Rewrite the following statement using a number in scientific notation. The diameter of a certain atom is about \( 0.54 \) nanometers. (Recall that nano- means "billionth.")

The measures of the angles in the triangle are A = 6.17°,B = 11.50°, C = 162.33° and that's the solution to the triangle using the Law of Sines.

To solve the triangle using the Law of Sines, we can use the following formula:

(a/sin A) = (b/sin B) = (c/sin C)

First, let's convert the given angle B from degrees and minutes to decimal form:

B = 11° 30' = 11.5°

Next, we can plug in the given values into the formula and solve for the unknowns:

(3.7/sin A) = (6.5/sin 11.5°)

Cross-multiplying and rearranging gives us:

sin A = (3.7 * sin 11.5°) / 6.5

Using a calculator, we can find the value of sin A:

sin A = 0.1076

Now, we can use the inverse sine function to find the measure of angle A:

A = sin^-1(0.1076) = 6.17°

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C:

C = 180° - A - B = 180° - 6.17° - 11.5° = 162.33°

So, the measures of the angles in the triangle are:

A = 6.17°
B = 11.5°
C = 162.33°

Round your answers to two decimal places, we have:

A = 6.17°
B = 11.50°
C = 162.33°

And that's the solution to the triangle using the Law of Sines.

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Answer:

To simplify this expression, we first need to evaluate the expression inside the parentheses:

10 - 9 + 6 = 7

Now we can substitute this value back into the original expression:

10 + 28 ÷ 7 (7) = 10 + 4(7) (since 28 ÷ 7 = 4)

= 10 + 28

= 38

Therefore, 10 + 28 divided by 7 (10-9+6) equals 38.

Answer: 9/4

Step-by-step explanation:

Answer:

15/4 feet

Step-by-step explanation:

When given a mixed number like [tex]3\frac{3}{4}[/tex], you multiply the denominator by the whole number and add the numerator.

In this case, multiply 3 x 4 and then add 3. After finding that value, put it over the original denominator, giving 15/4

Answer:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

not intersect.

To determine if two lines intersect in R3, we need to solve for both parameters (t and s) in the two equations and then check if the values are equal.

For Line 1: x = 2 - t, y = -3 + 5t, z = t. We can solve for t by setting all three equations equal to each other, giving t = x - 2 = y + 3 = z.

For Line 2: P = (4,-1,16) + s (1,4,-7). We can solve for s by setting the three equations equal to each other, giving s = (x - 4) / 1 = (y + 1) / 4 = (z - 16) / -7.

If the two values of t and s are equal, then the lines intersect at the point (x, y, z). If they are not equal, then the lines do not intersect.

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The probability of at most one price hike in one year is 0 + 0 = 0.

No price hikes in a randomly selected one and a half year:

The probability of no price hikes in one year is 0, since the average is 4. Therefore, the probability of no price hikes in one and a half years is also 0.

Four price hikes in 2 years:

The average number of price hikes in one year is 4, so the average number of price hikes in 2 years is 8. The probability of exactly 4 price hikes in 2 years is therefore 0, since it is less than the average.

At most one price hike in one year:

The probability of at most one price hike in one year is the sum of the probabilities of 0 and 1 price hikes. The probability of 0 price hikes is 0, as mentioned before. The probability of 1 price hike is also 0, since it is less than the average of 4. Therefore, the probability of at most one price hike in one year is 0 + 0 = 0.

Overall, the probability of no price hikes in a randomly selected one and a half year, four price hikes in 2 years, and at most one price hike in one year are all 0, since they are all less than the average number of price hikes.

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The width of the walkway is approximately 0.343 feet or about 4.12 inches.

Let's suppose that the pathway is x feet wide.

The total length of the garden with the walkway is 8 + 2x feet (since there is a walkway on both sides of the garden), and the total width of the garden with the walkway is 12 + 2x feet.

