You have deposited SEK 10,000 in an account that gives 2% interest every year. How much have you received in interest after two years?

One-Step Equations:

Number one: x + 6 = 8

Solve: To begin, you must subtract 6 on both sides to get x by itself.

x = 8 When you subtract 6 on both sides, you get x = 8 which is your answer. This is a one-step equation, meaning it only took us a single step in order to solve this equation.

Number two: x - 5 = 15

Solve: To solve this one-step equation, first, start off by adding 5 on both sides. Since it's only one step, your answer will be x = 20. All we had to do was add 5 to isolate the variable.

Two equations that contain fractions:

Number one: x - 1/2 = 2/4

Solve: x - 1/2 = 2/4

To begin, we have to add 1/2 to get x by itself. Since 2/4 and 1/2 don't have common denominators, all we have to do is multiply 1/2 by 2/2 to get a common denominator of 4. 1/2 x 2/2 is equal to 2/4. 2/4 + 2/4 is 4/4 which is equal to 1. Your answer is x = 1.

Number two: x + 3/4 = 2/4

Solve: To begin, we have to subtract 3/4 on both sides. Since 2/4 and 3/4 have a common denominator of 4, we can go ahead and subtract right away. 2/4 - 3/4 is equal to -1/4. x = -1/4.

One equation using distributive property:

Number one: 3(x + 2) = 18

Solve: To begin, we have to distribute the 3 to x and 2 (multiply). We get 3x + 6 = 18. To get x by itself, we have to first subtract 6 on both sides. We then get 3x = 12. Now, divide by 3 on both sides so that x is completely isolated, and we get x = 4.

One equation with decimals:

Number one: x + 0.25 = 0.75

Solve: To begin, we have to subtract 0.25 on both sides. When we do this, 0.75 - 0.25, we get x = .50 We can also write this as a fraction .50 is the same thing as 1/2. x = 1/2 or .50

One real-world problem:

Number one: Maria went to the store and she had 20 dollars to spend. She got a notebook for 5 dollars, and she wanted to buy pens with the rest. Each ben cost 5 dollars, how many pens can she buy in total?

Solve: We know that Maria had a total of 20 dollars in total and she already spent 5 dollars. We also know that each pen cost 5 dollars. When knowing this we can write this equation: 5x + 5 = 20. Since we don't know how many pens she's going to buy, we can just write a variable, in this case, x. Now we solve. Just like always, we need to isolate the variable. To do this, we have to first subtract 5. We then get, 5x = 15. Now, divide by 5 on both sides and we get x = 3. That means that Maria can buy a total of 3 pens.

Answer:

basicly everything that the other person said but the first answer is wrong, if you subtract 6 from both sides then the answer would be 2

Step-by-step explanation:

i edited it and also made it look a little more child like lol:

One-Step Equations:

Number one: x + 6 = 8

Solve: subtract 6 on both sides to get x by itself.

x = 2  

Number two: x - 5 = 15

Solve: add 5 on both sides.  

x = 20

Two equations that contain fractions:

Number one: x - 1/2 = 2/4

Solve: find a common denominator by multiplying 1/2 by 2 for both sides

x = 1.

Number two: x + 3/4 = 2/4

Solve: subtract 3/4 on both sides.

One equation using distributive property: 3(x + 2) = 18

Solve: distribute the 3 to x and 2. 3x + 6 = 18. subtract 6 on both sides. We then get 3x = 12. divide by 3 on both sides,

x = 4

One equation with decimals:

Number one: x + 0.25 = 0.75

Solve: subtract 0.25 on both sides.

X = 0.5

One real-world problem: Maria went to the store and she had 20 dollars to spend. She got a notebook for 5 dollars, and she wanted to buy pens with the rest. Each pen cost 5 dollars, how many pens can she buy in total?

Solve: 5x + 5 = 20. subtract 5 on both sides. divide by 5 on both sides and we get x = 3. That means that Maria can buy a total of 3 pens.

Pascal's Triangle is used to simplify the process of binomial expansion

The correct response:

Pascal's Triangle is an array of numbers arranged in a triangular pattern

that gives a binomial expansion coefficients.

