The first term in a sequence is 72. The pattern follows the rule add 31. What are the next four terms?

Answer:  False

Reason: It should be x-a instead of x+a

Answer:

Step-by-step explanation:

C

[tex]\Large\textsc{answer :}[/tex]

x≤-7

[tex]\Large\textsc{calculations :}[/tex]

First , use the distributive property :

3(x-4)≥5x+2

3x-12≥5x+2

Subtract 5x on both sides :

3x-5x-12≥2

Now , add 12 on both sides :

3x-5x≥2+12

3x-5x≥14

Subtract the x's :

-2x≥14

Divide by -2 on both sides and watch what happens :

x≤-7 (notice that the inequality sign changed from "greater than or equal to" to "less than or equal to")

If we divide both sides of an inequality by a negative number , we change the inequality sign .

[tex]\footnotesize\textit{hope helpful~}[/tex]

Answer:

1/5

Step-by-step explanation:

there are 15 pens totally, there are 3 red pens.

probability-> 3/15=1/5

Answer:

$18.Hope it helps.....

use tan since you are given the opposite and adjacent sides

tan θ = [tex]\frac{opp}{adj}\\\\[/tex]

tan θ = [tex]\frac{2}{12}[/tex]

use the inverse of tan to find the angle

θ = [tex]tan^{-1}(\frac{2}{12})[/tex]

θ = 9.462322208...

θ = 9.46°

The experimental probability that the bottle landed on its base by the data recorded is; 3/10.

It follows from the frequency recorded for the bottle landing on it's base and side that; base = 9 and side = 21.

The total possible outcome is 30.

On this note, the required probability is; 9/30 = 3/10.

Read more on probability;

https://brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

Discussion

The object of this is make w by itself on one side of the equation.

Equation

x = 3 (y + w) - 1               Add 1 to both sides of the equation.

x + 1 = 3(y + w) - 1 + 1      Combine

x + 1 = 3(y + w)                 Remove the Brackets

x + 1 = 3y + 3w                 Notice y and w are affected by the 3. Subtract 3y

x + 1 - 3y = 3y-3y + 3w   Combine

x + 1  = 3w                       Divide both sides by 3

(x +1)/3 = 3w/3  

(x + 1)/3 = w

Answer: (x + 1)/3 = w

Random sampling is the selection of clusters first from the community. Then the correct option is C.

Random sampling is the method of selecting the subset from the set to make a statical inference.

A researcher for an airline interviewed all of the passengers on five randomly selected flights.

Cluster sampling is a strategy in which the research splits the overall population into distinct clusters (groups).

Then random sampling is the selection of clusters first from the community.

More about the sample method link is given below.

https://brainly.com/question/15125943

#SPJ1

Answer:

61 Degree Angle

Step-by-step explanation:

Supplementary angles are two angles that add up to 180 degrees. So in this case, 119 + 61 = 180.

Answer:

volume

Step-by-step explanation:

the amount of space enclosed by an object or shape, how much 3-dimensional space

Answer: I think it’s $15.71

Step-by-step explanation:

Answer:

red I think

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Answer:

14/15

Step-by-step explanation:

P(S or T) = P(S) + P(T) = 3/5 + 1/3

= 9/15 + 5/15 = 14/15

Answer:

x= y−2/3

Step-by-step explanation:

1 Subtract 2 from both sides.

y-2=3x

2 Divide both sides by 3.

y−2/3 =x

3 Switch sides.

x= y−2/3

Answer:

535km

Step-by-step explanation:

train speed = 321/3 km per hour = 107kmh

in 5 hours, travel distance = speed x time = 107 x 5 = 535km

Answer: z=29 x=119 y=61

Step-by-step explanation:

A ray is 180 degrees and you can go from there. Hope this helps!

Answer:

c

Step-by-step explanation:

Answer:

How many hours a week do you watch televison?

Step-by-step explanation:

In order for Mike to organize a survey about this particular topic, it's important that he asks concise questions that provide him with generalized data about multiple days of the week. Because of this, he wouldn't want to ask any questions that solely focus on specific days, so we can use process of elimination to get rid of answer choices C and D. Both of these options are too specific, and only ask about 1 or 2 days instead of a larger period of time. Using the same logic, we can get rid of option A. Option A is also too specific, but for a different reason. This question is only asking about students who watch televison for an hour everyday. Remember, for good surveys, more results provide a better sample of data. So it's important that the questions asked are coherent, but also don't limit the amount of data received either.

[tex]\huge[\sum_{k=0}^{4}(k)][/tex] [tex] = 0+1+2+3+4=\boxed{10} [/tex]

=[tex]\huge(\binom {5}{2}) [/tex] [tex] =(5!)/(3! \times 2!) = (5\times 4)/(2)= \boxed{10}[/tex]

Since there are 5 teams..

The number of matches played in a 5 team round Robin is 10.

A round-robin tournament is a sports competition where each player or team competes against every other player or team; each contestant faces off against the other contestant in turn. A round-robin tournament differs from an elimination tournament in that participants are eliminated after a set number of losses.

From 5 teams we choose 2 to form combinations (need combinations of 2 different teams to play a match).

Here, 5C2 = 5!/2!(5-2)!

= 5×4×3×2!/2!×3!

= 10

Hence, the number of matches played in a 5 team round Robin is 10.

To learn more about the permutation and combination visit:

https://brainly.com/question/28065038.

#SPJ7

Answer:

(1,4)

Step-by-step explanation:

Since x is already "alone", you can plug 3y-11 into the x-value for the first equation to get 3(3y-11)+5y=23. Now distribute 3 to the numbers in the parentheses. In the end, the solution to this is (1,4).

Answer:

x=1, y=4

Step-by-step explanation:

Substitute x = 3y - 11

3(3y - 11) + 5y = 23 |

Simplify

|14y – 33= 23 |

Isolate y for 14y-33=23

y=4

For x =3y - 11

Substitute y = 4

X=3• 4- 11

Simplify

X=1,

Answer:

3.6 in

Step-by-step explanation:

1/2 ft= 6in

1/5 ft= 2.4 in

so 6-2.4= 3.6 in

Hope this helps :)

Answer: i think option c

Step-by-step explanation:

Answer:

1. right, 2. median, 3. range or the IQR

Step-by-step explanation:

Answer:

For the answers, it would be: 1. right, 2. median, and 3. range or IQR.

Answer:

Number 1

Step-by-step explanation:

Vertex is (−1,−13)

[tex]~~~~~6x^2 +12x -7 =0\\\\\implies x^2 +2x - \dfrac 76=0\\\\\implies x^2+2x = \dfrac76\\\\\implies x^2 +2x +1 = \dfrac 76 +1\\\\\implies (x+1)^2 = \dfrac{13}6\\\\\implies x+1 = \pm \sqrt{ \dfrac{13}6}\\\\\implies x = -1 \pm\sqrt{\dfrac{13} 6}\\\\\text{Hence,}~ x = -1 +\sqrt{\dfrac{13} 6}~~ \text{and}~~ x = -1-\sqrt{\dfrac{13} 6}[/tex]

Answer:

Using the Empirical Rule, we find that .997 (99.7%) of students have grade point averages that are between 1.23 and 3.81.

Step-by-step explanation:

Calculate the z-scores corresponding to a GPA of 1.23 and 3.81.

We want to find the area between the z-scores of -3 and 3.

The Empirical Rule tells us that 99.7% of the data lies within three standard deviations under the normal curve.

Therefore, the area between -3 < z < 3 is about .997, or around 99.7%.

Answer:

[tex]\textsf{13)} \quad y=(x+5)^2+4[/tex]

[tex]\textsf{14)} \quad y=-\dfrac{1}{2}(x-2)^2-3[/tex]

Step-by-step explanation:

Vertex form of a parabola:  

[tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

From inspection of the graph, the vertex is (-5, 4)

[tex]\implies y=a(x+5)^2+4[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (-4, 5):

[tex]\implies a(-4+5)^2+4=5[/tex]

[tex]\implies a(1)^2+4=5[/tex]

[tex]\implies a+4=5[/tex]

[tex]\implies a=1[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=(x+5)^2+4[/tex]

From inspection of the graph, the vertex is (2, -3)

[tex]\implies y=a(x-2)^2-3[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (0, -5):

[tex]\implies a(0-2)^2-3=-5[/tex]

[tex]\implies a(-2)^2-3=-5[/tex]

[tex]\implies 4a-3=-5[/tex]

[tex]\implies 4a=-2[/tex]

[tex]\implies a=-\dfrac{1}{2}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]\implies y=-\dfrac{1}{2}(x-2)^2-3[/tex]

#1

Equation

As there is no y inetercept present and the function is same as general quadratic equation y=x^2 just change in coordinates a=1

Final equation

#2

y=a(x-2)²-3

Use (4,-5)

Equation