Two-lined salamanders have weights that are normally distributed and on average 13.6 grams with a standard deviation of 2.2 grams. A random sample of 8 two-lined salamanders is selected and weighed.

The probability that the sample mean is between 13.6-x and 13.6+x is around 0.68 (more precisely, 0.6827), for some value of x. What is the value of x ?

Answer:

Step 1: Calculate percentage discount

=> $97,899.99 × 25/100

=> 97,899.99/1 × 25/100

{multiply the numerator by the numerator and the denominators by the denominators}

=> 2,447,499.75/100

divide 24,474.9975 by 100

=> 24,474.9975

=> 24,474.9975

{Substract 24,474.9975 from 97,899.99.}

=> 97,899.99 - .24,474.9975

=> 73,424.9925

Step 2: Calculate sales tax rate

Sales tax rate = price × rate/100

=> 73,424.9925 × 3.75/100

=> 275,343.7/100

=> 2,753.437

Add to 73,424.9925

=> 73,424.9925 + 2,753.437

=> 76,178.4295

=> 76,178.4 { Rounded to 1 dp)

Therefore, the total price of the purchases is 76,178.4295

Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

\(\frac{125}{5} = 25 mpg\\\)

2. Divide miles you want to travel by the mileage per gallon you got on the first step

\(\frac{400}{25} = 16 gallons\)

Answer:

The slope is going to be 5 and the y-intercept is going to be (0,9)

Step-by-step explanation:

What is an expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The number before x in an expression is going to be the slope of the equation. and the number by itself is your y-intercept of the equation.

What is your y-intercept?

The y intercept is the point on which your line crosses on the y axis.

The line will cross on the number 9 which causes 9 to be the y-intercept.

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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Use the definition of absolute value.

\(|x| = \begin{cases} x & \text{if } x \ge0 \\ -x & \text{if } x < 0 \end{cases}\)

The absolute value is always non-negative. So if \(x\) is already non-negative, \(|x|=x\) is unchanged. But if \(x\) is negative, then \(|x|=-x\) because multiplying \(x\) by -1 makes it positive.

Now, if \(x>1\), then by the definition of absolute value,

\(x > 1 \implies x - 1 > 0 \implies \boxed{|x - 1| = x - 1}\)

The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) = 3x - 5

Here, g(x) is not given clearly.

But we can identify the given function as an inverse of each other.

Let's suppose the ordered pairs are:

[x, f(x)] and [x, g(x)]

The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.

f(0) = -5 so for (0, -5) on the f(x) list then (-5,0) must be on the g(x) list

f(1) = -2 so for (1, -2) on the f(x) list then (-2, 1) must be on the g(x) list

f(2) = 1 so for (2, 1) on the f(x) list then (1, 2) must be on the g(x) list

Let's suppose:

g(x) = (x+5)/3

g(-5) = 0

g(-2) = 1

g(1) = 2

So the ordered pair (-5, 0), (-2, 1), and (1, 2) are in the list of g(x).

Thus, the functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.

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Answer:

376.8

Step-by-step explanation:

formula for SA=2×π×r×h  +  2×π×r²

r = 4

r²= 16

h = 11

π= 3.14..

substitute:

SA= (2 × 3.14 × 4 × 11) + (2× 3.14 × 16)

276.32  + 100.48 = 376.8

Using translation concepts, it is found that the triangles are congruent, as triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

From the vertices of the triangles MNP and QRS, the following transformation was applied:

(x,y) -> (-x,-y).

Which is a 180º rotation about the origin, that is, triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.

Rotations do not change the side lengths, only the orientation of the triangle, hence the triangles QRS and MNP are congruent.

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Answer:

Step-by-step explanation:

+ At time 0 (beginning), the volume is 5 (feet^3) of sand.

+ After 1 minute, it lefts: 90% of 5 = 0.9*5

+ After 2 minutes, it left 90% of (0.9*5) = 0.9*(0.9*5)

or

\(5.(0.9)^{2}\)

+ After 3 minutes, it left 90% of    \(5.(0.9)^{2}\)

or

\(5.(0.9)^{3}\)

.......

+ After x minutes, it left 90% of    \(5.(0.9)^{x-1}\)

or

\(5.(0.9)^{x}\)

So the answer is \(5.(0.9)^{x}\), that means C

Answer:

lol i dont know but yo dog smell like evolution and natural selection?

Step-by-step explanation:

Answer:

11.) 180-38=142 12.)24.5 13.)im not sure but want to say 10

Step-by-step explanation:

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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Answer:

f(2) = 0 and f(6) = -4

Step-by-step explanation:

First, find f(x) when x = 2

Plug in 2 as x in the function:

f(x) = -(x - 2)​

f(2) = -(2 - 2)

f(2) = -(0)

f(2) = 0

Next, find f(x) when x = 6. Plug in 6 as x in the function:

f(x) = -(x - 2)​

f(6) = -(6 - 2)

f(6) = -(4)

f(6) = -4

So, f(2) = 0 and f(6) = -4

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Answer:

Yes they do :)

(o´▽`o)ﾉ x

Answer:

0.54 ltres

Step-by-step explanation:

30/100 x 1.8 = 0.54 l

The answer for blanks in statements are, an x-intercept of 1 , -3, x>1 , increasing , 7.5.

Many mathematical and real-world phenomena are described by functions. Modeling real-world occurrences like population increase, interest rates, or physical motion is frequently done using them. There are many distinct features that functions can have, including continuity, differentiability, and periodicity. Functions can also be linear or nonlinear.

The domain and range of functions are crucial components. The set of all potential input values makes up the domain of a function, whereas the set of all possible output values makes up the range. The behaviour of a function, such as whether it is increasing, decreasing, or constant, can also be used to categorize it. A function's graph shows the relationship between its input and output values graphically.

Function h has an x-intercept of 1 and a y-intercept of -3.  The function is positive for x>1 and increasing on all intervals of x. The average rate of change for the function on the interval [0, 2] is 7.5

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Answer:

50.3cm²

Step-by-step explanation:

Formula: The area of a circle is found by A = πr²

Given:

Plug in:

A = πr² → A = (3.142)(4)²

            → A = (3.142)(16)

            → A = 50.272

"1 decimal places",  round up to 50.3

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

When 33 is divided into 86, the quotient is 2 and the remainder is 20.

Answer:

  f(1) = -1

  f(n) = f(n-1) -1

Step-by-step explanation:

The first term is -1. Each term is 1 less than the previous. These equations say that.

  f(1) = -1

  f(n) = f(n-1) -1

Answer:

D = 100 - 2p

Where p is the price in dollars of the product and D is the number of products that can be sold at that price

And we need to interpret the slope of this function mean in the context of the problem. And for this case the slope is m=-2 and it means that for every increase in the price in 1 $ we will have a decrease the number of products in two units

Step-by-step explanation:

For this problem we know the following function given:

D = 100 - 2p

Where p is the price in dollars of the product and D is the number of products that can be sold at that price

And we need to interpret the slope of this function mean in the context of the problem. And for this case the slope is m=-2 and it means that for every increase in the price in 1 $ we will have a decrease the number of products in two units

Answer:

3/5

Step-by-step explanation:

one year has 12x2 fortnight so 24

A.her yearly salary is

B.now we do the opposite operation, divide

C. we look for the difference with a subtraction

Answer:

Nine hundred fourteen point two three eight

OR

Nine hundred one ten 4 one two tenths three hundredths and eight thousandths

The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

The total surface area of the can is therefore:

A = 2πr² + 2πrh

We know that the volume of the can is 810 cm³, which is given by:

V = πr²h

We can solve this equation for h to get:

h = V/(πr²)

Substituting this expression for height h into the equation for the surface area, we get:

A = 2πr² + 2πr(V/(πr²))

Simplifying, we get:

A = 2πr² + 2V/r

Now we have an equation for the surface area of the can in terms of the radius, r.

To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.

dA/dr = 4πr - 2V/r² = 0

Solving for radius r, we get:

\(r = (810/\pi)^1^/^3\)

r=∛810/3.14

r=6.35 cm

Now find h:

h = 810/πr²

h=810/3.14×6.35²

h=810/126.6

h=6.39 cm

Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

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Answer:

30

Step-by-step explanation:

24/4=6

42/7=6

6 x 5=30