Pascal's Triangle is presented in the form;

\({}\)                   1

               1    \({}\) 1

             1 \({}\)    2     1

         1      3     \({}\)3      1

   1   \({}\)     4      6     4       1

1\({}\)        5      10    10     5       1

Therefore, we have;

(x + y)⁰ = 1

(x + y)¹ = x + y

(x + y)² = x² + 2·x·y + y²

(x + y)³ = x³ + 3·x²·y + 3·y²·x + y³

(x + y)⁴ = x⁴ + 4·x³·y + 6·x²·y² + 4·x·y³ + y⁴

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The coefficients of the above, binomial expansion corresponds to the

values on each row on the Pascal's Triangle.

Therefore;

Alby's statement that the numbers in Pascal's Triangle are the values of the

exponents on the variables in a binomial expansion, is not correct.

The correct option is therefore;

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Answer:

No. The values in Pascal's Triangle are the values of the coefficients in a binomial expansion.

Step-by-step explanation:

Answer: 12 outcomes

Step-by-step explanation:

When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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To solve for x at an angle, you must first understand what type of angle you are working with. If the angle is a right angle, you can use the Pythagorean theorem to solve for x. If the angle is an obtuse angle, you can use the law of cosines to solve for x. If the angle is an acute angle, you can use the law of sines to solve for x.

To solve for x at a right angle using the Pythagorean theorem, you must have the lengths of the two neighboring sides of the triangle. The sum of the squares of the two sides is equal to the square of the hypotenuse, according to the Pythagorean theorem. By rearranging the components and solving for x, this equation may be used to find x.

To use the law of cosines to solve for x at an obtuse angle, you must know the lengths of all three sides of the triangle. According to the law of cosines, the square of one side's length equals the sum of the squares of the other 2 sides minus twice the product of the other 2 sides multiplied by the cosine of the obtuse angle. You can use this equation to solve for x by rearranging the terms and solving for x.

To apply the law of sines to solve for x in an acute angle, you should first know the lengths of the triangle's two sides as well as the acute angle's measurement. According to the law of sines, the ratio of one side's length to the sine of the opposite angle equals the ratio of the other side's length to the sine of the acute angle. By rearranging the terms and solving for x, you may use this equation to solve for x.

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Answer:

c. 122.1 cm

Step-by-step explanation:

so l * w + \(\frac{\pi r^2}{2}\)

since 6 cm is the diameter

6/2 = 3

the radius (or r) is 3

so 18 * 6 + \(\frac{3.14 * 3*3}{y}\)

108 + \(\frac{3.14*9}{y}\)

108 + \(\frac{28.26}{2}\)

108 + 14.13 = 122.13

simplified: 122.1 cm

hope this helps:)

Answer:

C. 122.1

Step-by-step explanation:

The area of a semicircle is HALF of the area of the circle. As the area of a circle is \(\pi r^2\). So, the area of a semicircle is \(\frac{1}{2}(\pi r^2)\), where r is the radius.

18 × 6

= 108

108 \(cm^2\) is the area of the rectangle,

For the semicircle, we know the diameter is equal to 6 cm,

(Remember that Diameter is equal to the radius times 2 (r × 2)),

To find the radius, divide the diameter by 2,

6 ÷ 2

= 3

The radius of the semicircle is 3 cm

Now use the equation \(\frac{1}{2}(\pi r^2)\) to find the area of the semicircle,

\(\frac{1}{2} (\pi 3^2)\)

(Remember pie is 3.14...)

Slove:

\(\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\)

\(=\frac{1}{2}\pi 3^2\)

\(\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\)

\(=\frac{1\pi 3^2}{2}\)

\(\mathrm{Multiply:}\:1\pi =\pi\)

\(=\frac{3^2\pi }{2}\)

\(3^2=9\)

\(=\frac{9\pi }{2}\)

\(\frac{9\pi }{2} =\left(\mathrm{Decimal:\quad }\:14.13716\dots \right)\)

Now take the decimal 14.13716.... and round to the nearest tenth,

14.13

(Remember 4 or less keep it the same, 5 or more bring the value up one more)

3 less than 5 so keep the 1 the same,

14.1

Now add 108 and 14.1,

108 + 14.1

= 122.1

Therefore the total area of the shape is 122.1 \(cm^2\). Answer ⇒ C.

Answer:

p=117.25

Step-by-step explanation:

441/4=110.25

110.25+7=117.25

103.25

Step-by-step explanation:

rewrite

4p - 28 = 441

-28. -28

----- -----

0. 413

413÷4= 103.25

Answer:

b. 12

Step-by-step explanation:

2*2*2*2 - 8* 2 divided by 4= 12

Answer:

17

Step-by-step explanation:

anddo the work you cheater

The required measure of the indicated angle b is 101°.

