Solve the following system of equations graphically on the set of axes below.

y = 2/3 x + 3
y = - 4/3 x - 3
Plot two lines by clicking the graph.

Answer: see below. the answers are bolded.

Step-by-step explanation:

1. Since x+55 forms a straight line, x+55 = 180. Solve that equation and you get x = 125. All interior angles in a triangle = 180. That means: 55+45+y = 180. Solve that equation and you get y = 80.

2. 110+x forms a straight line. 110+x = 180. Solve that equation and you get x = 70. Now that you have x, and you know that the interior angles of a triangle add up to 180, set up an equation. 70 + 65 + y = 180. Solve, and

y = 45

Hope I helped :)

The difference between the interquartile range of Matt's remaining vacation days an Linda's remaining vacation days is given as follows:

-3.5.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

Matt's ordered data-set is given as follows:

5, 9, 11, 12.

Hence the quartiles are:

Hence the IQR is of:

IQR = 11.5 - 7 = 4.5.

Linda's ordered data-set is given as follows:

0, 6, 9, 13.

The quartiles aret

The IQR is of:

IQR = 11 - 3 = 8.

Hence the difference is of:

4.5 - 8 = -3.5.

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53 = 43 + v, so substitute each number for V and see if it equals 53.

v = 8 >>> NO

53 = 43 + 8 >>> Nope. This is 51

v = 10 >>> YES

53 = 43 + 10 = 53 >>> Yup! This works.

v = 96 >>> NO

53 = 43 + 96 >>>> Nope, this doesn't add up.

V = 6 >>> NO

53 = 43 + 6 = 49 >>> Nope this doesn't add up.

The simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|

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

2|5k-3/5+1/10k

Express properly

So, we have

2|5k - 3/5 + 1/10k|

Collect the like terms in the expression

So, we have the following representation

2|5k - 3/5 + 1/10k| = 2|5k  + 1/10k - 3/5|

Evaluate the like terms

This gives

2|5k - 3/5 + 1/10k| = 2|51/10k - 3/5|

Expand the brackets

2|5k - 3/5 + 1/10k| = |51/5k - 6/5|

Hence, the simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|

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Answer:

The answer is zero.

Step-by-step explanation:

Using the law of sines, the value of a in the given triangle, to the nearest tenth, is calculated as: 19.9.

The law of sines that we would apply is given as:

sin A/a = sin B/b = sin C/c.

Given the following:

a = ?

A = 64 degrees

b = 17

B = 50 degrees

Plug in the values into the equation, sin A/a = sin B/b:

sin 64/a = sin 50/17

Cross multiply:

a * sin 50 = sin 64 * 17

Divide both sides by sin 50

a * sin 50 / sin 50 = sin 64 * 17 / sin 50

a ≈ 19.9 [nearest tenth]

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The value of a to the nearest tenth is 20.0

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Using sine rule to solve for a;

The side opposite to angle 64 is a and the side opposite to angle 50 is 17

a/sinA = b/sinB

a/sin64 = 17/sin50

asin50 = 17sin64

0.766a = 17 × 0.899

0.766a = 15.283

a= 15.283/0.766

a = 20.0( nearest tenth)

Therefore the value of a is 20.0

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After 7 years, you will have approximately $[tex]24,156.36[/tex] in your savings account.

To calculate the final amount in your savings account after 7 years with continuous compounding, we can use the formula for compound interest with continuous compounding:

[tex]\[ A = P \times e^{rt} \][/tex]

Where:

- A is the final amount in the account

- P is the initial principal (the amount you deposit)

- e is Euler's number (approximately 2.71828)

- r is the interest rate (expressed as a decimal)

- t is the time period in years

In this case, you have won $12,000 in the lottery, so P = $12,000. The interest rate is [tex]7.5\%[/tex], which is equivalent to [tex]0.0.75[/tex] in decimal form. The time period is [tex]7[/tex] years.

Plugging these values into the formula, we get:

[tex]\[ A = 12000 \times e^{0.075 \times 7} \][/tex]

Calculating the exponential term:

[tex]\[ e^{0.075 \times 7} \approx 2.013 \][/tex]

Substituting this back into the equation:

[tex]\[ A = 12000 \times 2.013 \]\[ A \approx 24156.36 \][/tex]

So, after 7 years, you will have approximately $[tex]24,156.36[/tex] in your savings account.

