use implicit differentiation to find the derivative dy dx. b. find the slope of the curve at the given point. cos(y)

Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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Answer:

21 calouris

Step-by-step explanation:

5250/250

Answer:

500

Step-by-step explanation:

250 X 7 = 1750

5250 - 1750 = 3500

3500 divided by 7 =500

Yes, If there are any outliers in the data set, the standard deviation will be large since the deviation from the mean will have increased. Therefore, if the outliers are eliminated, the standard deviation will be reduced, probably reflecting the true features of the population.

The impact on the standard deviation increases with the outlier's extremeness. Outliers make your data more variable, which reduces statistical power. Therefore, eliminating outliers can make your findings statistically significant. A removal of an outlier will have an impact on the mean. The standard deviation will decrease if the outlier was larger than the mean.

The standard deviation will increase if the outlier was less extreme than the mean. It's best to get rid of outliers only when there's a good cause to. Some outliers in your dataset represent normal population variance and ought to be left alone. They are referred to as real outliers.

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The average rate of change of a function f is given by:

Answer:

(a) \(Area = 232.23\ cm^2\)

(b) \(Area = 52.78\ cm^2\)

(c) \(Area = 373.06cm^2\)

Step-by-step explanation:

The area of a circle:

\(Area = \pi r^2\)

Where

\(\pi = 3.14\)

Solving (a):

\(r = 8.6cm\)

\(Area = \pi r^2\)

\(Area = 3.14 * (8.6cm)^2\)

\(Area = 3.14 * 73.96cm^2\)

\(Area = 232.2344cm^2\)

\(Area = 232.23\ cm^2\) --- Approximated

Solving (b):

\(r = 4.1cm\)

\(Area = \pi r^2\)

\(Area = 3.14 * (4.1cm)^2\)

\(Area = 3.14 * 16.81cm^2\)

\(Area = 52.7834cm^2\)

\(Area = 52.78\ cm^2\) --- Approximated

Solving (c):

\(r = 10.9cm\)

\(Area = \pi r^2\)

\(Area = 3.14 * (10.9cm)^2\)

\(Area = 3.14 * 118.81cm^2\)

\(Area = 373.0634cm^2\)

\(Area = 373.06cm^2\) --- Approximated

Answer:

you betta do ya best it might be 34

Step-by-step explanation:

Answer: the answer is 2/5

Step-by-step explanation: e

Answer:

The rate of change is M= -9/13 (M= negative nine over thirteen)

Step-by-step explanation:

the answer would be 48 green marbles

Step-by-step explanation:

48/6=8

So, each person would get 8 marbles each

Answer:

True

Step-by-step explanation:

If the discriminant \(D=b^2-4ac < 0\), then there are two complex roots

If the discriminant \(D=b^2-4ac > 0\), then there are two real roots

If the discriminant \(D=b^2-4ac=0\), then there is only one real root

Answer:

\(\frac{1}{9^3}\) or \(\frac{1}{729}\)

Step-by-step explanation:

When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.

Option D is the correct answer i.e., the mean because the data distribution is skewed to the right.

From the given box plot we can get to know that there are more values towards the right end than the left end. Therefore it means that the data is skewed towards the right.

As we know when both sides of the median have the same number then it is a symmetrical box plot.

Whenever we deal with skewed graphs, the best option to choose from mean and median is always the median. This is because due to a large number of data values on one side, the mean will always be closer to that side. The median is not largely affected in this case.

Therefore, the correct answer would be option D. The median, because the data distribution is skewed to the right

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The complete question is:

Given the box plot, will the mean or the median provide a better description of the center?

a. The Mean, because the data distribution is symmetrically

b. the median, because the data distribution is symmetrical.

c. the mean because the data distribution is skewed to the right.

d. the median, because the data distribution is skewed to the right

3x-4y=12 best describes the graph of the line.

Hence, 3x-4y=12 best describes the graph of the line.

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Answer:

Wait nvm sorry point A is at (1,-5) so the answer is B

Step-by-step explanation:

Answer:

25(x)= 200

Step-by-step explanation:

Total = 200

Per day = 25

x = how many days

25(x)= 200

25(8)= 200

- Sorry i am just a little confused by the question but i hope this helps. Have a great day!

Answer:

x+25=200

Step-by-step explanation:

The choice that had statements that are all true is (a) Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2

The complete question is added as an attachment

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

The number line

On the number line, we have the following

A = -4

B = -2 1/2

C = 1

D = 1 3/4

When the above values are compared with the list of options, we have

Option (A) = true

This is so because in (a)

Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2

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Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.

Using this rule, we can find the derivative of h(x) as follows:

h(x) = (x + 2) / (x - 2)

h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator

h'(x) = (-2 - 2x) / (x - 2)^2

Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.

Step-by-step explanation:

( 6 − 7 i ) ( − 8 + 3 i )

First FOIL:

( 6 − 7 i ) ( − 8 + 3 i )  = -48 + 18i + 56i -21i^2

Combine like terms

                                 = -48 + 74i -21i^2

Convert i^2 = -1

                                 = -48 + 74i -21(-1)

And simplify

                                 = -48 + 74i + 21

                                 = -27 + 74i

Answer:

12756pi km

Step-by-step explanation:

Circumference = pi * diameter

Diameter = radius * 2

kilometer = meter/1000

6378000*2= 12756000

diamter = 12756000 meters

12756000/1000 = 12756 kilometers

diameter = 12756 kilometers

12756pi km= circumference

The inequality that describes the given word problem is;

x + 1.5 < 48

Let x represent how tall Keenan was last summer. Thus;

x = Keenan's height last summer in inches

If he was x inches last summer, and has since grown an additional 1.5 inches up to date, then it means that his total height now is;

x + 1.5 inches.

The conditons state "riders must be at least 48 inches tall to ride the Night Eagle roller coaster". So it means that his height must be equal to 48 inches, or larger than 48 inches, to make him eligible to ride the roller coaster.

But since he is still too short to ride, this means the expression x+1.5 is smaller than 48 and as such the inequality of this problem is;

x + 1.5 < 48

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Answer:

-8x(8yz)(-8)

Step-by-step explanation:

(-2x^2yz^-2)4

-8x(8yz)(-8)

Answer:

a = 18

b = 3

hope it helps

have a nice day

Answer:

  \(a=\dfrac{\Delta v}{t}\)

Step-by-step explanation:

Acceleration is the change in velocity per unit time. It is usually represented by the letter "a". An appropriate formula is ...

  \(\boxed{a=\dfrac{\Delta v}{t}}\)

The required equation for determining the acceleration from a velocity-time graph is \(a=\dfrac{\Delta v}{t}\)equation is a=delta v over t.

We know that,

Acceleration is known as the rate of change of velocity per unit time.

The velocity vs time graph is the graph plotted between the change in velocity with the change in time.

\(a=\dfrac{\Delta v}{t}\)

Hence the required equation for determining the acceleration from a velocity-time graph is \(a=\dfrac{\Delta v}{t}\).

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Answer: 0.1974

Step-by-step explanation:

Let X be a random variable that denotes the gas mileage (in miles per gallon) of the individual sedan.

Given: Population mean: \(\mu=20\)

Standard deviation: \(\sigma=2\)

The probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5:

\(P(19.5<x<20.5)=P(\dfrac{19.5-20}{2}<\dfrac{x-\mu}{\sigma}<\dfrac{20.5-20}{2})\\\\=P(-0.25<z<0.25)=2P(0.25)-1 [P(-z<Z<z)=2P(Z<z)-1]\\\\=2(0.5987)-1=0.1974\)

The required probability=0.1974

Step-by-step explanation:

square root of 19 + 6 =324 + 36= 360

360÷51.84 =6.9444444

From the application of mathematical rules, BODMAS, the square roots of 19 + 6 squared divided by 7.2 squared ≈ 5.053343388

Square root of 19

√19 ≈ 4.358898944

6 squared

6² = 36

7.2 squared

7.2² = 51.84

Dividing,

36 ÷ 51.84

≈ 0.694444444

Addition,

4.358898944 + 0.694444444

≈ 5.053343388

Therefore,

√19 + 6² ÷ 7.2²

≈ 4.358898944 + 0.694444444

≈ 5.053343388

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Answer:

It takes one minute for both of them to eat one scoop.

Step-by-step explanation:

How long does it take them to eat 1 scoop of ice cream working together?

Jada: 2/5 = 0.4 per minute

Noah: 3/5 = 0.6 per minute

0.4+0.6 = 1 scoop per minute

How long does it take for Noah to eat his 3 scoops of ice cream in 5 minutes?

5 minutes???

The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.

f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)

= 1 - 5√(9 - x) / √(9 - x)

= 1 - 5 / √(9 - x).

To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.

Setting f'(x) = 0:

1 - 5 / √(9 - x) = 0

5 / √(9 - x) = 1

(√(9 - x))^2 = 5^2

9 - x = 25

x = 9 - 25

x = -16.

The critical point is x = -16.

We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.

Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).

For x < -16:

Plugging in a test value, let's say x = -17, into the derivative:

f'(-17) = 1 - 5 / √(9 - (-17))

= 1 - 5 / √(9 + 17)

= 1 - 5 / √26

≈ 1 - 0.97

≈ 0.03.

Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).

For -16 < x < 9:

Plugging in a test value, let's say x = 0, into the derivative:

f'(0) = 1 - 5 / √(9 - 0)

= 1 - 5 / √9

= 1 - 5 / 3

≈ 1 - 1.67

≈ -0.67.

Since f'(0) is negative, the function is decreasing in the interval (-16, 9).

For x > 9:

Plugging in a test value, let's say x = 10, into the derivative:

f'(10) = 1 - 5 / √(9 - 10)

= 1 - 5 / √(-1)

= 1 - 5i,

where i is the imaginary unit.

Since the derivative is not a real number for x > 9, we cannot determine the sign.

Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

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Answer: 15

Step-by-step explanation: 15 ÷ 5 = 3

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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