Answer:
y = -4x - 10
Step-by-step explanation:
y-6=-4(x+4)
1: distributive property
y-6= -4x - 16
2: add 6 both sides
y = -4x - 10
What are the 4 types of values?
Thousands, hundreds, tens and ones are four types of values and there are many more.
What is value?Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.
What is the value of 4?The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.
Thousands, hundreds ,tens and ones are four types of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.
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I really need help What is the image point of (9,3) after the transformation r x-axis ∘D 1/3?
The image point of (9,3) after the transformation r x-axis is (-9, -3 ).
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
Since we know that Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Therefore, Under a counterclockwise
a point (x, y ) → (- x, - y ) , thus
(9, 3 )→ (-9, -3 )
Therefore, the image point of (9,3) after the transformation r x-axis is (-9, -3 ).
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Suppose we are interested in investigating the prevalence of diabetes in the Canadian retirement-age population. Suppose we collect a simple random sample of 145 Canadians of retirement age (65+), and ask each whether or not they have diabetes. We find that the sample proportion of individuals who have diabetes in our sample is 0.20. a. Who are the individuals in this study? What is the variable in this study? b. Suppose, only for the purpose of part (b) of this question, that the true proportion of Canadians of retirement age who have diabetes is actually 0.25. i. If we were to take many SRSs of size 145, what would be the approximate sampling distribution of the resulting sample proportions? Show your work. ii. Based on this sampling distribution, what is the probability of observing a sample proportion as small as what we observed (0.20)? Show your work. c. As mentioned above, the sample proportion of individuals who have diabetes in our sample is 0.20. Using this value, construct a 95% confidence interval for the true proportion, p. Show your work
a. The individuals in this study are Canadians of retirement age (65+). The variable in this study is whether or not they have diabetes.b. Suppose, only for the purpose of part (b) of this question, that the true proportion of Canadians of retirement age who have diabetes is actually 0.25.
i. If we were to take many SRSs of size 145, the approximate sampling distribution of the resulting sample proportions would be a normal distribution with a mean of 0.25 and a standard deviation of \(sqrt((0.25(1-0.25))/145)=0.04/12=0.0333.\)This is because the sample size is large (n > 30) and we assume the sampling distribution to be normal.
ii. Based on this sampling distribution, the probability of observing a sample proportion as small as what we observed (0.20) is calculated as follows: Z = (0.20 - 0.25) / 0.0333 = -1.50P(Z < -1.50) = 0.0668 or 6.68%.
Therefore, the probability of observing a sample proportion as small as what we observed (0.20) is 6.68%.
c. Using the sample proportion of 0.20, the 95% confidence interval for the true proportion p is calculated as follows:
Margin of error = 1.96 x sqrt((0.20(1-0.20))/145) = 0.055
Interval = 0.20 ± 0.055 = (0.145, 0.255)
Therefore, we are 95% confident that the true proportion of Canadians of retirement age who have diabetes is between 0.145 and 0.255.
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Help please I don’t understand
Answer:
x=0.75645 in radians
x=43.34175 in degrees
Step-by-step explanation:
cos(x)=8/11
Answer:
approximately 46.66
Step-by-step explanation:
label the following sides as 11=h and 8=o.
circle the missing angle x
remember SohCahToa
since you have h and o that means you are using (sin) on your calculator and since the angle is missing you do the inverse of sin multiplied by (8/11)
1) To the nearest tenth of a foot, what is the distance from the wall to
the base of the ladder?
A) 1.9 feet
B)2.1 feet
C)4.5 feet
D)10.7 feet
the answer might be C=4.5 feet
2 triangle Figures, A 2m volume 30cu m, B 5m what is the volume of B?? Please help me with this one.
The volume of B is given as follows:
468.75 m³.
How to obtain the volume of B?The volume of B is obtained applying the proportions in the context of the problem.
The ratio between the side lengths is given as follows:
Figure A/Figure B = 2/5
As the side lengths are given in units, and the volume is given in cubic units, the ratio of the volumes is given as follows:
Va/Vb = (2/5)³
Va/Vb = 8/125.
Then the volume of B is obtained as follows:
30/Vb = 8/125
8Vb = 30 x 125
Vb = 30 x 125/8
Vb = 468.75 m³.
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The graph below shows a company’s profit f(x) in dollars depending on the price of pens x, in dollars, sold by the company What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing and what do they represent about the sale and profit? What is an aproxímate average rate of change of the graph from x=3 to x=5 and what does this rate represent?
Solution:
Given:
\(\begin{gathered} f(x)=profits \\ x=price\text{ of pens} \end{gathered}\)From the graph, the x-intercept exists at (0,0) and (6,0).
The maximum value is (3,120).
The x-intercept represents the break-even points. The company was not in profit or loss when no pen was sold and when 6 pens were sold, the profit was $0 at these two points.
The maximum value of the graph represents the maximum profit made by the company. The company made a maximum profit of $120 when 3 pens were sold.
The interval where the function is increasing is from negative infinity to x = 3. This shows that the more pen sold, the higher the profit made.
The interval where the function is decreasing is from x = 3 to positive infinity. This shows that the less pen sold, the lower the profit made.
The approximate average rate of change of the graph from x = 3 to x = 5 is;
\(\begin{gathered} ARC=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\ where: \\ x_1=3 \\ x_2=5 \\ f(x_1)=120 \\ f(x_2)=60 \\ \\ Hence, \\ ARC=\frac{60-120}{5-3} \\ ARC=\frac{-60}{2} \\ ARC=-30 \end{gathered}\)The rate represents a decrease of $30 for every pen sold across the decreasing interval.
) find the number of ways to distribute 10 identical cards into 3 boxes, where each box has at least one card.
Numbers of ways to distribute 10 identical cards into 3 boxes is 36
Combination is is a way of selecting items from a collection where the order of selection does not matter.
Formula of combination:
Let a x-combination of a set is a subset of x distinct elements of S. If the set has n elements, the number of x-combinations is equal to the binomial coefficient.
ⁿCₓ = n(n-1)(n-2)(n-3). . . (n-x+1) / (x-1)(x-2)(x-3) . . . .(1)
which can be written as ⁿCₓ = n! / (n-x)! x! , when n > x
ⁿCₓ = 0 , when n < x
Where n = distinct object to choose from
C = Combination
x = spaces to fill
According to the question,
Number of identical cards : n =10
Number of box cards are being distributed : x = 3
Number of ways to distribute when no condition is given : ⁿ⁺ˣ⁻¹Cₓ₋₁
If we place one one card in each box then
Number of cards left with us = 10 - 3
= 7
Now, condition of at least one cards in each box is satisfied ,
Then total number of ways to distribute 7 cards into 3 = ⁷⁺³⁻¹C₃₋₁
=> ⁹C₂ = 9! / (9 - 2)! 2!
=> 9×8×7! / 7!2!
=> 9×8/2
=> 9×4
=>36 ways
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how do you find B and M in y = 9 - 5x ?
For the linear function y = 9 - 5x, it is found that:
The coefficient M is the slope of M = -5.The coefficient B is the intercept of B = 9.How to identify coefficients m and b in a linear function?A linear function, in slope-intercept format, is modeled according to the following rule below:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).In the context of this problem, the linear function is modeled as follows:
y = 9 - 5x.
In standard format, with the slope in front, we have that:
y = -5x + 9.
Meaning that the coefficients are given as follows:
m = -5, which is the slope of the function.b = 9, which is the intercept of the function.More can be learned about linear functions at https://brainly.com/question/24808124
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if rs=44 and qs=68 find qr.
Answer:
qr=68r/s
Step-by-step explanation:
rs=44
s=44/r
qs=68
q(44/r)=68
44q/r=68
44q=68r
q=68r/44
rs=44
r=44/s
qr=(68r/44)(44/s)=68r/s
solve n-3 = 4 x 3 - n/ 7
Solve n-3 = 4 x 3 - n/7 : n = 105/8
What is Algebra?
Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.
To solve the equation :
n-3 = 4 x 3 - n/7
Solve for n
n-3 = 4 x 3 - n/7
n - 3 = 12 - n/7
n = 12 + 3 - n/7
n = 15 - n/7
n = (105 - n)/7
7n = 105 - n
7n + n = 105
8n = 105
n = 105/8
Hence, solution for n-3 = 4 x 3 - n/7 is n = 105/8
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5+5?????????????????????????????????????????/
Answer:
Hello There!!
