what is the slope y intercept and equation?

Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for quality control. Suppose a random sample of 50 amplifiers is taken from a month's production..

What is the probability that less than 40 of the amplifiers will meet the company's quality standards? b) What is the probability that between 40 and 45 inclusive of the amplifiers will meet the company's quality standards? c) What is the probability that more than 45 of the amplifiers will meet the company's quality standards? a) In order to solve for the probability that less than 40 amplifiers will meet the company's quality standards, we can use the binomial distribution formula: P(X < 40) = Σi=0^39 C(50, i) (0.85)i(1-0.85)50-i

This can be solved using a computer, calculator, or by using a binomial probability table. Using a binomial table, we can find that P(X < 40) = 0.024. Therefore, there is a 0.024 probability that less than 40 amplifiers will meet the company's quality standards. b) To solve for the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards, we can use the binomial distribution formula again. We need to solve for P(40 ≤ X ≤ 45): P(40 ≤ X ≤ 45) = Σi=40^45 C(50, i) (0.85)i(1-0.85)50-i This can also be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(40 ≤ X ≤ 45) = 0.435. Therefore, there is a 0.435 probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards. c) To solve for the probability that more than 45 amplifiers will meet the company's quality standards, we can use the binomial distribution formula one more time. We need to solve for P(X > 45): P(X > 45) = Σi=46^50 C(50, i) (0.85)i(1-0.85)50-i Once again, this can be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(X > 45) = 0.056. Therefore, there is a 0.056 probability that more than 45 amplifiers will meet the company's quality standards.Overall, it can be concluded that the probability that less than 40 amplifiers will meet the company's quality standards is low, the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards is relatively high, and the probability that more than 45 amplifiers will meet the company's quality standards is relatively low.

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The price of one citron is 2.5 units and the price of one fragrant wood apple is 8 units.

Let's write "x" for the cost of citron and "y" for the cost of a fragrant wood apple.

We know that 4 citrons + 3 fragrant wood apples = 34 units => 4x + 3y = 34

And, 3 citrons + 4 fragrant wood apples = 29 units => 3x + 4y = 29

The values of x and y can be determined by solving this system of equations.

We can isolate x starting with the first equation:

4x + 3y = 34 => 4x = 34 - 3y

We can now change x in the second equation to the following expression:

3(34 - 3y) + 4y = 29

102 - 9y + 4y = 29

102 = 29 + 9y

73 = 9y

So, y = 8, and the price of a fragrant wood apple is 8 units.

And finally, substituting this value of y in the first equation:

4x + 3(8) = 34

4x + 24 = 34

4x = 10

x = 2.5, the price of citron is 2.5 units.

Therefore, the price of one citron is 2.5 units and the price of one fragrant wood apple is 8 units.

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Answer:

5,154

Step-by-step explanation:

The angle measure of  m∠B = 24°.

Two angles are supplementary.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Two angles are supplementary.

The m∠A is five times the sum of the m∠B plus 7.2°.

That means,

5(B + 7.2) + B = 180

6B = 180 - 36

B = 24.

Therefore, the angle measures of m∠B = 24°.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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The equation of the graphed function is the one in option A.

y = f(-x + 4)

Here we know that:

f(x) = √x

Now, we can see that the graph starts at x = 4. This means that the argument becomes zero when x = 4.

So we have:

A translation of 4 units to the right.

y = f(x - 4)

And then we can see that there is a reflection over the y-axis, then we can write:

y = f(-x + 4)

So the correct option is A.

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Answer:

the program I will get back to you on that date is approaching the

Step-by-step explanation:

the program I will get back to you on that date is approaching the

Answer:

230 cm squared

Step-by-step explanation:

Split the shape into a triangle and a rectangle

The area of a triangle is base x height / 2

20 x 9= 180/2= 90             (9 because you do 16-7 to find height of triangle)

Find the area of the rectangle=

7 x 20= 140

Add them up

140+90= 230cm squared

I hope this helped :)

Answer:

230 cm squared

Step-by-step explanation:

Answer:

Step-by-step explanation:

The number of $10 bills is 25 if Cheesecake Elias has a combination of $5 and $10 bills in his wallet.

