if m(x)= sin²(x), then m'(x)=? A. cos²x+sin²x. B.sinx²-cos²x C. 2cos²x-sinx D. cos²-sin²x​

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

It will take Sarah approximately 15.9 years to pay off the loan.

To determine how long it will take Sarah to pay off the loan, we can use the formula for the number of periods required to pay off a loan:

\(\(n = \frac{{\log\left(\frac{{P \cdot r}}{{P - M \cdot r}}\right)}}{{\log(1 + r)}}\)\)

Where:

n is the number of periods (in this case, the number of months)

P is the principal amount (loan amount), which is $300,000

r is the monthly interest rate, which is 0.525% or 0.00525 (expressed as a decimal)

M is the monthly payment, which is $1,925

Substituting the values into the formula, we have:

\(\(n = \frac{{\log\left(\frac{{300,000 \cdot 0.00525}}{{300,000 - 1,925 \cdot 0.00525}}\right)}}{{\log(1 + 0.00525)}}\)\)

Using a calculator to evaluate the logarithms and perform the division, we find that \(\(n \approx 190.6\)\) months.

Since we are asked to determine the time to the nearest tenth of a year, we divide 190.6 by 12 to convert it into years:

\(\(\frac{{190.6}}{{12}} \approx 15.9\) years\)

Therefore, it will take Sarah approximately 15.9 years to pay off the loan.

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Answer: A. To find the equation that models this relation, we can plot the data and look for a trend.

From the graph, we can see that the data follows an exponential growth pattern. The equation for exponential growth is:

y = ab^x

where y is the final population, a is the initial population, b is the growth rate, and x is the time in hours.

Using the data from the table, we can find the value of b:

b = y/x

where y is the population after x hours.

For example, after 2 hours, the population is 5000:

b = 5000/2 = 2500

We can repeat this process for each time period and find the average value of b:

b = (2500 + 3125 + 3906.25 + 4882.81 + 6103.51 + 7629.38) / 6 = 4275.5

Now that we have the value of b, we can find the equation that models the relation:

y = 2000(4275.5)^x

Rounding to one decimal place:

y = 2000(4.3)^x

B. Using the equation, we can find the population after 12 and 24 hours:

y = 2000(4.3)^12 ≈ 8,898,335.7

y = 2000(4.3)^24 ≈ 7.42 x 10^13

Step-by-step explanation:

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

She will have $375,769.33 in her retirement plan at the time of retirement.

Explanation:

According to the question,

Periodic Payments(P) = $200

Rate of Return(r) = 12%(annual)

                           \(=\frac{12}{12}%\)  

                           = 1% monthly

                           = 0.01

Number of payments(n) = 65 - 40

                                        = 25(annual)

                                        = 25 × 12 monthly

                                        = 300 monthly

Future value =?

The formula for calculating future value is:

Future Value = \(P[\frac{(1+i)^{n}-1 }{i}]\)

                      = \(200[\frac{(1+0.01)^{300}-1 }{0.01}]\)

                      = \(200[\frac{19.7884663-1}{0.01}]\)

                      = 200[1878.84663]

                      = 375,769.326

                      = 375,769.33

Final Answer:

Therefore, the future value of her retirement when she retires is

$ 375,769.33 .

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In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Answer: Coupon B is more profitable

Answer:

See below ~

Step-by-step explanation:

Sample Space : {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}

Event (first toss = heads)

Answer:

Sample Space is 3, {HTH, THH, TTT, THT, HTT, HHH}

Step-by-step explanation:

The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

Answer:

Step-by-step explanation:

If angle 5 = 4x + 15, and angle 4 = 6x - 5, and angle 5 = angle 4, then:

4x + 15 = 6x - 5 and

20 = 2x so

x = 10. Now sub this back in for x in angle 5's expression:

angle 5 = 4(10) + 15 ---> 40 + 15 ---> angle 5 = angle 4 = 55 degrees

Answer:

0.5

Step-by-step explanation:

2.2 is approximately 2.

