convert decimal number 0.25 in rational numbers ​

We are given with a rectangle whose length is 27 miles , and breadth is (3y + 1) miles and we are asked to find it's area . As , we know that , the area of a rectangle with Length and Breadth , L and B is given by Area = L × B respectively . Now , using this same formula in our question we have ;

\({:\implies \quad \sf Area=27\times (3y+1)}\)

\({:\implies \quad \sf Area=27\times 3y + 27\times 1}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{Area=81y+27\:\: sq\:\: mi.}}}\)

The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate \(= (1 + r/m)^m - 1\)

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate \(= (1 + 0.145/2)^2 - 1\)  

Simplifying the expression inside the parentheses:

Nominal rate \(= (1 + 0.0725)^2 - 1\)

Calculating the exponent:

Nominal rate \(= (1.0725)^2-1\)

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

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Answer: 60mph

Step-by-step explanation:

500-300 = 200

200 = distance traveled in 2 hrs

100 = distance traveled every hour

100=2x+20, x being the slower train

80=2x

x=40

40+20 = 60, the speed of the faster train

Answer:

i have the same question some one help

Step-by-step explanation:

30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

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Answer:

Step-by-step explanation:

The answer is B

The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²

We will use the following points to find the area of the sector;

First of all, the angle that is formed in a full rotation is 2π.

The area of a circle is given by the formula; A = πr²

The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π

Thus, the area of a sector is given by the formula;

A = (θ/2π) * πr²

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Answer:

Rectangular prism)1344

Rectangular pyramid)138.53

Cylinder)326.73

Cone)400.21

Triangular prism) I don't know the answer because I can't tell what sides the length is for

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16

Answer:

-----------------

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

Answer:

112.5

67.5

Step-by-step explanation:

We know the ratio is:

5:3

So, we can write it as:

5x+3x=180, with 5x being one angle, and 3x being the other

combine like terms

8x=180

divide both sides by 8

x=22.5

5(22.5)=112.5

3(22.5)=67.5

So, one angle is 112.5 and the other is 67.5.

Hope this helps!

Step-by-step explanation:

Our Equation:

*153/18 = 8.5 as a decimal.

\(x(8.5)=104\)

Divide each side by 8.5:

\(x=12.235\) \(rounded\) \(to\) \(the\) \(thousandths\) \(or\) \(\frac{208}{17}\)

Answer:

(36, 13)

Step-by-step explanation:

to find the midpoint you have the add the x and the y and then divide by two

to find one of the endpoints you just do the opposite

you multiply the midpoint by 2

and then subtract the remaining endpoint from it

(11, -1) --> (22, -2)

now subtract T from it

(36, 13)

that is your answer

The point estimate for sales when advertising is $3000 is $5412.

Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.

If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:

Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412

So, the required amount is $5412.

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The area of the region in the curves is 9 square units

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

f(x) = 4 - 2x² and g(x) = 2x.

In the region that lies inside the curves, we have

x = -2 and 1

So, we have

[-2, 1]

This represents the interval

For the surface generated around the region bounded by the curves, we have

A = ∫[a, b] [f(x) - g(x)] dx

This gives

A = ∫[-2,1] [4 - 2x² - 2x] dx

Integrate

A = 4x - x² - 2x³/3 [-2,1]

Expand

A = |4(-2) - (-2)² - 2(-2)³/3 - (4(1) - (1)² - 2(1)³/3)|

Evaluate

A = 9

Hence, the area of the region in the curves is 9 square units

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Question

If R is the region bounded above by the graph of the function f(x) = 4 - 2x² and below by the graph of the function g(x) = 2x, find the area of the region . This question requires you show your ability to us apply Calculus. Show all working.​

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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(a) There are 20 ways to choose 2 colors without replacement when the order is relevant. (b) There are 10 ways to choose 2 colors without replacement when the order is not relevant.

(a) If the order of the choices is relevant, then we need to use the permutation formula. The number of ways to choose 2 colors from 5, without replacement and with order considered, is given by P(5,2) = 5!/(5-2)! = 5x4 = 20.

(b) If the order of the choices is not relevant, then we need to use the combination formula. The number of ways to choose 2 colors from 5, without replacement and with order not considered, is given by C(5,2) = 5!/(2!3!) = 10.

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The ordered pair that represents the point plotted and labeled A include the following: (−1, 2).

In Mathematics and Geometry, the translation of a graph to the left simply means a digit would be subtracted from the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph upward means a digit would be added to the numerical value on the y-coordinate (y-axis) of the pre-image.

g(x) = f(x) + N

Note: "Point A is one unit left and two units up from the origin. "

Since point A is one unit left and two units up from the origin (0, 0), we can logically deduce the following:

(x, y)                   →           (x - 1, y + 2)

Origin (0, 0)        →           (0 - 1, 0 + 2) = point A (-1, 2).

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Answer:

A: -2 + 3i

B: -1 + -1i

C: 3 + -4i

D: 4 + 1i

Step-by-step explanation:

These are the answers, Basically just normal graphing. run/rise.

I hope this helps! :)))))

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer:

Step-by-step explanation:

answer is 9.66

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

Your answer is 11.8

Step-by-step explanation:

-1.8 degrees is 11.8 degrees warmer than -13.6. Hope this helps you!

Answer:

5.

Step-by-step explanation:

15.90 / 3.18 =

Answer:

each bar costs $3.

Step-by-step explanation:

The inequality that describes the problem is:

3x > 18

This inequality states that the total cost of the soap bars, represented by 3x, is greater than Colleen's budget of $18. The variable x represents the number of bars of soap Colleen bought. So, if x represents the number of bars of soap Colleen bought, 3x represents the total cost of those bars, since each bar costs $3.

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To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume is 824 cubic inches, we can rearrange the formula to solve for the radius:

824 = πr²h

Since the height is not given, we cannot find the exact radius. However, we can still determine the relationship between the height and radius if the volume remains the same.

b. If the height of the cylinder is changed, but the volume stays the same, the radius will change inversely proportional to the height. This means that as the height increases, the radius will decrease, and vice versa. This relationship ensures that the volume remains constant.

Therefore, we cannot determine the exact radius without knowing the height, but we can conclude that the radius and height have an inverse relationship.

Answer:

I don't know

Step-by-step explanation:

it depends on your definition and question

Answer:

\(y=-\frac{1}{4}x+5\)

Step-by-step explanation:

Given the point (8,3) and slope of 4, we can write an equation in point-slope form.

We know that any line perpendicular to another line has a opposite reciprocal. The opposite reciprocal of 4 is \(-\frac{1}{4}\).

Now, to write this in point slope form.

Point slope formula:

\(y-y_1=m(x-x_1)\)

New equation:

\(y-3=-\frac{1}{4}(x-8)\)

Simplify:

\(y=-\frac{1}{4}x+5\)

Here is the equation :)