11.2.1: using the binomial theorem to find coefficients in binomials. (a) what is the coefficient of x3y4 in (-3x 4y)7? (b) what is the coefficient of x2y7 in (5x - y)9? (c) what is the coefficient of x5y3 in (3x - 4y)8?

The solution of system of equations is (6,-2) or (0,6)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

(6,-2) and (0,6)

The given line graph has coordinates (6,-2) and (0,6)

The given table of values contain the same points (6,-2) and (0,6)

So, the solution of system of equations is (6,-2) or (0,6)

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Answer:

I think the first one is the best answer but you might be expected to say variable. I cannot choose one answer. It all depends what you have been told or what your teacher has said about it.

Myself, I would pick A.

Step-by-step explanation:

Symbols (like letters) that are used to represent numbers which are unspecified.

The problem is that variable is also a possible answer. The problem is that a variable is usually a letter. Symbols do are not used for variables in anything but counting systems.

When you look up the word variable it is defined as a symbol. But that is too confining.

Answer:

the option C

Step-by-step explanation:

have a great day

Answer:

six rolls will cost $3.60

Step-by-step explanation:

unit rate is $0.60 per roll and you multiply that by 6

Answer:

y = -2x + 5

I hope you have a better day tomorrow :)

Answer:

y=2x+5

Step-by-step explanation:

Thx for the points ;)

Answer:

24.35

Step-by-step explanation:

Answer:

when y=1 then x=0.5

Step-by-step explanation:

The graph is provided.

The equation y=4x-1 can be graphed by first graphing the -1 which is the y-intercept in the y=mx+b form. 4=m that is our slope. you can find the lines second point by moving 4 up and 1 to the right. rise/run =4/1. So when you move 4 up and 1 right you get another point on the line (1,3).

You can find out x=0.5 when y=1 by just tracing your finger over the graph and the point when y equals 1 the line intercepts x=0.5. Another screenshot is given.

I hope this helps!

the standard form (ax^2 + bx + c = 0) and intercept form (a(x-x1)(x-x2) = 0) are less helpful for directly determining the hang time

The vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. In the context of hang time, the vertex form allows us to directly read the value of "h," which corresponds to the time at which the ball reaches its highest point, or the peak of its trajectory. The value of "k" represents the height of the ball at its highest point. By identifying the vertex coordinates (h, k), we can determine the time (hang time) it takes for the ball to reach the ground.

In contrast, the standard form (ax^2 + bx + c = 0) and intercept form (a(x-x1)(x-x2) = 0) are less helpful for directly determining the hang time. While they can provide information about the roots or intercepts of the quadratic equation, they do not provide immediate insights into the time the ball spends in the air.

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The population that gives the size of the maximum sustainable yield is 572.45 thousand whales.

To find the population that gives the maximum sustainable yield, we need to determine the maximum point of the function f(p) = -0.0005p^2 + 1.07p. This can be done by finding the vertex of the quadratic equation.

The equation f(p) = -0.0005p² + 1.07p is in the form of f(p) = ap² + bp, where a = -0.0005 and b = 1.07. The x-coordinate of the vertex can be found using the formula x = -b / (2a).

Substituting the values of a and b into the formula, we get:

x = -1.07 / (2 × -0.0005)

x = 1070 / 0.001

x = 1070000

Therefore, the population size that gives the maximum sustainable yield is 1070000 whales.

To find the size of the yield, we need to substitute this population value into the function f(p) = -0.0005p² + 1.07p.

f(1070) = -0.0005 ×(1070²) + 1.07 × 1070

f(1070) = -0.0005× 1144900 + 1144.9

f(1070) = -572.45 + 1144.9

f(1070) = 572.45

The size of the maximum sustainable yield is 572.45 thousand whales.

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Answer:

6c + 4f = 26

Step-by-step explanation:

The probability that the committee contains at least one man is 1 - (probability of selecting only women).

To find the probability, we need to determine the total number of possible committee combinations and the number of combinations with at least one man. There are 9 people (6 women + 3 men) to choose from, and we want to choose a committee of 4.

Total combinations = C(9,4) = 9! / (4!(9-4)!) = 126
Combinations of only women = C(6,4) = 6! / (4!(6-4)!) = 15

To find the probability of at least one man, we'll subtract the probability of selecting only women from 1:

P(at least one man) = 1 - (15/126) = 1 - 0.119 = 0.881

The probability that the committee contains at least one man is approximately 0.881, or 88.1%.

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\((7 + 3) + 42 \times (7 - 3) \)

\(10 + 42 \times 4\)

\(10 + 168\)

\( 178\)

Answer:

178

Step-by-step explanation:

Make sure to follow the order of operations:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

The expression to represent the probability that one marble is yellow and the other marble is red is P(Y and R) = \((^8C_1 \times ^5C_1)\) / \(^{25}C_2\).

Option A is the correct answer.

We have,

P(Y) represents the probability of selecting a yellow marble from the bag.

= \(^8C_1 / ^{25}C_1\)

P(Y) represents the probability of selecting a red marble from the bag.

= \(^5C_1 / ^{25}C_1\)

Now,

The probability that one marble is yellow and the other marble is red.

P(Y and R) = \(^8C_1 \times ^5C_1\) / \(^{25}C_2\)

Thus,

The expression to represent the probability that one marble is yellow and the other marble is red is:

P(Y and R) = \((^8C_1 \times ^5C_1)\) / \(^{25}C_2\)

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The complete question:

A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from the bag. What expression would give the probability that one marble is yellow and the other marble is red?

