How do you pronounce B"?

Answer:

8 cm

Step-by-step explanation:

divide 400 by 50 which is 8.

Answer:

a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.

b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.

c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.

d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.

Step-by-step explanation:

We have a normal distribution, with mean 190 and standard deviation 7.4.

We take samples of size n=45 from this population.

Then, the sample means will have a distribution with the following parameters:

[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]

The probability that the sample mean is less than 189 can be calculated as:

[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]

The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:

[tex]P(M<M^*)=0.75[/tex]

The third quartile corresponds to a z-value of z*=0.6745.

[tex]P(z<z^*)=0.75[/tex]

Then, we can calculate the sample mean for the third quartile as:

[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]

The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.

Answer:

R= sqrt 445

Y = 19

Step-by-step explanation:

Radius is the square root of 445

Find y

So, First step is to substitute what you have

-9^2 + y^2 = 445

 81 + y^2 = 445

-81               -81

y^2 =364

Y is about 19

Let me know if I'm incorrect

Hope this helps :)

Answer:

The leg measures 2 I believe

Step-by-step explanation:

Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.

The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

Let the length of the perpendicular be x.

Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]

Hence, the length of one leg of the triangle is 2√2 cm.

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Answer:

Perimeter = 317 m

Step-by-step explanation:

Given track is a composite figure having two semicircles and one rectangle.

Perimeter of the given track = Circumference of two semicircles + 2(length of the rectangle)

Circumference of one semicircle = πr  [where 'r' = radius of the semicircle]

                                                       = 25π

                                                       = 25 × 3.14

                                                       = 78.5 m

Length of the rectangle = 80 m

Perimeter of the track = 2(78.5) + 2(80)

                                     = 157 + 160

                                     = 317 m

Therefore, perimeter of the track = 317 m

Answer:

33

Step-by-step explanation:

2/5x40=16

40-16=24

24+9=33

33 marbles

2/5 is .4

Multiply .4 by 40 to get 16

Subtract 16 from 40 to get 24

Add 9 to 24 to get 33

Hope it helps <3

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Answer:

Step-by-step explanation:

Step-by-step explanation:

Log T = 11.8 + 1.5.M (with T is the amount of energy released by the earthquake, Log refers to the logarithm to the base 10)

-->T = [tex]10^{11.8 +1.5*6.5}[/tex] ≈3.458 *[tex]10^{21}[/tex]

Answer:  2.00 x 10¹⁰⁹

Step-by-step explanation:

log T = 11.8 + 1.5M

Given: M = 6.5

log T = 11.8 + 1.5(6.5)

log T = 11.8 + 9.75

log T = 21.55

      T = 10²¹⁻⁵⁵

      T = 1.995 x 10¹⁰⁹

      T = 2.00 x 10¹⁰⁹       rounded to the nearest hundredth

Answer:

The test statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=23.6[/tex] represent the sample mean

[tex]s=8.6[/tex] represent the sample standard deviation

[tex]n=28[/tex] sample size  

[tex]\mu_o =25[/tex] represent the value that we want to test

t would represent the statistic

System of hypothesis

We want to test if the true mean is lower than 25, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 25[/tex]  

Alternative hypothesis:[tex]\mu < 25[/tex]  

The test statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11[/tex]    

Answer:

m = 0

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the coordinates into the formula:

m = (-3 + 3)/(4 - 6)

m = 0/-2

m = 0

Hey there! :)

Answer:

x = -1.

Step-by-step explanation:

[tex]\frac{1}{x-4}+ \frac{x}{x-2}= \frac{2}{x^{2}-6x+8 }[/tex]

Make each fraction have a common denominator:

[tex]\frac{1(x-2)}{x^{2}-6x+8}+ \frac{x(x-4)}{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]

Simplify:

[tex]\frac{x-2}{x^{2}-6x+8}+ \frac{x^{2}-4x }{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]

Disregard the denominator and solve the numerators:

x - 2 + x² - 4x = 2

Combine like terms:

x² - 3x - 2 = 2

x² - 3x - 4 = 0

Factor:

(x - 4)(x + 1)

***Only one of these solutions works because if x = 4, the denominator of the first fraction would be 0, which is undefined. Therefore, the only possible solution is x = -1.

Answer:

a) 95% confidence intervals are

(64.188, 72.652)

b) Mike use  

(t₀.₀₂₅ , ₆)= 2.4469

Step-by-step explanation:

Step(i):-

Given data

    x    :     65    71    74    61    66    70   72

Mean of 'x'

     x⁻ = ∑ x / n

[tex]x^{-} = \frac{65+71+74+61+66+70+72}{7} = 68.42[/tex]

 x       :     65          71        74          61        66         70          72

x - x⁻   :    -3.42     2.58     5.58      -7.42      -2.42    1.58        3.58

(x-x⁻)² :      11.69   6.65     31.13     55.05     5.85      2.49      12.81

∑((x-x⁻)²) =  125.67

Variance

             S² = ∑((x-x⁻)²) / n-1 = [tex]\frac{125.67}{6} = 20.945[/tex]

Standard deviation S = √20.945 =4.576

Step(ii):-

95% confidence intervals are determined by

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} +t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Degrees of freedom

ν =n-1 = 7-1 =6

[tex]t_{\frac{\alpha }{2} , n-1 } = t_{(\frac{0.05}{2} , 6)}[/tex]   = (t₀.₀₂₅ , ₆)= 2.4469

[tex](68.42 - 2.4469 \frac{4.576}{\sqrt{7} } , 68.42 +2.4469\frac{4.576}{\sqrt{7} })[/tex]

( 68.42 - 4.232, 68.42 + 4.232)

(64.188, 72.652)

Conclusion:-

95% confidence intervals are

(64.188, 72.652)

Answer:

64.19 to 72.67

Step-by-step explanation:

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24  

    Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24  

(b) The​ P-value is 0.004.

(c) Reject Upper H 0 because the​ P-value is less than the alpha = 0.01 level of significance.

(d) There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Step-by-step explanation:

We are given that a simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x overbar = 18.3 and the sample standard deviation is found to be s = 6.3.

Let [tex]\mu[/tex] = population mean

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24      {means that the population mean is 24}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24     {means that the population mean is different from 24}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 18.3

            s = sample standard deviation = 6.3

            n = sample size = 15

So, the test statistics =  [tex]\frac{18.3-24}{\frac{6.3}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                    =  -3.504

The value of t-test statistics is -3.504.

(b) Now, the P-value of the test statistics is given by;

               P-value = P( [tex]t_1_4[/tex] < -3.504) = 0.002 or 0.2%

For the two-tailed test, the P-value is calculated as = [tex]2 \times 0.002[/tex] = 0.004 or 0.4%.

(c) Since the p-value of the test statistics is less than the level of significance as 0.002 < 0.01, so we will reject our null hypothesis.

(d) This means that we have sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Answer:

[tex] c = 77.6 [/tex]

Step-by-step explanation:

You may have entered the measure of a side as the measure of an angle.

[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]

[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]

[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]

[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]

[tex] c = 77.6 [/tex]

You are correct. Good job!

Answer:

f(t) = 100,000 ⋅ 0.012 t

Step-by-step explanation:

Answer:

  B. ∠2 and ∠3 are complementary

Step-by-step explanation:

The substitution property of equality lets you put ∠2 in place of ∠1 in the statement ...

  ∠1 and ∠3 are complementary.

  ∠2 and ∠3 are complementary . . . . using ∠2 for equal ∠1 in the above

Answer: ∠2 and ∠3 are complementary

Step-by-step explanation:

Answer:

  384.6 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the trig relation involving sides adjacent and opposite the angle. Here, the road distance is adjacent to the angle of depression, and the altitude is opposite. So, you have ...

  Tan = Opposite/Adjacent

  tan(7.5°) = (300 ft)/(distance to car 1)

  tan(9°) = (300 ft)/(distance to car 2)

Solving for the distances, we have ...

  distance to car 1 = (300 ft)/tan(7.5°) ≈ 2278.73 ft

  distance to car 2 = (300 ft)/tan(9°) ≈ 1894.13 ft

Then the separation between the cars is ...

  distance apart = 2278.73 ft - 1894.13 ft

  distance apart = 384.6 ft

Answer:

The suitcase originally weighed 44kg.

Step-by-step explanation:

1- 0.25= 0.75 (multiplier)

33÷0.75=44

The suitcase originally weighed 44kg

Answer:

10.55% probability

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the CDs are chosen is not important. So we use the combinations formula to solve this question.

1 Bach CD, from a set of 4.

1 Beethoven CD, from a set of 6.

1 Brahms CD, from a set of 3.

1 Handel CD, from a set of 2.

So, D=144

4 CDs from a set of 4+6+3+2 = 15.

So, T= 1365

p= D/T= 144/1365 = 0.1055

10.55% probability that she will choose one by each composer

Answer: G = (19) × (26) × (16)

Step-by-step explanation:

The isomorphism classes of Abelian groups of order 12 are Z₄ ⊕ Z₃ and Z₂ ⊕ Z₂ ⊕ Z₃

SO Let us calculate the orders of some of the elements of G

We have

4² = 16,

4³ = 64

    = 19,

and

4^4 = 19.4

      = 76

      = 31.

furthermore,

4^5 = 31.4

       = 124

       = 34

and

4^6 = 34.4

      = 136

      = 1

Hence, 4 and 34 each have order 6, 16 and 31 each have order 3, and 19 has order 2.

Next, we calculate

11² = 121

    = 31

and

11³ = 11.3

    = 341

    = 26

this is the calculation needed.

26² = 11^6

      = 31³

       = 1

since we already showed that 31 has order 3. This means that 26 has order 2

Since G has two distinct elements of order 2, it cannot be isomorphic to . We conclude

that G = Z₂ ⊕ Z₂ ⊕ Z₃

Finally, we will express as an internal direct product.

The previous calculations show that

(19) = { 1, 19 }

and (26) = { 1, 26 }

are cyclic subgroups of G of order 2 with trivial intersection. We have

(19) × (26) = { 1, 19, 26, 44 }

since

(16) = { 1, 19, 26, 44 }

has trivial intersection with (19) × (26),  conclude that

G = (19) × (26) × (19)

Answer:

32

Step-by-step explanation:

Mean = Average = The data values added together/ the number of data values.

The mean of 5 numbers is 22.6=

[tex]\frac{12+16+n+23+30}{5} = 22.6[/tex]

Multiply both sides by 5.  22.6 becomes 113

12+16+23+30+n=113

n+81 = 113

n= 32

The value of n is 32.

The arithmetic mean of m values [tex]x_1,x_2,..., x_m[/tex] is

[tex]\frac{x_1+x_2+...+x_m}{m}[/tex]

The given

mean = [tex]\frac{12+16+n+23+30}{5}=22.6[/tex]

⇒12+16+n+23+30=22.6×5=113

⇒n=113-81=32

Hence, n=32

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Answer:  B) contain the points E and F

Step-by-step explanation:

Dilation of 2 means to multiply both the x- and y-coordinates by 2

see image below

The only option that is true that E'F' contains points E and F

Answer:

  contains the points E and F

Step-by-step explanation:

The center of dilation is an invariant point. It doesn't move, regardless of the dilation factor.

Likewise, any line through the center of dilation will not move. It is not rotated or translated by dilation--it simply is stretched (or compressed) along its length. It is still an infinite line, and it still goes through all of the points it went through before dilation.

The line through the center of dilation that contains points E and F, after dilation, ...

  contains the points E and F.

Answer:

The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.

Step-by-step explanation:

We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.

Let X = Number of hits made by a baseball player

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 7 at-bats

            r = number of success = exactly 2 hits

            p = probability of success which in our question is batting average

                   of a baseball player, i.e; p = 0.25

SO, X ~ Binom(n = 7, p = 0.25)

Now, the probability that he has exactly 2 hits in his next 7 at-bats is given by = P(X = 2)

          P(X = 2) =  [tex]\binom{7}{2}\times 0.25^{2} \times (1-0.25)^{7-2}[/tex]

                        =  [tex]21 \times 0.25^{2} \times 0.75^{5}[/tex]

                        =  0.3115

Answer:

[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

Replacing we got:

[tex]\bar X=58.875[/tex] represent the mean

[tex]s=5.083[/tex] represent the sample standard deviation for the sample  

[tex]n=8[/tex] sample size  

[tex]\mu_o =60[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 60[/tex]  

Alternative hypothesis:[tex]\mu < 60[/tex]  

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Answer:

a. 75,000

b. 50,000

c. 75,000

Step-by-step explanation:

The computation of allocating the joint cost using the physical units method is shown below:

[tex]Allocation\ rate = \frac{Joint\ costs}{Total\ number\ of\ products}[/tex]

[tex]= \frac{\$200,000}{300 + 200 + 300}[/tex]

[tex]Allocation\ rate = \frac{200,000}{800}[/tex]

= 250

For face cream

[tex]= Unit\ produced\times Allocation\ rate[/tex]

= [tex]300\times 250[/tex]

= 75,000

For body lotion

[tex]= Unit\ produced\times Allocation\ rate\\\\ = 200\times 250[/tex]

= 50,000

For Liquid soap

[tex]= Unit\ produced\times Allocation\ rate\\\\ = 300\times 250[/tex]

= 75,000

hence, we simply applied the above formula by multiplying the units produced with the allocation rate so that each one allocation cost could come

Answer:

f(2) = 5

Step-by-step explanation:

Simply plug in 2 for x:

f(2) = 2(2) + 1

f(2) = 4 + 1

f(2) = 5

Answer:

[tex] {1000}^{m} \div {100}^{n} \\ \\ {10}^{3m} \div {10}^{2n} [/tex]

Since they have the same base and are dividing we subtract the exponents

That's

[tex] {10}^{3m - 2n} [/tex]

So

Hope this helps you

Answer:

[tex]\boxed{ z = 3m-2n}[/tex]

Step-by-step explanation:

=> [tex]1000^m / 100^n[/tex]

=> [tex](10)^{3m} / (10)^{2n}[/tex]

Using rule of exponents [tex]a^m/a^n = a^{m-n}[/tex]

=> [tex]10 ^{3m-2n}[/tex]

Comparing it with [tex]10^z[/tex], we get

=> z = 3m-2n

Answer:

Midpoint of segment AB= (-0.5, 0)

Step-by-step explanation:

The midpoint coordinates of the midpoint has the x coordinate on .5 and the y coordinate on 0.

Answer:

Xavier's age = 23

Yifei's age = 27

Step-by-step explanation:

Represent Yifei's age with Y and Xavier's age with X;

Given that the sum of their ages is 124;

X + Y = 124

Also, given that Yifei is 4 years older

Y = X + 4

Required

Find their age when they got married

From the parameters above, we've been able to form a simultaneous equation

[tex]X + Y = 124[/tex]

[tex]Y = X + 4[/tex]

Substitute X + 4 for Y in the first equation

[tex]X + X + 4 = 124[/tex]

[tex]2X + 4=124[/tex]

Subtract 4 from both sides

[tex]2X + 4 - 4 = 124 - 4[/tex]

[tex]2X = 120[/tex]

Divide both sides by 2

[tex]\frac{2X}{2} = \frac{120}{2}[/tex]

[tex]X = 60[/tex]

Substitute 60 for X in the second equation

[tex]Y = X + 4[/tex] becomes

[tex]Y = 60 +4[/tex]

[tex]Y = 64[/tex]

To get their ages when they got married; we simply subtract 37 from their current ages

Xavier's age = 60 - 37

Xavier's age = 23

Yifei's age = 64 - 37

Yifei's age = 27

Step-by-step explanation:

f(g(x))=[tex]\sqrt{g(x)}[/tex]

--> g(x) >= 0 --> x-9>=0 --> x>=9