6) Molly invests $7,747 in a retirement
account with a fixed annual interest rate
compounded 2 times per year. After 16
years, the balance reaches $31,685.08.
What is the interest rate of the account?

Step-by-step explanation:

\(U _{ {12}^{th} } = a {r}^{(n - 1)} \\ = 5 \times {5}^{12 - 1} \\ = 244140625 \\ {12}^{th} \: term \: is \: 244140625\)

Polynomial function is a function which the power of degree is more than two

g(x) = log 2x is a polynomial function

If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its  possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.

Percent error = 1%

Kilogram of iron ore = 500 kilograms

First step is to find the 1% of 500 kilograms

= .01 × 500 kilograms

= 5

Second step is to find the possible reading

Possible reading :

500 - 5

=495

500 + 5

= 505

Therefore we can conclude that  based on the above analysis the possible reading can be between 495 and 505.

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The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

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The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

The domains are all real numbers except the the values that makes the denominator zero

x - 1 = 0

x=1

That is; the domain is all real numbers except x=1

Answer:

the answer is 1 because the power of any no. 0 is always 1

Answer:

x - 7 = 2

Step-by-step explanation:

A number = x

minus seven = - 7

is two =  "= 2 "

Answer:  They need to have the same numerator to be equivalent

Example:

The fractions 1/7 and 2/7 are not equal because \(1 \ne 2\). So simply having the same denominator is not enough to have the fractions be the same overall.

Answer: If the numerators are equivalent.

Step-by-step explanation: If both denominators are the same, for example, 1/4 and 3/4, the fraction with the greater number (in this case, 3/4) is greater. If both fractions have exactly the same numerator and denominator, then they are equivalent.

Answer:

$36

Step-by-step explanation:

$48 × (100 - 25)% = $36

The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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The z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

The mean of the set of data is equal to the sum of all the quantities in the data, and divide by the no of quantities.

Given:

The standard deviation, d = 182.56,

The mean, m = 265.95,

The observation value, X = 235.90

Calculate the z score by the following formula given below,

Z = (X - m) / d,

Here, Z is the Z score,

Z = 235.90 -  265.95 / 182.56

Z =  -0.165

Therefore, the z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

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Answer:

i am pretty sure it is a (-4,1)

Step-by-step explanation:

hope this helps!

if i get it right plz mark brainliest.

thx!

Answer:

A. (-4,1)

Step-by-step explanation:

edge 2020

Answer:

86% is the percent of the book has Sarah left to read?

Answer: You divide it, get your answer, move the decimal point to the right twice, and that's you're percent.

Step-by-step explanation:

1/4=.25

.25 > 25%

Answer:

The answer is 25%

Step-by-step explanation:

To change decimal to percentage multiply by 100

1/4×100%

=25%

Answer:

switch them up

Step-by-step explanation:

Answer:

Multiply the normal price of the item by .25 and then subtract that from the normal price.

Step-by-step explanation

\(x -(x*.25)\)  

x is the item

Step-by-step explanation:

100%-25%= discounted price= 75%

You do the discounted price divided by 75 to find 1%

do that times 100 to find the pre-discounted price.

e.g

find the original price of a sweater when it was on sale of 25%. the sale price is £15.00.

£15.00 = 75%

15.00 divided by 75 = 1% =£0.20

£0.20 x 100 = pre-sale price = £20.00

The price of the sweater before the sale is £20.00.

You are welcome xx

A ship captain is mapping a trip and wants to know the distance the ship will travel over certain time intervals. time (hours)distance (miles). 0.5, 12.5. 1, 25. 1.5, 37.5. Assuming that the ship travels at a constant speed, what is its speed? ... You can see that every 30 minutes or 0.5 hours, the ship's distance ...

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

I don't understand I'm sorry.....

Answer:

Step-by-step explanation:

First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03

That means that there was a gain of $7.03 per share for Archie.

That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:

(7.03x100)= 703

The answer then is:

Archie gained $703 from selling all of his shares.

The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

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Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

The answer is D because for it to be a function x-value can only have one output. For D, 8 has two outputs 1 and 4.

Answer:

\(f(a) = 2a + 8\)

\(f(x + h) = 2x + 2h + 8\)

\(\frac{f(x + h) - f(x)}{h} = 2\)

Step-by-step explanation:

Given

\(f(x) = 2x + 8\)

Required

\(f(a)\)

\(f(x + h)\)

\(\frac{f(x + h) - f(x)}{h}\)

Solving for f(a)

Substitute a for x in the given parameter

\(f(x) = 2x + 8\) becomes

\(f(a) = 2a + 8\)

Solving for f(x+h)

Substitute x + h for x in the given parameter

\(f(x + h) = 2(x + h) + 8\)

Open Bracket

\(f(x + h) = 2x + 2h + 8\)

Solving for \(\frac{f(x + h) - f(x)}{h}\)

Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)

\(\frac{f(x + h) - f(x)}{h}\) becomes

\(\frac{2x + 2h + 8 - (2x + 8)}{h}\)

Open Bracket

\(\frac{2x + 2h + 8 - 2x - 8}{h}\)

Collect Like Terms

\(\frac{2x - 2x+ 2h + 8 - 8}{h}\)

Evaluate the numerator

\(\frac{2h}{h}\)

\(2\)

Hence;

\(\frac{f(x + h) - f(x)}{h} = 2\)

Answer:

there is not a common factor

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

She needed to subtract 36 from both sides of the equation, instead she added 36 to the right side.

By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.

In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:

(t, h) = (0 s, 5 ft)

Second, the final height of the ball is equal to:

h = 5 ft

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The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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