The area covered by the garden and the walkway is the product of the length and width, which is:

[tex](8 + 2x) \times (12 + 2x) = 192[/tex]

Expanding this equation, we get:

[tex]96 + 32x + 16x + 4x^2 = 192\\4x^2 + 48x - 96 = 0[/tex]

Dividing both sides by 4, we get:

[tex]x^2 + 12x - 24 = 0[/tex]

Using the quadratic formula, we get:

x = (-12 ± [tex]\sqrt{ (12^2 - 41(-24))) / (2\times1}[/tex])

x = (-12 ±[tex]\sqrt{(288)) / 2}[/tex])

x = (-12 ± [tex]12\sqrt{(2)) / 2}[/tex]

x = -6 ± [tex]6\sqrt{(2)}[/tex]

Since the width of the walkway cannot be negative, we take the positive value of x:

[tex]x = -6 + 6\sqrt{(2)} \\x= 0.343 feet[/tex]

Therefore, the width of the walkway is approximately 0.343 feet or about 4.12 inches.

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Answer: 8 times per minute

Step-by-step explanation: 50 (1-84%) = 8

0 and variance 1.

For (a), L follows a Chi-squared distribution with 6 degrees of freedom. This is because L is a sum of squares of 6 random variables (the 5 Yi - Y plus Y^3).

For (b), J follows a Student's t-distribution with 6 degrees of freedom. This is because it is the ratio of two independent normally distributed random variables with mean 0 and variance 1.

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The answers are explained in the solution below.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given are some operation based on multiplication,

1) 26 x 3/4 = 78/4

2) 9 x 7/10 = 63/10

3) 2/5 x 32 = 64/5

4) 1/8 x 400 = 400/8 = 50

5) 15 x 4/5 = 60/5 = 12

6) 3/11 x 66 = 198/66 = 18

7) 45 x 3/8 = 135/8

8) 3/10 x 12 = 36/10 = 18/5

9) 55 x 2/5 = 110/5 = 22

10) 5/6 x 40 = 200/6 = 100/3

11) 7/9 x 54 = 378/54 = 7

12) 600 x 5/12 = 3000/12

= 250

13) 2/3 x 21 = 42/3 = 14

14) 500 x 3/5 = 1500/5 = 300

15) 72 x 5/8 = 360/8 = 45

16) 2/9 x 35 = 70/9

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Answer:

6

Step-by-step explanation:

24h/6g= 4 hours per gaurd

Answer:

tgv7cutc

Step-by-step explanation:

txr. thh5d tdhg6643gchctc

The equation 3(5)+3(4), which also simplifies to 27, is the same as Karen's expression.

A collection of letters and/or numbers that denotes a mathematical quantity or connection is known as an expression in mathematics. It can be evaluated or simplified using mathematical principles and may contain variables, constants, and operators (such as +, -, x,, etc.). Numerical values, relationships between values, and mathematical processes can all be represented using expressions. For instance, the expression "3x + 5" illustrates the connection between the numbers 3 and 5 and the variable x, and it can be assessed for various values of x to yield various numerical outcomes.

given

Karen's formula is 3(5+4), which can be written as 3(9) = 27.

The equation 3(5)+3(4), which also simplifies to 27, is the same as Karen's expression.

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Loni needs to do 4,450 sessions in the first year to break even.

What is total revenue?

Total revenue is the total amount of money earned by a business from the sale of its products or services during a particular period of time.

To break even, the total revenue Loni makes should be equal to the total cost of running the nail salon. Let's calculate the total cost first:

Total Cost = Rent + Other expenses + Start-up cost + Cost of supplies per session x Number of sessions

Total Cost = $24,000 + $50,000 + $15,000 + $10 x Number of sessions

Total Cost = $89,000 + $10 x Number of sessions

Now, to break even, the total revenue should be equal to the total cost:

Total Revenue = Total Cost

$30 x Number of sessions = $89,000 + $10 x Number of sessions

$20 x Number of sessions = $89,000

Number of sessions = $89,000 / $20

Number of sessions = 4,450

Therefore, Loni needs to do 4,450 sessions in the first year to break even.

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Answer: 11.1 ft

Step-by-step explanation:

([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).

To fix \(G\) as a group and set \([g,h]:=g h g^{-1} h^{-1}\), and then set
\[[G,G] := \left\{\left[g_{1}, h_{1}\right] \cdots\left[g_{s}, h_{s}\right]: g_{1}, \ldots, g_{s}, h_{1}, \ldots, h_{s} \in G\right\}\), we can start by noticing that this is a subset of the Cartesian product of \(G\) with itself, and since \(G\) is a group, this subset must also be a group. Therefore, \([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).

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Yes, Laura will have enough money to buy the computer before her brother's birthday.

Cost is the total amount of money, time, and resources required to produce or acquire a product, service, or outcome. It involves the initial outlay of money, time, and resources necessary to produce or acquire something. In addition, it involves any ongoing expenses required to maintain or improve that something. Cost can be a one-time purchase, a long-term investment, or a recurring expense.

At the time of her purchase, Laura had $427 which is $59 short of the $486 computer. She earns $42 each week from babysitting, so if she saves every penny she earns for the next 7 weeks she will have enough money to buy the computer. She will have $294 after the first week of saving, $336 after the second week, $378 after the third week, $420 after the fourth week, $462 after the fifth week, $504 after the sixth week, and $546 after the seventh week. The $546 is more than enough money to purchase the computer before her brother's birthday.

Additionally, the computer's price drops $14 each day, so if Laura waits an extra week to purchase the computer, it will cost her even less. She will have $588 after the eighth week and would only need to spend $400 to purchase the computer.

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Answer:

attached is the answer

Step-by-step explanation:

HI

THIS IS THE ANSWER

I HOPE IT HELPS

GOOD LUCK

∠T has a cosine ratio of 15/17.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

PQR and STU are the similar triangles.

With the help of cosine function we can find the measure of T.

Cosine = Adjacent side/ hypotenuse

The adjacent side is thirty and hypotenuse is thirty four.

Plug in these values in the above formula.

∠T=30/34

Divide numerator and denominator by 2

∠T=15/17

Hence, ∠T has a cosine ratio of 15/17.

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The cosine value of θ is approximately -0.7071.

We know that:

sin(θ) = √(3/2)

Using the trigonometric identity:

sin^2(θ) + cos^2(θ) = 1

We can find cos(θ) by first finding sin^2(θ) and then solving for cos(θ):

sin^2(θ) + cos^2(θ) = 1

cos^2(θ) = 1 - sin^2(θ)

cos(θ) = ± √(1 - sin^2(θ))

Since cos(θ) is negative, we can choose the negative square root:

cos(θ) = - √(1 - sin^2(θ))

Substituting sin(θ) = √(3/2), we get:

cos(θ) = - √(1 - 3/2)

cos(θ) = - √(1/2)

cos(θ) = - √2/2

Since cos(θ) is negative and given cos(θ) < 0, we have:

cos(θ) = - √2/2

Therefore, cos(θ) is approximately -0.7071.

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If Andy traveled 10 miles and paid a $12 tip to his drive. Sammy traveled 15 miles and paid a $9 tip to his driver. the cost per mile to ride the Uber is $0.60.

Let the cost per mile to ride the Uber be "x".

Then, Andy paid a total of 10x + 12 dollars for his 10-mile trip.

Similarly, Sammy paid a total of 15x + 9 dollars for his 15-mile trip.

Since both customers paid the same amount, we can set their total costs equal to each other and solve for "x":

10x + 12 = 15x + 9

Subtracting 10x and 9 from both sides:

3 = 5x

Dividing by 5:

x = 0.6

Therefore, the cost per mile to ride the Uber is $0.60.

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Answer: x intercepts = -5/2 or x = -13/2    

the y intercepts y = 16.5

vertex  ( -9/2 , -4)

Step-by-step explanation:

Answer:

The roots and x-coordinates of the equation are

[tex]-\frac{5}{2}[/tex] and [tex]-\frac{13}{2}[/tex]

The vertex of the parabola is

[tex]-4.5[/tex]

Step-by-step explanation:

Given

[tex]0=x^2+9x+16.25\\y=x^2+9x+16.25[/tex]

Complete the Square, X intercepts, and Roots

[tex]0=x^2+9x+16.25[/tex]

Write [tex]16.25[/tex] as a fraction.

