finding the slope of (1, 1), (-1,-4) from two points

The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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The answer for it is diagram B because it does not cross or have parallel lines

Answer:

y intercept is 3, slope is 2

The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.

The estimated regression equation developed in part (a) to predict overall customer satisfaction is given by:

Overall Satisfaction = 0.3151*Trade Price + 0.3132*Speed of Execution + 1.5026

The coefficient of determination (R2) is a measure of how well the equation fits the data and is calculated as the proportion of the variation in overall satisfaction that is explained by the model. In this case, the R2 = 0.39, which means that 39% of the variation in overall satisfaction can be explained by the trade price and speed of execution variables.

To determine the overall significance of the relationship, the F test was used. The F statistic was calculated to be 17.874, which was significant at the 0.05 level (p-value = 0.000), indicating that the model was an effective predictor of overall customer satisfaction.

The t tests were then used to determine the significance of each independent variable. The t statistic for Trade Price was 2.639 (p-value = 0.009), indicating that the variable was significant at the 0.05 level, while the t statistic for Speed of Execution was 2.565 (p-value = 0.012), indicating that the

The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.

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Answer:

g(x) = x^2 + 5

Step-by-step explanation:

You notice that g(x) is essentially just f(x) but moved upwards.

Using the formula a(x-h)^2 + k, you know that there is no vertical or horizontal stretch, so a is 1. You also know that h is 0 because there is no horizontal movement.

Lastly, you have k. Because the graph is moved up by 5, k = 5.

The equation is g(x) = x^2 + 5.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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100 - 3(3 x 7 - 4 x 5)

Simplify

97(21 - 20)  

Simplify

97(1)

Now, multiply.

97 x 1 = 97

So the answer to the equation above, is 97.

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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Answer:

15

Explanation:

The y-intercept of a line is the point where it intersects the y-axis. This happens when x = 0; therefore, the y-coordinate of the y-axis is found by putting x = 0 in the equation given. This gives

which is our answer!

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

$89.70 or $192.30

Step-by-step explanation:

All you have to do is multiply 26 by 3.45 and you get your answer. Which if you use a calculator it would say 89.7, to find the answer you just add a zero to the end.

If you're doing the second answer you multiply 30 by 3.45, then you take 26 and multiply by 3.45, after that you add them together and you get your answer.

The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

From the question, we have the following equations that can be used in our computation:

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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Answer:

Cash, Bonds, Stocks and Mutual funds

Step-by-step explanation:

The four major categories of securities are:  

These 4  major categories are evaluated as given below:  

Answer:

462.30m

Step-by-step explanation:

1 month = $462.30

You multiply by the number of months to find how much she made over that time so $462.30 * m = 462.30m

Answer:

Step-by-step explanation:

An example of time-ordered typical sample statistics is shown in the Control chart. It is used to process the Mean bar.

A control chart is a statistical tool for monitoring the effectiveness of a process over time. It has the form of a graph with two additional lines representing the upper control limit and lower control limit. The central line in the graph represents the mean or average of the data.

Control charts are a type of graph used in production control to assess the effectiveness of exceptional production procedures under challenging circumstances. Control charts are actually the tools used in control strategies. These curves were produced using historical data.

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Answer:

if they are parallel it would almost be opposite but they would be negative instead of positive

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

a) -8/9

b) The series is a convergent series

c) 1/17

Step-by-step explanation:

The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.

If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r

a is the first tern of the series.

a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;

∑(-8)^(n−1)/9^n

= ∑(-8)^(n−1)/9•(9)^n-1

= ∑1/9 • (-8/9)^(n−1)

From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9

The common ratio r = -8/9

b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.

c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.

S∞ = a/1-r

Given a = 1/9 and r = -8/9

S∞ = (1/9)/1-(-8/9)

S∞ = (1/9)/1+8/9

S∞ = (1/9)/17/9

S∞ = 1/9×9/17

S∞ = 1/17

The sum of the geometric series is 1/17

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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Answer:

The value of the middle-most observation is called the median of the data.

First arrange the given numbers in ascending order,

2,2,3,5,7,9,9,10,11

Here n=9, which is odd.

Where, n is the number of the given number.

median = value of  

Given in the question:

a.) A group of 12 students and 3 teachers pay $72 for admission to a private research center.

b.) Another group of 14 students and 4 teachers pay $87.

Let,

x = Cost per student

y = Cost per teacher

Let's interpret the scenario of given a and b into an equation. These equations will be the linear systems to be used in getting the cost.

Given a: A group of 12 students and 3 teachers pay $72 for admission to a private research center.

Given b: Another group of 14 students and 4 teachers pay $87.

Conclusion: The linear systems you would use to find the cost of one student ticket and one teacher ticket are 12x + 3y = 72 and 14x + 4y = 87.

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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Answer:

I don't know what the unit of measurement is, so I'll say the distance is 21. As for the average speed, its average speed is 8 per second.

Step-by-step explanation:

Distance: 21

Speed: 7

There :3

Answer:

Nicole is 13 years old because x + 5 = 18

Step-by-step explanation:

Answer:

The number of possible outcomes is;

Explanation:

Given that you flip a coin and roll a 6 sided die.

The number of outcomes for each is;

The combined total number of possible outcomes is;

The number of possible outcomes is;

Y=-x+3 is the slope-intercept form equation for the line.

The slope or gradient of a line is a numerical representation of a line's steepness and direction in mathematics. The reason for this usage is unknown, although it first appears in English in O'Brien (1844), who wrote "y = mx + b," and in Todhunter (1888), who wrote "y = mx + c." The letter m is widely used to signify slope.

The slope can be calculated by comparing the "vertical change" to "horizontal change" between any two distinct points on a line. In cases when the ratio is expressed as a quotient ("rise over run").

From the above graph,

The line is passing through the points (-1, 4) and (3, 0)

Let the slope intercept form be

y= mx +c

Slope m=(0-4/3+1)

=-4/4

= -1

y= -x+c

The equation is passing through the point (3, 0)

-3+c=0

c=3

y= -x+3

Therefore, y=-x+3 is the slope-intercept form equation for the line.

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The number of days until Stephen and John are on the same page would be 6 days

The page they would be on would be 64 pages

Assuming that the number of days can be denoted as x, the equation for the number of pages that Stephen has read in total is:

= 22 + 7 x

The number of pages that John has read in total is:

= 10 + 9 x

To find the number of pages, equate these:

22 + 7 x = 10 + 9x

22 - 10 = 9x - 7 x

12 = 2 x

x = 12 / 2

x = 6 days

The page they would be on is:

= 10 + 9 x

= 10 + 9 ( 6 )

= 64 pages

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The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

Answer:

Step-by-step explanation:

Let's call the weight of each container "w". We can set up two equations based on the information given:

Equation 1: 3w = 70.8 (the weight of 3 containers holding 9 gallons)

Equation 2: 5w = 118.0 (the weight of 5 containers holding 15 gallons)

To solve for "w", we can first solve Equation 1 for "w":

3w = 70.8

w = 70.8/3

w = 23.6

Now we can substitute this value of "w" into Equation 2 and solve for the total weight of 5 containers:

5w = 118.0

5(23.6) = 118.0

So each container weighs 23.6 pounds.