Use the concept of a triangle is defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

In the given figure,

Interior angle = 79°

And the corresponding exterior angle = b

If we combine both angles,

Then it becomes a complete angle of the line.

Since we know that,

The complete angle of a line = 180 degrees.

Therefore,

79° + b =  180°

Subtract 79° on both sides,

b = 101°

Hence,

The measure of angle b is 101°.

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a. The efficiency of Expedition Everest is approximately 87.8%.

b. The utilization of Expedition Everest is approximately 94.7%.

c.  The demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.

To calculate the efficiency and utilization of Expedition Everest, we need to compare the actual number of riders with the design capacity and effective capacity.

Given:

Demand = 3,000 riders/hour

Average riders = 1,800 riders/hour

Design capacity = 2,050 riders/hour

Effective capacity = 1,900 riders/hour

a. Efficiency:

Efficiency is calculated as the average riders divided by the design capacity, multiplied by 100%.

Efficiency = (Average riders / Design capacity) * 100%

= (1,800 / 2,050) * 100%

≈ 87.8%

Therefore, the efficiency of Expedition Everest is approximately 87.8%.

b. Utilization:

Utilization is calculated as the average riders divided by the effective capacity, multiplied by 100%.

Utilization = (Average riders / Effective capacity) * 100%

= (1,800 / 1,900) * 100%

≈ 94.7%

Therefore, the utilization of Expedition Everest is approximately 94.7%.

c. Capacity Analysis:

To determine if the operation is overcapacity or undercapacity, we compare the demand with the effective capacity.

Demand > Effective capacity

3,000 > 1,900

Since the demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.

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The tοtal weight οf all the tennis balls in the fully packed bοx is apprοximately 31 pοunds.

Geοmetry is a branch οf mathematics that deals with the study οf pοints, lines, angles, shapes, and their prοperties, as well as space and the relatiοnships between οbjects in space.

1. First, we need tο cοnvert all the dimensiοns οf the bοx tο inches: 1 ft = 12 inches, sο the dimensiοns οf the bοx in inches are 12 in * 13 in * 19 in. The diameter οf a tennis ball is 2.6 inches, sο the radius is 1.3 inches.

Tο find the maximum number οf tennis balls that can be packed in the bοx, we need tο find hοw many can fit in each dimensiοn. In the 13-inch dimensiοn, we can fit 5 tennis balls (since 5 * 2.6 = 13). In the 19-inch dimensiοn, we can fit 7 tennis balls (since 7 * 2.6 = 18.2, which is less than 19).

Fοr the height οf the bοx, we need tο find hοw many layers οf tennis balls can fit. The height οf a tennis ball is 2.6 inches, sο we can fit 7 layers in the 12-inch dimensiοn (since 7 * 2.6 = 18.2, which is less than 12).

Therefοre, the maximum number οf tennis balls that can be packed in the bοx is 5 x 7 x 7 = 245.

2. The vοlume οf each tennis ball is (4/3)π(1.3)^3 cubic inches, which is apprοximately 9.14 cubic inches. Sο the tοtal vοlume οf 245 tennis balls is 245 x 9.14 = 2238.3 cubic inches.

The weight οf οne cubic inch οf tennis balls is 0.014 pοund, sο the weight οf 2238.3 cubic inches is 2238.3 x 0.014 = 31.33 pοunds, rοunded tο the nearest pοund.

Hence, the tοtal weight οf all the tennis balls in the fully packed bοx is apprοximately 31 pοunds.

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Answer:

about 0.3

Step-by-step explanation:

8/9 is about 0.89

0.89/3 = about 0.3

Answer: x = 2 and y = 5

Step-by-step explanation:

y = 2x + 1

3x + y = 11

Substitute

3x + (2x + 1) = 11

5x + 1 = 11

Subtract both sides by 1

5x = 10

Divide both sides by 5

x = 2

y = 2x + 1

Substitute

y = 2 (2) + 1

y = 4 + 1

y = 5

Answer:

x = 7

Step-by-step explanation:

The right angle is composed of the 2 given angles, so sum to 90°

4x + 40 + 6x - 20 = 90

10x + 20 = 90 ( subtract 20 from both sides )

10x = 70 ( divide both sides by 10 )

x = 7

Answer:

8 times

Step-by-step explanation:

volume if cube = l³

volume of small cube = (3x)³ = 27x³

Volume of Large cube = (6x)³ = 216x³

216x³/27x³ = 8

The volume of large cube = 8 × Volume of small cube

Given:

The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.

