The graph is a straight line that passes through the points P and Q How can I state the coordinates of P and Q. How can i determine the gradient of the line segment PQ? How do I do a equation of the line PQ ? How can I find the length of Line PQ? How can I find the mid point of PQ?

Answer:

38.4 Megabytes

2.4 x 16 = 38.4

Step-by-step explanation:

To find the value of x for which f(x) = g(x), we can equate the two functions:

f(x) = g(x)

x^2 - 1 = 3x

Bringing all the terms to one side, we get:

x^2 - 3x - 1 = 0

Using the quadratic formula, we can solve for x:

x = [ -(-3) ± sqrt((-3)^2 - 4(1)(-1))] / 2(1)

Simplifying the expression:

x = [3 ± sqrt(13)] / 2

Therefore, the values of x for which f(x) = g(x) are (3 + sqrt(13))/2 and (3 - sqrt(13))/2.

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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Answer:

Engineer: 9.5 hr

Assistant: 4.5 hr

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Given the engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour, and a customer received a bill for $425 for a certain job:

Given the assistant worked 5 hours less than the engineer:

Therefore, the system of equations that represents the problem is:

\(\begin{cases}40x+10y=425\\ \quad \qquad \;\;\;y=x-5\end{cases}\)

Substitute the second equation into the first equation to eliminate y:

\(40x+10(x-5)=425\)

Solve the equation for x to find the number of hours the engineer worked:

\(\begin{aligned}40x+10(x-5)&=425\\40x+10x-50&=425\\50x-50&=425\\50x&=475\\x&=9.5\end{aligned}\)

Therefore, the engineer worked 9.5 hours.

Substitute the found value of x into the second equation and solve for y to find the number of hours the assistant worked:

\(\begin{aligned}y&=x-5\\y&=9.5-5\\y&=4.5\end{aligned}\)

Therefore, the assistant worked 4.5 hours.

Answer:

C(3, −3), D(−2, −3)

Step-by-step explanation:

The distance from point A to point B is 5 units.

The width of the rectangle is 5 units.

The length must be 6 units to have an area of 30 square units.

Points C and D must be 6 units below points A and B.

Their coordinates must be (-2, -3) and (3, -3).

Answer: C(3, −3), D(−2, −3)

Answer:

The answer is A.

Step-by-step explanation:

You have to multiply by converting the second fraction into upside down :

\( \frac{4x + 1}{6x} \div \frac{x}{3x - 1} \)

\( = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} \)

\( = \frac{(4x + 1)(3x - 1)}{x(6x)} \)

\( = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } \)

\( = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } \)

It should be noted that the probability that a student will earn at least one 5 will be 0.3152.

Test P(x). P(at least one 5)

1. 0.4. 0.2

2. 0.45. 0.36

3. 0.15. 0.488

Therefore, the probability that a student in the AP curriculum will earn at least one 5 will be:

= (0.4 × 0.2) + (0.45 × 0.36) + (0.15 × 0.488)

= 0.3152

In conclusion, the correct option is 0.3152.

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Answer:

$34.99

Step-by-step explanation:

49.99 - 14.997=

34.99

Answer:

the answer is 34.99

if you want me to explain i will ")

Answer:

To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.

Step-by-step explanation:

The unknown angle in the cyclic quadrilateral is as follows:

m∠CML = 109 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find m∠CML as follows:

Using the arc angle and opposite angle of a quadrilateral theorem,

6x + 25 = 1 / 2 (7x + 14 + 106)

6x + 25 = 1 / 2(7x + 120)

6x + 25 = 7 / 2 x + 60

6x - 7 / 2 x  = 60 - 25

6x - 3.5x = 35

2.5x = 35

divide both sides by 2.5

x = 35 / 2.5

x = 14

Therefore,

m∠CML = 6x + 25 = 6(14) + 25 = 84 + 25 = 109 degrees

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Answer: \(f^{-1} (x) = \sqrt{x} +1\)

Step-by-step explanation:

\(y = x^2 - 2x + 1\)

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

\(x = y^2 - 2y +1\)

\(x = (y-1)^2\), (factor!)

±\(\sqrt{x} = y - 1\)

So, the inverse "function" is:

\(f^-1(x)\) = ±\(\sqrt{x} +1\)

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

\(f^{-1} (x) = \sqrt{x} +1\)

Answer:

50

Step-by-step explanation:

Given the trend line equation :

y = 9x + 5

Exercise time if she runs 5 miles :

From the trend line equation :

y = exercise time

x = miles ran

If she runs 5 miles ; then x = 5

y = 9(5) + 5

y = 45 + 5

y = 50

The equations that can be used to solve for y, the length of the room, are: y(y + 5) = 750, y² – 5y = 750, and y(y – 5) + 750 = 0.

It states that when multiplying a number by a group of numbers added together, you can multiply the number by each individual number in the group and add the products together to get the same answer.

In order to find the length of the room, we need to solve for y in each of the equations given.

First, let's solve for y in the equation y(y + 5) = 750. We can use the distributive property to expand the equation to y² + 5y = 750.

Then, we can subtract 750 from both sides of the equation to get y² + 5y - 750 = 0.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

Second, let's solve for y in the equation y² – 5y = 750.

To solve this equation, we can add 5y to both sides to get y² = 5y + 750. Then, we can divide both sides by y to get y = 5y + 750.

We can then subtract 5y from both sides to get y - 5y = 750. Finally, we can divide both sides by 5 to get y = 150.

Third, let's solve for y in the equation y(y – 5) + 750 = 0.

To solve this equation, we can use the distributive property to expand the equation to y² – 5y + 750 = 0.

Then, we can subtract 750 from both sides to get y² – 5y = -750.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

In conclusion, the equations that can be used to solve for y, the length of the room, are y(y + 5) = 750, y2 – 5y = 750, and y(y – 5) + 750 = 0. The solutions for y are y = -25 and y = 30.

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Answer:

Pls give us the statements

Evaluating the function in the values of the domain we will get some coordinate pairs. The graph of these is in the image at the end.

Here we have the function:

3x - y = 1

And we want to graph this in the domain (-3, -1, 0, 4)

To do so, we need to evaluate the function (the values of x) in the values of the domain.

Solving the equation for y we get:

y = 3x - 1

Now, when x = -3

y = 3*-3 - 1 = -10

when x = -1

y = 3*-1 - 1 = -4

when x = 0

y = 3*0 - 1 = -1

When x = 4

y = 3*4 - 1 = 11

So we have the points (-3, -10), (-1, -4),  (0, -1), (4, 11)

The graph of these points is on the image below.

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

x=0.1

Step-by-step explanation:

Answer:

e. The mayor uses a significance level of 0.05 and n = 1,000 voters.

Step-by-step explanation:

Power of a test:

For a high power of a test, two conditions are needed:

Large significance level.

Large sample.

In this question:

A significance level of 0.05 will lead to a higher power than a significance level of 0.01, which means that the answer is between options d and e.

A test with a sample of 1000 has a higher power than a test with a sample of 500, and thus, the answer is given by option e.

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

\(\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537\)

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

\(\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712\)

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

\(H_0: \mu_1 - \mu_2 = 0\)

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

\(H_1: \mu_1 - \mu_2 \neq 0\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

From the two samples:

\(X = \mu_1 - \mu_2 = 1276 - 1439 = -163\)

\(s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144\)

Test statistic:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-163 - 0}{77.3144}\)

\(z = -2.11\)

The test statistic is z = -2.11.

Answer:

A

Step-by-step explanation:

Because the cost per pie is less.

Gracie's statement is not necessarily correct about the tens digit in a dividend is less than the divisor and the divisor has one digit. Gracie says the quotient must have a 0 in the tens place.

What is dividend?

In mathematics, a dividend is the number that is being divided in a division problem. For example, in the division problem 18 ÷ 3 = 6, 18 is the dividend.

Gracie's statement is not necessarily correct. Let's look at a couple of examples to see why.

Example 1:

Dividend = 25

Divisor = 4

In this case, the tens digit of the dividend (2) is less than the divisor (4). The quotient is 6 with a remainder of 1. There is no 0 in the quotient, so Gracie's statement is incorrect.

Example 2:

Dividend = 35

Divisor = 4

In this case, the tens digit of the dividend (3) is also less than the divisor (4). The quotient is 8 with a remainder of 3. Again, there is no 0 in the quotient, so Gracie's statement is still incorrect.

From these examples, we can see that Gracie's statement is not always true. It is possible for the tens digit of the dividend to be less than the divisor, and for the quotient to not have a 0 in the tens place.

The only time Gracie's statement would be true is if the remainder is 0 after dividing the dividend by the divisor. In that case, the quotient would indeed have a 0 in the tens place. However, this is not always the case.

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Ellie's growth rate is 2.4 pounds per month.

To find Ellie's growth rate in pounds per month, we divide the change in weight by the time period. Let's calculate it using the given information:

Determine the change in weight:

Change in weight = 0.6 pounds

Determine the time period:

Time period = 0.25 months

Calculate the growth rate:

Growth rate = Change in weight / Time period

Substituting the values:

Growth rate = 0.6 pounds / 0.25 months

To divide by a fraction, we multiply by its reciprocal:

Growth rate = 0.6 pounds * (1 / 0.25 months)

Simplifying the fraction:

Growth rate = 0.6 pounds * 4 months

Multiplying:

Growth rate = 2.4 pounds per month

Therefore, Ellie's growth rate is 2.4 pounds per month. This means that, on average, she gains 2.4 pounds every month.

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The given expression is

To find the day, we have to evaluate the function where y < 100.

Then, apply a logarithm on each side

Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

The range of the graphed function in this problem is given as follows:

[-9, 9].

The values of y in this function are between -9 and 9, inclusive, hence the range of the function is given as follows:

[-9, 9].

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Answer:

21 boys

Step-by-step explanation:

 Girls            Boys

     6                  7            <= reflects the 6:7 ratio mentioned in the problem

----------   =    ----------

     18                 x

Cross multiply to determine x:  

6x = 7(18), or x = 7(3), or x = 21

There are 21 boys when we have 18 girls.

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses