What is the five-number summary for this data set?
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.

It is True that Using flowcharts, programmers can break large systems into subsystems that are easier to understand and code.

A flowchart  serves a picture  consisting the separate steps of a process which is in sequential order and can be used to  break large systems into subsystems during programing.

If a more cohesive module is needed, it can be formed into one unit, having the performance of  multiple functions.

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Answer:

Below in bold.

Step-by-step explanation:

Part A

At the x-intercepts  f(x) = 0, therefore:

2x^2 - 3x - 5 = 0

(2x - 5)(x + 1) = 0

x = 5/2, -1)

So the x intercepts are (-1, 0) and (5/2, 0).

Part B

The Coefficient  of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.

Convert f(x) to vertex form, by completing the square:

f(x) = 2x^2 - 3x - 5

= 2(x^2 - 3/2x) - 5

= 2[(x - 3/4)^2 - 9/16] - 5

= 2(x - 3/4)^2 -18/16 - 80/16

= 2(x - 3/4)^2 - 49/8

So the coordinates of the vertex are

(3/4, -49/8)  or

(0.75, -6.125) in decimal form.

Part C

To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.

The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).

You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.

Suggest   x = - 2  and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 =  11.

- that is the point (-2,11) and the other would be  x = 4,  f(x) = 15. (4, 15)

Once you have plotted these points draw a smooth u shaped curve through them.

In order to find how many times they will blink at the same time we need to find the common multiple of 4 and 6 between 1 and 60.

The first bulb blinks after every 4 seconds, means it blinks in multiple of 4.

The multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.

The second bulb blinks after every 6 seconds, means it blinks in multiple of 6.

The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

The common multiple of 4 and 6 = 12, 24, 36, 48, 60.

∴

in sixty seconds they will blink 5 times at the same time.

The equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).

Given that x = -6, it means the directrix is horizontal.

Equation of parabola that opens left or write is expressed as;

( y - k )² = 4p( x - h )

Given that;

First, we find the vertex.

The vertex( h, k ) is halfway between the directrix and the focus.

Hence, x coordinate of the vertex is;

x = ( x coordinate of focus + directrix ) / 2

x = ( -4 + (-6) ) / 2

x = -10/2

x = -5

y coordinate of the vertex will be the same as that of the focus.
y = 8

Hence vertex will be;

( -5, 8 )

Next, we find the distance p from the focus to the vertex and from the vertex to the directrix.

Subtract x coordinate of vertex from x coordinate of focus.

p = -4 - ( -5 )

p = -4 + 5

p = 1

Now, we substitute these values into the equation.

( y - k )² = 4p( x - h )

( y - (8) )² = 4(1)( x - (-5) )

( y - 8)² = 4( x +5 )

Therefore, the equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).

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Answer:

Step-by-step explanation:

Hello!

apply distributive law

[tex]a(b - c) = ab - ac[/tex]

2(3-8y)=2.3-2.8y

=6-16y

Hope it helps!

Answer:

12.50h = 2500.75

Step-by-step explanation:

He earned $12.50 for 1 hour of work.

For 2 hours, he earned $12.50 × 2.

For 3 hours, he earned $12.50 × 3.

For h hours, he earned $12.50 × h which can be simply written as 12.50h

He earned altogether $2500.75, so 12.50h must equal 2500.75.

Answer: B 12.50h = 2500.75

Answer:

[tex]12.50 h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

12.50 x h = 2500.75

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

[tex]h=\frac{2500.75}{12.50}[/tex]

= 200.6 Hours

The measure of angle C is 35°.

Given that, ΔABC≅ΔDEF, ∠A=70°, ∠E=3x and ∠F=x+10.

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

In ΔABC and ΔDEF, corresponding angles are equal.

That is, ∠A=∠D=70°, ∠B=∠E=3x and ∠C=∠F=x+10

Now, ∠A+∠B+∠C=180° (∵angle sum property)

⇒70°+3x+x+10=180°

⇒4x=100°

⇒x=25°

Thus, ∠C=x+10=35°.

Therefore, the measure of angle C is 35°.

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Answer:

=> -2.22

Step-by-step explanation:

=> 2.35 + ( -4.57)

=> 2.35 - 4.57

=> - 2.22

Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object or land is taken, especially for use in a scientific research and experiment such as direct comparison.

From the odometer on Missy's car, we have the following information:

Initial reading = 23,678 miles.

Final reading = 25,127 miles.

Trip = Final reading - Initial reading

Trip = 25,127 - 23,678

Trip = 1,449 miles.

Lubrication mileage = 16,000 kilometers.

Total mileage = 68,000 kilometers.

Lubrication time = Total mileage/Lubrication mileage

Lubrication time = 68,000/16,000

Lubrication time = 4.25 ≈ 4.

Next Lubrication time = (16,000 × 0.25) + 68,000

Next Lubrication time = 16,000 - (16,000 × 0.25) + 68,000

Next Lubrication time = 80,000 kilometers.

Rate = $29 per mile

Speed limit = 35 mph

Missy's car speed = 43 mph

Difference = 43 - 35

Difference = 8 mph.

Ticket = 29 × 8

Ticket = $232.

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Answer:

distance = 10

2/7 /(22) = 10

The exact value of cos(c+d) is (D) [tex]cos(c+d) = \frac{21+24\sqrt{7} }{100}[/tex].

To find the exact value of cos(c+d):

In the second quadrant:

In the third quadrant:

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

[tex]\frac{21+24\sqrt{7} }{100}[/tex] ≈ [tex]0.84498[/tex]

To prove: Perhaps you want to work this out using the trignometric identities.

cos(c) = -√(1 -sin(c)²) = -7/25

sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is: cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

Therefore, the exact value of cos(c+d) is (D) [tex]cos(c+d) = \frac{21+24\sqrt{7} }{100}[/tex].

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The complete question is given below:

What is the exact value of cos(c+d), given sine c = start fraction 24 over 25 end fraction for c in quadrant ii and cosine d = negative three-fourths for d in quadrant iii?

(A) Negative StartFraction 47 Over 100 EndFraction

(B) Negative 1 and StartFraction 3 Over 100 EndFraction

(C) StartFraction 21 minus 24 StartRoot 7 EndRoot Over 100 EndFraction

(D) StartFraction 21 + 24 StartRoot 7 EndRoot Over 100 EndFraction

Substitute [tex]y=\sin^{-1}\left(\frac x4\right)[/tex], so that

[tex]dy = \dfrac{dx}{4\sqrt{1-\left(\frac x4\right)^2}} = \dfrac{dx}{\sqrt{16 - x^2}}[/tex]

Then the integral is

[tex]\displaystyle \int \frac{\left(\sin^{-1}\left(\frac x4\right)\right)^2}{\sqrt{16-x^2}} \,dx = \int y^2 \, dy[/tex]

and by the power rule,

[tex]\displaystyle \int y^2 \, dy = \frac13 y^3 + C[/tex]

so that the original integral is

[tex]\displaystyle \int \frac{\left(\sin^{-1}\left(\frac x4\right)\right)^2}{\sqrt{16-x^2}} \,dx = \boxed{\frac13 \left(\sin^{-1}\left(\frac x4\right)\right)^3 + C}[/tex]

Best guess for the function is

[tex]\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}[/tex]

By the ratio test, the series converges for

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1[/tex]

When [tex]x=1[/tex], [tex]f(x)[/tex] is a convergent [tex]p[/tex]-series.

When [tex]x=-1[/tex], [tex]f(x)[/tex] is a convergent alternating series.

So, the interval of convergence for [tex]f(x)[/tex] is the closed interval [tex]\boxed{-1 \le x \le 1}[/tex].

The derivative of [tex]f[/tex] is the series

[tex]\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n[/tex]

which also converges for [tex]|x|<1[/tex] by the ratio test:

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1[/tex]

When [tex]x=1[/tex], [tex]f'(x)[/tex] becomes the divergent harmonic series.

When [tex]x=-1[/tex], [tex]f'(x)[/tex] is a convergent alternating series.

The interval of convergence for [tex]f'(x)[/tex] is then the closed-open interval [tex]\boxed{-1 \le x < 1}[/tex].

Differentiating [tex]f[/tex] once more gives the series

[tex]\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)[/tex]

The first series is geometric and converges for [tex]|x|<1[/tex], endpoints not included.

The second series is [tex]f'(x)[/tex], which we know converges for [tex]-1\le x<1[/tex].

Putting these intervals together, we see that [tex]f''(x)[/tex] converges only on the open interval [tex]\boxed{-1 < x < 1}[/tex].

