Find the mode for the following distribution.
Number Frequency
16
3
20
5
24
9
28
7
32
7
36
5
40
3
24
28
32
28 and 32

Answer:

w > -3

Step-by-step explanation:

2w<9+5w

Subtract 5w from each side

2w-5w<9+5w-5w

-3w <9

Divide each side by -3 remembering to flip the inequality

-3w/-3 > 9/-3

w > -3

Answer:

w>-3

Step-by-step explanation:

Answer:

B. 4x² - 20x  + 26

Step-by-step explanation:

→Set it up, like so:

(2x - 5)² + 1

4x² - 20x + 25 + 1

→Add like terms (25 and 1):

4x² - 20x + 26

Answer:

[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]

[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]

And we can use the normal standard distribution table or excel and we can  find the probability with this difference:

[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]

Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 10000[/tex] represent the mean

[tex] \sigma = 714.2857[/tex] represent the deviation

[tex] n = 49[/tex] represent the sample size selected

For this case since the sample size is large enough n>30 we have enough evidence to use the central llmit theorem and the distribution for the sample mena would be given by:

[tex] \bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}}) [/tex]

And we want to find the following probability:

[tex] P(9832 < \bar X< 10200)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we use the z score formula for the limits  given we got:

[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]

[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]

And we can use the normal standard distribution table or excel and we can  find the probability with this difference:

[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]

Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251

Answer:

0.4929 = 49.29% probability that he voted in favor of Scott Walker

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Having a college degree.

Event B: Voting for Scott Walker.

They found that 57% of the respondents voted in favor of Scott Walker.

This means that [tex]P(B) = 0.57[/tex]

Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree

This means that [tex]P(A|B) = 0.33[/tex]

Probability of having a college degree.

33% of those who voted for Scott Walker(57%).

45% of those who voted against Scott Walker(100 - 57 = 43%). So

[tex]P(A) = 0.33*0.57 + 0.45*0.43 = 0.3816[/tex]

What is the probability that he voted in favor of Scott Walker?

[tex]P(B|A) = \frac{0.57*0.33}{0.3816} = 0.4929[/tex]

0.4929 = 49.29% probability that he voted in favor of Scott Walker

Answer:

11453

Step-by-step explanation:

Answer: There is a 0.88% chance of pulling three red marbles in a row.

Step-by-step explanation:

First pull = 4/15 (26.67%)

second pull = 3/14 (21.43%)

Third pull = 2/13 (15.38%)

You need to multiply these three fractions to get the probability of pulling three reds in a row, doing that will get you 4/455 or 0.88%

Answer:

m=2

Step-by-step explanation:

-2.73m-10.92=-6m-4.38

3.27m=6.54

m=2

Answer: See below

Step-by-step explanation:

[tex]i[/tex] is an imaginary number.

[tex]i=\sqrt{-1}[/tex]

[tex]i^2=-1[/tex]

.

2.

.

I hope it helps you

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.

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Answer:

a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

b) We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]  

d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Step-by-step explanation:

Information provided

[tex]\bar X=23400[/tex] represent the sample mean

[tex]s=1412[/tex] represent the sample standard deviation

[tex]n=18[/tex] sample size  

[tex]\mu_o =22100[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic (variable of interest)  

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

Part a

We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

Part b

We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

Part c

The statistic is given by:

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

Replacing the info we got:

[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]    

Part d

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Answer:

g(x)= 1/4 |x-2| + 1

Step-by-step explanation:

line:

points on same line:

slope based on the points

And the line is moved to the right by 2 units:

So the function becomes:

Considering movement up by 1 unit as well:

This is the final of equation for the line.

Answer:

Please read the complete answer below!

Step-by-step explanation:

You have the following function:

[tex]f(x)=x^3-3x^2-9x+4[/tex]   (1)

a) To find the interval on which f is increasing or decreasing, you first calculate the critical points of f(x).

