A recent national survey found that high school students watched an average (mean) of 7.1 movies per month with a population standard deviation of 1.0. The distribution of number of movies watched per month follows the normal distribution. A random sample of 33 college students revealed that the mean number of movies watched last month was 6.2. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students? State the null hypothesis and the alternate hypothesis.

Answer:

3 · |x+6|

Step-by-step explanation:

Write out what you see. "Three times" is 3 · something; "the absolute value of the sum of a number and 6" is |number + 6|. We'll use x for our number. Put it all together and you get 3 · |x+6|

The expression of the statement, Three times the absolute value of the sum of a number and 6 is  [tex]\[3\left| n+6 \right|\][/tex] .

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Answer: a = 9, b = 48, c = -1

Step-by-step explanation:

"a" represents the points you receive if an Ace is picked.  It is given that you get 9 points ----> a = 9

"b" represents the number of cards that are Not an Ace.  4 cards in the deck are Aces so 52 - 4 = 48 cards are Not an Ace -----> b = 48

"c" represents the points you receive if Not an Ace is picked.  It is given that you lose 1 point ----> c = -1

Answer:

Here is the rest of the page

Step-by-step explanation:

Answer:

The margin of error is  [tex]E = 1.96 * \frac{ 0.92}{\sqrt{28 } }[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  [tex]n = 28[/tex]

     The  sample  mean is  [tex]\= x = 2.4 \ hr[/tex]

      The  standard deviation is  [tex]\sigma = 0.92 \ hr[/tex]

Given that the confidence level is 95% the the level of significance can be evaluated as

             [tex]\alpha = 100 -95[/tex]

            [tex]\alpha = 5 \%[/tex]

             [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is  [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

          [tex]E = 1.96 * \frac{ 0.92}{\sqrt{28 } }[/tex]

         [tex]E = 0.3408[/tex]

Step-by-step explanation:

Hello, there!!

The answer would be 41/9.

The reason for above answer is to change any mixed fraction into improper fraction we should follow a simple step:

look here,

=[tex] \frac{4 \times 9 + 5}{9} [/tex]

we get 41/9.

Hope it helps...

The given fraction into the improper fraction should be [tex]\frac{41}{9}[/tex]

Given that,

[tex]= 4\frac{5}{9}\\\\ = \frac{41}{9}[/tex]

Here we multiply the 9 with the 4 it gives 36 and then add 5 so that 41 arrives.

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Answer:

Step-by-step explanation:

(f/g) = (3 - 2x ) / (1/x + 5) You could go to the trouble to simplify all of this, but the easiest way is to just put in the 8 where you see an x

(f/g)8 = (3 - 2*8) / (1/8 + 5)

(f/g)/8 = (3 - 16 / (5 1/8)          1/8 = 0.125

(f/g) 8 = - 13 / ( 5.125)

(f/g)8 = - 2.54

Answer:

x=nπ3, n∈I

Step-by-step explanation:

sin x + sin 5x = sin 2x + sin 4x

⇒⇒   2 sin 3x cos 2x = 2 sin 3x cos x

⇒⇒   2 sin 3x(cos 2x - cos x) = 0

⇒    sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒    sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I

or    cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x

⇒   2x=2nπ±x  ⇒  x=2nπ, 2nπ3⇒   2x=2nπ±x  ⇒  x=2nπ, 2nπ3 , n∈I, n∈I

But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I

Answer:

A: y= 1/4x - 7

if it is perpendicular, then it creates 4 right angles. so that new line would pass through (0,-7) and something else that isnt important. but the slope, or m, would be 1/4, and the y intercept would be -7. so the new equation is y=1/4x-7

Answer:

Evaluate 8P6 P 6 8 using the formula nPr=n!(n−r)! P r n = n ! ( n - r ) ! . 8!(8−6)! 8 ! ( 8 - 6 ) ! Subtract 6 6 from 8 8 . 8!(2)! 8 ! ( 2 ) ! Simplify 8!(2)! 8 !

Step-by-step explanation:

evaluate" usually means to put a value in for the variable, but you don't give us a value for p. also, it is unclear if you ...

The value of the expression [tex]^8P_6[/tex] is 20160.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.

The value of the expression is calculated as:-

[tex]^8P_6=\dfrac{8!}{8!-6!}=\dfrac{8!}{2!}[/tex]

[tex]^8P_6 =\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2}[/tex]

[tex]^8P_6[/tex] = 20160

Hence, the value is 20160.

