(a) The heights of male students in a college are thought to be normally distributed with mean 170 cm and standard deviation 7.
The heights of 5 male students from this college are measured and the sample mean was 174 cm.
Determine, at 5% level of significance, whether there is evidence that the mean height of the male students of this college is higher than 170 cm.
[6]
(b) (i) The result of a fitness trial is a random variable X which is normally distributed with mean μ and standard deviation 2.4 . A researcher uses the results from a random sample of 90 trials to calculate a
98% confidence interval for μ . What is the width of this interval?
[4]
(ii) Packets of fish food have weights that are distributed with standard deviation 2.3 g. A random sample of 200 packets is taken. The mean weight of this sample is found to be 99.2 g. Calculate a 99% confidence interval for the population mean weight.
[4]
(c) (i) Explain the difference between a point estimate and an interval
Estimate. [2]
(ii) The daily takings, $ x, for a shop were noted on 30 randomly chosen days. The takings are summarized by Σ x=31 500 and
Σ x2=33 141 816 .
Calculate unbiased estimates of the population mean and variance of the shop’s daily taking. [4

Answer:

C. y=7/9x+17/9

Step-by-step explanation:

Take the slope. slope= m = y2-y1/x2-x1

=5-(-2)/4-(-5)

=7/9

Then put it into point-slope form.

y-y1=m(x-x1)

=y-5=7/9(x-4)

Simplify.

y=7/9x-28/9+5

y=7/9x+17/9

Answer:

C

Step-by-step explanation:

First find the slope (change in y/ change in x) which is positive 7/9.

Then use y=mx+b and plug in the slope, and one of the given points to solve for b.

5= 7/9*4+b

5=28/9+b

5-28/9=b

45/9-28/9=b

17/9=b

Then with the slope and y intercept(b) you get the equation shown in answer c.

Hope that helps!

Answer:

[tex]-\frac{77}{24}[/tex]

Step-by-step explanation:

1. rewrite the equation in standard form: [tex]4\cdot \frac{3}{2}\left(y-\left(-\frac{41}{24}\right)\right)=\left(x-\left(-\frac{3}{2}\right)\right)^2[/tex]

2. find (h,k), the vertex. the vertex is [tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex]

3. find the 'focal length' of the parabola - the focal length is the distance between the vertex and the focus. from the vertex we can see that the focal length, p, = 3/2

4. Parabola is symmetric around the y-axis and so the asymptote is a line parallel to the x-axis, a  distance p from the [tex]\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex] y coordinate which is at  [tex]-\frac{41}{24}\right)[/tex]. Set up the equation:

[tex]y=-\frac{41}{24}-p[/tex]

5. substitute and solve:

[tex]y=-\frac{41}{24}-\frac{3}{2}[/tex]

[tex]y = -\frac{77}{24}[/tex]

hope this helps, ask me questions if you still don't understand.

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

Assuming the faces are numbered 1 to 12, there are 9 faces with values less than 10. Since the outcomes are equally probable and mutually exclusive, the probability of any of the 9 is the sum of their individual probabilities:

  P(n < 10) = 9×1/12 = 9/12 = 3/4

Step-by-step explanation:

the item angle on the left line is also 130 degrees, as these 2 equally long lines create a triangle with 2 equal sides.

the two internal angles are the complement from 130 to 180 degrees, as every straight line stands for 180 degrees.

so, 180-130 = 50 degrees.

=> both internal angles are 50 degrees.

that makes the angle at the bottom tip of the triangle the complement of both 50 degree angle to 180, because the sum of all angles in a triangle is always 180 degrees.

so, 180 - 50 - 50 = 80 degrees.

and the outside angles of that triangle tip angle are each half of the complement of these 80 degrees to 180 (resistive to the bottom horizontal line).

180 - 80 = 100

100/2 = 50

so, both outside bottom angles are again 50 degrees.

Answer:

If you buy per dozen, each buns costs about 91 cents.

You will save $4.11 if you buy per dozen.

Step-by-step explanation:

1.25 * 12= $15

10.89/12= .9075 = .91 cents

15-10.89= $4.11

Answer:

1. 6 (2a-3b)

6×2a - 3b

=12a-18b

2. a(2ab+3)

a×2ab+3

=2a²b + 3a

3. (x-4)(3x)

=3x² - 12x

just kembangkan... answer my question plss..help me.

