emily invests $6,398 in a retirement account with a fixed annual interest rate compounded continuously .After 16 years the balance Reaches $9,483.80. What is the interest rate of the account?

Answer:

385865

Step-by-step explanation:

this is not correct question because I can't see this

We can conclude after answering the provided question that Joel cannot inequality satisfy the constraints by purchasing two games and six puzzles because 6 + 2 is less than 9.

In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the two sides until only the variables remain. However, a number of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

puzzles while adhering to the constraints?

Let x be the number of puzzles that Joel can buy and y be the number of games that Joel can buy.

Joel has a total spending limit of $96. As a result, we can write the first inequality as follows:

8x + 12y ≤ 96

x + y ≥ 9

s: x ≥ 0 ≥ 0

To see if Joel can satisfy the constraints by purchasing two games and six puzzles, we enter x = 6 and y = 2 into the inequalities:

8x + 12y ≤ 968(6) + 12(2) ≤ 9672 ≤ 96 (True) (True)

x + y ≥ 96 + 2 ≥ 9 (False) (False)

Joel cannot satisfy the constraints by purchasing two games and six puzzles because 6 + 2 is less than 9.

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Step-by-step explanation:

[tex]2 {}^{a} = 16[/tex]

Since our variable is in the exponent, we take the logarithm of both sides in order to solve for a.

The log base is 2 In order to cancel out base 2,

[tex]a = log_{2}(16) [/tex]

[tex]a = 4[/tex]

The triangles that translate to triangle X are A and F.

Triangle ABC is translated to triangle A'B'C', 5 square(s) to the right and 4 square(s) down.

Triangles can be translated by moving each of their vertices a certain distance in a certain direction. The distance and direction of the translation can be described using vector notation.

For example, a translation of a triangle by the vector <a, b> would move each vertex of the triangle a units to the right and b units up. The resulting translated triangle would have the same shape and size as the original triangle, but would be located in a different position in the plane.

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Image transcribed:

Select all of the triangles below which are translations of triangle X.

Triangle ABC is translated to triangle A'B'C'.

Fill in the gaps below to describe the translation.

Triangle ABC is translated to triangle A'B'C'.

Fill in the gaps below to describe the translation.

___ square(s) to the left/right and ___ square(s) up/down

A

B

C

A'

B'

C'

The solutions to the equation, 0.4x² + x = 0.7, are approximately x = -1.54 and x = 0.29.

From the question, are solve the given quadratic equation.

To solve the equation 0.4x² + x = 0.7, we can start by rearranging it to the standard quadratic form ax² + bx + c = 0:

0.4x² + x - 0.7 = 0

Then, we can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 0.4, b = 1, and c = -0.7, so we have:

x = (-1 ± √(1² - 4(0.4)(-0.7))) / 2(0.4)

x = (-1 ± √(1 + 1.12)) / 0.8

x = (-1 ± √(2.12)) / 0.8

x ≈ -1.54 or x ≈ 0.29

Hence, the solutions are -1.54 and 0.29

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To solve this problem, we need to use vector addition to find the resultant velocity of Julia.

Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.

The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.

The velocity of the river is 3 km/hr in the negative y-axis direction.

To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.

Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:

|V| = √(Vx² + Vy²)

where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.

Vx = 8 km/hr

Vy = -3 km/hr

|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr

The direction of the resultant velocity can be calculated as:

θ = tan⁻¹(Vy / Vx)

θ = tan⁻¹(-3 / 8) = -20.56°

The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).

Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).

Answer:

Step-by-step explanation:

The hypotenuse length is not given here. So we have to find it.

We take hypotenuse length as X

by using the Pythagoras theorem

x² = 6²+10²

x= √136

x=2√34

the perimeter of the garden = 6+10+2√34

                                                = 16+2√34

                                                = 5.8+16

                                                =21.8m

Answer:

156 M

Reasoning you add How far He has walked from his starting point

Step-by-step explanation:

Answer: 156 m here u go

The simplest form of the fraction in this problem is given as follows:

t^6.

The fraction in the context of this problem is defined as follows:

2(t^4)³/2t^6.

The numeric constant of both the numerator and the denominator is of two, hence it can be simplified, as follows:

(t^4)³/t^6.

At the numerator, we apply the power of power rule, meaning that when we have a single base elevated to multiple exponents, we can multiply the exponents, hence:

(t^4)³ = t^(4 x 3) = t^12.

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence the simplified expression is given as follow:

t^12/t^6 = t^(12 - 6) = t^6.

