The figure shown is composed of two congruent triangles and a square. Measurements are given in inches. 1 4 7 What is the total area of the figure in square inches? Enter your answer in the box. X 2 5 8 5 in. 0 4 in. 5 in. 3 6 9 6 in. pla 5 in. 4 in. 5 in.​

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.

More can be learned about the interquartile range at brainly.com/question/12323764

#SPJ1

RQT = 159

RQS = 69

==============================================

Explanation:

Draw a segment connecting R and S.

Triangle SRQ is a right triangle due to Thale's Theorem. That theorem is a special case of the inscribed angle theorem. The 90 degree angle R is opposite the diameter SQ.

Minor arc QR = 42 degrees. Half of this is 42/2 = 21, which is the measure of inscribed angle RSQ. This inscribed angle subtends minor arc QR.

Focus on triangle SRQ. We have two known angles (R = 90 and S = 21). Let's use them to find the missing angle.

The inside angles of any triangle always add to 180 degrees.

S+R+Q = 180

21+90+Q = 180

111+Q = 180

Q = 180-111

Q = 69

Angle RQS is 69 degrees.

----------------

We'll add angle SQT onto the previous result to get angle RQT.

angle RQT = (angle RQS) + (angle RQT)

angle RQT = (69) + (90)

angle RQT = 159 degrees

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

Learn more about collinear on

https://brainly.com/question/1649376

#SPJ1

Answer: 678

Step-by-step explanation: ii

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

Answer:

The answer is zero.

Step-by-step explanation:

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

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

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

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

The amount of walking space between two tables at the point where they are the closest is 0.9 m.

We are given that;

The space allowed per chair = 45 cm.

Number of tables=30

Now,

we find the length of a side of a square that contains a table by adding twice the radius of a table to twice the space allowed per chair. The formula is: side length=2×radius+2×space per chair

Plug in the given values and simplify. The calculation is: side length=2×0.9+2×0.45=2.7

Now subtract the diameter of a table from the side length to get the walking space between two tables. The formula is: walking space=side length−diameter

Plug in the given values and simplify. The calculation is: walking space=2.7−1.8=0.9

To express our answer in meters. walking space=0.9 m

Therefore, by the algebra the answer will be 0.9 m.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

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!

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.

For similar questions on Transactions

https://brainly.com/question/26138968
#SPJ11

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.
For similar question on probability.

https://brainly.com/question/30768613

#SPJ11

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|

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The number of questions asked in a day is A = 110

Given data ,

To determine the number of questions being asked in a day, we need to divide the total number of questions by the number of days.

Now ,  12 people are collectively asking 775 questions in a 7-day period.

So , the number of questions being asked in a day, we divide 775 by 7

A = 775 / 7

On simplifying the equation , we get

A ≈ 110.71

Hence , 110.71 questions are being asked in a day

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

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

Read more about odds at

https://brainly.com/question/16363997

#SPJ1

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.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

Answer:

it is 20.00 hope this answer helps.

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.

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

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

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.

Read more on confidence interval here:https://brainly.com/question/15712887

#SPJ1

Answer:

Step-by-step explanation:

so how to help you but you do a good job

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).

To learn more about the transformations click here :

brainly.com/question/11352944

#SPJ1

Answer:11.7

Step-by-step explanation:

σ =√137.63265306122

σ= 11.731694381513

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

Learn more about long division:
https://brainly.com/question/28824872
#SPJ1

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 :)

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.

For more such questions on savings account: https://brainly.com/question/30101466

#SPJ11

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.

for such more question on equation

https://brainly.com/question/16983571

#SPJ11