A. P(Y and R) = \(^8C_1 ~^5P_1 ~^{25}P_2\)

B. P(Y and R) = \(^8C_1 ~^5P_2 ~^{25}P_2\)

C. P(Y and R) = \(^8C_1 ~^5P_2 ~^{25}P_2\)

D. P(Y and R) = \(^8C_3 ~^5P_1 ~^{25}P_2\)

Answer:

\(v = \frac{4}{3} \pi {r}^{3} = \frac{4}{3 } \times \pi \times {3}^{3} = 36\pi = 113.04\)

Answer:

one, x = 7

Step-by-step explanation:

7(x - 2) + 5 = 3 (2x - 1) + 1

reduce:

7x - 14 + 5 = 6x - 3 + 1

x = 7

Answer:

15 cups of coffee

which represents the total number of cups of coffee purchased from the card

Step-by-step explanation:

A = 45 - 3x

45 - 3x = A

45 - 3x = 0

( I kinda got lost here, but if it is a real problem for you like it was for me, I used Cymath, it was really helpful. )

I hope this helps.

Every time the same instrument is used for a measurement, it produces consistent results, which denotes: -reliability.

The degree to which a measurement tool produces consistent, repeatable estimates of what is believed to be a true score at the core.

The same set of people receives the same instrument again. The correlation between the results on the two instruments is what defines dependability. The scores ought to be comparable if the outcomes remain constant over time. How long to wait between the two administrations is the key to test-retest reliability.

Reliability is defined as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions.

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Answer:

I dont get it, what is this?

Step-by-step explanation:

The probability that a randomly chosen person has diabetes is approximately 10.45%.

The probability that a randomly chosen person has diabetes can be calculated by dividing the number of people with diabetes by the total population. Using the given data, we have:

Total population = 100%Probability of having diabetes = 10.5%Number of people with diabetes = 34.2 million

To find the probability of a randomly chosen person having diabetes, we divide the number of people with diabetes by the total population as follows:

Probability of having diabetes = (Number of people with diabetes / Total population) x 100%

= (34.2 million / 327 million) x 100%

= 0.1045 or 10.45%

Therefore, the probability that a randomly chosen person has diabetes is approximately 10.45%.

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Answer:

99

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The coordinates of the image of point Y following these modifications are thus -2.

After these adjustments, the image of point Y has coordinates that are -2.

The coordinates of the image of point Y following these modifications are thus -2.

The complete question is,
The figure below is translated up 2 units and then rotated 180° counterclockwise. What are the coordinates of the image of point Y after these transformations?

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Answer:

112y + 154z

Step-by-step explanation:

-14(-8y-11z) = 112y + 154z

Two minus makes one plus.

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

You need to either graph the equation or manipulate the equation into the standard form for a circle  ( often requiring 'completing the square' procedure)

circle equation:

        (x-h)^2 + (y-k)^2  = r^2    where (h,l) is the center   r = radius

x^2  - 6x      +     y^2 + 10 y  = 2    'complete the square for x and y

x^2 -6x +9    +     y^2 +10y + 25   = 2  + 9   + 25      reduce both sides

(x-3)^2           +  (y+5)^2    = 36     (36 is 6^2   so r = 6)

   center is  3, -5

For instance, the parent function for the quadratic family is y = x². Other functions in the quadratic family, such as y = -(x - 2)² + 3 or y = 3(x + 1)² - 4, are derived from the parent function through transformation.

A family of functions is a group of functions with graphs that display one or more similar characteristics.

The Parent Function is the simplest function with the defining characteristics of the family.

Functions in the same family are transformations of their parent functions.
A family of functions refers to a group of functions that share a common characteristic.

The common characteristic may be the shape of their graphs or the type of equation that they follow.

Examples of functions that belong to the same family are quadratic functions, exponential functions, and trigonometric functions. A

family of functions is defined by its parent function, which is the simplest function that belongs to the family.

Functions in the same family can be derived from the parent function through transformations such as translation, reflection, and dilation.

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The integer that represents the given situation is a positive 31.

The temperature being 31 degrees above zero means that it is warmer than the freezing point of water. In this context, "above zero" refers to the Celsius or Fahrenheit scale, where zero represents the freezing point of water. Therefore, a temperature of 31 degrees above zero is a positive value indicating a warm temperature.

In this case, it can be assumed that the temperature is being measured in Celsius since 31 degrees above zero on the Fahrenheit scale would correspond to a very high temperature of approximately 87 degrees Fahrenheit. Overall, the integer that represents this situation is positive 31, which signifies a warm temperature above the freezing point.

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Answer:24

Step-by-step explanation:

Answer:-1/12

Step-by-step explanation:

16x=64x+4

16x-64x-4

-48x=4

x=4/-48

Ans:-1/12

Answer:

\(\huge\boxed{\sf x = -1/12}\)

Step-by-step explanation:

\(\sf 16x = 64x+4\\\\Subtract \ 64x \ to \ both \ sides\\\\16x-64x=4\\\\-48x = 4\\\\Divide \ -48 \ to \ both \ sides\\\\x= 4 / -48\\\\x = - 1 / 12\\\\\rule[225]{225}{2}\)

Hope this helped!

a

(4.5, 0) and (5, 0)

The x-intercept of the parabola represents the point where the parabola graph intersects the x-axis. In other words, these are the x values where the y coordinate is 0.

Using the information given, we can observe that the parabola falls from the left, passes through the point (3, 2), reaches the minimum point, then rises to the right and passes through the point (6, 2) .

Since the parabola intersects the x-axis at the x-intercept, we can conclude that the x-intercept is the point where the y-coordinate is 0. In this case, x values of 4.5 and 5 will have a y coordinate of zero. So the x-intercepts of the parabola are (4,5,0) and (5,0).