Answer:
\(a = p*q\\b = (p*s)+(q*r)\\c = r*s\)
Step-by-step explanation:
The standard form of trinomial is given as:
\(ax^2+bx+c\)
And the factored form is:
\((px+r)(qx+s)\)
In order to find the values of a,b and c in terms of p,q,r and s we will take the factored form, multiply it and then compare it with the standard form.
So,
\((px+r)(qx+s)\\=px(qx+s)+r(qx+s)\\= pqx^2+psx+qrx+rs\\= pqx^2+(ps+qr)x+rs\)
Now comparing it with the standard form of trinomial
We will compare the co-efficients of x^2, x and the constant
By comparing, we get
\(a = pq = p*q\\b = ps+qr = (p*s)+(q*r)\\c = rs = r*s\)
Hence,
\(a = p*q\\b = (p*s)+(q*r)\\c = r*s\)
divide 2x²+5x+2 by 2x+1
Step-by-step explanation:
hope it helps you mark me as brainlist
Toasty Hands is a manufacturer of battery-powered heated gloves. Its top of the line model currently sells for $279, and it expects sales of 440,000 pairs in the next year. Its estimate of the demand for gloves suggests that if it cuts the price to $239 it could sell 540,000 pairs. What is the absolute value of the elasticity coefficient for Toasty Hands' gloves? Round your answer to two decimals. 1st attempt
The absolute value of the elasticity coefficient for Toasty Hands' gloves is 394,265.23.
The elasticity coefficient is calculated as follows:
Elasticity coefficient = (Change in demand)/(Change in price) * (Original price)/(Original demand)
In this case, the change in demand is 540,000 - 440,000 = 100,000 pairs. The change in price is 239 - 279 = -40. The original price is $279, and the original demand is 440,000 pairs.
Plugging these values into the formula, we get:
Elasticity coefficient = (100,000)/(-40) * (279)/(440,000) = -394,265.23
The absolute value of the elasticity coefficient is 394,265.23. This means that the demand for Toasty Hands' gloves is elastic, meaning that a small change in price will lead to a large change in demand.
Here is a more detailed explanation of the calculation:
The change in demand is calculated by subtracting the original demand from the new demand. In this case, the new demand is 540,000 pairs, and the original demand is 440,000 pairs. So the change in demand is 540,000 - 440,000 = 100,000 pairs.
The change in price is calculated by subtracting the original price from the new price. In this case, the new price is $239, and the original price is $279. So the change in price is 239 - 279 = -40.
The original price is $279, and the original demand is 440,000 pairs.
Plugging these values into the formula, we get the elasticity coefficient of -394,265.23.
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Pete earns $8.50 per hour plus tips. On Tuesday, he received $16 in tips. How many hours did Pete work if he earned a total of $50 on
Tuesday?
Answer:
4 hours .
Step-by-step explanation:
4x8.50=34
34 + 16=50
Answer:
He worked 4 hours i think
Step-by-step explanation:
Take 50 and subtract his tips ($16)
then divide your answer by how much he makes an hour ($8.50)
P varies directly with s and t. If p=10 when s=-8 and t=12, find t when p=6 and s=15
In which quadrant does 0 lie if the following statements are true: cos 0 > and sin> 0
The angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the angle θ lies.
Recall that there are four quadrants in a Cartesian coordinate system: Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.
Since cos(θ) > 0, the angle θ must be in a quadrant where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.
Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
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Instructions: Use the model to fing the area of the shaded region.
Answer: \(\frac{1}{3}\) yds²
Step-by-step explanation:
To find the area, we will multiply 2/3 by 2/4. When multiplying fractions, you multiply straight across.
\(\displaystyle \frac{2}{4} *\frac{2}{3} =\frac{2*2}{4*3} =\frac{4}{12} =\frac{1}{3}\)
We can also use the model, see attached.
b. Take 50 readings c. Determine sample size using a confidence level of 90% and 5% of accuracy. N=( E r
×x
Z α/2
×S
) 2
The sample size required to achieve a 90% confidence level and 5% accuracy is 67. The z-score for the 90% confidence level is 1.645.
The sample size is calculated using the following formula: N = (er × zα/2 × s)²
where:
N is the sample sizeer is the desired accuracyzα/2 is the z-score for the desired confidence levels is the standard deviation of the populationIn this case, we are given that the desired accuracy is 5%, the confidence level is 90%, and the standard deviation of the population is unknown.
The z-score for the 90% confidence level is 1.645.
