Green Red Blue Yellow

Event A: lands on yellow.
Event B: lands on green.
Events A and B are_______ events.​

Answer:

f(n) = 6n + 12

Step-by-step explanation:

There is a common difference in consecutive number of seats, that is

42 - 36 = 36 - 30 = 30 - 24 = 24 - 18 = 6

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 18 and d = 6 , then

f(n) = 18 + 6(n - 1) = 18 + 6n - 6 = 6n + 12

Answer:

a. (3.83952, 5.16049)

b. (7.32, 8.88)

c. The difference in the range of the confidence intervals suggest that taking the zinc loz-enges reduces the overall duration of cold symptoms

d. The assumptions required for the validity validity of a t-test include that the data is sampled from a source that have data that are normally distributed

Step-by-step explanation:

The given parameters are;

The number of participants that took zinc lozenges, n₁ = 25

The number of participants that took a placebo, n₂ = 23

The mean duration of the symptoms for the zinc lozenge group, [tex]\overline x_1[/tex] = 4.5 days

The standard deviation of overall duration, s₁ = 1.6 days

The mean duration of the symptoms for the placebo group, [tex]\overline x_2[/tex] = 8.1 days

The standard deviation, s₂ = 1.8 days

a. The 95% confidence interval if everyone in the population were to take zinc lozenges is given as follows;

[tex]CI=\bar{x}_1\pm t_{\alpha/2} \times \dfrac{s_1}{\sqrt{n_1}}[/tex]

n₁ = 25, the degrees of freedom (df) = n₁ - 1 = 24

The t-value for 95% confidence interval, with df = 24, with t = 2.064

Therefore, we have;

[tex]CI_{zl}=4.5 \pm 2.064 \times \dfrac{1.6}{\sqrt{25}}[/tex]

[tex]CI_{zl}[/tex] = 4.5 ± 0.66048

[tex]CI_{zl}[/tex] = (3.83952, 5.16049)

b. The 95% confidence interval if everyone in the population were to take the placebo is given as follows;

[tex]CI_p=\bar{x_2}\pm t_{\alpha/2} \times \dfrac{s_2}{\sqrt{n_2}}[/tex]

n₂ = 23, the degrees of freedom (df) = n₂ - 1 = 22

The t-value for 95% confidence interval, with df = 22, with t = 2.074

Therefore, we have;

[tex]CI_p =8.1 \pm 2.074 \times \dfrac{1.8}{\sqrt{23}}[/tex]

[tex]CI_p[/tex] = 8.1 ± 0.7784

[tex]CI_p[/tex] = (7.32, 8.88)

c. Based on the difference in the range of the 95% confidence interval for the mean duration of cold symptoms of the group that take zinc lozenges, (3.83952, 5.16049), and the mean of the group that are on a placebo, (7.32, 8.88), there is sufficient statistical evidence to suggest that there is a difference between the mean and taking zinc lozenges reduces the overall duration of cold symptoms more than if taking placebo

d. The assumptions required for validity when carrying out a t-test include;

i) The measurement scale is ordinal or continuous

ii) The sample is a simple random sample

iii) The data gives a normal distribution curve

iv) The sample size is reasonably large

v) The variance are homogeneous

Among these assumptions, the data must be randomly sampled from the population of interest and that the data variables follow a normal distribution

The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation

Answer:

Ummmm its just a black screen

Step-by-step explanation:

Answer:

I am not completly sure, cause the answer might be a bit more complex but, for the spinner on the left 4/8 and the right 1/8 chances

Step-by-step explanation:

Answer: 5/8 is the correct answer.

Step-by-step explanation: The other dude is completely wrong.

