A light year, the distance light travels in 1 year, is approximately 5.9×10^12 miles. A nearby galaxy is approximately 5.1×10^6 light years from our galaxy. Find the distance in miles between our galaxy and the nearby galaxy.

There are actually 5040 ways of arranging the letter knitting.

The system of equations is:

x = 2y

x*$10 + y*8 = $84

Solving it, we see that he worked 3 hours landscaping and 6 hours washing cars.

First, we need to define the variables:

We know that Alexander worked twice as many hours washing cars as he worked hours landscaping, then:

x = 2y

We also know that he earned a total of $84, then:

x*$10 + y*8 = $84

So the system of equations is:

x = 2y

x*$10 + y*8 = $84

To solve it, we just replace the first equation into the second one:

(2y)*$10 + y*8 = $84

y*$28 = $84

y = $84/$28 = 3

So He worked 3 hours landscaping, and:

x = 2*y = 2*3 = 6

6 hours washing cars.

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Marisol did a mistake while grouping the terms in Step 1, with the sign. Thus, Marisol should go back and group the terms in Step 1 as (6x³ - 22x²) - (9x - 33). Hence, the second option is the correct choice.

The polynomial Marisol had was 6x³ - 22x² - 9x + 33.

The steps she did in the grouping of terms and factoring out the GFC out of the groups were:

Step 1: (6x³ - 22x²) - (9x + 33).

Step 2: 2x²(3x - 11) -3(3x + 11).

After this Marisol was unable to get a common factor to proceed further.

The mistake that Marisol did was in Step 1, as while grouping -9x and +33, she took the minus sign out, which will make -9x to become 9x, but 33 to become -33.

This is where she made the mistake and writing - (9x + 33) in place of - (9x - 33).

Thus, her steps should have been:

Step 1: (6x³ - 22x) - (9x - 33),

Step 2: 2x²(3x - 11) -3(3x - 11), which gives her a common factor (3x - 11), to continue with the third step:

Step 3: (2x² - 3)(3x - 11).

Refer to the attachment for the complete question, as the given question is incomplete.

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Answer:

1. 1/27 2. 1/16

Step-by-step explanation:

First can be rewritten as (1/9)^(1/2 * 3) and anything to the power of 1/2 is a sqrt. So it is sqrt(1/9)^3. Then (1/3)^3 which is 1/27

Second, the negative bring the number to the bottom, 1/(32)^4/5. Then can be written as [tex]\sqrt[5]{1/32}[/tex]^4. 5th root of 1/32 is 1/2 then 1/2^4 is 1/16

Answer:

3/8=15/40

Step-by-step explanation:

Multiply both the numerator and the denominator of the first term by 5 and you'll see that it's the same fraction.

Answer:

D. g(x) = 5x^2

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A point of the function g(x) is known: (1, 5)

The proper function is

[tex]g(x)=5x^{2}[/tex]

Demonstration calculating g(1)

[tex]g(1)=5(1)^{2} =5(1)=5[/tex]

The point (1, 5 ) belongs to this function

Hope this helps

Answer:

C

Step-by-step explanation:

When the run part (the difference between x-coordinates of the two points on the line) is 1, the slope is an integer.

Answer:

C , D , B

Step-by-step explanation:

Trigonometry is given by three formulas :

SOH - CAH - TOA

Hope this helped and have a good day

Using the line of best-fit, it is found that:

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are:

(0,0), (1,2), (2,6).

Hence, using a calculator, the estimate for the battery after x minutes is given as follows:

y = 3x - 0.333.

50% power is obtained when y = 50, hence:

50 = 3x - 0.333

x = 50.333/3

x = 16.8 minutes.

90% power is obtained when y = 90, hence:

90 = 3x - 0.333

x = 90.333/3

x = 30.1 minutes.

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The relative frequency of the third class is 3/20.

Relative frequency measures how often a value appears relative to the sum of the total values. It is determined by dividing the frequency of a class by the total frequency.

Relative frequency = frequency of the third class / total frequency

6/(3 + 10 + 6 + 15 + 6)

6/ 40 = 3/20

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Answer:

10.3. and One solution

Step-by-step explanation:

I had this question, tho it might be different

The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]

An equation is an expression that shows the relationship between two or more numbers and variables.

Complex number is in the form z = a + bi, where a, b are real numbers.

Given the complex number z = 1 + 3i

In polar form: r = √(1² + 3²) = 3.16

Ф = tan⁻¹ (3/1) = 71.57⁰

The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]

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The 98% confidence interval of the proportion of all Americans who think that living on their own makes someone feels like an adult is (29.0%, 31.0%)

The given parameters are:

The number of success is then calculated as;

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 2000 * 28\%[/tex]

Evaluate

[tex]\bar x = 560[/tex]

Hence, 560 successes would be found in the sample of 2000 Americans

The proportion that lives on their own is:

p = 30%

The z-score for 98% confidence interval is

z = 2.326

The confidence interval is calculated as:

[tex]CI = \bar p \pm z * \sqrt{\frac{\bar p(1 - \bar p)}{ n}[/tex]

So, we have:

[tex]CI = 30\% \pm 2.326 * \sqrt{\frac{30\%(1 - 30\%)}{2000}[/tex]

Evaluate

[tex]CI = 30\% \pm 1\%[/tex]

Expand

CI = (30% - 1%, 30% + 1%)

Evaluate

CI = (29%, 31%)

Hence, the 98% confidence interval is (29.0%, 31.0%)

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By SSS congruency criteria ΔABC ≅ ΔDEF

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The given vertices of the triangles are;

ΔABC: A(−4, −3), B(0, 0), C(2, −3)

ΔDEF:  D(3, 1), E(6, -3), F(3, −5)

The lengths of the sides of ΔABC are

AB = √((0+4)² + (0+3)²) = √25 = 5

BC = √((2-0)² + (-3 - 0)²) = √13  

AC = √((2+4)² + (-3 +3)²) = √36 = 6

The lengths of the sides of ΔDEF are;

DE = √25=5

EF = √13

DF = √36 = 6

As,

AB= DE, BC = EF , AC= DF

So, By SSS congruency criteria ΔABC ≅ ΔDEF

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The equation that results from completing the square in the following equation. x^2−20x+75=0 is (x+2)^2 = 10

The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.

GIven;

x^2−20x+75=0

Subtract 75 from each side

x^2−20x+75 - 75 = -75

Take the coefficient of x

20

Divide by 2

10

Square it

100

Add it to each side

x^2 +5x + 100 = -75 + 100

(x+2)^2 = 10

Take the square root of each side

x+2 = 10

x = 8

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Answer:

all real numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

You are going from a very small number (like - 100000) to a very large number (like + 100000).

But neither of those could be the answer. They are either not small enough or not large enough. The domain must look like this.

- ∞ < x < ∞

Answer: So the domain is all the real numbers.

Answer:

Step-by-step explanation:

The Compositions of Reflections Over Intersecting Lines Theorem states that if we perform a composition of two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.

hope it helps! (✿◠‿◠)

The result concluded is equivalent to a single rotation transformation of the original object.

When a graph is reflected along an axis, say x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.

The Compositions of Reflections Over Intersecting Lines states that if we perform a composition of two reflections over two lines that intersect.

The result concluded is equivalent to a single rotation transformation of the original object.

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Answer: [tex]55^{\circ}[/tex]

Step-by-step explanation:

The measure of the third unknown arc is

[tex]360^{\circ}-70^{\circ}-110^{\circ}=180^{\circ}[/tex].

So, [tex]x=\frac{180^{\circ}-70^{\circ}}{2}=\boxed{55^{\circ}}[/tex]

Hence, the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."

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[tex]\bf{-8x+4\leq 36 }[/tex]

Subtract 4 from both sides.

[tex]\bf{-8x\leq 36-4 }[/tex]

Subtract 4 from 36 to get 32.

[tex]\bf{-8x\leq 32 }[/tex]

Divide both sides by −8. Since −8 is <0, the inequality direction is changed.

[tex]\bf{x\geq \dfrac{32}{-8} }[/tex]

Divide 32 by −8 to get −4.

[tex]\bf{x\geq -4 \ \ \Rightarrow \ \ \ Answer }[/tex]

Question :

Solution :

⇒ -8x + 4 ≤ 36

⇒ -8x ≤ 36 - 4

⇒ -8x ≤ 32

⇒ -x ≤ 32 / 8

⇒ -x ≤ 16 / 4

⇒ -x ≤ 8 / 2

⇒ -x ≤ 4

⇒ x ≥ -4

a) The speed of the boat is 3/5 ft/sec

b) The rate at which the angle changes is 8/125 rad/sec

A right angled triangle is a type of the triangle with one of its angles 90°.

The longest side of the triangle is called the hypotenuse which is the side that faces the right angle. other sides are called the adjacent sides.

Analysis:

The analysis is in the attached file below.

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Answer:

We first need to know the graph of the basic function belonging to the trigonometric family, which is sin x.

Now we need to apply basics of functions to get the graph of y = -sinx from y = sinx

If x is the input in the y = sinx , then sin x will be the output which will be represented on the  y axis. Eg :

If x = pi/2

then output will be y = sin(pi/2) = 1

Hence in the graph of sinx, at x =pi/2 the value of y is 1.

Once we have understood this, we can use the same logic in the case

y = -sinx

If x = pi/2

then output will be y = - sin(pi/2) = -1

Here we can see that the output of y = - sin x will be the exact negative of  of the output of y = sinx

Hence all portions of the graph of  y = sinx in the +y axis will come down to the -y axis for y = -sin x, i.e we will be taking mirror image of the graph along the x axis. Below are the graphs of y=sinx and y= - sinx respectively for your reference:

(image courtesy Microsoft graphic calculator)

Pooling can be referred to the process of how an insurance company can pay a large benefit even if it hasn't collected that amount from an individual's or company premium in this type of context.

This is referred to as a type of protection against financial loss or other forms of incidents or risks and there are different types which cater for different purpose or reasons and they include life, vehicle insurance etc. The insurance plan is usually sold by designated insurance companies and are accessible to the public.

Pooling is the process which involves the smaller firms purchasing better interest rates which helps to lessen the cost of coverage. This also ensures that benefits are paid at the right time so as to avoid hassle and other forms of issues which may arise from this important process.

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The average rate of change within the function f(x)=[tex]x^{2} -x-1[/tex]is -2.

Given The function f(x)=[tex]x^{2} -x-1[/tex]

We have to search out the typical rate of change of function within the interval (-2,1).Interval is largely a variety between numbers lying on the quantity line which may be a line on which different numbers are plotted.

We know that average rate of change =f(b)-f(a)/(b-a)

we have to first know the values of function at different values of x.

f(x)=[tex]x^{2} -x-1[/tex]

f(1)=1-1-1

=-1

f(-2)=4+2-1

=5

b=-2

a=1

put within the formula:

A=-1-5/1+2

=-6/3

=-2

Hence average rate of change of the function within the interval (-2,1) is -2.

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Answer:

f(5) = 45

Step-by-step explanation:

If f(x) = 2x²-5 , f(5) =

f(5) = 2(5)² - 5

f(5) = 2(25) - 5

f(5) = 50 - 5

f(5) = 45

Answer:

The choice D.

Step-by-step explanation:

[tex]f(x) = {( \frac{1}{6} })^{x} \\ \\ f(3) = {( \frac{1}{6} })^{3} = \frac{ ({1})^{3} }{( {6})^{3} } = \frac{1}{216} [/tex]

Answer:

260 cm^2

Step-by-step explanation:

The area of a parallelogram is calculated by multiplying its height and base:

The base for this parallelogram is given as 20 and the height is 13

13*20 = 260

The area is stated in square units so the answer is 260 cm^2

The amount loaned at the interest rate of 11% is $3000.

The amount loaned at the interest rate of 7% is $16,500

0.11a + 0.07b = 1485 equation 2

Where:

a = amount loaned at the interest rate of 11%

b = = amount loaned at the interest rate of 7%

In order to determine how much was loaned at 7%, take the following steps:

Multiply equation 1 by 0.11:

.11a + 0.11b = 2145 equation 3

Subtract equation 2 from equation 3:

0.04b = 660

Divide both sides by 0.04:

b = 16,500

Subtract 16,500 from 19,500 :

19,500 - 16,500 = $3000

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