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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

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:

-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:

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 (✿^‿^)

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

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:

The best and most correct answer among the choices provided by the question is

The statement that points out his most serious omission is "What if the electric bill increases?".

Step-by-step explanation:

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:

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:

a

Step-by-step explanation:

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:

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:

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:

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:

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

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:

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:

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:

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:

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.

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:

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°

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:

b

Step-by-step explanation:

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:

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:

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

Step-by-step explanation: