You make an initial deposit of $2,500 in an account that offers 6% simple interest per year. How much will be in the account after 4 years?

Enter the correct answer in the box.

The number of boxes containing both pens and pencils is 2.

What is set?

A set is defined as a well-defined collection of distinct objects. It is denoted by the capital letters of the English alphabet. Its value remains the same for every individual.

Calculation for the number of boxes containing both pens and pencils

Total number of boxes is given by the union of two sets A and B; i.e. A∪B= 20

Boxes having pencils is given by the set A = 13

Boxes having pens is given by the set B = 9

Boxes having neither pens nor pencils, A'∩B' = 3

Boxes containing both pens and pencils are given by the intersection of the sets, A∩B

A∩B = A + B - A∪B

= 13 + 9 - 20

= 2

Hence, the number of boxes containing both pens and pencils is 2.

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Answer:

no solution exists:

Step-by-step explanation:

x²−1x+10=0

Step 1: Simplify both sides of the equation.

x²−x+10=0

Step 2: Subtract 10 from both sides.

x²−x+10−10=0−10

x²−x=−10

Step 3: The coefficient of -x is -1. Let b=-1.

Then we need to add (b/2)^2=1/4 to both sides to complete the square.

Add 1/4 to both sides.

x²−x+ 1/4=−10+ 1/4

x²−x+ 1/4=−39 /4

Step 4: Factor left side.

(x  -1/2)² = −39 /4

Step 5: Take square root.

x  −1 /2 =±√ −39 /4

Step 6: Add 1/2 to both sides.

x  =−1/2  + 1/2 = 1/2 ±√ -39/4

x = 1/2 ±√ -39/4

No real solutions.

Answer:x=-5

Step-by-step explanation:

y2-y1/x2-x1

-5-x/ 1-6-> -5-x/-5

-10/-5=2

The position of point A of the triangle is -4 units from the x-axis.

A coordinate plane is a 2D plane created by the junction of the x-axis and y-axis, two perpendicular lines. A coordinate system in geometry is a way to use one or more integers or coordinates to determine the positions of the points.

Here in the given diagram, there is a triangle ABC. The coordinates of the vertex of the triangle are,

A ( -4,2 )

B ( 1, -5 )

C ( 3,1 )

The distance of point A from the x-axis is -4 units.

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Answer:

yes

Step-by-step explanation:

yes

The answers will be :

a. The equation of perpendicular bisector of QR is y = \(\frac{-5}{3}\) x + 3.

b. The slope of median of triangle passing through point R is 1/4.

c. The slope of the altitude of the triangle that passes through point R doesn't exists.

What is slope of a line segment ?

Slope is the ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.

It is given that the vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).

a.

The midpoint (M) of QR will be equal to

( \(\frac{-2 + 8}{2} , \frac{-5 + 1}{2}\) )

or

M = (-3 , 2)

Now , slope of line QR will be ;

\(m_{QR}\) = \(\frac{1+5}{8+2}\)

\(m_{QR}\) = 6 / 10

We know that :

m × \(m_{QR}\) = -1

m = -10 / 6

or

m = -5 / 3

Equation of line will be given as :

y + 2 = \(\frac{-5}{3}\) ( x - 3 )

y = \(\frac{-5}{3}\) x + 3

b.

The midpoint of PQ will be :

= (\(\frac{-6 - 2}{2} , \frac{1 - 5}{2}\))

= ( -4 , -2)

The slope of median of triangle that passes through point R will be ;

m = \(\frac{-2 - 1}{-4-8}\)

m = -3 / -12

m = 1/4

or

m = 0.25

c.

Slope of altitude of triangle that passes through point Q will be :

m = \(\frac{1 - 1}{-6-8}\)

m = 0 / -14

m = 0

The slope in this case doesn't exist.

Therefore the answers will be :

a. The equation of perpendicular bisector of QR is y = \(\frac{-5}{3}\) x + 3.

b. The slope of median of triangle passing through point R is 1/4.

c. The slope of the altitude of the triangle that passes through point R doesn't exists.

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Answer:

3rd one

Step-by-step explanation:

Answer:C

Step-by-step explanation:took test

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

a) To find the volume of the torus using the shell method, the integral can be set up as ∫2πy(2πr)dy.

b) To find the volume of the torus using the washer method, the integral can be set up as ∫π(R²-r²)dx.

c) The volume of the torus can be found by evaluating one of the two integrals obtained in parts (a) and (b).

a) The shell method involves considering cylindrical shells with height dy and radius y. Since the torus is formed by revolving a circle of radius 3 centered at (8,0) about the y-axis, the radius of each shell is y and the height is 2πr, where r is the distance from the y-axis to the circle. Therefore, the integral to find the volume of the torus using the shell method is ∫2πy(2πr)dy.

b) The washer method involves considering infinitesimally thin washers with inner radius r and outer radius R. In the case of the torus, the inner radius is the distance from the y-axis to the circle, which is y, and the outer radius is the radius of the circle, which is 3. Therefore, the integral to find the volume of the torus using the washer method is ∫π(R²-r²)dx.

c) To find the volume of the torus, one of the two integrals obtained in parts (a) and (b) can be evaluated. The specific integral to evaluate depends on the chosen method (shell or washer). By substituting the appropriate values into the integral and evaluating it, the volume of the torus can be calculated.

