6. A parabola has focus (-1, 6) and directrix y = 4. Determine whether each point on
the list is on this parabola. Explain your reasoning.
a. (-1,5)
b. (1,7)
c. (3,9)

The average of cost computers was $1,915.79​ 35 years ago. The correct answer would be an option (D).

The percentage is defined as a ratio expressed as a fraction of 100.

Let the average computer cost was x 35 years ago.

As per the question, we have

76% of x = $1,456

76% is expressed as 0.76 in decimal form

0.76x = 1,456

x = 1,456/0.76

x = 1,915.7947

Rounded to the nearest cent, and we get

x = 1,915.79

Thus, the average of cost computers was $1,915.79.

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The coordinates of the fourth vertex of the parallelogram are (11, -7).

What is a parallelogram?

A parallelogram is a quadrilateral with opposite sides that are parallel to each other. The opposite sides of a parallelogram are also equal in length.

The fourth vertex of a parallelogram can be determined by finding the vector that connects one vertex of the parallelogram to the opposite vertex, and then adding that vector to the third vertex given in the problem.

The vector that connects the first vertex (-3, 1) to the third vertex (5, -5) is (8, -6). To find the fourth vertex, we add this vector to the second vertex (3, -1) :

(3,-1) + (8, -6) = (11, -7)

Hence, the coordinates of the fourth vertex of the parallelogram are (11, -7).

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The required probability for the given delta airlines is given by :

a. Probability of flight late no more than 5 minutes is 0.25.

b. Probability of flight late more than 10 minutes is 0.5

c. Expected flight time is equal to 130 minutes.

Flight time from Cincinnati to Tampa = 2 hours 5 minutes

Actual time distributed between 2 hours and 2 hours 20 minutes

2 hours = 120 minutes

2 hours 20 minutes = 140 minutes

f(x) =  [tex]\left \{ {{\frac{1}{( 140 - 120)} , 120 \leq x\leq 140\atop {0 , x = 0 }} \right.[/tex]

a. Probability of flight no more than 5 minutes late

[tex]\int_{130}^{125} \frac{1}{20} dx[/tex]

= 1 / 4

= 0.25

b. Probability of flight  more than 10 minutes late

[tex]\int_{135}^{125} \frac{1}{20} dx[/tex]

= 1/2

= 0.5

c. Expected flight time in minutes

= [tex]\int_{140}^{120} \frac{x}{20} dx[/tex]

= 130 minutes

Therefore, the required probability are given by :

a. Probability of flight late no more than 5 minutes is 0.25.

b. Probability of flight late more than 10 minutes is 0.5

c. Expected flight time is equal to 130 minutes.

The above question is incomplete , the complete question is :

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.  What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? What is the expected flight time, in minutes?

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Answer:

D. 4x² - x / x² - x - 2

Step-by-step explanation:
First cross multiply then sum the results:

cross:

x(x + 2) = x² + 2x

3x(x - 1) = 3x² - 3x

sum the results of the cross:

x² + 2x + 3x² - 3x

4x² - x (this goes at the top)

Then multiply the bottom:

(x - 1 )(x + 2)

x² + 2x - x - 2

x² - x - 2 (this stays at the bottom)

Fraction ends up like:

4x² - x / x² - x - 2

The variation in the values is due to random error. Hence, it can be reduced by taking more observations to estimate the measure of the mass of the ring.

One way to minimize experimental error in this situation is to take multiple measurements and use the average of those measurements as the final value. This helps to account for any small fluctuations or inaccuracies in the individual measurements.

Also, it is important to ensure that the balance is properly calibrated and that the ring is placed on the balance in the same way each time.

Other ways to minimize experimental error include using a more precise measuring instrument, such as a digital scale, and ensuring that the lab environment is controlled and stable (i.e. no drafts or vibrations that could affect the measurements).

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The complete question is -

You measure the mass of a ring to be used in your experiment three times using the same balance and get slightly different values: 17.46 g, 17.42 g, and 17.44 g. How can you minimize experimental error?

Answer:

49. a)  A - C - 1

49. b)  1 - 2R

49. c)  2Q - P

50.  x = 103

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm}\underline{Log laws}\\\\$\log_axy=\log_ax + \log_ay$\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\$\log_ax^n=n\log_ax$\\\\$\log_ab=c \iff b=a^c$\\\\&\log_aa=1$\\ \end{minipage}}[/tex]

Part a

Given:

[tex]\log_5 9=A[/tex]

[tex]\log_5 6=B[/tex]

[tex]\log_5 11=C[/tex]

[tex]\begin{aligned}\log_5 \dfrac{9}{55}&=\log_5 9 - \log_5 55\\&=\log_5 9 - \log_5 (11 \cdot 5)\\&=\log_5 9 - (\log_5 11 + \log_5 5)\\&=\log_5 9 - \log_5 11 - \log_5 5\\&=A-C-1\\\end{aligned}[/tex]

Part b

Given:

[tex]\log_3 10=R[/tex]

[tex]\log_3 4=S[/tex]

[tex]\log_3 11=T[/tex]

[tex]\begin{aligned}\log_3 \dfrac{3}{100}&=\log_3 3 - \log_3 100\\&=\log_3 3 - \log_3 (10 \cdot 10)\\&=\log_3 3 - \log_3 10^2\\&=\log_3 3 - 2\log_3 10\\&=1-2R\\\end{aligned}[/tex]

Part c

Given:

[tex]\log_3 4=P[/tex]

[tex]\log_3 10=Q[/tex]

[tex]\log_3 7=R[/tex]

[tex]\begin{aligned}\log_3 25&=\log_3 \dfrac{100}{4}\\&=\log_3 100 - \log_3 4\\&=\log_3 (10 \cdot 10) - \log_3 4\\&=\log_3 10^2 - \log_3 4\\&=2 \log_3 10 - \log_3 4\\&=2Q-P\end{aligned}[/tex]

The error was in line 4 of the calculation.  The log law

was not applied correctly.

The correct solution is:

[tex]\begin{aligned}3 \log (x-3) + 1 & = 7\\3 \log (x-3) & = 6\\\log (x-3) & = 2\\x-3&=10^2\\x&=3+10^2\\x&=103\end{aligned}[/tex]

The correct alternative is -

Given is the graph of the function.

The correct alternatives are -

Therefore, the correct alternative is -

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Answer: Midpoints (-3/2)

Step-by-step explanation:

Midpoint formula is (x1+x2)/2 , (y1+y2)/2

Plugin x values and solve
(-1 +-5)/2 = -3

Plugin y values and solve
(-5+9)/2 = 2

The midpoint is -3/2

I hope this helped you :D

The value of the expression 3x + 4y² when x = -3 and y = 5 is 91.

Given the expression in the question;

3x + 4y²

To determine the value of the expression when x = -3 and y = 5, plug in x = -3 and y = 5 for every x and values in the expression and simplify.

3x + 4y²

3( -3 ) + 4( 5 )²

Simplify

Take the square of 5

3( -3 ) + 4( 25 )

Multiply 3 and -3

-9 + 4( 25 )

Multiply 4 and 25

-9 + 100

Add -9 and 100

91

Therefore, the value of the expression is 91.

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Answer:

11

Step-by-step explanation:

Now:

Shawn: 23

Yu Yan: 15

x years ago:

Shawn: 23 - x

Yu Yan: 15 - x

x years ago, Shawn was 3 times as old as Yu Yan.

23 - x = 3(15 - x)

23 - x = 45 - 3x

2x = 22

x = 11

Check:

11 years ago Shaw was 23 - 11 = 12, and Yu Yan was 15 - 11 = 4.

12 is indded 3 times 4.

Answer: 11

Totally correct about the mentioned before is 2.5%. This is because the z-score for this situation is (494 - 686) / 96 = -2. According to the Empirical Rule, approximately 95% of observations will fall within 2 standard deviations of the mean. In this case, the question is asking for the percent of students who scored less than 494, which is below 2 standard deviations, so the answer is 2.5%.

The Empirical Rule states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data would get fall within 3 standard deviations of the mean. So if we know the mean and standard deviation of a normal distribution, we can use this rule to estimate the percentage of data that falls within a certain range.

In this specific question, the mean of Math Level 2 SAT subject test score was 686 with a standard deviation of 96. We were asked to find the percent of students who scored less than 494. To find this we first calculated the z-score which is (494 - 686) / 96 = -2.

Since the z-score is -2 it means that it's 2 standard deviation below the mean, and according to the Empirical rule 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. So the answer is 2.5%.

