A case-control study was conducted to evaluate the relationship between artificial sweeteners and bladder cancer. 3,000 cases and 3,000 controls were enrolled in the study. Amongst the cases, 1,293 had used artificial sweeteners in the past, while 1,707 had never used artificial sweeteners. Among the controls, 855 had used sweeteners and 2,145 had not. Calculate the odds of being a case.

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.

Answer:

(14,4) (21, 6) (28,8) If they had six losses, they would have 21 wins

Step-by-step explanation:

According to the information given, for every 7 wins, they lose 2 games. That means in order to finish the table, we have to find multiples of 7 and 2. If they won 14 games, they would have 4 losses. This is because since 14 is twice the value of 7, they would have lost twice the number of games.

The next would be 21 wins since 7x3 is 21 and 6 losses since 2x3 is 6

The last one would be 28 wins (7x4) and 8 losses (2x4)

If they had six losses, they would have 21 wins

Answer:

10.69% probability that all 12 flights were on time

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it was on time, or it was not. The probability of a flight being on time is independent of any other flight. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

83% of recent flights have arrived on time.

This means that [tex]p = 0.83[/tex]

A sample of 12 flights is studied.

This means that [tex]n = 12[/tex]

Calculate the probability that all 12 flights were on time

This is P(X = 12).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 12) = C_{12,12}.(0.83)^{12}.(0.17)^{0} = 0.1069[/tex]

10.69% probability that all 12 flights were on time

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:

I noticed a pattern:

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

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

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

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: Anything above 2

Step-by-step explanation:

Answer: 3,4,5,6,7,8,9 (Any of these digits work)

Step-by-step explanation:

We want to find a digit that makes the number greater than 3260.2. There are many digits that can fit in there.

3318.7≥3260.2

Here, we plugged in a 3. that makes this sentence true because 3318.7 is greater than or equal to 3260.2. Since 3 works, we know that any digit greater than 3 would fit.

Answer:

1 = 95

2 = 77

3 = 85

4 = 103

Step-by-step explanation:

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

Slope is the change in y over the change in x

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

Slope = 1/1

Slope = 1

Answer:

4. f(x) = 8x^4 – 3x + 5x^2​

Step-by-step explanation:

In choices 1., 2., and 3., each function is a 2nd degree function since the term with the highest degree has an exponent of 2 on x. In choice 4., the function is a 4th degree function since there is a term with x^4, and that is the highest exponent on x.

Answer: 4. f(x) = 8x^4 – 3x + 5x^2​

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:

150 yards

Step-by-step explanation:

Since 1 yard = 3 feet,

You can divide 450 by 3 to express it in yards.

450 ÷ 3 = 150

So, the pyramid is 150 yards high.

Answer:

150 yards

Step-by-step explanation:

Answer:

we dont see aa figure

Step-by-step explanation:

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:

  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: 22.3 quarter

Step-by-step explanation:

Answer:

13.896 kg

Step-by-step explanation:

Answer:

D) 86 – 18x – 8 = 12x + 18

X = 2

Step-by-step explanation:

86 – 2 (9x + 4) = 12x + 18

This question has a straight forward answer...

It's just to open up the bracket and ensure that the negative sign before the bracket multiply the values in the bracket exactly.

So opening up the bracket gives us this as the answer

86 - 18x -8 = 12x +18

86-18-8 = 12x+ 18x

60 = 30x

X = 2

If [tex]f(x)=\mid x\mid[/tex] and [tex]g(x)=x+2[/tex] then [tex]f(g(x))=\mid x+2\mid[/tex].

The domain is [tex]x\in(-\infty, +\infty)=\mathbb{R}[/tex].

The range is [tex]y\in[2,+\infty)[/tex].

Hope this helps.

Answer:

Step-by-step explanation:

with range there is a horizontal line under the > sign, just as a side note:D

BRANLIEST?

Answer:

A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.

Step-by-step explanation:

Confidence interval:

x% confidence

Of a sample

Between a and b.

Interpretation: We are x% sure(or there is a x% probability/chance) that the population mean is between a and b.

In this question:

92% confidence interval for the average height of football players is (63.2, 65.9).

Interpretation: We are 92% sure that the true average height of all college football players, that is, the population mean, is in this interval.

The correct answer is:

A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.

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:

First choice

Step-by-step explanation:

Start by arranging the exponents of 10 in ascending order.

9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7 * 10^3

The exponents are in ascending order, -8, -6, 3, 3

Since the last two exponents are equal, we must compare the numbers that multiply the powers of 10. They are 2.5 and 7. Since 2.5 < 7, ascending order is 2.5, 7. That means the line above is in ascending order.

Answer: First choice

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.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The rectangle has an area of 60 square feet. Find its dimensions (in ft) if the length of the rectangle is 4 ft more than its widh.

smaller value ___________________ ft

larger value ____________________ ft

Answer:

Smaller value = 6 ft

Larger value = 10 ft

Step-by-step explanation:

Recall that the area of a rectangle is given by

[tex]Area = W \times L[/tex]

Where W is the width and L is the length of the rectangle.

It is given that the rectangle has an area of 60 square feet.

[tex]Area = 60 \: ft^2 \\\\60 = W \times L \\\\[/tex]

It is also given that the length of the rectangle is 4 ft more than its width

[tex]L = W + 4[/tex]

Substitute [tex]L = W + 4[/tex] into the above equation

[tex]60 = W \times (W + 4) \\\\60 = W^2 + 4W \\\\W^2 + 4W - 60 = 0 \\\\[/tex]

So we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method  

[tex]W^2 + 10W - 6W - 60 \\\\W(W + 10) – 6(W + 10) \\\\(W + 10) (W - 6) = 0 \\\\[/tex]

So,

[tex](W + 10) = 0 \\\\W = -10 \\\\[/tex]

Since width cannot be negative, discard the negative value of W

[tex](W - 6) = 0 \\\\W = 6 \: ft \\\\[/tex]

The length of the rectangle is  

[tex]L = W + 4 \\\\L = 6 + 4 \\\\L = 10 \: ft \\\\[/tex]

Therefore, the dimensions of the rectangle are

Smaller value = 6 ft

Larger value = 10 ft

Verification:

[tex]Area = W \times L \\\\Area = 6 \times 10 \\\\Area = 60 \: ft^2 \\\\[/tex]

Hence verified.

Answer:

  20 minutes

Step-by-step explanation:

Melissa works as fast as two Bettys, so working together, they get the job done at the rate 3 Bettys could do it. That time is (60 minutes)/3 = 20 minutes.

Working together, Betty and Melissa can mow the lawn in 20 minutes.

_____

You can also think in terms of mowing rates as lawns per minute. The total mowing rate is ...

  Betty's rate + Melissa's rate = (1/60 lawns/min) +(1/30 lawns/min)

  = (1/60 +2/60) lawns/min = 1/20 lawns/min

The inverse rate is then ...

  20/1 min/lawn

Together, they take 20 minutes to mow 1 lawn.

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:

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:

Jill bought 16 books and Sam bought 9 books

Step-by-step explanation:

Let the number of books that Jill bought be j.

Let the number of books that Sam bought be s.

Jill bought 7 more books than Sam:

j = 7 + s

They bought 25 books altogether:

j + s = 25

Put j = 7 + s into the second equation:

7 + s + s = 25

7 + 2s = 25

2s = 25 - 7 = 18

s = 18/2 = 9 books

Therefore:

j = 7 + s = 7 + 9

s = 16 books

Jill bought 16 books and Sam bought 9 books.