Let s(t)=[tex]\sqrt{x+16}[/tex] be the position function. Use the Definition to find the velocity at t=0.

The standard deviation of the fitness center is larger than the standard deviation of the last shipment

The given parameters are:

Distribution: Normal distribution

The last shipment

Mean weight = 2.7 grams

Standard deviation = 0.1 gram.

Fitness center

Mean weight = 100.2 pounds

Standard deviation = 0.1 pound

In the above parameters, we can see that the fitness center has a larger mean weight than the last shipment, while they both have the same standard deviation

This means that the standard deviation of the fitness center is larger than the standard deviation of the last shipment

And so, the distribution of the fitness center is more dispersed

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0 is correct, though...

[tex]\dfrac{\frac1x - \frac13}{x + 3}[/tex]

is continuous at [tex]x=3[/tex], so

[tex]\displaystyle \lim_{x\to3} \frac{\frac1x - \frac13}{x + 3} = \frac{\frac13 - \frac13}{\frac13 + 3} = \frac0{\frac{10}3} = 0[/tex]

What was probably intended was the limit

[tex]\displaystyle \lim_{x\to3} \frac{\frac1x - \frac13}{x - 3}[/tex]

which requires a little more finesse because the function is not continuous at [tex]x=3[/tex].

Rewrite it as

[tex]\dfrac{\frac1x - \frac13}{x - 3} = \dfrac{3 - x}{3x(x-3)} = -\dfrac{x-3}{3x(x-3)}[/tex]

When [tex]x\neq3[/tex], we can cancel [tex]x-3[/tex] so that

[tex]\displaystyle \lim_{x\to3} \frac{\frac1x-\frac13}{x-3} = \lim_{x\to3} -\frac1{3x} = -\frac1{3\times3} = -\frac19[/tex]

The length of each equal side of the isosceles right triangle will be 11 cm.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The hypotenuse of an isosceles right triangle is √242 cm.

In an isosceles right triangle, the two legs of the isosceles right triangle are congruent.

Let x be the other leg.

(√242)² = x² + x²

242 = 2x²

x² = 121

x = 11 cm

The length of each equal side of the isosceles right triangle will be 11 cm.

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Answer:

b, c, a

Step-by-step explanation:

Part (b)

[tex]f(3)=-3^3 + 4(3)^2-2(3)+2 \\ \\ =-27+36-6+2 \\ \\ =9-4 \\ \\ =\boxed{5}[/tex]

Part (c)

[tex]f(-2)=-(-2)^3+4(-2)^2-2(-2)+2 \\ \\ =16+16+4+2 \\ \\ =\boxed{38}[/tex]

Answer: 4:1

Step-by-step explanation:

36 men: 9 ladies

36/9=

4/1 ==> 4 men: 1 lady

4:1

Answer: second quadrant

Step-by-step explanation:

Answer:72 bracelets

Step-by-step explanation:

24*3

72 bracelets

If she can make 4 bracelets with 12 beads, you divide to get three. Three times 24 is 72 bracelets

The answer would be 4/21 if divided 2/7 by 1.5 which is the correct option (C).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have to determine the divide 2/7 by 1.5

⇒ 2/7 ÷ 1.5

Here 1.5 = 3/2

⇒ 2/7 ÷ 3/2

Apply the division operation between both term

⇒ (2/7)/(3/2)

Reciprocal the terms, we get

⇒ (2/7)×(2/3)

⇒ (2×2)/(7×3)

⇒ 4/21

Therefore, the answer would be 4/21

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Answer:

4.02 inches

Step-by-step explanation:

48.24/12= monthly average

=4.02 inches

Answer:

A) x = m - n - p

Step-by-step explanation:

m - x = n + p

subtract m from both sides

m - x (- m) = n + p (- m)

m cancels out on the left and stays on the right

- x = n + p - m

divide by -1 because this is the constant in front of x

visualize as -1*x if it helps (anything multiplied by 1 is that number)

(- x / -1) = (n / -1) + (p/ -1) - (m/ -1)

the positives become negative and the negatives become positive

x = -n - p + m or x = m - n - p

Answer:

Y= 1/2

Gradient= y2-y1/x2 -x2=m

Given that:

y2=1

y1=Y

x1=-4

x2=-5

1-y/-4-(-5) =2

1 - y/-4+5 =2

cross multiply

2(1-y) = -4+5

2-2y =1

-2y =1-2

-2y = -1

divide both sides by the coefficient of y

Y = 1/2

The value of m<DEC is given as 35 degrees

In the given figure, to find the missing value of angle DEC, we can easily relate this to angle on a straight line.

The law states that the sum of all angles on a straight line are equal to 180 degrees.

[tex]m < CEF + m < DEC = 180^0\\145^0 + m < DEC = 180^0\\m < DEC = 180^0 - 145^0\\m < DEC = 35^0[/tex]

The value of the angle m<DEC is equal to 35 degrees.

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No: g(x) of not the inverse function of f(x)

Given data

f(x) = -4 ( -2x + 9 )^3 - 8

g(x) = - cube root ( -5x + 6 ) + 2

f(x) = -4 ( -2x + 9 )^3 - 8

dividing through by - 4 gives

= ( -4 ( -2x + 9 )^3 ) / -4 - ( 8  / -4)

= ( -2x + 9 )^3 -  ( -2 )

=  ( -2x + 9 )^3 + 2

finding the cube root

= ( -2x + 9 )^3 + 2

= cube root ( ( -2x + 9 )^3 + 2 )

= ( -2x + 9 ) +  cube root ( 2 )

( -2x + 9 ) +  cube root ( 2 ) ≠ g(x) = - cube root ( -5x + 6 ) + 2

The equation solved is not equal to g (x), therefore we can say that g(x) of not the inverse function of f(x)

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The domain is all real numbers and the range is 21 for the given function that is f(x) = 21.

According to the question, the domain can take only those values through which expression can be defined. And the range is the set of values for the given function.

Therefore, the function is: f(x) = 21

So, for this expression, the variable 'x' can take any real values from the interval of (-∞ , ∞).

And the range is 21 for the given function.

Hence the domain is (-∞ , ∞) and the range is 21.

What is domain and range in the function?

The domain of a function can be defined as the complete set of all the possible values for the dependent variables. Similarly, the range of the function can be expressed as the set of all the values which can be assumed by the expression of the function.

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The best estimate of the product of 8 and 629 is 5600

The statement is given as

The best estimate of the product of 8 and 629

Express as a product

So, we have

8 x 629

Round 629 to the smallest hundred greater than 629

So, we have

8 x 629 = 8 x 700

Evaluate the product

8 x 629 = 5600

Hence, the best estimate of the product of 8 and 629 is 5600

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The equation of a line passing through the origin and parallel to the line passing through the points (8, 3) and (10, 8) is 2y - 5x = 0.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's suppose the equation of that line as the slope-intercept form is

y = mx + c

Where m is the slope while c is the y-intercept.

Now this line is parallel to a line that passes through points  (8, 3) and

(10, 8) thus meaning the slope of both lines must be the same.

So,

Slope associated with points  (8, 3) and (10, 8) ⇒

m = difference in y's coordinate / difference in x's coordinate

m = (8 - 3)/(10 - 3)

m = 5/7

So our equation will be y = (5/7)x + c

Since it is passing through the origin or (0,0) so it will satisfy the coordinate.

Therefore,

0 = (5/7)0 + c ⇒ c = 0

It means y = (5/7)x ⇒ 7y - 5x = 0 will be the equation.

Hence "The equation of a line passing through the origin and parallel to the line passing through the points (8, 3) and (10, 8) is 2y - 5x = 0".

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The given question is an incomplete complete question as follows;

The equation of a line passing through the origin and parallel to the line passing through the points (8, 3) and (10, 8).

The domain of the quadratic equation is all non-negative real numbers.

The picture indicates the case of the launch of an object from the top of a building. The height of the object (f(x)), in feet, as a function of time, (x), in seconds. Both height and time are represented by non-negative real numbers and hence the following solutions do not make sense in the context of problem:

Now we proceed to fill the blanks in the four paragraphs:

f(- 2) = 0, meaning that - 2 second after the object was launched, the object was 0 feet above the ground. This interpretation does NOT make sense in the context of the problem.

f(0.5) = 100, meaning that 0.5 seconds after the object was launched, the object was 100 feet above the ground. This interpretation make sense in the context of the problem.

f(6) = - 224, meaning that 6 seconds after the object was launched, the object was - 224 feet above the ground. This interpretation does NOT make sense in the context of the problem.

Based on the observation above, it is clear that an approximate domain for the function is all non-negative real numbers.

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===========================================================

Explanation:

The preimage (-6,-2) shifts to the image point (-4,-4)

Focus on the x coordinates. The jump from -6 to -4 is an increase of 2. So we have x become x+2

Now focus on the y coordinates. The jump from -2 to -4 is -2, so y becomes y-2

The translation rule we use is [tex](\text{x},\text{y})\to (\text{x}+2,\text{y}-2)[/tex] which shifts the point 2 units to the right and 2 units down.