You calculate the derivative f(x) respect to x:

[tex]\frac{df}{dx}=3x^2-6x-9[/tex]    (2)

Next, you equal the derivative to zero, and then you find the roots of the polynomial by using the quadratic formula:

[tex]3x^2-6x-9=0\\\\x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(-9)}}{2(3)}\\\\x_{1,2}=\frac{6\pm12}{6}\\\\x_1=-1\\\\x_2=3[/tex]

Then, the critical points are x=-1 and x=3

Next, you calculate df/dx for a values of x to the left and to the right of the critical points x1 and x2. If df/dx < 0 the function is decreasing, if df/dx > 0 the function is increasing.

for x = -1.01

[tex]\frac{df(-1.01)}{dx}=3(-1.01)^2-6(-1.01)-9=0.12[/tex]

Then, in the interval (-∞,-1), the function is increasing

for x = -0.99

[tex]\frac{df(-0.99)}{dx}=3(-0.99)^2-6(-0.99)-9=-0.11[/tex]

In the interval (-1,3) the function is decreasing

for x = 3.01

[tex]\frac{df(3.01)}{dx}=3(3.01)^2-6(3.01)-9=0.12[/tex]

In the interval (3,+∞) the function is increasing

b) To find the local minimum and maximum you use the second derivative of the function:

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

you evaluate the second derivative for the critical points x1 and x2, if the second derivative is positive, you have a local minimum. If the second derivative is negative, you have a local maximum:

for x1 = -1

[tex]6(-1)-6=-12<0[/tex]

x=-1 is a local maximum

for x2 = 3

[tex]6(3)-6=12>0[/tex]

x=3 is a local minimum

c) upward concavity: (-1,3)

downward concavity: (-∞,-1)U(3,+∞)

The inflection points are calculated with the second derivative equal to zero:

[tex]6x-6=0\\\\x=1[/tex]

For x = 1 you have an inflection point

Answer:

[tex]\dfrac{1}{10}[/tex]

Step-by-step explanation:

Probability of the captain hitting the pirate ship [tex]=\dfrac{1}{2}[/tex]

Probability of the pirate hitting the captain's ship [tex]=\dfrac{1}{5}[/tex]

If both fire cannons at the same time, the probability that both the pirate and the captain hit each other's ship

=P(Captain Hits AND Pirate Hits)

=P(Captain Hits) X P(Pirate Hits)

[tex]=\dfrac{1}{2} X \dfrac{1}{5}\\\\=\dfrac{1}{10}[/tex]

Answer:

Due to the higher z-score, Norma should be offered the job

Step-by-step explanation:

Z-score:

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.

In this question:

Whoever has the higher z-score should get the job.

Norma:

Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.

This means that [tex]X = 84.2 \mu = 67.4, \sigma = 14[/tex]

So

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

[tex]Z = \frac{84.2 - 67.4}{14}[/tex]

[tex]Z = 1.2[/tex]

Pierce:

Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16.

This means that [tex]X = 276.8, \mu = 264, \sigma = 16[/tex]

So

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

[tex]Z = \frac{276.8 - 264}{16}[/tex]

[tex]Z = 0.8[/tex]

Reyna:

Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8.

This means that [tex]X = 7.62, \mu = 7.3, \sigma = 0.8[/tex]

So

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

[tex]Z = \frac{7.62 - 7.3}{0.8}[/tex]

[tex]Z = 0.4[/tex]

Due to the higher z-score, Norma should be offered the job

Answer:

4

Step-by-step explanation:

T(n) = n² + 3

T(1) = 1² + 3 = 1 + 3 = 4

Answer:

a) [tex]V(t) = 24 - 2t[/tex]

b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Step-by-step explanation:

The volume of the tank in terms of the time can be described by the following equation:

[tex]V(t) = V(0) - at[/tex]

In which V(0) is the initial volume and a is the hourly decrease rate.

a. Write a formula that expresses v in terms of t.

The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]

Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]

Then

[tex]V(t) = V(0) - at[/tex]

[tex]V(t) = 24 - 2t[/tex]

b. As t increases from 3 to 6, v varies from _________ to _________

[tex]V(t) = 24 - 2t[/tex]

[tex]V(3) = 24 - 2*3 = 18[/tex]

[tex]V(6) = 24 - 2*6 = 12[/tex]

So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Answer:

7/10=0.7

3+0.7=3.7

3.7

Hope this helps

Step-by-step explanation:

Answer:

230,000

Step-by-step explanation:

You have round in the ten thousands space which is the 3, knowing that the next number is 8 and it is greater than 5 the 3 will round up to a 4

Answer:

34) 75

35) 60

36) 210

Step-by-step explanation:

34) Area of a rectangle:

L x B

= 15 x 5

= 75

35) Area of a trapezium :

½ h (sum of || sides)

= ½ x 6 x (12+8)

= 3 x 20

= 60

36) Area of a regular hexagon:

3BH

= 3 x 7 x 10

210

Hope it helps....

