An endocrinologist is interested in the effects of depression on the thyroid. It is believed that healthy subjects have a mean thyroxin (a hormone related to thyroid function) level of 7.0 micrograms/100 ml and a standard deviation of 1.6 micrograms/100 ml. The endocrinologist wants to assess whether the mean thyroxin level is different for those with depression. She samples 35 subjects with depression and obtains a sample mean of 7.82 micrograms/100 ml for thyroxin. What null and alternative hypotheses should she test

Answer:

D

Step-by-step explanation:

Using the Mean Value Theorem, sin xsin y ≤ x − y| for all real numbers x and y, sinx is uniformly continuous on R.

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the derivative of the function is equal to the average rate of change of the function over [a, b].

Applying this theorem to the function f(x) = sin x on the interval [x, y], we can find a point c between x and y where the derivative of f(x) is equal to the average rate of change of f(x) over [x, y].

Since the derivative of sin x is cos x, we have cos c = (sin y - sin x) / (y - x). Rearranging the inequality, we get sin y - sin x ≤ cos c (y - x). Now, using the fact that |cos c| ≤ 1, we can rewrite the inequality as sin y - sin x ≤ |y - x|. Thus, sin xsin y ≤ x - y| for all real numbers x and y.

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Answer:

Legs - the sides that form the right angle of a right triangle.

Hypotenuse - the side opposite the right angle of a right triangle.

Step-by-step explanation:

Every triangle has 3 sides.

Certain special triangle have specific names assigned to their sides.

A right triangle has one right angle and two acute angles. The two sides that form the right angle of a right triangle are called legs. The third side of the right triangle is called hypotenuse. The hypotenuse is opposite the right angle and does not help form the right angle.

The statement is False.

(a) Let x be an integer. If 4x² + 3x + 7 is odd, then x must be even.Statement (a) is false.

Here is the explanation:We know that an integer is odd if and only if it can be represented in the form of 2k + 1, where k is any integer.Let us assume that x is an odd integer. Then, we can write x as 2k + 1, where k is any integer.Substituting the value of x in 4x² + 3x + 7, we get;4x² + 3x + 7 = 4(2k + 1)² + 3(2k + 1) + 7= 4(4k² + 4k + 1) + 6k + 3 + 7= 16k² + 16k + 4 + 6k + 10= 16k² + 22k + 14= 2(8k² + 11k + 7)which is an even integer as it is a multiple of 2.

Therefore, we have proven that if x is odd, then 4x² + 3x + 7 is even.So, we have disproved the statement as it is not true for all integers. It's only true for odd integers only. Therefore, statement (a) is false.

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Answer:

Circumference ~ 53.4

Step-by-step explanation:

Use the distance formula to get the radius of the circle. The radius is about 8.5. Now put 8.5 into the formula 2(pi)r for the Circumference. Rounding to the nearest tenth the answer is 53.4

Answer: x=17 and 98

Step-by-step explanation:

Those two angles are supplementary so just add them together and make it equal to 180.

Answer: h = 6

explanation:

first u get h by itself

4h + 6 = 30

subtract 6 from both sides

4h = 24

divide by 4 on both sides

h = 6

Answer:h=3/13

Step-by-step explanation: Subtract 6  from both sides of the equation 4h+6-6=30h-6 you simplify 4h=30h-6. Subtract 30h  from both sides of the equation then you get -26h=-6 then you divide both sides of the equation by the same term -26h/-26=-6/-26 and your answer is 3/13.

Answer:

54 sq ft

Step-by-step explanation:

6ft x 3 ft = 18 sq ft

9 ft x 4 ft = 36 sq ft

18 sq ft + 36 sq ft = 54 sq ft

The choices should be in sq ft, not in sq cm

The value of area in sq cm would be far greater than the value of area in sq ft.

i think your answer is B. 27x

Answer:

No

Step-by-step explanation:

Use the Pythagorean Theorem to check on this.  

Does 8^2 + 8^2 = 12^2?  Does 64 + 64 = 144?  NO.  So this is not a right triangle.

Answer:

x=49

Step-by-step explanation:

Answer:

P'(0, -4)

Step-by-step explanation:

when a coordinate (x, y) is rotated by 180 degrees, the resulting coordinate will be (-x, -y). Note that each coordinate is negated when rotated about 180 degrees

Given the coordinate P (0, 4). When rotated by 180 degrees, the resulting coordinate will be at P'(0, -4)

The probability P(Z < -2.33 or Z > 2.33) is approximately 0.0198.

To find the probability P(Z < -2.33 or Z > 2.33) using the standard normal distribution, we can calculate the individual probabilities and then add them together.

Using a standard normal distribution calculator

The value for P(Z < -2.33) is approximately 0.0099.

P(Z < -2.33), which is approximately 0.0099.

we can add the two probabilities together

P(Z < -2.33 or Z > 2.33) = P(Z < -2.33) + P(Z > 2.33)

= 0.0099 + 0.0099

= 0.0198

Therefore, the probability P(Z < -2.33 or Z > 2.33) is approximately 0.0198

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The pizza is divided into 6 equal pieces in total: 3 initial slices, each further divided into 2 equal pieces.

A pizza is cut into 3 equal slices. Each slice is then cut into 2 equal pieces. How many pieces of pizza are there in total?

To solve this problem, we can use our definition of multiplication. Multiplication is repeated addition. In this case, we are repeatedly adding 2 to itself 3 times. This gives us 2 + 2 + 2 = 6. Therefore, there are 6 pieces of pizza in total.