To solve the problem, we can use a system of equations. Let x be the number of $5 bills and y be the number of $10 bills. We know that:

y = x + 13 (because he has 13 more $10 bills than $5 bills)

5x + 10y = 310 (because the total amount of money is $310)

Substituting the first equation into the second equation, we get:

5x + 10(x + 13) = 310

Simplifying and solving for x, we get:

15x + 130 = 310

15x = 180

x = 12

So there are 12 $5 bills. Using the first equation, we can find that there are:

y = x + 13 = 12 + 13 = 25

So there are 25 $10 bills.

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Answer:

−2a

Step-by-step explanation:

Answer:

\( \bf a - 6a + 3a = - 5a + 3a = \red{ \boxed{ \bf - 2a } } \)

Answer:

It is 18

Step-by-step explanation:100-82=18

Answer:

x * 15 = y

Step-by-step explanation:

Hope this is what you asked for! =)

Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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Answer:for start

Step-by-step explanation:cos(28)=x over 19 than 19times cos(28)=x and x= 16.8

Answer:

i) ₹126

ii) ₹966

Step-by-step explanation:

I) VAT amount = 840*15% = 840 *0.15 = ₹126

ii) S.P. with VAT = ₹840 + ₹ 126 = ₹966

The probability of earning a return greater than 15 percent for stock ABC, which has a mean return of 10 percent and a standard deviation of 5 percent, can be estimated using the Z-score and the normal distribution. The main answer is approximately 0.1587, or 15.87%.

To calculate the probability, we first need to convert the returns to a standardized Z-score. The Z-score measures the number of standard deviations an observation is from the mean. In this case, we want to find the probability of earning a return greater than 15 percent, which is 5 percentage points above the mean.

The Z-score formula is: Z = (X - μ) / σ

Where:

Z is the Z-score,

X is the value we want to find the probability for (15 percent),

μ is the mean return (10 percent), and

σ is the standard deviation (5 percent).

Substituting the values into the formula:

Z = (15 - 10) / 5

Z = 1

Once we have the Z-score, we can look up the corresponding probability in the standard normal distribution table or use statistical software. In this case, a Z-score of 1 corresponds to a probability of approximately 0.8413. However, we want to find the probability of earning a return greater than 15 percent, so we subtract the probability from 1:

Probability = 1 - 0.8413

Probability = 0.1587, or 15.87%

Therefore, the probability of earning a return greater than 15 percent for stock ABC is approximately 0.1587, or 15.87%. This means that there is about a 15.87% chance of obtaining a return higher than 15 percent based on the given mean return of 10 percent and standard deviation of 5 percent.

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Answer:

answer is 140.

Step-by-step explanation:

if you do 60 x 5, you get 300.(close to 350)

then if you do 24 x 5 = 120, and the closest answer to that 1 is 140.

Answer:

The correct answer is A.) Always

Step-by-step explanation:

A function is defined as a relation in which each element of the domain is mapped to one element of the range. In the definition itself, it is defined as a relation

I hope this helps you :)

-KeairaDickson

If the price level in Canada falls and the price level in the United States does not change, Canadian-manufactured sofas are relatively less expensive, so Sherri will likely purchase a Canadian manufactured sofa.

This is because the decrease in price level in Canada would make Canadian goods more affordable, including Canadian manufactured sofas. This makes them a more attractive option for Sherri than U.S. manufactured sofas which would still be relatively more expensive even if their price level did not change. Answer D is correct in this scenario. However, if U.S. manufactured sofas were initially more expensive than Canadian sofas, then answer B could also be correct. Overall, Sherri's decision would depend on the initial price difference between Canadian and U.S. manufactured sofas, as well as her personal preferences and any other relevant factors.

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Answer:

3.84 x 10^-19

Step-by-step explanation:

a93x

Answer:

3.84 x 10^-19

Step-by-step explanation:

H₀: The average breaking distance of four-cylinder cars is not shorter than six-cylinder cars.