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The solution to the expression using laws of exponents is: t⁶

Some of the laws of exponents are:

1) Product of powers rule: This means that we are to add the powers together when multiplying like bases.

2) Quotient of powers rule: This means that we are to subtract powers when dividing like bases.

3) Power of powers rule: This means that we are to multiply powers together when raising a power by another exponent.

4) Power of a product rule: This means that when any base is to be multiplied by an exponent, distribute the exponent to each part of the base.

We are given the expression:

2(t⁴)³/2t⁶

2 is common to both numerator and denominator and they will cancel out to give: (t⁴)³/t⁶

Using power of power rule on the numerator, we have:

t¹²/t⁶

Using quotient of powers rule, we have:

t¹²/t⁶ = t¹²⁻⁶

= t⁶

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Answer:

2×2×7=28

Step-by-step explanation:

28÷2=14

14÷2=7

Prime numbers 2, 2, and 7 make 28

The radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.

Radius is a line segment that extends from the center of a circle or sphere to its circumference. It is the distance from the center to the edge of the circle or sphere. It is also used to measure the length of an arc of a circle. Radius is a necessary measure when calculating the area of a circle or sphere, as well as the volume of a sphere.

The arc length of a semicircle is given by the formula s = πr,
where r is the radius of the semicircle. In this case,
we are given the radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.

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The arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.

What is an arc?

An arc is part of a circle's circumference. It is a segment of a curved line that is formed when a straight line intersects a circle or a curved shape. Arcs can be measured in length, angle, or radius, depending on the context.

To find the arc length of a semicircle, we need to know the radius of the circle and the angle subtended by the arc at the center of the circle.

Let's assume the radius of the semicircle is 'r'. Since it is a semicircle, the angle subtended by the arc at the center of the circle is 180 degrees or π radians.

The formula for arc length is given by:

arc length = radius x angle in radians

In this case, the angle is π radians and the radius is 'r'. Therefore, the arc length of the semicircle is:

arc length = r x π

We can leave the answer in terms of π or substitute the value of π to get a numerical answer. For example, if the radius of the semicircle is 4 units, the arc length will be:

arc length = 4 x π

arc length ≈ 12.57 units (using π ≈ 3.14)

Therefore, the arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.

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Answer:

b = 62°

Step-by-step explanation:

We Know

A triangle sum is 180°

We know two angles, one is 68.5° and the other is 49.5°.

Find angle b

We Take

180 - (68.5 + 49.5) = 62°

So, b = 62°

Step-by-step explanation:

the length of the diagonal is calculated out of the length and width by using Pythagoras (after all, one length, one width and the diagonal are creating a right-angled triangle).

25² = length² + width²

length = 2×width + 10

we are using the second in the first equation :

25² = (2×width + 10)² + width²

625 = 4×width² + 40×width + 100 + width²

525 = 5×width² + 40×width

105 = width² + 8×width

width² + 8×width - 105 = 0

a quadratic equation

ax² + bx + c = 0

has the general solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 1

b = 8

c = -105

width = (-8 ± sqrt(8² - 4×1×-105))/(2×1) =

= (-8 ± sqrt(64 + 420))/2 =

= (-8 ± sqrt(484))/2 =

= (-8 ± 22)/2 = -4 ± 11

width1 = -4 + 11 = 7

width2 = -4 - 11 = -15

a negative size of the length of a side of a shadow does not make any sense, so, our valid solution is

width = 7 in.

and then

length = 2×width + 10 = 2×7 + 10 = 14 + 10 = 24 in.

As a result, chairs in modern movie theatres are about 21.05% larger than those from theatres built 30 years ago.

By reducing the value through the overall value and multiplying the outcome by 100, the percentage may be calculated. The proportion is calculated using the method (value/total value)100%.

We can use the formula for percentage increase to solve this problem:

% increase = (new value - old value) / old value × 100%

The new value is the current average width of a movie theater seat, which is 23 inches. The old value is the width of a movie theater seat from 30 years ago, which is 19 inches.

% increase = (23 - 19) / 19 × 100% ≈ 21.05%

Therefore, current movie theater seats are approximately 21.05% wider than a theater seat from 30 years ago.

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The surface area (A) of a cylinder is given by the formula A = 2πr² + 2πrh, where r is the radius of the cylinder and h is its height.

In this case, the radius of the cylinder is 3x - 2 cm, and its height is x + 3 cm. Substituting these values into the formula, we get:

A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)

Simplifying this expression, we get:

A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π

A = 24πx² - 10πx - 12π

So the surface area of the cylinder is 24πx² - 10πx - 12π.

