Need help with #6 please help

Answer: A quadratic of the form $ax^2 + bx + c$ has rational roots if and only if its discriminant, $b^2 - 4ac$, is a perfect square. In this case, the discriminant is $(20)^2 - 4(3)(c) = 400 - 12c$. So, we need to find the positive integers $c < 100$ that make $12c$ a perfect square.

The perfect squares that are less than $100$ are $1,4,9,16,25,36,49,64,81$, so the possible values for $c$ are $33,44,55,66,77,88$.

So, the positive integers $c$, with $c < 100$, that make the quadratic have rational roots are $33,44,55,66,77,88$

Step-by-step explanation:

The earliest time at which they can be finished moving all of the boxes is: d. 9:44 a.m

To determine the earliest time at which Quincy and Celine can finish moving all of the boxes, we need to determine the maximum amount of time it will take for them to move all of the boxes. We can do this by calculating the time it will take for each person to move each type of box individually, and then adding those times together.

Quincy takes 1 minute to move a small box and 2 minutes to move a large box. Celine takes 2 minutes to move a small box and 3 minutes to move a large box.

Time to move 16 small boxes: 16 boxes * 1 minute/box = 16 minutes

Time to move 10 large boxes: 10 boxes * 2 minutes/box = 20 minutes

Total time for Quincy: 16 minutes + 20 minutes = 36 minutes

Time to move 16 small boxes: 16 boxes * 2 minutes/box = 32 minutes

Time to move 10 large boxes: 10 boxes * 3 minutes/box = 30 minutes

Total time for Celine: 32 minutes + 30 minutes = 62 minutes

To get the earliest time they can finish moving all the boxes, we take the maximum of the two times:

Max(36 minutes, 62 minutes) = 62 minutes

Start time: 9:00 a.m.

End time: 9:00 a.m. + 62 minutes = 9:62 a.m.

So the earliest time they can finish moving all the boxes is 9:62 a.m.

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Use the data to create a stemplot.

Twenty-four workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes.

20 35 42 52 65 20 60 49 24 37 23 24

22 20 41 25 28 27 50 47 58 30 32 48

The data in a stem-and-leaf plot:

3/0257

2/0002344578

4/12789

5/028

6/05

Another presentation that is similar to a histogram is a stemplot. In statistics, a stemplot is a tool for presenting quantitative data in a graphical format, similar to a histogram, namely to assist in visualizing the shape of the data distribution which is often used in exploratory analysis. Stemplots were introduced by Arthur Bowley in the early 1900's. However, its general use only began in 1980 after John Tukey's published Exploratory Data Analysis in 1977.

Stem-and-leaf plots provide more information about true values than histograms. As in a histogram, the length of each bar corresponds to the number of events that fall into a given interval. On Histograms. we can only see the frequency value of the data but we don't know what the actual number value is. In contrast to the histogram, in SLP besides we can know the frequency value, we can also know what the actual data value is. This is done by dividing the observed values into two components, stem and leaf.

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a. (-1,5) is on the parabola

b. (1,7) is NOT on the parabola

c. (3,9) is NOT on the parabola

a. (-1,5)

The distance from the point (-1,5) to the focus (-1,6) is sqrt((-1-(-1))^2 + (5-6)^2) = sqrt(0+1) = 1

The distance from the point (-1,5) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(5-4) = 1

Since the distances are equal, the point (-1,5) is on the parabola.

b. (1,7)

The distance from the point (1,7) to the focus (-1,6) is sqrt((1-(-1))^2 + (7-6)^2) = sqrt(2^2 + 1^2) = sqrt(5)

The distance from the point (1,7) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(7-4) = 3

Since the distances are not equal, the point (1,7) is not on the parabola.

c. (3,9)

The distance from the point (3,9) to the focus (-1,6) is sqrt((3-(-1))^2 + (9-6)^2) = sqrt(4^2 + 3^2) = sqrt(16+9) = sqrt(25)

The distance from the point (3,9) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(9-4) = 5

Since the distances are not equal, the point (3,9) is not on the parabola.