Answer:

Step-by-step explanation:

35. 75

area of rectangle : A = b x h

                                  = 15 X 5

                                   = 75

36. 60

area of trapezoid : A = (b1 + b2) x h

                                                2

                                  = (8+12) x 6

                                            2

                                   = 60

37. 210

area of regular polygon : A = P x a  (P no. of sides) (a is apothem)

                                                   2

                                           = (6 x 10) x 7

                                                       2

                                           = 210

Answer:

Option A.

The heartbeat has a pattern of 60 + (5 x minutes) and linear graphs are straight. The only way the linear graph is straight if there is a pattern.

Step-by-step explanation:

Answer:

385 ways

Step-by-step explanation:

Given;

7 red balls

10 white balls

In how many ways can 4 balls be selected if there are more than 2 red balls.

Selecting 4 balls which must contain more than 2 red balls, will be 3 red balls and 1 white ball to make it 4 in total, or all the 4 balls selected will red balls.

= 3 red balls and 1 white ball  OR 4 red balls

= 7C₃ x 10C₁  + 7C₄

[tex]= \frac{7!}{4!3!} *\frac{10!}{9!1!} \ \ + \ \frac{7!}{3!4!} \\\\= (35*10) \ + \ 35\\\\= 350 \ + 35\\\\= 385 \ ways[/tex]

Therefore, there are 385 ways of selecting 4 balls, if there are more than 2 red balls.

Answer:

360 x 30% = answer

30% = 30/100 = 0.3

360 x 0.3 = 108

108 is the answer

Hope this helps

Step-by-step explanation:

Answer:

108 pages

Step-by-step explanation:

30% of 360=108

360*.30=108

Answer:

A)1/18

B)1/6

C)13/18

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW,

The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?

CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION

Answer:

65!

65! = 8. 2547650592 * 10^ 90 approximately

Step-by-step explanation:

A random number generator randomly generates a number from 1 to 65.

Once a specific number is generated, the generator will not select that number again until it is reset.

The number of ways it can be used is = 65!

65! = 8. 25476505* 10^ 90 approximately

Answer:

[tex]x_{2} = 0.0000[/tex]

Step-by-step explanation:

The formula for the Newton's method is:

[tex]x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}[/tex]

Where [tex]f' (x_{i})[/tex] is the first derivative of the function evaluated in [tex]x_{i}[/tex].

[tex]x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}[/tex]

Lastly, the value of [tex]x_{2}[/tex] is determined by replacing [tex]x_{1}[/tex] with its numerical value:

[tex]x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}[/tex]

[tex]x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}[/tex]

[tex]x_{2} = 0.0000[/tex]

Answer:

c. line

Step-by-step explanation:

the intersection of two planes is called a line

Answer:

Hello dear,

two planes intersect and forms line

so yaa your answer is C)

Hope I helped you ;)

please thank me !!!

satsriakal ji

Answer:

10000

Step-by-step explanation:

3.34x=33400

x=10000

The number is x=10000.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

let, the number = x

now, we get,

3.34x=33400

x=10000

Hence, The number is x=10000.

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Answer:

The recoil velocity of the gun is [tex]0.72\,\,\frac{km}{h}[/tex]  and is pointing in opposite direction to the velocity of the bullet.

Step-by-step explanation:

Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).

We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg

In mathematical terms, we have:

[tex]5\, kg * v= 0.01 \,kg\,* 360\,\frac{km}{h} \\v=\frac{0.01\,*360}{5} \,\,\frac{km}{h}\\v=0.72\,\,\frac{km}{h}[/tex]

Answer:

9.9

Step-by-step explanation:

remember your distribution rules.

x/3.3=3 make sure x is by itself. so take 3*3.3

When you have x divided by a number equaling a number take the number it equals to and multiply by the number that x is being divided by.

3=x/3.3

move 3.3 by multiplying it by 3 which gives you 9.9.

The solution of x in equation 3 = x / 3.3 is,

⇒ x = 9.9

We have to given that;

Expression is,

⇒3 = x / 3.3

Now, We can simplify the equation for x as;

⇒ 3 = x / 3.3

Multiply by 3.3 both side,

⇒ 3 × 3.3 = x

⇒ 9.9 = x

⇒ x = 9.9

Thus, Solution is,

⇒ x = 9.9

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