Answer:

13 square units

Step-by-step explanation:

We need to find the distance between the points using the  

Pythagorean Theorem, a² + b² = c²

(3,6) and (6,5); 6 - 3 = 3 and 6 - 5 = 1

3² + 1² = c²

9 + 1 = c²

c = √10

(6,5) and (5,1); 6 - 5 = 1 and 5 - 1 = 4

1² + 4² = c²

1 + 16 = c²

c = √17

√17 + √10 = 13.038

Based on the triangle midsegment theorem, the true statements are:

DE║AC

2DE = AC

If a line segment joins two sides of triangle and divides them at their midpoint, the divided segments will be congruent, and thus, the line segment joining the two sides is a midsegment of the triangle. According to the triangle midsegment theorem, the midsegment will be parallel to the third side that is not divided and also would be 1/2 its length. That is, the third side is twice the midsegment of that triangle.

In the image given, considering triangle ABC, we can make the following conclusions based on the triangle midsegment theorem:

D and E are midpoints of sides AB and BC respectively because they are divided by segment DE equally.

The midsegment is DE.

DE would be parallel to the third side, line segment AC.

Length of AC would be twice the length of DE

In conclusion, the true statements based on the triangle midsegment theorem are:

DE║AC

2DE = AC

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Answer:

B. - Three T-Shirts and Seven Sweatshirts: $37.5 + $203 =240.50

   - Six T-Shirts and Five Sweatshirts: $75 + $145 = $220

Step-by-step explanation:

A. - Three T-Shirts and Seven Sweatshirts: $27 + $213.50 = $240.50

   - Six T-Shirts and Five Sweatshirts: $54 + $152.5 = $206.5

B. - Three T-Shirts and Seven Sweatshirts: $37.5 + $203 =240.50

   - Six T-Shirts and Five Sweatshirts: $75 + $145 = $220

C. - Three T-Shirts and Seven Sweatshirts: $35.01 + $210 = $245.01

   - Six T-Shirts and Five Sweatshirts: $70.02 + $150 = $220.02

Mark as Branliest Please! :)

Answer: Step 1

Step-by-step explanation: The order of operations states that multiplication must be done before addition. However, in step 1, 3x3-2 turns into 3x1 which is wrong. It should be 9-2 because you need to do the multiplication first.

The correct option regarding the point at which the linear functions intersect is given by:

C) The lines don't intersect.

A linear function is modeled by:

y = mx + b

In which:

For line m, we have that the y-intercept is of b = 8. When x changes by 4, y changes by 8, hence the slope is of 2, and the equation is:

y = 2x + 8.

Line n, in slope-intercept format, is given by:

-8x + 4y = 24

4y = 8x + 24

y = 2x + 6

Hence:

2x + 8 = 2x + 6

0x = -2

Which is impossible, hence they do not intersect and option C is correct.

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Check the picture below.

The solution to the following mathematical problems are;

Solve using

BODMAS

5² -3⁴ / (2³-5)(6² ÷ 9)

= 25-81 / (8-5)(36÷9)

= -56 / (3)(4)

= -56/12

= - 14/3

20² ÷ {3(5-9)² + 2}

= 400 ÷ {3(-4)² + 2}

= 400 ÷ {3(16) + 2}

= 400 ÷ (48+3)

= 400 ÷ 50

= 8

84/12 + (5-7)² -72 ÷ 6×2

= 7 + (-2)² - 12 × 2

= 7 + (4) - 24

= 11 - 24

= -13

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Answer:

The answer is 314

Step-by-step explanation:

You need to do

3.14(pie) times the radius times the height divided by 3

Answer:

C. 314 [tex]in^{3}[/tex]

Step-by-step explanation:

The volume of a cone is: 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h'

1/3 x 3.14 x [tex]5^{2}[/tex] x 12

1/3 x 3.14 x 25 x 12

1/3 x 3.14 x 300

100 x 3.14

V = 314

331.5 inches²  is the area of the octagon, rounded to the nearest square inch.

What is octagonal in shape?

