The population of a city decreases by 3.3% per year. If this year's population is 72,000, what will next year's population be, to the nearest individual?

The tangent vector to the curve at t = n is given by the derivative of the parametric equations: [tex]\frac{dx}{dt} = nt \ and\ \frac{dy}{dt} = n't^2[/tex]

To find the principal unit normal vector to a curve at a specified value of the parameter, you will need to do the following:

Here is an example to illustrate this process:

Suppose we have a curve given by the parametric equations [tex]x = t^2[/tex] and y = t^3. The tangent vector to the curve at t = 2 is given by the derivative of the parametric equations:

[tex]\frac{dx}{dt} = 2t \ and\ \frac{dy}{dt} = 3t^2[/tex]

Evaluating these at t = 2, we find that the tangent vector is (4,12).

The normal vector to the curve at t = 2 is perpendicular to the tangent vector, so we can find it by rotating the tangent vector 90 degrees counterclockwise. This can be done by taking the negative of the second component and swapping the components: (-12,4).

To normalize the normal vector, we divide it by its magnitude:

[tex](-12,4)\sqrt((-12)^2 + 4^2) = (-12\sqrt164,4\sqrt164) = (-0.73,0.24)[/tex]

This is the principal unit normal vector to the curve at t = 2.

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The simplest form of expression 125^(2/3) is 25.

This expression can be solved using exponents. Exponent means a quantity, describing the power to which base number is raised. In other words , Exponent refers to the number of times a number is used in a multiplication. The 4 types of exponents are: positive, negative, zero, and rational. Positive exponents tell you how many times to multiply a base by itself.

In order to solve this expression , we use properties of exponents.

Hence , using the property - [tex]x^{m} x^{n} = x^{mn}[/tex]

and rewriting 125 as cube of 5

i.e. [tex]125=5^{3}[/tex]

→ [tex](5^{3})^{2/3}[/tex]

Now , cancelling the 3s

→ [tex]5^{2}[/tex] = 25

Therefore the answer after simplification is 25.

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The given fraction in percentage is 86%.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

percentage, a relative value indicating the hundredth parts of any quantity. We must divide the amount by the sum to get the percentage, then multiply the result by 100.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 of 100 questions correctly on a test (75/100).

To get the percentage, multiply the given fraction by 100.

(43/50)*100= 86%

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Question: Rewrite the fraction in the sentence below as a percentage.

The number of ounces of water that would be wasted in one day is 12.173 ounces.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys. The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

Given,

The faucet drips per every minute.

1 min -------1/4 ml

for 60 min -----?

x=(1/4)×60

x=15 ml

For one day,

15 ml×24 hours=360 ml

Therefore, 360 ml=12.173 ounces.

Hence, the number of ounces of water that would be wasted in one day is 12.173 ounces.

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For both part (a), the two nonnegative numbers, x and y must be 0 and 20 for the sum of their squares to be as large as possible, and 10 and 10 for the sum of their squares to be as small as possible. For part (b), x must be 20 and y should be 0 for largest possible result, whereas for smallest possible result x must be 0 and y should be 20.

Nonnegative numbers are numbers which are greater than or equal to zero.

For a much straightforward and easy way of solving such questions we can simply use the trial and error method.

For part (a), we can start off by taking both the numbers as 10. The sum of their squares will now be 100. If we take the numbers as 12 and 8, the sum of their squares will be 208. As we can see by increase one of the numbers we get a larger result. Thus, the largest possible values will be 20 and 0, which will give a result of 400. While carrying out this trial and error method we also found out that the minimum result was obtained when both the numbers were 10.

For part (b), a similar approach can be taken. Through trial and error method we observe that  20 + (0)^1/2 gives the largest possible result, whereas 0 + (20)^1/2 gives the smallest possible result.

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Answer:

9/20 or 0.45

Step-by-step explanation:

The least common multiple of 12, 20 and 6 is 60. Reducing the fractions to the denominator 60 we have:

[tex] \bold{ \dfrac{7}{12} + \dfrac{4}{20} - \dfrac{2}{6} = \dfrac{35}{60} + \dfrac{12}{60} - \dfrac{20}{60} } \\ \\ \bold{= \frac{35 + 12 - 20}{60} = \frac{27}{60} = \frac{9}{20} }[/tex]

If any addend is an integer, an I is placed as denominator and the same operation is done.

