what is the sum of the first 5 terms of the geometric series: 1+3+9+…+19,686

a. 212
b. 58
c. 136
d. 121

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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By adding the set of parentheses as shown above, we get an expression [tex]65 e^{0.68} \simeq 17.09[/tex]

In mathematics, exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bⁿ, where b is the base and n is the power; this is pronounced as "b to the n".

One possible way to create an expression using parentheses to get a value of 17 is:

((8 ÷ 2) + (9 × 9) - (10 × 2)) exponent 0.5

First, we evaluate the multiplication and division operations inside parentheses, since they have higher precedence than addition and subtraction.

[tex]((8 \div 2) + (9 \times 9) - (10 \times 2)) = (4 + 81 - 20) = 65[/tex]

Then, we raise the result to the power of 0.68 which is the same as taking the square root:

65 exponent 0.68 ≈ 17.09

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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.

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:

(-5,3)

Step-by-step explanation:

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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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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Answer:

20 Kg

Step-by-step explanation:

let b represent the weight of 1 bag of sand

after using [tex]\frac{1}{4}[/tex] of 1 bag there is [tex]\frac{3}{4}[/tex] bag left along with the unused bag , then

[tex]\frac{3}{4}[/tex] b + b = 35 ( multiply through by 4 to clear the fraction )

3b + 4b = 140

7b = 140 ( divide both sides by 7 )

b = 20

that is one full bag weighs 20 Kg

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

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 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:1300

Step-by-step explanation:

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

Answer:

385865

Step-by-step explanation:

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

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:

1048576

Step-by-step explanation:

2^20=1048576

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°

Answer: -1/2x

Step-by-step explanation:

Rise over run method if you know it is really helpful

the result by 5 and adds 4 one last time to get the final output value. This can also be written in shorthand as:=(f o f o f) (X) = 5(5(5X + 4) + 4) + 4 = 125X + 124.

How to solve a  function?

To find (f o f o f) (X), we need to apply the function f three times to X. Let's start by finding (f o f) (X):

(f o f) (X) = f(f(X)) = f(5X + 4) = 5(5X + 4) + 4 = 25X + 24

Now, we need to apply f to (f o f) (X) to get the final result:

(f o f o f) (X) = f((f o f) (X)) = f(25X + 24) = 5(25X + 24) + 4 = 125X + 124

Therefore, (f o f o f) (X) = 125X + 124.

In words, the function (f o f o f) (X) takes any input value X, multiplies it by 5, adds 4, multiplies the result by 5 again, adds 4, and finally multiplies the result by 5 and adds 4 one last time to get the final output value. This can also be written in shorthand as:

(f o f o f) (X) = 5(5(5X + 4) + 4) + 4 = 125X + 124.

This process of applying a function multiple times to an input value is known as function composition, and it is a fundamental concept in mathematics and computer science.

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The solution of the given system of equation is x = 6 and y = -6.

The places where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.

The two equations are x + y = 0 and 5x + 4y = 6.

The first equation can be written as:

x = - y

Substituting the value of x in equation 2 we have:

5(-y) + 4y = 6

-5y + 4y = 6

-y = 6

y = -6

Substitute the value of y in equation 1:

x - 6 = 0

x = 6

Hence, the solution of the given system of equation is x = 6 and y = -6.

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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?

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]

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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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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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{6\dfrac{2}{3} - 4\dfrac{1}{3}}\\\\\mathtt{\rightarrow \dfrac{6\times3 + 2}{3} - \dfrac{4\times3 + 1}{3}}\\\\\mathtt{\rightarrow \dfrac{18 + 2}{3} - \dfrac{12 + 1}{3}}\\\\\mathtt{\rightarrow \dfrac{20}{3} -\dfrac{13}{3}}\\\\\mathtt{\rightarrow\dfrac{7}{3}}\\\\\mathtt{\rightarrow2 \dfrac{1}{3}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{2\dfrac{1}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/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 portion of the Earth that you can see from the hot air balloon is approximately 68.1 miles.

What is horizon ?

The horizon is the apparent boundary where the Earth's surface seems to meet the sky. It's the line that separates the visible portion of the Earth's surface from the portion that is not visible due to the curvature of the Earth. The horizon appears to be a straight line, but it is actually a curved line due to the spherical shape of the Earth. The distance to the horizon depends on the observer's height above the ground, as well as the radius of the Earth. The higher the observer, the farther away the horizon appears.

The distance from the balloon to the horizon is the same as the radius of the Earth plus the height of the balloon. So in this case, it's 1.5 + 4000 = 4001.5 miles.

Now we need to find the distance AC, which is the distance from the center of the Earth to point C. To do this, we can use the Pythagorean theorem:

AC² + BC² = (radius of Earth)²

AC² + (4001.5)² = (4000)²

AC² = (4000)² - (4001.5)²

AC ≈ 68.2 miles

Now we can find the distance BD using similar triangles. In the triangle ABD, we know that AB is the radius of the Earth, which is 4000 miles. We also know that AC is 68.2 miles, and we want to find BD. So we can set up the following proportion:

BD / AB = AC / AD

Solving for BD, we get:

BD = AB * (AC / AD)

To find AD, we can use the Pythagorean theorem again:

AD² = AB²+ BD²

AD² = (4000)²+ (BD)²

AD ≈ 4000.3 miles

Now we can plug in the values we have:

BD = AB * (AC / AD)

BD = 4000 * (68.2 / 4000.3)

BD ≈ 68.1 miles

So the portion of the Earth that you can see from the hot air balloon is approximately 68.1 miles. Rounded to the nearest tenth, the answer is 68.1 miles.

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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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Using matrix method solve + 2 = 3 5 − = 7. the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations:

x + 2y = 3

5x - 2y = 7

using matrix methods, we can represent the system as a matrix equation:

AX = B

where

A = [1 2; 5 -2]

X = [x; y]

B = [3; 7]

To solve for X, we need to find the inverse of A:

A^-1 = 1 / det(A) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate of A.

det(A) = (1 * -2) - (2 * 5) = -12

adj(A) = [-2 -2; -5 1]

So, A^-1 = -1/12 * [-2 -2; -5 1] = [1/6 1/6; 5/6 -1/6]

Now, we can solve for X:

X = A^-1 * B = [1/6 1/6; 5/6 -1/6] * [3; 7] = [2; 1]

Therefore, the solution to the system of equations is x = 2 and y = 1.

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