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(a) Take the Laplace transform of both sides:

[tex]2y''(t)+ty'(t)-2y(t)=14[/tex]

[tex]\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s[/tex]

where the transform of [tex]ty'(t)[/tex] comes from

[tex]L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)[/tex]

This yields the linear ODE,

[tex]-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s[/tex]

Divides both sides by [tex]-s[/tex]:

[tex]Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}[/tex]

Find the integrating factor:

[tex]\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C[/tex]

Multiply both sides of the ODE by [tex]e^{3\ln|s|-s^2}=s^3e^{-s^2}[/tex]:

[tex]s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}[/tex]

The left side condenses into the derivative of a product:

[tex]\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}[/tex]

Integrate both sides and solve for [tex]Y(s)[/tex]:

[tex]s^3e^{-s^2}Y(s)=7e^{-s^2}+C[/tex]

[tex]Y(s)=\dfrac{7+Ce^{s^2}}{s^3}[/tex]

(b) Taking the inverse transform of both sides gives

[tex]y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right][/tex]

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that [tex]\frac{7t^2}2[/tex] is one solution to the original ODE.

[tex]y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7[/tex]

Substitute these into the ODE to see everything checks out:

[tex]2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14[/tex]

Answer:

claire has to leave at 3:50 from her house.

Answer:

She needs to leave by 3:50 to get there on time.

Step-by-step explanation:

4:15 - 0:25 = 3:50.

Answer:

In this question, we shall be accepting the null hypothesis H0 since the critical value is greater than the test statistic value

Step-by-step explanation:

Here in this question, we want to make a conclusion about the null hypothesis H0.

To make or give the correct conclusion about the null hypothesis in this case, we shall need to compare the absolute value of the test statistic used against the value of the critical value.

Hence, we draw a conclusion if the test statistic is larger or smaller than the critical value.

From the value given in the question, we can see that the test statistic given as 1.68 is lesser in value compared to the critical value given as 1.96.

In this kind of case, the conclusion that we shall be drawing is that we will accept the null hypothesis H0 and reject the alternative hypothesis

Answer:

r = 0.023104906

Step-by-step explanation:

Given half life = T = 30 yrs.

Decay constant = r.

Using the decay constant formula:

[tex]r=\frac{\ln2}{T}\\r=\frac{\ln2}{30}\\r=0.023104906[/tex]

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Answer:

ST, RS, RT

Step-by-step explanation:

Angles of a triangle add up to 180°.

2x + 11° + 3x + 23° + x + 42° = 180°

6x + 76° = 180°

x = 17⅓

m∠R = 2x+11° = 45⅔°

m∠S = 3x+23° = 75°

m∠T = x+42° = 59⅓°

The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.

ST, RS, RT

Answer:

  35 cm

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.

  1 L = 1000 cm³, so 99 L = 99,000 cm³

  60 cm diameter = 2 × 30 cm radius

So, we have ...

  99,000 cm³ = π(30 cm)²h

  99,000/(900π) cm = h ≈ 35.01 cm

The oil is 35 cm deep in the drum.

Answer:

15.8 sq. in. of paper will be required.

Step-by-step explanation:

The problem is that a drinking cup does not have a cover, so only the lateral surface area counts.

I.e. We need only the first term.

A = pi r l = pi * 1.5 * sqrt(3^2+1.5^2)

= 15.81 sq. in.

Answer:

csctheta= [tex]\frac{\sqrt{13} }{3}[/tex]

Step-by-step explanation:

answer is provided on top

The value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]. Cosec is found as the ratio of the hypotenuse and the perpendicular.

The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle

The given data in the problem is;

[tex]\rm cot \theta = \frac{2}{3}[/tex]

The [tex]cot \theta[/tex] is found as;

[tex]\rm cot \theta = \frac{B}{P} \\\\ \rm cot \theta = \frac{2}{3} \\\\ B=2 \\\\ P=3 \\\\[/tex]

From the phythogorous theorem;

[tex]\rm H=\sqrt{P^2+B^2} \\\\ \rm H=\sqrt{2^2+3^2} \\\\ H=\sqrt{13} \\\\[/tex]

The value of the cosec is found as;

[tex]\rm cosec \theta = \frac{H}{P} \\\ \rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]

Hence the value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex].

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Answer:

see below

Step-by-step explanation:

Scientific notation is a * 10 ^b

a must be a number between 1 ( including 1 ) and less than 10

12 is greater than 10 so it is not scientific notation

Answer:

87; 2%

Step-by-step explanation:

An exponential growth model is defined as :

F(x) = A( 1 + r)^x

Where;

A = Initial amount,

r = rate of increase

x = time

Comparing the exponential growth function with the exponential growth model given;

f(x)=87(1.02)^x

A = 87 = Initial amount

The growth rate of the model expressed as a percentage :

Taking :

(1 + r) = 1.02

1 + r = 1.02

r = 1.02 - 1

r = 0.02

Expressing r as a percentage :

0.02 * 100% = 2%

Answer:

Below

Step-by-step explanation:

Let T be triangle, C the circle and S the square.

● T + T + T = 30

● 3T = 30

Divide both sides by 3

● 3T/3 = 30/3

● T = 10

So the triangle has a value of 10.

●30 T + C + C = 20C + S + S = 13T +C ×S/2

Add like terms together

●30 T + 2C = 20C +2S= 13T + C×S/2

Replace T by its value (T=10)

● 300 + 2C = 20C + 2S = 130 + C×S/2

Take only this part 20C + 2S = 130 + C × S/2

● 20C + 2S = 130 + C×S/2 (1)

Take this part (300+2C = 20C+2S) and express S in function of C

● 20C + 2S = 300 + 2C

Divide everything by 2 to make easier

● 10 C + S = 150+ C

● S = 150+C-10C

● S = 150-9C

Replace S by (5-9C) in (1)

● 20C + 2S = 130 + C×S/2

● 20C + 2(150-9C) = 130 +C× (150-9C)/2

● 20C + 300-18C= 130 + C×(75-4.5C)

● 2C + 300 = 130 + 75 -4.5C^2

● 2C +300-130 = 75C - 4.5C^2

● 2C -75C + 170 = -4.5C^2

● -73C + 170 = -4.5C^2

Multiply all the expression by -1

● -4.5C^2 +73C+ 170= 0

This is a quadratic equation, so we will use the discriminant method.

Let Y be the discriminant

● Y = b^2-4ac

● b = 73

● a = -4.5

● c = 170

● Y = 73^2 - 4×(-4.5)×170= 8389

So the equation has two solutions:

● C = (-b +/- √Y) /2a

√Y is approximatively 92

● C = (-73 + / - 92 )/ -9

● C = 18.34 or C = -2.11

Approximatively

● C = 18 or C = -2

■■■■■■■■■■■■■■■■■■■■■■■■■

● if C = 18

30T + 2C = 300 + 36 = 336

● if C = -2

30T + 2C = 300-4 = 296

Answer:

the first  partial sum  [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]

the second partial sum  [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]

the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]

the fourth  partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]

the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]

the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]

Step-by-step explanation:

The term of the sequence are given as : [tex]\dfrac{1}{2}[/tex], [tex]\dfrac{1}{2^2}[/tex], [tex]\dfrac{1}{2^3}[/tex], [tex]\dfrac{1}{2^4 }[/tex] ,  .  .  .  

The nth term for this sequence is , [tex]\mathtt{a_n =( \dfrac{1}{2})^n}[/tex]

The nth partial sum of the sequence for [tex]\mathtt{a_1,a_2,a_3.... a_n}[/tex] is [tex]\mathtt{S_n}[/tex]

where;

[tex]\mathtt{S_n = a_1 +a_2+a_3+ ...+a_n}[/tex]

The first partial sum  is:  [tex]\mathtt{S_1= a_1}[/tex]

[tex]\mathtt{S_1= (\dfrac{1}{2})^1}[/tex]

[tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]

Therefore, the first  partial sum  [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]

The second partial sum is: [tex]\mathtt{S_2= a_1+a_2}[/tex]

[tex]\mathtt{S_2= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2}[/tex]

[tex]\mathtt{S_2= \dfrac{1}{2} + \dfrac{1}{4}}[/tex]

[tex]\mathtt{S_2= \dfrac{2+1}{4} }[/tex]

[tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]

Therefore, the second partial sum  [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]

The third partial sum is : [tex]\mathtt{S_3= a_1+a_2+a_3}[/tex]

[tex]\mathtt{S_3= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3 }[/tex]

[tex]\mathtt{S_3= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}}[/tex]

[tex]\mathtt{S_3= \dfrac{4+2+1}{8}}[/tex]

[tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]

Therefore, the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]

The fourth partial sum : [tex]\mathtt{S_4= a_1+a_2+a_3+a_4}[/tex]

[tex]\mathtt{S_4= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 }[/tex]

[tex]\mathtt{S_4= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}[/tex]

[tex]\mathtt{S_4= \dfrac{8+4+2+1}{16}}[/tex]

[tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]

Therefore, the fourth  partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]

The fifth partial sum : [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5}[/tex]

[tex]\mathtt{S_5= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 }[/tex]

[tex]\mathtt{S_5= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}}[/tex]

[tex]\mathtt{S_5= \dfrac{16+8+4+2+1}{32}}[/tex]

[tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]

Therefore, the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]

The sixth partial sum: [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5+a_6}[/tex]

[tex]\mathtt{S_6= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 +(\dfrac{1}{2})^6 }[/tex]

[tex]\mathtt{S_6= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64} }[/tex]

[tex]\mathtt{S_6= \dfrac{32+16+8+4+2+1}{64}}[/tex]

[tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]

Therefore, the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]

Answer:

y = -4x - 6.

Step-by-step explanation:

We are given (-5, -3), (-1, -2), and (3, -1) for points of a line. First, we need to find the slope.

