A group of up to 40 people are going to a trip to Washington DC. Some will travel in a van that holds 12 people, and the rest will buy train tickets. Write an inequality that can be used to find the number of train tickets that the group will need.

Answer:

x=98°

Step-by-step explanation:

The angles of a triangle must equal 180°.

To get the third angle (G) you must do: 180°-53°-45°

That will give you 82°

Anglr G and angle x create a straight line which is 180°.

so to get the answer you must do 180°-G=x

180°-82°=98°

Therefore x=98°

Answer:

The 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]

The data provided is:

S = {112, 120, 98, 55, 71, 35, 99, 142, 64, 150, 150, 55, 100, 132, 20, 70, 93}

Compute the sample mean and sample standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{17}\times[112+120+98+...+93]=92.1176\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 25041.7647}=39.56[/tex]

The critical value of t for 95% confidence level and n - 1 = 16 degrees of freedom is:

[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 16}=2.120[/tex]

*Use a t-table.

Compute the 95% confidence interval for the hemoglobin reading for all the patients in the hospital as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]

     [tex]=92.1176\pm 2.120\times\frac{39.56}{\sqrt{17}}\\\\=92.1176\pm 20.3408\\\\=(71.7768, 112.4584)\\\\\approx (72, 112)[/tex]

Thus, the 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).

Answer:

P(Math or English) = 0.89

Step-by-step explanation: This solution will only be applicable if finding the probability that a randomly selected student is taking a math class or an English class.

Lets study the meaning of or , and on probability. The use of the word or means that you are calculating the probability

that either event A or event B happened

Both events do not have to happen

The use of the word and, means that both event A and B have to happened

The addition rules are: # P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

at the same time)

P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they

have at least one outcome in common)

The union is written as A ∪ B or “A or B”.

The Both is written as A ∩ B or “A and B”

Lets solve the question

The probability of taking Math class 69%

The probability of taking English class 70%

The probability of taking both classes is 50%

P(Math) = 69% = 0.69

P(English) = 70% = 0.70

P(Math and English) = 50% = 0.50

To find P(Math or English) use the rule of non-mutually exclusive

P(A or B) = P(A) + P(B) - P(A and B)

P(Math or English) = P(Math) + P(English) - P(Math and English)

Lets substitute the values of P(Math) , P(English) , P(Math and English)

in the rule P(Math or English) = 0.69 + 0.70 - 0.50 = 0.89

P(Math or English) = 0.89

P(Math or English) = 0.89

This solution will only be applicable if we are to find the probability that a randomly selected student is taking a math class or an English class.

Step-by-step explanation:

a) The diameter of the wheel is the distance between the minimum and maximum.  In other words, it's double the amplitude.

d = 2 × 14 = 28.

b) The period of the wave is:

720 = 2π / T

T = π/360

So the time for 3 revolution is:

3T = π/120

3T = 0.026 seconds

c) The minimum here is when cosine = 1.

h(t) = -14(1) + 14

h(t) = 0

This makes sense, since the minimum height is when the nail is at the bottom of the wheel, or at the ground.

Answer:

B (48)

Step-by-step explanation:

One particular property of medians is the 2/3 ratio. Basically, the centroid separates the median into two line segments, and the longer line segment is 2/3 of the median length. So, 72 x 2/3 is 48.

Answer:

Step-by-step explanation:

Can u help me

Answer:

cant see the picture

Step-by-step explanation:

Answer:

873

Step-by-step explanation:

so the equation is: 5x+1

sum is:

[tex] \frac{first \: one \: + \: last \: one}{2} \times quantity \: of \: terms \\ [/tex]

we have 6( 5×1+1) to 91 (5×18+1)

so we have 18 terms

then:

[tex] \frac{91 + 6}{2} \times 18 = 873[/tex]

Answer:

  A.  (2, 4)

Step-by-step explanation:

The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...

  (x, 2x)

That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).

It is the case that you have (x, 2x) for (2, 4).

The point (2, 4) lies on the graph of y = 2x.

Answer:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Step-by-step explanation:

Info given

50, 53, 55, 43, 50, 47, 58.

We can calculate the sample mean and deviation with this formula:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}[/tex]

represent the mean height for the sample  

[tex]s=5.014[/tex] represent the sample standard deviation for the sample  

[tex]n=7[/tex] sample size  

represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

Hypothesis to test

We want to test if the true mean is equal to 51, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 51[/tex]  

Alternative hypothesis:[tex]\mu \neq 51[/tex]  

The statistic is given by:

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

Replacing we got:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Answer:

I noticed a pattern:

3 * 2 + 6 = 12 and 2 * 2 + 5 = 9

This means that a*b = 2a + b.

Answer:

option 1

Step-by-step explanation:

[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]

[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]

[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]

Answer:

Quadrant II.

Step-by-step explanation:

Quadrant | has positive x and y coordinates.

Quadrant || has negative x and positive y coordinates.

Quadrant ||| has negative x and y coordinates.

Quadrant |V has positive x and negative y coordinates.

Since -3 is negative and 15 is positive, the answer is Quadrant II.

Hey there! I'm happy to help!

We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)

We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.

We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.

[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]

So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!

15(18+r)=21(18-r)

We use the distributive property to undo the parentheses.

270+15r=378-21r

We subtract 270 from both sides.

15r=108-21

We add 21 to both sides.

36r=108

We divide both sides by 36.

r=3

Therefore, the speed of the river is 3 mph.

You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!

Have a wonderful day!

Answer:

A digit that makes this sentence true is 4.

Step-by-step explanation:

Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:

4

5

6

7

8

and

9

Out of any of these you can choose, I chose 4.

9514 1404 393

Answer:

   3, or any greater digit

Step-by-step explanation:

Suppose the digit is 'd'. Then the value on the right is ...

  69.436 +100d

Subtracting the value on the left, we want the difference greater than 0.

  69.436 +100d - 352.934 > 0

  100d -293.498 > 0 . . . . simplify

  100d > 293.498 . . . . . . . add 293.498

  d > 2.93498 . . . . . . . . . . divide by 100

That is d is any single digit greater than 2.9. Those digits are ...

  d ∈ {3, 4, 5, 6, 7, 8, 9}

Any digit 3 or greater makes the sentence true.

Slope is the change in y over the change in x

Slope = (1-0) /( -3 - -4)

Slope = 1/1

Slope = 1

Answer:

n = r - 2.5

Step-by-step explanation:

We have the following data:

7 4.5

8 5.5

10 7.5

12 9.5

Now, what we will do is what happens if we subtract each one:

7 - 4.5 = 2.5

8 - 5.5 = 2.5

10 - 7.5  = 2.5

12 - 9.5 = 2.5

The difference is always kept constant, therefore the equation would be:

n = r - 2.5

Answer:

1/8

Step-by-step explanation:

Total cards = 8

Card with 4 = 1

P(4) = 1/8

Answer:

a) [tex]654.16-2.01\frac{165.4}{\sqrt{52}}=608.06[/tex]    

[tex]654.16+2.01\frac{165.4}{\sqrt{52}}=700.26[/tex]    

b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]

So the answer for this case would be n=189 rounded up to the nearest integer

Step-by-step explanation:

Part a

[tex]\bar X=654.16[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=165.4 represent the sample standard deviation

n =52represent the sample size  

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

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom aregiven by:

[tex]df=n-1=52-1=51[/tex]

Since the Confidence is 0.95 or 95%, the significance [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.01[/tex]

Now we have everything in order to replace into formula (1):

[tex]654.16-2.01\frac{165.4}{\sqrt{52}}=608.06[/tex]    

[tex]654.16+2.01\frac{165.4}{\sqrt{52}}=700.26[/tex]    

Part b

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for this case wuld be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]

So the answer for this case would be n=189 rounded up to the nearest integer

Answer:

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Step-by-step explanation:

Step(i):-

Given mean of the life time of a bulb = 510 hours

Standard deviation of the lifetime of a bulb = 25 hours

Let 'X' be the random variable in normal distribution

Let 'x' = 552

[tex]Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628[/tex]

Step(ii):-

The  probability of a bulb lasting for at most 552 hours.

P(x>552) = P(Z>1.63)

               = 1- P( Z< 1.63)

               =  1 - ( 0.5 + A(1.63)

              =   1- 0.5 - A(1.63)

              =   0.5 -A(1.63)

              =   0.5 -0.4485

             =  0.0515

Conclusion:-

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Answer:

a. t>w

Step-by-step explanation:

Sin t= 0.29

t = sin^-1(0.29)

t= 16.86°

Sin w= 0.43

W = sin^-1(0.43)

W= 25.47°

Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°

For t= 180°-16.86°

t = 163.14°

For w = 180°-25.47°

W= 154.53°

163.14°>154.53°

t>w

Answer:

[tex]\boxed{\sf \ \ \ a=-2, \ b = 1 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

saying that the function is continuous means that you cannot have a "jump" in the graph of the function

so we want

a*(-3)+b=7 and a*4+b=-7

it comes

   (1) -3a + b = 7

   (2) 4a + b = -7

(2)-(1) gives 4a + b + 3a - b =7a = -7-7 = -14

so a = -14/7 = -2

we replace in (1)

b = 7 + 3*(-2) = 7 - 6 = 1

hope this helps

Answer:

c and I will talk to you later today or tomorrow morning and then I will

Step-by-step explanation:

email to you later today to see you and the kids are doing well and that you

Answer:

11.5

Step-by-step explanation:

Put the numbers in order from smallest to largest

2,2,6,9,9,11,11,12,32,43,46,54,54,59

The median is the middle number

There are 14 numbers so the middle is between 7 and 8

2,2,6,9,9,11,11,    12,32,43,46,54,54,59

Take the average of the 7th and 8th numbers

(11+12)/2 = 11.5

The median is 11.5

Answer: 11.5

Step-by-step explanation:

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

2   2   6   9   9   11   11   12   32   43   46   54   54   59    

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median= 11+12/2=11.5

Answer: 22.3 quarter

Step-by-step explanation:

Answer:

13.896 kg

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x + 3 = 6[/tex]

Move constant to R.H.S and change its sign:

[tex]x = 6 - 3[/tex]

Calculate the difference

[tex]x = 3[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

we dont see aa figure

Step-by-step explanation:

Assuming the coin is not weighted and is a fair and standard coin - the chance of flipping head is 1/2. You can either flip head or tails, there are no other possible outcomes.

Answer:

1 = 95

2 = 77

3 = 85

4 = 103

Step-by-step explanation:

Inscribed angles are half their arc that their 2 lines intersect.

Answer:

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

Step-by-step explanation:

The axis of symmetry is found by h = -b/2a  where ax^2 +bx +c

A. f(x) = x^2 + 4x + 3

  h = -4/2*1 = -2    x=-2

B. f(x) = x^2 - 4x - 5

h = - -4/2*1 = 4/2 =2  x=2  not -2

C. f(x) = x^2 + 6x + 2

h =  -6/2*1 = -3/2 =  x=-3/2  not -2

D. f(x) = -2x^2 - 8x + 1

h = - -8/2*-2 = 8/-4 =-2  x=-2  

E. f(x) = -2x^2 + 8x - 2

h = - 8/2*-2 = -8/-4 =2  x=2  not -2

Answer:

Hey there! The answer to this question is

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1