2 divided by 4 is 0.5, so 2.2 divided by 4 must be close to 0.5.

Answer: 0.5

Answer:

16.97056

Step-by-step explanation:

The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

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Answer:

I will translate and will be right with you

Step-by-step explanation:

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

Answer:

the slope intercept form of the equation is y= - \(\frac{4}{3}\)x -8

so the correct graph will be going negative from left to right, and will go through the point (0,-8)

The true statements of the rectangle are as follows:

The statements that are true in the option are highlighted with point listing.

Generally a rectangle has 2 opposite sides equal to each other.

The perimeter of a rectangle can be express as follows:

perimeter = 2l +2w

where

w = width

l = length

The area of a rectangle can be express as follows

area = lw

The last 2 statement are not true statement because the volume of a rectangle cannot be found as it is a 2 dimensional figure and the units for area is squared but it was express in cm³(centimetre cube)

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Answer:

B and C

Step-by-step explanation:

On solving the provided question, we can say that in the given graph the function will be so, g(x) = -1/2 |x|

Mathematicians use graphs logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

in the given graph

we have two lines that are straight from the origin, so the function must be in modulus

so, g(x) = -1/2 |x|

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Answer:

\(336m^2\)

Step-by-step explanation:

\(6*8=48\)

\(10*12=120\)

\(8*12=96\)

\(6*12=72\)

Add all these up

\(48+120+96+72=336\)

Hope this helps

The solution of the function 3f(1) - 4g(-2)  is -19.

The functions can be solved as follows;

f(x) = 7x - 4

g(x) = 11 - x²

Therefore, let's solve the composite function as follows:

A composite function is generally a function that is written inside another function.

Hence,

3f(1) - 4g(-2) = ?

f(1) = 7(1) - 4 = 7 - 4 = 3

g(-2) = 11 - (-2)² = 11 - 4 = 7

Therefore,

3f(1) - 4g(-2) = 3(3) - 4(7) = 9 - 28 = -19

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Answer:a A. 4x-7/2x(x-2)

got it right on the test

Step-by-step explanation:

Answer:

C - formula of area of rectangle is l×w

so 23×16

The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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Answer:

c

Step-by-step explanation:

got it from my math book

Answers:

1. -2y^3+9y-3y-16

2. 14x^3-23x^2+19x-24

Hi!

I'm really sorry but I'm not sure how to solve these equations however I have searched online and this is what it has said. I hope it is what you are looking for! I have attached screenshots of the working out above in order of each question. You may want to double check but the first two are for the first question and second two are for the second question.

The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

From the question, we have the following parameters that can be used in our computation:

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

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Answer:

VW = 36

Step-by-step explanation:

From the question, we are given:

VW = 5x - 4, UV = 2x,

UW = 52

Hence,

UV + VW= UW

2x + 5x - 4 = 52

7x = 52 + 4

7x = 56

x = 56/7

x = 8

VW = 5x - 4,

VW = 5(8) - 4

VW = 40 - 4

VW = 36

Answer: 1/3

The answer is 1/3

Step-by-step explanation:

Have a nice day :)

The scale factor from figure A to figure B is 1/3.

The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii. The scaling factor indicates how much a figure has increased or decreased from its initial value.

In the question, we are informed that figure B is a scaled copy of figure A.

We are asked to find the scale factor from figure A to figure B.

To find the scale factor, we need to find the dimension of a particular side of figure A, and the corresponding side of figure B, then the ratio of these dimensions gives the scale factor.

Dimension of figure A = 9 units {From the attachment},

Dimension of figure B = 3 units {From the attachment}.

The scale factor is the ratio of the dimension of figure B, to the dimension of figure A.

Thus, the scale factor = 3:9 = 1:3 or 1/3.

Thus, the scale factor from figure A to figure B is 1/3.

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