Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x = the average of the 49 races. Part (a) two decimal places.) Give the distribution of X. (Round your standard deviation to two decimal places)Part (b) Find the probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) __ min Part (d) Find the median of the average running times ___ min

The weight becomes 1/4 of its original value when the distance is multiplied by 2.

According to the question, "the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth." We need to determine the effect on the weight when the distance is multiplied by 2.

Let w be the weight of a body, d be the distance from the center of the earth, and k be the constant of variation. According to the question,

w = k / d²

When the distance is multiplied by 2, the new distance is 2d. Therefore, the new weight is given by:

w' = k / (2d)²

w' = k / 4d²

w' = w / 4

Therefore, the weight becomes 1/4 of its original value when the distance is multiplied by 2.

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Question 7. C (rectangular pyramid)

Question 8. 17 cm

Answer:

Question 7:C rectangular pyramid

Question 8: C 120 in

A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160

Step-by-step explanation:

In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.

To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].

This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).

To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).

We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).

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Tο shift the graph tο the right, we can simply add a pοsitive cοnstant tο the x values οf each pοint befοre plοtting them. Fοr example, if we want tο shift the graph tο the right by 2 units.

The intersectiοn οf twο number lines creates a twο-dimensiοnal plane knοwn as a cοοrdinate plane. The x-axis, a hοrizοntal number line, and the y-axis, a vertical number line, are twο examples οf these number lines.

Tο graph the equatiοn 5x - 3y = 18 οn a cοοrdinate plane, we can fοllοw these steps:

1. Sοlve fοr y in terms οf x:

5x - 3y = 18

-3y = -5x + 18

y = (5/3)x - 6

2. Chοοse sοme values fοr x and use the equatiοn tο find the cοrrespοnding y values. Fοr example, we can chοοse x = 0, 3, and 6:

When x = 0: y = (5/3)(0) - 6 = -6

When x = 3: y = (5/3)(3) - 6 = -3

When x = 6: y = (5/3)(6) - 6 = 2

3. Plοt the pοints (0, -6), (3, -3), and (6, 2) οn the cοοrdinate plane.

4. Draw a straight line passing thrοugh these three pοints. This line represents the graph οf the equatiοn 5x - 3y = 18.

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Over a year, the Blue Valley Glacier typically moves about the same distance as the Silver Lake Glacier, and Blue Valley has the same variability in its annual movement compared to Silver Lake.

The median annual movement of the Blue Valley Glacier is 300.2 feet, and the interquartile range is 14 feet.

The interquartile range indicates the spread of the data within the middle 50% of the data

So we know that the annual movement of the Blue Valley Glacier falls within a range of 300.2 ± 7 feet (i.e. 293.2 to 307.2 feet)

Similarly, the median annual movement of the Silver Lake Glacier is 300.4 feet, and the interquartile range is also 14 feet

So the annual movement of the Silver Lake Glacier also falls within a range of 300.4 ± 7 feet (i.e. 293.4 to 307.4 feet)

Since the ranges for both glaciers overlap and have the same size, we can conclude that they typically move about the same distance over a year, and that the variability in the annual movement of Blue Valley is comparable to that of Silver Lake.

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The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.

Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.

The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.

P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3

(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.

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To estimate the distance traveled  we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.

A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.

The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.

Using the trapezium rule, the estimated area of each strip is:

Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s

Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s

Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s

Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s

The total estimated area is the sum of the areas of the 4 strips:

Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s

Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:

Estimated distance traveled is = |-4000| = 4000 meters

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Answer:

b = [tex]\frac{S-2la}{h+l}[/tex]

Step-by-step explanation:

S = bh + lb + 2la ( reversing the equation )

bh + lb + 2la = S ( subtract 2la from both sides )

bh + lb = S - 2la ← factor out b from each term on the left side

b(h + l) = S - 2la ← divide both sides by (h + l)

b = [tex]\frac{S-2la}{h+l}[/tex]

The concentration of hydrogen ions in a liter of the sports drink is approximately 3.98 x 10^(-3) moles per liter.

The pH of a substance is a measure of its acidity or basicity and is defined as the negative logarithm (base 10) of the hydrogen ion concentration [H+]. The formula for pH is given as pH = -log[H+].

To find the concentration of hydrogen ions in a liter of a sports drink that has a pH of 2.4, we can use the formula pH = -log[H+]. Rearranging this formula, we get [H+] = 10^(-pH).

Substituting the given value of pH into this expression, we get [H+] = 10^(-2.4).

It's worth noting that the hydrogen ion concentration is related to the acidity of a solution; the higher the hydrogen ion concentration, the more acidic the solution. The pH scale ranges from 0 (most acidic) to 14 (most basic), with a pH of 7 being neutral. The sports drink in question has a relatively low pH, indicating that it is quite acidic.