[tex]x^2+9x+16\frac{1}{4}=0[/tex]

[tex]x^2+9x+\frac{65}{4}=0[/tex]

Factor the left hand side.

Write [tex]x^2[/tex] as a fraction with a common denominator, multiply by [tex]\frac{4}{4}[/tex].

[tex]x^2*\frac{4}{4} +9x+\frac{65}{4}=0[/tex]

Combine [tex]x^2[/tex] and [tex]\frac{4}{4}[/tex].

[tex]\frac{x^2*4}{4} +9x+\frac{65}{4}=0[/tex]

Combine the numerators over the common denominator.

[tex]\frac{4x^2+65}{4} +9x=0[/tex]

To write [tex]9x[/tex] as a fraction with a common denominator, multiply by [tex]\frac{4}{4}[/tex].

[tex]\frac{4x^2+65}{4} +9x*\frac{4}{4} =0[/tex]

Combine [tex]9x[/tex] and [tex]\frac{4}{4}[/tex].

[tex]\frac{4x^2+65}{4} +\frac{36x}{4} =0[/tex]

Combine the numerators over the common denominator.

[tex]\frac{36x+4x^2+65}{4} =0[/tex]

For a polynomial of the form [tex]ax^2+bx+c[/tex], rewrite the middle term as a sum of two terms whose product is [tex]a*c=4*65=260[/tex] and whose sum is [tex]b=36[/tex].

[tex]\frac{36(x)+4x^2+65}{4} =0[/tex]

Rewrite 36 as 10 plus 26.

[tex]\frac{(10+26)x+4x^2+65}{4} =0[/tex]

Apply the distributive property.

[tex]\frac{4x^2+10x+26x+65}{4} =0[/tex]

Group the first two terms and the last two terms.

[tex]\frac{\left(4x^2+10x\right)+26x+65}{4} =0[/tex]

Factor out the GCF from each group.

[tex]\frac{2x\left(2x+5\right)+13\left(2x+5\right)}{4} =0[/tex]

Factor the polynomial by factoring out the GCF.

[tex]\frac{\left(2x+5\right)+\left(2x+13\right)}{4} =0[/tex]

Set the numerator equal to zero.

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

[tex]2x=5=0\\2x=13=0[/tex]

Solving for [tex]x[/tex] in each equation gives us

[tex]-\frac{5}{2}[/tex] and [tex]-\frac{13}{2}[/tex]

The final solution is

[tex]x=-\frac{5}{2} ,-\frac{13}{2}[/tex]

These values of [tex]x[/tex] are the roots of the equation and lie on the x-axis.

Vertex

We can use the formula [tex]\frac{-b}{2a}[/tex] to evaluate the vertex.

This formula is for a polynomial of the form [tex]ax^2+bx+c=0[/tex].

[tex]x^2+9x+16.25=0[/tex]

In this case

[tex]a=1\\b=9[/tex]

Inserting our values into the equation yields

[tex]\frac{-9}{2*1}[/tex]

[tex]\frac{-9}{2}=-4.5[/tex]

The amount that you owe will reach $15,000 after approximately 21.5 years.

Here is a step-by-step explanation of how to calculate this:
1. First, determine the number of compounds per year (n). In this case, since we are using an effective rate, n = 1.
2. Next, use the compound interest formula to find the final amount (A): A = P(1 + r/n)^(nt)
3. Plug in the given values for P ($10,000), r (0.021), n (1), and A ($15,000) and solve for t:
$15,000 = $10,000(1 + 0.021/1)^(1*t)
4. Simplify the equation and isolate t on one side:
1.5 = (1.021)^t
5. Take the natural logarithm of both sides:
ln(1.5) = t*ln(1.021)
6. Solve for t:
t = ln(1.5)/ln(1.021)
7. Use a calculator to find the value of t:
t ≈ 21.5

Therefore, the amount that you owe will reach $15,000 after approximately 21.5 years, rounded to the nearest tenth (0.1).

