Mark has taken four tests so far this quarter. His grades were 88%, 95%, 80%, and 92%. What is the mean of his test scores?

Answer:

b² + 10b + 21

Step-by-step explanation:

First: b²

Outer: 7b

Inner: 3b

Last: 21

b² + 7b + 3b + 21 =

b² + 10b + 21

Answer:

\((b + 3)(b + 7) \\ b(b + 7) + 3(b + 7) \\ b {}^{2} + 7b + 3(b + 7) \\ b {}^{2} + 7b + 3b + 21 \\ b {}^{2} + 10b + 21\)

hope this will help u :)

The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

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The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

We break up a number according to its place value and expand it to show the value of each digit.

Given that to write expanded form of 706.039

Expanded Factors Form:

706.039 = 7 × 100  + 0 × 10 + 6 × 1  + 0 × 0.1 + 3 × 0.01 + 9 × 0.001

Expanded Notation Form:

706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

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The function is y = 3(x+3)^2-9

The equation of a parabola is

y=a(x-h)^2+k

where (h,k) are the coordinates of the vertex and a, is a constant.

From the question, we have

(h,k)=(-3,-9)

⇒y=a(x+3)^2-9

To find a, substitute x=-2,y=-6

-6=a(-2+3)^2-9

⇒a=3

The equation, y=3(x+3)^2-9

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer: E

Step-by-step explanation:

Answer: As we know that the formula of outlier is

IQR = Q3 - Q1

= 52 - 32

= 20

52 + 1.5(20) = 82...

so anything above 82 is an outlier

now

32 - 1.5(20) = 2.

..anything below 2 is an outlier

so...the 83 is outlier

so correct option is D

hope it helps

Step-by-step explanation:

Answer:

9/5

Step-by-step explanation:

Answer:

$25.08

Step-by-step explanation:

$48 to which you apply the 50%

48/2= $24

then you add the sales tax:

24+4.5%= 25.08

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

a) The nonzero vector orthogonal to the plane through the points P, Q and R is (0, 10, -10).

b) The area of the triangle PQR is \(5\sqrt{2}\).

Step-by-step explanation:

The statement is incomplete. The complete question will be presented below:

Consider the points below: P(2, 0, 2),  Q(−2, 1, 3),  R(4, 2, 4)

(a) Find a nonzero vector orthogonal to the plane through the points

P, Q,  and R. (b) Find the area of the triangle PQR.

a) Let \(P(x,y,z) = (2,0,2)\), \(Q(x,y,z) = (-2,1,3)\) and \(R(x,y,z) = (4,2,4)\). First, we construct vectors PQ and PR by using the following formulas:

\(\overrightarrow{PQ} = Q(x,y,z) -P(x,y,z)\) (1)

\(\overrightarrow{PQ} = (-2,1,3)-(2,0,2)\)

\(\overrightarrow{PQ} = (-4,1,1)\)

\(\overrightarrow{PR} = R(x,y,z) -P(x,y,z)\) (2)

\(\overrightarrow{PR} = (4,2,4)-(2,0,2)\)

\(\overrightarrow{PR} = (2,2,2)\)

Then, we can find the nonzero vector orthogonal to the plane by means of the following cross product:

\(\vec S = \overrightarrow{PQ}\,\times\,\overrightarrow{PR}\)

Which can be solved by the following determinant (Law of Sarrus):

\(\vec S = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4&1&1\\2&2&2\end{array} \right |\)

\(\vec S = (2-2,2+8, -8-2)\)

\(\vec S = (0, 10,-10)\)

The nonzero vector orthogonal to the plane through the points P, Q and R is (0, 10, -10).

b) The area of the triangle is determined by the following formula:

\(A = \frac{1}{2}\cdot \|\overrightarrow{PQ}\,\times\,\overrightarrow{PR} \|\)

\(A = \frac{1}{2}\cdot \|\vec S\|\) (3)

\(A = \frac{1}{2}\cdot \sqrt{0^{2}+10^{2}+(-10)^{2}}\)

\(A = 5\sqrt{2}\)

The area of the triangle PQR is \(5\sqrt{2}\).

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

Answer:

-36-128b

Step-by-step explanation:

Simply take -36 out of the parentheses to get -36-128b.

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

2 quarts of 100% antifreeze.

Step-by-step explanation:

5 quarts/ .40 * x/ 1

.40x= 5

x=2

2 quarts of pure antifreeze must be added to 5 quarts of a 40​% antifreeze solution to obtain a 50​% antifreeze​ solution.

