P(Z>\frac{335-300}{25})=P(z>1.4)=0.0808[/tex]
b) Now choose an SRS of four twelfth-graders. What is the probability that his or her mean score is higher than 300? Higher than 335?
For this case since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
[tex] \bar X = \sim N(\mu = 300, \sigma_{\bar x} = \frac{35}{\sqrt{4}}=17.5)[/tex]
The new z score is given by:
[tex]z=\frac{\bar X -\mu}{\sigma_{\bar x}}[/tex]
And using the formula we got:
[tex]P(\bar X>300)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{300-\mu}{\sigma_{\bar x}})=P(Z>\frac{300-300}{17.5})=P(z>0)= 0.5[/tex]
We find the probabilities with the normal standard table or with excel.
And for the other case:
[tex]P(\bar X>335)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{335-\mu}{\sigma_{\bar x}})=P(Z>\frac{335-300}{17.5})=P(z>2)=0.0228[/tex]
ASAP! I NEED THIS DONE AS QUICKLY AS POSSIBLE WITH WORKING OUT
After t seconds, a particle P has position vector
r = [(3t³- t + 3)i + (2t²+ 2t - 1)j] m
(a) Find an expression for the velocity of P in terms of t
(b) Find an expression for the acceleration of P in terms of t
Answer:
See explanation.
Step-by-step explanation:
Let us first analyze some principle theory. By definition we know that the velocity ( [tex]v[/tex] ) is a function of a distance ( [tex]d[/tex] ) covered in some time ( [tex]t[/tex] ), whilst acceleration ( [tex]a[/tex] ) is the velocity achieved in some time. These can also been expressed as:
[tex]v = \frac{d}{t}\\[/tex] and [tex]a=\frac{v}{t}[/tex]
We also know that both velocity and acceleration are vectors (therefore they are characterized by both a magnitude and a direction). Finally we know that given a position vector we can find the velocity and the acceleration, by differentiating the vector with respect to time, once and twice, respectively.
Let us now solve our problem. Here we are givine the Position vector of a particle P (in two dimensional space of [tex]i-j[/tex] ) as:
[tex]r=(3t^3-t+3)i+(2t^2+2t-1)j[/tex] Eqn.(1)
Let us solve.
Part (a) Velocity: we need to differentiate Eqn.(1) with respect to time as:
[tex]v(t)=\frac{dr}{dt}\\\\ v(t)=[(3)3t^2-1]i+[(2)2t+2]j\\\\v(t)=(9t^2-1)i+(4t+2)j[/tex] Eqn.(2)
Part (b) Acceleration: we need to differentiate Eqn.(2) with respect to time as:
[tex]a(t)=\frac{dv}{dt}\\ \\a(t)=[(2)9t]i+4j\\\\a(t)=(18t)i+4j[/tex]
Thus the expressions for the velocity and the acceleration of particle P in terms of t are
[tex]v(t)=(9t^2-1)i+(4t+2)j[/tex] and [tex]a(t)=(18t)i+4j[/tex]
Six students from a statistics class reported the number of hours of television they watch per week. Here are their data: 8, 10, 5, 14, 3, 6. What is the standard deviation of the number of hours of television watched per week for this sample of six students?
Answer:
3.93
Step-by-step explanation:
Let x is the number of hours of television watched per week by six students.
X 8 10 5 14 3 6
Standard deviation for sample data is
[tex]Standard deviation=S=\sqrt\frac{{sum(x-xbar)^2} }{n-1}[/tex]
[tex]xbar=\frac{sum(x)}{n}[/tex]
[tex]xbar=\frac{8+10+5+14+3+6}{6}[/tex]
[tex]xbar=\frac{46}{6}[/tex]
xbar=7.67
[tex]sum(x-xbar)^2=(8-7.67)^2+(10-7.67)^2+(5-7.67)^2+(14-7.67)^2+(3-7.67)^2+(6-7.67)^2[/tex][tex]sum(x-xbar)^2=0.11+5.44+7.11+40.11+21.78+2.78=77.33[/tex]
[tex]Standard deviation=S=\sqrt\frac{{(77.33)} }{5}[/tex]
[tex]S=\sqrt15.466[/tex]
S=3.93
Punction gives the distance of a dog
from a post, in feet, as a function of time,
in seconds, since its owner left.
Find the value of $(20) and of f(140).
distance from post in feet
20
40
60
80
100 120 140
Function C gives the cost, in dollars, of buying n apples. What does each expression
or equation represent in this situation?
a. 8) = 4.50
b. C(2)
The distance of a dog from a post and the cost of buying apples can be represented by functions. We can find the values of these functions by substituting specific values and calculating the corresponding outputs.
Explanation:In this question, we are given a function that represents the distance of a dog from a post as a function of time. To find the value of f(20), we substitute 20 into the function and calculate the corresponding distance. To find the value of f(140), we do the same thing, substituting 140 into the function.
f(20) = 20 feet
f(140) = 140 feet
In the second part of the question, we are given a function C that represents the cost of buying n apples. To find the meaning of each expression or equation, we substitute the given value of n and calculate the corresponding cost.
C(8) = $4.50
C(2) represents the cost of buying 2 apples.
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What is the answer to 3 1/4 cans of red paint and 3 2/12 cans of yellow paint add up to how many cans of orange paint? I know it is 6 cans of orange paint, but don't know the fraction.
The number of orange cans of paint is 6
Solution:
Given that,
[tex]\text{Number of cans of red paint } = 3\frac{1}{4}\\\\\text{Number of cans of yellow paint } = 3\frac{2}{12}[/tex]
Let us convert the mixed fractions to improper fractions
Multiply the whole number part by the fraction's denominator.
Add that to the numerator.
Then write the result on top of the denominator
[tex]\rightarrow 3\frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{13}{4}\\\\\rightarrow 3\frac{2}{12} = \frac{12 \times 3 + 2}{12} = \frac{38}{12}[/tex]
Now we have to add red cans of paint and yellow cans of paint to get orange cans of paint
[tex]\text{Number of cans of orange paint } = \frac{13}{4} + \frac{38}{12}[/tex]
Take L.C.M for denominators
The prime factors of 4 = 2 x 2
The prime factors of 12 = 2 x 2 x 3
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 3
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 = 12
[tex]\text{Number of cans of orange paint } = \frac{13}{4} + \frac{38}{12}[/tex]
[tex]\text{Number of cans of orange paint } = \frac{13 \times 3}{4 \times 3} + \frac{38}{12}\\\\\text{Number of cans of orange paint } = \frac{39}{12} + \frac{38}{12}\\\\\text{Number of cans of orange paint } = \frac{77}{12} = 6.4 \approx 6[/tex]
Thus the number of orange cans of paint is 6
Sebuah tangga yang panjangnya 5m bersandar pada dinding rumah. Tinggi dinding yang di capai tangga tersebut adalah 3,5m, jarak ujung bawah tangga terhadap dinding?
The distance between the base of the ladder and the wall is approximately 3.57 meters.
Explanation:To find the distance between the base of the ladder and the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the base of the ladder represents one side of the triangle, the height of the ladder represents another side, and the distance between the base of the ladder and the wall represents the hypotenuse.
Using the given information, we can calculate the distance as follows:
d^2 = 5^2 - 3.5^2
d^2 = 25 - 12.25
d^2 = 12.75
d ≈ √12.75
d ≈ 3.57m
Therefore, the distance between the base of the ladder and the wall is approximately 3.57 meters.
A veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine, and that the number of milligrams, m, varies directly with the weight of the dog, w. The vet uses these steps to find the amount of medicine to give a 10-pound dog. Step 1 Find the constant of variation. k = StartFraction 0.5 Over 50 EndFraction = 0.01 Step 2 Write the direct variation equation. m = 0.01 w Step 3 Substitute 10 into the equation to find the dosage for a 10-pound dog. 10 = 0.01 w Step 4 Solve for w. 10 = 0.01 w. W = 1000. The 10-pound dog needs 1000 milligrams. In which step did the veterinarian make the first error? Step 1 Step 2 Step 3 Step 4
Answer:the veterinarian made the first error in step 3
Step-by-step explanation:
the number of milligrams, m, varies directly with the weight of the dog, w.
Assuming constant of variation is k, then,
m = kw
k = m/w = 0.5/50 = 0.01
Therefore,
m = 0.01w
In step 3, Substituting 10 into the equation to find the dosage for a 10-pound dog like 10 = 0.01w was error.
The correct step is
m = 0.01 × 10
m = 0.1 milligrams
Noah has a total of 47 video games he only buys action games in sports games he has 21 warehousing in the sports games how many Action games and how many sports game does he have
Question is not proper;Proper question is given below;
Noah has a total of 47 video games. he only buys action games and sports games. He has 21 more action games than sports games. how many action games, a, and sports games, s, does he own?
