The Derby Dragons have a mean height of 72.0 inches and a standard deviation of 1.2. The Aviston Aces have a mean height of 70.8 inches and a standard deviation of 0.7. The Ballwin Bears have a mean height of 73 inches and a standard deviation of 1.0. On average, which team is a taller? Which team has players whose heights are more consistent?

Answer:

Step-by-step explanation:

Answer:36 burgers were sold.

Step-by-step explanation:

Let x represent the total number of burgers, with or without cheese that was sold.

The total number of burgers with cheese that the fast food sold is 30.

if the ratio burger sold with cheese compared to without cheese was

5 : 1 , the total ratio would be the sum of both proportions. It becomes

5 + 1 = 6

Therefore

5/6 × x = 30

5x/6 = 30

Cross multiplying by 6, it becomes

5x = 30 × 6 = 180

x = 180/5 = 36

Therefore, the number of burgers without cheese sold would be

36 - 30 = 6

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.

Answer:

Non Arguement passage.

Step-by-step explanation:

The passage given is a non arguement passage , the passage is more of a report especially the introductory part where the author said ''Since the 1950s a malady called whirling disease has invaded U.S. fishing streams, frequently attacking rainbow trout.'' this highlighted phrase is a report gathered or investigated by the author which was gotten as a result of his own personal findings or from history. For an argument passage, the introductory part will have portrayed what the author implied, there will be an indication of the authors stance or favoured opinion which of course will be backed by evidence from his or her findings. as such, there is nothing of such which may serve as a precursor to indicate or informed us if the passage is that of an arguement. Again, the passage is a report and not an argument. as nothing can be inferred from the paragraph to point to us if it is an argument passage.

However, there is a conclusion in the passage and conclusions has arrived by the author must have been from a detailed findings and research, if possible an experimental study before a conclusion can be reached as the last line of the paragraph says ''A parasite deforms young fish, which often chase their tails before dying, hence the name.'' The conclusion is that parasite are known to cause deformation in young fish.

The percent decrease of the number of students home sick is 24.14%.

Solution:

The number of students home this last week was 145

This week there were only 110 students home sick

To find: Percent decrease

The percent decrease is given by formula:

[tex]\text{Percent Decrease } = \frac{\text{Final value-initial value}}{\text{Initial value}} \times 100[/tex]

Here given that,

Initial value = last week = 145

Final value = this week = 110

Substituting the values in formula, we get,

[tex]\text{Percent Decrease } = \frac{110-145}{145} \times 100\\\\\text{Percent Decrease } = \frac{-35}{145} \times 100\\\\\text{Percent Decrease } = -24.14[/tex]

Here negative sign denotes decrease in percent

Thus the percent decrease of the number of students home sick is 24.14%.

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.

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.

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]

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

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]

Answer:

B. [tex]-6b-4[/tex]

Step-by-step explanation:

Given expression is [tex]-6(b+2)+8[/tex]

Simplifying the expression now

Lets use distributive property of multiplication to solve it.

As given, [tex]-6(b+2)+8[/tex]

Distributing -6 with b and 2.

= [tex](-6b-12)+8[/tex]

Opening the parenthesis

= [tex]-6b-12+8[/tex]

= [tex]-6b-4[/tex]

∴ As from the given options, [tex]-6b-4[/tex] is the correct choice.

Answer:

B

Step-by-step explanation:

Its right got it from khan

Answer:

22.8 MPG

Step-by-step explanation:

356 divided by 15.6 = 22.8

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.

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:

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.

The distance between the base of the ladder and the wall is approximately 3.57 meters.

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.

Answer: 240

Step-by-step explanation:

The percent error For Diego measurement is 4.3 % decrease

Solution:

Given that, Diego measured the length of a pain to be 22 cm

The actual length of the pen is 23 cm

To find: percent error

Percent error is the difference between a measured and actual value, divided by the actual value, multiplied by 100%

The formula for percent error is given as:

[tex]\text{Percent error } = \frac{\text{Measured value - actual value}}{\text{Actual value}} \times 100[/tex]

Here given that,

Measured value = 22 cm

Actual value = 23 cm

Substituting the values in formula,

[tex]Percent\ Error = \frac{22-23}{23} \times 100\\\\Percent\ Error = \frac{-1}{23} \times 100\\\\Percent\ Error = -0.043 \times 100\\\\Percent\ Error = -4.3[/tex]

Here, negative sign denotes percent decrease

Thus percent error For Diego measurement is 4.3 % decrease

Answer:

Option C) population

Step-by-step explanation:

We are given the following situation in the question:

A researcher is curious about the average IQ of registered voters in the state of FL.

Sample:

It is a part of a population. It is always smaller than the population.

Statistic:

Any numerical value or any other measure describing a sample of a population is known as statistic.

Population:

It is the universal data set. Every observation belongs to this group which is of interest. Sampling is done within population to obtain small groups of sample.

Parameter:

Any numerical value or any other measure describing the population is known as a parameter.

In this situation, the entire group of registered voters in FL is an example of a population because it contains all the individual for variable of interest.

Variable of interest:

Average IQ of registered voters in the state of FL.

Individual of interest:

Registered voters in the state of FL.

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

Answer:

The constant of proportionality is 2.5 dollar per cupcake and then the required equation would be [tex]y=2.5x[/tex].

Step-by-step explanation:

Given:

Let the number of cupcakes be represent by [tex]'x'[/tex]

Also let the total cost be represented by [tex]'y'.[/tex]

We know that two proportional quantities are in for;

[tex]y=kx[/tex]

where, k⇒ represents constant of proportionality.

Now we know that;

1 dozen = 12

Half dozen = 6

Now Given:

half dozen cupcakes cost $15.

So Let us substitute [tex]x=6[/tex] and  [tex]y=15[/tex] in above equation we get;

[tex]15 =k \times 6[/tex]

Dividing both side by 6 we get;

[tex]\frac{15}{6}=\frac{k6}{6}\\\\k= 2.5 \ \$/cupcake[/tex]

Hence the constant of proportionality is 2.5 dollar per cupcake and then the required equation would be [tex]y=2.5x[/tex].

Final answer:

The constant of proportionality relating the number of cupcakes to the cost is $2.50 per cupcake. The equation representing the relationship is C = $2.50 × n.

Explanation:

To find the constant of proportionality for the number of cupcakes and total cost, we use the given information: half a dozen cupcakes (which is 6 cupcakes) cost $15. Therefore, we can divide 15 by 6 to find the cost per cupcake.
C = k × n

Where C is the total cost, n is the number of cupcakes, and k is the constant of proportionality (cost per one cupcake). First, find the constant:
k = C/n = $15/6 cupcakes = $2.50 per cupcake

The equation that represents the relationship between the number of cupcakes (n) and the total cost (C) is:
C = $2.50 × n

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]

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

Learn More

Laws of sines :https://brainly.com/question/12980528

Keywords: Laws, sines, tenth

#LearnwithBrainly

Answer:

C

Step-by-step explanation:

I just finished the test :)

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]

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

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.

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.

When analyzing data on homes in a neighborhood, focus on variables like value, size, year built, and basement presence. The sample data set of lawn areas is quantitative and continuous.

Data Analysis Process:

When collecting data on homes in a neighborhood, you can analyze it by looking at variables like value, size, year built, and basement presence. To make sense of the data, you can calculate statistics like the median home value and the variation in values to get a clearer picture of the housing market.

Data Types:

The areas of lawns in square feet sampled from five houses represent quantitative data, specifically continuous data, as they can take on any value within a range without restrictions.

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]

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.

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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