Looking at the concentrations.

100% of x quarts is x quarts of antifreeze.

30% of 5 quarts is .3(5) quarts antifreeze.

Adding that we have 5+x quarts and we want

50% of that to be antifreeze so the total is

.5(x + 5)

x + .3(5) = .5(5+x)

x + 1.5 = 2.5 + .5x

x - .5x = 2.5 - 1.5

.5x = 1

x = 1/.5 = 2 quarts pure antifreeze.

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The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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Answer:(2x+7)+(2x+7)

Step-by-step explanation:

what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer

Answer:

C

Step-by-step explanation:

70+20=90 and thats a right angle which is 90°

Answer:

-13

Step-by-step explanation:

-3(2) = -6

2(-6) -1

-12-1= -13

Answer:

the answer is= 2.5

Step-by-step explanation:

good luck!

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

I believe it will be 55.9 or 56 along the roadway

Step-by-step explanation:

Hope this Helped

The  number of 50¢ coins is 200, number of  25¢ coins is 360

and number of  10¢ coins is 160.

The quantitative relation between two or more amounts showing the number of times one value is contains or contained within other.

Now the given ratio is 5 : 9 : 4.

and total amount of the coins is $206.

There are three types of coins in the bag, 50¢, 25¢ and 10¢.

Suppose x be the the ratio of coins in the bag.

Hence, number of  50¢ coins = 5x

number of  25¢ coins = 9x

number of  10¢ coins = 4x

Now, given total amount = $206

and since $1 = 100¢

⇒ ($0.5)(5x) + ($0.25)(9x) + ($0.1)(4x) ¢ = $206

Solving them,

⇒ 2.5x + 2.25x + 0.4x = 206

⇒ 5.15x = 206

⇒ x = 40

Therefore,

number of  50¢ coins = 5*40 = 200

number of  25¢ coins = 9*40 =  360

number of  10¢ coins = 4*40 =  160

Hence, number of 50¢ coins is 200, number of  25¢ coins is 360

and number of  10¢ coins is 160.

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Answer:

Colour ---- Probability

Blue ----- 0.2

Red ------- 0.4

Yellow ------ 0.4

Step-by-step explanation:

Given

Colour ---- Probability

Blue ----- 0.2

Red -------

Yellow ------

Required

Complete the table

In probability, all probabilities add up to 1.

i.e.

\(P(Blue) + P(Red) + P(Yellow) = 1\)

Substitute 0.2 for P(Blue)

\(0.2 + P(Red) + P(Yellow) = 1\)

\(P(Red) + P(Yellow) = 1 - 0.2\)

\(P(Red) + P(Yellow) = 0.8\)

From the question, we understand that the frequency of yellow and red balls are the same.

Hence:

\(P(Red) = P(Yellow)\)

\(P(Red) + P(Yellow) = 0.8\) becomes

\(P(Red) + P(Red) = 0.8\)

\(2P(Red) = 0.8\)

Make P(Red) the subject

\(P(Red) = 0.4\)

Recall that:

\(P(Red) = P(Yellow)\)

Hence,

\(P(Yellow) = 0.4\)

So, the complete table is:

Colour ---- Probability

Blue ----- 0.2

Red ------- 0.4

Yellow ------ 0.4

\(\displaystyle\frac{3}{16}\)

Probability represents the likelihood of an event occurring. Complex probability is the likelihood of a series of events occurring.

Independent Events

The question states that the marbles are replaced after being recorded. This means that the separate drawing of marbles is independent of each other. So, the probability of an event occurring does not change based on events that happened earlier.

This is important to this question because it means that probability does not change based on if the one red marble was drawn first or second.

Probability of a Red

First, we need to find the probability of drawing a red marble. Probability is represented as the number of successful outcomes (drawing a red) over the number of possible outcomes (number of marbles). Out of the total 12 marbles, 3 of them are red. So, the probability of drawing a red is \(\displaystyle\frac{3}{12}\).

The Complement

In probability, the complement is the likelihood of an event not occurring. So, in this situation, the complement is the likelihood of not drawing a red. Out of the total 12 marbles, 9 are NOT red. So, the complement is \(\displaystyle\frac{9}{12}\).

Complex Probability

To find the probability of 2 different events both occurring, multiply the probabilities together.

Then, we can simplify the fraction by dividing by 9

This means that the probability of drawing exactly one red is 3/16.