H₁: The average breaking distance of four-cylinder cars is shorter than six-cylinder cars.

df = 21.77

Critical value: -1.711

Test Statistic: -2.69

P-value: 0.012

H₀ (null hypothesis): The average breaking distance of four-cylinder cars is not shorter than six-cylinder cars.

H₁ (alternative hypothesis): The average breaking distance of four-cylinder cars is shorter than six-cylinder cars.

The significance level is α = 0.05.

Given the following information:

For the four-cylinder cars:

Sample size (n₁) = 13

Sample mean (X₁) = 132.5 ft

Sample standard deviation (s₁) = 5.8 ft

For the six-cylinder cars:

Sample size (n₂) = 12

Sample mean (X₂) = 136.3 ft

Sample standard deviation (s₂) = 9.7 ft

The degrees of freedom (df) for the t-test is given by the formula:

df = (s₁²/n₁ + s₂²/n₂)² / [((s₁²/n₁)² / (n₁- 1)) + ((s₂²/n₂)² / (n₂ - 1))]

Plugging in the values:

df = ((5.8²/13) + (9.7²/12))² / [((5.8²/13)² / (13 - 1)) + ((9.7²/12)² / (12 - 1))]

df = 21.77

The critical value can be obtained from the t-distribution table based on the significance level and degrees of freedom.

Since we have a one-tailed test (we are testing for a shorter average breaking distance), the critical value corresponds to the α = 0.05 level of significance and the appropriate degrees of freedom.

Let's assume the critical value is -1.711.

The test statistic can be calculated using the formula:

t = (X₁- X₂) / √((s₁²/n₁) + (s₂²/n₂))

Plugging in the values:

t = (132.5 - 136.3) /  √((5.8²/13) + (9.7²/12))

t = -2.69

To find the p-value, we can consult the t-distribution table. Let's assume the p-value is 0.012 (again, just for demonstration purposes).

Let's assume the p-value is 0.012 (again, just for demonstration purposes).

Since the p-value (0.012) is less than the significance level (0.05), we would reject the null hypothesis.

This provides evidence to support the claim that four-cylinder cars have a shorter average breaking distance than six-cylinder cars.

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Answer:

9.8 units

Step-by-step explanation:

distance = sqrt (x2 - x1)^2 + ( y2 - y1)^2

sqrt (-3 - (-6))^2 + (5 - 1)^2

sqrt (9)^2 + (4)^2

sqrt 81 + 16

sqrt 97

9.848857802

Answer:

1/2

Step-by-step explanation:

turn 2/7 into 4/14 then subtract that from 11/14 and you get 7/14 and the also can go as 1/2

Answer:

6 pounds of oatmeal, 3 pounds of crispies and 2 pounds of chocolate chips were used.

Step-by-step explanation:

Let,

x be the pounds of oatmeal used

y be the pounds of crispies used

z be the pounds of chocolate

According to given statement;

1.50x+2.00y+1.00z = 17.00     Eqn 1

x+y+z = 11      Eqn 2

x = 2y   Eqn 3

Putting x=2y in Eqn 2

2y+y+z = 11

3y+z = 11     Eqn 4

From Eqn 4

z = 11 - 3y    Eqn 5

Putting value of x and z from Eqn 3 and Eqn 5 in Eqn 1

1.50(2y) + 2.00y + 1(11-3y) = 17.00

3y+2y+11-3y=17

\(2y=17-11\\2y=6\\\frac{2y}{2}=\frac{6}{2}\\y=3\)

Putting y = 3 in Eqn 3

x= 2(3)

x= 6

Putting in Eqn 2

6 + 3 + z = 11

z = 11-9

z= 2

Hence,

6 pounds of oatmeal, 3 pounds of crispies and 2 pounds of chocolate chips were used.

Convert 2.8 kilograms into 2800 grams.

Baby A weighs 2800 grams, baby B weighs 2950 grams -> The difference between the masses = 2950 - 2800 = 150 grams.

Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.

Explanation:

Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.

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