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The area of the glacier at the start of last year was 56.31 km², based on a percentage reduction of 0.2%.

A percentage decrease represents the difference between the starting and ending values, expressed as a percentage of the starting value.

In working out the percentage reduction, we determine the difference between the ending and starting values.  This difference is divided by the starting value and multiplied by 100.

The current area of the glacier = 56.20 km²

The percentage reduction = 0.2%

Proportionately, the current area, in percentage terms = 99.8% (1 - 0.2%)

99.8% = 56.20 km²

100% = 56.31 km²

Thus, to 2 decimal points, the area of the glacier at the start of last year was 56.31 km².

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A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.

The square has four sides, hence:

360/4 = 90º.

The other figure has three sides, which are similar, hence:

360/3 = 120º.

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Answer: If you are reporting on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, you are using a population.

A population is a complete set of all the individuals or elements that share a common characteristic, such as all breast cancer patients seen at a hospital in a given year. A sample, on the other hand, is a subset of a population that is selected for analysis or study.

In this case, since you are reporting on all breast cancer patients seen at the hospital last year, you are using the entire population of breast cancer patients, rather than just a sample of them.

Step-by-step explanation:

If a plot of the residuals shows a curved pattern, it indicates that a straight line is not a good model for the data. This does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve.

When a least-squares regression line is fit to a set of data, it is used to determine the linear relationship between two variables. If a plot of the residuals (the difference between the observed values and the predicted values from the regression line) shows a curved pattern, it indicates that a straight line is not a good model for the data. This could mean that there is a nonlinear relationship between the two variables or that the data contains outliers that are not accounted for by the regression line. However, it does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve. To determine if the regression line is an accurate model for the data, it is important to visually inspect the plot of the residuals and assess whether the pattern is random or systematic. If the pattern is random, it indicates that the regression line is a good model for the data. If the pattern is systematic, it indicates that the regression line is not a good model for the data and alternative models should be considered.

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The function best represents the data in the scatter plot is y = 2x + 20.

The function of the straight line has the general formula: y = mx + c

where m is the slope of the line, and c is the y-intercept

So first, we will need to find the slope (m):

The slope can be calculated with the points (x₁, y₁) and (x₂, y₂) as follows:

m = (y₂ - y₁)/(x₂ - x₁)

= 120 - 60/50 - 20

= 60/30

= 2/1

So, now we have the slope of our equation y = 2x + b but we still need to find b (or where the y intersects.)

Now, consider the ordered pair (20, 60)

y = 2x + b

60 = 2 × 20 + b

b = 60 - 40

b = 20

Now, put the value of b in y = 2x + b, and we get

y = 2x + 20

Also, b can not be -20 because this is a positive y-intercept, and we know it has a slope of 2.

Therefore the function is y = 2x + 20

--The given question is incomplete; the complete question is

"A picture is enlarged by keeping its width the same and increasing its length. The scatter plot below shows the perimeter of the picture (y) for different lengths (x):

Plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140

Which function best represents the data in the scatter plot?

y = 2x − 20

y = 2x + 20

y = x − 20

y = x + 20"--

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The number of kilometers that Darlene runs is given as follows:

2.4 kilometers.

The distance that Darlene runs is obtained applying the proportions in the context of the problem.

The proportion is applied to convert the mixed number to decimal, adding the integer part to the division of the numerator by the denominator.

The distances are given as follows:

Hence the total distance is of:

1 + 1.4 = 2.4 km.

She ran 1 km in the morning.

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In this case, there are 8 letters, so the total number of 4-letter words possible is 8^4 = 4096.

(b) In this case, each letter can be used only once, so we must choose 4 different letters out of 8 letters. This can be done using the combination formula C(8,4) = 70.

(c) Since each word must begin with the letter A, the remaining 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.

(d) The letter C must be at the end, so the first 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.

(e) The second letter must be a vowel, so the first letter can be chosen out of 4 letters (A, E, I, O). The remaining 3 letters can be chosen out of 7 letters. This can be done using the combination formula C(4,1) x C(7,3) = 140.

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Answer: The slope of the line is 2/3.

The line is not solid, it is dashed.

The area below the line is shaded.

A solution to the inequality is (2,3).

The x-intercept of the boundary line is (-3/2,0)

All the statements except the first one are true about the graph of y< 2/3 x +1.

Step-by-step explanation:

Manufacturing should pay $2206.80, Selling should pay $7356.0and Administration should pay $2452.00

Generally, To find out how much each department should pay, you can use the proportion of the cost that corresponds to their respective ratio.

First, calculate the total ratio by adding the three ratios together:

1/10 + 1/3 + 1/9 = 0.544

Then, divide the total cost by the total ratio to find the unit cost:

$12,005 / 0.544 = $22068.01

Next, multiply the unit cost by the ratio for each department to find out how much they should pay:

Manufacturing: $22068.01 x 1/10 = $2206.80

Selling: $22068.01 x 1/3 = $7356.0

Administration: $22068.01 x 1/9 = $2452.00

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A: The probability of selecting a Democrat is 84/212 = 0.3968 or 39.68%.

B: The probability of selecting an Independent and Female respondent is 16/212 = 0.075 or 7.5%.

C: The probability of selecting a Republican given that the respondent is Male is 45/69 = 0.6522 or 65.22%.

D: The probability of selecting a Republican or Female respondent is 126/212 = 0.5962 or 59.62%.

E: The events being a Republican independent of being a Male, P(Republican/Male) = P(Republican) which means these events are independent.

What is the probability?

Probability is a mathematical concept that quantifies the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a) To find the probability of selecting a Democrat, we need to add up the number of Democratic respondents and divide by the total number of respondents. In this case, the number of Democratic respondents is 36 + 48 = 84. The total number of respondents is 84 + 45 + 24 + 33 + 16 = 212. So the probability of selecting a Democrat is 84/212 = 0.3968 or 39.68%.

b) To find the probability of selecting an Independent and Female respondent, we need to find the number of Independent and Female respondents, and divide by the total number of respondents. In this case, the number of Independent and Female respondents is 16. The total number of respondents is 212, so the probability of selecting an Independent and Female respondent is 16/212 = 0.075 or 7.5%.

c) To find the probability of selecting a Republican given that the respondent is Male, we need to use conditional probability formula. P(Republican/Male) = P(Republican and Male) / P(Male)

In this case, the number of Republican and Male respondents is 45. The number of Male respondents is 45+24 = 69

So the probability of selecting a Republican given that the respondent is Male is 45/69 = 0.6522 or 65.22%.

d) To find the probability of selecting a respondent that is Republican or Female, we need to find the number of Republican or Female respondents and divide by the total number of respondents. In this case, the number of Republican or Female respondents is 45 + 33 + 48 = 126. The total number of respondents is 212, so the probability of selecting a Republican or Female respondent is 126/212 = 0.5962 or 59.62%.

e) To answer whether the events being a Republican independent of being a Male or not, we need to check the independence of the events. Events A and B are independent if and only if P(A/B) = P(A) = P(B)

In this case, P(Republican/Male) = 0.6522 and P(Republican) = (45+33)/212 = 0.4906

So the events being a Republican independent of being a Male, P(Republican/Male) = P(Republican) which means these events are independent.

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Answer: C

If you leave behind 0.5 then instead of 24 the correct answer would be 22.

Answer:

Yes, (x-3) is a factor of (x^4-13x^2+36) using synthetic division.

Synthetic division:

| x -3 |

x^4 -13x^2+36

x^3 -10x^2+27x-108

The remainder is zero, so (x-3) is a factor of the polynomial (x^4-13x^2+36).

Step-by-step explanation:

The sequence (3n-2/n)n=1 converges to 1.

To show that (3n-2/n)n=1 converges, we need to find the limit as n approaches infinity.

Using algebraic manipulation, we have the following steps

lim (3n-2/n)n = lim (3-2/n)^n

lim (3n-2/n)n = (3-2/∞)^∞

lim (3n-2/n)n = 1^∞

lim (3n-2/n)n = 1

The basic definition of convergence states that a sequence converges if the limit of the sequence as n approaches infinity is equal to a finite number

Since the limit of (3n-2/n)n as n approaches infinity is 1, we can conclude that the sequence converges to 1.