Answer:

-1456

-864

4

-11

-5,25

-1,93

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rate of change is:

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{(x+2)(x+3)^2(x-3)}{(x-4)^2(x+4)}[/tex]

Step-by-step explanation:

i'm going to assume what you have looks like

[tex]\frac{x^2-9}{\frac{x^2-16}{\frac{x^2+5x+6}{x-4}}}[/tex]

Let's start by factoring everything

x²-9= (x+3)(x-3)

x²-16= (x+4)(x-4)

x²+5x+6=(x+3)(x+2)

x-4= x-4

which means what we have looks like

[tex]\frac{(x+3)(x-3)}{\frac{(x+4)(x-4)}{\frac{(x+3)(x+2)}{x-4}}}=\frac{(x+3)(x-3)}{(x+4)(x-4)}\div\frac{x-4}{(x+3)(x+2)}=\frac{(x+3)(x-3)}{(x+4)(x-4)}*\frac{(x+3)(x+2)}{x-4}=\frac{(x+3)^2(x-3)(x+2)}{(x+4)(x-4)^2}[/tex]

And I think that's as simplified as it can get

Answer:

10 cm³

Step-by-step explanation:

The total surface area of a cube = 6 cm²

The formula for the surface area of the cube is :

A = 6a², a is the side of the cube

6 = 6a²

a = 1 cm

Now, the length of the formed cuboid = 2 cm

Breadth = 1 cm

Height = 1 cm

Required volume of the formed cubiod is :

V = 2(lb+bh+hl)

Put all the values,

V = 2(2(1)+1(1)+2(1))

V = 10 cm³

So, the required volume of the formed cuboid is equal to 10 cm³

Step-by-step explanation:

[tex]\frac{120+30}{\frac{66}{1126}-8*3+17-4*4 }[/tex]

[tex]\frac{-42225}{6458}[/tex]

Answer:

Step-by-step explanation:

I'll show you how to do the first one; the other are exactly the same, so pay attention.

The formula for arc length is

[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:

[tex]AL=\frac{40}{360}*2(3.1415)(3)[/tex]. I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):

[tex]AL=\frac{1}{9}*2(3.1415)(3)[/tex] which makes

AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:

[tex]A_s=\frac{1}{9}*(3.1415)(3)^2[/tex] which simplifies a bit to

[tex]A_s=\frac{1}{9}*(3.1415)(9)[/tex]. As you can see, the 9's cancel each other out, leaving you with

[tex]A_s=3.14[/tex] units²

Answer:

Step-by-step explanation:

[tex]Arc \ Length = 2 \pi r \frac{ \theta}{360}[/tex]

[tex]Sector \ Area = \pi r^2 \frac{ \theta }{360}[/tex]

[tex]1) Arc \ Length = 2 \pi \times 3 \times \frac{40}{360} = 2\pi \times 3 \times \frac{1}{9} = \frac{2}{3} \pi = 2.09[/tex]

  [tex]Sector \ Area = \pi \times 9 \times \frac{40}{360} = 9\pi \times \frac{1}{9} = \pi = 3.14[/tex]

[tex]2) Arc \ Length = 2 \pi \times 5 \times \frac{88}{360}= 7.68[/tex]

  [tex]Sector \ Area = \pi \times 25 \times \frac{88}{360} = 19.2[/tex]

[tex]3) Arc \ Length = 2 \pi \times 6 \times \frac{260}{360} = 27.22[/tex]

  [tex]Sector \ Area = \pi \times 36 \times \frac{260}{360} = 81.68[/tex]

Hope This Helps!!!

Hope This Helps!!!Have A Great Day!!!

Answer:

Step-by-step explanation:

radius of circle is 12

also there is 2 right angles in the triangle if you wanted to solve this problem yourself

but here's the answer:

arc angle of the triangle inside the sircle is double the angle closest to x.

(the pointy area of the triangle is half the angle length of the arc)

i can add more though:

Answer:

First : Unbiased

Second : Biased

Answer:

Max

Step-by-step explanation:

the function given that h = -16t³+64t+10

the general function Equation:

h = at²+bt+c

=> t at the highest point is defined by t = -b/2a

= -64/2(-16) = -64/-32 = 2 second

the total times that the ball hits the ground

= 2× 2 seconds = 4 seconds.

so, Max is right

Answer:

Solution given:

Let h=0=when the ball hit the ground,the height=0.

h= -16t^2 + 64t + 10.

0=16t²-64t-10

8t²-32t-5=0

∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]

taking positive

t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]

t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]

So

t=4.15seconds closer to 4seconds.So

Max is closer.

Answer:

At least 12

Step-by-step explanation:

I created 12 different number patterns greater than 540. I hope I was able to help you out :)

Answer:

x = sqrt(33)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

4^2 + x^2 = 7^2

16 + x^2 = 49

Subtract 16 from each side

x^2 = 49-16

x^2 = 33

Take the square root of each side

sqrt(x^2) = sqrt(33)

x = sqrt(33)

[tex]\quad\quad\quad \boxed{ \tt{\color{blue}{c}^{2} = {a}^{2} + {b}^{2} }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{\color{blue}{a} = \sqrt{ {c}^{2} - {b}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{\color{black}{a} = \sqrt{ {c}^{2} - {b}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {c}^{2} - {b}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {7}^{2} - {4}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {49} - {16} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt \color{black}{{x} = \sqrt{ 33} }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt \color{green}{{x} = \sqrt{ 33} }}[/tex]

_________

#LetsStudy

Answer:

Step-by-step explanation:

multiply both sides by 8

do over and write g=8x5

solve 8x5=40

g=40

Answer:

95

Step-by-step explanation:

14 + (42 + 7) + 32

14 + 49 + 32

63 + 32

95

Answer:

95

Step-by-step explanation:

Let's use BEDMAS to solve this (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)

1. Calculate the brackets.

42 + 7 = 49

2. Add 14 + 49 + 32

14 + 49 + 32 = 95

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

Have a great summer :)

Answer:

Area of four walls is 3960 square feet.

Step-by-step explanation:

length, L = 30 ft

Width, W = 50 ft

height, H = 6 ft

The area of walls is

= 2 (L W + W H + H L)

= 2 (30 x 50 + 50 x 6 + 6 x 30)

= 2 (1500 + 300 + 180)

= 3960 square feet

Answer/Step-by-step explanation:

How much tile would he need to cover the floor?

Answer: 1500 Ft^2

If the height of the basement is 6 ft, how much wall area is there to paint?

Answer: 960 Ft^2

Answer:

$213,200,000 or 2.132*10[tex]^{5\\}[/tex]

Step-by-step explanation:

82000*2600

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

Work Shown:

(5 oranges)/(2 dollars) = (20 oranges)/(x dollars)

5/2 = 20/x

5x = 2*20 .... cross multiply

5x = 40

x = 40/5 .... dividing both sides by 5

x = 8

20 oranges cost $8

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

Another way to approach the problem is to note that the jump from "5 oranges" to "20 oranges" is "times 4".

5*4 = 20

So we'll apply the "times 4" operation to the old cost of $2 to get the new cost being 2*4 = 8 dollars

Answer:

$8

Step-by-step explanation:

if 5 oranges cost $2 then 1 orange costs 2/5 of a dollar, or 40 cents

20 oranges multiplied by 40 cents is $8

or you can set up a proportion:

2/5 = x/20

cross-multiply to get:

5x = 40

x = 8

Answer:

x = ±3 sqrt(2)

Step-by-step explanation:

x^2 = 18

Take the square root of each side

sqrt(x^2) = sqrt(18)

x = ± sqrt(18)

x =±sqrt(9*2)

x = ±sqrt(9) sqrt(2)

x = ±3 sqrt(2)

[tex]\longrightarrow{\blue{ 2 \: ( \: 32 \: y + 3 \: x \: )}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]64 \: y + 6 \: x[/tex]

[tex] = 2 \: ( \: 32 \: y + 3 \: x \: )[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

2 ( 32y + 3 x)

Step-by-step explanation:

64 y + 6x

factor out 2 from the equation

2 ( 32y + 3 x)

Answer:

x = - 10

Step-by-step explanation:

Expand the equation first then simplify it

Answer:

30-12=18

18-18=0

Step-by-step explanation:

2x + 12 = 30

X represents the snacks, 2 represents the $2 per snack, 12 represents the $12 entry fee, and 30 represents the $30 Olivia had.

goodStep-by-step explanation:

Answer:

Click the second one, I truly hope that worked! :)