Find the derivative of each function. Simplify each derivative and express all exponents as positive values.

The circumference of circle is 150.72 millimetres.

In simpler terms, circumference in the perimeter of circle. Thus, it will represent the measure of length of the line of circle. The relationship between circumference of circle and it's diameter will be represented as formula -

C = πd, where C is circumference and d is diameter.

Keep the value of diameter in the formula to find the exact circumference of the circle.

Circumference = 3.14×48

Performing multiplication to find the circumference of the circle

Circumference = 150.72 millimetres.

Therefore, the circumference of the circle with 48 millimetres diameter is 150.72 millimetres.

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A conclusion which can be made from the given information about quadrilateral EFGH is that: A. the quadrilateral is both a parallelogram and a rectangle.

A quadrilateral can be defined as a type of polygon that has four (4) sides, four (4) vertices, four (4) edges and four (4) angles.

In Geometry, there are different types of quadrilateral and these include the following:

In this scenario, we can reasonably infer and logically deduce that quadrilateral EFGH is both a parallelogram and a rectangle because the length of its diagonal are equal and it has adjacent sides of equal of length.

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Part B

What is the median recovery time?

Remember that

For a normal distribution, mean = median = mode

so

The median is 4 days

Part C

What is the Z-score for a patient that took 5.7 days to recover?

Remember that

z =(x - μ)/σ

where

μ=4 days

σ=1.6 days

X=5.7 days

substitute

z=(5.7-4)/1.6

z=1.0625

Part D

What is the probability of spending more than 4.5 days in recovery?

z =(x - μ)/σ

μ=4 days

σ=1.6 days

x=4.5 days

Find out z

z=(4.5-4)/1.6

z=0.3125

using a z-score table values

P(X>4.5)=0.3773

Part E

What is the probability of spending between 3.5 and 4.3 days in recovery?

For x=3.5 -------> z=(3.5-4)/1.6=-0.3125

For x=4.3 -----> z=(4.3-4)/1.6=0.1875

using a z-score table values

P(3.5 < X < 4.3)=0.1970

Part F

Remember that

If your score is in the 85th percentile, it means that 85% of the scores are below your score and 15% are above your score

using a z-score table values

the value of Z=1.036

Find out the value of x

1.036=(x-4)/1.6

solve for x

x=5.6576 days

Let's us tabulate the data that is on the scatterplot.

As you can see in the fourth column, "Sold More Trucks than Cars?", some rows say "Yes" and some say "No".

Let's take a look at Employee No.1. Employee No.1 sold 4 trucks and sold 2 cars. Therefore, employee no.1 was able to sell more trucks than cars and thus, the answer to the fourth column is "Yes."

The same is done for all the employees.

In the end, there are 6 employees who were able to sell more trucks than cars.

13.75h = 50 This is the answer

I think it euqation 4

Answer: I believe the answer would be B

Step-by-step explanation: Multiply m(8) and n(8) together to get (mn)(8) and you would get 150.

Answer

Explanation

Given:

we can rewrite the expression as follows:

Explanation

Give that

To get the value of

we will have

The value (f o g) (x) is

The graph is

Thus, the Domain is

[tex]7/10^2[/tex] is ten times [tex]7/10^3[/tex] or  [tex]7/10^3[/tex] is one-tenth of [tex]7/10^2[/tex].

[tex]10^2[/tex]  and [tex]10^3[/tex] are written in the exponent form.

Exponent

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

We are given two numbers [tex]7/10^2[/tex] and [tex]7/10^3[/tex].

We have to find the relationship between the two given numbers.

We know that,

[tex]7/10^2[/tex] can be written as 7/100 and [tex]7/10^3[/tex] can be written as 7/1000.

We can write,

7/1000 = (7/100) *(1/10)

Hence, 7/1000 is one-tenth of 7/100.

Also, we can write,

7/100 = (7/1000)*10

Hence, 7/100 is ten times 7/1000.

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This statement is justified by the angle addition postulate.

Answer

The length of the missing leg = 12 m

Explanation

The triangle presented is a right angled triangle because one of its angles is equal to 90 degrees.

The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

Hypotenuse side = 15 m

a = 9 m

b = d = ?

a² + b² = (hyp)²

9² + d² = (15)²

81 + d² = 225

d² = 225 - 81

d² = 144

d = √144

d = 12 m

Hope this Helps!!!

Answer:

We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem,

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

If one leg is 9 , that's our a value.

If the hypotenuse is 15 , that's our c value.

Now we just have to find the b value.

Plugging in the variables,

[tex] {9}^{2} + {b}^{2} = {15}^{2} [/tex]

[tex] {9}^{2} = 81 \\ {15}^{2} = 225 \\ 81 + {b}^{2} = 225[/tex]

Subtract 81 from both sides.

[tex] {b}^{2} = 144[/tex]

Square root both sides.

[tex] \sqrt{ {b}^{2} } = b \: and \: \sqrt{144 = 12 } [/tex]

so b = 12

Answer:

242

Step-by-step explanation:

I used Desmos.

Answer:

hope it helps

Step-by-step explanation:

The value of the missing variable x in the given triangle is; x = 15

We know that sum of angles on a straight line is 180 degrees. That means the angle on the horizontal line of (9x + 16)° inside the triangle will be;

180 - (9x + 16)°

Now, we know that sum of angles in a triangle is 180 degrees. Thus;

180 - (9x + 16)° + 5x - 14 = 90

180 - 4x - 30 = 90

150 - 4x = 90

150 - 90 = 4x

60 = 4x

x = 60/4

x = 15

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Answer:

I would say B, because the entire purpose and main theme of  The Interlopers is to show the futility and uselessness of feuds and arguments, and that sometimes its best to just live and let live, just to keep it short.

Let's draw the ramp to better understand the problem:

For us to be able to determine how long the ramp will be, we will be using the Cosine Function.

We get,

Therefore, the answer is 57.2165 feet.

Answer:

Yep! Got it alllllll right.

The area of a flat ring whose inside and outside diameters are 4cm and 10cm is  66cm²

The region encircled by a circle with radius r is known as πr² in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

Circular ring's inner diameter (d) is equal to 4 cm.

Circular ring's inner radius (r) is 2 cm.

The circumference of the ring (D) is 10 cm.

Circular ring's (R) outer radius is 5 cm.

To locate

the circumference of the ring.

Solution:

The following formula can be used to calculate the area of a circular ring whose inner and outer diameters are given:

Area of a circle equals (R2 - r2).

= 22(5^2-2^2) / 7

= 66cm²

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A sequence of transformations that maps ABC to A'B'C' is a Rotation of 90° counterclockwise about the origin followed by a Translation of 2 units right.

This is further explained below.

Generally, The purpose of translation is to convey the meaning of a text written in one language into another language using texts written in those respective languages.

In conclusion, A rotation of 90 degrees anticlockwise around the origin, followed by a translation of 2 units right, is the sequence of transformations that maps ABC to A'B'C'.

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The given equation is

This equation belongs to an uptrend line because the variable x is positive. The line has to have a y-intercept at -1 because that's the constant term.

Following the characteristics of the equation, we can deduct that the correct graph is A.

The given system is

Let's isolate y in the first equation.

Then, we replace the equation we've got in the second equation of the system.

Now, we solve for x.

We use this value to find y.

Answer:

the amount of money sam has borrowed was 2400

he paid interest 2%

total intreast 48$

48÷3 = $16 a year

2%= $16

16×5= $80 for 10%

$80× 10= 800

800×3= 2400 total amount was borrowed

so 2400-2%= 2352

2400- 2352= 48

step1

translation in x direction is left or right

translation in y direction is down or up

so

translation 6 units righ is the same that

x+6

translation 6 units up is the same that

y+6

For (-5,-5) we have -----> (-5+6,-5+6)-------> (1,1)

For (-5,-4) we have -----> (-5+6,-4+6) ----> (1,2)

For (-3,-5) we have ----> (-3+6,-5+6) -----> (3,1)

the solution is the option A

According to the solving the matrix will be  BF = [tex]\left[\begin{array}{ccc}4&0&-3\\15&9&6\end{array}\right][/tex]

A matrix is a rectangular array as well as table of characters, numbers, or expressions that is set up in rows and columns to represent a mathematical object or a characteristic of one. As an illustration, consider a matrix containing two rows as well as three columns..

In the field of optics, matrices are employed to model refraction and reflection. Quantum mechanics, electrical circuits, and resistor conversion all benefit from the usage of matrices. In electric circuits, matrices are utilized to solve equations relating to the AC network.

B = [tex]\left[\begin{array}{ccc}2&-1&2\\3&-1&-2\end{array}\right][/tex]

F = [tex]\left[\begin{array}{ccc}3&1&1\\-2&-2&1\\-2&-2&-2\end{array}\right][/tex]

Now solving for BF:

B = [tex]\left[\begin{array}{ccc}2&-1&2\\3&-1&-2\end{array}\right][/tex]  x F = [tex]\left[\begin{array}{ccc}3&1&1\\-2&-2&1\\-2&-2&-2\end{array}\right][/tex]

BF = [tex]\left[\begin{array}{ccc}6+2-4&2+2-4&2-1-4\\9+2+4&3+2+4&3-1+4\end{array}\right][/tex]

BF = [tex]\left[\begin{array}{ccc}4&0&-3\\15&9&6\end{array}\right][/tex]

According to the solving the matrix will be  BF = [tex]\left[\begin{array}{ccc}4&0&-3\\15&9&6\end{array}\right][/tex].

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The complete table of the algae area is:

Day 1  2 3 4 5 6

Area 1/2 1 2 4 8 16

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

The initial area exists given as;

A(1) = 1/2 square meters

When it doubles every day, we have:

A(n) = 2 × A(n - 1) where A(1) = 2

So, we contain the following values

A(2) = 1/2 × 2 = 1

A(3) = 1 × 2 = 2

A(4) = 2 × 2 = 4

A(5) = 4 × 2 = 8

A(6) = 8 × 2 = 16

Therefore, the complete table is:

Day 1  2 3 4 5 6

Area 1/2 1 2 4 8 16

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Answer:

Perpendicular

Explanation:

Given the coordinates

A(-2,-5), B(4.7) C(0, 2) and D(8,-2)​, we are to determine whether AB is parallel, perpendicular to CD or neither

To do this, we need to find he slope of AB and CD first. Using the formula for calculating slope as shown;

m = y2-y1/x2-x1

For AB:

slope = 7-(-5)/4-(-2)

Slope = 7+5/4+2

Slope of AB = 12/6

Slope of AB = 2

For CD

Slope of CD = -2-2/8-0

Slope of CD = -4/8

Slope of CD = -1/2

Note that for AB to be perpendicular to CD, the product of their slope must be -1.

Given

mAB = 2

mCD = -1/2

Taking their product

mAB * mCD = 2 * -1/2

mAB * mCD = -1

Since the product is -1, hence AB is PERPENDICULAR to CD

[tex]b \div 5 = - 30 \\ \frac{b}{5} = - 30[/tex]

I CONVERTED b÷5 SO THAT I CAN USE CROSS MULTIPLICATION

[tex]b = - 30(5) \\ b = - 150[/tex]

b is -150

HOPE THIS HELPS.

The temperature fell from 0°F  to  [tex]-6\frac{3}{5}[/tex].or below O°F in [tex]2\frac{1}{5}[/tex]hours.  the temperature change per hour is  -3 degree

When two independent temperature readings are subtracted, or when calculating the amount of temperature rise or fall, the result is a temperature difference, also referred to as a delta temperature (T).

We are aware that throughout the course of hours, the temperature dropped from 0 to= [tex]-6\frac{3}{5}[/tex].

Therefore, we will divide the change in temperature by the number of hours to determine the rate of change of the temperature.

In order to solve for that, we shall convert the mixed number into improper fractions.

[tex]-6\frac{3}{5}=\frac{-33}{5}degrees\\ 2\frac{1}{5} =\frac{11}{5}hours\\[/tex]

Hourly temperature change =[tex]\frac{\frac{-33}{5} }{\frac{11}{5} }[/tex]

=-3

As a result, there was a -3 degree shift in temperature every hour.

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x is case of almonds and y is case of walnuts.

Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.

H-E-B orders no more than 200 bags of almonds and walnuts at a time.

So,

x + y < 200

where x and y refers to the number of bags

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

H-E-B pays $24 per case of almonds and $27 per case of walnuts, but will not order more than $300 total at any one time.

But keep in mind that : Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.

So,

24 * (x/15) + 27 * (y/17) < 300

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

The constraints are:

x + y < 200

(24/15) x + (27/17) y < 300

So, the graph of the previous constraints is as following :

Let's begin by listing out the information given to us: