What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …

Answer:

0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 160, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]

Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170.

This is the pvalue of Z when X = 170 subtracted by the pvalue of Z when X = 150. So

X = 170

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{170 - 160}{5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 150

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{150 - 160}{5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.

Answer:

10 people

Step-by-step explanation:

Count the x's for more than 1 scarf, which is 2 or 3 scarfs

2 = 9

3 =1

total = 10

Answer:

only allow 3 decimals

90.284 is the answer we removed all others except for 3

I'm assuming the limit is supposed to be

[tex]\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}[/tex]

Multiply the numerator by its conjugate, and do the same with the denominator:

[tex]\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)[/tex]

so that in the limit, we have

[tex]\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]

Factorize the first term in the denominator as

[tex]x^2-3x=x(x-3)[/tex]

The [tex]x-3[/tex] terms cancel, leaving you with

[tex]\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]

and the limand is continuous at [tex]x=3[/tex], so we can substitute it to find the limit has a value of -1/18.

Answer:

1.56 hours

Step-by-step explanation:

300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.

Answer:

i thought the question said a 'HORSE' fills a hot tub...

Step-by-step explanation:

lol dont mind me i just want points :D

Answer:

d = 61.25 m

Step-by-step explanation:

The number of seconds, t it takes for an object to fall a distance of d meters can be found using the formula :

[tex]t=2\sqrt{\dfrac{d}{g}}[/tex] .....(1)

It is required to find the distance covered by ab object in 5 seconds

Solving equation (1) for d. So,

[tex]d=\dfrac{t^2g}{4}[/tex]

Putting all the values we get :

[tex]d=\dfrac{(5)^2\times 9.8}{4}\\\\d=61.25\ m[/tex]

So, the distance covered by the object is 61.25 m.

The object will fall at a distance of 122.5 meters.

Acceleration is the rate of change of velocity with time, both in terms of speed and direction.

Given that, t = √(2d/g).

t = √(2d/g

t√(g/2) = √d

t²(g/2) = d

Or, d = t²(g/2)

Substitute g = 9.8 and t = 5:

d = 5²(9.8/2)

d = 122.5 meters

Hence, the object will fall at a distance of 122.5 meters.

Learn  more on acceleration here:

https://brainly.com/question/12550364

#SPJ2

Answer:

By plotting the graph of f(x)=lnx, you can conclude that when x is small, dy/dx has a larger value. For instance, the gradient of the curve when x=0.5 is 2. However, as you move along the x axis, you will see that the graph levels off, indicating a decrease in the slope, or dy/dx. For example, if x=10, dy/dx = 0.1 and when x=20, dy/dx= 0.05 and so on. Eventually, when x is large enough the value of dy/dx will be negligible.

Thus, as x increases, the slope decreases.

Answer:

Explanation shown below

Step-by-step explanation:

f(x)=lnx;

The rate of change is defined as dy/dx;

dy/dx[Inx] = 1/x

and dy/dx is defined as the slope

The nature of the slope is as x increases ; the slope decreases and conversely meaning as x decreases, the slope increases.

Answer:

36π

Step-by-step explanation:

area=πr²

=πx6x6

6x6=36

area = 36π

Answer:

B. F(x) = 3(x - 2)² - 2

Step-by-step explanation:

→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.

→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.

→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.

→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.

This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."

Complete Question

The complete question is shown on the first  and second uploaded image

Answer:

a

  [tex]\= HK = \= t + \= u[/tex]

b

  [tex]\= GL = \= s - \= t[/tex]

c

[tex]\= JH = \= u + \= s[/tex]

Step-by-step explanation:

Now looking at the diagram

Following the direction of the unit vectors [tex]\= u , \= s, \= t[/tex]

     [tex]\= {HK} = \= {KI} + \= KL[/tex]

=>   [tex]\= HK = \= t + \= u[/tex]

And  

    [tex]\= GL = \= GH + \= GF[/tex]  jjj

=>   [tex]\= GL = \= s - \= t[/tex]

Also

    [tex]\= JH = \= JG + \= JI[/tex]

=>  [tex]\= JH = \= u + \= s[/tex]

Answer:

5,586.17

Step-by-step explanation:

A = $ 5,586.17

A = P + I where

P (principal) = $ 4,000.00

I (interest) = $ 1,586.17

Compound Interest Equation

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

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer:

The sample size required is 289.