Answer:
Noah has 34 action games and 13 sports games.
Step-by-step explanation:
Given:
Total number of games he has = 47
Let the number of action games be 'a'.
Let the number of sports game be 's'.
So we can say that;
Total number of games he has is equal to sum of the number of action games and the number of sports games.
framing in equation form we get;
[tex]a+s = 47 \ \ \ \ \ eqaution \ 1[/tex]
Also Given:
He has 21 more action games than sports games.
so we can say that;
[tex]a=s+21 \ \ \ equation\ 2[/tex]
Now Substituting equation 2 in equation 1 we get;
[tex]a+s=47\\\\s+21+s=47\\\\2s+21=47[/tex]
Subtracting both side by 21 we get;
[tex]2s+21-21=47-21\\\\2s = 26[/tex]
Dividing both side by 2 we get;
[tex]\frac{2s}{2}=\frac{26}{2}\\\\s=13[/tex]
Now Substituting the value of 's' in equation 2 we get;
[tex]a=s+21=13+21=34[/tex]
Hence Noah has 34 action games and 13 sports games.
Use the law of sines to find the value of y. Round to the nearest tenth.Law of sines: sin(A)/a = sin (B)/b= sin(C)/cTRiangleXYZXY=2XZ=yangle of y= 75angle of z = 50
y=2.50 units
Step-by-step explanation:
Given that angle ∠Y=75°, ∠Z=50°, side XY=2 units, and side XZ is y then applying the sine rule for this case,
x/sin ∠x =y/sin y =z/sin z
2/sin 50°=y/sin 75°
2 sin 75° =y sin 50°
y= 2 sin 75°/sin 50°
y=2.50 units
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Answer:
C
Step-by-step explanation:
I just finished the test :)
simplifying inside parentheses first pt. 2
Answer:
The answer to your question is the second option
Step-by-step explanation:
Process
Simplify using exponents laws, first inside the parentheses and then outside the parentheses.
[tex][\frac{a^{-2}b^{2}}{a^{2}b^{-1}} ]^{-3}[/tex]
a) Simplify a
a⁻² a⁻² = a⁻⁴
b) Simplify b
b² b¹ = b³
c) Write the result
[tex][\frac{b^{3}}{a^{4}}]^{-3}[/tex]
d) [tex][\frac{a^{4}}{b^{3}}]^{3}[/tex]
e) Simplify
[tex]\frac{(a^{4})^{3}}{(b^{3})3}[/tex]
f) Result
[tex]\frac{a^{12}}{b^{9}}[/tex]
Julia purchased a new car and traveled 356 miles before refueling. If she needed 15.6 gallons of gas to fill the car's tank, estimate her gas mileage.
Answer:
22.8 MPG
Step-by-step explanation:
356 divided by 15.6 = 22.8
Please help asap, brainliest,thanks, and 50 points. Thank you soooo much! <3
Answers:
1) [tex]x^{8} y^{8}[/tex]
2) [tex]y^{3} \sqrt{y}[/tex]
3) [tex]5x^{4} \sqrt{6}[/tex]
4) [tex]\sqrt{7}[/tex]
5) [tex]\frac{\sqrt{z}}{z}[/tex]
Step-by-step explanation:
1) [tex]\sqrt{x^{16} y^{36}}[/tex]
Rewriting the expression:
[tex](x^{16} y^{36})^{\frac{1}{2}}[/tex]
Multiplying the exponents:
[tex]x^{\frac{16}{2}} y^{\frac{36}{2}}[/tex]
Simplifying:
[tex]x^{8} y^{8}[/tex]
2) [tex]\sqrt{y^{7}}[/tex]
Rewriting the expression:
[tex]\sqrt{y^{6} y}=(y^{6} y)^{\frac{1}{2}}[/tex]
Multiplying the exponents:
[tex]y^{\frac{6}{2}} y^{\frac{1}{2}}[/tex]
Simplifying:
[tex]y^{3} y^{\frac{1}{2}}=y^{3} \sqrt{y}[/tex]
3) [tex]\sqrt{150 x^{8}}[/tex]
Rewriting the expression:
[tex]\sqrt{(6)(25) x^{8}}[/tex]
Since [tex]\sqrt{25}=5[/tex]:
[tex]5x^{4}\sqrt{6}[/tex]
4) [tex]\frac{7}{\sqrt{7}}[/tex]
Multiplying numerator and denominator by [tex]\sqrt{7}[/tex]:
[tex]\frac{7}{\sqrt{7}} (\frac{\sqrt{7}}{\sqrt{7}})=\frac{7}{7\sqrt{7}}[/tex]
Simplifying:
[tex]\sqrt{7}[/tex]
5) [tex]\frac{5z}{\sqrt{25 z^{3}}}[/tex]
Rewriting the expression:
[tex]\frac{5z}{5z \sqrt{z}}[/tex]
Simplifying:
[tex]\frac{1}{\sqrt{z}}[/tex]
Since we do not want the square root in the denominator, we can multiply numerator and denominator by [tex]\sqrt{z}[/tex]:
[tex]\frac{1}{\sqrt{z}}(\frac{\sqrt{z}}{\sqrt{z}})[/tex]
Finally:
[tex]\frac{\sqrt{z}}{z}[/tex]
if you want to comeplete baby step 1 so that you have $1,000 in your savings account, and you are able to put in $125 a week, how many weeks will it take to have $1000?
