Use the empirical rule to answer the following question.

in an experiment, 200 runners were asked to run for 6 minutes on a treadmill. their heart rates after 6 minutes were normally distributed, with a mean of 110 bpm and a standard deviation of 10 bpm.

a. what percent of the runners had heart rates between 100 and 120 bpm?

b. what percent of the runners had heart rates between 110 and 130 bpm?

c. what percent of the runners had heart rates over 90 bpm?

Part B

Answer:

Here is an example of a systems equation with 3 variables:

x+y+z=2

6x-4y+5z=31

5x+2y+2z=13

Step-by-step explanation:

Using elimination:

x+y+z=2

5x+2y+2x=13

5x+2y+2x=13

- 2x-2y-2z-4

____________

3x=9

x=9

Using substitution:

9+y+z=2

y=z-7

9+z-7+z=2

2+2z=2

z=0

Using substituion again:

9+y=2

y=-7

The domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)

The domain means all the possible values of the x and the range means all the possible values of the y.

The table is shown below.

Let the logarithm function with the variables x and y. Then we have

y = logₐ x

At x = 25, the value of y will be 2. Then the value of a will be

2 = logₐ 25

2 = 2 logₐ 5

1 = logₐ 5

Then 1 can be written as

1 = log₅ 5

Then on comparing, the value of a will be

a = 5

Then the logarithm function will be

y = log₅ x

Then the domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Instead of using a t-test, alternative statistical tests can be employed when the null hypothesis makes specific claims about the data. These tests are chosen based on the type of data and the specific hypothesis being tested.

When the null hypothesis makes claims about the data that go beyond a simple comparison of means, using a t-test may not be appropriate. Alternative statistical tests can be used in such situations to address specific hypotheses.

For example, if the null hypothesis involves comparing proportions, a chi-square test or Fisher's exact test can be used. These tests are suitable for analyzing categorical data and determining if there is a significant difference between observed and expected frequencies.

Similarly, if the null hypothesis involves comparing means across more than two groups, analysis of variance (ANOVA) or its non-parametric counterpart, the Kruskal-Wallis test, can be employed. These tests allow for the comparison of means across multiple groups and can provide valuable information about the overall differences between groups.

The selection of an appropriate test depends on various factors. The nature of the variables being analyzed, such as categorical or continuous, influences the choice of test. Sample size also plays a role, as some tests require larger sample sizes to yield accurate results. Additionally, each test has certain assumptions associated with it, and researchers need to ensure these assumptions are met before applying the test.

By using alternative tests that are suitable for the specific hypotheses being tested, researchers can gain a deeper understanding of their data. This approach allows for more accurate statistical inferences and can provide valuable insights into the relationships and differences present in the dataset.

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Answer:

(x+2)^2 - 6

Step-by-step explanation:

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\(slope = \frac{3 - 9}{ - 10 - 15} \\ \)

\(slope = \frac{ - 6}{ - 25} \\ \)

\(slope = \frac{6}{25} \\ \)

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Answer:

The slope is \(\frac{6}{25}\) or \(0.24\).

Step-by-step explanation:

This is the formula to calculate the slope from two given points: \(slope=\frac{y_2-y_1}{x_2-x_1}\) . Now, substitute (x1, y1) and (x2, y2) for (15,9) and (-10,3). \(slope=\frac{3-9}{-10-15}\) . That equation becomes \(slope=\frac{-6}{-25}\) . You have to change \(\frac{-6}{-25}\) to \(\frac{6}{25}\) . The slope is 6/25 or in decimal form, 0.24.

Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation:

Answer: 323.75

Step-by-step explanation:

92.5 x 3.5 = 323.75

Step-by-step explanation:

\(distance \: covered \: on \: saturday = (6x - 5)miles \\ \\ distance \: covered \: on \: sunday = (4x + 8)miles \\ \\ difference \: in \: distance = \\ \\ \: \: \: (6x - 5) - (4x + 8) \\ \\ 6x - 5 - 4x - 8 \\ \\ \: D.)2x - 13 \: \:✓✓✓ \\ \\ hope \: it \: helps \: you \: \: ....\)

Answer:

1:1

Step-by-step explanation:

The ratio from the initial figure PQ: QR is 1:1 because the figure is a square.

The ratio of P'Q': Q'R' is still 1:1 because even if we dilated the figure we actually compare the sides P'Q' to Q'R' that had the proportions preserve.

Based on the IQR values, we conclude that Bus 18 is more consistent than Bus 47, as it has smaller IQR. This means the travel times of students on Bus 18 are more tightly clustered around the median, and are fewer outliers in data.

A line plot is a type of graph that displays data as points or dots along a number line. Each dot or point represents a single data value, and the number line shows the range of the data. Line plots are useful for displaying small to moderate-sized data sets and for identifying the central tendency and variability of the data.