The outcomes for beets or plants beet is $ 5000 , $3000 and $1000.

Given :

a farmer wants to decide if he should plant beets or sweet potatoes. no matter what he plants he will get either a good, average, or bad crop yield.

For beets, a good yield will give him a profit of $5,000, average will profit $3,000 and, and a bad yield will give a profit of $1,000. for sweet potatoes, the profit for good, average, and bad yields are as follows: $6,000, $3,000, and $0. for either crop, the probability of good yield is 0.4, the probability of average yield is 0.5 and the probability of a bad yield is 0.1.

Outcomes of beets = good yield , average and bad yield.

so

= $ 5000 , $3000 and $1000

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(a) There are 21 different ways to choose two different restaurants.

(b)There are 42 different ways to choose two different restaurants.

(c) There are 49 different ways to choose two different restaurants.

In the given question,  suppose Ches Tahoe restaurant is one of the 7 largest restaurants in x city.

a. We would like to choose two different restaurants from them. So we have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants.

So different ways:

n = [tex]^{7}C_{2}[/tex]

Using, [tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]

n = [tex]\frac{7!}{2!(7-2)!}[/tex]

After solving

n = 21

There are 21 different ways to choose two different restaurants.

b. We would like to choose two different restaurants. one is for our lunch and the other one is for our dinner. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one for our lunch and the other one for our dinner.

So different ways:

n = [tex]^{7}P_{2}[/tex]

Using, [tex]^{n}P_{r} = \frac{n!}{(n-r)!}[/tex]

n = [tex]\frac{7!}{(7-2)!}[/tex]

After solving

n = 42

There are 42 different ways to choose two different restaurants.

c. We would like to choose two restaurants. one is for your lunch and the other one is for your dinner. We are OK for going to the same restaurants. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one is for your lunch and the other one is for your dinner OK to the same

So different ways:

n = (7)^2

n = 49

There are 49 different ways to choose two different restaurants.

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S=1.86 with t in seconds is the equation for free fall at the surface of Mars. The rock's speed at time zero is 3.72 m/s.

By differentiating the position function with respect to time, it is possible to determine the velocity or rate of change of a moving object's position with respect to time. The absolute value of the velocity is the same as the speed.

The rock's travel distance (s) is given as a function of time (t).

[tex]\lim_{h \to \0}o\\s'(t)= \frac{1.86(t th)^{2}-1.86t^{2} }{h} \\= \frac{1.86t^{2}+3.72th+1.86h^{2-1.86t^{2} } }{h} \\[/tex]

[tex]\lim_{h \to \0} o[/tex] → [tex]3.72t+1.86h[/tex] → [tex]3.72(1)\\[/tex] [tex]= 3.72 m/s[/tex]

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In case of a normal distribution, the mean, median, and mode are equal . So option A is correct

What is normal distribution?

The most significant continuous probability distribution in probability theory and statistics is the normal distribution, also referred to as the gaussian distribution. On occasion, it is referred to as a bell curve.

The probability distribution of data is expressed mathematically as a normal distribution. It is symmetrical from both ends and has only one mode. The equal mean, median, and mode of the given data are highlighted by the normal distribution.

The options are b) It has two modes. c) It is asymmetrical. and d) the points of the curve meet the x-axis at z are incorrect.

Therefore, The correct option is A, the equal mean, median, and mode of the given data are highlighted by the normal distribution.

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The graph of the linear function y = 36 - 4x that represents this situation is given by the image shown at the end of the answer.

To graph the linear function, these three steps are taken:

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are detailed as follows:

Initially, he has 36 overdue activities, hence the intercept is of:

b = 36.

And thus the coordinates of the y-intercept are given as follows:

(0,36).

Each day, he can do 4 activities, meaning that the number of remaining activities decays by 4, and thus the slope is of:

m = -4.

Thus the definition of the function is presented as follows:

y = -4x + 36.

The x-intercept of the function is the value of x when the output variable assumes a value of 0, hence it is obtained as follows:

-4x + 36 = 0

4x = 36

x = 9.

Thus the coordinates of the x-intercept are given as follows:

(9,0).

Finally, a line is traced connecting the y-intercept (0,36) and the x-intercept (36,0).

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Answer: The slope of a negative line can be calculated using (y2 - y1)/(x2 - x1)

Step-by-step explanation:

Example:

(2, -4) (3, -5)

(y2 - y1)/(x2 - x1)

-5 - -4 / 3 - 2

-1/1

Slope = -1

Answer:

Step-by-step explanation:

Answer:

y = (-256)/5

Step-by-step explanation:

Solve for y:

y/32 + 8/5 = 0

Put each term in y/32 + 8/5 over the common denominator 160: y/32 + 8/5 = (5 y)/160 + 256/160:

((5 y)/160 + 256/160) = 0

(5 y)/160 + 256/160 = (5 y + 256)/160:

(1/160 (5 y + 256)) = 0

Multiply both sides of (5 y + 256)/160 = 0 by 160:

(160 (5 y + 256))/160 = 160×0

(160 (5 y + 256))/160 = 160/160×(5 y + 256) = 5 y + 256:

(5 y + 256) = 160×0

0×160 = 0:

5 y + 256 = 0

Subtract 256 from both sides:

5 y + (256 - 256) = -256

256 - 256 = 0:

5 y = -256

Divide both sides of 5 y = -256 by 5:

(5 y)/5 = (-256)/5

5/5 = 1:

Answer: y = (-256)/5

Answer:

Endothermic reactions absorb energy

Step-by-step explanation:

The monthly cost for 66 minutes of calls will be $15.84.

Monthly cost is the payment or the bill amount that needs to be paid at the end of the month.

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes)

The monthly cost for 45 minutes of calls = $14.40

The monthly cost for 102 minutes = $19.53

The above values can be paired in groups so as to satisfies the coordinates of a linear function

(45,14.40)  and (102,19.53)

Finding the slope of the graph using these points

slope, m=Δy/Δx

m=Δy=19.53 - 14.40 = 5.13

Δx=102 - 45 = 57

m = 5.13/57 =0.09

Finding the equation of the linear function using m = 0.09, and point (45,14.40)

m=Δy/Δx

0.09=y-14.40/x-45

0.09(x-45)=y-14.40

0.09x-4.05=y-14.40

0.09x-4.5+14.40=y

y=0.09x + 9.9

So for 66 minutes, the cost will be;

x = 66, y = ?

y=0.09*66 + 9.9

y=5.94+9.9 = $15.84

The monthly cost for 66 minutes of calls is $15.84.

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The stock's average nominal risk premium is 6.70%, while its average real return is 7.47%.

The inflation rate can be obtained from the consumer price index or the GDP deflator. The real rate of return is the actual yearly rate of return after accounting for factors like inflation. It is computed by adding the nominal rate to the inflation rate and dividing the result by three.

The annual return factored in after taxes and inflation is known as the real rate of return. Taxes and inflation are not included in a nominal rate of return, which is what it is called. The same goes for a rate of return that is calculated using taxes or inflation.

From the information given, the average return will be calculated thus:

Average return = 0.540 / 5

                          = 0.108

Average return = 10.80%

Therefore, the average real return will be:

= [( 1 + Average return) / (1+ inflation rate)] - 1

substitute the values in the above equation, we get

= [(1+0.1080) / (1+0.081)] - 1

simplifying the above equation,

= 0.0747

= 7.47%

Also, the average nominal risk premium will be:

= Average Return - Risk free rate

= 0.1080 - 0.041

= 0.067

= 6.70%

Therefore, the stock's average nominal risk premium is 6.70%, while its average real return is 7.47%.

The complete question is:

You’ve observed the following returns on Yamauchi Corporation’s stock over the past five years: −10 percent, 24 percent, 21 percent, 11 percent, and 8 percent. The average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.1 percent. a. What was the average real return on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What was the average nominal risk premium on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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No, these results indicate that people who eat more chocolate have a lower body mass index (BMI). The negative slope of -0.168 means that as chocolate consumption increases, BMI decreases. The significant p-value of 0.003 indicates that the results are statistically significant and not due to chance.

In a mathematics problem or experiment, a variable is a quantity that can change. To indicate a variable, we often use a single letter. Generic symbols used frequently for variables include the letters x, y, and z.

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. For instance, the linear equation x+9=4 has 9 and 4 as constants and x as a variable.
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Answer: 7

Step-by-step explanation: I got 7. Here's how I got it:

Use the process of elimination. The 2 cannot be divided by 3, because the number (3) we are dividing by, is greater than the primary number (2). If we divided 3 by 2, we would result in a decimal. Then, I took an estimate. I got rid of the 3 because that number would be a low number to divide by 3.

Then I started plugging in numbers:

(6*2) + 5 + 1 + 4 = 22

As we know, 22 is NOT a product of 3.

So, it has to be 7, but I'll prove my answer:

(7*2) + 5 + 1 + 4 = 24

And yes, 24 can be divided by 3 8 times. I hope this helps.

Clarification: I multiply 6 and 7 by 2 because both numbers would go into the 2 boxes.

On solving the provided question, An expression that finds the sum of x and y => X + Y

a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples -  2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.

An expression that finds the sum of x and y -

=> X + Y

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Answer:

Step-by-step explanation:

3,808

Answer: 3808

Step-by-step explanation:

2 times 34 = 68

68 times 56 = 3808

Answer is 3808

the first statement is false, and the 2nd statement is true.

the sign > indicates it is greater than the next value and the sign < indicates it is less than the next value.

In mathematics the above signs are used to compare two mathematical expressions.

7<5 cannot be possible as positive 7 is always greater than positive 5

in the next positive 3 is greater than positive 1 so it is true.

hence, 7<5 is false and 3>1 is true.

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Answer:1= 80 percent

2= 87.5 percent

Step-by-step explanation:

The surface area of the pyramid is 41. 29 In²

The formula for determining surface area of a square pyramid is expressed as;

Surface area = a² + 2a [tex]\sqrt{\frac{a^2}{4 } + h^2[/tex]

Where;

Substitute the values

Surface area = [tex]4^2 + 2(4) \sqrt{\frac{4^2}{4} } + 6[/tex]

Find the squares

Surface area = [tex]16 + 8 \sqrt{\frac{16}{4} + 6 }[/tex]

Divide the values

Surface area = 16 + 8√10

Surface area = 16 + 8(31.16)

expand the bracket

Surface area = 16 + 25. 29

Surface area = 41. 29 In²

Hence, the value is 41. 29 In²

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The area of the ring between these two circles if the radius of the larger and the smaller circle is 10 and 6 is 200.96.

Given:

two circles have the same center $c.$

the larger circle has radius $10$

and the smaller circle has radius $6.$

we are asked to determine the  the area of the ring between these two circles.

⇒ Area of the ring =  Area of larger circle - area of smaller circle

⇒ Area of circle = πr²

⇒ Area of larger circle  = π(10)²

= 100π

⇒ Area of small circle = π(6)²

= 36π

Area of the ring =  Area of larger circle - area of smaller circle

Area of the ring = 100π - 36π

= 64π

= 200.96

Hence the area of the ring is 200.96

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For the binomial distribution, √npq formula finds the standard deviation.

See the image below for the complete solution to the question:

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Answer:     the mathematics books must be together but the other books can be arranged in any order? Answer:

Step-by-step explanation:

There are some disadvantages to using this type of data collection is:

"Information available from the question"

In the question:

After gathering data on the effectiveness of company meetings, you decide to conduct a survey to obtain measurable qualitative and quantitative feedback. you will mail a survey to several companies.

To write the disadvantages to using this type of data collection.

Now, According to the question:

There are some disadvantages to using this type of data collection is:

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Answer: [-6,2]

Step-by-step explanation:

Domain of a function means what x can we put into the function to get a numerical answer - for what x the function is defined. On the graph you can see that it's in the interval from -6 to 2. e.g. you cannot know the answer for x=7 , -6.5 or any x outside of the domain

There is correlation but not causation between GPA and the number of text messages. that is option A is correct.

How one variable changes in relation to another is indicated by the correlation coefficient. A score of 1 shows a complete positive correlation, with a positive correlation being one where both variables move in the same direction. While 0 indicates there is no linear connection, a number of -1 indicates a complete negative correlation.

Given to us is that The data have a -0.9 correlation coefficient.

That is, there is a significant inverse relationship between the quantity of texts and each student's grade point average (GPA).

Hence, choice A is right.

There is correlation but not causation between GPA and the number of text messages.

option B,C,D are incorrect because we know that correlation does not imply causation that is correlation does not imply  a cause and effect between the two variable. correlation between variables means that relationship between two variables not the change in one variable , is the cause of the change in the variable. causation indicates that one event is the result of the occurrence of the other event.

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