Answer:
8 weeks
Step-by-step explanation:
$125*8 = $1000
Answer:it will take you 8 weeks to have $1,000 in your savings account
Step-by-step explanation:
If you want to comeplete baby step 1 so that you have $1,000 in your savings account, and you are able to put in $125 a week. It means that the number of weeks that it will take you to have $1000 in your savings account would be
1000/125 = 8 weeks.
Researchers working the mean weight of a random sample of 800 carry-on bags to e the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300?
(A) The bias will decrease and the variance will remain the same.
(B) The bias will increase and the variance will remain the same.
(C) The bias will remain the same and the variance will decrease.
(D) The bias will remain the same and the variance will increase.
(E) The bias will decrease and the variance will decrease.
Final answer:
Increasing the sample size from 800 to 1,300 for estimating the mean weight of carry-on bags keeps the bias the same but decreases the variance, meaning that the sample will have lower variability around the true population mean.
Explanation:
When researchers working to estimate the mean weight of carry-on bags increase the sample size from 800 to 1,300, the correct effect on the bias and variance of the estimator is that the bias will remain the same and the variance will decrease. Bias is a measure of the systematic error of an estimator, and changing the sample size does not generally affect the estimator's systematic error if the estimator is unbiased to begin with. On the other hand, increasing the sample size leads to a decrease in variance which measures the spread of the sample means around the true population mean. Therefore, the larger the sample size, the closer the sampling distribution of the mean will be to the population mean, thus reducing variability, as indicated by a smaller standard deviation and a narrower confidence interval. Therefore, the correct answer is (C): The bias will remain the same and the variance will decrease.
gina pasted 3 stickers in a book. if she added one sticker to her collection every day, what equation represents the relationship between x (number of days) and y (number of stickers)?
Answer:
The answer to your question is
Number of stickers = number of days + 3
Step-by-step explanation:
- To find the equation of the line that represents the situation, first, find the slope.
Slope = m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = [tex]\frac{4 - 3}{1 - 0} = \frac{1}{1} = 1[/tex]
- Find the equation of the line
y - y1 = m(x - x1)
y - 4 = 1(x - 1)
y - 4 = x - 1
y = x - 1 + 4
y = x + 3
y = number of stickers
x = days
Number of stickers = number of days + 3
Answer:
is x = y + 3
Step-by-step explanation:
Radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time t (in weeks), then dQ dt = −rQ, where r > 0 is the decay rate.
A) If 500 mg of a mystery substance decays to 83.01 mg in 5 weeks, determine the decay rate r.
B) Find an expression for the amount of this substance present at any time t.
C) Find the time required for the substance to decay to one-half its original amount.
Answer:
Step-by-step explanation:
If a jar wrench whose handle extends 17 cm from the center of the jar is attached to the lid, what is the minimum force required to open the jar?
The minimum force required to open the jar using the wrench is 41.5 N, calculated based on the given torque of 8.9 N∙m and the effective radius of 0.2145 m.
Calculate the minimum force required to open the jar using the jar wrench:
1. Identify the torque required:
The problem states that the torque required to open the jar is 8.9 N∙m. This means that you need to apply a force that creates a twisting moment of 8.9 N∙m to overcome the friction between the lid and the jar.