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The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

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The odds against stopping on a number less than 12 is 5 ; 11

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

Sections in the spinner = 16

This means that the probability of getting a number less than 12 is

P(Number less than 12) = Sections less than 12/Sections in the spinner

There are 11 sections less than 12

So, we have

P(Number less than 12) = 11/16

When represented as odds, we have

P(Number less than 12) = 16 - 11 : 11

Evaluate the difference

P(Number less than 12) = 5 : 11

Hence, the odds against stopping on a number less than 12 is 5 ; 11

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The cost of 13 yards of material sold at #1000 per yard would be:

13 x #1000 = #13,000

The solution to the equation is x = 1.6.

Let's start by distributing the 3 on the right side of the equation:

25 + 2x = 12x + 9

Next, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side. To do this, we'll subtract 2x from both sides:

25 = 10x + 9

Then, we'll subtract 9 from both sides:

16 = 10x

Finally, we'll divide both sides by 10:

x = 1.6

So the solution to the equation is x = 1.6.

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The coordinates of point A' are (4,1) in the given rectangle.

According to the shown figure, the coordinate of the given rectangle can be written as:

The coordinates of vertice A are (4, 3)

As we know that the x-coordinate of the reflected point will be the same as the x-coordinate of the original point.

Therefore, the x-coordinate of point A' will be:

x-coordinate of A' = 4

Here, the y-coordinate of point A is 3, which is 1 unit above the line y = 2. So, the reflection of point A across the line y = 2 will be 1 unit below the line y = 2.

So, the y-coordinate of point A' will be:

y-coordinate of A' = 2 - 1 = 1

Therefore, the coordinates of point A' are (4,1).

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The total deer population for year 8 will be D. about 2081 deer.

To calculate the total deer population, we use the mark-recapture formula where: N = M * C/R

M = Total number of deer population captured and marked

C = Total number of deer population that had or did not have a mark

R = Total deer population recaptured and marked

So, for the given problem, the figures are as follows:

M = 1608

C = 110

R = 85

N = 1608 * 85 = 176,880/85 = 2080.94

So, the estimated deer population is about 2081 deer.

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Transactions are larger than others Bank B may be the cheaper option even if you make more than 35 transactions.

To compare the cost of using Bank A and Bank B need to consider the total cost based on the number of transactions.

Let's say you make x transactions in a month.

For Bank A the monthly cost is a fixed fee of $45 regardless of the number of transactions.

For Bank B the monthly cost is a fee of $20 plus $0.70 for each transaction.

So the total cost for Bank B is:

Total cost = $20 + $0.70x

The break-even point where the total cost of Bank A and Bank B are equal need to solve the following equation:

45 = 20 + 0.70x

Subtracting 20 from both sides, we get:

25 = 0.70x

Dividing both sides by 0.70, we get:

x = 35.71

If you make more than 35 transactions in a month Bank A is the cheaper option.

If you make fewer than 35 transactions Bank B is the cheaper option.

Analysis assumes that all transactions are of the same amount.

To compare the total cost of both banks based on the actual amounts of the transactions.

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The probability that Nippon will get 100% on the quiz by random guessing is 1/16.

To calculate the probability of Nippon getting a 100% on the quiz by guessing on all 4 true-false questions, you need to consider the probability of guessing correctly on each individual question.
The probability of guessing correctly on a single true-false question is 1/2, as there are two possible answers (true or false).

Since there are 4 questions, you need to find the probability of guessing correctly on all 4 questions.
To do this, you multiply the probabilities of guessing correctly on each individual question: [tex](1/2) \times  (1/2) \times  (1/2) \times  (1/2).[/tex]
When you multiply these probabilities, we  get (1/16), which is the probability of Nippon getting 100% on the quiz by guessing on all 4 true-false questions.
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Answer: 678

Step-by-step explanation: ii

Answer:

it is 20.00 hope this answer helps.

Part A: The table that displays a complete list of possible outcomes would be = Table B, that is option B.

Part B: The probability that the chosen events will take place = 0.3.

To calculate the probability of the given event the formula that should be used is given below. That is;

Probability = possible outcome/sample space

The total number of blues balls = 1

The total number of red balls = 2

The total number of yellow balls = 2

The total number of balls = 5, while total number of colour = 3

For part A: the possible sample outcomes = (H,B), (HR), (HY), (TB), (TR), (TY).

For part B:

Using the formula the possible outcome = 2

Sample space = 7

Probability = 2/7 = 0.3

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Answer:

[tex]g(x) = f(x) - 4[/tex]

Step-by-step explanation:

We have been given a graph for f(x) and a table for g(x) and we have to find the transformation to map f(x) to g(x)

Let's find the function values for f(x) and g(x) at specific (easily distinguishable) x values for both

x               f(x) from graph                        g(x) from table

0                         4                                                0

1                          3                                                -1

2                          4                                                0

The function values for f(x) for x =  -1 and x = 3 are a bit difficult to read since they do not cross at  a grid intersection          

From the above table we see that for a specific x, g(x) value is 4 less than the f(x) value

Therefore the transformation is
g(x) = f(x) - 4    

Therefore g(x) is shifted downward by 4 points

I have plotted both f(x) and g(x) using the transformation; You can see the points fit

[tex]-------------------------------[/tex]

Ignore this part if you wish

The equation for f(x) is
f(x) = (x - 1)² + 3  in vertex form

or

f(x) = x² − 2x + 4​ in polynomial form

g(x) will then be
x² - 2x + 4 - 4 = x² -2x

The 95% confidence interval of the mean is approximately (26.4121, 39.3879) lbs.

since df = n - 1 = 20 - 1 = 19). You can find this value using a t-distribution table or an online calculator.

For a 95% confidence level and 19 degrees of freedom, the t-score is approximately 2.093.

Now, let's calculate the margin of error (E):

E = 2.093 * (14.8 / √20)

E ≈ 6.4879

Finally, we'll find the confidence interval:

Lower Bound = x - E = 32.9 - 6.4879 ≈ 26.4121 lbs

Upper Bound = x + E = 32.9 + 6.4879 ≈ 39.3879 lbs

The 95% confidence interval of the mean is approximately (26.4121, 39.3879) lbs.

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The above is a long division problem, where 40 is the divisor and 10 is the dividend. the answer is 00.250 or 0.250. Long division is also called synthetic division.

       00. 250___________________

40 | 10.000

  -   0

      1 0

 -       0

     1 0 0

-        80
         2 0 0

-         2 0 0

             0   0

-                0      

                 0

Note that the answer is given in three decimal places that is 0.250

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a. The values of k for which points A, B, and C are collinear are k = 3 and k = -2.

b. The value of k for which AB is parallel to CD is k = 13.

a. slope AB = (k+4-9)/(k+1-0) = (k-5)/(k+1)

The slope of AC is:

slope AC = (k+3-9)/(2k-0) = (k-6)/(2k)

Since A, B, and C are collinear, slope AB = slope AC. Therefore, we have:

(k-5)/(k+1) = (k-6)/(2k)

2k(k-5) = (k+1)(k-6)

2k^2 - 10k = k² - 5k - 6

k = 3 or k = -2

(b)  The slope of AB is:

= (k+4-9)/(k+1-0) = (k-5)/(k+1)

The slope of CD is:

= (k+6-k-3)/(2k+2-2k) = 3/2

Since AB is parallel to CD, slope AB = slope CD. Therefore, we have:

(k-5)/(k+1) = 3/2

2(k-5) = 3(k+1)

k = 13

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With the values provided, we can find both the volume and surface area.

Volume:

Formula = pi x r^2 x h

---r is the radius, h is the height

Volume = pi x (3)^2 x 7

Volume = pi x 36 x 7

Volume = 252pi mi^3 = 791.68 mi^3

Surface Area:

Formula = 2 x pi x r x h + 2 x pi x r^2

---r is the radius, h is the height

Surface Area = 2 x pi x 3 x 7 + 2 x pi x (3)^2

Surface Area = 42pi + 18pi

Surface Area = 60pi mi^2 = 188.50 mi^2

Hope this helps!

The inequality that represents the graph is:

x≥ -3

The inequality that represents the graph is:

x < 2

We have,

11.

From the number line,

The dot is in -3 and it extends infinitely to the right.

So,

The inequality that represents the graph is:

x≥ -3

And,

From the number line,

The open dot is in 2 and it extends infinitely to the left.

So,

The inequality that represents the graph is:

x < 2

Thus,

The inequality that represents the graph is:

x≥ -3

The inequality that represents the graph is:

x < 2

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Answer:11.7

Step-by-step explanation:

σ =√137.63265306122

σ= 11.731694381513

Answer:

5 (19 + 12)

Step-by-step explanation:

You add up the red and black pens and multiply by 5, which indicates the 5 bags

Answer:

Step-by-step explanation:

so how to help you but you do a good job

Answer:

216.

Step-by-step explanation:

To solve this expression, you can first simplify the expression inside the parentheses:

45 - (25 + 8) = 45 - 33 = 12

Then you can substitute this simplified expression back into the original equation and multiply by 18:

(12) X 18 = 216