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Answer:

Step-by-step explanation:

You can use the equations:

x = 2y

where x is the number of $10 bills and y the number of $5 bills and:

10x+5y = 125

Solving gives x=10 and y = 5, or in other words there are 10 $10 bills and 5 $5 bills

Duncan's height is closest to the mean.

Duncan (32nd percentile) has a z-score of z = 0.4677 and Shane (62nd percentile) has a z-score of z = 0.3055 when using "Table A" or "normalcy" on a TI calculator. Now that we have the z-score formula, we can create

−0.4677 = (32 − μ)/σ

and

Duncan and Shane are 3-year-old boys. Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. shane is 34.0 inches tall and is at the 62nd percentile of the distribution.

0.3055 = (34 − μ)/σ

Since the boys' heights fall under the same distribution, it should be noted that and will have the same values in each equation. Consequently, this is a set of linear equations.

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Answer:

the slope is -1/3 and the coordinates are (0,-6) and (3,-7). Below is a picture of the equation graphed.

Step-by-step explanation:

Answer: 16/81

Step-by-step explanation:

To do this you have to do 2^4 which is 16.
Next, you have to do 3^4 which is 81
This gives you 16/81.

Now check if you can simplify it.
You can't so this is your answer :D

I hope this was able to help you :D

The verbal expression that best represents the equation 2(n - 7) = -14 is: c) seven less than twice a number is equal to negative fourteen.

Verbal expression can be defined as the way of writing mathematical expression into words or translating  equation into words.

Now let interpret this  equation 2(n - 7) = -14 into verbal expression.

n = a number

2n = twice a number

2n - 7 = seven less than twice a number

-14 = negative fourteen

Therefore we can conclude that the correct option is C.

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The different combinations of the five-digit number formed are enough to create ID numbers.

What is meant by combinations?

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant.

We first find the total number of 5-digit enrollment IDs that can be created using all possible combinations of numbers possible.

Since each digit of the five-digit number can be from 0-9, there are ten possible values for each digit.

So the total number of ways a five-digit number can be formed

= 10*10*10*10*10 = 100,000

For the given question, it is mentioned that only 75,000 students are expected to be enrolled in the next ten years,

Since 100,000 is greater than 75,000 the five-digit ID number will be enough.

But if the school is to last longer than ten years, it is safe to use a six or seven-digit ID number.

Therefore a five-digit Id number using symbols from 0-9 will be enough.

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Step-by-step explanation:

the sum of the area of the inner rectangle and the area of the 2 outer half-circles (that together are the area of one full circle).

the radius of the circles is 10 ft.

so, the diameter (= the width of the inner rectangle) = 2×10 = 20 ft.

so, the area of the inner rectangle is

30×20 = 600 ft²

the area of the combined full circle is

pi×r² = pi×10² = 100pi = 314.1592654... ft²

together that is

914.1592654... ft²

Answer: 720

Step-by-step explanation:

The system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 has the following solution: (x, y) = (1 / 24, 7 / 8)

In this question we find the case of a system of two linear equations with two variables, this case may have an unique solution. This system can be solved by algebraic properties.

First, write the system of linear equations:

4 · y - 12 · x = 3

y + 3 · x = 1

Second, clear y in the second equation:

y = 1 - 3 · x

Third, substitute in the first equation:

4 · (1 - 3 · x) - 12 · x = 3

Fourth, expand the expression and clear variable x:

4 - 12 · x - 12 · x = 3

4 - 24 · x = 3

24 · x = 4 - 3

24 · x = 1

x = 1 / 24

Fifth, determine the value of variable y:

y = 1 - 3 · (1 / 24)

y = 1 - 1 / 8

y = 7 / 8

The solution to the system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 is (x, y) = (1 / 24, 7 / 8).

The statement reports several typing mistakes. The system of linear equations is shown below:

4 · y - 12 · x = 3

y + 3 · x = 1

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