A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of 0.8 years. If you randomly purchase one item, what is the probability it will last longer than 14 years

Answer:

Option B, Americium-241, is the right answer.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:  c. (1/2) bc sin A

Step-by-step explanation:

You can find the area of a triangle using trigonometry if you know the lengths of two sides and the measure of the included angle using the following formula:

[tex]A=\dfrac{1}{2}ab\sin C[/tex]

Answer:

[tex]\Large \boxed{\mathrm{\bold{C} }}[/tex]

Step-by-step explanation:

We can find the area of the triangle when two sides are given and the angle in between the two sides.

[tex]\displaystyle A=\mathrm{\frac{1}{2} bc \cdot sinA}[/tex]

b and c are the sides and A is the angle in between b and c.

Answer:

The  correct option is   b

Step-by-step explanation:

From the question we are told that

   The  sample size is  [tex]n = 100[/tex]

    The  population  mean is  [tex]\mu = 2.5[/tex]

   The  sample  standard deviation is  [tex]\sigma = 0.2[/tex]

Generally the mean of the sampling distribution of sample means is mathematically represented as

       [tex]\mu_{\= x } = \mu[/tex]

=>    [tex]\mu_{\= x } = 2.5[/tex]

Answer:

a

The null hypothesis is  [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]

The  alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex]   (Manufacturers claim)

b

 [tex]t = 2.114[/tex]

c

Decision rule

    Reject the null hypothesis

d

There is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor

Step-by-step explanation:

From the question we are told that

   The first sample  size is  [tex]n_1 = 9[/tex]

    The second sample size is [tex]n_2 = 12[/tex]

    The first sample mean is  [tex]\= x_1 = 1260 \ feet[/tex]

     The  second sample mean is  [tex]\= x_2 = 1230[/tex]

     The  first standard deviation is  [tex]\sigma_1 = 24[/tex]

     The second standard deviation is  [tex]\sigma_2 = 37[/tex]

      The significance level is [tex]\alpha = 0.10[/tex]

The null hypothesis is  [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]

The  alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex]   (Manufacturers claim)

Generally the degree of freedom is mathematically represented as

       [tex]df = n_1 + n_2 -2[/tex]

       [tex]df = 9 + 12 - 2[/tex]

       [tex]df = 19[/tex]

Generally the pooled standard deviation  is mathematically represented as

      [tex]\sigma_p = \sqrt{ \frac{(n_1 - 1)\sigma_1^2 + (n_2-1 )\sigma_2^2 }{ (n_1 - 1 ) + (n_2 - 1 )} }[/tex]

      [tex]\sigma_p = \sqrt{ \frac{(9 - 1)24^2 + (12-1 )37^2 }{ (9 - 1 ) + (12 - 1 )} }[/tex]

      [tex]\sigma_p =32.17[/tex]

Generally the test statistics is mathematically represented as

      [tex]t = \frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma_p^2}{n_1 } +\frac{\sigma_p^2}{n_2 } } }[/tex]

    [tex]t = \frac{1260 - 1230 }{\sqrt{\frac{32.17^2}{9 } +\frac{32.17^2}{12 } } }[/tex]

    [tex]t = 2.114[/tex]

Generally the p-value is obtained from the student t distribution table and the value is

    [tex]p-value = P(t > 2.11) = t_{2.11 , 19} = 0.024173[/tex]

Given that the  [tex]p-value < \alpha[/tex]

The null hypothesis is rejected

Hence we can conclude that there is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor

3s=t+5

s=4

we substitute 4 for s in the equation

3*4=t+5

12=t+5

t=12-5

t=7

Answer:

Brainliest!

Step-by-step explanation:

3s = t+5

s = 4

so...

3 (4) = t+5

12 = t+5

t = 7

Answer:

Step-by-step explanation:

(1,15) and (2,30)

(30-15)/(2-1)= 15/1 = 15

Answer: 0.47

Step-by-step explanation:

Given that

n = 100, probability of rolling 1 = 1/6

binomial approximation

np = 100 ( 1/6) = 16.667

standard deviation = √ 100 × 1/6 ×5/6 = 3.7627

P ( 9 ≤ X ≤ 16 )

= P ( 8.5 < X < 16.5 )

so,

= P ((8.5 - 16.6667) / 3.7627 < Z < (16.5 - 16.6667) / 3.7627

= P ( -2.17 < Z < -0.04 )

= 0.484 - 0.015

= 0.47

Therefore the approximate probability that you will roll between 9 and 16 ones is 0.47

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are going to be using the compound interest formula

Given data

principal P= $5000

N is time = 7 years

rate r= 2.5%= 0.025

compounded monthly k= 112

final amount A=?

The expression for the compound interest is

[tex]A= P(1+\frac{r}{K} )^K^N[/tex]

substituting into the expression we have

[tex]A= 5000(1+\frac{0.025}{12} )^1^2^*^7\\\\ A= 5000(1.002 )^1^2^*^7\\\\ A= 5000(1.002 )^8^7\\\\A= 5010*1.18273815853 \\\\ A= 5925.51[/tex]

in seven years he will have $5925.51

Answer:

Amount after 10 years is $1472.775

Step-by-step explanation:

Amy deposited $750 in a saving account that pays 6.75% Interest compounded monthly for 10 years.

Principal amount= $750

Rate of interest= 6.75%

Time= 10 years

Number of times compounded= 10*12

Number of times compounded= 120

A= p(1+r/n)^(nt)

A= 750(1+0.0675/120)^(120*10)

A= 750(1+0.0005625)^(1200)

A= 750(1.0005625)^(1200)

A= 750(1.9637)

A= 1472.775

Amount after 10 years is $1472.775

Answer:

z = 1/9

Step-by-step explanation:

2z + 6z + 2 = 3 - 1z

2z + 6z + 1z = 3 - 2 (on rearranging)

9z = 1 (on solving)

z = 1/9

HOPE IT HELPS (✿^‿^)

Step-by-step explanation:

a) 12:40 = 3: 10

b) 40:12 = 10:3

c)

[tex]1. \: \frac{non \: fiction}{graphic \: novels} [/tex]

[tex]2. \: \frac{science \: fiction}{graphic \: novels} \: \: \: \: \: \: \: 3. \frac{science \: fiction}{non \: fiction} [/tex]

d)

Fiction books is 80.

Answer:

x=6

Step-by-step explanation:

BD is bisecting of <B

x/3=8/4    the theorem of  the bisecting

4*x=3*8

4x=24

x=24/4

x=6

Answer:

Here is the full question:

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) Σ_(n=1)^∞ (-1)^n+1 1/7^n n

Step-by-step explanation:

Σ_(n=1)^∞ (-1)^n+1 1/7^n n

We will use the function In (1 + x)

We will now give a power series expansion of the function while it is centered at x=0

This will give us In (1 + x) = Σ_(n=1)^∞[tex](-1)^{n+1}[/tex][tex]\frac{x^{n} }{n}[/tex]

Note that x= 1/7

Now let us equate the two equations

Σ_(n=1)^∞[tex](-1)^{n+1}[/tex][tex]\frac{1}{7^{n}n }[/tex] = ㏑(1 + x)|[tex]_{x = \frac{1}{7} }[/tex] = ㏑[tex]\frac{8}{7}[/tex]

Sum of the series will give ㏑[tex]\frac{8}{7}[/tex]

Answer:

the standard deviation for the number of restaurants specializing in seafood is 0.8944

Step-by-step explanation:

Given that :

Sum total number N of top restaurants in Chicago = 20

Four of the restaurants specialize in seafood,

then , the probability that a randomly selected restaurant from the top 20 in the list will specialize in seafood will be  p = 4/20

p = 0.2

sample size n = 5

Assuming X to be the random variable that follows a Binomial distribution that represent the number of restaurants specializing in seafood.

Then: [tex]X \sim Binomial (n,p)[/tex]

where;

n = 5  and p = 0.2

The standard deviation σ  can be determined by using the formula:

[tex]\sigma = \sqrt{np(1-p)}[/tex]

[tex]\sigma = \sqrt{5\times 0.2(1-0.2)}[/tex]

[tex]\sigma = \sqrt{1.0(0.8)}[/tex]

[tex]\sigma = \sqrt{0.8}[/tex]

σ = 0.894427191

σ [tex]\simeq[/tex] 0.8944

Answer:

C

Step-by-step explanation:

Starting at zero, it went back 2/5 to negative 2/5.  Then it went forward 4/5 to positive 2/5, which is the answer.

Answer:

a.  0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]

b. 0.6[tex]\overline {19}[/tex]  = [tex]\mathbf{\dfrac{613}{990}}[/tex]  

Step-by-step explanation:

Consider the following repeating decimal. 0.6[tex]\overline {19}[/tex]

a) Write the repeating decimal as a geometric series.

0.6[tex]\overline {19}[/tex] is being expressed as 0.6191919...

0.6[tex]\overline {19}[/tex] = 0.6 + 0.019 + 0.00019+ 0.0000019 + ...

0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}+ \dfrac{19}{100000}+ \dfrac{19}{10000000}+ ...[/tex]

0.6[tex]\overline {19}[/tex] = [tex]0.6+ \dfrac{19}{1000} \begin {bmatrix} 1 + \dfrac{1}{100} + \dfrac{1}{10000}+ ... \end {bmatrix}[/tex]

0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]

(b) Write the sum of the series as the ratio of two integers

0.6[tex]\overline {19}[/tex]  = [tex]0.6 + 0.019 ( \dfrac{1}{1-0.01})[/tex]

0.6[tex]\overline {19}[/tex]  =[tex]0.6 + \dfrac{19}{1000}\times \dfrac{100}{99}[/tex]

0.6[tex]\overline {19}[/tex]  = [tex]0.6 + \dfrac{19}{990}[/tex]

0.6[tex]\overline {19}[/tex]  = [tex]\dfrac{594+19}{990}[/tex]

0.6[tex]\overline {19}[/tex]  = [tex]\mathbf{\dfrac{613}{990}}[/tex]  

Answer:

6p^3−7p^2+11p−6

Step-by-step explanation:

1. You would want to foil it, which means multiplying one number from each parentheses to the next parentheses, like so:

3p * 2p ^ 2 = 6p^3

3p * -p = -3p

3p * 3 = 9p

-2 * 2p^2 = -4p^2

-2 * -p = 2p

-2 * 3 = - 6

2. Now add all of the numbers we foiled together, thus getting you:

6p^3−7p^2+11p−6

Answer:

y=4.5x

Step-by-step explanation:

I got it correct on Khan!

