please simplify this

Answer:

Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.

Test statistic t=2.238>tc=1.708.

The null hypothesis is rejected.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]

The significance level is 0.05.

The sample has a size n=26.

The sample mean is M=370.69.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=26-1=25[/tex]

The critical value for a  right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.

As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant.  The null hypothesis is rejected.

There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).

Let's raise i to various powers starting with 0,1,2,3...

i^0 = 1

i^1 = i

i^2 = ( sqrt(-1) )^2 = -1

i^3 = i^2*i = -1*i = -i

i^4 = (i^2)^2 = (-1)^2 = 1

i^5 = i^4*i = 1*i = i

i^6 = i^5*i = i*i = i^2 = -1

We see that the pattern repeats itself after 4 iterations. The four items to memorize are

i^0 = 1

i^1 = i

i^2 = -1

i^3 = -i

It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.

To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.

This means i^25 = i^1 = i

Likewise,

i^5689 = i^1 = i

because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely

Answer:

Angle P is congruent to itself due to the reflexive property.

Explanation:

Angle P must be congruent to angle S through corresponding angle theory.

Otherwise, it wouldn't prove ΔPQR is similar to ΔSTR.

Answer:

Angle P is congruent to itself due to the reflexive property.

Step-by-step explanation:

Answer:

ln e = 1

ln e 2x = 2x

ln 1 = 0

Step-by-step explanation:

ln e

ln(2.718282) = 1

In e 2x

ln(2.718282)(2)x = 2x

ln 1 = 0

Answer:

a) Test statistic

    Z = 1.265 < 1.96 at 0.05 level of significance

The battery life is not exceeds 40 hours

b)

p- value = 0.8962

Step-by-step explanation:

Step(i):-

Given sample size 'n' =10

Mean of the sample x⁻ = 40.5 hours

Mean of  of the Population μ = 40 hours

Standard deviation of the Population = 1.25 hours

Step(ii):-

Null Hypothesis:H₀: μ = 40 hours

Alternative Hypothesis :H₁ : μ < 40 hours

step(ii):-

Test statistic

               [tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

              [tex]Z = \frac{40.5 -40}{\frac{1.25}{\sqrt{10} } }[/tex]

             Z = 1.265

Level of significance = 0.05

Z₀.₀₅ = 1.96

Z = 1.265 < 1.96 at 0.05 level of significance

The battery life is not exceeds 40 hours

Step(iii):-

P - value        

P( Z < 1.265) = 0.5 + A( 1.265)

                     = 0.5 + 0.3962  

                    = 0.8962

P( Z < 1.265) = 0.8962

i ) p- value = 0.8962 > 0.05

Accept H₀

There is no significant

The battery life is not exceeds 40 hours

Answer:

$39,000

Step-by-step explanation:

This is the best answer because you recieve the most money. 2630*12 is 31560 dollars, and 665*52= $34580.

Answer:

7/8 chance

Step-by-step explanation:

There are 7 numbers that are either even or greater than 2: 2, 3, 4, 5, 6, 7, and 8. There is a 7/8 chance choosing either of those.

Answer:

7/8

Step-by-step explanation:

there are 6 numbers that are greater than 2: 3,4,5,6,7,8

there are 4 even numbers: 2,4,6,8

Answer:

Step-by-step explanation:

A) u = 4      v = 4/(sqrt)3

B) b = 5      c = 10

C) b = 2(sqrt)2     a = 4

D) m and n are both 7(sqrt)2/2

The missing side lengths for the three triangles are 10√3, 12, and 8. The first triangle is a 30-60-90 triangle, the second triangle is a 45-45-90 triangle, and the third triangle is a right triangle. The missing side lengths were found using the properties of special triangles and the Pythagorean Theorem.

Here are the missing side lengths for the following triangles:

Triangle 1:

The missing side length is 15.

The triangle is a 30-60-90 triangle, so the ratio of the side lengths is 1:√3:2. The hypotenuse of the triangle is 20, so the shorter leg is 10 and the longer leg is 10√3. The missing side length is the longer leg, so it is 10√3.

Triangle 2:

The missing side length is 12.

The triangle is a 45-45-90 triangle, so the ratio of the side lengths is 1:1:√2. The hypotenuse of the triangle is 12√2, so each of the legs is 12. The missing side length is one of the legs, so it is 12.

Triangle 3:

The missing side length is 8.

We can use the Pythagorean Theorem to find the missing side length. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is 10 and one of the other sides is 6. Let x be the missing side length.

[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]

100 = 36 +[tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 64

x = 8

Therefore, the missing side length is 8.