Note: The specific calculations to find the volume of the torus and the corresponding numerical result were not provided in the question, so the final answer in cubic units cannot be determined without further information.

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Answer:

x is -2

u is -2

You need to expand the brackets.

The steps are shown in the picture above. Hope this helps

Grace

2 cups black paint + 1 cup white paint

percent of white paint = (cups white paint / total cups of paint) × 100 = (1/3)×100 = 33.3%

Chase

7 cups black paint + 3 cups white paint

percent of white paint = (cups white paint / total cups of paint) × 100 = (3/10)×100 = 30%

Grace's gray is lighter since it has a greater percentage of white paint

Answer:

X = 10*9/5

= 2*9

= 18

Answer = 18

Answer:

\(x=18\)

Step-by-step explanation:

First way (equivalent fractions):

\(\frac{x}{10}=\frac{9}{5}\)

\(\frac{x}{10}=\frac{18}{10}\)

\(x=18\)

Second way (cross multiplication):

\(\frac{x}{10}=\frac{9}{5}\)

\(5x=90\)

\(x=18\)

Answer: 3750

Step-by-step explanation:

Answer:

1 is  6.45

Step-by-step explanation:

3.25+1.55+1.65=6.45

Answer:

e = 35

d = 124

f = 21

Step-by-step explanation:

Answer:

2(3 + 8k)

Step-by-step explanation:

GCF of 6 and 16 is 2.

6 + 16k = 2(3 + 8k)

Answer:

5

Step-by-step explanation:

The check digit is the very last digit on the right, the one by itself

5

jdhdusndjskdbkanxjsidnw

Answer: If Spencer chooses to solve for a quantity using inference by enumeration, the different probability terms that need to be multiplied together in the summation depend on the specific problem or scenario at hand. However, in general, when performing inference by enumeration, the process involves summing over all possible combinations of values for the variables involved.

Let's consider a simple example to illustrate this. Suppose Spencer is trying to calculate the probability of a specific event E occurring, given a set of variables {X1, X2, X3}. In this case, the probability of event E can be written as:

P(E) = Σ P(E, X1, X2, X3),

where Σ denotes the summation symbol, and P(E, X1, X2, X3) represents the joint probability of event E and variables X1, X2, and X3 occurring together.

To evaluate this expression using inference by enumeration, Spencer would need to consider all possible combinations of values for X1, X2, and X3. For example, if each variable can take on two values (0 or 1), then there would be 2^3 = 8 possible combinations. Spencer would calculate the joint probability for each combination and sum them up to obtain P(E).

The specific probability terms that need to be multiplied together in the summation depend on the structure and dependencies of the variables in the problem. If the variables are independent, the joint probability can be calculated by multiplying the individual probabilities. However, if there are dependencies between the variables, additional terms and conditional probabilities may be involved in the calculation.

It's important to note that as the number of variables or the number of possible values for each variable increases, the computational complexity of inference by enumeration grows exponentially, making it impractical for problems with large state spaces. In such cases, approximate methods like sampling or more efficient algorithms like variable elimination or belief propagation are often used.

One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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Answer:

B

Step-by-step explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC = \(\frac{opposite}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{4}{5}\)

cosABC = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{3}{5}\)

using the exact values

sin60° = \(\frac{\sqrt{3} }{2}\) , cos60° = \(\frac{1}{2}\)

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= ( \(\frac{4}{5}\) × \(\frac{1}{2}\) ) + (\(\frac{3}{5}\) × \(\frac{\sqrt{3} }{2}\) )

= \(\frac{4}{10}\) + \(\frac{3}{10}\) \(\sqrt{3}\)

= \(\frac{2}{5}\) + \(\frac{3}{10}\) \(\sqrt{3}\)

sin<ABc

cos<ABC

Now

The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

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The complexity of the algorithm is O(n^2)b and there is no algorithm that can evaluate a polynomial in sublinear time complexity.

Brute-force Algorithm:

a. In order to evaluate a polynomial given in the form p(x) = anxn + an-1xn-1 + … + a0 at a particular point x0, the brute-force method simply plugs in the value of x0 into the polynomial and evaluates the entire polynomial expression

Take an integer n and n+1 numbers a0, a1, a2, ...an.Let x be a real or complex number.

Evaluate p(x) as: p(x) = a0 + a1x + a2x2 + … + anx^nPseudo-code for brute-force algorithm to evaluate polynomial p(x) at point x0:

function evaluate_polynomial(polynomial_coefficients, point_x)

{ sum = 0; for i = 0 to n do{ term = polynomial_coefficients[i] * pow(point_x, i); sum = sum + term;} return sum;}

Complexity of the algorithm: O(n^2)b.

b. Linear Algorithm:

The evaluation of a polynomial at a given point can be carried out by using the Horner's rule algorithm which is in Theta(n).

Horner's rule algorithm works by computing the polynomial one coefficient at a time in the following

Take an integer n and n+1 numbers a0, a1, a2, ...an.

Let x be a real or complex number.

Evaluate p(x) as: p(x) = a0 + x(a1 + x(a2 + … + x(an-1 + xan)…)

Pseudo-code for linear algorithm to evaluate polynomial p(x) at point x0:

function evaluate_polynomial_horner(polynomial_coefficients, point_x) { n = polynomial_coefficients.size; result = polynomial_coefficients[n-1];

for i = n-2 to 0 do{ result = result * point_x + polynomial_coefficients[i];} return result;}

c. Complexity of the algorithm:

O(n)

Better-Than-Linear Algorithm:

It is not possible to evaluate a polynomial of degree n at a point x0 using an algorithm whose worst-case efficiency class is better-than-linear (O(n)).

Thus, there is no algorithm that can evaluate a polynomial in sublinear time complexity.

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Answer: C. 00:00 $927; Vince wrote the wrong number to represent the interest rate.

Step-by-step explanation:

Given that:

Amount borrowed (p) = 900

Simple interest (r) = 1.5% = 0.015

Time (t) = 2 years

Amount he'll pay back (A) :

A = P(1 + rt)

A = 900(1 + 0.015(2))

A = 900(1 + 0.03)

A = 900(1.03)

A = $927

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

well u haven't attached the question

Answer:

Step-by-step explanation:

Answer:

The answer would be C.

Step-by-step explanation:

C. 2 3/4

Please find the photograph for the square root of 3.

4√3

= 4 × 1.732

= 6.928

6.928

Hope it helps

In the given right triangle, AC ≈ 5.506 units, α ≈ 25°, and γ measures 0 degrees.

In the given right triangle, we are given that BC has a length of 5 units and angle β is 65 degrees. Let's label the vertices of the triangle as follows: A, B, and C. Angle β is opposite side BC.

To find the missing angles and sides, we can use trigonometric ratios such as sine, cosine, and tangent.

Since we know the opposite side (BC) and angle β, we can use the sine ratio, which states that the sine of an angle is equal to the ratio of the length of the side opposite to the hypotenuse.

sin(β) = BC/AC

Rearranging the equation, we have:

AC = BC/sin(β)

AC = 5/sin(65°)

AC ≈ 5/0.90631

AC ≈ 5.506

Therefore, the length of side AC is approximately 5.506 units.

Now, to find the missing angles, we can use the fact that the sum of angles in a triangle is 180 degrees.

Angle α = 90° - β

Angle α = 90° - 65°

Angle α = 25°

Thus, angle α measures approximately 25 degrees.

Lastly, we can find angle γ by subtracting angles α and β from 90 degrees.

Angle γ = 90° - α - β

Angle γ = 90° - 25° - 65°

Angle γ = 90° - 90°

Angle γ = 0°

Therefore, angle γ measures 0 degrees.

To summarize, in the given right triangle with BC = 5 units and β = 65 degrees, the missing side AC is approximately 5.506 units long. The missing angles are α ≈ 25 degrees and γ = 0 degrees.

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Given:

Selling price of radio for Masada = 63,000

Loss = 10%

To find:

The amount of money Masada paid for the radio?

Solution:

Let x be the amount of money Masada paid for the radio.

According to the question,

\(x-10\%\text{ of }x=63000\)

\(x-\dfrac{10}{100}x=63000\)

\(x-0.1x=63000\)

\(0.9x=63000\)

Divide both sides by 0.9.

\(x=\dfrac{63000}{0.9}\)

\(x=70000\)

Therefore, Masada paid 70,000 for the radio.

When we divide the 464 by 60 we get the following remainder in our answer that is 44.

The Remainder is the name for the value that is left behind after division. If an amount (reward) cannot be divided completely with another number, we are left with only a meaning (divisor). The remaining is the name for this amount. For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

7.733333333333333

=7 44/60 ⇔ 7 R 44

464 divided by 60

=7 with a remainder of 44

Here, we provide you the outcome of the dividing with remainder, often known as the Euclidean division, along with a brief explanation of the following terms:

464 divide by 60 yields a quotient and residual of 7 R 44.

464 is the dividend & 60 is the divisor; the division (numeric division) of 464/60 is 7; the remainder ("left over") is 44.

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