two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 100 miles per hour. The westbound train travels at 80 miles per hour. How long will it take for the two trains to be 252 miles apart? Do not do any rounding.

Answer:

The area formula of a triangle is (base * height) / 2 and the area of a square is s² where s is the length of one side.

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Answer:

x = 5 and y = -4

Step-by-step explanation:

y = - 3x + 11 ______(1)

5x + y = 21______(2)

Substitute (1) into (2).

5x + (-3x + 11) = 21

5x - 3x + 11 = 21

2x = 21-11

2x = 10

x = 10/2

x = 5

Now substitute x = 5 into (1).

y = -3(5) + 11

y = -15 + 11

y = -4

Hence, x = 5 and y = -4

Answer:

Hey there!

The solutions to a system are where the lines, or graphs intersect each other.

We see that the graphs intersect at (0, -4) and (2, 0).

Thus, the solutions are (0, -4) and (2, 0).

Hope this helps :)

Answer:

[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]

[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]

Step-by-step explanation:

The info given is:

[tex] X= 21[/tex] number of students who said that they planned to work in a rural community

[tex] n= 380[/tex] represent the sample size selected

[tex]\hat p =\frac{21}{380}= 0.0553[/tex] the estimated proportion of students who said that they planned to work in a rural community

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

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

Replpacing we got:

[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]

[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]

A mean for estimation is the minimum-maximum variation estimate's C.I. The % of pupils planning to work in a rural community alters between 0.0323 and 0.0783.

Confidence interval:

Let's [tex]p^{}[/tex] represent the sampling fraction of the people who promised to work in a rural area.

Sample size:

[tex]n = 380[/tex]

x: the large number the pupils expected to work in a rural setting

[tex]p^{} = \frac{x}{n} \\\\p^{} = \frac{21}{ 380} = 0.0553\\\\(1- \alpha)\ \ 100\%[/tex]confidence for true proportion:

[tex]( p^{}\ \pm Z_{\frac{\alpha}{2}} \times \sqrt{p^{} \times \frac{(1-p^{})}{n}} ) \\\\[/tex]

For [tex]95\%[/tex]confidence interval:

[tex]\to 1 - \alpha = 0.95[/tex]

When:

[tex]\to \alpha = 0.05[/tex]

Calculating the value of Z by using the table:

[tex]\to Z_{0.025} = 1.96[/tex]

When the  [tex]95\%[/tex] of the confidence interval:

[tex]\to (0.0553 \pm Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}})\\\\\to (0.0553 - Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380})},0.0553 + Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}))}\\\\[/tex]

by solving the value we get:

[tex]\to ( 0.0323 , 0.0783 )[/tex]

Find out more about the Confidence interval here:

brainly.com/question/2396419

Answer:

x = 5, AB=5, BC = 15

Step-by-step explanation:

AC = AB + BC (Segment Addition)

AC= 20, AB =x Bc = 3x,

20= x+3x 20=4x

x=5

AB=x, AB =5

BC=3x BC= 15

The segment addition postulate states gives the value of x as 5, given

that the sum of x and 3·x is 20.

Responses:

From the given diagram, we have;

[tex]\overline{AB}[/tex] = x

[tex]\overline{BC}[/tex] = 3·x

According to segment addition postulate we have;

[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches

Which gives;

x + 3·x = 20

Therefore;

4·x = 20

[tex]x = \dfrac{20}{4} = 5[/tex]

[tex]\mathbf{\overline{BC}}[/tex] = 3·x  

[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15

Learn more about segment addition postulate here:

https://brainly.com/question/1397818

Answer:

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Step-by-step explanation:

Confidence interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 290, \pi = \frac{261}{290} = 0.9[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]

Percentage:

Proportion multplied by 100.

0.8546*100 = 85.46%

0.9454*100 = 94.54%

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Based on the​ result, does the method appear to be​ effective?

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Answer:

p > α

0.7038 > 0.05

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of  cloth.

Step-by-step explanation:

We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of  cloth.

Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.

ANOVA:

The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.

Set up hypotheses:

Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

Set up decision rule:

We Reject H₀ if p ≤ α

OR

We Reject H₀ if F > F critical

ANOVA in Excel:

Step 1:

In the data tab, select data analysis

Step 2:

Select "Anova single factor" from the analysis tools

Step 3:

Select the destination of input data in the "input range"

Step 4:

Select "rows" for the option "Group By"

Step 5:

Tick the option "labels in first row"

Step 6:

Set alpha = 0.05

Step 7:

Select the destination of output data in the "output options"

Conclusion:

Please refer to the attached results.

The p-value is found to be

p = 0.7038

The F value is found to be

F = 0.475

The F critical value is found to be

F critical = 3.238

Since p > α

0.7038 > 0.05

We failed to reject H₀

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.