Solving for an area of a regular octagon, we can make use of the formula shown below:

Area = 1/2 × apothem × perimeter

In this problem, the following values were given such as:

Apothem = 10 inches

Perimeter = 66.3 inches

Put the values in the formula

Area = 1/2 × 10 × 66.3

Area = 331.5 inches²  

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Answer: C). 332 in.2

Step-by-step explanation:

on edg

Answer:

99cm

Step-by-step explanation:

A meter is equal to 100cm

The rope is a metre (m) long but a centimetre (cm) less.

100cm - 1cm = 99cm

Answer:A

Step-by-step explanation:

-3 to the left and up 4

Answer:

Step-by-step explanation:

Use pythagorean theorem (a^2+b^2=c^2). The diagonal represents c and the width represents b or a. 8^2+b^2=10^2->64+b^2=100->b^2=36->b=6. So your height would be 6.

The measures of the two different angles are 70° and 110°.

What is angle in parallelogram ?

Thus from the given question, we have:

(6n − 70)° + (2n + 10)° =  180°

8n - 60 =  180° + 60

8n = 240

n = 240/8

n = 30°

So that,

i. (6n − 70)° = (6[30] − 70)°

                    = 180 - 70

                     = 110°

ii. (2n + 10)° = (2[30] + 10)°

                   = 60 + 10

                   = 70°

Therefore, the measures of the two different angles are 70° and 110°.

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Answer: [D] 2(36-12)

Step-by-step explanation:

    First, we will simplify the given expression.

38 – 14 = 24

    Now, we will see if the other expressions are equivalent or not.

[A] 2(19-7) = 24

[B] 24 = 24

[C] (19-7)2 = 24

[D] 2(36-12) = 48

    The expression is NOT equivalent to the expression 38 – 14 is;

                   [D] 2(36-12)

Hi :)

Let's evaluate all these expressions

[tex]\boldsymbol{\boxed{38-14=24}}}[/tex]

  So Now the question boils down to --

What expression is NOT equivalent to [tex]\boldsymbol{24?}[/tex]

     [tex]\boldsymbol{2(19-7)}[/tex]

     [tex]\boldsymbol{2(12)}[/tex]

     [tex]\boldsymbol{24}[/tex]

Option (A) is ruled out, because we're looking for expressions that are not equivalent to 24.

   Well 24 is always equal to 24!

     [tex]\boldsymbol{(19-7)2}[/tex]

     [tex]\boldsymbol{(12)2}[/tex]

     [tex]\boldsymbol{24}[/tex]

    [tex]\boldsymbol{2(36-12)}[/tex]

     [tex]\boldsymbol{2(24)}[/tex]

     [tex]\boldsymbol{48}[/tex]

[tex]\tt{Learn\;More;Work\;Harder}[/tex]

:)

The probability for at least 1 page is 0.667 .

Probability is the department of arithmetic concerning numerical descriptions of the way likely an event is to occur, or how probable it is that a proposition is actual. The probability of an event is a number between 0 and 1, where, roughly speaking, zero shows the impossibility of the event, and 1 suggests truth.

Possibility = the wide variety of methods of achieving success. The whole wide variety of possible outcomes. As an example, the opportunity of flipping a coin and its being heads is ½ because there's 1 way of having a head and the total quantity of viable outcomes is 2 (a head or tail). We write P(heads) = ½.

The form opportunity is from old French probability (14 c.) and at once from Latin probabilities (nominative probabilitas) "credibility, possibility," from probabilistic (see likely). The mathematical sense of the time period is from 1718.

As there's an average of 1 misprint in line with the web page, the possibility of a minimum of 5 misprints is 1 - P(0, 1, 2, 3, or 4 misprints)

P(0) = e-1/0!

P(1) = e-1/1!

P(2) = e -1/2!

P(3) = e-1/3!

P(4) = e-1/4!  

P(0, 1, 2, 3, or 4 misprints) = e-1(1 + 1 + half of + 1/6 + 1/24) = 2 17/24 e-1 = .99634

Then, P(5 or more misprints) is 1 - .99634 = .00366

Then, the P(at the least 1 page in a 300-page ebook has at least 5 misprints) = 1 - P(0 pages have at least 5 misprints).

P(0 pages have at the least 5 misprints) = P(300 of 300 pages have 0, 1, 2, 3, or 4 misprints) =.99634 300

(you could view this as C(300, 300) p300 in case you desire) = 0.332881690573629

Then, P(1 or greater pages have at least 5 misprints) = 1 - 0.332881690573629 = 0.667118309426371

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