2. Determine the effective radius:
The effective radius is the distance from the center of rotation (the center of the lid) to the point where the force is applied (the end of the wrench handle).
In this case, the effective radius is the sum of:
The length of the wrench handle (17 cm = 0.17 m)
Half the diameter of the lid (4.45 cm = 0.089 m / 2, assuming a circular lid)
So, the effective radius is 0.17 m + 0.0445 m = 0.2145 m.
3. Apply the torque formula:
The formula for torque is: τ = rF
τ = torque (in N∙m)
r = effective radius (in meters)
F = force (in Newtons)
You can rearrange this formula to solve for force: F = τ / r
4. Calculate the force:
Plug in the values: F = 8.9 N∙m / 0.2145 m
Calculate: F = 41.5 N
Therefore, the minimum force required to open the jar using the wrench is 41.5 N.
The cost of four evening movie tickets is $33.40 the cost of 6 daytime tickets is 39.30 what is the difference between the cost of one evening ticket in one day time ticket
Answer:the difference between the cost of one evening ticket and one day time ticket s $1.8
Step-by-step explanation:
The cost of four evening movie tickets is $33.40. This means that the cost of one evening ticket would be
33.4/4 = $8.35
The cost of 6 daytime tickets is 39.30. This means that the cost of one daytime ticket would be
39.30/6 = $6.55
Therefore, the difference between the cost of one evening ticket and one day time ticket would be
8.35 - 6.55 = $1.8
Appropriately conducting and interpreting biostatistical applications require attention to a number of important issues. These include, but are not limited to, the following except:_______1. Clearly define the objective or research question2. Choosing an appropriate study design3. selecting a representative sample/ sufficient size4. Carefully collecting and analyzing the data5. Producing appropriate summary measures or statistics6. Generating appropriate measures of effect or association7. Quantifying uncertainty8. Appropriately accounting for relationships among characteristics9. Limiting inferences to the appropriate population.
Answer: None of the above
Step-by-step explanation:
Each of the presented points helps to describe how to collect and summarize data and how to make appropriate scientific inferences.
It provides a guide on how to use biostatistical principles with grounded mathematical and probability theory. It aims is to help understand and to interpret biostatistical analysis generally.
Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown to the right. The area of the photo will be half the area of the entire ad. What is the value of x?
The value of [tex]\( x \) i[/tex]s irrelevant; the relationship between the areas remains constant regardless of its value.
To find the value of[tex]\(x\), let's denote the length of the ad as \(L\) and the width as \(W\). The area of the entire ad is \(L \times W\). Since the area of the photo is half the area of the ad, its area is \(\frac{1}{2} \times L \times W\).[/tex]
Now, we're given a diagram indicating that the length of the photo is [tex]\(x\) and its width is \(\frac{1}{2}W\). Therefore, the area of the photo is \(x \times \frac{1}{2}W\)[/tex].
We set up an equation based on the given information:
[tex]\[\frac{1}{2} \times L \times W = x \times \frac{1}{2}W\][/tex]
We cancel out the common factor of[tex]\(\frac{1}{2}W\) from both sides:\[L = x\][/tex]
This means that the length of the ad is equal to [tex]\(x\). Since we're not given any specific measurements or constraints on \(x\), its value could be any positive real number. Thus, the value of \(x\) is irrelevant to the relationship between the areas of the photo and the entire ad. Regardless of \(x\)[/tex], the area of the photo will always be half the area of the ad.
If the standard deviation of the sampling distribution of sample means is 5.0 for samples of size 16, then the population standard deviation must be
Answer:
20
Step-by-step explanation:
The question states that the sample size is 16 and standard deviation of sampling distribution of sample mean also known as standard error is 5. This information can be written as
σxbar=standard error=5 ,n=sample size=16.
We have to find population standard deviation σ.
We know that
[tex]Standard error=\frac{population standard deviation}{\sqrt{n} }[/tex]
[tex]population standard deviation=\sqrt{n} *(standard erorr)[/tex]
[tex]\sqrt{n} =\sqrt{16} =4[/tex]
Population standard deviation=σ=4*5=20
What is the recursive rule for the sequence 1, −6, 36, −216, ... ? an=6⋅an−1 , a1=1 an=−6⋅an−1 , a1=1 an=−16⋅an−1 , a1=1 an=16⋅an−1 , a1=1
Answer:
Option 2) [tex]a_n = -6(a_{n-1})[/tex]
Step-by-step explanation:
We are given the following sequence in the question:
[tex]1, -6, 36, -216, ...[/tex]
We have to find the recursive relation for the sequence.
