Graph. (Shade. Dashed line. Solid line?)
x+3y≥3

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.

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

Check the picture below.

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: [tex]512a^{15}[/tex]

Step-by-step explanation:

[tex](a^5*2^3)^3[/tex]

First, lets solve the inside of the parenthesis

[tex](a^5*8)^3[/tex]

Now, distribute the power of 3 to both terms. Remember taking a power of an exponent is like multiplying them (in this case [tex](a^5)^3=a^{15}[/tex]

[tex]a^{15}*512[/tex]

Simplify

[tex]512a^{15}[/tex]

Answer:A

Step-by-step explanation:

-3 to the left and up 4

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:

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!

The sentence "If this is the last chance you have to speak to him, what do you want to tell him" will be the best response from the leader.

This refers to the act of imitating the character and behaviour of someone who is different from yourself which an example is a training exercise which involves imitating of another people.

Sometimes, during the role play, the member of the group can run out of words while presenting a role, hence, as the member states, "i don’t know what to say to my father", the sentence "If this is the last chance you have to speak to him, what do you want to tell him" will be the best response from the leader to induce the member to talk.

Therefore, the Option C is correct.

Missing word "a. What or whom do you want to get away from? b. What made you come if you didn't want to be here today? c. If this is the last chance you have to speak to him, what do you want to tell him? d. What do you imagine will happen if you don't talk about it?"

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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

Answer:

28

Step-by-step explanation:

Tangent is a line that touches the circle at one point and is perpendicular to the radius. Circle A has radius AB and tangent CB, so AB is perpendicular to CB. Therefore triangle ABC is a right angle, with angle B measuring 90 degrees. Since interior angles of a triangle add up to 180 degrees, measure of angle A is 180 - 90 - 62 = 28 degrees.

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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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:

10 ounces

Step-by-step explanation:

Answer:

  9.09 ounces

Step-by-step explanation:

The added water can be calculated by writing an equation for the amount of iodine in the diluted solution.

Let x represent the number of ounces of water added to the 60% solution. The total amount of iodine in the mixture is ...

  0.60(100) +0(x) = 0.55(100+x) . . . . . ounces of iodine in the mix

Simplify the equation:

  60 = 55 +0.55x

  5 = 0.55x . . . . . . . subtract 55

  x = 5/0.55 ≈ 9.09

9.09 ounces of pure water must be added to produce a 55% solution.

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.

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:

is there a picture I can look at?

Answer: Line

Step-by-step explanation:

The probability of obtaining the number of successes indicated in problems 51–58 is 0.42.

Probability is absolutely how in all likelihood something is to happen. every time we're unsure about the final results of an occasion, we can talk about the chances of sure results—how in all likelihood they may be. The analysis of occasions ruled by using probability is called facts.

The opportunity of an event may be calculated with the aid of the opportunity formula by means of truly dividing the favorable wide variety of results by way of the overall variety of feasible effects.

Probability is the department of mathematics regarding numerical descriptions of ways possibly an occasion is to occur, or how likely it's miles that a proposition is actual. The chance of an event is more than a few between zero and 1, in which, roughly talking, 0 shows the impossibility of the event and 1 suggests fact.

Cells x doute the no of surrell and

"p' denotes the probability of turrets

D= 5

H=pkin = 50-xo-5 = 250

σ = SD(X) = √√rbg

= √√5=x05x=5 = 14.№33

The probability of obtaining $45-26

= P(-5-250 < x-M 22605-250)

14.233

= P(-03864 < 2 2 0-7332)

8.4200

0.42

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Answer:

distance = 10

2/7 /(22) = 10

Answer:

=> -2.22

Step-by-step explanation:

=> 2.35 + ( -4.57)

=> 2.35 - 4.57

=> - 2.22

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.

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: 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.

Answer:

D

Step-by-step explanation:

Pq=opp/hyp

(135+12)=180

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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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].

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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While E will increase, C and D won't change.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

Due to the fact that the circle's equation is,

Nevertheless, we are aware of the circle's equation.

                           [tex]x^{2}+y^{2}+C x+D y+E=0[/tex]

(By figuring out the circle's equation[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex], where r is the radius and (h,k) is the center)

                         [tex]x^{2}+y^{2}+2 h x+2 k y+\left(h^{2}+k^{2}-r^{2}\right)=0[/tex]

The following equation is compared to the generic equation above.

Our results are C = 2h, D = 2k, and E [tex]=\left(h^{2}+k^{2}-r^{2}\right)[/tex]

As a result, C will be unchanged if r lowers ( because C is free from r)

D won't be effected ( because D is also free from r)

E will, however, rise if r falls.

E[tex]=\left(h^{2}+k^{2}-r^{2}\right)[/tex]

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Answer:

m∠6 = 54°

Step-by-step explanation:

Given the diagram, we know that line b is a straight line and angles 1 (the angle measuring 13x + 9°) and 2 are supplementary angles and thus add up to 180.  

We also know angles 2 and 7 (the angles measuring 5x + 9°) are alternate exterior angles and are therefore congruent.

So since angle 2 = 5x + 9, we can do:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 162

x = 9

Angles 7 and 6 are also congruent plugging x into angle 7 also gives us the measure of angle 6:

5(9) + 9 = 45 + 9 = 54°