PLEASE ANSWER
The perimeter of the rectangle below is 120 units. Find the length of side VY .
Write your answer without variables.

Answer:

4/5

Step-by-step explanation:

Call our unknown variable ‘x’

X(1/4)=1/5

Therefor, x=4/5

The moment of inertia for rotation about the z axis is  [tex]I & =\frac{a^2 M}{3}[/tex].

A triangular prism of mass m, whose two ends are equilateral triangles.

Two ends are equal.

The xy plane with side 2a, is centered on the origin with its axis along the z axis.

Find the moment of inertia for rotation the z-axis.

It is divide into 4 triangles with side 'a' k one side is 3cm.

[tex]$$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$[/tex]

It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.

Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.

[tex]$$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$[/tex]

[tex]$$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$[/tex]

⇒ Now, by using the [tex]$I_{\text {Big }}=I$[/tex]

⇒[tex]I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\[/tex]

⇒[tex]4 I & =I+a^2 m[/tex]

⇒[tex]4 I-I & =a^2 m \\[/tex]

⇒[tex]3 I & =a^2 M . \\[/tex]

⇒[tex]I \quad & =\frac{a^2 M}{3}[/tex]

Therefore, the moment of inertia is [tex]I & =\frac{a^2 M}{3}[/tex].

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Ans:-

[tex] \: [/tex]

[tex] \: [/tex]

Int b nd c can be divide by 12

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The Sum In The Form a( b + c ):-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

The correlation coefficient may assume any value between -1 and 1. Correct answer: letter D.

This means that the coefficient may be negative, zero, or positive, with a value of -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

The correlation coefficient is a numerical measure of the degree of linear dependence between two variables. It is a statistic that measures the strength of the relationship between two variables. A correlation coefficient of 1 indicates a perfect positive correlation, a coefficient of -1 indicates a perfect negative correlation, and a coefficient of 0 indicates no correlation between the two variables.

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As of December 21, the account's opening balance will be $ 4,000.66.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Given that, on December 18 of a leap year. Stacy opened a savings account by depositing $6000.

The account pays 1.45% interest, compounded daily.

To find the missing amounts in the table and determine what is her opening balance on December 21, the following calculations must be performed:

The interest rate must be divided by the number of days in the year.

0.0145 / 366 = 0.00003961748

December 18:

Opening balance = 0

Deposit = 6,000

Withdrawal = 0

Principal used to compute interest = 6,000

Day's interest rounded to the nearest cent = 0.24 ((6,000 x 0.00003961748) - 6,000)

Ending balance = $6000.24

On December 19 she deposited $500, and on December 20 she withdrew $2500.

December 19:

Opening balance = 6000.24

Deposit = 500

Withdrawal = 0

Principal used to compute interest = 6,500.24

Day's interest rounded to the nearest cent = 0.26 ((6,500.24 x 0.00003961748) - 6,500.24)

Ending balance = 6500.50

December 20:

Opening balance = 6500.50

Deposit = 0

Withdrawal = 2500

Principal used to compute interest = 4,000.50

Day's interest rounded to the nearest cent = 0.16 ((4,000.50 x 0.00003961748) - 4,000.50)

Ending balance = 4000.66

Therefore, as of December 21, the account's opening balance will be $ 4,000.66.

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The only table that shows a proportional relationship is; Table C

Proportional relationships are defined as relationships between two variables where their ratios are equivalent to each other.

Option A: The ratios of each value of x and its' corresponding y-value are;

1.5/1, 3/2, 6/3, 9/6

This does not show a proportional relationship because they are not all equal.

Option B:  The ratios of each value of x and its' corresponding y-value are;

1.5/3, 2.5/5, 3/7, 4.5/8

This does not show a proportional relationship because they are not all equal.

Option C:  The ratios of each value of x and its' corresponding y-value are;

50/1, 150/3, 200/4, 250/5

This shows a proportional relationship because they are all equal.

Option D:  The ratios of each value of x and its' corresponding y-value are;

6/2, 12/4, 18/5, 21/6

This does not show a proportional relationship because they are not all equal.

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2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and  range of the function is all positive real numbers

A relation is a function if it has only One y-value for each x-value.

The given function is:

f(x) = 2(3)ˣ

To find the initial amount, we need to find f(0):

f(0) = 2(3)⁰ = 2(1) = 2

So the initial amount is 2.

