Jocelyn invests $1,600 in an account that earns 2.5% annual interest. Marcus invests $400 in an account that earns 5.4% annual interest. Find when the value of Marcus's investment equals the value of Jocelyn's investment and find the common value of the investments at that time. If necessary, enter the year to the nearest tenth and the value to the nearest cent.

Answer:

The period of given function is  [tex]Period = 16\pi [/tex]

So, Option B is correct.

Step-by-step explanation:

In this question we need to find the period of the function y= 3 sin x/8

The formula used to find period of function is: [tex]\frac{2\pi }{b}[/tex]

We need to know the value of b.

To find the value of b we compare the standard equation with the equation of function given.

Standard Equation: y = a sin(bx - c) +d

Given Equation: y= 3 sin(x/8)

Comparing we get:

a= 3

b= 1/8

c= 0

d=0

So, we get the value of b i.e 1/8. Putting it in the formula to find period of given function.

[tex]Period = \frac{2\pi }{b}[/tex]

[tex]Period = \frac{2\pi }{\frac{1}{8}}[/tex]

Solving,

[tex]Period = 2\pi *8[/tex]

[tex]Period = 16\pi [/tex]

So, the period of given function is  [tex]Period = 16\pi [/tex]

option D is the answer.!!!!

Answer:

Step-by-step explanation:

The formula for the area of a circle of radius r is A = πr².

Here, the area is A = π(18 units)² = 324π units²  (Answer D)

Answer:

Both the mean and median will decrease, but the mean will decrease more than the median.

Step-by-step explanation:

Removing the wheel of cheese will decrease the median a little bit, because the median shifts from between two data points to the lower of the two data points:

       With the wheel of cheese, the median is the middle number, but there's no middle number in this data set! So, to find the median we take the mean of the two middle numbers, $4.79 and $5.19 which is $4.99.

       Without the wheel of cheese,

Removing the wheel of cheese will decrease the mean significantly, because the total cost will decrease by $39.99, and the number of items decreases by only 1.

Answer: B

Step-by-step explanation:

Answer:

The degree of a polynomial is the highest degree of its monomials with non-zero coefficients

Step-by-step explanation:

not sure

The maximum power of the polynomial x⁶ + 4x - 3 that is degree will be 6.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

A polynomial's degree is the greatest exponent of its variable term. The variable in this example is x, and the maximum exponent of x is 6, which is the degree of the polynomial. As a result, the polynomial x⁶ + 4x - 3 has a degree of 6.

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ANSWER

C. f(x) = (x+3)(x+5)

EXPLANATION

The given function is

[tex]f(x) = x^2 +8x+15[/tex]

The factored form of the function reveals the zeros of the function.

From the factored form, we apply the zero product principle to get the zeros.

From the given options, the factored form of the polynomial is

[tex]f(x) = (x+3)(x+5)[/tex]

Answer:

Step-by-step explanation:

[tex]3x^{2} + 5x-12=0[/tex]

[tex]-12=-5x-3x^{2}[/tex]

[tex](-12=-5x-3x^{2} ) * -1[/tex]

[tex]\sqrt{12=5x+3x^{2}[/tex]

Answer:

Step-by-step explanation:

what are the statements about the data?

Answer

C) The mean is greater than the median.

Step-by-step explanation:

To find the median, order the scores from LEAST to GREATEST.

400, 575, 575, 670, 720, 885, 1250.

The mean is the middle number, which is 670.

To find the mean, average the scores:  

400 + 575 + 575 + 670 + 720 + 885 + 1250

7

= 725

725 > 670; therefore, the mean is greater than the median.

Answer:

A. 18 divided by 2/9

Step-by-step explanation:

To determine the number of boos that will fit into a box that is 18 inches long, we divide the length of the box by the length of the books

18 inches  divided by 2/9 inches per book

This tells us how many books

copy dot flip

18 * 9/2

81 books

Answer:

Step-by-step explanation:

The formula for the area of a sector is

[tex]A_{s} =\frac{\theta }{360}*\pi r^2[/tex]

where theta is the angle given as 45 and r is the radius (7).  Plugging in we get

[tex]A_{s}=\frac{45}{360}*\pi  (7)^2[/tex]

Simplify a bit to get

[tex]A_{s}=\frac{1}{8}*49\pi[/tex]

which gives you, in terms of pi:

[tex]A_{s}=\frac{49\pi }{8}[/tex]

or if you need to use the decimal form, rounded to the hundredths position:

A = 19.24

The selection of "Yes" or "No" to state whether each data set is likely to be normally distributed is as follows: A) No. B) Yes. C) Yes. D) Yes

A normal distribution of data occurs when the majority of data points are relatively similar and the data set has a small range of values.

1. The number of coupons used at a supermarket is no.

2. The weights of the pumpkins that are delivered to a supermarket is yes.

3. The number of raisins in each 8-oz box of raisins at a supermarket is yes.

4. The amount of time customers spend waiting in the checkout line at a supermarket is yes.

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The selection of "Yes" or "No" to state whether each data set is likely to be normally distributed is as follows: A) No. B) Yes. C) Yes. D) No

1. The number of coupons used at a supermarket is likely to follow a discrete distribution rather than a normal distribution. Customers may use 0, 1, 2, or more coupons, but the number of coupons used is not continuous and typically has a lower bound of 0. The distribution may be skewed to the right with a large number of transactions involving no coupons and a decreasing frequency as the number of coupons increases.

2. The weights of pumpkins are likely to be normally distributed because they are a result of many different factors, such as genetics, soil quality, water intake, etc., which tend to produce a bell-shaped curve when combined. This is an example of a continuous measurement that can be modeled well with a normal distribution.

3. The number of raisins in each 8-oz box is likely to be normally distributed due to the central limit theorem. Although the distribution of raisins per box might be uniform or have some other distribution, when the sample size (number of raisins per box) is large, the distribution of the sample mean (total number of raisins in many boxes) will approach a normal distribution. Since an 8-oz box contains a large number of raisins, the count in each box should be approximately normal.

4. The amount of time customers spend waiting in the checkout line is likely not to be normally distributed. This is because the waiting time is bounded below by zero and may have an upper limit depending on the store's operating hours or customer patience. The distribution of waiting times is often skewed to the right, with many customers experiencing short waits and a few experiencing longer waits. This results in a distribution with a long tail on the right side, which is not characteristic of a normal distribution.

Answer:

option A

Step-by-step explanation:

We can find the standard form by expanding the equation:

y = 3(x-4)^2 - 22

y = 3(x^2 - 8x + 16) - 22

y = 3x^2 - 24x + 48 - 22

y= 3x^2 - 24x + 26

So the correct option is option A

Answer:

option A) y= 3x²-24x+26 ~apex

Step-by-step explanation:

D. -4/3

Let's solve your equation step-by-step.

9x2+24x+20=4

Step 1: Subtract 4 from both sides.

9x2+24x+20−4=4−4

9x2+24x+16=0

Step 2: Factor left side of equation.

(3x+4)(3x+4)=0

Step 3: Set factors equal to 0.

3x+4=0 or 3x+4=0

x= −4 /3

Hope This helps

Answer:

D. x = [tex]-\frac{4}{3}[/tex]

Step-by-step explanation:

Step 1: Subtract 4 from both sides.

9x^2 + 24x + 20 − 4 = 4 − 4

9x^2 + 24x + 16 = 0

Step 2: Factor left side of equation.

(3x+4)(3x+4) = 0

Step 3: Set factors equal to 0.

3x+4=0 or 3x+4=0

x = [tex]-\frac{4}{3}[/tex]

I hope this helps your assignment! Anyways, have a fantastic day! :D  

Answer:

F

Step-by-step explanation:

In congruent triangles, or similar triangles, the letters in the same place will also be congruent

Answer:

the answer is A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.

The best conclusion from the study is that the consumption of blueberries might be associated with lower cholesterol levels. However, it's important to note that correlation does not mean causation and other factors could be at play.

The statement that comes closest to an appropriate conclusion from the study is that the possible consumption of blueberries might be associated with lower cholesterol levels. However, it is important to remember that correlation does not necessarily imply causation. While the organization of farmers showed a connection between eating blueberries and lower cholesterol, this does not necessarily mean eating blueberries directly causes lower cholesterol. Other factors could be involved. For instance, those who eat blueberries daily might generally lead healthier lifestyles, contributing to lower cholesterol levels.

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Answer:

Step-by-step explanation:

65 - Acute

72 - Acute

96 - Obtuse

Answer:

(a)

Step-by-step explanation:

Given 3 sides of a triangle a, b and c where c is the longest side, then

• If a² + b² = c² ⇒ triangle is right

• If a² + b² > c² ⇒ triangle is acute

• If a² + b² < c² ⇒ triangle is obtuse

Here a = 65, b = 72 and c = 96

65² + 72² ? 96²

4225 + 5184 ? 9216

9409 > 9216 ⇒ triangle is acute

Monthly periodic rate = 1.95%

The APR is the annual periodic rate

The annual periodic rate is the monthly rate multiplied by 12, because there are 12 months in a year

APR = monthly periodic rate X number of months in a year

= 1.95% X 12

= 23.4%

By using the concept of Annual Periodic rate and Monthly periodic rate,

Annual periodic rate of Shelby = 23.4%

What is Annual Periodic Rate and Monthly periodic rate?

At first it is important to know about Periodic rate.

Periodic rate is the rate that can be charged on loans for a certain period.

If the periodic rate is calculated over a month then it is called monthly periodic rate.

If the periodic rate is calculated over a year then it is called Annual periodic rate.

Here,

Monthly periodic rate of Shelby = 1.95%

Annual periodic rate of Shelby = [tex]1.95 \times 12[/tex]

                                                   = 23.4%

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Answer:

the answer is 82

Step-by-step explanation:

The answer would be 82

Answer:

13

Step-by-step explanation:

Volume = length x width x height

2320.5 = l x 12.75 x 14

2320.5 = l x 178.5

2320.5/178.5 = l

l = 13

the answer for this question is (B) 5,-2

The equation for the volume of a cube is V=s^3, where V is volume and s is side length.  Plug in and solve:

V=4.5^3

V=4.5*4.5*4.5

V=91.125ft^3

Hope this helps!!

Answer:

Step-by-step explanation:

Observe in the attached image that the final balance in your account on 9/1 is $578.30.

Then:

*On 9/6 he makes a payment of $140.30

*On 9/8, he makes a withdrawal from an ATM of $120

This means that:

$140.30 + $120 = $260.30

Then:

*On 9/18 you receive a deposit of $356.22

This means that:

$356.22

So, we have:

Beginning Balance: $578.30.

Total Withdrawals: $260.30

Total Deposits: $356.22

Final Balance = Beginning balance + Total Deposits - Total Withdrawals

Final Balance= $578.30 + $356.22 - $260.30

Final balance= $674.22

Then:

Date     Description    Debits(-) Credits(+)    Balance

9/6        Auto Pay         140.30                       438.00

9/8         ATM               120.0                         318.00

9/18       Deposit                           356.22      674.22

The balance in Arianna's register after the transactions will be $587.88. Then the correct option is C.

A monetary transfer is a record of money entering and exiting your account and is known as a bank transaction.

Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and checks #149 on 9/14 in the amount of $240.67.

No other Transactions were made.

Then the balance be in Arianna's register will be

→ $ 578.37 + $ 310.25 - $ 60 - $ 240.67

→ $ 587.88

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Answer:

  B)  9/2

Step-by-step explanation:

Subtracting 5x+7 from both sides leaves 2x = 9.

Dividing the 9 into two parts, we find ...

  x = 9/2

Answer: 9/2 your welcome i got a 100% on the test by the way

Step-by-step explanation:

[tex]f(x)[/tex] is continuous on [0, 3] and differentiable on (0, 3), so the mean value theorem applies here. It says that there is some [tex]c[/tex] in the open interval (0, 3) such that

[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]

We have

[tex]f'(x)=-2\sin2x-e^{-x}[/tex]

so

[tex]-2\sin2c-e^{-c}=\dfrac{\cos6+e^{-3}-2}3\implies c\approx1.5418[/tex]

The original negative number in the problem is found by setting up the equation 6x = x - 20 and solving for x, which results in the original number being -4.

If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. To solve for the original number, we can set up an equation based on the given condition. Let's assume the original number is x.

According to the problem, 6 times x equals x subtracted by 20:

6x = x - 20

To solve for x, we'll first move all terms involving x to one side of the equation by subtracting x from both sides:

6x - x = -20

This simplifies to:

5x = -20

Now, divide both sides by 5 to isolate x:

x = -20/5

x = -4

Therefore, the value of the original number is -4.

Solution:  Second month = m

The equation is

m + 10205 = 21894

m = 11689

So the second month will be $11,894. :)

To solve for the second month's salaries, subtract the first month salary from the total for two months. The solution to the equation $21,894 - $10,205 gives this salary: $11,689.

The subject of this problem is a toy company's salary expenses over a course of two months. Let's denote the salary expenses for the second month as X. We know from the problem that the total salary expenses for the first two months (January and February) are $21,894. Furthermore, we know that the salary expenses for January are $10,205.

We can write an equation to express these facts as follows: X (which is the salary expenses for February) is equal to the total salary for the two months minus the salary for January, or in mathematical notation, X = $21,894 - $10,205.

We solve this math equation by subtracting $10,205 from $21,894, giving us X = $11,689. Therefore, the second month's salaries total $11,689.

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A) There is a positive correlation between plant growth and the time spent in light.

Hope this helps chu

Have a great day

The correlation coefficient helps us to know how strong is the relation between two variables. The correct option is A.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

Since in the given scatterplot as the value of the percent of the time the plant is exposed to light is increased there is a simultaneous growth in the height of the plant in inches.

Therefore, For the given scatterplot the conclusion that can be made is that there is a positive correlation between plant growth and the time spent in light.

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Answer:

81.75 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where a, b are the parallel bases and h is the perpendicular height

Calculate h using the right triangle and the sine ratio

sin30° = [tex]\frac{opposite }{hypotenuse}[/tex] = [tex]\frac{h}{10}[/tex]

Multiply both sides by 10

10 × sin30° = h, thus

h = 5

a = 12 and b = 8.7 + 12 = 20.7, hence

A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 20.7)

   = 0.5 × 5 ×32.7

   = 81.75 ft²

Answer: letter a should be the correct answer

Step-by-step explanation:

D is the answer for this question

Compute the surface element:

[tex]\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv[/tex]

[tex]\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}[/tex]

[tex]\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}[/tex]

So the integral is

[tex]\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)[/tex]

[tex]=\dfrac23(37^{3/2}-1)[/tex]

170^3 this is the answer just make sure you do you're work.