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The value of x that makes the average between 3.15 and x equal to 40 is 76.85.

In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:

(3.15 + x) / 2 = 40

To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.

To solve for x, we can start by multiplying both sides of the equation by 2:

3.15 + x = 80

Next, we can subtract 3.15 from both sides of the equation:

x = 76.85

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The probability that more heads are tossed using coin A than coin B is 5/16.

The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.

P(E) = Number of favorable outcomes/ Total number of possible outcomes

Coin toss:

There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is

1/2 = 0.5.

Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.

Let's calculate the possible outcomes when coin A is tossed three times.

There are 2 possible outcomes when one coin is tossed.

Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8

Likewise, the possible outcomes when coin B is tossed two times are:

The number of possible outcomes = 2 * 2 = 4

Therefore, the total number of possible outcomes = 8 * 4 = 32

Now, we will find out the cases where the number of heads is more when coin A is tossed three times.

HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT

Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)

Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes

P = 10/32P = 5/16

Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.

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The statement "Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment" is false.

A binomial experiment is an experiment that is repeated multiple times with each repetition having only two potential outcomes. In a binomial experiment, the probability of success remains constant from trial to trial.

The criteria for a binomial experiment are as follows:

P(x) = (ⁿCₓ)(pˣ)(q^(n-x))

Where p is the probability of success, q is the probability of failure (q = 1 - p), and ⁿCₓ is the combination formula.

Therefore, the statement "Ten cards are selected out of a 52-card deck without replacement and the number of Jacks is observed. This is an example of a "Binomial Experiment" being false. This is because the probability of drawing a jack changes with each trial, as the deck's composition changes after each card is drawn.

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The Area of Bella's garden as required to be determined in the task content is the difference of the area of the rectangular backyard and the right triangular fish pond.

It follows from the task content that the area of Bella's trapezoidal garden is to be determined from the given information.

Since the garden and the fish pond are from the rectangular backyard; the sum of their areas is equal to the area of the backyard.

Ultimately, the area of the garden is the difference of the area of the rectangular backyard and the right triangular fish pond.

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Answer:

1. n=6

2. n=19

3. n=15

4. n=20

5. n=40

6. n=16

7. n=19

8. n=6

9. n=2.4

10. n=30

Step-by-step explanation:

remember the priorities :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

inside every category you go usually from left to right, but you can use the commutative property where applicable.

4 + 5 - 3 = 4 + 5 - 3 = 4 + 5 - 3 = 4 - 3 + 5 = 6

8×3 - 5 = 24 - 5 = 19

15/3 + 10 = 5 + 10 = 15

8 + 3 - 1×2 = 8 + 3 - 2 = 9

14×3 - 2 = 42 - 2 = 40

(3 + 5)×2 = 8×2 = 16

10 + 7 + 2×1 = 10 + 7 + 2 = 19

16/8 + 4 = 2 + 4 = 6

7 + 5/5 = 7 + 1 = 8

20/4×6 = 5×6 = 30

Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.

Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.

Here,

The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:

2 × (length + width) = 2 × (175 m + 96 m) = 542 m

Therefore, the cost of fencing the garden at 17.50 per meter is:

Cost of fencing = length of fence × cost per meter

= 542 m × 17.50

= 9485

Hence, the cost of fencing the garden is ₹9485.

To find the cost of plowing the garden, we need to first calculate its area, which is given by:

Area = length × width

= 175 m × 96 m

= 16800 m²

Therefore, the cost of plowing the garden at 4.50 paise per square meter is:

Cost of plowing = area of garden × cost per square meter

= 16800 m² × 0.045

= 756

Hence, the cost of plowing the garden is ₹756.

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Answer: 72°

Step-by-step explanation:

To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.

Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).

Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.

Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°

The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].

Given:

Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]

Expand the equation

[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]

[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]

[tex]5^2 = 25[/tex]

Then, substitute the expanded expressions into the equation

[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]

Simplify and combine like terms

[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]

Rearrange the equation so that one side is 0

[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.

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Answer:153

Step-by-step explanation:

The total volume of the sample is 0.0067 m³ and the density of the sample is 2753.73 kg/m³.

An ore sample weighs 18.5 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 N. When the ore sample is immersed in water, the tension in the cord is given as 11.8 N.

Thus, the buoyancy force experienced by the ore sample is given by the difference between the weight of the sample in the air and the tension in the cord.

Buoyancy force experienced by the ore sample = Weight of the sample in the air - Tension in the cord

Buoyancy force experienced by the ore sample = (18.5 N) - (11.8 N)

Buoyancy force experienced by the ore sample = 6.7 N

Also, we know that the weight of the ore sample in air is equal to the weight of the ore sample when immersed in water.