To determine which bus is the most consistent, we need to look at the variability of data. The most appropriate measure of variability for this purpose is the interquartile range (IQR), which is the range of the middle 50% of the data.

From the given data, we can calculate the IQR for both buses as follows:

For Bus 18:

Lower quartile (Q1) = 8

Upper quartile (Q3) = 24

IQR = Q3 - Q1 = 24 - 8 = 16

For Bus 47:

Lower quartile (Q1) = 10

Upper quartile (Q3) = 34

IQR = Q3 - Q1 = 34 - 10 = 24

The range, which is the difference between the maximum and minimum values, is not as appropriate a measure of variability for this purpose, as it is heavily influenced by outliers. Therefore, we cannot use the range to determine the consistency of the data for either bus.

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The PDF of W = X², if X has an exponential distribution with parameter λ, is equal to fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0 and fW(w) = 0 for w < 0.

To find the probability density function (PDF) of the random variable W = X² when X has an exponential distribution with parameter λ,

Apply a transformation to the original PDF.

Let us denote the PDF of X as fX(x) and the PDF of W as fW(w). We want to find fW(w).

To begin, let us express W in terms of X,

W = X²

Now, find the PDF of W, which is the derivative of the cumulative distribution function (CDF) of W.

So, find the CDF of W first.

The CDF of W is ,

FW(w) = P(W ≤ w)

Substituting W = X², we have,

FW(w) = P(X² ≤ w)

To determine the probability of X² being less than or equal to w,

consider that X can take on both positive and negative values.

So,  split the calculation into two cases,

First case,

X ≥ 0

In this case, X² ≤ w implies X ≤ √w, since X is non-negative.

Thus, we have,

FW(w) = P(X² ≤ w) = P(X ≤ √w)

Since X has an exponential distribution, its CDF is given by,

FX(x) = 1 -\(e^{(-\lambda x)}\)  for x ≥ 0

for the case X ≥ 0, we have,

FW(w) = P(X ≤ √w) = FX(√w) = 1 -\(e^{(-\lambda \sqrt{w} )}\)

Second case,

X < 0

X² ≤ w implies X ≤ -√w, since X is negative.

However, for X < 0, X² is always non-negative.

The probability is always 0 in this case.

Combining both cases, we can write the CDF of W as,

FW(w) = 1 - \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

FW(w) = 0 for w < 0

Finally, to find the PDF fW(w), we take the derivative of the CDF with respect to w,

fW(w) = d/dw [FW(w)]

Differentiating, we have,

fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

fW(w) = 0 for w < 0

Therefore, the PDF of W = X², when X has an exponential distribution with parameter λ, is given by,

fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

fW(w) = 0 for w < 0

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The above question is incomplete, the complete question is:

If X has an exponential (λ) PDF, what is the PDF of W = X² ?

Answer:

see the attachment photo!

Answer: there you go

Step-by-step explanation:

The Binary Search Tree is as follows:

                                                   E

                                            /            \

                                         S                T

                                        /                    \

                                      I                       W

                                   /                            \

                                A                               M

                              /                                    \

                             C                                     G

                              \

                                D

The set of letters is {I, D, S, A, E, T, C, G, M, W} and len (I, D, S, A, a) = 5

Binary Search Tree:The binary search tree based on the alphabetical ordering of the letters is:

post-order sequence is: C, D, A, G, M, I, W, T, S, E.

To draw the binary search tree for the given post-order sequence, follow the steps below:

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When the molecular equation, hydrochloric acid (aq) + barium hydroxide (aq) ⟶ barium chloride (aq) + water, is balanced using the smallest possible integer coefficients, the values of these coefficients are: 2, 1, 1, and 2.

When the molecular equation, bromine trifluoride (g) ⟶ bromine (g) + fluorine (g), is balanced using the smallest possible integer coefficients, the values of these coefficients are: 1, 1, and 3.

To balance the given molecular equation, we need to determine the smallest possible integer coefficients for each compound involved. Let's start with the first equation:

Hydrochloric acid (HCl) is a strong acid that dissociates in water to form H⁺ and Cl⁻ ions. Barium hydroxide (Ba(OH)₂) is a strong base that dissociates to form Ba²⁺ and OH⁻ ions.

The balanced equation is:

2 HCl(aq) + (1) Ba(OH)₂(aq) ⟶ (1) BaCl₂(aq) + 2 H₂O(l)

In this balanced equation, we have two hydrochloric acid molecules reacting with one barium hydroxide molecule to form one barium chloride molecule and two water molecules.

Now let's move on to the second equation:

Bromine trifluoride (BrF₃) is a molecular compound that decomposes into bromine (Br) and fluorine (F) gases.

