Question 1 (10 points)
Is normal body temperature the same for men and women?
Medical researchers interested in this question collected data
from a large number of men and women. Random samples
from that data are recorded in the table below.
Body Temperature (°F)
Female
97.8
98.0
98,2
98,2
98.6
98.8
98.8
99.2
99.4
Male
96.9
97.4
97.8
97.8
97.9
98.0
98.1
98.6
98.8
Two random samples of body temperatures.
[Source: Journal of Statistics Education Data
Archive, www.amstat.org, April 15, 2002.]
a) Use a 95% confidence interval to estimate the mean
body temperature of men.
b) Use a 95% confidence interval to estimate the mean
body temperature of women.
c) Find the margin of error for the men and for the
women.
d) Which margin of error is larger? Why is it larger?

The correct statement is:

d. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.

What is binomial distribution?

In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure. For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. This distribution is also called a binomial probability distribution.

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial can result in only two outcomes (success or failure), and the probability of success is constant. Examples of situations that can be modeled by a binomial distribution include flipping a coin a fixed number of times or counting the number of defective items in a batch of products.

The normal distribution, on the other hand, is a continuous probability distribution that is often used to model naturally occurring phenomena, such as heights, weights, and test scores. The normal distribution is characterized by a bell-shaped curve, and it is used because many phenomena in nature follow a normal distribution pattern.

So, the binomial and normal distributions are both widely used in probability and statistics, but they are fundamentally different types of distributions.

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Answer:

250.50 - 35m = 300 - 45.25m

Step-by-step explanation:

Given :

International Business School :

Initial = 250.50

Spending per month = $35

Future Agricultural leaders club :

Initial = $300

Spending per month = 45.25

The number of months, m itvwi take for them to have the same amount of money :

Total spending after m months for both :

Initial - spending per month * number of months

International Business School :

250.50 - 35m - - - (1)

Future Agricultural Leaders Club :

300 - 45.25m - - - - - 2)

Equate both : (1) and (2)

250.50 - 35m = 300 - 45.25m

Answer:

250.50 - 35m = 300 - 45.25m

( option B )

The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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Assume that p(x) represents the density function for American men's heights in inches and that p(69) = 0.18. Consider the implications of this mathematical statement carefully. How many men in America are between 68.9 and 69.1 inches tall on average? Percentage, roughly.

If p(x) is the density function for the heights of American men, then p(69) = 0.18 means that the probability density at x = 69 inches is 0.18.

We can integrate the density function over the range [68.9, 69.1] to determine the approximate percentage of American men who are between 68.9 and 69.1 inches tall:

P(68.9 ≤ x ≤ 69.1) = ∫₀.₁₃ p(x) dx ≈ 0.036

So, approximately 3.6% of American men are between 68.9 and 69.1 inches tall.

We would anticipate p(75)  p(69) if American men are on average 69 inches tall because the distribution is most likely symmetric around the mean and taper off as we move away from the mean in either direction.

P(69) = 0.5 indicates that 50% of American men have heights that are less than or equal to 69 inches if P(h) is the cumulative distribution function of p. We can use the density function and integrate over the corresponding intervals to estimate P(68.9) and P(68.8):

P(x ≤ 68.9) ≈ ∫₀.₁₃ p(x) dx ≈ 0.5 - 0.036/2 ≈ 0.482

P(x ≤ 68.8) ≈ ∫₀.₂₃ p(x) dx ≈ 0.5 - 0.036 - 0.013 ≈ 0.451

So, approximately 48.2% of American men have heights less than or equal to 68.9 inches, and approximately 45.1% have heights less than or equal to 68.8 inches.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

The product of the radical expression is  - 49 + 13√7. option B is the correct answer

From the question, we have

(7-√7)(-6+√7)

= (7) × (-6) + (-√7) × (√7) + (-√7) × (-6) + (7)(√7)

= -42 - 7 + 6√7 + 7√7

= - 49 + 13√7

The product of the radical expression is  - 49 + 13√7

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

1., 2., 3., 5.

Step-by-step explanation:

2 2/3 x 1 1/2 =

= (2 * 3 + 2)/3 * (1 * 2 + 1)/2

= 8/3 * 3/2

= 24/6

= 4

Answer:

Write the mixed numbers as improper fractions.

Multiply the numerators to get 24.