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The probability of Heather getting exactly 12 out of 15 correct can be found using the binomial probability formula:

P(X = 12) = (15 choose 12) * (0.87)^12 * (0.13)^3
= (15! / (12! * 3!)) * (0.87)^12 * (0.13)^3
= 455 * 0.087 * 0.0022
= 0.0828

Therefore, the probability of Heather getting exactly 12 out of 15 correct is 0.0828, or 8.28%.

To round this answer to two decimal places, we can use the following formula:

0.0828 * 100 = 8.28%

So the final answer is 8.28%.

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The number lines for the given inequalities are drawn as shown in the figures below.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. On a number line, inequalities are represented by drawing a straight line and designating the endpoints with either an open or closed circle. An open circle indicates that the value is not included. A closed circle indicates that the value is included.

1) Number line A

 The closed circle at -2 means greater than or equal or less than or equal to -2.

Now the arrow is extending to the left.

So the inequality is numbers less than or equal to -2.

2) Number line B

 The open circle at -2 means greater than or less than  -2.

Now the arrow is extending to the left.

So the inequality is numbers less than  -2.

3) Number line C

  The closed circle at -2 means greater than or equal or less than or equal to -2.

Now the arrow is extending to the right.

So the inequality is all the numbers greater than or equal to -2.

4) Number line D

  The open circle at -2 means greater than or less than  -2.

Now the arrow is extending to the right.

So the inequality is all the numbers greater than  -2.

Therefore the number lines for the given inequalities are drawn as shown in the figures below.

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 The solution to the system of equations is (x, y) = (-5/3, -4/3).

What is system of linear equations?

A system of linear equations is a set of two or more equations with two or more variables that are to be solved simultaneously. Each equation in the system is linear, meaning it can be written in the form of ax + by + cz + ... = d, where a, b, c, and d are constants and x, y, z, and other variables are unknowns.

The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system. The solution of a system of linear equations is a set of values for the variables that make all of the equations true.

There are different methods to solve systems of linear equations, such as substitution method, elimination method, and matrix method. These methods involve manipulating the equations in the system to isolate one variable, substitute its value into another equation, and eventually find the values of all the variables.

Systems of linear equations are used in many areas of mathematics, science, engineering, and economics to model real-world situations and solve practical problems.

To solve the system of equations:

x + y = -3 (Equation 1)

y = 2x + 2 (Equation 2)

We can substitute Equation 2 into Equation 1 for y and solve for x:

x + (2x + 2) = -3

3x + 2 = -3

3x = -5

x = -5/3

Now that we know x, we can substitute it into either Equation 1 or Equation 2 to find y. Let's use Equation 2:

y = 2x + 2

y = 2(-5/3) + 2

y = -10/3 + 6/3

y = -4/3

Therefore, the solution to the system of equations is (x, y) = (-5/3, -4/3).

Comparing this solution to the answer choices, we see that option (b) is the correct answer:

(a) 5/3, 4/3

(b) -5/3, -4/3 <--- Correct answer

(c) -3/5, -3/4

(d) 3/4, 3/5

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The correct proportion regarding the similar polygons is given as follows:

x/19.2 = 48/8.

Similar polygons are polygons that share these two features listed as follows:

For this problem, we have that the two rectangles are similar, as they both have the same angle measures, and the side lengths form a proportional relationship.

The proportional relationship for the equivalent side lengths of the rectangles is given as follows:

x/19.2 = 48/8.

Meaning that the fourth option is the correct option.

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The value of x is 9 and the sides are 28,8

what is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always is 180 degrees.

From the given figure ,

we can say that the two triangles are similar ,

21 / 3x+1  =  6 / x-1

21 ( x-1) = 6 (3x+1)

21x - 21 = 18x + 6

21x - 18x = 21 + 6

3x = 27

x = 9

3x + 1 = 3* 9 + 1 = 28

x-1 = 9-1 = 8

Therefore, The value of x is 9 and the sides are 28,8

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