The balanced equation is:

(1) BrF₃(g) ⟶  (1) Br₂(g) + 3 F₂(g)

In this balanced equation, one molecule of bromine trifluoride decomposes to form one molecule of bromine and three molecules of fluorine.

Overall, it is important to balance chemical equations to ensure the conservation of atoms and the law of mass conservation. By using the smallest possible integer coefficients, we can achieve a balanced equation that accurately represents the reaction.

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The total cost of the mirror based on its area is obtained as $9.80.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of the bathroom mirror can be found by multiplying its length and width -

Area = Length × Width

Area = 5 feet × 4 feet

Area = 20 square feet

Since the mirror sells for $0.49 per square foot, we can find the total cost of the mirror by multiplying the area of the mirror by the cost per square foot -

Total Cost = Area × Cost per square foot

Total Cost = 20 square feet × $0.49 per square foot

Total Cost = $9.80

Therefore, the total cost of the bathroom mirror will be $9.80.

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2x and 4x + 108 are supplementary angles and that means they add up to 180 degrees.

2x + 4x + 108 = 180

Combine like terms

6x + 108 = 180

Subtract 108 from both sides.

6x = 72

Divide both sides by 6

x = 12

Answer:Yes

Step-by-step explanation: It came because your asking questions that you have to gather data for.

We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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To find the differential equation for a family of curves, we need to find an equation that relates the variables involved in the curves. For example, consider the family of curves given by:

y = mx + c

where m and c are constants. To find the differential equation for this family of curves, we can take the derivative of both sides with respect to x:

dy/dx = m

This is the differential equation for the family of curves.

To find the family of orthogonal trajectories, we need to find a new family of curves that intersect the original family of curves at right angles. We can use the fact that the product of the slopes of two perpendicular lines is -1. So, if the differential equation for the original family of curves is:

dy/dx = f(x, y)

then the differential equation for the family of orthogonal trajectories is:

dy/dx = -1/f(x, y)

To find a specific orthogonal trajectory, we need to solve this differential equation for y as a function of x.

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The equation of the tangent line to the curve f(x) = x³ - 2x² + 2x at x = 1 is y = -1x + 1. To find the equation of the tangent line at a specific point on a curve, we need to determine the slope of the curve at that point.

The slope of the curve at x = 1 can be found by taking the derivative of the function f(x).

The derivative of f(x) = x³ - 2x² + 2x can be found using the power rule. Taking the derivative term by term, we get:

f'(x) = 3x² - 4x + 2.

Now, we can substitute x = 1 into the derivative to find the slope at x = 1:

f'(1) = 3(1)² - 4(1) + 2 = 3 - 4 + 2 = 1.

The slope of the curve at x = 1 is 1. Since the tangent line shares the same slope as the curve at the given point, we can write the equation of the tangent line using the point-slope form.

Using the point-slope form, we have:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point (1, f(1)) and m is the slope. Plugging in the values, we get:

y - f(1) = 1(x - 1).

Simplifying further, we have:

y - f(1) = x - 1.

Since f(1) is equal to the function evaluated at x = 1, we have:

y - (1³ - 2(1)² + 2(1)) = x - 1.

Simplifying,

y - 1 = x - 1.

Finally, rearranging the equation,

y = -1x + 1.

Therefore, the equation of the tangent line to the curve f(x) = x³ - 2x² + 2x at x = 1 is y = -1x + 1.

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The value of sin(u+v) given tan u = 15/8 is -9/221

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the their angles.

A right-angled triangle has 3 sides, hypotenuse, opposite and adjacent. The following should be noted:

Sin = Opposite / Hypothenuse

Tan = Opposite / Adjacent

Cos = Adjacent / Hypothenuse

When tan u = 15/8

Opposite = 15

Adjacent = 8

Hypothenuse will be:

= ✓(15² + 8²)

= ✓(225 + 64)

= ✓289

= 17

Therefore sin u = 15/17

When cos v = -5/13, it should be noted that sin v will be -12/13.

Therefore, sin(u + v) will be:

= 15/17 + (-12/13)

= 15/17 - 12/13

= 195/221 - 204/221

= -9/221

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Answer:

The object has to be moving

miles per hour to escape the moon's gravity.

Answer:

Step-by-step explanation:

The object has to be moving 1400 miles per hour to escape the moon's gravity.

Peer-reviewed (refereed or scholarly) journals: Before an article is published in a journal, it is examined by a number of other experts in the subject to guarantee that it is of a high caliber. (The paper is more likely to be valid from a scientific standpoint, draw fair conclusions, etc.)

Peer review has been conducted on the publications in a refereed journal. The papers were evaluated for quality by reputable academics or subject-matter experts before being approved for publication, so this tells us that they are of a high caliber. Also known as "scholarly" or "peer-reviewed," these pieces are published in journals.

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Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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so the time needed is 3.1 years