To find the growth rate, we can use the formula:

growth rate = (f(x) - f(0)) / f(0) × 100%

= (2(3)ˣ - 2) / 2 × 100%

= (3ˣ - 1) × 100%

So the growth rate is (3ˣ - 1)×100%.

The domain of the function is all real numbers because the function is defined for all values of x.

The range of the function is all positive real numbers because the function is always positive for any value of x.

Specifically, the range of the function is (0, infinity).

Hence, 2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and  range of the function is all positive real numbers

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The number of apples for the lot will be 21.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 3 to 2. Tia wants to sell a total of 35 apples and oranges.

a /o = 3 / 2

a + o = 35

( 3 / 2)o + o = 35

5o = 70

o = 14

a + o = 35

a + 14 = 35

a = 21

Hence, the number of apples for the lot will be 21.

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Answer: 93 [tex]\frac{1}{3}[/tex] yards³

Step-by-step explanation:

      We will find the volume in feet with this formula:

                               V = LWH

V = LWH

V = (140)(4)(0.5)

V = 280 feet³

      There are 3 feet in a yard, and the question asks for yards, so we will divide:

280 feet³ / 3 = 93 [tex]\frac{1}{3}[/tex] yards³

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P(X + Y < 4) = 0.53 rounded to the first decimal place.

To find the probability P(X + Y < 4),

we need to find the values of x1 and x2 that satisfy the condition

X + Y < 4, and then sum up the corresponding probabilities in the table.

We can start by plotting the points (x1, x2) on a graph and finding the region where X + Y < 4.

This region can be determined by shading in the portion of the graph that is below the line X + Y = 4.

Next, we need to find the values of x1 and x2 in the table that fall within this region and sum up their probabilities.

This gives us P(X + Y < 4) = 0.20 + 0.14 + 0.11 + 0.08 = 0.53.

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The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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The center of mass coordinates of the given plane is -

COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex],  [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}

The center of mass is the point at which the whole mass of the body or system can be considered to be concentrated.

Given is the plane with the equation -

ρ(x, y) = (1 + x/2)

We can write the center of mass as -

X{C.M.} = [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex]

Y{C.M.} = [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]

Therefore, the center of mass coordinates of the given plane is -

COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex],  [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}

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The area of the rectangle will be equal to 11 square units.

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

A matrix is a structured table with columns and rows for arranging numbers, expressions, and even symbols. If the two matrices have equal row and column sizes, they can be added to, subtracted from, and multiplied element by element.

The area of the rectangle is calculated by finding the determinant of the matrix as below,

[tex]A = \left[\begin{array}{cc}3&-1&\\5&2&\\\end{array}\right][/tex]

A = ( 6 - ( -5 )

A = 6 + 5

Area = 11 square units

Hence, the value of the area of the rectangle is 11 square units.

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Considering the given data, we can calculate our answers of standard deviation as:

a) The range of times that covers the middle 68% of this distribution is 6.44 <= x <= 7.92

b) 97.9% of these men run a mile in more than 8.57 minutes.

(a) Using the 68-95-99.7 rule, we know that 68% of the data falls within 1 standard deviation of the mean. Hence, the middle 68% of times falls between the mean minus 1 standard deviation and the mean plus 1 standard deviation:

7.18 - 0.74 <= x <= 7.18 + 0.74

=> 6.44 <= x <= 7.92

(b) To find the percent of men who run a mile in more than 8.57 minutes, we need to find the area under the curve to the right of 8.57 minutes. This can be found by subtracting the area under the curve to the left of 8.57 from 100%. Using the standard normal distribution tables or a calculator, the standard score (z-score) for 8.57 can be found:

z = (8.57 - 7.18) / 0.74 = 2.10

Using standard normal distribution tables or a calculator, the area under the curve to the right of 2.10 can be found to be approximately 2.1%, so

100% - 2.1% = 97.9%

of these men run a mile in less than 8.57 minutes.

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Basically, there are two different types of geometric shapes such as: Two – Dimensional Shapes.

Define area of geometrical shape?

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Basically, there are two different types of geometric shapes such as: Two – Dimensional Shapes. Total area under graph = 15 + 12.56 + 3 + 20 = 50.56 sq. units

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

The area of shape is the space enclosed within the perimeter or the boundary of a given shape. We can calculate the area of shape for different geometrical shapes using specific mathematical formulae.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.

The area under the graph will be -

area of rectangle = length × breadth

= 5 × 3 = 15 sq. unit

area of circle = πr²

= 3.14 × 2 × 2

= 12.56 sq units

area of triangle = 1/2 × base × height

= 1/2 × 3 ×2

= 3 sq. units

area of trapezium = a + b / 2 . h

= 5 + 3 / 2 . 5

= 20 sq. units

area of triangle = 1/2 × 2 × 5 = 5 sq. units

Total area under graph = 15 + 12.56 + 3 + 20 = 50.56 sq. units

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Answer:

yes

Step-by-step explanation:

that is 3×3×3×3×3×3....×3 21 times and the other is 50 times,so u have to multiply 3²¹ with more 3s so u ger 3⁵⁰

Answer:

b = 8 cm

Step-by-step explanation:

Area: 1/2*base*height

1/2*base*3=12

3*base=24

base=24/3

base=8 cm

Radius of Circle B = 6 cm + 3 cm = 9 cm

Radius of Circle C = 9 cm + 3 cm = 12 cm

Radius of Circle D = 12 cm - 2 cm = 10 cm

What is a circle's straightforward definition?

Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed.

The area of a circle is given by the formula: A = πr^2, where A is the area and r is the radius.

The area of Circle A is A = π(6 cm)^2 = 36π cm^2

The area of Circle B is A = π(9 cm)^2 = 81π cm^2

The area of Circle C is A = π(12 cm)^2 = 144π cm^2

The area of Circle D is A = π(10 cm)^2 = 100π cm^2

To find how many times greater than the area of Circle A is the area of Circle D, we can divide the area of Circle D by the area of Circle A:

100π cm^2 / 36π cm^2 = 2.78

The area of Circle D is 2.78 times greater than the area of Circle A.

Note: since π is a constant, we can ignore it for the purposes of comparing the areas of the circles. It will always be the same value and it will cancel out when dividing.

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1) Where ΔTRA ≅ ΔVAR the conjecture is that [tex]\overline{VA}[/tex] ≅ [tex]\overline{TA}[/tex] and that [tex]\overline{TR}[/tex] =[tex]\overline{AV}[/tex]

2) Where ΔABC ≅ DEC the conjecture is that ΔACE ≅ Δ BCD

3) Where Δ REH ≅ ΔAEC and ΔREH and ΔAEC are isosceles triangles, the conjecture is that [tex]\overline{RE}[/tex] ≅ [tex]\overline{EH}[/tex] and [tex]\overline{AE}[/tex] ≅ [tex]\overline{EC}[/tex]

In mathematics, a conjecture is a speculative conclusion or assertion that is stated without evidence.

Some conjectures, such as the Riemann hypothesis (which is still a conjecture) or Fermat's Last Theorem (which was a conjecture until it was proved in 1995 by Andrew Wiles), have affected much of mathematical history as new fields of mathematics have been formed to prove them.

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The answer indicates that the lines at x = 9 & x = -5 both vertical and have no slope. They can't be parallel as a result.

Parallel in mathematics refers to two bars that never cross one another; picture an equal sign. Comparatively, the word "parallel" denotes similarity or simultaneous occurrence. Three close friends' similar lives might be shown in a tale.

Equal slope lines are parallel. The lines x = 9 & x = -5, on the other hand, are vertical and have no slope. They can't be parallel as a result. In actuality, vertical lines are never parallel to one another; rather, they always form a 90-degree angle (perpendicular).

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Answer: 19.3

Step-by-step explanation: To solve this we can find numbers whose squares are close to 372. We know 20x20 = 400 and 19x19 = 361 so it has to be between these two.372 is closer to 361 meaning the square root of it is less than 19.5. Now we can just test numbers. 19.4x19.4 = 376ish and 19.3x19.3 is 372.49. This number is close enough so 19.3 is our answer.

[tex]e^y-e^{-y}=x\implies e^y-\cfrac{1}{e^y}=x\implies \cfrac{(e^y)^2-1}{e^y}=x \\\\\\ e^{2y}-1=xe^y \implies e^{2y}-xe^y=1[/tex]

now, we're going to do some "completing the square" on the left-side, that is, we'll make it a perfect square trinomial by using our very good friend Mr Zero, 0.