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

Let's apply this rule to the point (3,-1)

[tex](\text{x},\text{y})\to (\text{x}+2,\text{y}-2)\\\\(3,-1)\to (3+2,-1-2)\\\\(3,-1)\to \boldsymbol{(5,-3)}\\\\[/tex]

The preimage (3,-1) shifts to the image (5, -3)

Answer:6,7,8,9x4

Step-by-step explanation:

the purpose is to solve th equation5789x4

Answer: Question: 306 × 673 = 205,938  Estimate: 300 × 700 = 210,000

See more below

Step-by-step explanation:

306 round to the nearest hundred is 300 because 306 ≥ 300

And 673 rounds to 700 because its to the nearest hundred. Here is the problem.    

    306

  × 673

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

  205,938

So, 205, 938 is underestimate to 210,000

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The estimated the product of 306×673 by first rounding each number to the nearest hundred is: the estimated product of 306 and 673 is 210000.

Given: 306 × 673 = 205,938  

Estimate: 300 × 700 = 210,000

306 round to the nearest hundred is 300 because 306 ≥ 300

And 673 rounds to 700 because its to the nearest hundred.

Now, we have,

   306

 × 673

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

 205,938

Now, multiply the rounded numbers:

300 * 700 = 210000

So, the estimated product of 306 and 673 is 210000.

So, We have,

205, 938 is underestimate to 210,000.

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Answer:

[tex]\dfrac{11}{8}[/tex]

Step-by-step explanation:

Slope formula

[tex]\textsf{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.}[/tex]

Define the points:

[tex]\textsf{Let}\:(x_1,y_1)=(5,7)[/tex]

[tex]\textsf{Let}\:(x_2,y_2)=(-3,-4)[/tex]

Substitute the defined points into the formula:

[tex]\implies \textsf{Slope}=\dfrac{-4-7}{-3-5}=\dfrac{-11}{-8}=\dfrac{11}{8}[/tex]

Therefore, the slope of (5, 7) and (-3, -4) is 11/8.

The linear function is V(x) = 800x + 2400.

Given,

The cost of computer when purchased (the initial book value), V = 2400 (x = 0)

Company chooses to depreciate for 3 years using straight line method.

The book value after 3 years = 0 (x = 3)

We have to write a linear function that expresses the book value of the computer as a function of its age V(x).

Here, the value is depreciating over 3 years.

That is 2400 in 3 years = 2400/3 = 800

That is depreciating $800 in a year.

Now we can write the equation as:

V(x) = 800x + 2400

When we consider slope-intercept form, we can check that the above given equation of a line passes through two points: (0, 2400) and (3, 0)

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The order from the least to the greatest is 0.1, 1/4, 40%, 9/7.

The numbers given are in improper fraction, decimals, proper fraction and percentage.

Improper fraction is a fraction in which the numerator is greater in value than the denominator. Proper fraction is a fraction in which the numerator is less in value than the denominator. A decimal is a number that consists of integers and non-integers separated by a decimal point. Percentage is the fraction of an amount expressed as a number out of 100.

For ease, all the numbers would be converted to percentages :

9/7 x 100 = 128.57%

0.1 = 10%

1/4 x 100 = 25%

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Given conditions:

6th term (T6) = -2

first term (a) = 18

n = 6, r = ?

Formula for finding the nth term of a GP:

[tex]tn = a {r}^{n - 1} [/tex]

Where:

T = the given value for the number of term(s)

n = the given number of term

a = The first term

r = The common ratio

Replacing for the values:

[tex] - 2 = 18 {r}^{6 - 1} \\ - 2 = 18 {r}^{5} [/tex]

Dividing both sides by 18, we have:

[tex] {r}^{5} = \frac{ - 2}{18} [/tex]

Now, we have to fifth root both sides to find the value of r.

[tex] \sqrt[5]{ {r}^{5} } = \sqrt[5]{ \frac{ - 2}{18} } [/tex]

Therefore:

Common ratio, [tex]r = -0.0638165752[/tex] [tex]≈ -0.064[/tex] to 3 decimal places.

The current assets total of  Adventure Travel. at December 31, 20XX is $44,300

What are current assets?

Current assets are short-term resources owned by Adventure Travel which are used in its daily operations such as the cash, accounts receivable as well the office supplies which are current assets until consumed

In other words, in a bid to determine current assets total, we sum up the cash, accounts receivable and the office supplies of the company since there are no other current assets aside the aforementioned ones.

Current assets total=cash+ accounts receivable+ office supplies

cash=$25,000

accounts receivable=$ 15,000

office supplies=$4,300

current assets total=$25,000+$15,000+$4,300

current assets total=$44,300

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