Sarah is going to invest $280 and leave it in an account for 9 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Sarah to end up with $410?

9514 1404 393

Answer:

  C.  0.25, 1, 2, 4.75

Step-by-step explanation:

The solutions are the x-values of the points where the curves intersect. There are 4 intersection points to the right of the y-axis. Choice C is the only one with four (4) positive values for x.

Answer: hello your question is incomplete below is the complete question

Let X and Y be two independent standard normal random variables, i.e., each follows the distribution N (0, 1). Now, define two new random variables as Z = 11 - X + X²Y, W = 3-Y. find cov ( Z, W )

answer : Cov ( Z, W ) = -1

Step-by-step explanation:

Z = 11 - X + X²Y

w = 3 - Y

Cov ( Z, W ) = Cov ( 11 - x + x^2 Y , 3 - Y )

  = Cov ( 11, 3 ) - Cov ( 11, Y ) - Cov(x,3) + cov (x,y) + cov(x^2y, 3) -cov (x^2y, y )

attached below is the remaining part of the detailed solution

hence

Cov ( Z, W ) = -1

Answer:

Its only 5 point but ok

its $3.44 per quart

Step-by-step explanation:

Answer:

38/45

Step-by-step explanation:

4/10+4/9 Simplify.

2/5*4/9    Find a common denominator (45).

2/5*9/9=18/45

4/9*5/5=20/45

18/45+20/45=38/45

Hope this helps and have a great day C:

Answer:

the missing side is 90 because is a right triangle

ANSWER

-1,-1 is P

-4, -3 is R

-2,  -3 is Q

I think this is the answer hope it helps :)

Answer: 45°

Step-by-step explanation: All the angles of a triangle have to equal 180.

95 + 40 + x = 180

135 + x = 180

180-135 = 45.

Answer:

FNB bank

Step-by-step explanation:

FNB = 18000 * 0.056* 8 = 8064

Nedbank = 18000*0.066* 6 = 7128

Standard = 18000*0.072*5=6480

FNB is the best choice for Steven

Answer:

15 weeks

Step-by-step explanation:

I just answered this one not too long ago

It will take 15 weeks for Emanuel to lose at most 251 pounds.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, Emanuel is trying to lose weight, he starts 2017 weighing 296 pounds.

If he plans to burn enough calories to lose 3 pounds per week,

We need to find that how many weeks will pass before Emanuel is at most 251 pounds,

So, let the number of weeks be x,

We will use here the concept of equations solving,

So, establishing the equations,

296 - 3x = 251

296 - 251 = 3x

45 = 3x

x = 15

Hence, it will take 15 weeks for Emanuel to lose at most 251 pounds.

Learn more about equations, click;

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Answer:

Step-by-step explanation:

From the information given:

The probability distribution at the end of 6 months is determined as follows:

After 6 months;

Mean of probability distribution =  value of Initial cash  + [tex]\alpha[/tex]T  

=2.0 +(0.1 × 6)

=2.6

After 6 months;

The probability distribution's standard deviation is estimated by using the following formula:

Standard deviation:

[tex]= b\sqrt{T}[/tex]

[tex]= 0.4 \times \sqrt{6}[/tex]

= 0.9798

Hence, after 6 months;

The company's cash position is supposed to be allocated monthly, with the following expenses.

Mean                            2.6

Standard deviation     0.9798

Variance                      0.96

After 12 months, the probability distribution is as follows:

Mean = value of Initial cash  + [tex]\alpha[/tex]T

= 2.0 +(0.1 × 12)

= 3.2

The standard deviation is:

The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]

[tex]= 0.4 \times \sqrt{12}[/tex]

= 1.3856

Hence, after 6 months;

The company's cash position is supposed to be allocated monthly, with the following expenses.

Mean                            3.2

Sandard deviation      1.3856

Variance                      1.92

b)  

in 6-month distribution, the probability of the negative value of the cash position is as follows.

Now, for us to find the negative cash distribution;

We need to estimate the z -scores value.

The z-score inform us greatly on the concept of how far a particular data point is from the mean.

For a normal distribution;

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

Here;

the value of x = zero as a result that if it exceeds zero. the cash position will be negative.

∴

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]

[tex]z = -2.6536[/tex]

Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.

As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.

For 12 months distribution:

The Probability of negative cash position is calculated as follows:

[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]

Using the standard distribution tables,

N(-2.31) equals 0.0104 or 1.04 percent.

As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year  

c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]

This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.

To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.

The first step is to go over the z-score formula in more detail, as seen below.;

[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]

Now, compute the derivative of this equation with respect to T as follows:

[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]

Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:

[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]

As a result, the time period in which achieving a negative cash condition is = 20 months.

Answer:

12 students

Step-by-step explanation:

CLEAN THAT IPAD FOR HIM

Answer:

12 students went to the beach fewer than 2 times.

Step-by-step explanation:

Just count the total number of dots that come before 2.

By the polynomial remainder theorem, the remainder is

f (2) = 2⁵ + 5×2³ + 4 = 32 + 40 + 4 = 76

(The theorem says a polynomial p(x) has remainder p(c) upon dividing it by x - c.)

Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

The number of sides is 3 on each piece of paper, altogether there are 6 sides.

The total number of angles on a triangle is 180°, altogether the sum of both triangles is 360°

Answer:

1)

mean - 5

median - 5

mode - 6

range - 7

2)

mean - 444

median - 453

mode - 345

range - 198

3)

mean - 6

median - 6

mode - 8

range - 7

4)

mean - 10

median - 9

mode - 9

range - 17

5)

mean - 5

median - 4

mode - 3

range - 7

6)

mean - 143

median - 148

mode - 157

range - 33

12) 9

13) 10

14) 10, 5

15)

If the price of swimming lessons went up to mean and mode would change.

mean - 9.66666667 (9.6 repeating)

median - 10

mode - 10

range - 13

Answer:

wow thats alot of "stuff"

Step-by-step explanation:

Answer:

For the first, top one, it is Outcome

For the second one, it is Event

For the third one, it is Trial

For the fourth one, it is Experimental Probability

For the fifth one, it is Probability

Answer:

I think it's 4.5

Step-by-step explanation:

I divided the servings by the packages and I got 4.5 for each of them.

ANSWER

l

Or

Or

EXPLANATION

The given line has slope,

and

We can find the equation in the point slope form, which is given by,

We substitute the point and slope to get,

We can also simplify further to get,

We make y the subject to get,

This is called the slope intercept form.

We could also write in standard form to get

Or

Answer:

wx-x=d

wx = d + x

x = d/w + x/w

Step-by-step explanation:

Answer:

x = d/(w-1)

Step-by-step explanation:

factor out 'x' as first step:

x(w - 1) = d

now divide by w-1:

x = d/(w-1)

Answer:

D. 6

Step-by-step explanation:

[tex]36 {}^{ \frac{1}{2} } = \sqrt{36} = 6[/tex]

Answer:

30cm3

Step-by-step explanation:

Volume=Base area *height

Base area is a triangle=1/2 *base*height

1/2*3*4=6cm2

Height=5cm

Volume=6*5=30cm3

Answer:

10 m³

Step-by-step explanation:

My apologies for attaching the explanation in a pic, brainly wouldn't let me upload my text answer for some reason.

Answer:

47.1

Step-by-step explanation:

l= rø

or, l= 18 × 5π/6

or, l= 15π

l = 47.1

9514 1404 393

Answer:

  C - 24 square root of 2

Step-by-step explanation:

In case you haven't memorized the fact that the diagonal of a square is √2 times the side length, you can figure it from the Pythagorean theorem.

  d² = s² + s² . . . . square of hypotenuse is sum of squares of sides

  d² = 2s²

  d = s√2 = (24 ft)√2 = 24√2 ft

Answer:

54 unit ^2

Step-by-step explanation:

Well a formula for a rectangle is a=lw

So 6*9=54

The area is 54

Since the area of the figure changed by a factor of 25, a factor by which the dimensions of the pentagon were multiplied include the following: C. 5.

In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:

(Scale factor of dimensions)² = Scale factor of area

(Scale factor of dimensions)² = 25

Scale factor of dimensions = √25 = 5

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Answer:

c.5

Step-by-step explanation:

Answer:

8/15

Step-by-step explanation:

In a right triangle, where B is an acute angle, the tan B is equal to the measure of the side opposite B divided by the measure of the shorter side at B

tanB = 16/30 = 8/15

Answer:

[tex]x = \frac{\sqrt{70} }{10}, - \frac{\sqrt{70} }{10}[/tex]

Answer:

Rounded to the nearest cent, over 5 years she will earn $ 916.89.

Step-by-step explanation:

Since Tabitha found an annuity that pays 7.0% annual interest, compounded semiannually, and she decided to invest $ 650 semiannually in this annuity for 5 years, to determine how much interest she will earn during the 5 years the following calculation must be performed:

650 x (1 + 0.07 / 2) ^ 5x2 = X

650 x (1 + 0.035) ^ 10 = X

650 x 1,035 ^ 10 = X

916,889 = X

Thus, rounded to the nearest cent, over 5 years she will earn $ 916.89.

Answer: 1125.41

Step-by-step explanation:

First, let’s find out how much is in the account after 5 years. We will use the savings annuity formula

A(t)=d((1+r/n)n⋅t−1)r/n

to find the value of A(5). We know that r=0.07, d=$650, n=2 compounding periods per year and, t=5 years. Substitute these values into the formula.

A(5)=$650 ((1+0.07/2)5⋅2−1)/(0.07/2)

Simplifying gives

A(5)=$650 ((1.035)10−1)/(0.035),

thus

A(5)=$7,625.41.

The sum of all deposits D5 is given by 5⋅2⋅$650=$6,500. Now, substitute these numbers into

A(5)=D5+I5

and solve for I5. This gives

$7,625.41=$6,500+I5,

yielding the total interest paid as $1,125.41. Enter 1125.41 as the answer.