The product of a number and 2 is 1. Find eight times the number.

Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

Answer:

x < -7/6

Step-by-step explanation:

In a equation that show a greater than or less than sign can be a equal sign .

Answer: your so bad

Step-by-step explanation:

hahahaahahahahahhahahahahahahaha

Answer:

A. Yes

B. yes

C. Yes

D. No

E. Yes

Step-by-step explanation:

Good luck!

Answer D

Step-by-step explanation:

Answer: 13. -68

14. 36

15. -36

16. -3

17. 10

18. -4

19. 1310 ft

20. 330 ft

Step-by-step explanation:

13. 34*(-2)=-68

14. -9*(-4)=

-(9*(-4))=

-(-36)=36

15. 12*(-3)=-36

16. -12/4=-3

17. -20/(-2)=

20/2=10

18. 200/(-50)=-4

19. -1640*(-1)-(-330*(-1))=

1640-(-330*(-1))=

1640-330=1310 ft

20. -990*(-1)-(-660*(-1))=

990-(-660*(-1))=

990-660=330 ft

Answer:

m= -1/2

Step-by-step explanation:

Answer:

72 outfits possible,

1/72 chance of selecting a particular outfit

Step-by-step explanation:

For each of the 3 sweaters, there are 4 shirts to choose from, and for each of those 4 shirts, there are 6 pants to choose from. Therefore, there are totally \(3\cdot 4\cdot 6=72\) outfits to choose from (order is fixed and therefore negligible). A specific outfit would represent 1 of these 72 outfits. Therefore, the probability of selecting a particular outfit is \(\boxed{\frac{1}{72}}\)

1. Using Radicals the number √17 has a value of 4.123.

2. √510 =260100.

3. √4x = 2√x.

Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).

When multiplying or dividing, it is standard practise for the final result to contain the same number of significant figures as the number with the fewest significant figures. The division of two numbers can be calculated using the following formula: Dividend Divisor = Quotient + Remainder. The number that is being divided in this case is known as the dividend.

The number that divides the number (dividend) into equal parts is known as the divisor.

1. \(\sqrt{17}\\\) = 4.123 (The values of the number √17 is 4.123.)

2.  √510

= 510^2

=(500+10)^2

=500^2+10^2+2×500×10

=250000+100+10000

=260100.

3. √4x = 2√x.

because 4 = 2*2

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The given function y = -1 + 3x^5/4 is a solution of the given differential equation \(3x^2 * 2y' + 3y = x - 1.\)

To verify that the function y = -1 + 3x^5/4 is a solution of the given differential equation, we need to substitute this function into the differential equation and check if it satisfies the equation.

The first step is to calculate the derivative of y with respect to x, denoted as y'. Taking the derivative of -1 with respect to x gives us 0, and taking the derivative of 3x^5/4 with respect to x gives us (15/4)x^1/4.

Substituting these values into the differential equation, we get:

\(3x^2 * 2(15/4)x^1/4 + 3(-1 + 3x^5/4) = x - 1\)

Simplifying the equation further, we have:

\(45/2 x^7/4 - 3 + 9/4 x^5/4 = x - 1\)

Combining like terms, we get:

\(45/2 x^7/4 + 9/4 x^5/4 - 3 - x + 1 = 0\)

This equation holds true for all x, indicating that the given function y = -1 + 3x^5/4 is indeed a solution to the given differential equation.

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Answer:

220y^3

Step-by-step explanation:

Find the volume as if it was a rectangular prism - 8*8*5 = 320y^3

Find the Volume of the Missing section - 5*4*5 = 100

Subtract the missing section from the first number - 320-100=220y^3

Answer:

The partial products are:

18 + 1.2 + 0.42

The sum: 19.62

Step-by-step explanation:

This has to do with understanding what place value is.

3 ones = 3 * 1 = 3

6 * 3 ones = 18

2 tenths = \( 2 * \frac{1}{10} = 2*0.1 = 0.2 \)

6 * 2 tenths = 1.2

7 hundredths = \( 7 * \frac{1}{100} = 7*0.01 = 0.07 \)

6 * 7 hundredths = 0.42

The partial products are:

18 + 1.2 + 0.42

The sum = 19.62

Answer:

Answer:

The partial products are:

18 + 1.2 + 0.42

The sum: 19.62

Step-by-step explanation:

This has to do with understanding what place value is.

3 ones = 3 * 1 = 3

6 * 3 ones = 18

Step-by-step explanation:

In shape (i), there are two electron domains around the central atom. This means that the electron-domain geometry is linear. However, there are two bonding pairs and no lone pairs of electrons around the central atom, resulting in the molecular geometry also being linear.

The concept of electron-domain geometry and molecular geometry is essential in understanding the properties of molecules. The electron-domain geometry is determined by the number of electron domains (bonding or lone pairs) around the central atom in a molecule. On the other hand, the molecular geometry is determined by the arrangement of atoms in the molecule, taking into account the presence of lone pairs.

Knowing the electron-domain geometry and molecular geometry of a molecule is crucial in predicting its polarity and reactivity. For instance, polar molecules have an asymmetric distribution of electron density, while nonpolar molecules have a symmetric distribution. This difference in polarity affects the physical and chemical properties of a molecule, such as boiling point, melting point, and solubility.

In summary, in shape (i), both the electron-domain geometry and molecular geometry are linear, which means that the central atom has two bonding pairs and no lone pairs. Understanding the electron-domain and molecular geometry of molecules is essential in predicting their properties and behavior.

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If a matrix A is 5 x 3 and the product AB is 5x7, the size of B is 3x7.

The product of two matrices A and B, denoted as AB, is possible only if the number of columns of A is equal to the number of rows of B. In this case, A is 5x3, which means it has 3 columns.

And since the product AB is 5x7, it means the resulting matrix has 7 columns. Therefore, the number of columns of B must be equal to 7. And since A has 3 columns, the number of rows of B must be equal to 3 for the product to be possible.

Thus, the size of B is 3x7.

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The width of the two paths is 5 m.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.

Let the width of the two paths be x.

Thus, the total area covered by the paths is = (30×x) + (40×x) - x²

The total area covered by the paths is 325 m².

Equate both of them.

⇒ (30×x) + (40×x) - x² = 325

⇒ 30x + 40x  - x² = 325

⇒ x² -70x + 325 = 0

Solving the above equation, we get

x = 65 or x = 5

The valid solution is x = 5.

Thus, the width of the two paths is 5 m.

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Tenemos precio de lista de $25 para el libro.

Si aplicamos un descuento del 25%, este descuento representa:

Ahorramos $6.25.

El precio que pagamos el libro es $18.75.

The eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scalar multiple of itself. In other words, if A is a square matrix and v is an eigenvector of A, then Av = λv, where λ is the eigenvalue associated with v.

Given the eigenvalues and eigenvectors for matrix A as λ1 = 2, v1 = [-5 1]ᵀ and λ2 = 6, v2 = [5 4]ᵀ, we can say that:

- Av1 = λ1v1 = 2[-5 1]ᵀ = [-10 2]ᵀ
- Av2 = λ2v2 = 6[5 4]ᵀ = [30 24]ᵀ

Therefore, the eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

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Answer:

area of circle F = 9 pi

Step-by-step explanation:

An interesting problem, combining geometry and algebra.

It has not been indicated, but it will be assumed that GH is a tangent to the circle F, hence the tangent-secant theorem from point H applies.

Produce HF to point E on the circumference such that EJ forms a diameter of circle F.

By the tangent-secant theorem,

HG^2 = HJ*HE

Substitute given values,

(x+2)^2 = 2*(2*(2x-1)+2)

Expand algebraically

x^2+4x+4 = 2(4x-2+2)

x^2+4x+4 = 8x

x^2-4x+4 = 0

Factor

(x-2)^2 = 0

=>

x=2

Substitute x=2 into radius FG = 2(x)-1 = 3

Therefore area of circle F

= pi r^2

= pi (3)^2

= 9 pi

Answer:

\(y = \tan(x + \frac{x^2}{2})\)

Step-by-step explanation:

Poorly formatted question; The complete question requires that we prove that \(y=\tan(x+\frac{x\²}{2})\)

When

\(\frac{dy}{dx} =1+xy\²+x+y\²\) and \(y(0)=0\)  

We have:

\(\frac{dy}{dx} =1+xy\²+x+y\²\)

Rewrite as:

\(\frac{dy}{dx} =1+x+xy\²+y\²\)

Factorize

\(\frac{dy}{dx} = (1+x)+y\²(x+1)\)

Rewrite as:

\(\frac{dy}{dx} = (1+x)+y\²(1+x)\)

Factor out 1 + x

\(\frac{dy}{dx} = (1+y\²)(1+x)\)

Multiply both sides by \(\frac{dx}{1 + y^2}\)

\(\frac{dy}{1+y\²} = (1+x)dx\)

Integrate both sides

\(\int \frac{dy}{1+y\²} = \int (1+x)dx\)

Rewrite as:

\(\int \frac{1}{1+y\²} dy = \int (1+x)dx\)

Integrate the left-hand side

\(\int \frac{1}{1+y\²} dy = \tan^{-1}y\)

Integrate the right-hand side

\(\tan^{-1}y = x + \frac{x^2}{2} + c\)

\(y(0)=0\) implies that: \((x,y) = (0,0)\)

So:

\(\tan^{-1}y = x + \frac{x^2}{2} + c\) becomes

\(\tan^{-1}(0) = 0 + \frac{0^2}{2} + c\)

This gives:

\(0 = 0 +0 + c\)

\(0 =c\)

\(c = 0\)

The equation \(\tan^{-1}y = x + \frac{x^2}{2} + c\) becomes

\(\tan^{-1}y = x + \frac{x^2}{2} + 0\)

\(\tan^{-1}y = x + \frac{x^2}{2}\)

Take tan of both sides

\(y = \tan(x + \frac{x^2}{2})\) --- Proved

i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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Answer:

(1/3) Pi r^2 h

Step-by-step explanation:

The volume of a cone (or pyramid, for that matter) is 1/3 the area of the base times the height.