Answer:

1. Point estimate M (sample mean): 83.33

2. The lower bound is $73.36 and the upper bound is $93.30. One can be______% confident that the mean travel tax for all cities is between these values.

3. A. The researcher could decrease the level of confidence.

Step-by-step explanation:

A point esimate for the population mean travel tax can be done with the sample mean.

We can calculate the sample mean as:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(67.85+78.62+70.28+84.03+79.28+87.72+101.54+97.28)\\\\\\M=\dfrac{666.6}{8}\\\\\\M=83.33\\\\\\[/tex]

2. We have to calculate a 95% confidence interval for the mean.

The sample mean is M=83.33.

The sample size is N=8.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

We calculate the sample standard deviation as:

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((67.85-83.33)^2+(78.62-83.33)^2+(70.28-83.33)^2+. . . +(97.28-83.33)^2)}\\\\\\s=\sqrt{\dfrac{994.49}{7}}\\\\\\s=\sqrt{142.07}=11.92\\\\\\[/tex]

The standard error is:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{11.92}{\sqrt{8}}=\dfrac{11.92}{2.828}=4.214[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=8-1=7[/tex]

The t-value for a 95% confidence interval and 7 degrees of freedom is t=2.36.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.36 \cdot 4.214=9.97[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 83.33-9.97=73.36\\\\UL=M+t \cdot s_M = 83.33+9.97=93.30[/tex]

The 95% confidence interval for the mean travel tax is (73.36, 93.30).

We can be 95% confident that the true mean travel tax is within this interval.

3.. If we have no access to additional data, we can not decrease the standard deviation or increase the sample size.

The only way to have a narrower confidence interval is decreasing its level of confidence. With the same sample information, the lower the confidence, the narrower is the interval.

Step-by-step explanation:

[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

The quadratic formula is honestly the most straightforward way of solving here.

Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:

1) a=1, b=0, c=8

This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)

2) a=-9, b=4, c=-10

This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.

3) a=1, b=8, c=17

This reduces to x=(-4+i), (-4-i)

So those are the answers for each.

Please Refer to the screenshot. Hope this helps!

Answer:

all squares are quadrilaterals

Answer:

z = -17.67 + i3.43

Step-by-step explanation:

Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -

z = 18( cos169 + isin169 ),

z = r(cos Ф + i sin Ф)

Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -

sin169 is positive, while cos169 is negative, thus -

a = -17.6692893021...,

b = 3.43456191678...

Rectangular Form, z = -17.67 + i3.43

Hope that helps!

Answer:

B

Step-by-step explanation:

area of top on triangle=1/2×4×3=6m²

area of four top triangles=6×4=24 m²

area of bottom square=4×4=16 m²

area of four side rectangles=4×(4×5)=80 m²

Total area= 24+16+80=120m²

Answer:

The general term is

Sn = -(-2)ⁿ.3¹⁻ⁿ

step by step Explanation:

we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

The expected number of the people at the reception whose favorite snack will be chips is 1152

Step-by-step explanation:

Given

The data in the above table and

Reception = 3600

Required

Predict the number of the people at the reception whose favorite snack will be chips.

The first step is to determine the total number of samples;

[tex]Total = Brownies + Cookies + Chips + Other[/tex]

[tex]Total = 32 + 22 + 56 + 65[/tex]

[tex]Total = 175[/tex]

The next step is to determine the fraction of people whose favorite is chips

[tex]Fraction = \frac{Chips}{Total}[/tex]

[tex]Fraction = \frac{56}{175}[/tex]

The product of the above fraction and the expected number of people in the reception is the solution to this question;

[tex]Expected\ Number = \frac{56}{175} * 3600[/tex]

[tex]Expected\ Number = \frac{56* 3600}{175}[/tex]

[tex]Expected\ Number = \frac{201600}{175}[/tex]

[tex]Expected\ Number = 1152[/tex]

Hence, the expected number of the people at the reception whose favorite snack will be chips is 1152

Answer:

The statistic for this case would be:

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

And replacing we got:

[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]

Step-by-step explanation:

For this case we have the following info:

[tex] n =700[/tex] represent the sample size

[tex] X= 305[/tex] represent the number of employees that earn more than 50000

[tex]\hat p=\frac{305}{700}= 0.436[/tex]

We want to test the following hypothesis:

Nul hyp. [tex] p \leq 0.4[/tex]

Alternative hyp : [tex] p>0.4[/tex]

The statistic for this case would be:

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

And replacing we got:

[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]

And the p value would be given by:

[tex] p_v = P(z>1.922)= 0.0274[/tex]

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]

1) Calculating the first derivative

[tex]f'(x)=2x[/tex]

2) Now, let's work to find the critical points

Set this

[tex]2x=0\\x=0[/tex]    

0, belongs to the interval. Plug it in the original function

[tex]f(0)=(0)^2+8\\f(0)=8[/tex]

3)  Making a table x, f(x) then compare

x|  f(x)

-1 | f(-1)=9  

0 | f(0)=8   Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.    

