Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100mm cigarettes is obtained, and the tar content of each cigarette is measure. The sample has a mean of 19.4 mg and a standard deviation of 3.52 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest about the effectiveness of the filters? What are the hypotheses? Identify the test statistic. Identify the P-value Identify the critical value(s). State the final conclusion that addresses the original claim. A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. B. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. C. Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. D. Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. What do the results suggest, if anything, about the effectiveness of the filters? A. The results are inconclusive because the sample size is less than 30. B. The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes. C. The results do not suggest that the filters are effective. D. The results suggest that the filters are effective. E. The results suggest that the filters increase the tar content.

Step-by-step explanation:

∫ 9 arctan(1/x) dx

If u = 9 arctan(1/x), then:

du = 9 / (1 + (1/x)²) (-1/x²) dx

du = -9 dx (1/x²) / (1 + (1/x²))

du = -9 dx / (x² + 1)

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ln(x² + 1)

Evaluate from x=1 to x=√3.

[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]

[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]

(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)

(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)

(6π√3 − 9π)/4 + 9/2 ln(2)

Answer:

[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]

Step-by-step explanation:

We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].

Now let's say that u = arctan(1/x). The value of 'du' would be as follows:

du = - x / (1 + x²) * dx

If we apply integration by parts, v = 1, and of course u = arctan(1/x):

=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]

Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':

=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx

=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du

=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du

=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )

=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |

So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;

[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]

Now computing the boundaries we have the following answer:

[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]

Answer:

1/16ft²

Step-by-step explanation:

If 26 rolls fits into 1 5/8 ft² pan, then for us to get the number of square feet for each roll, we will fillw the steps;

26rolls = 1 5/8ft²

1 roll = xft²

26 rolls = 13/8 ft²

1roll = xft²

Cross multiply

26×x = 1×13/8

26x = 13/8

Ceoaa multiply

26x×8 = 13

208x = 13

x =13/208

x = 1/16 ft²

Hence the baker uses 1/16ft² for each roll

The equation of a line in slope intercept form with slope (-2/3) and point (10,-5) is y = (-2/3) - 1.

The slope is the rate of change of y-axis with respect to x-axis.

We know that equation of a line in slope intercept form is y = mx + b.

To find the y-intercept b we will substitute the value of m and point (x,y).

∴ The equation of the line in slope intercept form with slope -2/5 and points (10,-5) is,

-5 = -(2/5)×10 + b.

-5 = -4 + b.

b = -1.

So the given equation of the line is y = (-2/3)x - 1.

learn more about slope here :

https://brainly.com/question/3605446

#SPJ5

Answer:

54

Step-by-step explanation:

Substitute n into the equation:

-2(3)[5+3-8-3(3)]

-6[-9]

+54

Answer:

$29.16

Step-by-step explanation:

Each gallon of gas is $2.16.

13.5 gallons of gas is 2.16 (13.5) = $29.16.

Answer:

It's 3.

Step-by-step explanation:

3x2=6

3x4=12

3x5=15

Answer:

Grams

Step-by-step explanation:

Pencils are pretty light, so they should be measured in grams.

Answer:

grams :)

Step-by-step explanation:

I looked it up

Answer:

x-40%-16%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Density = mass/volume = 20/6.47

Answer:

357,340

Step-by-step explanation:

Locate the tens place:

357,335

Check the number to the right:

357,335

If the number is greater than or equal to 5, then we round up. If the number is less than or equal to 4, we round down.

The number next to the tens place is a '5'. We round up.

357,335 ≈ 357,340

Hope this helps.

Answer:

357340

Step-by-step explanation:

Answer:

the order of operations tells us how to solve a problem.

first is P for parentheses. this means you solve all the expressions within the parentheses. this ensures a simplified expression before moving on.

second is E for exponents. this means you solve all the expressions with exponents. by doing this before MDAS, you do not raise the wrong values.

third and fourth is M/D for multiplication/division. the / is between these two because these steps are interchangeable. you can multiply or divide first. the results will be the same.

this also applies to the fifth and sixth, which are A/S for addition/subtraction.

Looks like the integral should be

[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]

Expand the denominator:

[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]

Notice that

[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]

In order to use this substitution, expand the integral as

[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]

In the first integral, use the previously mentioned substitution:

[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]

[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]

In the second integral, complete the square in the denominator:

[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]

Now substitute

[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]

so that

[tex]\sec t=\dfrac{8x+13}5[/tex]

Then

[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]

and the integral becomes

[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]

[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]

[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]

So, the integral is

[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]

Answer:

false

plz tell me if im wrong i hope i helped

Answer:

20 miles/hour

Step-by-step explanation:

40 miles in 2 hours,

thus,

         40/2 miles  in 2/2 hours = 20 miles in 1 hour.

Therefore, Tim bikes 20 miles per hour.  

Answer:

Answer:54

4 1/2times 12

Convert 4 1/2 to an improper fraction.

9/2 times 12

Cancel the common factor of 2

9 times 6

Multiply

9 by 6 the you'll get 54

Answer:

D

Step-by-step explanation:

♡ The Question ♡

Graph the solution of 5 ≤ 9 - 4a

A) A

B) B

C) C

D) D

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Answer ♡

-I believe the answer should be the first choice, A!

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*  

♡ The Explanation/Step-By-Step ♡

-No Explanation/Step-By-Step provided!  

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ Tips ♡

-No Tips provided!

First, let's get the total amount of coins inside the box.

7 quarters + 4 dimes + 4 nickels + 3 pennies = 18 total coins.

(7 quarters / 18 coins) * 100 = 38.89% chance of picking a quarter

(4 dimes / 18 coins) * 100 = 22.22% chance of picking a dime

(4 nickels / 18 coins) * 100 = 22.22% chance of picking a nickel

(3 pennies / 18 coins) * 100 = 16.67% chance of picking a dime

Since the quarters have a higher percentage of being picked, we can expect to draw $0.25 from the box

Answer:

-3x<12

/-3  /-3

x<-4

Step-by-step explanation:

The diagonal of a rectangle = sqrt(w^2 + l^2)

w = width

l = length

In this problem,

The diagonal = 20 in

w = x

l = 2x + 8

Let's plug our numbers into the formula above.

20in = sqrt((x)^2 + (2x + 8)^2)

Let's simplify the inside of the sqrt

20 in = sqrt(5x^2 + 32x + 64)

Now, let's square both sides.

400 = 5x^2 + 32x + 64

Subtract 400 from both sides.

0 = 5x^2 + 32x - 336

Factor

0 = (5x - 28)(x + 12)

Set both terms equal to zero and solve.

x + 12 = 0

Subtract 12 from both sides.

x = -12

5x - 28 = 0

Add 28 to both sides.

5x = 28

Divide both sides by 5

x = 28/5

The width cant be a negative number so now we know that the only real solution is 28/5

Let's plug 28/5 into our length equation.

Length = 2(28/5) + 8 = 56/5 + 8 = 96/5

In conclusion,

Length = 96/5 inches

Width = 28/5

Answer:

-72

Step-by-step explanation:

-32 + (2-6)(10)

-32 + (-4)(10)

-32 + -40

-72

Answer:

-72

Step-by-step explanation:

Use PEMDAS and solve from left to right.

2 - 6 = -4

Parenthesis means multiplication.

-4 x 10 = -40

Then you add the negatives.

-32 + -40 or

-32 - 40 = -72

Answer:

$7075 or 7718

Step-by-step explanation:

91100-6200=84900

84900/11= 7718.18181818 or rounded= 7718

(This is if the december month doesnt count.)

84900/12=7075

(If december is included.)

Answer:

her monthly salary = 84900/12= 7075 dollars

Step-by-step explanation:

total earns= 91100 dollars

actual salary does not include bonus

her actually salary : 91100-6200= 84900

her monthly salary = 84900/12= 7075 dollars

Answer:

40/4 shaded in squares

Step-by-step explanation:

for 0.4, since 100 is a whole, multiply by 100.

0.4*100=40

shade in 40 squares

for 0.04, multiply by 100

0.04*100=4

shade in 4 squares

Answer:

20%

Step-by-step explanation:

100 divided by 5 =20 20x1=20

Answer:

6 1/2 cubic feet

Step-by-step explanation:

A carton has a length of 2 1/6 feet

The width is 1 1/5 feet

The height is 2 1/2 feet

Therefore the volume of the carton can be calculated as follows

= length × width × height

= 2 1/6 × 1 1/5 × 2 1/2

= 13/6 × 6/5 × 5/2

= 390/60

= 13/2

= 6 1/2 cubic feet

Hence the volume of the carton is 6 1/2 cubic feet

A and B is not, because if you were to make the A bigger it'll be the same as B, so I think is C