Therefore, the sample size is:
N = (0.05 × 1.645 × s)²
We do not know the standard deviation of the population, so we must estimate it. We can use the sample standard deviation from the 50 readings that were taken.
The sample standard deviation is 1.5.
Therefore, the sample size is:
N = (0.05 × 1.645 × 1.5)² = 67
Therefore, the sample size required to achieve a 90% confidence level and 5% accuracy is 67.
Here are the steps involved in calculating the sample size:
Identify the desired accuracy and confidence level.Calculate the z-score for the desired confidence level.Estimate the standard deviation of the population.Substitute the values into the sample size formula.Calculate the sample size.The answer is 67.To know more about formula click here
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Over what interval is the function in this graph constant?10-1010-10A. 6 S XS 10B. -10 5 XS-4C. 1 S XS6D. -4$X$1
In a graph, constant functions are represented as horizontal lines. According to this, the function is constant from 1 to 6.
It means that the correct choice is C. 1≤x≤6
Consider a market served by a monopolist, Firm A. A new firm, Firm B, enters the market and, as a result, Firm A lowers its price to try to drive Firm B out of the market. This practice is known as
Predatory pricing. Predatory pricing occurs when a dominant firm intentionally sets its prices below the cost of production or below its competitors' prices in order to eliminate competition and deter new entrants into the market.
In this scenario, Firm A, the monopolist, engages in predatory pricing by reducing its prices in response to the entry of Firm B into the market. The aim is to make it financially difficult for Firm B to survive and eventually force it out of the market. By lowering its prices, Firm A hopes to attract customers away from Firm B and regain its monopoly power.
Predatory pricing is considered an anti-competitive practice and is often illegal in many jurisdictions. It can harm competition, limit consumer choice, and lead to higher prices in the long run. Regulatory bodies and competition authorities closely monitor such practices and may take legal action against firms found engaging in predatory pricing.
Overall, predatory pricing is a strategy employed by dominant firms to protect or strengthen their market position by driving out competitors. However, it is important for regulators to enforce antitrust laws to ensure fair competition and protect the interests of consumers and smaller market players.
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Given the graph of the function f(x), find each of the following.
† y
a. f(-4) 2
b.
f(0) O
C.
f (2) -1
d. f (5) -1
Answer:
a) 2 ; b) 0; c) -2 ; d) -1
Step-by-step explanation:
a) f(-4)=2 ;
b) f(0)=0;
c) f(2)= -2 ;
d) f(5)= -1
Mr. Sharma has the option of selecting a rectangular plot of size 45 m × 25 m or a square plot of
size 35 m at the same price. Which one should he prefer and why?
Answer:
Square Plot
Step-by-step explanation:
Let us compare the Area of both plots
Rectangular Plot : L X B = 45 x 25 = 1125 M^2
Square Plot : S X S = 35 x 35 = 1225 M^2
Area of Square Plot > Area of Rectangular Plot
Therefore he should prefer the Square Plot as it has more area.
Hope it helps.
"The probability of event A given event B is denoted by OP (A or B) OP (A and B) O P(A/B) OP(BIA)
the correct notation to represent the probability of event A given event B is P(A|B).
The correct notation for the probability of event A given event B is P(A|B), which is read as "the probability of A given B." This notation represents the conditional probability of event A occurring, given that event B has already occurred.
On the other hand, OP (A or B) represents the probability of either event A or event B occurring, or their union. This is not the same as the probability of A given B.
Similarly, OP (A and B) represents the probability of both event A and event B occurring, or their intersection. This is also different from the probability of A given B.
OP(A/B) and OP(BIA) are not standard notations in probability theory and are not commonly used to represent conditional probabilities. The correct notation for conditional probability is P(A|B).
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help please
with number 4
Please help 50 points!
Simplify the expressed
Answer:
Step-by-step explanation:
\(\frac{x^{2} -x-12}{x+4} * \frac{2x^{2}-32 }{x^{2} -8x+16}\) rewrite as multiplication
\(\frac{x^{2} +3x-4x-12}{x+4} * \frac{2(x^{2}-16) }{x^{2} -8x+16}\) look to factor
\(\frac{x(x+3)-4(x+3)}{x+4} * \frac{2(x-4)(x+4) }{(x-4)^{2}}\) , difference of 2 squares and perfect square
\(\frac{(x+3)(x-4)}{x+4} * \frac{2(x-4)(x+4) }{(x-4)^{2}}\), finish factoring and simplify
2(x+3)
Examples of distribution
Answer:
see below
Step-by-step explanation:
5(2a+2b+2c)
you must distribute the 5 among the values in parenthesis
4(x-3)
you must distribute the 4 among the values in parenthesis
Hope this helps! :)
Can someone help me with this please :)
Answer:
47.25
Step-by-step explanation:
9 times 10.5=94.5/2=47.25
evaluate
x
— + 6(x-12) when x=12
4
Answer:
3
Step-by-step explanation:
x=12
12/4 + 6(12-12)
12/4 +6(0)
12/4 + 0
3+0
3
Determine the constant of proportionality(k) write the proportional
relationship between and x and y. (Hint: the proportionality is written in the y = k(x)
Answer:
The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k
Step-by-step explanation:
hope it helps
Someone please help am kind of stuck 10 points awarded and brainless please help and thank you
Answer:
157.92 + d = ?