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.

Answer:

Step-by-step explanation:

The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.

There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.

  C(1, 1), D(4, 1)

Options

Answer:

[tex](E)0.7+0.4-0.2=0.9[/tex]

Step-by-step explanation:

In probability theory

[tex]P$(A or B)=P(A)+P(B)$-$P(A and B)[/tex]

Let the event that the show had animals in it = A

P(A)=0.7

Let the event that the show aired more than 10 times =B

P(B)=0.4

P(A and B)= 0.2

[tex]P$(A or B)$=0.7+0.4-0.2=0.9[/tex]

Therefore, the equation which  shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:

[tex]0.7+0.4-0.2=0.9[/tex]

The correct option is E.

Answer:

There is enough paint to cover the tank with one layer of paint.

Step-by-step explanation:

Given the cilindrical configuration of the tank and supposing that only external face must be painted, the surface area of the section (lateral wall + lid) can be calculated by the following expression:

[tex]A_{s} = 2\pi\cdot r\cdot h + \pi\cdot r^{2}[/tex]

Where [tex]r[/tex] and [tex]h[/tex] represent the radius and the height of the cube, respectively.

If [tex]r = 0.55\,m[/tex] (a diameter is two times the length of radius) and [tex]h = 1.4\,m[/tex], the intended surface area is:

[tex]A_{s} = 2\pi\cdot (0.55\,m)\cdot (1.1\,m)+\pi\cdot (0.55\,m)^{2}[/tex]

[tex]A_{s} \approx 4.751\,m^{2}[/tex]

It is known that 250 mL of paint are needed to cover a square meter of the surface area, the needed amount of paint to cover the required area is estimated by simple rule of three:

[tex]Q = \frac{4.751\,m^{2}}{1\,m^{2}}\times (250\,mL)[/tex]

[tex]Q = 1187.75\,mL\,(1.188\,L)[/tex]

In consequence, there is enough paint to cover the tank with one layer of paint.

Answer:

Step-by-step explanation:

Given the 3* 3 matrices [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex], to compute the determinant using the first row means using the row values [0 4 1 ] to compute the determinant. Note that the signs on the values on the first row are +0, -4 and +1

Calculating the determinant;

[tex]= +0\left[\begin{array}{cc}-3&0\\3&1\\\end{array}\right] -4\left[\begin{array}{cc}5&0\\2&1\\\end{array}\right] +1\left[\begin{array}{cc}5&-3\\2&3\\\end{array}\right] \\\\= 0 - 4[5(1)-2(0)] +1[5(3)-2(-3)]\\= 0 -4[5-0]+1[15+6]\\= 0-20+21\\= 1[/tex]

The determinant is 1 using the first row as co-factor

Similarly, using the second column [tex]\left[\begin{array}{c}4\\-3\\3\end{array}\right][/tex] as the cofactor, the determinant will be expressed as shown;

Note that the signs on the values are -4, +(-3) and -3.

Calculating the determinant;

[tex]= -4\left[\begin{array}{cc}5&0\\2&1\\\end{array}\right] -3\left[\begin{array}{cc}0&1\\2&1\\\end{array}\right] -3\left[\begin{array}{cc}0&1\\5&0\\\end{array}\right] \\\\= -4[5(1)-2(0)] - 3[0(1)-2(1)] -3[(0)-5(1)]\\= -4[5-0] -3[0-2]-3[0-5]\\= -20+6+15\\= -20+21\\= 1[/tex]

The determinant is also 1 using the second column as co factor.

It can be concluded that the same value of the determinant will be arrived at no matter the cofactor we choose to use.

Answer:

if m is supposed to be the equals (=) sign then x = 25

Step-by-step explanation:

45 = (2x-5)

+5         +5

50 = (2x)

÷2     ÷2

25 = x

Answer: 70

Step-by-step explanation:

Answer:

sorry but are you dyin why do u need help why do you need someone to save you just say i need answers to this equation pls

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.

Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.

Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

Learn more about horizontal asymptotes here -

https://brainly.com/question/14357352

#SPJ2

Answer:

c

Step-by-step explanation:

Answer: 52.8

Step-by-step explanation: it’s on khan ,

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:

-4/8

Step-by-step explanation:

Using rise over run would give you -4/8. Since the rise is going downward four times the number would be negative. Since the run is going to the right 8 times it would be positive.

Answer:  the slope is -1/2

Step-by-step explanation:  The rise is -4. Easy to see from the y-intercept, 4 below the origin. The run is 8, again easy to see from the distance between the x-intercept at -8, 8 unite away from the origin.

So slope = rise/run -4/8   simplify (by LCM, 4) So you get slope = -1/2