Learn more about side lengths here: brainly.com/question/18725640

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Area of one side of a U.S. dime is approximately 254  square millimeters.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that  U.S. dime has a diameter of about 18 millimeters.

We need to find the area of one side of a dime to the nearest square millimeter.

Diameter=18 millimeters

Diameter is two times of radius

D=2R

18=2R

Divide both sides by 2

Radius is 9 millimeters.

Area of dime=πr²

=3.14×(9)²

=3.14×81

=254 square millimeters.

Hence, area of one side of a U.S. dime is approximately 254  square millimeters.

To learn more on Circles click:

https://brainly.com/question/11833983

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Answer:

  50.18°

Step-by-step explanation:

  ∠BAD = ∠BAC +∠CAD

  102° = (8x+17)° +(9x+11)° . . . . . substitute given values

  102 = 17x +28 . . . . . . . . . . simplify, divide by degrees

  x = (102 -28)/17 = 74/17 . . . . . solve for x

Then the angle of interest is ...

  ∠CAD = (9x +11)° = (9(74/17) +11)° = 50 3/17°

  ∠CAD ≈ 50.18°

Answer:

See Explanation below

Step-by-step explanation:

This question has missing details because the number of video games is not stated;

However, you'll arrive at your answer if you follow the steps I'll highlight;

The question requests for the number of arrangement; That means we're dealing with permutation

Let's assume the number of video games is n;

To arrange n games, we make use of the following permutation formula;

[tex]^nP_n = \frac{n!}{(n-n)!}[/tex]

Simplify the denominator

[tex]^nP_n = \frac{n!}{0!}[/tex]

0! = 1; So, we have

[tex]^nP_n = \frac{n!}{1}[/tex]

[tex]^nP_n = n![/tex]

Now, let's assume there are 3 video games;

This means that n = 3

[tex]^3P_3 = 3![/tex]

[tex]^3P_3 = 3 * 2 * 1[/tex]

[tex]^3P_3 = 6\ ways[/tex]

So, whatever the number of video games is; all you have to do is; substitute this value for n;

Answer:

50°

Step-by-step explanation:

ABCD is a kite.

Therefore, AB = BC

[tex]\therefore m\angle BCA= m\angle BAC = 40\degree \\

\because BD \perp AC.. (Diagonals \: of\: kite) \\

\therefore y + 90\degree + m\angle BCA = 180\degree \\

\therefore y + 90\degree + 40\degree = 180\degree \\

\therefore y = 180\degree - 130\degree \\

\huge\red {\boxed {y = 50\degree}} [/tex]

Answer:

b median

Step-by-step explanation:

Answer:

  orthocenter

Step-by-step explanation:

The red segment is an altitude of the triangle, as are the two legs. The intersection point of the altitudes is the orthocenter.

__

This is basically a vocabulary question.

Answer:

z-Axis. The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the -axis is the axis about which the azimuth coordinate. is measured.

Step-by-step explanation:

Answer:

Option D is correct.

There are 34 nickels in the piggy bank.

Step-by-step explanation:

A piggy bank contains pennies, nickels and dimes.

Let the number of pennies be p

Let the number of nickels be n

Let the number of dimes be d

Also, note that 1 penny = $0.01

1 nickel = $0.05

1 dime = $0.10

- The number of dimes is 15 more than the number of nickels.

d = 15 + n

- There are 140 coins altogether totaling $7.17.

p + n + d = 140

0.01p + 0.05n + 0.1d = 7.17

Bringing the 3 equations together

d = 15 + n (eqn 1)

p + n + d = 140 (eqn 2)

0.01p + 0.05n + 0.1d = 7.17 (eqn 3)

Substitute (eqn 1) into (eqn 2)

p + n + d = 140

p + n + (15 + n) = 140

p + 2n + 15 = 140

p = 140 - 15 - 2n = 125 - 2n

p = 125 - 2n (eqn 4)

Substitute (eqn 1) and (eqn 4) into (eqn 3)

0.01p + 0.05n + 0.1d = 7.17

0.01(125 - 2n) + 0.05n + 0.1(15 + n) = 71.7

1.25 - 0.02n + 0.05n + 1.5 + 0.1n = 7.17

0.1n + 0.05n - 0.02n + 1.5 + 1.25 = 7.17

0.13n + 2.75 = 7.17

0.13n = 7.17 - 2.75 = 4.42

0.13n = 4.42

n = (4.42/0.13) = 34

d = 15 + n = 15 + 34 = 49

p = 125 -2n = 125 - (2×34) = 125 - 68 = 57

Hence, there are 57 pennies, 34 nickels and 49 dimes in the piggy bank.

Hope this Helps!!!

Answer:

Length =  502 ft

Width = 212 ft

Step-by-step explanation:

Recall the formula for the perimeter of a rectangle of length "L" and width "W":

Perimeter = 2 L + 2 W = 1428  ft

Now, since the length is 78 ft more than twice the width, then we can write this in mathematical form as:

L = 2 W +78

so, 2 W = L -7 8

and now replace "2 W" with it equivalent  "L - 78"  in the first perimeter equation and solve for "L":

2 L + L - 78 = 1428

3 L = 1428 + 78

3 L = 1506

L = 1506/3

L = 502 ft

Then the width W can be obtained via:

2 W = L - 78

2 w = 502 -78

2 W = 424

w = 212 ft

Answer:

324000000000000000000000

Answer:

His monthly income is 9000 Rs

Answer:

y = [tex]\frac{1}{2}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Parallel lines have equal slopes

line M crosses the y- axis at (0, 3) ⇒ c = 3

y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M

Answer:

Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die. But with a second dice, there will be 24 different possibilities.

Step-by-step explanation:

   1     2        3 4   5     6

1 (1, 1)   (1, 2)   (1, 3)   (1, 4)  (1, 5)   (1, 6)

2 (2, 1)   (2, 2)  (2, 3)  (2, 4) (2, 5)  (2, 6)

3 (3, 1)   (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

4 (4, 1)   (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4, 6)

5 (5, 1)   (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

6 (6, 1)   (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)

Answer:

the answer is A

Step-by-step explanation:

Answer:

(4b)•(0.5a) = (4•0.5)(a)(b) = 2ab

Step-by-step explanation:

Answer:

(x, y) = (-8/3, -60)

Step-by-step explanation:

y = 30x + 20

y = 10 * 2 - 80 → y = 20 - 80

y = 30x + 20

y = -60

30x + 20 = -60

x = -8/3

(x, y) = (-8/3, -60)

Hope this helps! :)

Answer:

3.15 dollars

Step-by-step explanation:

The sales tax rate is 7% = 0.07

So, we need to multiply the listed price and the sales tax rate.

= 45 * 0.07 = 3.150 (3.15)

Hope this helps and please mark as the brainliest

Answer:

a = ±4√5

Step-by-step explanation:

Solve for c.

3√c = 9

√c = 9/3

√c = 3

c = 3²

c = 9

Put b=2√2 and c=9, solve for a.

a² + (2√2)² + 9² = 169

a² + 8 + 81 = 169

a² = 169 - 81 - 8

a² = 80

a = ±√80

a = ±4√5

Answer:

80%

Step-by-step explanation:

The numbers 5 or even are 4, 5, 6, and 8.

4 numbers out of 5.

4/5 = 0.8

Convert to percentage.

0.8 × 100 = 80

P(5 or even) = 80%

Answer:

80% chance

Step-by-step explanation:

There are 4 numbers that fit the rule, 4, 5, 6, and 8. There is a 4/5 chance spinning one of those numbers or 80% chance.

Answer:  c) SAS Postulate

Step-by-step explanation:

DP = PC              Sides are congruent

∠ADP ≡ ∠BCP    Angles are congruent (angles are between the sides)

AD = BC             Sides are congruent

To finish the proof, we can state that ΔADP ≡ ΔBCP by the Side-Angle-Side (SAS) Postulate

Answer:

15.87%

Step-by-step explanation:

We have to calculate the value of z:

z = (x - m) / (sd / n ^ (1/2))

where x is the value to evaluate, m is the mean, n is the sample size and sd is the standard deviation, we replace:

p (x <60,527) = z = (x - m) / (sd / n ^ (1/2))

p (x <60,527) = z = (60,527 - 60) / (5/90 ^ (1/2))

z = 1

if we look in the attached table, for z = 1 it is 0.8413

p (x> 60,527) = 1 - 0.8413

 p (x> 60,527) = 0.1587

Therefore the probability is 15.87%

Answer:

Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Also, Two events are said to be independent if the outcome or occurrence of the first does not affects the outcome or occurrence of the second so that the probability is not changed.

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Answer:E. P(B\A)≠P(B)

Step-by-step explanation:

Answer:

about 10

Step-by-step explanation:

62.8 = 2 pi r/2

62.8/2 = pi r

31.4/pi = pi r/pi

about 10 = r

Answer: x=-3/4

Step-by-step explanation:

Since we know f(x)=6, we can set it equal to the equation.

6=9+4x           [subtract 9 on both sides]

-3=4x              [divide both sides by 4]

x=-3/4