9514 1404 393

Answer:

  10 minutes

Step-by-step explanation:

The current legal tender conversion rate is 50 kobo = 0.50 naira. Then the airtime balance is ...

  (300 NGN)/(0.50 NGN/s) × (1 min)/(60 s) = 300/(0.50×60) min = 10 min

Answer:

I guess this is the answer hope it helps

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

[tex]\lambda = \frac{29742}{365} = 81.485[/tex]

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]

0% probability that on a given day, 50 radioactive atoms decayed.

Answer:

z=3x/4+1 x=4z/3-4/3

Step-by-step explanation:

it right answer is Clovis 2.5% it answer

Answer:

11

Step-by-step explanation:

I'm assuming that [.] fldenote absolute value even tho the absolute value function is represented by (|.|)

value of [-7] will be positive that us 7.

= 7 + 4

= 11

Answer:

Hence the answers are,

a) Probability that in the past 12 months the car had more than one problem = P(X > 1) is 0.2716.

b) The Probability that in the past 12 months the car had almost two problems = P( X < 2) is 0.9160.

c) The Probability that in the past 12 months the car had zero problems = P(X= 0 ) is 0.3606.

Step-by-step explanation:

Let's take X to be the number of problems per car.

By considering the given statement, X follows a Poisson Distribution with Mean (X) = 1.02.

The Poisson probability formula is :

e Pr( X = k) = e- k! k= 0,1,2...

a)

The Probability that in the past 12 months the car had more than one problem = P(X > 1)

[tex]P(X > 1) =1- P(X < 1) \\\\=1- (P(X = 0) + P(X = 1)-1.021.02 e + 1.021.02 =1-6 0!\\= 1-0.3606 + 0.3678\\= 1-0.7284\\= 0.2716[/tex]

b)

The Probability that in the past 12 months the car had almost two problems = PX < 2)

[tex]Pr(X < 2) = Pr(X = i) = Pr(X = 0) + Pr(X = 1) + Pr(X = 2)\\-1.021.020 -1.021.02 -1.021.02 e e + e + 0! 1! 2!\\= 0.3606 + 0.3678 + 0.1876\\= 0.9160[/tex]

c)

The Probability that in the past 12 months the car had zero problems = P(X= 0 )

[tex]- 1.021.02 e 0!\\= 0.3606[/tex]

Answer:

a) k = 0.00012491389

b) The Shroud of Turin was 755 years old at the time of this data.

Step-by-step explanation:

(a) Find the value of the constant k in the differential equation C' = -kC.

First we find the differential equation, by separation of variables. So

[tex]\int \frac{C^{\prime}}{C} dt = -\int k dt[/tex]

So

[tex]\ln{C} = -kt + K[/tex]

In which K is the constant of integration, representing the initial amount of substance. So

[tex]C(t) = C(0)e^{-kt}[/tex]

Half-life of 5549 years.

This means that [tex]C(5549) = 0.5C(0)[/tex]. We use this to find k. So

[tex]C(t) = C(0)e^{-kt}[/tex]

[tex]0.5C(0) = C(0)e^{-5549k}[/tex]

[tex]e^{-5549k} = 0.5[/tex]

[tex]\ln{e^{-5549k}} = \ln{0.5}[/tex]

[tex]-5549k = \ln{0.5}[/tex]

[tex]k = -\frac{\ln{0.5}}{5549}[/tex]

[tex]k = 0.00012491389[/tex]

So

[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]

(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 contained in freshly made cloth of the same material. How old was the Shroud of Turin at the time of this data?

This is t for which [tex]C(t) = 0.91C(0)[/tex]

So

[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]

[tex]0.91C(0) = C(0)e^{-0.00012491389t}[/tex]

[tex]e^{-0.00012491389t} = 0.91[/tex]

[tex]\ln{e^{-0.00012491389t}} = \ln{0.91}[/tex]

[tex]-0.00012491389t = \ln{0.91}[/tex]

[tex]t = -\frac{\ln{0.91}}{0.00012491389}[/tex]

[tex]t = 755[/tex]

The Shroud of Turin was 755 years old at the time of this data.

Answer:

2 days

Step-by-step explanation:

Lets say that in one day, one cow eats 1 block of grass. So, six cows in three days would eat 18 blocks of grass in total. So 18 blocks of grass is how much we have. that means nine cows would eat that much in 2 days.

Step-by-step explanation:

The graph of Fx), shown below in pink, has the same shape as the graph of G(x)-x, but it is shifted to the right two units. Complete its equation below Enter exponents using the caret (a), for example, enter x as x 4. Do not include Fx)-in your answer. .5 5 F(x) = Answer: 0

The equation of the graph is,

⇒ G (x) = (x - 3)⁴

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of function G (x) is shown in image.

Here, The graph is 3 units left to function F (x) = x⁴.

Hence, The equation of the graph is,

⇒ G (x) = (x - 3)⁴

Thus, The equation of the graph is,

⇒ G (x) = (x - 3)⁴

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Use the circular formula and divide the volume by 2

Step-by-step explanation:

Answer:

12.56

Step-by-step explanation:

3.14(8)/2

=12.56

Answer:A

Step-by-step explanation:

Answer:

3x² + 13x + 4

Step-by-step explanation:

I did the steps in my book

Answer:

it can be in point intercept form

Step-by-step explanation:

Answer:

it can be point intercept from

Answer:

The solution set is: (-1,3)

We want to find the set of the x-values of the points that belong to the given graph and have an y-value larger than zero.

The set is: s = (-1, 3)

To find the set, we need to see the x-values of the points on the graph such that y > 0.

y > 0 means that we only look at the region of the graph that is above the x-axis.

We can see that this region goes from x =-1 to x = 3

Then for all the x-values between x = -1 and x = 3 the points p(x, y) on the graph have an y-value larger than zero.

Notice that because the value must be larger than zero, then the particular x-values:

x = -1 and x = 3 are not in the set.

So the set must be written as:

s = (-1, 3)

This is the set in the interval notation.

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Answer:A. This is the formula for the area of a trapezoid: a+b/2 x height (a and b being the bases)

Step-by-step explanation: Use the formula. 10+12=22. 22/2 is 11. 11 x 16 is 176. Therefore, the answer is A.

Answer:

Option B, 29°

Step-by-step explanation:

The diagram is a angle bisecting diagram which divides the 58° angle into two 29° angles.

Answered by GAUTHMATH

Answer:

The null hypothesis is [tex]H_0: p \leq x[/tex], in which x is the proportion tested.

The alternative hypothesis is [tex]H_1: p > x[/tex]

Step-by-step explanation:

A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than x.

This means that at the null hypothesis, we test if the proportion is of at most x, that is:

[tex]H_0: p \leq x[/tex]

Suppose that we suspect otherwise and carry out a hypothesis test.

The opposite of at most x is more than x, so the alternative hypothesis is:

[tex]H_1: p > x[/tex]

Answer:

ok so if she gets paid 372 we just multiply this by 4 since there's 4 weeks in a month then we multiply by 4 so

372*4*12=17856

now we just multiply 831.33 by 2 since she is paid semimonthly and we multiply by 12

831.33*2*12=19951.92

now we just subtract

19951.92-17856=2095.92

so she gets paid 2095.92 more dollars per year

Hope This Helps!!!

Answer:

The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.

Step-by-step explanation:

At the null hypothesis, we test if there was no increase, that is, the mean is 0, so:

[tex]H_0: \mu = 0[/tex]

At the alternative hypothesis, we test if there was an increase, that is, the mean is greater than 0, so:

[tex]H_1: \mu > 0[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%.

This means that [tex]n = 104, X = 6.9, s = 55[/tex]

Value of the test-statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{6.9 - 0}{\frac{55}{\sqrt{104}}}[/tex]

[tex]t = 1.28[/tex]

P-value of the test:

The p-value of the test is a right-tailed test(test if the mean is greater than a value), with 104 - 1 = 103 df and t = 1.28.

Using a t-distribution calculator, this p-value is of 0.1017.

The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.

Answer:

hour= 1.25

MINUTES ANSWER= 75 minutes

Step-by-step explanation:

hope that helps>3

Answer:

5/4 hour= 75 minutes

--------------------------------

[tex]\textbf{HOPE IT HELPS}[/tex]

[tex]\textbf{HAVE A GREAT DAY!!}[/tex]

Answer:

4

Step-by-step explanation:

Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.

We can see that this is a 30-60-90 degree triangle.

The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].

We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.

The value of x in the triangle is 4.

What is the Pythagorean theorem ?

The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees

The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.

8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to

'a' , or 4.

2a=8

a=4

x=a=4

so, the the value of x in the triangle is 4.

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