Cones have bases that are circles, so their areas are Pi r^2, usually written \(\pi r^2\), Pi times the radius squared.

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

Answer:

draw a line where y is equal to 5 and shade in the graph below to represent the greater than

Step-by-step explanation:

The confidence interval about the given mean age is (40.7, 34.3). Since the given mean age of 38.8 years is in the obtained interval, there is no sufficient evidence to conclude that the mean age had changed.

The formula for the confidence interval is

C.I = \(\bar x\) ± z(σ/√n)

Where \(\bar x\) - sample mean; z or z(α/2) - test value; σ - standard deviation of the sample; n - sample size;

Consider the hypothesis,

null hypothesis H0: μ = 38.8

alternate hypothesis Ha: μ ≠ 38.8

It is given that,

sample size n = 32

sample mean \(\bar x\) = 37.5

standard deviation σ = 9.2

Constructing a 95% confidence interval about the mean age:

a) Finding the significance level:

= 1 - (95/100)

= 1 - 0.95

∴ α = 0.05

b) Finding the z-value for the obtained significance level:

z(α/2) = z(0.05/2)

∴ z = 1.96 (From the distribution table)

c) Calculating the lower and upper bounds:

C.I = \(\bar x\)  ± z(σ/√n)

On substituting,

C.I = 37.5 ± (1.96)(9.2/√32)

⇒ 37.5 ± (1.96)(1.626)

⇒ 37.5 ± 3.186(≅3.2)

Upper bound = 37.5 + 3.2 = 40.7

Lower bound = 37.5 - 3.2 = 34.3

Thus, the interval is from 34.3 years to 40.7 years.

Hence the given mean age of 38.8 is included in the interval, the evidence is insufficient to conclude that there is a change in the mean age.

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Answer:

68 ft

I've attached the Trignometric ratio theory as well

hope you understood :)

\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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Chelsea made a mistake in simplifying the equation 3(x-3). To find the solution to 4x-5=2(3(x-3)), we first simplify the expression inside the parentheses.

Now, to isolate the variable x, we need to move the terms with x to one side of the equation. Let's subtract 4x from both sides, which gives us -5-4x=6x-18-4x. Simplifying this, we get -5-4x=2x-18.

Next, let's move the constant terms to the other side. Adding 18 to both sides, we get -5-4x+18=2x-18+18. Simplifying this, we get -4x+13=2x.

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Chelsea made a mistake when subtracting the variable term from both sides. By identifying this error and correctly following the steps, we find that the solution to the equation 4x - 5 = 2 3(x - 3) is x = -7.

Chelsea made a mistake in her work when finding the solution to the equation 4x - 5 = 2 3(x - 3). To determine where she went wrong, let's analyze her steps.

Step 1: Distribute 3 to (x - 3): 4x - 5 = 2 3x - 6.
Step 2: Combine like terms: 4x - 5 = 6x - 12.
Step 3: Move the variables to one side and the constants to the other side. Chelsea may have mistakenly subtracted 4x from both sides instead of 6x. This would result in: -5 = 2x - 12.
Step 4: Solve for x. Chelsea may have then incorrectly added 12 to both sides instead of adding 5, leading to: 7 = 2x.
Step 5: Divide both sides by 2: x = 7/2.

Upon reviewing her work, Chelsea should have subtracted 6x from both sides in Step 3, not 4x. This would have resulted in the equation 2x - 5 = -12. Correctly following the steps would lead to the correct solution: x = -7.

Therefore, Chelsea made a mistake when subtracting the variable term from both sides. By identifying this error and correctly following the steps, we find that the solution to the equation 4x - 5 = 2 3(x - 3) is x = -7.

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Answer:

  CD = 3 -√3

Step-by-step explanation:

The ratio of leg lengths in a 30°-60°-90° triangle is ...

  1 : √3 : 2

The longest leg of ΔABD is 2√3, so we must multiply all of these ratio values by √3 to see the actual lengths of the triangle sides.

  AB : BD : AD = 1 : √3 : 2 = √3 : 3 : 2√3

That is ...

  AB = √3

  BD = 3

__

The lengths of the legs in isosceles right triangle ABC are the same, so ...

  BC = AB = √3

Then the length of interest is ...

  CD = BD -BC

  CD = 3 -√3 . . . . . . . a=3, b=-1