Consider two consecutive positive integers such that the square of the second integer added to 3 times the first is equal to 105

Answer:

[tex]\huge\boxed{a_3=9,216}[/tex]

Step-by-step explanation:

[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]

Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ [tex]\r p , \ \r q[/tex], ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of [tex]\alpha[/tex] ​?

Answer:

a

   [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

   [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

   [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e                        [tex]\r q = 1- \r p[/tex]

b

   [tex]\alpha = 10\%[/tex]

Step-by-step explanation:

Here

    [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

    [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e  

      [tex]\r q = 1- \r p[/tex]

      [tex]\r q = 1- 0.12[/tex]

      [tex]\r q = 0.88[/tex]

     [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as

     [tex]\alpha = ( 100 - C )\%[/tex]

Where  [tex]C[/tex] is the confidence level which is given in this question as  [tex]C = 90 \%[/tex]

So  

    [tex]\alpha = ( 100 - 90 )\%[/tex]

    [tex]\alpha = 10\%[/tex]

Answer:

D. The linear parent function

Step-by-step explanation:

Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.

Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;

m= gradient of the straight line graph

x= the independent variable

y= the dependent variable

c= the vertical intercept

Answer:

The linear parent function :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

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

5x = 10

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{10}{5} [/tex]

Calculate

[tex]x = 2[/tex]

Now, substitute the given value of X in the equation

3x + y = 3

[tex]3 \times 2 + y = 3[/tex]

Multiply the numbers

[tex]6 + y = 3[/tex]

Move constant to R.H.S and change it's sign

[tex]y = 3 - 6[/tex]

Calculate

[tex]y = - 3[/tex]

The possible solution of this system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equation

[tex]2 \times 2 - ( - 3) = 7[/tex]

[tex]3 \times 2 - 3 = 3[/tex]

Simplify the equalities

[tex]7 = 7[/tex]

[tex]3 = 3[/tex]

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

The correct answer is D. 23

Explanation:

Histograms similar to other graphs represent numerical information, usually by using bars, as well as ranges. For example, in the case presented the information presented belongs to the scores obtained in a test, which are shown using ranges. Moreover, it is possible to know the total of people that took the test by adding each of the frequencies, as the frequency in the y-axis shows the number of times the range repeated and it is expected each grade registered belongs to 1 person. This means the total of people is equal to 2 (score from 60-69) + 9 (score from 70-79) + 7 (score from 80-89) + 5 (score from 90-99) = 23 people.

Answer:

the answer is 23

Step-by-step explanation:

hopes this helps:)

Answer:

The frequency of f(x) is two times the frequency of the parent function.

Step-by-step explanation:

We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.

Then, for the parent function, we get:

[tex]1 = 2\pi f_1[/tex]

or solving for [tex]f_1[/tex]:

[tex]f_1=\frac{1}{2\pi }[/tex]

At the same way, for f(x), we get:

[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]

But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:

[tex]f_2=2f_1[/tex]

It means that the frequency of f(x) is two times the frequency of the parent function.

Answer:

X=20

Step-by-step explanation:

The answer is C

Answer

[tex]P= 0.144[/tex] ways

the coin can land tails either exactly 8 times or exactly 5 times in

[tex]0.144[/tex] ways

Step by step explanation:

THis is a binomial distribution

Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.

P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹

p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³

p=(9)+p(3)

p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴

P= (0.5)¹⁴ [C(14,9) + C(14,3)]

P= (0.5)¹⁴ [2002 * 364]

P= 1/16384 * (2002 +364)

P= 91091/2048

P= 0.144

Hence,the coin can land tails either exactly 8 times or exactly 5 times in

[tex] 0.144[/tex] ways

Answer:

x = 80

y = 130

Step-by-step explanation:

The 2 angles are supplementary. so, x-30 + x+50 = 180.

We solve and get 2x = 180-20

x = 80

y = x+50, because of parallel rules.

y = 130

Answer:

x = 80

y = 130

Step-by-step explanation:edge 2020

Answer:

2/3

Step-by-step explanation:

The equation for direct variation is: y = kx, where k is a constant.

Here, we see that y varies directly with x when y = 6 and x = 72, so let's plug these values into the formula to find k:

y = kx

6 = k * 72

k = 6/72 = 1/12

So, k = 1/12. Now our formula is y = (1/12)x. Plug in 8 for x to find y:

y = (1/12)x

y = (1/12) * 8 = 8/12 = 2/3

Thus, y = 2/3.

~ an aesthetics lover

Answer:

Step-by-step explanation: I hope i'm right

[tex]y \alpha x\\y=kx....(1)\\6=72k\\\frac{6}{72} =\frac{72k}{72} \\\\1/12 =k\\y = 1/12x=relationship-between;x-and;y\\x =8 , y =?\\y = \frac{8}{12} \\Cross-Multiply\\12y =8\\12y/12 = 8/12\\\\y = 2/3[/tex]

Answer:

27

Step-by-step explanation:

First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.

Answer:

Step-by-step explanation:

Perimeter of rectangle is 2(l) + 2(w).

The perimeter is given 100 units.

2(4x-1) + 2(3x+2) = 100

Solve for x.

8x-2+6x+4=100

14x+2=100

14x=98

x=7

Plug x as 7 for the side WX.

4(7) - 1

28-1

= 27

Answer:

Hey there!

The perimeter can be expressed as 140+140+68[tex]\pi[/tex]

This is equal to 493.52 m

Hope this helps :)

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I think. I just multiplies the 3 numbers. Hope this helps (:

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I just multiplies the 3 numbers.

Answer:

18

Step-by-step explanation:

23^0 - 15^1 + 18^0 + (43 - 12) =

= 1 - 15 + 1 + 31

= -14 + 1 + 31

= -13 + 31

= 18

Answer:

-7 > x

Step-by-step explanation:

3(x-4)>5x+2

Distribute

3x-12>5x+2

Subtract 3x from each side

3x-12-3x>5x-3x+2

-12 > 2x+2

Subtract 2 from each side

-12-2>2x+2-2

-14 > 2x

Divide by 2

-14/2 > 2x/2

-7 > x

Answer:

[tex]\boxed{x<-7}[/tex]

Step-by-step explanation:

3(x-4)>5x+2

Expand brackets.

3x - 12 > 5x+2

Subtract 3x and 2 on both sides.

-12 - 2 > 5x - 3x

-14 > 2x

Divide both sides by 2.

-7 > x

Switch sides.

x < -7

Answer:

5,000

Step-by-step explanation:

If it decreases by 5% a year, it'll decrease by 75% in 15 years

i.e 1 year = 5%

15 years = x

Cross multiply

x = 75%

Therefore, since it decreases by 75%

100 - 75 x 20,000 = 5,000

100

Answer:

I think it is [tex]\frac{6x-18}{x^{4} }[/tex]

Step-by-step explanation:

Answer:

[tex]-5<x<26[/tex].

Step-by-step explanation:

We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.

Angle opposite to larger side is larger.

Since, 14 < 15, therefore

[tex]2x+10<62[/tex]

[tex]2x<62-10[/tex]

[tex]2x<52[/tex]

[tex]x<26[/tex]          ...(1)

We know that, angle can not not negative.

[tex]2x+10>0[/tex]

[tex]2x>-10[/tex]

[tex]x>-5[/tex]        ...(2)

From (1) and (2), we get

[tex]-5<x<26[/tex]

Therefore, the range of values of x is [tex]-5<x<26[/tex].

Answer:

D. 6

Step-by-step explanation:

here, as given set Q consists { 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36}

and set Z contains {3, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, .... }

so be comparing both, we can see that the numbers 6, 12, 18, 24, 30 and 36 is repeated.

Hey there! I'm happy to help!

We want to find the volume of this  rectangular waterbed. This means the amount of space it takes up. To find the volume of a rectangular prism, you just multiply together the three side lengths.

7×5×1=35 cubic feet

Now, we need to see how many gallons fit into 35 cubic feet. We see that one gallon is equal to 0.13 cubic feet. So, we can set up a proportion to find how many gallons are needed. We will use g to represent our missing number of gallons.

[tex]\frac{gallons}{cubic feet} = \frac{1}{0.13} =\frac{g}{35}[/tex]

In a proportion, the products of the diagonal numbers are equal. This means that 35, which is 1 multiplied by 35, is equal to 0.13g, which is from multiplying 0.13 by the g.

0.13g=35

We divide both sides by 0.13/

g≈269.23

When rounded to the nearest whole gallon, we will need 269 gallons of water to fill the waterbed.

I hope that this helps! Have a wonderful day! :D

Answer:

Step-by-step explanation:

Since the waterbed is rectangular, its volume would be determined by applying the formula for determining the volume of a cuboid which is expressed as

Volume = length × width × height

Therefore,

Volume of waterbed = 7 × 5 × 1 = 35 cubic feet

1 US gallon = 0.133680556 cubic feet

Therefore, converting 35cubic feet to gallons, it becomes

35/0.133680556 = 261.81818094772 gallons

Rounding up to whole gallon, it becomes 262 gallons

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!

Answer:

The position of the particle is described by [tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Step-by-step explanation:

The position function is obtained after integrating twice on acceleration function, which is:

[tex]a(t) = 2\cdot t + 5[/tex], [tex]\forall t \geq 0[/tex]

Velocity

[tex]v(t) = \int\limits^{t}_{0} {a(t)} \, dt[/tex]

[tex]v(t) = \int\limits^{t}_{0} {(2\cdot t + 5)} \, dt[/tex]

[tex]v(t) = 2\int\limits^{t}_{0} {t} \, dt + 5\int\limits^{t}_{0}\, dt[/tex]

[tex]v(t) = t^{2}+5\cdot t + v(0)[/tex]

Where [tex]v(0)[/tex] is the initial velocity.

If [tex]v(0) = -5[/tex], the particular solution of the velocity function is:

[tex]v(t) = t^{2} + 5\cdot t -5, \forall t \geq 0[/tex]

Position

[tex]s(t) = \int\limits^{t}_{0} {v(t)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_{0} {(t^{2}+5\cdot t -5)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_0 {t^{2}} \, dt + 5\int\limits^{t}_0 {t} \, dt - 5\int\limits^{t}_0\, dt[/tex]

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + s(0)[/tex]

Where [tex]s(0)[/tex] is the initial position.

If [tex]s(0) = 6[/tex], the particular solution of the position function is:

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Answer:

Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex]

Step-by-step explanation:

Given information:

The particle is moving with an acceleration that is function of:

[tex]a(t)=2t+5[/tex]

To find the expression for the position of the particle first integrate for the velocity expression:

AS:

[tex]V(t)=\int\limits^0_t {a(t)} \, dt\\v(t)= \int\limits^0_t {(2.t+5)} \, dt\\\\v(t)=t^2+5.t+v(0)\\[/tex]

Where, [tex]v(0)[/tex] is the initial velocity.

Noe, if we tale the [tex]v(0) =-5[/tex] ,

So, the velocity equation can be written as:

[tex]v(t)=t^2+5.t-5[/tex]

Now , For the position of the particle we need to integrate the velocity equation :

As,

Position:

[tex]S(t)=\int\limits^0_t {v(t)} \, dt \\S(t)=\int\limits^0_t {(t^2+5.t-5)} \, dt\\S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+s(0)[/tex]

Where, [tex]S(0)[/tex] is the initial position of the particle.

So, we put the value [tex]s(0)=6[/tex] and get the position of the particle.

Hence, Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex].

For more information visit:

https://brainly.com/question/22008756?referrer=searchResults

Answer:

sin = -√2 / 2

cos = √2 / 2

tan = -1

Step-by-step explanation:

Θ is in quad IV

sin = -√2 / 2

cos = √2 / 2

tan = -1

Answer:

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]

  = [tex]-\frac{36}{7}[/tex]

y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]

  = [tex]\frac{40}{7}[/tex]

Therefore, coordinates of pint B will be,

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Answer:

8 hours

Step-by-step explanation:

25%= 2 hrs

100%=8 hrs

brainliest plsssssssssssssssssssss

       -zylynn

Answer:

a) P(B'|A) = 0.042

b) P(B|A') = 0.625

Step-by-step explanation:

Given that:

80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered

Of the aircraft that are discovered, 63% have an emergency locator,

whereas 89% of the aircraft not discovered do not have such a locator.

From the given information; it is suitable we define the events in order to calculate the probabilities.

So, Let :

A = Locator

B = Discovered

A' = No Locator

B' = No Discovered

So; P(B) = 0.8

P(B') = 1 - P(B)

P(B') = 1- 0.8

P(B') = 0.2

P(A|B) = 0.63

P(A'|B) = 1 - P(A|B)

P(A'|B) = 1- 0.63

P(A'|B) = 0.37

P(A'|B') = 0.89

P(A|B') = 1 - P(A'|B')

P(A|B') = 1 - 0.89

P(A|B') = 0.11

Also;

P(B ∩ A) = P(A|B) P(B)

P(B ∩ A) = 0.63 × 0.8

P(B ∩ A) = 0.504

P(B ∩ A') =  P(A'|B) P(B)

P(B ∩ A') = 0.37 × 0.8

P(B ∩ A') = 0.296

P(B' ∩ A) = P(A|B') P(B')

P(B' ∩ A) = 0.11 × 0.2

P(B' ∩ A) = 0.022

P(B' ∩ A') =  P(A'|B') P(B')

P(B' ∩ A') = 0.89 × 0.2

P(B' ∩ A') = 0.178

Similarly:

P(A) = P(B  ∩  A ) + P(B'  ∩  A)

P(A) = 0.504 + 0.022

P(A) = 0.526

P(A') = 1 - P(A)

P(A') = 1 - 0.526

P(A') =  0.474

The probability that it will not be discovered given that it has an emergency locator is,

P(B'|A) =  P(B' ∩ A)/P(A)

P(B'|A) = 0.022/0.526

P(B'|A) = 0.042

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

The probability that it will be discovered given that it does not have an emergency locator is:

P(B|A') = P(B ∩ A')/P(A')

P(B|A') = 0.296/0.474

P(B|A') = 0.625

Answer:

what

Step-by-step explanation:

Answer:

H0 :

a. mu is greater than or equal to $108.50

Ha:

c. mu is less than or equal to $108.50

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence

In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.

Answer:

The statement

the product of 60 and the number of seconds is written as

60 * s

Hope this helps you