Step-by-step explanation:
Here is your answer:5+5 eqauls 10.
hope this helps,have a great day!!
~Pinky~
A fresh fish retailer receives a shipment of sardines in sealed packs. Together, there were 3 pounds in 12 packs. If the retailer received 48 packs of sardines, how many pounds were in the shipment?
Answer:
So, the question is asking how many pounds are there in 48 shipments if ever 12 shipments are 3 pounds, so what you want to do is so how many times 12 will go into 48 and then multiply that by 3!
48/12 = 4
4 * 3 = 12
The total 48 shipments weigh 12 pounds!
Step-by-step explanation:
Hope it helps! =D
Answer:
The weight of one pack of sardines is 3 pounds / 12 packs = 0.25 pounds/pack
So the weight of 48 packs of sardines is 0.25 pounds/pack * 48 packs = 12 pounds.
HELP ASAP
The table shows input and output values of a function given a rule. Which function
represents the rule?
Input: x, a number; Output: y, 3 less than 2 times x
Input, x: -2 -1 0 1 2
Output, y: -7 -5 -3 -1 1
y=2x+3
y=2x-3
y=-3x+2
y=2x
Answer:I think its A.
Step-by-step explanation:
I'm too lazy too explain you got your answer please be happy
Do you have $20 to spend on a taxi fare ride cost five dollars +250 per kilometer right in any quality determine the distance in kilometers de you can write for $20
Answer: 6
just beleive me
Which equations for the measures of the unknown
angles x and y are correct? Check all that apply.
x = costa
x= sin" E)
x= tan'a
y= sin "(a)
y = cos-'
The correct equations for the measures of the unknown angles x and y are:
x = cos(a), y = sin(a).
The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:
sin(a) = opposite side / hypotenuse
cos(a) = adjacent side / hypotenuse
tan(a) = opposite side / adjacent side
In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).
The inverse trigonometric functions\((sin^-1, cos^-1, tan^-1)\) are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:
\(sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))\)
So, the correct equations for the measures of the unknown angles x and y are:
\(x = cos^-1(x)y = sin^-1(y)\)
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which of the following could be the graph of f(x)=-a(x+b)^1/2 if both a and b are positive numbers
Answer:
Option D.
Step-by-step explanation:
We have the function:
f(x) = -a*(x + b)^(1/2)
Where:
a > 0
b > 0
Now, as a is positive and we have the coefficient "-a", we will have that the function is always negative.
Why? because (x + b)^(1/2) is always positive.
then: -a*(x + b)^(1/2) is always negative.
We also should see that the domain is not the set of all real numbers, because if:
x + b < 0, then we have the square root of a negative number, and we know that this is a complex number.
The only option that meets these two conditions is option D.
Answer
C
Step-by-step explanation:
Got it mf wrong
This type of research is intended to be carried out by any professional, in any type of school, to investigate a problem. The findings are limited in their generalizability. a. Historical research. b. Survey research. c. Action research. d. Ethnographic study.
The correct option is:
c. Action research
What type of research is conducted by professionals in any type of school to investigate a problem, with findings that may have limited generalizability?
The type of research conducted by professionals in any type of school to investigate a problem, with findings that may have limited generalizability, is known as action research.
c. Action research.
Action research is a type of research that is intended to be carried out by professionals in any type of school setting to investigate a specific problem or issue. The focus of action research is on practical solutions and making improvements within a particular context.
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which of the following is an si base unit for measuring temperature? 1) Celsius 2) Degrees 3) Fahrenheit 4) Kelvin
The SI base unit for measuring temperature is 4) Kelvin. Temperature is a physical quantity that measures the degree of hotness or coldness of an object or a system.
The International System of Units (SI) is a globally accepted system of measurement. In SI, temperature is measured using the Kelvin (K) scale, which is the SI base unit for temperature.
The Kelvin scale is based on the absolute zero point, which is the lowest possible temperature where all molecular motion ceases. Absolute zero is defined as 0 Kelvin (0 K). Temperature increments on the Kelvin scale are equivalent to increments on the Celsius scale, with 1 Kelvin being equal to 1 degree Celsius.
The other options listed, such as Celsius and Fahrenheit, are not SI base units for temperature but are commonly used in everyday contexts. Celsius (°C) is widely used in many countries and is based on the Celsius scale, which sets the freezing point of water at 0°C and the boiling point of water at 100°C at sea level. Fahrenheit (°F) is used mainly in the United States and a few other countries and has its freezing point at 32°F and boiling point at 212°F at sea level. However, neither Celsius nor Fahrenheit is considered an SI base unit for temperature.
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I-Ready
Describe Angle Relationships in Triangles - Quiz - Level H
The figure shoys a triangle with unknown angles.
Which equation shows the relationship between the angles in the triangle?
mL1 + mL2 + mL3 = 360°
mL1 + mL2 + mL3 = 180°
mL1 + mL2 = 360° + mL3
mL1 + mL2 = 180° + mL3
The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.
What is the relationship between the angles of the triangle?The equation that shows the relationship between the angles in the triangle is determined as follows;
The sum of angles in a triangle is equal to 180 degrees.
So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;
angle 1 + angle 2 + angle 3 = 180
We can re-write the equation as follows;
m∠1 + m∠2 + m∠3 = 180
Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.
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The length of one kind of fish is normally distributed. The average length is 2.5 inches, with a standard deviation of 0.4 inches. What is the probability that the average length of 100 randomly selected fishes is less than 2.4 inches
There is only a 0.62% chance that the average length will be less than 2.4 inches. Therefore, we can conclude that it is unlikely for the average length of 100 randomly selected fish to be less than 2.4 inches.
Use the central limit theorem, which states that the distribution of sample means will be approximately normal regardless of the distribution of the population, as long as the sample size is large enough.
In this case, we are given that the length of one kind of fish is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.4 inches. We want to find the probability that the average length of 100 randomly selected fish is less than 2.4 inches.
To apply the central limit theorem, we need to calculate the mean and standard deviation of the sampling distribution of the sample mean. The mean of the sampling distribution will be equal to the population mean, which is 2.5 inches. The standard deviation of the sampling distribution can be calculated using the formula:
standard deviation = population standard deviation / square root of sample size
In this case, the population standard deviation is 0.4 inches, and the sample size is 100, so:
standard deviation = 0.4 / sqrt(100) = 0.04 inches
Now that we have the mean and standard deviation of the sampling distribution, we can use the z-score formula to find the probability of obtaining a sample mean of less than 2.4 inches:
z = (sample mean - population mean) / standard deviation
z = (2.4 - 2.5) / 0.04 = -2.5
Using a standard normal distribution table, we can find that the probability of obtaining a z-score of -2.5 or less is approximately 0.0062. This means that the probability of obtaining a sample mean of less than 2.4 inches is approximately 0.0062.
In other words, if we were to randomly select 100 fish from this population and calculate the average length, there is only a 0.62% chance that the average length would be less than 2.4 inches. Therefore, we can conclude that it is unlikely for the average length of 100 randomly selected fish to be less than 2.4 inches.
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A diver is 4 meters below sea level. What integer represents the location of the diver?
Answer:
-4
Step-by-step explanation:
When talking about integers key words like below or anything being Loss means Negative.And anything relating to an positive like above or receive means positive which means anything that your gaining or getting.
A system of inequalities is shown.
A graph of two parabolas. The first is a solid upward opening parabola with a vertex at 1 comma 3 and passing through negative 1 comma 7 and 3 comma 7 with shading inside the parabola. The second is a dashed downward opening parabola with a vertex at 0 comma 4 and passing through negative 2 comma 0 and 2 comma 0 with shading inside the parabola.
