The salary scale for a senior officer starts at N57000
per annum. A rise of N2800 is given at the end of each
Find the total amount of money that the officer will
year.
earn in 14 years.​

Answer:

Step-by-step explanation:

With regards to the factor 'walking device used', the ANOVA conducted on the cadence data revealed a main effect of walking device, and also with the results of the experiment giving rise to a p - value less than 0.05, we can reject the null hypothesis which says, there is no effect of the walking device factor.

We can thus conclude that there is not enough statistics evidence to prove that there is no interaction between the two factors or that there is no effect of the walking device given the cadence data.

Answer:

Step-by-step explanation:

In order to solve this, we'll set up a proportion.

Since y is inversely related to the square of x, therefore:

                   y=4/63 ----->9 (square of x)

                   y=?  ---------->25 (square of x)

According to the inverse relation:

                     y=4/63------->25  

                     y=?------------->9 and y=4/175

Answer:

Step-by-step explanation:

x represents the number of miles you have walked

y represents your distance from home in miles.

The relationship between these two variables can be expressed by the following equation: y=x+5

The dependent variable is that whose value changes whenever the value of the independent variable is changed.

From the equation above:

We can clearly see that y changes for different values of x.

Therefore:

Answer:

1dependant

2independant

Step-by-step explanation:

Answer:

The  interval is  [tex]0.7187 < p < 2.421[/tex]

Step-by-step explanation:

From the question we are told that

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

       The  population  proportion is [tex]p = 0.81[/tex]

       The  confidence level is  C =  98%

The level of significance is mathematically evaluated as

     [tex]\alpha = 100 -98[/tex]

    [tex]\alpha = 2%[/tex]%

    [tex]\alpha = 0.02[/tex]

Here this level of significance represented the left and the right tail

The degree of  freedom is evaluated as

     [tex]df = n-1[/tex]

substituting value  

    [tex]df = 100 - 1[/tex]

     [tex]df = 99[/tex]

Since we require the critical value of one tail in order to evaluate the  98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2

The  critical value of  [tex]\frac{\alpha}{2}[/tex] and the evaluated degree of freedom is  

      [tex]t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33[/tex]

this is obtained from the critical value table  

The standard error is mathematically evaluated as

             [tex]SE = \sqrt{\frac{p(1-p )}{n} }[/tex]  

substituting value  

           [tex]SE = \sqrt{\frac{0.81(1-0.81 )}{100} }[/tex]  

           [tex]SE = 0.0392[/tex]  

The 98%  confidence interval is evaluated as

      [tex]p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }[/tex]

substituting value  

     [tex]0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392[/tex]

      [tex]0.7187 < p < 2.421[/tex]

Answer:

Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%

Alternate Hypothesis, [tex]H_A[/tex] : p < 51%

Step-by-step explanation:

We are given that less than 51% of workers got their job through networking. We have to express the null and alternative hypotheses in symbolic form for this claim.

Let p = population proportion of workers who got their job through networking

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%

Alternate Hypothesis, [tex]H_A[/tex] : p < 51%

Here, the null hypothesis states that greater than or equal to 51% of workers got their job through networking.

On the other hand, the alternate hypothesis states that less than 51% of workers got their job through networking.

Hence, this is the appropriate hypothesis that can be used.

Answer:

D

Step-by-step explanation:

3x, 4y, and 7z must be equal to the LCM of 3, 4, and 7 in order to be the smallest value. The LCM is 84 which means x = 28, y = 21 and z = 12. 28 + 21 + 12 = 61.

Answer:

61

Step-by-step explanation:

3x=4y=7z

x =4/3 y

x = 7/3 z

Since they have to be integers

y and z must be multiples of 3

y = 7/4 z

Since they have to be integers

z must be multiple of 4

Z must be a multiple of 12

Let z = 12

Then

y = 7/4 *12

y = 21

x = 7/3 *12

x = 28

x+y+z

28+ 21+12

61

Hey there! :)

Answer:

∠A = 15.6°

Step-by-step explanation:

Use trigonometry to solve for ∠A. Since this involves the opposite and adjacent sides, tangent will be used. Therefore:

24/86 = arc tan x (inverse of tangent)

0.279 = arc tan x

x = 15.59° ≈ 15.6°.

Therefore:

∠A = 15.6°

Answer:

33

Step-by-step explanation:

An = 6n+3

so the first five terms in sequences is A5= 6*5 +3 = 33

Answer:

diana

Step-by-step explanation:

Answer:

I think it’s Diana I’m sorry if I’m wrong :P

Answer:

d. number of items-discrete; total time-continuous

Step-by-step explanation:

Continuous:

Real numbers, can be integer, decimal, etc.

Discrete:

Only integer(countable values). So can be 0,1,2...

In this question:

You can purchase 0, 1, 2,...,10,...,100,... items, so the number of items is discrete.

You can spend for example, 0.5 hours in the store, or 2.5 minutes, that is, can be decimal numbers. So the total time is continuous

The correct answer is:

d. number of items-discrete; total time-continuous

Answer:

Step-by-step explanation:

Please, share the instructions that come with each problem.  Thanks.

2a -a + 1 = can be simplified to a + 1.

x + y + x + 2 = cannot be simplified.

2(x + 4) + 2x =

3x + 2(x - 2) =​ can be expanded and then simplified:  

   3x + 2x - 4 = 5x - 4

Answer:

a. interaction

Step-by-step explanation:

In statistics, interaction occurs when the effect of one variable depends on the value of another variable.

In this case, Trish's analysis shows that the effect of alcohol consumption in a persons reaction time also depends on that person's quality of sleep, highlighting a clear case of interaction.

Answer:

Critical value zc = 1.6449.

As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that more than 22% of the population will like the new soft drink.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22\\[/tex]

The significance level is 0.05.

The sample has a size n=400.

The sample proportion is p=0.25.

[tex]p=X/n=100/400=0.25[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{400}}\\\\\\ \sigma_p=\sqrt{0.000429}=0.0207[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.25-0.22-0.5/400}{0.0207}=\dfrac{0.0288}{0.0207}=1.3881[/tex]

As this is a right-tailed test, there is only one critical value and it is, for a significance level of 0.05, zc=1.6449.

As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.

Answer:

A =1017.9 cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi * (18)^2

Using the pi button

A =1017.87602 cm^2

Rounding to 1 decimal place

A =1017.9 cm^2

Answer:

123454321

Step-by-step explanation:

it's a palendrome, made out of a number of numbers in the sqquence.

Answer:

[tex]P(141.8<X<218)=P(\frac{141.8-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{218-\mu}{\sigma})=P(\frac{141.8-173.6}{49.8}<Z<\frac{218-173.6}{49.8})=P(-0.639<z<0.892)[/tex]

And we can find this probability with this difference and using the normal standard table:

[tex]P(-0.639<z<0.892)=P(z<0.892)-P(z<-0.639)=0.814-0.261= 0.553[/tex]

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(173.6,49.8)[/tex]  

Where [tex]\mu=173.6[/tex] and [tex]\sigma=49.8[/tex]

We are interested on this probability

[tex]P(141.8<X<2188)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(141.8<X<218)=P(\frac{141.8-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{218-\mu}{\sigma})=P(\frac{141.8-173.6}{49.8}<Z<\frac{218-173.6}{49.8})=P(-0.639<z<0.892)[/tex]

And we can find this probability with this difference and using the normal standard table:

[tex]P(-0.639<z<0.892)=P(z<0.892)-P(z<-0.639)=0.814-0.261= 0.553[/tex]

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

Answer:

105/136 ≈ 0.772

Step-by-step explanation:

There are 3 socks and 2 colors, so they are either all the same color or 2 will be different colors.

P(different colors)

= 1 − P(same color)

= 1 − ₁₀C₃/₁₇C₃ − ₇C₃/₁₇C₃

= 1 − 120/680 − 35/680

= 1 − 155/680

= 1 − 31/136

= 105/136

≈ 0.772

Answer:

1. Critical value t=±2.447

2. The null hypothesis is failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the birth weight significantly differs from 6.6 lbs.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=6.6\\\\H_a:\mu\neq 6.6[/tex]

The significance level is 0.05.

The sample has a size n=7.

The sample mean is M=7.56.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.18.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.18}{\sqrt{7}}=0.446[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.56-6.6}{0.446}=\dfrac{0.96}{0.446}=2.152[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=7-1=6[/tex]

For a two-tailed test with 5% level of significance and 6 degrees of freedom, the critical value for t is ±2.447.

As the test statistic t=2.152 is under 2.447 and over -2.447, it falls in the acceptance region, so the effect is not significant. The null hypothesis is failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.

Sample mean and standard deviation calculations:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{7}(9+7.3+6+. . .+6.6)\\\\\\M=\dfrac{52.9}{7}\\\\\\M=7.56\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{6}((9-7.56)^2+(7.3-7.56)^2+(6-7.56)^2+. . . +(6.6-7.56)^2)}\\\\\\s=\sqrt{\dfrac{8.32}{6}}\\\\\\s=\sqrt{1.39}=1.18\\\\\\[/tex]

ANSWER :

Percentage = 50%

(if it odd and even then its 100%)

Answer:

100%

Step-by-step explanation:

There is a 100% chance rolling an odd or even since all the faces of this die are odd or even.

Answer:

Length = 47 in

Radius = 47/π in

Step-by-step explanation:

Let 'h' be the length of the package, and 'r' be the radius of the cross section.

The length and girth combined are:

[tex]L+G=141=h+2\pi r\\h=141-2\pi r[/tex]

The volume of the cylindrical package is:

[tex]V=A_b*h\\V=\pi r^2*h[/tex]

Rewriting the volume as a function of 'r':

[tex]V=\pi r^2*h\\V=\pi r^2*(141-2\pi r)\\V=141\pi r^2-2\pi^2 r^3[/tex]

The value of 'r' for which the derivate of the volume function is zero yields the maximum volume:

[tex]V=141\pi r^2-2\pi^2 r^3\\\frac{dV}{dr}=282\pi r-6\pi^2r^2=0\\ 6\pi r=282\\r=\frac{47}{\pi} \ in[/tex]

The length is:

[tex]h=141-2\pi r=141-2\pi*\frac{47}{\pi}\\h=47\ in[/tex]

The dimensions that yield the maximum volume are:

Length = 47 in

Radius = 47/π in

Answer:

work shown and pictured

Answer:

112

Step-by-step explanation:

Original Score equals 14 right?

If chase doubles his original Score daily it will be

14*2 (Tuesday)=28

28×2 (Wednesday)=56

56×2 (Thursday)=112

Therefore,

Chase's Final score Equals 112

The number of points did he score on Thursday is 112.

Given that,

Based on the above information, the calculation is as follows:

On Monday = 14

On Tuesday = (14) (2) = 28

On Wednesday = (28) (2) = 56

On Thursday = (56) (2) = 112

Therefore, we can conclude that the number of points did he score on Thursday is 112.

Learn more: brainly.com/question/24169758

Answer:

n = 8

Step-by-step explanation:

The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.

It has a common ratio of 3 => [tex] \frac{6}{2} = \frac{18}{6} = \frac{54}{18} = 3 [/tex]

Thus, the sum of the first n terms of a geometric sequence is given as [tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

Where,

[tex] a_1 [/tex] = first term of the series = 2

r = common ratio = 3

[tex] S_n [/tex] = sum of the first n terms = 6,560

Plug in the above values into the formula

[tex]6,560 = \frac{2(1 - 3^n)}{1 - 3}[/tex]

[tex] 6,560 = \frac{2(1 - 3^n)}{-2} [/tex]

[tex] 6,560 = \frac{1 - 3^n}{-1} [/tex]

Multiply both sides by -1

[tex] -6,560 = 1 - 3^n [/tex]

Subtract 1 from both sides

[tex] -6,560 - 1 = - 3^n [/tex]

[tex] -6,561 = - 3^n [/tex]

[tex] 6,561 = 3^n [/tex]

Evaluate

[tex] 3^8 = 3^n [/tex]

3 cancels 3

[tex] 8 = n [/tex]

The value of n = 8

Answer:

160°

Step-by-step explanation:

1/2 (Major arc AB - Minor arc AB) = 20°

Major arc AB = 200°

Minor arc AB = 160°

central angle = minor arc AB = 160°

The value of variable x is,

⇒ x = 150°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Line segment ac and segment bc are tangent to circle O.

Now, We get;

∠A + ∠B + ∠C + ∠O = 360°

90° + 90° + 30° + x = 360°

x = 360° - 210°

x = 150°

Hence, The value of variable x is,

⇒ x = 150°

Learn more about the angle visit:;

https://brainly.com/question/25716982

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Answer:

[tex]\frac{d}{dy}(-3x^{2} -12) = -6x[/tex]

0 = -6x

0 = x

[tex]-3(0)^{2} -12 = -12[/tex]

(0,-12)

Step-by-step explanation:

Answer:

between 108-110?

Step-by-step explanation:

60% or 200 = 120 people

90% of 120 = 108

question doesnt look complete so this is the best I could come up with...‍♀️

Answer:

  independent: day number; dependent: hours of daylight

  d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

  1.79 fewer hours on Feb 10

Step-by-step explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

__

b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

  d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

  d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

__

c) d(41) = 10.34, so February 10 will have ...

  12.13 -10.34 = 1.79

hours less daylight.

Answer:

1/9

Step-by-step explanation:

Separate the fraction (1/9) from the variable x:

y = (1/9)x.

1/9 is the constant of proportionality.

Answer:

in this experiment we only have two  sample space which is only true or false.

because all the answers will have to fall between this sample space.

Step-by-step explanation:

we cannot actually or fully understand the above answer without first of all defining or explaining what sample space actually means.

Sample space: this is the set of all possible outcome that may come from an experiment.or we can say simply say it is the range of values that the experiment depends on.