Step-by-step explanation:

Let p be population proportion of people that would buy the product.

It is provided that the nationwide poll on this type of product and price was run earlier this year, with percentages running from 75% to 80%.

Assume that the sample proportion of people that would buy the product is, [tex]\hat p=0.75[/tex].

A 95% Confidence Interval is to be constructed with a margin of error of 5%.

We need to determine the sample size required for the 95% Confidence Interval to be within 5% of the actual value.

The formula to compute the margin of error for a (1 - α)% confidence interval of population proportion is:

[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The critical value of z for 95% confidence interval is,

z = 1.96.

Compute the sample size required as follows:

[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\ \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}[/tex]

         [tex]=[\frac{1.96\cdot \sqrt{0.75(1-0.75)} }{0.05}]^{2}\\\\=(16.9741)^{2}\\\\=288.12007081\\\\\approx 289[/tex]

Thus, the sample size required is 289.

Answer:

10-19 ⇒ 3

50-59 ⇒ 4

Answer:

# of ties    # of racks

 10-19               3

50-59              4

Step-by-step explanation:

Using the Stem and Leaf plot, our data is:

11, 12, 16

21

32, 34, 36, 37, 39

41, 45

51, 52, 53, 56

# of ties    # of racks

 10-19               3 (11, 12, 16)

50-59              4 (51, 52, 53, 56)

Answer: D  180 degrees rotation about the origin.then a dilation by a scale factor of one-third.

Step-by-step explanation:

A( -9,3)    B(-9,6)  C (0,3)  

After a rotation of 180 degrees you will have the new points as

A (9,-3)   B( 9,-6)  C (0, -3)

The you after dilating it by a scale factor of 1/3

you will get the coordinates

A ( 3,-1)  B( 3,-2)   C(0,-1)  

which match is what was given in the question.

Answer:

a 180° rotation about the origin, then a dilation by a scale factor of One-third

Step-by-step explanation:

took the test

Answer:

x=2

Step-by-step explanation:

Original width = 6

New width 6+x+x

Orignal length 12

New length  12+x+x

A = l*w

160 = ( 6+2x) ( 12+2x)

Factor

160 = 2( 3+x) 2(6+x)

Divide each side by 4

40 = (3+x) (6+x)

FOIL

40 = 18+ 6x+3x+ x^2

40 = 18 +9x+x^2

Subtract 40 from each side

0 = x^2 +9x -22

Factor

0 = (x +11) (x-2)

Using the zero product property

x +11 =0   x-2 =0

x= -11   x=2

Since we cannot have a negative  sidewalk

x =2

Answer:

2

Step-by-step explanation:

Original width = 6

New width = 6 + x + x = 6 + 2x

Orignal length = 12

New length = 12 + x + x = 12 + 2x

A = l * w

160 = (6 + 2x)(12 + 2x)

160 = 2(3+x) * 2(6+x)

160 = 4 * (3 + x)(6 + x)

160/4 = (3 + x)(6 + x)

40 = 18 + 6x + 3x + x^2

40 = 18 + 9x + x^2

x^2 + 9x - 22 = 0

= x^2 + 11x - 2x - 22 = 0

= x(x + 11) - 2(x + 11) = 0    

= (x + 11) (x - 2) = 0

x = - 11, 2

Since we cannot have a negative width because it's a dimension,

x = 2 is right

Answer:

The answer is 2.5ft².

Step-by-step explanation:

Given that the area of trapezoid formula is A = 1/2×(a+b)×h where a and b is the length and h is the height. Then substitute the following values into the formula :

[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]

Let a = 1.2,

Let b = 0.8,

Let c = 2.5,

[tex]area = \frac{1}{2} \times (1.2 + 0.8) \times 2.5[/tex]

[tex]area = \frac{1}{2} \times 2 \times 2.5[/tex]

[tex]area = 2.5 {feet}^{2} [/tex]

Answer:

Step-by-step explanation:

We will examine and outline the details of this chi-square test and then conclude in context.

(A) A population of women have just been treated for a urinary tract infection.

(B) Since the chi-square test is done for categorical variables, we will pick out the variable involved here.

That variable is: "UTI Recurrence"

Hence, we are looking at the recurrence of a urinary tract infection, among samples of the population of women who have recently been treated of it.

(C) There are three samples from this population and they are distinguished thus:

SAMPLE 1: Those drinking cranberry juice daily

SAMPLE 2: Those taking lactobacillus drink

SAMPLE 3: Those abstaining from both drinks (the placebo sample)

(D) The result of the test gave good evidence that SAMPLE 1 has the lowest value of the categorical variable involved; as compared to the values from SAMPLE 2 and SAMPLE 3.

In other words, on the average (average here is equal to mode or frequency of occurrence of the variable), the lowest number of UTI recurrences stems from Sample 1, as compared to the numbers of UTI recurrences in the other two samples

Answer:

Step-by-step explanation:    AS YOU KHOW THW ABSOLUTE VALUE OF A QUESTION IS NUMBER ITSELF IF THERE IS MINUS SIGH THEN THE  SIGH OF A NUMBER WILL BECOME PLUS OR IF THERE IS A PLUS SIGH THEN THERE IT WILL REMAIN AS IT IS. IF THERE IS NO NUMBER WITH THE MINUS SIGH THEN THE MINUS SIGH WILL REAMIN AS IT IS.

+2 +9  -   +2

The answer has same sigh, then Plus answer will you get is

+11 - 2 then you will minus the answer will be

+9

HOPE IT HELP YOU

Answer:

16.25%

=0.163 (correct to 3 decimal places)

Step-by-step explanation:

The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).

[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]

From the given table:

Population Under 15 years = 2600

Population of the working class (between 15-64) = 16000

Therefore:

[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]

=0.163 (correct to 3 decimal places)

the answer is 180°

Step-by-step explanation:

because it rotated 2x and 90+90 is 180

Answer:

The number of possible outcomes in each trial of this game is 12

Step-by-step explanation:

Given

Rolling of a 6 sided die followed by tossing of a fair coin

Required

Number of possible outcomes

The first step is to list out the possible outcomes of rolling a die and tossing a coin

Rolling a fair die = {1,2,3,4,5,6}

Tossing a coin = {Head, Tail}

Let Head be represented by H and Tail be represented by T;

So,

Rolling a fair die = {1,2,3,4,5,6}

Tossing a coin = {H, T}

The question states that a roll of a 6 sided die is followed by a toss of a fair coin

This means that each trial is {A roll of die and A toss of coin}

So, the sample space is as follows

Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

Number of outcomes in the sample space is 12.

Hence, the number of possible outcomes in each trial of this game is 12

Answer:

the total number of possible outcomes in each trial of this game is 12

Step-by-step explanation:

uhhhhhh none :) kk bye <3

Answer:

valarie had 28 pencils , she gave 15 pencils away to people. How many pencils will she have left?

Step-by-step explanation:

hope this helps:)

Answer:

10.

A. 10240

6.

B. 2^18 = 262144

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

the answer is b because

Answer:

n how many ways can a president, vice president, and a secretary be chosen? It is 12X11X10. Permutation of n things taken r at a time: nPr=n!/(n-r)! 12P3=12*11*10*9!/9!= 12*11*10=1320 ways.

Step-by-step explanation:

Answer:

The Transformations are R(O , -90°) & R(O , 270)

Step-by-step explanation:

* Lets revise the rotation of a point

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

 (270° anti-clockwise or -90°)

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise (-180°) or  

anti-clockwise (180°) around the origin

* Lets solve the problem

∵ One vertex of a triangle is located at (0, 5) on a coordinate grid

∵ The image of the point after the transformation is (5 , 0)

- The coordinates are switched with each other

∴ There is no rotation with 180° or -180° because in the rotation with

 180° and -180° around the origin we change only the signs of the

 coordinates without switch them

∴ There is a rotation with 90° are 270° or -90°

- The zero has no sign

- When we rotate the point (0 , 5) by -90° or 270° around the origin

 we will change the sign of x-coordinate and switch the two

 coordinates

∴ The image of the point is (y , -x)

∵ x = 0 and y = 5

- There is no sign for zero, so we switch the coordinates only

∴ The vertex is located at (5, 0)

∴ The Transformations are R(O , -90°) & R(O , 270)

Answer:

R(O , -90°) & R(O , 270)

Step-by-step explanation:

Answer:

55.9139785%

Step-by-step explanation:

Is means equals and of means multiply

52 = P * 93

Divide each side by 93

52/ 93 = P

.559139785

Change to percent form

55.9139785%

Step-by-step explanation:

The last option 45 and 46

Answer:

its 4-5 not 45-46 \

Step-by-step explanation: