Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.
a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?

Answer:

864

Step-by-step explanation:

AT= 2Area base+ph

AT= 2(12*12) +(12*4)12

AT=2 (144)+576

AT= 288+576

AT=864"

Answer:

t-shirts = 8, hats= 15

Step-by-step explanation:

let the no of of t-shirt be x

and the no of hats be y

[tex]x+y= 23-----------1[/tex]

[tex]8x+10y= 154---------2[/tex]

solving equations 1 and 2 simultaneously we have

multiplying equation 1 by 8 and subtracting from 2 we have

[tex]8x+8y=184-------------4\\-8x+10y=154------------2[/tex]  

[tex]=0x-2y=30[/tex]

[tex]y=\frac{-30}{2} \\y=-15[/tex]

y= 15

substituting y= 15 in equation 1 to find x we have

[tex]x+15=23\\x=23-15\\x= 8[/tex]

x=8

Answer:

x = 2, y = 5

Step-by-step explanation:

Hello,

   y=6x-7

   9x-2y=8

can be written as

   (1) 6x - y = 7

   (2) 9x -2y = 8

(2)-2*(1) gives

   9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6

   <=> -3x=-6

   <=> x = 6/3=2

and we replace it in (1)

  y = 6*2-7=12-7=5

hope this helps

Answer:

61,925 miles

Step-by-step explanation:

Given :

The p-value of the tires to outlast the were warranty were given in the the question as = 0.96

Checking the normal distribution table, The probability that corresponds to 0.96

from the Normal distribution table is 1.75.

Mean : 'μ'= 60000 miles

Standard deviation : σ=1100

The formula for z-score is given by

: z= (x-μ)/σ

1.75=(x-60000)/1100

1925=x-60000

x=61925

Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.

Answer:

Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.

The domain is all of the x values. Therefore the domain is {-1, 2}.

The range is all of the y values. Therefore the range is {-4, -3, 2}.

We don't use ( ) or [ ] because T is a discrete relation.

Answer:

24*26= 624 students

hope this helps!

Answer:

624 seats

Step-by-step explanation:

Total classrooms = 24

Each classroom has seats = 26

Total Number of seats = 24*26

=> 624 seats

Answer:

Step-by-step explanation:

hope its helpful

Answer:

4, 10, and 20.

Step-by-step explanation:

20 is a composite number because it has more than 2 factors.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

1 is neither prime nor composite.

2, 5 are prime numbers because they only have 2 factors.

4, 10, 20 are composite numbers because they have more than 2 factors.

Answer:

Hey there!

40 is 25% of 120.

We can see that 30 is 25% of 120, because 0.25(120)=30.

Hope this helps :)

Answer:

30 is 25% of 120

Step-by-step explanation:

What is 25% of 120

Is means equals and of means multiply

What = 25% * 120

What = .25 * 120

What =30

30 is 25% of 120

Answer:

19/9 because it equals to 2.111..  Which is greater than 1

Step-by-step explanation:

By the way if it's right can i get brainliest.

Answer:

1 < 19/9

Step-by-step explanation:

1  vs 19/9

Rewriting 19/9 as 9/9 + 9/9+ 1/9

1 vs 1+1 +1/9

1 vs 2 1/9

1 < 19/9

Answer:

5 [tex]\frac{1}{3}[/tex], 10 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex] ÷ 1 [tex]\frac{1}{3}[/tex] = 2

Thus to obtain a term in the sequence multiply the previous term by 2, thus

a₅ = [tex]\frac{8}{3}[/tex] × 2 = [tex]\frac{16}{3}[/tex] = 5 [tex]\frac{1}{3}[/tex]

a₆ = [tex]\frac{16}{3}[/tex] × 2 = [tex]\frac{32}{3}[/tex] = 10 [tex]\frac{2}{3}[/tex]

Answer:

x = 8

Step-by-step explanation:

To find the possible value of x in the given trapezoid MNOP with median QR, recall that one of the properties of a trapezoid is that the median length = ½ of the sum of the length of the parallel bases

Thus, ½ of [x + (3x + 8)] = 20

Let's find x

½*[x + (3x + 8)] = 20

½*[x + 3x + 8)] = 20

½*[4x +8] = 20

Multiply both sides by 2

4x + 8 = 20*2

4x + 8 = 40

Subtract 8 from both sides

4x = 40 - 8

4x = 32

Divide both sides by 4

x = 32/4

x = 8

Answer:

I think its 8 ‍♂️

Step-by-step explanation:

The order to us solve is:

Let's go:

[tex]25(1.2\times 3 - 1.25) + 3.45\\25(3.6-1.25)+3.45\\25\times 2.35 + 3.45\\58.75+3.45\\62.2[/tex]

Therefore, the result is 62.2.

Answer:

4.0375

Step-by-step explanation:

.25(3.6-1.25)+3.45

.25(2.35)+3.45

.5875+3.45

4.0375

HOPE  THIS HELPS:)

Answer:

Y=1/4x-4

Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25

Answer: 57769.8 in²

Let A be the area of the shaded region

We have a relation that can help us calculate its area

A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle

A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²

Answer:

818.4

Step-by-step explanation:

Answer:

The corresponding definite integral may be written as

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]

The answer of the above definite integral is

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]

Step-by-step explanation:

The given limit interval is

[tex]\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i[/tex]

[tex][a, b] = [-8, 6][/tex]

The corresponding definite integral may be written as

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]

[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]

Bonus:

The definite integral may be solved as

[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98[/tex]

Therefore, the answer to the integral is

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]

Answer:

9/26

Step-by-step explanation:

Answer:

Step-by-step explanation:

25-3 =22 have a cat or a dog

15 +16 =31 students are in the class if every person has either a cat or a dog

But we have 22

so 31 - 22 = 9 have both cat and dog

the probability is 9/25

Answer:

{ 6,12}

Step-by-step explanation:

The intersection is what the two sets have in common

{3, 6, 9, 12, 15}∩ {1, 6, 12, 18, 24}

= { 6,12}

Answer:

[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]

Now we can substitute in the equation

[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]

so the new equation is

[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]

the auxiliary equation is

[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]

so the solutions of the new equation are

[tex]y(t)=ae^{2t}+be^{-10t}[/tex]

with a and b real

as

[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]

[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]

hope this helps

do not hesitate if you have any questions

Answer:

9/24 or 37.5%

hope this helps :)

Hi,  

first thing you must do with a  probability problem is to count how many thing you have in your universe.

Here we are dealing with sweets. So let's count  :  5 +4+8+4+3 = 24  

and there is  5 yellow  so probability to pick up a yellow is  5/24

and there is 4 orange  so probabilitu to pick up a orange is  4/24

To say  :   Ola will pick orange or  yellow  mean  if she pick either one of the two sort is good.  So you add the proba of each :   5/24 +4/24 = 9/24

and then you must reduce if you can :   9/24 = 3*3 /8*3 =  3/8

So the probability that Ola pick a  yellow or orange sweet is  3/8 = 0.375

Answer:

21.84 years

Step-by-step explanation:

From the compound interest formula;

F = P(1+r)^t .......1

ln(F/P) = tln(1+r)

t = ln(F/P)/ln(1+r) .......2

Where;

F = Final value = $45,117

P = Initial value = $15,540

r = rate = 5% = 0.05

t = time

Substituting the values into equation 2;

t = ln(45117/15540)/ln(1.05)

t = 21.84542292124 years

t = 21.84 years

It will take Bob 21.84 years

Answer:

sqrt(70)/7

Step-by-step explanation:

sqrt(10/7)

sqrt ( a/b) = sqrt(a)/ sqrt(b)

sqrt(10) / sqrt(7)

But we don't leave a sqrt in the denominator, so multiply by sqrt(7) /sqrt(7)

sqrt(10) /sqrt(7) * sqrt(7) / sqrt(7)

sqrt(70)/ sqrt(49)

sqrt(70)/7

Trigonometry is the study of the properties of triangles and trigonometric functions and of their applications.  

I'm not sure how you'd want me to answer your question though, but stay safe!!

- eli <3

Answer:

At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0

The significance level is 0.05.

The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.

[tex]p_1=X_1/n_1=24/400=0.06[/tex]

The sample 2, of size n2=400 has a proportion of p2=0.1.

[tex]p_2=X_2/n_2=40/400=0.1[/tex]

The difference between proportions is (p1-p2)=-0.04.

[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]

As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Answer:

  2 1/4

Step-by-step explanation:

The volume of soil needed is ...

  (14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³

The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.

  You need to order 2 1/4 cubic yards.

___

There are 3 ft or 36 inches to a yard.

Answer:

a) diagonal box = 12.9 in

b) diagonal base = 8.2 in

Step-by-step explanation:

w = 8 in

h = 10 in

L = 2 in

required:

a) diagonal of the box

b) diagonal of its base

referring into the attached image

a) the diagonal of the box = sqrt ( w² + h² + L²)

  diagonal box = sqrt (8² + 10² + 2²)

  diagonal box = 12.9 in

b) diagonal of its base = sqrt ( w² + L²)

   diagonal base = sqrt ( 8² + 2²)

   diagonal base = 8.2 in

Answer:

This equation displays the distributive property which states that a(b + c) = a(b) + a(c).

Answer:

Distributive property

Step-by-step explanation:

4(x+3)=4x+12

This example shows distributive property because 4 is distributed (multiplied) to x +3. When 4 is distributed, it will equal 4x+12!!

Hope it helps!!!!

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

[tex]y=z=0\implies x=2\implies (2,0,0)[/tex]

[tex]x=z=0\implies y=2\implies(0,2,0)[/tex]

[tex]x=y=0\implies 2z=2\implies z=1\implies(0,0,1)[/tex]

Plane 2, 4x + 4y + z = 8:

[tex]y=z=0\implies4x=8\implies x=2\implies(2,0,0)[/tex]

[tex]x=z=0\implies4y=8\impliesy=2\implies(0,2,0)[/tex]

[tex]x=y=0\implies z=8\implies(0,0,8)[/tex]

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

[tex]\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}[/tex]

Answer:

y=2x+6

Step-by-step explanation:

The slope is 2x and the y-intercept is 6. It is shown how to graph it in the attachment.

Answer:

c = 20.5x + 5.59

Step-by-step explanation:

c = mx + b

c = mx + 5.59

108.09 = m(5) + 5.59

5m = 102.5

m = 20.5

c = 20.5x + 5.59

Answer:

Step-by-step explanation:

Area of a rectangle = l × w

where l is the length

w is the width

length of a rectangle is 11 yds more than twice the width is written as

l = 11 + 2w

Area = 63 yd²

(11+2w)w = 63

2w² + 11w - 63 = 0

Solve the quadratic equation

( w + 9) ( 2x - 7) = 0

w = - 9 w = 7/2 or 3.5

Since width is always positive w is 3.5 yd

l = 11 + 2(3.5)

l = 11 + 7

l = 18 yd

The length is 18 yd

The length is 18 ydThe width is 3.5 yd

Hope this helps you