Hope this helps ;)

The equation that describes the proportional relationship between x and y is: y = 4.5x.

To write the equation of a proportional relationship between variables x and y, find the constant of proportionality, which is k = y/x, then plug in the value of k into y = kx.

Constant of proportionality (k) = 9/2 = 22.5/5 = 36/8 = 4.5

Substitute k = 4.5 into y = kx.

y = 4.5x.

The equation is: y = 4.5x.

Learn more about the proportional relationship on:

https://brainly.com/question/15618632

#SPJ6

Answer:

a). Radius r of the small sector= 12cm

b). Perimeter of the shape= 68 cm

c). Angle= 47.7°

Step-by-step explanation:

a). Radius of the big sector= 24 cm

Arc if the big sector= 20 cm

Arc of the small sector= 10 cm

For the radius r of the small sector

r/10 = 24/20

r=(10*24)/20

r= 24/2

r= 12 cm

Radius r of the small sector= 12cm

b). Perimeter of the shape

= Total length of the shape

Let's note that the other side of the sector is also the radius= 24 cm

Perimeter= 20+24+24

Perimeter of the shape= 68 cm

c) the angle

Length of arc = 2πr*(angle/360)

Let angle = b

Length of arc = 20cm

20= 2*3.14*24*(b/360)

(20*360)/(2*3.14*24)= b

47.7°= b

Angle= 47.7°

Answer:

$94.50

Step-by-step explanation:

3(50)=150 $1.50

4(40)=160 160(5)=800 $8.00

5(50)=250 250(10)=2500 $25.00

6(40)=240 240(25)=6000  $60.00

60+25+8+1.5=$94.50

Answer:

The answer is D 10 to the power of -4.

Step-by-step explanation:

When the decimal point moves left, the power of becomes negative. Therefor the answer is D.

Have a good day.

Multiply by [tex]A^{-1}[/tex] on the right of both sides of [tex]A^3=I[/tex], then use the fact that matrix multiplication is associative.

If [tex]A^3=I[/tex], then

[tex]A^3A^{-1}=IA^{-1}[/tex]

[tex]A^2(AA^{-1})=A^{-1}[/tex]

[tex]A^2I=A^{-1}[/tex]

[tex]\implies A^2=A^{-1}[/tex]

Answer:

-70[tex]\frac{73}{100}[/tex]

Hope It Help

Unclear question. However, I inferred you want to know about hypotehsis test.

Step-by-step explanation:

Remember, any hypothesis test is divided into two types. They are:

Using this question example, here's the hypothesis statements ma sound:

Null hypothesis; There is a significant impact by the explanatory variables on engine overhaul time.

Alternate hypotheses; There is no impact by impact by the explanatory variables on engine overhaul time.

Answer:

64,186,300 square miles

I'm sorry if I misunderstood.

Good luck mate! :)

Please add Brainliest if you'd like, not that it matters.

Remember to try your best every day!

Answer:

See the attachment for formatted formulas

Step-by-step explanation:

Let X11, X12, ……,X1n  and X21 , X22……., X2n be two small independent random samples from two normal populations with means u1 and u2  and the standard deviations σ1 and σ2 respectively. If σ1= σ2 (=σ) but unknown then the unbiased pooled or combined estimate of the common variance σ2 (the term variance means that each population has the same variance) is given by

Sp2  = ((n_1-1)  s_(1^2 )+ (n_2-1) s_2^2)/(n_1+n_2-2)

Where

S12 = 1/(n_1- 1) ∑▒〖 (X_1i- X`_1)〗^2  and

S22 = 1/(n_2- 1) ∑▒〖 (X_2j- X`_2)〗^2

The test statistic

t = ((X_1`-X_2`)- (μ_1- μ_2))/(√(s_p&1/n_1 )+ 1/n_2 )

Has t distribution with v= n1 + n2 – 2 degrees of freedom.

It is used as a test statistic for testing hypotheses about the difference between two population means.

The procedure for testing hypothesis H0: μ_1- μ_2= ∆_0 in case of small independent samples when σ_1= σ_2 is as follows.

H0: μ_1- μ_2= ∆_0  against the appropriate alternative.

t = ((X_1`-X_2`)- ∆_0  )/(√(s_p&1/n_1 )+ 1/n_2 )

Which has t distribution with v= n1 + n2 – 2 degrees of freedom.

Answer:

t must be 7

Step-by-step explanation:

Replace s with 4 and solve for t in the original equation:

3 s = t + 5

3 (4) = t + 5

12 = t + 5

12 - 5 = t

7 = t

So t must be 7