We can also use math drawings to solve this problem. Here is a math drawing that shows how to find the product of 1/3 * 2/3:

The first row of the math drawing shows 1/3 of a pizza. The second row shows 2/3 of a pizza. The third row shows the product of 1/3 * 2/3. As you can see, the product is 6 pieces of pizza.

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Answer:

1/3

Step-by-step explanation:

From the figure, we know that the median of Amy is 40 and the median of Megan is 35.

Therefore the difference in their medians is = 40 - 35

                                                                         = 5

We see that Q1 of Megan is 25 and Q3 is 40. Therefore, her interquartile range is given by Q3 - Q1 = 40 - 25

                                           = 15

So, the difference of the medians is the multiple of the interquartile range.

So the multiple is = 5/15

                             = 1/3 (IQR of Megan)

Answer:

Yes, I can describe the difference of the two medians as a multiple of the interquartile range as shown below.

Step-by-step explanation:

The difference of the medians for the two data sets is 69 − 60 = 9. The interquartile ranges for the data sets are 9 ounces and 8 ounces.

This shows that the difference of the medians is about 1 times, or nearly equal to, the interquartile range of either data set.

For Genivieve, the multiple is 1:

9 = m(9)

m = 1

For Mindy, the multiple is 1.125:

9 = m(8)

m = 1.125

(This is the answer on edumentum)

Answer:

It's A I think. I did the math on math.way and it was differeten the the answers you have.

Step-by-step explanation:

Answer:

9 students is the correct answer :(

Multiply the length by width by the height/3

7 x 6 x 8/3 = 112 in^2

The answer is 112 in^2

Answer:

112

Step-by-step explanation:

The calculated product of the vectors a and b is 17

From the question, we have the following parameters that can be used in our computation:

a = (4, 1, 1/5) and b = (6,-4, -15)

The product of the vectors can be calculated using

a * b = Sum of products of each position

Using the above as a guide, we have the following:

a * b = 4 * 6 + 1 * -4 + 1/5 * -15

Evaluate the expression

a * b = 17

Hence, the product of the vectors a and b is 17

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The new mAs should be approximately 45 mAs.
The intensity of radiation at a given distance can be calculated using the inverse square law:

Intensity2 = Intensity1 × (Distance1/Distance2)^2

Given:
Intensity1 = 100 mR
Distance1 = 100 cm
Distance2 = 200 cm

Using the above formula, we can calculate the new intensity at 200 cm:

Intensity2 = 100 mR × (100 cm/200 cm)^2
Intensity2 = 100 mR × (1/4)
Intensity2 = 25 mR

To maintain the same exposure at the new distance, the new mAs needs to be adjusted accordingly. We can use the exposure maintenance formula:

mAs2/mAs1 = (kVp2/kVp1) × (Distance1/Distance2)^2 × (Gridratio2/Gridratio1)^2

Given:
mAs1 = 30 mAs
kVp1 = 120 kV
kVp2 = 138 kV
Gridratio1 = 5:1
Gridratio2 = 10:1

Substituting the given values into the formula, we can solve for mAs2:

mAs2/30 mAs = (138 kV/120 kV) × (100 cm/200 cm)^2 × (10/5)^2
mAs2/30 mAs = (1.15) × (0.5)^2 × (4)
mAs2/30 mAs = 1.15 × 0.25 × 4
mAs2/30 mAs = 0.115

Simplifying, we find:
mAs2 = 30 mAs × 0.115
mAs2 ≈ 3.45 mAs

Therefore, the new mAs should be approximately 45 mAs (rounded to the nearest whole number) to maintain exposure at 200 cm with a 10:1 grid and 138 kV.

To maintain exposure at a new distance of 200 cm with a 10:1 grid and 138 kV, the radiograph technician should set the new mAs to approximately 45 mAs. This adjustment takes into account the changes in distance, kV, and grid ratio while ensuring that the radiation intensity remains consistent.

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Answer: B

Step-by-step explanation:

4.2 / 0.25 = 21

0.4 · 21 = 8.4

8.4 + 2.5 = 10.9

Answer: 3, The initial velocity of the rocket

Answer:

the initial velocity of the rocket

Step-by-step explanation:

Answer:

x^3+3x^2-46

Step-by-step explanation:

The standard deviation of the distribution of sample means is approximately 2.331.

The mean of the distribution of sample means, also known as the sampling distribution mean, is equal to the population mean. In this case, the population mean (μ) is given as 31.3. Therefore, the mean of the distribution of sample means is also 31.3.

The standard deviation of the distribution of sample means, also known as the standard error, can be calculated using the formula:

Standard Error = Population Standard Deviation / √(Sample Size)

In this case, the population standard deviation (σ) is given as 18.4, and the sample size (n) is 62. Plugging these values into the formula, we get:

Standard Error = 18.4 / √(62)

Standard Error ≈ 2.331

Therefore, the standard deviation of the distribution of sample means is approximately 2.331.

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Answer:

1. d

2. c

3. b

4. f

5. a

6. e

Step-by-step explanation:

Good Luck

Answer:

x=1 and y=1

Step-by-step explanation:

see attachment

Answer:

y=x^28x+31

Step-by-step explanation:

Answer:   y= x 4 − 6 y = 1 x − 2

Step-by-step explanation:

Answer:

Any number below 3

(2, negative infinity)

Answer:

here's the answer with steps

x + 2 < 5

-2 -2

x < 3