Weight of the ore sample = Weight of the displaced water

Weight of the ore sample = Buoyancy force experienced by the ore sample

Weight of the ore sample = 6.7 N

The density of the ore sample

Density is given by the formula Density = Mass/Volume

Where Density is measured in kg/m³

Mass is measured in kg

Volume is measured in m³

Also, the density of water is given as 1000 kg/m³.

The density of the ore sample = Mass/Volume

Mass = Density x Volume

Volume of the ore sample can be obtained from volume of the displaced water.

Volume of the displaced water = Weight of the ore sample/Density of water

Volume of the displaced water = (6.7 N)/(1000 kg/m³)

Volume of the displaced water = 0.0067 m³

Density of the ore sample = (18.5 N)/(0.0067 m³)

Density of the ore sample = 2753.73 kg/m³

Therefore, 0.0067 m³ is the sample's total volume and 2753.73 kg/m³ is the density of the sample.

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The zeroes of the function are -12 and 5.

Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.

According to the question:

To find the zeros of the function

f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.

So we start with the equation:

x² + 7x - 60 = 0

Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:

x² + 7x - 60 = (x + 12)(x - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x + 12 = 0 or x - 5 = 0

Solving for x, we get:

x = -12 or x = 5

The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.

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Answer: 198 families live farther than 1 mile from the square.

Step-by-step explanation:

We know that there are 238 families that live within 1 mile of the village square. To find the number of families that live farther than 1 mile from the square, we can subtract 238 from the total number of families:

436 - 238 = 198

Therefore, 198 families live farther than 1 mile from the square. We can do this subtraction mentally without needing a calculator.

Answer:

0% (0/40)

Step-by-step explanation:

I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food

The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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 The 32 ways to get a five-card combination containing two jacks and three aces.

(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.

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When evaluating a data set or statistics, the things to consider are sample size and data quality. It's important to consider these things because they provide insight into the validity of the data and the accuracy of the statistics that are being used.

When presented with a dataset or statistics, there are several things to consider.

Here are two examples of what you need to consider when evaluating a dataset or statistics:

1. Sample size: It's important to consider the sample size because small sample sizes are more likely to be biased. For example, a small sample size might be unrepresentative of a larger population. A sample size of 30 is commonly used to distinguish between small and large samples in statistics. Larger sample sizes are often more representative of the population and produce more reliable statistics.

2. Data quality: The quality of the data is also an important consideration. When evaluating statistics, you must ensure that the data is accurate, relevant, and up-to-date. This is important because using incorrect or outdated data can lead to incorrect conclusions. Additionally, if the data is missing or incomplete, you may not be able to get an accurate picture of the population that the dataset is supposed to represent. This can skew the results, making them less reliable or even completely useless. Therefore, data quality is an important consideration when evaluating statistics.

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The formula relating I and P is I = kP

a) When P= $800, then I = $48

b) When I = $72, then P = $1200

If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:

I = kP

where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:

I/P = 6/100 = 0.06 = k

Now we can use this value of k to answer the given questions,

a) When P = 800, the formula relating I and P is:

I = kP

I = 0.06 × 800

I = 48

Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.

b) When I = 72, the formula relating I and P is:

I = kP

72 = 0.06P

Solving for P:

P = 72/0.06

P = 1200

Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.

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Answer:

Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck​

Step-by-step explanation:

Let's start by subtracting the base fee from the total cost:

$143.43 - $16.95 = $126.48

Now, we can divide the remaining cost by the cost per mile:

$126.48 ÷ $0.93/mile ≈ 136 miles

Therefore, Stacy drove the truck for approximately 136 miles.

Answer:

not sure if this sign � was important did it the best way I could

Step-by-step explanation:

To solve this problem graphically, we will first set up a system of inequalities based on the given information:

x ≥ 8 (Fatoumata must work at least 8 hours lifeguarding)

y ≤ 12 - x (Fatoumata can work at most 12 total hours)

15x + 10y ≥ 140 (Fatoumata must earn a minimum of $140)

To graph these inequalities, we can plot the points (8,0), (12,0), and (0,14) on a coordinate plane and draw lines connecting them. The line between (8,0) and (12,0) represents the constraint on the number of hours Fatoumata can work, while the line between (8,0) and (0,14) represents the constraint on the amount of money she must earn. The shaded region that satisfies all three inequalities is the feasible region.

To find one possible solution, we can pick any point within the feasible region. One such point is (8,6), which represents working 8 hours lifeguarding and 6 hours tutoring. This point satisfies all three inequalities:

x ≥ 8 is true since x = 8

y ≤ 12 - x is true since y = 6 ≤ 12 - 8

15x + 10y ≥ 140 is true since 15(8) + 10(6) = 180 ≥ 140

Therefore, one possible solution is for Fatoumata to work 8 hours lifeguarding and 6 hours tutoring to earn at least $140 while not exceeding 12 total hours worked.

The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.

VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.

If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.

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The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.