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a. The total interest paid on the 25-year mortgage is $110411.

b. The total interest paid on the 30-year mortgage is $135644.

What is the meaning of APR?

Annual percentage rate (APR) is the term used to describe the annual interest produced by a sum that is levied against borrowers or distributed to investors. APR is a percentage that expresses the actual yearly cost of borrowing money over the course of a loan or the income from an investment. This does not account for compounding and includes any fees or additional costs related to the transaction. Consumers can compare lenders, credit cards, or investment products using the APR as a benchmark figure.

Given that, the amount that is borrowed is $220,000.

If you borrow it for 25 years, you will pay $1,101.37 monthly.

The amount that you need to pay is (1,101.37×12×25) = 330411.

The total interest is =  (330411 - 220,000) = $110411.

If you borrow it for 30 years, you will pay $987.90 monthly.

The amount that you need to pay is (987.90×12×30) = 355644.

The total interest is =  (355644 - 220,000) = $135644

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The results of operations between functions:

Case A: (f + g) (x) = x / (x + 9) + x³

Case B: (f - g) (x) = x / (x + 9) - x³

Case C: (f · g) (x) = x⁴ / (x + 9)

Case D: (f / g) (x) = 1 / [x² · (x + 9)]

Function (f / g) (x) has the following domain: x ∈ R - {- 9, 0}.

According to function theory, we can obtain a function with more complexity by operations between two functions, the most common operations are listed below:

Now we proceed to determine the resulting function:

Case A:

(f + g) (x) = f(x) + g(x)

(f + g) (x) = x / (x + 9) + x³

Case B:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = x / (x + 9) - x³

Case C:

(f · g) (x) = f (x) · g (x)

(f · g) (x) = [x / (x + 9)] · x³

(f · g) (x) = x⁴ / (x + 9)

Case D:

(f / g) (x) = f(x) / g(x)

(f / g) (x) = [x / (x + 9)] / x³

(f / g) (x) = 1 / [x² · (x + 9)]

The domain of (f / g) (x) is the set of all values of x-values such that the function exists. In this case, we must determine the values of the denominator of (f / g) (x) such that it is not equal to zero.

x² · (x + 9) = 0

x = 0 or x = - 9

The domain of (f / g) (x) is: x ∈ R - {- 9, 0}.

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The increase in the y-coordinatesis then calculated by dividing it by the change in the x-coordinates.

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The binomial variable with mean 17 transformers and standard deviation √2.55 transformers.

In math standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random.

Here let us assuming the variable is a binomial variable.

Then we have written it as in the following form,

=> Mean = number of samples * probability

And the value of standard deviation is calculated as

=> Standard Deviation = √mean (1 − probability)

Here we know that the value of mean is calculated as,

=> 85% * 20 = 0.85*20 = 17 transformers

Then the value of Standard deviation is calculated as,

=> √mean * (1 − 0.85)

Apply the values on the formula, then we get,

=> √17 * 0.15 =√2.55 transformers.

Hence the random variable is a binomial variable.

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The value of x that solves the equation is x = 28.10, and there are 4 eggs per batch.

Particularly x is not in that equation, but we can write:

5x = 140.50

To solve for x, we need to divide both sides by 5, then we will get:

5x/5 = 140.50/5

x = 140.50/5

x = 28.10

To find this, we need to take the quotient between the number of eggs and the number of batches, so we will get:

12 eggs.

3 batches.

12/3 = 4

This means that you need 4 eggs per batch.

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The following systems are :

a) Non-linear

b) Linear

c) Linear

d) Non-linear

e) Linear

a) Non-linear: The equation is non-linear because it contains a product of two variables (x1 - 1) and (x2 + 1). A linear equation only contains variables and their coefficients, not products of variables.

b) Linear: The equation is linear because it only contains variables and their coefficients.

c) Linear: The equation is linear because it only contains variables and their coefficients and the sum of variables.

d) Non-linear: The equation is non-linear because it contains the sine and cosine functions, which are non-linear.

e) Linear: The equation is linear because it only contains variables raised to a constant power (e raised to a constant power) and their coefficients.

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Answer:

w=7/9

Step-by-step explanation:

6=7/w-3

Move the terms

6=7/w-3, w [tex]\neq[/tex] 0

Calculate

-7/w=-3-6

Multiply both sides

-7/w=-9

Swap the sides

7=9w

Divide both sides

9w=7

w=7/9, w [tex]\neq[/tex] 0

w=7/9

The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:

Shift right of 7 units and reflection over the x-axis.

The glide reflection is a combination of a reflection with a translation.

The vertices of the original triangle are given as follows:

A(-3,-2), B(-6,-5) and C(-1,-4).

The vertices of the reflected triangle are given as follows:

A'(4,2), B'(1,5) and C'(6,4).

Hence the composite rule is given as follows:

(x,y) -> (x + 7, -y).

Meaning that the glide reflection is defined as follows:

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Answer:

Plane B

Step-by-step explanation:

Plane A: 2800/5 = 560 m/h

Plane B: 3885/7 = 555 m/h

All the equations are matched with the line graph are given below.

And the letter code is AEBG.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Given:

All the equations are matched with the line graph:

A: y = 3x + 1 → Line 1

B: y = -2x + 2 → Line 3

G: y = -1/2x + 2 → Line 4

E : y = x+ 4 → Line 2

The letter code is AEBG.

Therefore, the letter code is AEBG.

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If the ratio of dolphins to penguins is 2:5, then for every 2 dolphins, there are 5 penguins. If there are 30 penguins, you can use this ratio to find out how many dolphins there are. To find out how many dolphins there are, you can set up a proportion:

(number of dolphins) / (number of penguins) = (2) / (5)

You know that the number of penguins is 30, so you can substitute that in and solve for the number of dolphins:

(number of dolphins) / 30 = 2 / 5

Multiply both sides by 30 to solve for the number of dolphins:

number of dolphins = (2/5) * 30 = 6

So, if there are 30 penguins, there would be 6 dolphins.

Options

The scale factor for the dilation in this problem is given as follows:

2.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The equivalent side lengths in this problem are given as follows:

The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:

k = 8/4 = 2.

(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).

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Answer:

Step-by-step explanation:

0.462

Answer:

0.462 :) hope this helps and please put me as brainiest thankyou !!

Step-by-step explanation:

The solution to an equation is 10.Solving an equation refers to the process of determining its solution.

Make the available

14to obtain the desired amount:

x – 6 + x = 14

Put similar phrases together to get:

2x – 6 = 14

Adding 6 to both sides yields:

2x = 20

x = 10.

The complete question is,

1 4 (4x 24) + x = 14 must be solved.

By dividing the 1 by 4, you can obtain:

Put similar phrases together to get:

Adding 6 to both sides yields:

x =

Consequently, is the necessary response.

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The amount that he pays for the cooler alone without the tax will be $7.37.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

His total bill, with tax, was $7.95. He paid 6 percent sales tax.

Let 'x' be the total bill without the sales tax. Then the equation is given as,

107.95% of x = $7.95

1.0795x = $7.95

x = $7.37

The amount that he pays for the cooler alone without the tax will be $7.37.

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a. The shape of the sampling distribution is normal by the Central Limit Theorem.

b. The mean is 0.23.

c. The standard error is 0.125, which means that the sample proportions differ by around 0.125 from the mean of 0.23.

d. The probability is 0.2877 = 28.77%.

By the Central Limit Theorem, each sample has at least 10 successes and at least 10 failures, and the shape of the distribution is normal.

For each sample, the mean and the standard error are specified as follows:

Hence, the distribution of differences, the mean, and the standard error are specified as follows:

Using the z-score formula, the probability that the difference is greater than 30 is 1 subtracted by the p-value of Z when X = 0.3, Therefore:

Z = (0.3 - 0.23)/0.125

Z = 0.56

Z = 0.56

1 - 0.7123 = 0.2877 = 28.77%.

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The complete question is:

At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS of 30 seniors and a separate SRS of 30 juniors. Let ^ps-^pj be the difference in the sample proportion of seniors and juniors that have parking passes.

a. What is the shape of the sampling distribution of ^ps-^pj? Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

d. What is the probability that the difference in sample proportions (senior-junior) of students with parking passes is greater than 30%?

Answer: This is known as Gay-Lussac's Law.

The relationship states that the pressure and volume of a gas are directly proportional at constant temperature. Therefore, if the pressure is increased by 25%, the volume must be decreased by 25% to maintain the constant product of pressure and volume.