Answer:1300

Step-by-step explanation:

Rate of Interest for 2 years. 650 for one times 2.

Investing R10,000 at 14% compounded twice a year for one year will give a return of approximately R1,449.49.

The interest rate charged on a loan or generated on an investment is represented as a percentage over a year and is known as the annual percentage rate (APR). It does not account for compounding and simply considers the basic interest rate.

The total interest gained on an investment over the course of a year, taking into account the effect of compounding, is known as the annual percentage yield (APY), on the other hand.

The compound interest is given as:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

For investing at 14% compounded twice:

[tex]A = R10,000(1 + 0.14/2)^{(2t)}\\A = R10,000(1.07)^{2t}[/tex]

Investment for t = 1 we have:

A = R10,000(1.07)²

A ≈ R11,449.49

Hence, Investing R10,000 at 14% compounded twice a year for one year will give a return of approximately R1,449.49.

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The type of sampling used in each case are:

Statement A → Stratified random sampling.

Statement B → Cluster sampling

Statement C → Simple random sampling

Statement D → systematic sampling

There are different ways that samples are classified such as:

1) Convenience sampling: This is where samples are drawn from a conveniently available pool.

2) Random Sampling: This is when we put all the options into a particular hat and drawn some of them.

3) Systematic Sampling: This is when every nth element is taken. For example, we want to survey something in the school, and then we interview every 10th person.

4) Cluster Sampling: This usually divides a population into groups, referred to as clusters, and each element in that cluster is surveyed.

5) Stratified Sampling: This will divide the population into groups. However, unlike cluster sampling, here, only some elements of the group are surveyed.

From the given problem:

Statement A is Stratified random sampling.

Statement B is Cluster sampling

Statement C is Simple random sampling

Statement D is systematic sampling

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Answer:

Approx. 4.47

Step-by-step explanation:

To calculate the standard deviation for the data, we need to follow these steps:

1. Calculate the mean (average) of the data:

mean = (13 + 17 + 9 + 21) / 4 = 15

2. Calculate the difference between each data point and the mean:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

3. Square each difference:

(-2)^2 = 4

2^2 = 4

(-6)^2 = 36

6^2 = 36

4. Calculate the variance by taking the average of the squared differences:

variance = (4 + 4 + 36 + 36) / 4 = 20

5. Calculate the standard deviation by taking the square root of the variance:

standard deviation = sqrt(variance) = sqrt(20) ≈ 4.47

Therefore, the standard deviation for the data is approximately 4.47.

The interest earned during the third month of the 7th year is $3,613.55.

What is interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

Let PMT be the monthly payment, r be the monthly interest rate, and n be the total number of payments. Then:

FV = PMT × [(1 + r)n - 1]/r

In this case, we want to find PMT, given that FV = $900,000, r = 0.038/12, and n = 10 × 12 = 120:

[tex]$900,000 = PMT * {[(1 + 0.038/12)}^{120} - 1]/(0.038/12)[/tex]

Solving for PMT, we get:

PMT = $682.48

[tex]FV = $682.48 * [(1 + 0.038/12)^87 - 1]/(0.038/12)\\\\ = $89,324.47\\\\PV = $682.48 * [(1 + 0.038/12)^83 - 1]/(0.038/12) \\\\= $85,710.92[/tex]

The interest earned during the third month of the 7th year is:

$89,324.47 - $85,710.92 = $3,613.55

Therefore, the interest earned during the third month of the 7th year is $3,613.55.

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The radical expression √2 -3√2 + 5√2 when simplified has its value to be 3√2

To combine √2, -3√2, and 5√2 into a single simplified radical, we need to first group the terms with the same radicand (the number inside the square root).

In this case, all three terms have a radicand of 2.

Adding -3√2 and 5√2, we get 2√2.

Then, combining this with √2, we have 3√2 as the simplified radical form of the expression.

Thus, the simplified radical form of √2 -3√2 + 5√2 is 3√2.

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Answer:

1048576

Step-by-step explanation:

2^20=1048576

An exponential expression with base 25 and a single, simplified exponent is [tex](25)^{-28}[/tex]

In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

Generally speaking, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the law of indices for powers of the same base number, we have the following:

[tex](25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}[/tex]

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Answer:

9

Step-by-step explanation:

the distance between the two points is just the difference in x-values: -7-2 = 9.

Answer:

The distance between two points  (-7, 5) and (2, 5) is [tex]\sqrt{35}[/tex]

Step-by-step explanation:

Given: Points (-7, 5) and (2, 5)            

We have to find the distance between the given points (2, 5) and (5, 7)

Consider the given points (2, 5) and (5, 7)

Distance between two points is calculated using formula

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1^2}[/tex]

[tex](x_1,y_1)=(-7,5), \ (x_2,y_2)=(2,5)[/tex]

Thus, [tex]D=\sqrt{(5- (-7))^2+(5-2)^2}=\sqrt{35}[/tex]

Thus, The distance between two points  (-7, 5) and (2, 5) is [tex]\sqrt{35}[/tex]

Answer: -1/2x

Step-by-step explanation:

Rise over run method if you know it is really helpful

now, if we take a looksie at the denominators on all sides, hmmm 2 and 3, so we can get an LCD of 6, so let's multiply both sides by 6 to do away with the denominators.

[tex]4-\cfrac{x-2}{2}=x+\cfrac{1-2x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( 4-\cfrac{x-2}{2} \right)~~ = ~~6\left( x+\cfrac{1-2x}{3} \right)} \\\\\\ 24-3(x-2)~~ = ~~6x+2(1-2x)\implies 24-3x+6~~ = ~~6x+2-4x \\\\\\ 30-3x=2x+2\implies 30=5x+2\implies 28=5x\implies \cfrac{28}{5}=x\implies 5\frac{3}{5}=x[/tex]

The area of the shaded region under the standard normal curve with z = 0.49 is 1.

The area of the shaded region under the standard normal curve with z = 0.49 is 1.

What is curve?

In mathematics, a curve is a continuous and smooth (i.e., differentiable) mathematical object that represents a path or a trajectory. Curves can be defined in different ways, depending on the context in which they are used.

What is area of curve?

The area of a curve refers to the amount of space enclosed by a curve on a two-dimensional plane. Finding the area of a curve can be a challenging problem, especially when the curve is not a standard geometric shape such as a circle or rectangle.

To find the area of the shaded region under the standard normal curve with z = 0.49, we need to use a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we find that the area to the left of z = 0.49 is 0.6864. This means that the area to the right of z = 0.49 is 1 - 0.6864 = 0.3136.

Since the normal curve is symmetric about the mean (z = 0), the area to the left of z = -0.49 is also 0.6864. Therefore, the area between z = -0.49 and z = 0.49 is:

0.6864 (area to the left of z = 0.49) + 0.3136 (area to the right of z = 0.49) = 1

So the area of the shaded region under the standard normal curve with z = 0.49 is 1.

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Using simple mathematical operations we know that 19.03 min will be required to make 88 pretzels by 5 makers.

In mathematics, an operation is a function that transforms zero or more input values ​​into well-defined output values.

The number of operands is the arity of the operation.

The four basic operations in mathematics for all real numbers are:

Addition (sum; '+') Subtraction (difference formation; '-') Multiplication (product formation; '×') Division (quotient formation; '÷')

So, insert values as follows: t is time

2*6/44 = 5*t/88

t = 8*88/444*5 = 0.3171 hours

0.3171*60 = 19.026 min

Therefore, using simple mathematical operations we know that 19.03 min will be required to make 88 pretzels by 5 makers.

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Complete question:

If 2 pretzel makers can make 444 pretzels in 6 hours, how long does it take 5 pretzel makers to make 88 pretzels?

Please provide specific data sets, and I would be happy to help you calculate the mean absolute deviation and determine which one has a MAD of 0.64.

Hello! Based on your question, you'd like to know which data set has a mean absolute deviation (MAD) of 0.64. Unfortunately, without any specific data sets provided, I am unable to directly calculate the MAD for you. However, I can help explain the concept of mean absolute deviation and how to calculate it for a given data set.

Mean absolute deviation is a measure of dispersion or variability within a data set. It helps in understanding how spread out the data points are from the mean (average) of the data set. To calculate the MAD, follow these steps:

1. Compute the mean of the data set by adding all the data points and dividing the sum by the total number of data points.
2. Calculate the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value of the result.
3. Add all the absolute deviations obtained in step 2.
4. Divide the sum of absolute deviations by the total number of data points to get the mean absolute deviation.

When you find a data set with a MAD of 0.64, it indicates that, on average, the data points are 0.64 units away from the mean. Keep in mind that a smaller MAD value means the data points are closer to the mean, indicating less variability, whereas a larger MAD value indicates more variability within the data set.

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