[tex]2\cdot n\cdot e^y=xe^y\implies n=\cfrac{xe^y}{2e^y}\implies n=\cfrac{x}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]e^{2y}-xe^y=1\implies e^{2y}-xe^y + n^2 - n^2=1\implies e^{2y}-xe^y+n^2=1+n^2 \\\\\\ (e^y)^2-xe^y+\left( \cfrac{x}{2} \right)^2=1+\cfrac{x^2}{4}\implies \left( e^y -\cfrac{x}{2} \right)^2=1+\cfrac{x^2}{4} \\\\\\ e^y -\cfrac{x}{2}=\sqrt{1+\cfrac{x^2}{4}}\implies e^y =\sqrt{1+\cfrac{x^2}{4}}+\cfrac{x}{2} \\\\\\ \ln(e^y)= \ln\left(\cfrac{x}{2}+ \sqrt{1+\cfrac{x^2}{4}} \right)\implies {\Large \begin{array}{llll} y=\ln\left(\cfrac{x}{2}+ \sqrt{1+\cfrac{x^2}{4}} \right) \end{array}}[/tex]

Answer: 70

Step-by-step explanation: To find this answer, we must use PEMDAS. So, we have parentheses (adding) and multiplying. The P is first, so we solve for parentheses first. So, 2 + 5 = 7. So, now we multiply. 10 * 7 = 70. Therefore 70 is our answer. I hope this helped!

Answer:

[tex]f(x) = {x}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {(a + 5)}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {a}^{2} + 25 + 10a + 7 \\ \dashrightarrow \: \: \boxed{ f(a + 5) = {a}^{2} + 10a + 32}[/tex]

hope helpful! :)

If an algebraic expression (x²)³ × x⁴ / x² [tex]x^{(2^3)}[/tex], then the simplified expression is [tex]x^{(2^3)}[/tex] using the exponent laws.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Consider the expression, as follows:

(x²)³ × x⁴ / x²

Use the exponent law "[tex]a^m \times a^n = a^(m+n)[/tex]" to simplify the first term:

(x²)³ × x⁴ = x⁽²ˣ⁶ ⁺⁴⁾ = x¹⁰

Use the exponent law "[tex]a^m / a^n = a^{(m-n)}[/tex]" to simplify the second term:

x¹⁰ / x² = x⁽¹⁰⁻²⁾ = x⁸

Use the exponent law "[tex](a^m)^n = a^(mn)[/tex]" to simplify the first term:

[tex]x^8 = x^{(24)} = x^{(2^3)}[/tex]

Simplified expression: [tex]x^{(2^3)[/tex]

Note: The laws used in this example are:

[tex]a^m \times a^n = a^(m+n)\\a^m / a^n = a^{(m-n)}\\(a^m)^n = a^{(m\timesn)}[/tex]

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Answer:

x = 40/3

Step-by-step explanation:

x+5/3=15

x + 5/3 = 45/3

x = 40/3

Let's check

40/3 + 5/3 = 15

45/3 = 15

15 = 15

SO, x = 40/3 is the correct answer.

The probability that the proportion of a sample is higher than 0.30 can be estimated using the Central Limit Theorem (CLT) which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a large sample size (n >= 30), we can use the normal distribution to approximate the distribution of the sample means.

Assuming the sample size is large, the standard error (SE) of the sample mean is given by

SE = sqrt(p * (1 - p) / n), where p is the population proportion (0.27) and n is the sample size.

With this information, we can find the Z-score corresponding to 0.30 using the formula: Z = (0.30 - 0.27) / SE

Since we don't know the sample size, we'll assume a conservative sample size of 30.

With a sample size of 30, the SE is approximately 0.039, and the Z-score is approximately 0.77.

Using a standard normal table, we can find the probability of a Z-score being greater than 0.77 is approximately 0.22.

Therefore, the approximate probability that the proportion who exercise at least five days per week is higher than 0.30 is 0.22.

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Answer:

Yes

Step-by-step explanation:

Yes, they do since if you multiply the y by 2.5 it will give you all the answers you entered

The total value of the account after 18 years, deposit of $100,000 with monthly compounding and a rate of 5%, is given as follows:

$245,501.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]P = 100000, r = 0.05, n = 12, t = 18[/tex]

Hence the balance is given as follows:

A(18) = 100000 x (1 + 0.05/12)^(12 x 18)

A(18) = $245,501.

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