Step-by-step explanation: Since you don't the amount of what his grandmother gave him you substitute the "number" for a letter. Example A or D.
I hope this helps.
Suppose that the mean score for a critical reading test is 580 with a population standard deviation of 115 points. What is the probability that a random sample of 500 students will have a mean score of more than 590? Less than 575? Solve using Excel.
the mean score for a critical reading test, using Excel, the probability that a random sample of 500 students will have a mean score of more than 590 can be calculated to be approximately 0.408.
To calculate the probabilities using Excel, we can utilize the standard normal distribution. First, we need to convert the sample means to z-scores by using the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). For the sample mean of more than 590, we can calculate the probability of z being greater than the corresponding z-score using the formula "=1-NORM.S.DIST(z-score,TRUE)". In this case, the z-score is (590 - 580) / (115 / sqrt(500)), which gives approximately 0.408.
Similarly, for the sample mean of less than 575, we calculate the probability of z being less than the corresponding z-score using the formula "=NORM.S.DIST(z-score,TRUE)". The z-score is (575 - 580) / (115 / sqrt(500)), which gives approximately 0.084.
Therefore, the probability that a random sample of 500 students will have a mean score of more than 590 is approximately 0.408, and the probability that the sample mean is less than 575 is approximately 0.084.
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the heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. what can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 centimeters? write the answer below.
We can be 98% that the margin of error is given as follows:
2.35 centimeters.
How to obtain the margin of error?We have the standard deviation for the sample, hence the t-distribution is used for this problem.
The equation for the margin of error, using the t-distribution, is given as follows:
\(M = t\frac{s}{\sqrt{n}}\)
The parameters are given as follows:
t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 50 - 1 = 49 df, is t = 2.4049.
The remaining parameters, the sample size and the standard deviation for the sample, have values given as follows:
n = 50, s = 6.9.
Hence the margin of error is given as follows:
M = 2.4049 x 6.9/square root(50) = 2.35 centimeters.
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meso- and medi- (meso/derm; medi/al) mean:
"meso-" and "medi-" both relate to the middle or intermediate position, but they may be used in different contexts and have distinct origins (Greek and Latin, respectively).
The prefixes "meso-" and "medi-" have different meanings:
Meso-: The prefix "meso-" generally means "middle" or "intermediate." It is derived from the Greek word "mesos," which carries the same meaning. In scientific and medical terminology, "meso-" is often used to indicate something that is located in the middle or intermediate position.
For example:
Mesoderm: The middle germ layer in the early development of an embryo.
Mesozoic: The era between the Paleozoic and Cenozoic eras, often referred to as the "Age of Reptiles."
Medi-: The prefix "medi-" typically means "middle" or "between." It is derived from the Latin word "medius," which conveys a similar sense. In various contexts, "medi-" is used to indicate something that is in the middle or intermediary position.
For example:
Median: Referring to the middle value in a set of numbers or the middle line or point dividing something into equal halves.
Mediastinum: The central area within the thoracic cavity, located between the lungs, which contains the heart, great vessels, and other structures.
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How to solve this maths equation??? pls help me, its urgent!!! asap
Answer:
x = \(\frac{3wyz}{4wz+wy-2yz}\)
Step-by-step explanation:
Given
\(\frac{2}{w}\) + \(\frac{3}{x}\) - \(\frac{4}{y}\) = \(\frac{1}{z}\)
Multiply through by wxyz to clear the fractions
2xyz + 3wyz - 4wxz = wxy ( subtract wxy from both sides )
2xyz + 3wyz - 4wxz - wxy = 0 ( subtract 3wyz from both sides )
2xyz - 4wxz - wxy = - 3wyz ( factor out x from each term on the left side )
x(2yz - 4wz - wy) = - 3wyz ( divide both sides by (2yz - 4wz - wy )
x = \(\frac{-3wyz}{2yz-4wz-wy}\) ( multiply numerator/ denominator by - 1 )
x = \(\frac{3wyz}{4wz+wy-2yz}\)
What is the answer and please explain how you got it!
Answer:
B- The sales price = the original price - 25% of the originial price
Step-by-step explanation:
What is the surface area of the rectangular pyramid below? (assume they are in cm²) Awnser Choices:
A. 320cm²
B. 440 cm²
C. 471 cm²
D. 251.6 cm²
The Surface area of the rectangular pyramid that is given in the image is: C. 471 cm².
How to Find the Surface Area of a Rectangular Pyramid?The surface area is simply the space covered by the faces of the pyramid . Therefore:
Surface area = area of the rectangular face + the four triangular faces
Note that there are two pairs of identical triangular faces.
Area of the first pair of triangular faces = base * height = 10 * 16.2 = 162 cm²
Area of the second pair of triangular faces = base * height = 12 * 15.8 = 189.6 cm²
Area of the rectangular face = length * width = 12 * 10 = 120 cm².
Surface area of the rectangular pyramid = 120 + 189.6 + 162 = 471.6 cm².
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FIND THE AREA OF THE TRIANGLE!! GEOMETRY!!! SHOW WORK!!
Answer: 72
Step-by-step explanation: Because if you do 18 + 24 + 30
the perimeter of a right triangle is 24 ft, and one of its legs measures 6 ft. Find the length of the other leg and the hypotenuse.
a) 6 ft, 12ft
b) 5 ft, 13 ft
c) 8 ft, 10 ft
d) 7 ft, 11 ft
Answer:
Step-by-step explanation:
We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).
By pythagoras we know that
\(h^2= a^2+b^2.\)
and the perimeter is \(P=h+a+b\).
Since P=24 and a=6 we have these equations:
\(h^2=36+b^2\\24=h+6+b\)
From the last equation we have \(h=18-b\). Replace h in the first equation we get that
\((18-b)^2=36+b^2\)
\(18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8\)
and h=18-8=10
What the least common denominator of the 2, 3/7, 3,4 ?
The least common denominator of the number 2, 3, 4, 7 is found to be 42.
Here, the least common denominator of the following numbers is asked,
2, 3, 4, 7
Now, first understand the meaning of least common denominator, it is basically meant that what is that least common value that will divide all of the four above mentioned numbers. So, it is actually ased about the least common multiple (LCM).
We can find the value which will be a multiple of all those numbers,
4 is multiple of 2 but 3 and 7 are not.
6 is a multiple of 2 and 3 but 7 is not.
42 is the number that is multiple of 6 as well as 7 and it also the smallest number doing so.
So, the least common denominator of 2, 3, 4, 7 is 42.
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Complete question - What is the least common denominator of 2, 3, 7, 4.
For a research project, students are asked to study how often students at an online high school look at social
media while doing schoolwork.
1. Sofie decides to develop a survey.
(a) Give an example of a question she could ask on her survey.
(b) How could Sofie select a simple random sample of students to take her survey?
(c) She gives out 80 surveys but receives only 32 completed surveys. What are the sample and
population for Sofie’s research?
(d) Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. If
Sofie uses only the completed surveys, what conclusion could she make about the percent of all high
school students who use social media while doing schoolwork?
(a) Example question: "How often do you look at social media while doing schoolwork?
(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.
(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.
(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.
(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."
(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.
(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.
To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.
Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.
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Find Sn for the following geometric sequences described.
From the question, the sum of each of the geometric sequence are;
1) 31 3/4
2) 340
3) 11/16
4) -6, 12, -24
What is geometric sequence?
We have that;
Sn = a(1 -\(r^n\))/1 - r
Sn = 16(1 \(- (1/2)^7\))1 - 1/2
Sn = 16(1 - 1/128)/1/2
Sn = 16(127/128) * 2
Sn = 31 3/4
2) Un = a\(r^n\) -1
256 = \(4(4)^n-1\)
64 =\(4^n-1\)
\(4^3 = 4^n-1\)
n = 4
Sn= \(4(4^4 - 1)\)/4 - 1
Sn = 340
3) Since we have a5 then n = 5
Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)
Sn = 33/32 * 2/3
= 11/16
4) 30= a(1 -\((-2)^4\))/1 - (-2)
30 = a(-15)/3
30 = -5a
a = 30/-5
a = -6
Then the first three terms are;
-6, 12, -24
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