[tex]a_1 =1\\a_2 = -6 = -6(1) = -6(a_1)\\a_3 = 36 = -6(-6) = -6(a_2)\\a_4 = -216 = -6(36) = -6(a_3)[/tex]
Thus, continuing in the following manner, we get,
[tex]a_n = -6(a_{n-1})[/tex]
Thus, the recursive rule is given by
Option 2) [tex]a_n = -6(a_{n-1})[/tex]
Answer:
Step-by-step explanation:
In 2014, the populations of China and India were approximately 1.355 and 1.255 billion people,45 respectively. However, due to central control the annual population growth rate of China was 0.44% while the population of India was growing by 1.25% each year. If these growth rates remain constant, when will the population of India exceed that of China?
Answer:
in the year 2023
Step-by-step explanation:
Initial population of China = 1.355 billion
Initial population of India = 1.255 billion
Annual population growth rate of China = 0.44% = 0.0044
Annual population growth rate of India = 1.25% = 0.0125
Now,
Final population = P₀ [tex]\times e^{\text{rate}\times t}[/tex]
Here,
P₀ = initial population
t = time
Thus,
Population of India > Population of China
1.255[tex]\times e^{\text{0.0125}\times t}[/tex] > 1.355[tex]\times e^{\text{0.0044}\times t}[/tex]
or
[tex]e^{0.0081t}[/tex] > 1.07968
taking natural log both sides
0.0081t > ln (1.07968 )
or
0.0081t > 0.0766
or
t > 9.465
Hence,
9.465 year after 2014
i.e
in 2014 + 9.465 = 2023.46
in the year 2023
Using the formula for exponential growth and the provided population data for China and India, we can approximate that India's population will exceed China's in roughly 20 years.
Explanation:In order to determine when India's population will exceed that of China, we can use the formula for exponential growth, which is P = P_0 * ert , where P is the future population, P_0 is the initial population, r is the growth rate, and t is time. As per the data provided, for China, P = 1.355 billion, r = 0.44%, and for India, P = 1.255 billion, r = 1.25%. We have to find time t when population of India will exceed that of China. This requires solving the equation: 1.355 * e0.0044t = 1.255 * e0.0125t.
This equation can be solved using algebra and logarithms. However, by making some approximations and using a spreadsheet or calculator, we can find that the population of India will exceed that of China after approximately 20 years, based on the growth rates provided.
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Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is -99. Which equation can be used to find m, the midpoint of the two numbers?
Answer:
[tex]m = \dfrac{a^2-99}{2a}[/tex]
Step-by-step explanation:
on a number line, m is the point that is the midpoint of two other points.
the distance between each of the points to the midpoint is 10 units..
if a is the point 10 units less than m
and b is the point 10 units greater than m,
then,
[tex]m = a+10[/tex]
[tex]m = b-10[/tex]
we can add the two equations to form the midpoint formula.
[tex]2m = a+b[/tex]
we also know that the product of both numbers equal -99.
[tex]ab = -99[/tex]
we can substitute either 'a' or 'b' to the equation of m.
[tex]2m = a-\dfrac{99}{a}[/tex]
[tex]m = \dfrac{a^2-99}{2a}[/tex]
and this is the equation for the midpoint of the two numbers.
Answer:
c
Step-by-step explanation:
Which operations would create an equivalent system of equations with opposite like terms?
3x-3y = 3
4x+5y = 13
The first equation can be multiplied by 5 and the second equation by 3.
The first equation can be multiplied by -4 and the second equation by-3.
The first equation can be multiplied by 4 and the second equation by -4.
The first equation can be multiplied by 3 and the second equation by 5.
Answer:the first equation can be multiplied by 5 and the second equation by 3
Step-by-step explanation:
The operation that would create an equivalent system of equations with opposite like terms is that the first equation can be multiplied by 5 and the second equation by 3, the correct option is A.
What is System of Equation?The system of equation is set of equations which have a common solution.
The equations are
3x-3y = 3
4x+5y = 13
The value of x and y can be determined using Elimination Method.
In elimination method like terms have to be created to make an equivalent system,
The first equation can be multiplied by 5 and the second equation by 3 to solve the equations.
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PLZ, HELP WORTH 30 PTS!!!! WILL MARK BRANLIEST!!!
Answer:
Therefore the equation of the required line is y = [tex]\frac{-1}{2}[/tex]x + 2 or 2y + x = 4.
Step-by-step explanation:
i) when x = -2 then y = 3 so the line from x = -2 to x = 2 has the point (-2, 3)
ii)when x = 2 then y = 1 so the line from x = -2 to x = 2 has the point (2, 1)
iii) if two points in a line are given then slope of equation passing through the lines is given by
slope m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{1 - 3}{2 - (-2)}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
So from the general equation of a line y = mx + c
we get y = [tex]\frac{-1}{2}[/tex]x + c and substituting for x and y with (-2, 3) respectively we get
3 = 1 + c. Therefore c = 2.
Therefore the equation of the required line is y = [tex]\frac{-1}{2}[/tex]x + 2 or 2y + x = 4.
Suppose that you have an enormous grapefruit that is 92% water (by weight). The grapefruit weights 100 pounds. If the water content of the grapefruit evaporates until it is 90% water (by weight), then approximately how much does the grapefruit now weigh?
Answer:
The weight of grapefruit is now 80 pound.
Step-by-step explanation:
Consider the provided information.
Let the x is the weight loss. The weight of grapefruit is 100 pounds and water is 92%. After evaporation water is 90%.
Thus the weight loss is:
[tex]0.92\times100-0.90(100 - x) = x[/tex]
[tex]92-90+0.90x=x[/tex]
[tex]2=x-0.90x[/tex]
[tex]2=0.1x[/tex]
[tex]x=20[/tex]
Hence, the weight loss is 80 pounds.
Therefore, New weight is 100 - 20 = 80 pounds
The weight of grapefruit is now 80 pound.
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance johnathan could of ran any day this week
An inequality that shows the distance Johnathan could of ran any day this week is:
[tex]x\leq 3.5[/tex]
Solution:
Let "x" be the distance Johnathan can run any day of this week
Given that,
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles
Therefore,
Number of days ran = 5
The most he ran in 1 day = 3.5 miles
Thus, the maximum distance he ran in a week is given as:
[tex]distance = 5 \times 3.5 = 17.5[/tex]
The maximum distance he ran in a week is 17.5 miles
If we let x be the distance he can run any day of this week then, we get a inequality as:
[tex]x\leq 3.5[/tex]
If we let y be the total distance he can travel in a week then, we may express it as,
[tex]y\leq 17.5[/tex]
The area of a rectangular plot is 36 square meters. The length of the plot (in meters) is one more than twice its width. Find the length and width of the plot.
length (m) ______.
width (m) ______.
Answer:
4m width and 9m length
Step-by-step explanation:
Let the width of the rectangle be x
Length is 1 more than twice width= 1 + 2x
Area of rectangle is L * B
x(2x + 1) = 36
2x^2 + x = 36
2x^2 + x -36 = 0
2x^2 + 9x - 8x -36 = 0
Solving this:
(2x+9)(x - 4) = 0
X = 4 or -4.5
Distance cannot be negative, so x = 4m
The length is thus 2(4) + 1 = 9m
Final answer:
The width of the plot is 4 meters and the length is 9 meters.
Explanation:
To solve this problem, we can let the width of the plot be x meters. According to the problem, the length of the plot is one more than twice its width, so the length would be 2x + 1 meters. The area of a rectangle is given by the formula A = length * width. So we have the equation (2x + 1) * x = 36. Expanding and rearranging, we get 2x² + x - 36 = 0.
Factoring this quadratic equation, we get (2x + 9)(x - 4) = 0. Setting each factor equal to zero and solving for x, we find x = -4/2 and x = 4. Since the width cannot be negative, we discard x = -4/2 and conclude that the width of the plot is 4 meters. Substituting this value back into the equation for the length, we find the length is 2(4) + 1 = 9 meters.
A individual has a body fat percentage of 17.7% and weighs 129 pounds.How many pounds of his weight is made up of fat?Round ur answer to the nearest tenth
Answer: 21.9 pounds of his weight is made up of fat.
Step-by-step explanation:
The total weight of the individual is 129 pounds. The individual has a body fat percentage of 17.7%.
Therefore, the number of pounds of his body that is made up of fat would be
17.7/100 × 129 = 0.177 × 129 = 21.93 pounds.
Approximating to the nearest tenth, it becomes 21.9 pounds.