Which system is represented in the graph?
y < x2 – 2x + 4
y < x2 + 4
y ≥ x2 – 2x + 4
y < –x2 + 4
y ≥ x2 – 2x + 4
y ≤ –x2 + 4
y > x2 – 2x + 4
y ≤ x2 + 4
The system which is represented in the graph is: y > \(x^{2}\) – 2x + 4
y ≤ \(x^{2}\) + 4
(h, k) = (1, -4), p = \(\frac{1}{4}\)
\(y > x^{2} -2x-3\)
rewrite y > \(x^{2} -2x-3\) in the standard form
\(4.\frac{1}{4} (y-(-4))=(x-1)^{2}\)
y ≤ \(x^{2}\) + 4
therefore parabola properties are:
(h,k) = (1, -4), p= \(\frac{1}{4}\)
The basic parabola has the accompanying properties: It is symmetric about the y-axis, which is an axis of symmetry. The base worth of y occurs at the beginning, which is a base-defining moment. It is also called the vertex of the parabola. The arms of the parabola go on indefinitely.
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A 150-pound person uses 4.8 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 250
calories?
Answer:
52.083
Step-by-step explanation:
1 min = 4.8 calories
? min=250calories
at the age speed
250/4.8 calories
=52.083min
Will make brainliest! Show work please!
The missing sides of the right triangle are DE = 4.195 and DF = 6.527 and the missing angle is 50°.
How to determine the missing sides and angles of a right triangle
In this question we find a right triangle with a known side and two known angles. The missing sides can be found by following trigonometric functions:
tan F = DE / EF
cos F = EF / DF
And the angle D is found by the following expression:
D = 90° - F
If we know that EF = 5 and F = 40°, then missing sides and angle are, respectively:
DE = EF · tan F
DE = 5 · tan 40°
DE = 4.195
DF = EF / cos F
DF = 5 / cos 40°
DF = 6.527
D = 90° - 40°
D = 50°
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how to know which way to solve a quadratic equation
Answer:
Practice -- lots of it
Step-by-step explanation:
I usually choose a solution method that I believe will find the desired answer for me in the least number of simple steps. What constitutes a "simple" step depends on a number of things:
the given information and/or the given form of the equationfamiliarity with all of the different solution processesfamiliarity with arithmetic facts (multiplication tables, squares)familiarity with quadratic forms: difference of squares, perfect square binomials, product of binomials, vertex formavailability of a graphing calculatorwhether an approximation will serve the purpose.__
I often choose a graphing calculator as my first approach to solving a quadratic. It easily shows the roots, and can show the vertex. (Sometimes, scaling the graph is required, so I actually prefer to use a touch-screen for the purpose. It is easier to "pinch" than to type in possible graph limits by trial and error.) The answer is generally provided to 3 or 4 significant figures, which is usually enough to tell if the solution is rational or irrational.
The easiest way to describe an integer (or rational) solution to someone else (on Brainly, for example) is usually to show the factoring of the quadratic. Finding the roots with a graphing calculator significantly aids the factoring process. (It is much easier to "find" the solution if you know the solution before you start looking.)
__
As we said at the beginning, the answer to your question is "practice." Many curricula try to offer opportunities to practice. I find most of these pretty annoying. What I suggest is that you find your own internal motivation to practice solving different kinds of quadratics in several different ways. That is, solve the same quadratic by ...
using the formulacompleting the squarefactoringgraphing (with a graphing calculator)scaling and/or translation and/or transformation*It might take you a couple of hours of work to learn the best way to solve an equation in under 5 minutes.
In this process, you will discover what you need to know to choose a method that works nicely for you. I believe you will find that total familiarity with arithmetic facts (sums, products, squares) and operations on all the different ways to represent numbers (integer, decimal, fraction, percent, scientific notation) will help you significantly.
_____
* Additional comment
Some "area" problems give you the difference of dimensions (length and width), and ask you to find the dimensions that give a specific area. This can be solved by (x)(x -d) = A. If you don't immediately recognize factors of A that differ by d, then you might have to resort to the quadratic formula to solve this.
Another approach is to let the variable represent the average dimension. Then the equation becomes (x -d/2)(x +d/2) = A, which is a "difference of squares" form that is much more easily solved. The solution for x is √(A +(d/2)²), and all you have to do is add and subtract d/2 from that solution to find the dimensions. This is an example of what I mean by transforming the problem.
A number is multiplied by 3. Next, 6 is added to the product. Then, the sum is divided by 8. If the result is 6, what is the number?
Answer:
14
Step-by-step explanation:
14 x 3 = 42
42 + 6 = 48
48 ÷ 8 = 6
Therefore, the answer is 14.
Answer:
14
Step-by-step explanation:
let us call the number x for now
the number (x) is multiplied by 3 to give us
3x
then,
it is added to 6 to give
3x + 6
then, our sum is divided by 8:
(3x + 6) / 8
according to the question, the result is 6
therefore,
3x + 6 / 8 = 6
if we cross multiply,
3x + 6 = 8 ( 6 )
3x + 6 = 48
collecting like terms,
3x = 48 - 6
3x = 42
divide through by 3 to give
3x / 3 = 42 / 3
x = 14
therefore, x = 14
to reassure us of our answer,
since (3(x) + 6) / 8 = 6
and we know that x = 14,
therefore,
(3(14) + 6) / 8 = 6
(42 + 6) / 8 = 6
48 / 8 = 6
6 = 6
therefore, we are now sure that x = 14
hope this helps
thanks
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied.
Surveying 20 college students and recording their favorite TV showSurveying 20 college students and recording their favorite TV show.
Choose the correct answer below.
A. No, because there are more than two possible outcomes and the trials are not independent.
B. Yes comma because all 4 requirements are satisfied.Yes, because all 4 requirements are satisfied.
C. No comma because there are more than two possible outcomes.No because there are more than two possible outcomes.
D. No, because the probability of success does not remain the same in all trials.
The given procedure does not result in a binomial distribution because it does not satisfy the criteria of having only two possible outcomes and independent trials.
No, this procedure does not result in a binomial distribution. In order for a distribution to be binomial, it must meet four criteria: (1) there must be a fixed number of trials; (2) the trials must be independent; (3) there must be only two possible outcomes (i.e., success or failure); and (4) the probability of success must remain the same in all trials.
In the given procedure, there are more than two possible outcomes (i.e., the different TV shows that the college students can choose) and the trials are not independent. Therefore, the procedure does not satisfy two of the four criteria necessary for a binomial distribution.
A binomial distribution can be described by the formula:
\(P(x) = nCx * p^x * (1 - p)^(n - x)\)
where n is the number of trials, x is the number of successes, and p is the probability of success. Since the given procedure does not meet the criteria for a binomial distribution, this formula does not apply.
The given procedure does not result in a binomial distribution because it does not satisfy the criteria of having only two possible outcomes and independent trials.
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I need steps for this....
The discriminant is 60 and the equation has two real roots with parabola intersecting x - axis at two points.
We are given that the equation is \(-3x^{2} +6x +2 = 0\)
The formula for discriminant is given by
D = \({b^{2} -4ac}\) where the equation is of the form \(ax^{2} + bx + c = 0\)
Therefore,
a = -3
b = 6
c = 2
Putting these values in formula of discriminant, we get
D = \({6^{2} - 4(-3)(2) }\)
D = 36 +24
D = 60
For the quadratic equation \(ax^{2} + bx + c = 0\) , the expression D = \(b^{2} - 4ac\) is called the discriminant.
The value of the discriminant shows how many roots does the quadratic equation has:
If D > 0 then the quadratic equation has two distinct real roots.If D = 0 then the quadratic equation has one repeated real root.If D < 0 then the quadratic equation has no real roots.Now, since D = 60 > 0, we can say that the equation has two real roots and therefore, the parabola is intersecting the x-axis at two places.
To learn more about discriminant of quadratic equations, refer to:
https://brainly.com/question/9970081
The temperature in the morning was -3.5 °F. By noon, the temperature had dropped by 1.5 °F. Write an addition expression to represent this scenario.
Answer: (-3.5 + (-1.5))
Step-by-step explanation:
Given the expression :
The temperature in the morning was -3.5 °F. By noon, the temperature had dropped by 1.5 °F. Write an addition expression to represent this scenario.
Morning temperature : - 3.5°F
By Noon : change (drop) in temperature
Addition expression to represent the scenario :
A drop in temperature means a further reduction in the initial temperature level :
Addition expression :
(Morning temperature + ( - drop in temperature))
(-3.5 + (-1.5))