Multiply the denominators to get 6.

Write the improper fraction as a mixed number.

The product is 4.

Step-by-step explanation:

the other person is wrong

I purposely got this question wrong so I can see the right answers

these are the correct answers

(edge)

The volume of the new touch tank is 16000 feet³.

Given that,

An aquarium is expanding its touch tank exhibit and is going to double the dimensions of the original tank.

A tank is in the shape of a rectangular prism.

Let l, w and h be the dimensions of the original tank.

Then if the dimensions are doubled, then the new dimensions of the new touch tank will be 2l, 2w and 2h.

Volume of the original tank = 2000 feet³

That is,

lwh = 2000

If all the dimensions are doubled,

2l . 2w . 2h = 8 lwh

                  = 8 × 2000

                  = 16000 feet³

Hence the volume of the new touch tank is 16000 feet³.

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Answer:

Step-by-step explanation:

b

Answer: 42$

Step-by-step explanation: 35.00+20%=42$

The value of the z-score for the value of sample 48 will be negative 0.4.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The mean is 50 and the standard deviation is 5.

Then the value of the z-score for the value of sample 48 will be

z = (x - mean) / (standard deviation)

Then we have

z = (48 - 50) / (5)

z = -2 / 5

z = -0.4

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The outward flux of the vector field F across the boundary of the region D, which is the cube bounded by the planes x = ±1, y = ±1, and ±1, can be found using the divergence theorem.

The outward flux is the integral of the divergence of F over the volume enclosed by the boundary surface.The first step is to calculate the divergence of F. The divergence of a vector field F = P i + Q j + R k is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In this case, div(F) = ∂/∂x(5y - 4x) + ∂/∂y(-4z - 5y) + ∂/∂z(-3y - 2x). Simplifying these partial derivatives, we have div(F) = -4 - 2 - 3 = -9.

Applying the divergence theorem, we can relate the flux of F across the boundary surface to the triple integral of the divergence of F over the volume enclosed by the surface. Since D is a cube with sides of length 2, the volume enclosed by the surface is 2^3 = 8.

Therefore, the outward flux of F across the boundary of D is given by ∬S F · dS = ∭V div(F) dV = -9 * 8 = -72. The negative sign indicates that the flux is inward.

In summary, the outward flux of the vector field F across the boundary of the cube D, as described by the given vector components, is -72. This means that the vector field is predominantly flowing inward through the boundary of the cube.

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Answer:

2 x^3 ( x-3)

----------------------------

5 (x+3)

Step-by-step explanation:

12 x^4 ( x-3) (x+5)

----------------------------

30x (x+3) (x+5)

Cancel the x+5

12 x^4 ( x-3)

----------------------------

30x (x+3)

Rewriting 12x^4 and 30x

6*2 x^3 *x ( x-3)

----------------------------

6*5 x (x+3)

Canceling 6x

2 x^3 ( x-3)

----------------------------

5 (x+3)

Answer:

3. equivalent

4. not equivalent

Step-by-step explanation:

Answer:

what are you doing step bro!!??

Step-by-step explanation:

9514 1404 393

Answer:

  C +2D = 3s -21

Step-by-step explanation:

Use the substitution property of equality.

  C = s -5

  D = s -8

Then the value of your expression is ...

  C +2D = (s -5) +2(s -8)

  = s -5 +2s -16

  C +2D = 3s -21

The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.

Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.

1. y = x² + 8x + 18

To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.

The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2

. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.

The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.

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Answer:

A(n) = 5.1×n + 4.5

Step-by-step explanation:

A(n) = A(n-1) + 5.1

A(1) = 9.6

A(n) - A(n-1) = 5.1  ,where n ≥ 1

This means that (A(n)) is an arithmetic sequence where :

The common difference r = 5.1

and

The first term A(1) = 9.6

Therefore

A(n) = A(1) + (n - 1)×r

       = 9.6 + (n - 1)×5.1

       = 9.6 + 5.1×n - 5.1

       = 5.1×n + (9.6 - 5.1)

       = 5.1×n + 4.5

Answer:

4/10

Step-by-step explanation:

This is because 4 water bottler are distributed to 10 girls

Answer:

2/5 of a bottle

Step-by-step explanation:

since there are 10 girls sharing 4 bottles of water, the equation is 4/10. This fraction can be further simplified into 2/5 and that's the answer. Hope this helps. :)

Answer:

x = m × p - n

Step-by-step explanation:

\(m = n + \frac{x}{p} \)

We can first multiply both sides by p.

\(m \times p = n + x\)

And now we only have n left with x, so we subtract n on both sides.

\(m \times p - n = x \\or \\ x = m \times p - n\)

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x+4)^2.(x+4)^2

= x^4 +16x^3+96x^2+256x+256

Answer:

?

Step-by-step explanation:

Answer:

Student has made an error

Step-by-step explanation:

If two figures are said to be congruent, this implies that area of both is same and both as exactly same or copy or each other.

But from the graph, it can be stated that height of figure JKLM is 4 units whereas that of other is 6 unit.

Hence explained !

EXPLANATION:

Given;

We are told that a baseball team scores in each of their first 5 innings. After that they do not score a run for the next 10 innings.

Let x represent the inning of the game and y represent the total number of runs.

Required;

Sketch a graph that shows the relationship between x and y.

Step-by-step explanation;

With each run the team scores points, that simply means as x increases, y also increases. That signifies a positive relationship between both variables. A positive relationship will be an upward sloping line (from left to right). At the point where the team does not score any more points, the line does not rise.

So the innings (the x-axis) moves towards the right while the runs does not move at all up till 10 innings.

This is best described by the graph labelled C.

ANSWER:

Graph C best represents the situation described

Answer:

Mean: 4.7

Mode: 2

Median: 4.5

Step-by-step explanation:

Answer:

3,4

Step-by-step explanation:

The first blanck answer is 3 because 3/4 is also known as .75 as a decimal and if you do 3 divided by .75 you get 4 meaning 4 is your second black answer

Hope this Helped!!!

Answer:

French toast recipe calls for 3/4 cup milk per beaten egg. An equivalent ratio to this rate is 3 cups milk for every 4 beaten eggs.

Step-by-step explanation:

hope it helps brainliest would also be appreaciated

Based on the coordinate map the library is located at -2, -2, while the police station could be located at -2, 3.

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Answer:

1/2 ÷ 3/10 = 1/2 × 10/3

1/2 miles per 3 and 1/3 hours

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by the inverse of that fraction.

In other words: a ÷ (b/c) = a × (c/b)

So for the first part of problem 11,

1/2 ÷ 3/10 = 1/2 × 10/3

This can be simplified and written out for the second part of problem 11 as,

1/2 miles per 3 and 1/3 hours

Answer:  The correct answer:

  " \(\frac{10}{3}\) " ; is the value for the first blank space for Problem #11 ;

_______________________

And for the final answer:

_______________________

 " \(1\frac{2}{3}\) miles per hour " .

_______________________

Step-by-step explanation:

_______________________

\(\frac{1}{2}\) ÷ \(\frac{3}{10}\)  =  \(\frac{1}{2}\) * \(\frac{10}{3}\)  ;

 →  {since "dividing by a number" is the same thing as "multiplying by the reciprocal of that said number."} .

_______________________

So:  " \(\frac{10}{3}\) " ; is the reciprocal of " \(\frac{3}{10}\) " ;

We can put: " \(\frac{10}{3}\) " ; in the "first answer box" in "Problem # 11 ".

_______________________

Now, we can continue solving the problem:

_______________________

We have:

_______________________

" \(\frac{1}{2}\) * \(\frac{10}{3}\) " ;

_______________________

Let us Cancel out the "2" ; and change to a "1" ; and

         Cancel out the "10" ; and change to a "5" ;

 →  {since: " [10 ÷ 2 = 5] " ;  and since:  " [2 ÷ 2 = 1] " ;

And we can rewrite the expression as:

_______________________

"  \(\frac{1}{1} * \frac{5}{3}\) " ;

→ \(\frac{1}{1} * \frac{5}{3} = 1 * \frac{5}{3} = \frac{5}{3} = 1\frac{2}{3}\) ;  which is our answer:  in miles per hour.

_______________________

The correct answer:

  " \(\frac{10}{3}\) " ; is the value for the first blank space for Problem #11 ;

_______________________

And for the final answer:

_______________________

 " \(1\frac{2}{3}\) miles per hour " .

_______________________

Hope this is helpful to you!

 Wishing you the best!

_______________________