Required:

What test score is 0.8 standard deviations below the mean?

Explanation:

Answer:

answered the question.

Answer:

1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

There are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$. For a number to end in the digit $3$ in base-$b$ representation, it must be congruent to $3$ modulo $b$.

We can rewrite $2013$ as $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$. Now, if $2013$ is congruent to $3$ modulo $b$, it means that $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$ is also congruent to $3$ modulo $b$.

Simplifying the expression, we have $2000 + 0 + 10 + 3$. Since the base-$b$-representation is formed by multiplying each digit by the corresponding power of $b$, we can rewrite the expression as $2 \cdot b^3 + 1 \cdot b^1 + 3 \cdot b^0$. We can now observe that the constant term $3 \cdot b^0$ will always be congruent to $3$ modulo $b$. However, the other terms $2 \cdot b^3$ and $1 \cdot b^1$ will not be congruent to $3$ modulo $b$ for any positive value of $b$. Therefore, the base-$b$-representation of $2013$ cannot end in the digit $3$ for any value of $b$.

Hence, there are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$.

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Answer:

a and b

Step-by-step explanation:

............. ...... ..

Answer:

The answer is B

Step-by-step explanation:

\(\frac{x}{4}=16\\\mathrm{Multiply\:both\:sides\:by\:}4\\\frac{4x}{4}=16\cdot \:4\\\mathrm{Simplify}\\x=64\)

Answer:

y= -3/5x-4

Step-by-step explanation:

After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.

a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y'  is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
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Answer:

x = 5

Step-by-step explanation:

I just solved the equation!

5 - 4(2-x) = 17

-4(2-x) = 12 (subtract by 5 on both sides)

2 - x = -3 (divide by 4 on both sides)

-x = -5 (subtract by 2 on both sides)

x = 5 (divide by -1 on both sides (two negatives cancel out!))

:)

Answer:

x = 5

Step-by-step explanation:

1) Subtract 5 from both sides.

-4(2-x)=17-5

2) Simplify 17 - 5 to 12.

-4(2-x)=12

3) Divide both sides by -4.

2-x=-12/4

4) Simplify 12/4 to 3.

2-x=-3

5) Subtract 2 from both sides.

-x=-3-2

6) Simplify - 3 - 2 to -5.

-x=-5

7) Multiply both sides by -1.

x = 5

Check the answer:

5-4(2-x)=17

1) Let x=5.

5-4*(2-5)=17

2) Simplify 2-5 to 3.

5-4*-3=17

3) Simplify 4 * -3 to -12.

5-(-12)=17

4) Remove parentheses.

5+12=17

5) Simplify 5 + 12 to 17.

17 = 17

All done !

Answer:

x

Step-by-step explanation:

Answer:

y-axis

Step-by-step explanation:

points are (x,y)

since the y-coordinate does not change, but the x-coordinate does, it rotates around the y-axis.

reflection just means it rotates 180 degrees (out of the paper, not around)

Answer:

A: b^3. B. X^3

Step-by-step explanation:

When dividing subtract the exponents is the property.

Answer:

A: \(b^3\) B: \(X^3\)

Step-by-step explanation:

\(A: b^7 - 4\\= b^3\)

B: \(X^5 - 2 \\=X^3\)

Answer:

The vertex of the graph is (-1,0)

Step-by-step explanation:

A vertex has different definitions

It refers to the point where we have the axis of symmetry

It can also be the point at which the graph changes direction

From the graph we have here, the vertex lie on the horizontal axis

It has an ordered pair value of (-1,0)

Given the rain barrel is shaped like a right circular cylinder. Therefore, volume of the rain barrel is approximately 3166.04 cubic inches.

To find the volume of the rain barrel, we can use the formula for the volume of a right circular cylinder, which is V = πr^2h. We are given the height and diameter of the rain barrel, so we can calculate its radius and then use the formula to find its volume.

Explanation:

The diameter of the rain barrel is 22 inches, so its radius is half of that, or 11 inches. The height of the rain barrel is 26 inches. We can now use the formula for the volume of a right circular cylinder to find the volume of the rain barrel:

V = πr^2h

V = π(11^2)(26)

V = π(121)(26)

V = 3166.04 cubic inches

Therefore, the volume of the rain barrel is approximately 3166.04 cubic inches.

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Answer:

$16200

Step-by-step explanation:

24 times 350=8400

8400+7000+800