A water faucet is turned 1/7 to the right and then 3/4 to the right again. How far is the water faucet turned?

Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The first four terms of the binomial series are  1,  x³/5,  (12/25)x⁶ and  respectively.

The binomial provided to us is (1+x^3)^-1/5.

To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.

\((1+x)^n = 1 + nx + [n(n - 1)/2!] x^{2} + [n(n - 1)(n - 2)/3!] x^{3} +...\)

As we can see here,

The value of x = x³,

The value of n = -1/5.

We get,

\((1+x^{3})^{-\frac{1}{5} } = 1 - \frac{1}{5} (x^{3} ) + [\frac{-1}{5} (\frac{-1}{5} -1)/2!]x^{6} + [\frac{-1}{5} (\frac{-1}{5} -1)(\frac{-1}{5} -2)/3!]x^{27} +\)

From the expansion, we can see,

First term = 1

Second term = x³/5

Third term = (12/25)x⁶

Fourth term = (-13/125)x²⁷

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The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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Answer:

okay, so we have a wall that is 60 ft. The area of the wall because the wall is a square is just side squared. So the area of the wall is \(60^{2}\), which is 30 600 square feet. The mirror is 20 ft by 60 ft. So the area of the mirror, because its a rectangle is length times width, so that's 20 a 60 so 20 x 60 is gonna give me 1200 square feet. So if we take the area of the mirror and put that over the area, the wall we get 1200 over 30 600, which reduces to one over three. So the mirror is one third the area of the wall.

Step-by-step explanation:

Let's take the first 2 x and y values and use them. First, you need to fill in your formula: y2-y1/x2-x1. It should look like this: 5-2/4-2. Then solve and you should get 3/2. You can't simplify it. So, this is your slope.

Next, you need to put this is into another formula. The formula is y-y1=m(x-x1). Take the first coordinate pair and plug it in for x1 and y1. Plug in your slope for m. When it's filled in, you should have y-2+3/2(x-1). It's hard to explain how to solve it so i'll just write it out.

y-2=3/2(x-2)

y-2=3/2x-3

y=3/2x-1

So, we have our equation in slope intercept form so that we have our slope and our y-intercept.

Y-intercept: -1

Slope: 3/2

Please put this as brainliest it took awhile and I hope this helped :) reply with questions if you still need help or have questions about the steps

Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Answer:

144ft^3

Step-by-step explanation:

To start, we have your formula: \(V=\frac{1}{2} (bh) (l)\)
b = base length of the triangle.
h = height of the triangle.
l = length of the prism

Fill in for each of those values:
\(V = \frac{1}{2} (6x6)(8)\)

\(V=\frac{1}{2} (36)(8)\)

\(V=(18)(8)\)

\(V=144\)

Your answer, because it is a 3D shape, should be cubed, so:
\(V=144ft^{3}\)

Answer:

Austin earned a higher score

Step-by-step explanation:

47/50 (Austin's score) = 94/100 (denominator is now 100) = 94% (converted to percentage) > 92% (Marty's score)

Hope this helps!

Answer:

Austin earned a higher score.

Step-by-step explanation:

Marty 50 * 0.92 = 46 points

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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hello

to solve this question, we need to follow some steps

collect like terms

divide both sides by the coefficient of k

from the calculations above, the value of k is 4

Answer:

20 weekday hours and 16 weekend hours

Step-by-step explanation:

all u do is take 5 hours and multiple them by 4 weekdays so it gives u 20 hours and then u multiple 8 hours by 2 which is 16 hours

All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

If the diameter increases by 10%,

new diameter = d+⅒ = 1.1d

also new radius = 0.55r

Height also increasesby 10%,

New height = h+⅒h = 1.1h

hence diameter of larger can =

π*(0.55)²*1.1= 1.0453

hence percentage change in volume

is 4.53% which can be rounded off to

The perimeter of the shape is 10 inches.

It's important to note that the perimeter of a shape or calculated by adding all the sides together.

In this case, this is a rectangle and the perimeter will be:

Perimeter = 2(length + width)

Length = 4 inches

Width = 1 inch

Perimeter = 2(length + width)

Perimeter = 2(4 + 1)

Perimeter = 10 inches.

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Answer:

x = 1851851.851....

Step-by-step explanation:

Given statement:

2.7% of x equals 50,000.

When we convert the statement into an equation, we get;

⇒ 2.7% × x = 50,000

A percentage is always written as (Percent)/100 in fraction form. Thus;

⇒ 2.7/100 × x = 50,000

Using cross multiplication:

To determine the value of x, we need to isolate it. This can be done by dividing the cooeficient of x both sides.

Divide both sides by 2.7

Answer:

Percent in decimal form:

\(\sf 2.7\% = \dfrac{2.7}{100} = 0.027\)

Therefore:

27% of X = 50000

\(\sf \implies 0.027 \cdot X=50000\)

\(\sf \implies X=\dfrac{50000}{0.027}\)

\(\sf \implies X=\dfrac{50000 \times 1000}{0.027 \times 1000}\)

\(\sf \implies X=\dfrac{50,000,000}{27}\quad \textsf{(as a fraction)}\)

\(\sf \implies X=1,851,852\quad \textsf{(nearest whole number)}\)

The statement that relative frequency is the difference of two frequencies from two different class is B. False.

To understand relative frequency, it is best to look at it from the relationship it has with cumulative frequency which is that while the cumulative frequency of a class is the total of the frequencies of that class and all previous classes, the relative frequency of a class is the proportion of the data that falls into that class.

Relative frequency is therefore not the difference found between two frequencies of different classes.

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shifted left 3 units

Graphed Below:

Answer: She started with 28 pieces of candy.

Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.

Answer:

She started with 28 candies.

Explanation:

Let the total amount of candies be c

Build equation:

→ remaining: c - 8

→ each gets: (c - 8)/5

Here given each gets 4 candies

So,

(c - 8)/5 = 4

c - 8 = 5(4)

c - 8 = 20

c = 20 + 8

c = 28

Answer:

Volume = 4

Step-by-step explanation

The Formula for Volume is length x width x height. You multiply 2 2/3 x 1 1/8 and you get 3 which is the base. then you multiply the base by 1 1/3 which is 4. So the carton's volume is 4.

The graph of the function y = -2x + 1/3 is added as an attachment

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

y = -2x + 1/3

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Step-by-step explanation: To solve for x in this literal equation, I would first distribute the C through the parentheses to get y = cx + cb.

Now subtract cb from both sides to get y - cb = cx.

Finally, divide both sides by c to get y - cb / c = x.

Answer:

A) DF= 11

B) JH= 13.6

C) GJ= 23.6

D) m∠F= 105

E) m∠G= 34

F) m∠J= 41

Step-by-step explanation:

The loan will increase to $39599.29 in 5 years

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

Using the above as a guide, we have the following:

Amount = P * (1 + r)ᵗ

Where

P = Principal = 35000

r = Rate = 2.5%

t = time = 5

Substitute the known values in the above equation, so, we have the following representation

Amount = 35000 * (1 + 2.5%)⁵

Evaluate

Amount = 39599.29

Hence, the amount is 39599.29

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Step-by-step explanation:

7. The two coordinates are (0, 4) and (1, -4).

 To find the slope you would need to use the formula \(\frac{y_{2}- y_{1} }{x_{2}- x_{1} }\)

 \(y_{2}\) = (-4), \(y_{1}\) = 4

 \(x_{2}\) = 1, \(x_{1}\) = 0

\(\frac{(-4)-4}{1-0}\) = \(\frac{-8}{1}\) = -8

8. The coordinates, (1, 4) and (0, -2)

(-2) -4 / 0 -1 = -6 / -1 = 6

Sorry for not formatting 8

9. The coordinates (-1, 3) and (4, -1)

(-1) - 3/ 4 - (-1) = -4/ 5

10. The coordinates (1, -1) and (2, -2)

(-2)- (-1) / 2 -1 = -1 / 1 = -1

Hope this helps!!!