(-2 - -3) / (-1 - -5) = (-2 + 3) / (-1 + 5) = 1 / 4.

A perpendicular bisector would have a slope of -4, which is the negative reciprocal of 1/4.

Now that we have the slope, we can say that the equation is y = -4x + b. To find what is b, we can say that y = -2 and x = -1.

-2 = -4(-1) + b

-2 = 4 + b

b + 4 = -2

b = -6

So, the equation of the perpendicular bisector is y = -4x - 6.

Hope this helps!

Answer:

y = -4x - 6.

Step-by-step explanation:

Just took the test and got it right

Classica aplicação de regra de 3:

é dito que: 1 milha = 1,6km

Logo, eis a regra de 3:

  milha           km

     1   --------    1,6

     X  --------   240

1,6X = 240.1

X = 240/1,6

Logo 240km equivalem a 150milhas

Answer:

We accept H₀  data from the survey is not enough to claim that 50% of the proportion indicated in previous studies have change

Step-by-step explanation:

To get conclusions about the survey we need to develop a hypothesis test of proportion

According to previous studies, (p₀ ) 50 % of staff and customers use public transportation, and we got from a survey 0f 1002 people 483 responded they also use then  p = 483/1002 then

n sample size is   1002  and  p = 0,482    (48,2 % )

Test Hypothesis

Null hypothesis                                   H₀            p  =  p₀

Alternative hypothesis                       Hₐ            p  <  p₀

CI =  95 %    α  = 5 %     α = 0,05    and from z-table we find z score for that value    z(c)  =  - 1,64

z(s)  =  (  p  -  p₀ ) /  √ (p₀*q₀)/ n         p₀ = q₀  = 0,5

z(s)  =  - 0,018* 31,65 / 0,5

z(s)  =  - 1,1394

To compare

z(s)  and  z(c)          -1,1394 > 1,64

Then z(s) is inside the acceptance region. We accept H₀ , because we don´t have enough evidence to claim that the survey results indicate a change in

the original proportion

Step-by-step explanation:

Using Sine Rule

[tex] \frac{ \sin(a) }{ |a| } = \frac{ \sin(b) }{ |b| } = \frac{ \sin(c) }{ |c| } [/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(38) }{a} [/tex]

[tex]a = \frac{5( \sin(38))}{ \sin(42) } [/tex]

[tex]a = 4.6[/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(100) }{b} [/tex]

[tex]b= \frac{5( \sin(100))}{ \sin(42) } [/tex]

[tex]b = 7.4[/tex]

Answer and Step-by-step explanation:

This is a complete question

Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80​% of the time. Identify the null​hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

The computation is shown below:

The null and alternative hypothesis is

[tex]H_0 : p = 0.80[/tex]

[tex]Ha : p < 0.80[/tex]

[tex]\hat p = \frac{x}{ n} \\\\= \frac{74}{97}[/tex]

= 0.7629

Now Test statistic = z

[tex]= \hat p - P0 / [\sqrtP0 \times (1 - P0 ) / n][/tex]

[tex]= 0.7629 - 0.80 / [\sqrt(0.80 \times 0.20) / 97][/tex]

= -0.91

Now

P-value = 0.1804

[tex]\alpha = 0.01[/tex]

[tex]P-value > \alpha[/tex]

So, it is Fail to reject the null hypothesis.

There is ample evidence to demonstrate that less than 80 percent of the time reports that these polygraph findings are accurate.

Answer:

[tex] y = - 2 [/tex]

Step-by-step explanation:

Given that the 2 triangles are congruent based on the Hypotenuse-leg theorem, this implies that:

[tex] x - y = x + 2 [/tex] , and [tex] 2x - y = 4x + 2y [/tex]

Using the expression, [tex] x - y = x + 2 [/tex], solve for y:

[tex] x - y - x = x + 2 - x [/tex]

[tex] - y = 2 [/tex]

[tex] y = - 2 [/tex]

Answer:

The first picture's answer would be (6, 21)

Step-by-step explanation:

You have to find the points on the 8th and the 9th day, and then you would add them together, and then divide by two finding the average, which would be 24 and 18, so when added, you get 42, divided by 2 you get 21. You look on the graph for the point with 21, and you find it is on 6.

Answer:

6.02

six point zero two

Step-by-step explanation:

Answer:

602 / 100= 6,02

Step-by-step explanation:

602 to divide 100 = 6,02

Answer:

x and y can have many values

Step-by-step explanation:

-24x - 12y = -16

Then: 24x + 12y = 16

We know: 6x + 3y = 4

X and Y can have a lot of valoues.

6x + 3y = 4

3 ( 2x + y) = 4

2x + y= 4/3

2x+y= 1.333...

Answer:

  his path

Step-by-step explanation:

In order to determine the total distance driven from one place to another, you need to know the path taken.