A groundhog lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to double its distance under the surface. It then climbs straight down another 4 feet. Its final position is deeper than 10 feet under the surface.

What was the groundhog's original position, p, relative to the surface?

Enter your answer in the box to complete the inequality.

The probability that a randomly selected utility bill is,

a) P(X < 68) ≈ 0.016 or 1.6%

b) P(81 < X < 90) ≈ 0.1476 or 14.76%

c) P(X > 120) ≈ 0.0912 or 9.12%

To find the probability in each case, we can use the standard normal distribution by converting the given values into z-scores.

a) To find the probability that a randomly selected utility bill is less than $68, we need to find P(X < 68). First, we calculate the z-score using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (68 - 100) / 15 = -2.1333

Using a standard normal distribution table or a calculator, we can find the corresponding cumulative probability for z = -2.1333, which is approximately 0.016. Therefore, the probability P(X < 68) is approximately 0.016 or 1.6%.

b) To find the probability that a randomly selected utility bill is between $81 and $90, we need to find P(81 < X < 90). We calculate the z-scores for both values:

z1 = (81 - 100) / 15 = -1.2667

z2 = (90 - 100) / 15 = -0.6667

Using the standard normal distribution table or a calculator, we find the cumulative probability for z1 and z2: P(z1) ≈ 0.1038 and P(z2) ≈ 0.2514. Then, we subtract P(z1) from P(z2) to find the probability between the two values:

P(81 < X < 90) ≈ P(z1 < Z < z2) ≈ P(z2) - P(z1) ≈ 0.2514 - 0.1038 ≈ 0.1476 or 14.76%.

c) To find the probability that a randomly selected utility bill is more than $120, we need to find P(X > 120). We calculate the z-score:

z = (120 - 100) / 15 = 1.3333

Using the standard normal distribution table or a calculator, we find the cumulative probability for z = 1.3333, which is approximately 0.9088. Since we want the probability of X to be greater than 120, we subtract this value from 1:

P(X > 120) ≈ 1 - P(z) ≈ 1 - 0.9088 ≈ 0.0912 or 9.12%.

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This gives us a dendrogram with three levels, where the first level has two clusters {{7,10},{20,28}} and {35}, the second level has two clusters {{7,10,20,28},35}, and the third level has only one cluster {{7,10,20,28,35}}.

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

To perform hierarchical clustering using single linkage, we start by treating each point as its own cluster, and then iteratively merge the two closest clusters until only one cluster remains. We use the single linkage method, which defines the distance between two clusters as the minimum distance between any two points in the clusters.

First, we calculate the pairwise distances between each point:

  7    10   20   28   35

7   -    3    13   21   28

10  3    -    10   18   25

20  13   10   -    8    15

28  21   18   8    -    7

35  28   25   15   7    -

Next, we find the two closest points/clusters and merge them:

  7,10  20   28   35

7,10  -    10   18   25

20    10   -    8    15

28    18   8    -    7

35    25   15   7    -

The closest points/clusters are 7 and 10, so we merge them to form a new cluster {7,10}.

  7,10  20,28  35

7,10  -    18     25

20,28 18   -      7

35    25   7      -

The closest points/clusters are now {20,28} and 35, so we merge them to form a new cluster {{20,28},35}.

 7,10  {20,28,35}

7,10  -    7

{20,28,35} 7    -

The closest points/clusters are now {7,10} and {{20,28},35}, so we merge them to form a new cluster {{{7,10},{20,28}},35}.

Hence, This gives us a dendrogram with three levels, where the first level has two clusters {{7,10},{20,28}} and {35}, the second level has two clusters {{7,10,20,28},35}, and the third level has only one cluster {{7,10,20,28,35}}.

The dendrogram can be visualized as in the attached image.

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Answer:

c

Step-by-step explanation:

here they give you an angle C≅angle G,  then a side DG≅ side CA and then an angle A≅angle D  so is the

Angle-Side-Angle theorem or ASA

Answer:

11 ounces cost 9.90$.  

Step-by-step explanation:

Each ounce cost .90 cents.

Hope this helped!

Answer:

\(x {}^{3} \)

Step-by-step explanation:

\(\frac{(x {}^{5} )}{( {x}^{2} )}\)

\(x {}^{3} \)

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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Answer:

18 men = 36 tons in 6 hours

Step-by-step explanation:

3 men = 1 ton in 1 hour

6 men = 2 ton in 1 hour

9 men = 3 tons in 1 hour

with this you find a pattern

3 men = 2 tons in 2 hours

3 men = 3 tons in 3 hours

3 men = 6 tons in 6 hours

6 men = 12 tons in 6 hours

9 men = 18 tons in 6 hours

12 men = 24 tons in 6 hours

15 men = 30 tons in 6 hours

18 men = 36 tons in 6 hours

(This is how i worked it out)

Answer:

18 people

Step-by-step explanation:

Method A:

3 man-hours to stack 1 ton

36 tons is 36 times 1 ton, so it takes 36 times as long to stack.

36 * 3 man-hours to stack 36 * 1 ton, or

108 man-hours to stack 36 tons

To do the job in 6 hours instead of 108, you need to do 108/6 = 18 times as much work per hour, so you need 18 times as many people.

18 * 1 person = 18 people

Answer: 18 people

Method B:

1 person works 3 hours and stacks 1 ton. That same person works another 3 hours and stacks another ton. In a total of 6 hours, 1 person stacked 2 tons. Since you need 36 tons stacked in the same 6 hours, and 36 = 18 * 2, you need 18 times the number of people, so you need 18 people.

Answer:

3003

Step-by-step explanation:

This is a combination since the order doesn't matter

15 C 10

The formula

15!

-------

10! (15-10)!

15*14*13*12*11

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

5*4*3*2*1

3003

The answers are

picture 1 : all the options

Picture 2:  option b

picture 3: option d

picture 4: option e

picture 5: option A, B and E

A line segment refer to a lime that has known definite ends. This is used most times to represent shapes of definite lengths. such that the length of the line corresponds to the length of the shape the line segment represents

The answer is all the options

the line segment pm is equal to mp hence the answer is mp - option b

A ray is a line with arrow head pointing to a particular direction.

The correct option is option d

line yp is equal in length to py therefore the answer is py

The correct option is option e

A ray is a line with arrow head pointing to a particular direction

The correct options are option A, B and E

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Based on the information given, we can assume that when a coin is tossed 50 times, the difference between the number of heads and the number of tails is x. Additionally, we are told that the probability function p(x) is equal to 12.

To understand this better, we need to consider the probability of getting different values of x.

For example, if we get 25 heads and 25 tails, then x is equal to 0. If we get 30 heads and 20 tails, then x is equal to 10.

If we get 20 heads and 30 tails, then x is equal to -10.

Since we are told that p(x) is equal to 12, we can assume that the probability of getting any value of x is 12%. This means that the probability of getting x = 0, x = 10, or x = -10 is all 12%.

To find out the actual number of times we can expect to get each value of x, we need to use the binomial distribution formula.

This formula takes into account the number of trials (in this case, 50 coin tosses), the probability of success (getting heads), and the value of x.

Overall, the information given tells us that we can expect to get a difference of 10 more heads than tails or 10 more tails than heads about 12% of the time when tossing a coin 50 times.

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To calculate the amount of each monthly payment for a $150,000 mortgage at an interest rate of 6% per year with equal  payments for twenty years,  use the formula for the monthly payment on a mortgage.

The formula is: P = (r * PV) / (1 - (1 + r)^(-n))

Where: P = Monthly payment

r = Monthly interest rate (annual interest rate divided by 12)

PV = Present value or loan amount

n = Total number of payments (number of years multiplied by 12)

Let's calculate the monthly payment: PV = $150,000

r = 6% / 12 = 0.005 (monthly interest rate)

n = 20 years * 12 = 240 months

P = (0.005 * 150,000) / (1 - (1 + 0.005)^(-240))

P = (750) / (1 - (1.005)^(-240))

P ≈ $1,109.02

Therefore, the amount of each monthly payment for this mortgage would be approximately $1,109.02.

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a) f is strictly increasing function then f is one to one

b) f: R-> R such that f(x) = x^n where n is even is not one to one

suppose that f is strictly increasing function

we have to prove that f is one to one

let us assume f(x1) = f(x2)

we have to prove x1=x2

since f is strictly increasing function

then x2>x1 and x1> x2

this implies that x1=x2

and Hence f is one to one function

b) f:R->R such that f(x) = x^ n where n is even is not one to one

because f(1)= f( -1)

but -1 is not equal to 1 therefore f is not one to one function

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Step-by-step explanation:

since we have the slope and a point, let's start with the point-slope form first, and then we transform it into the slope-intercept form.

the general slope-intercept form is

y = ax + b

"a" being the slope and b the y-intercept (the y-value when x = 0).

the general point-slope form is

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is a point on the line.

so, in our case

y - -16 = -2(x - 6)

y + 16 = -2x + 12

y = -2x - 4

that's it.

Answer:

19.2

What is 40 percent (calculated percentage %) of number 48? Answer: 19.2.

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

40/100=0.4

0.4 *48=19.2

Question 5

1) Given

2) Definition of congruent segments

3) Reflexive property of equality

4) Addition property of equality

5) Substitution

6) Commutative property of addition

7) Segment addition postulate

8) Substitution

9) Segments with equal measure are congruent

Question 6

1) Given

3) Segment addition postulate

4) Substitution

5) Subtraction property of equality

7) SSS

The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.

Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.

The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

Considering that,

We need to find for the peripheral income capability, find the interest capability.

Recollect that the pay is zero assuming no things are sold:

R'(x) = 0.06x² - 0.05x + 138

p(x) is what.

That's what we know,

MR = dTR/dx = 0.06x² - 0.05x + 138

Incorporating the marginal revenue function , we get complete income capability,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x

= (0.06x³)/3 - (0.05x²)/2 + 138 x

TR = 0.02 x³ - 0.025 x² + 138 x

TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x

P = ( 0.02 x³ - 0.025 x² + 138 x)/x

P = 0.02x² - 0.025x + 138

In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

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The hypotenuse is cm and the two other sides are cm and cm. The area of the triangle is (cm²) / 2.

To work out the area of a triangle, we can use the formula:

area = (base x height) / 2.
Given that one side of the triangle is perpendicular to the base and measures cm,

we can consider this as the height of the triangle.
Let's label the base as b and the height as h.
From the given information, we know that the base of the triangle is cm. So, b = cm.
To find the height, we need to use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is cm and the two other sides are cm and cm.
Applying the Pythagorean theorem, we have: cm² = cm² + cm².
Simplifying the equation, we get: cm² = cm².
Now, we can solve for cm: cm² - cm² = 0.
Therefore, cm = cm.
Now, we have the base (b = cm) and

the height (h = cm). Plugging these values into the formula, we have:
Area = (base x height) / 2 = (cm x cm) / 2.
Simplifying further, we get:
Area = (cm²) / 2.
As we need to give our answer in the form where A is an integer.

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The complete question is,

________is a triangle. is perpendicular to . cm, cm, cm work out the area of triangle . give your answer in the form where is an integer.

Answer:

90 in

Step-by-step explanation:

360/60 = 6

15*6 = 90

Answer: You have awnsered a & b, but when you fill out the equation, you get y=30.

Step-by-step explanation:

* y= 4(7) + 2

* y= 28 + 2

* y= 30

(a) \($\frac{\partial Q}{\partial x}\)\(-\)\(\frac{\partial P}{\partial y} = 0$\), and the line integral of \($F.dr$\) around any closed curve is zero.

(b) \($\oint_C F.dr = ab\int_{0}^{2\pi} (\cos^2 t - \sin^2 t)e^{b\sin t} dt$\)cannot evaluate the line integral of F.dr around the given closed curve using Green

(a) We want to use Green's theorem to evaluate the line integral of F.dr around the circle \($x^2 + y^2 = a^2$.\)

Green's theorem states that:

\($\oint_C F.dr = \iint_R (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) dA$\)

where \($F = P\hat{i} + Q\hat{j}$\) is a vector field,\($C$\) is a closed curve in the plane, and \($R$\) is the region bounded by\($C$\).

In this case, we have:

\($F = y\hat{i} - x\hat{j}$\)

\($P = 0$\)and\($Q = y$\)

\($\frac{\partial Q}{\partial x}\) = 0 and \($\frac{\partial P}{\partial y} = 0$\)

Therefore, \($\frac{\partial Q}{\partial x}\)\(-\)\(\frac{\partial P}{\partial y} = 0$\), and the line integral of \($F.dr$\) around any closed curve is zero.

(b) We want to use Green's theorem to evaluate the line integral of\($F.dr$\)around the closed curve C defined by\($x = a\cos t$, $y = b\sin t$, $0 \leq t \leq 2\pi$.\)

Green's theorem states that:

\($\oint_C F.dr = \iint_R (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) dA$\)

where \($F = P\hat{i} + Q\hat{j}$\) is a vector field, C is a closed curve in the plane, and R is the region bounded by C.

In this case, we have:

\($F = xe^{y}\hat{i} + (ye^{y} + e^{y})\hat{j}$\)

\($P = xe^{y}$\)and \($Q = ye^{y} + e^{y}$\)

\($\frac{\partial Q}{\partial x}\)= 0 and \($\frac{\partial P}{\partial y} = xe^{y} + e^{y}$\)

Therefore,

\($\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = -xe^{y}$\)

The region R enclosed by C is an ellipse with semi-axes a and b, and its area is given by\($A = \pi ab$\). Using polar coordinates, we have:

\($x = a\cos t$\)

\($y = b\sin t$\)

\($\frac{\partial x}{\partial t} = -a\sin t$\)

\($\frac{\partial y}{\partial t} = b\cos t$\)

\($dA = \frac{\partial x}{\partial t} \frac{\partial y}{\partial t} dt = -ab\sin t \cos t dt$\)

Thus, we have:

\($\oint_C F.dr = \iint_R (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) dA = \int_{0}^{2\pi} \int_{0}^{ab} (-xe^{y}) (-ab\sin t \cos t) drdt$\)

\($= ab\int_{0}^{2\pi} (\cos^2 t - \sin^2 t)e^{b\sin t} dt$\)

This integral does not have a closed-form solution, so we need to use numerical methods to approximate its value.

Therefore, we cannot evaluate the line integral of F.dr around the given closed curve using Green

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To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.

By calculating,

600/10=60 and 59 students which is less than 10% of the population.

A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.

Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values

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The mean of the random variable x, which represents the number of rotten apples chosen, is 1.2, and the standard deviation is approximately 0.979.

What is standard deviation?

Standard deviation is a statistical measure that quantifies the dispersion or variability of a dataset. It indicates how much individual data points differ from the mean value. A larger standard deviation suggests greater diversity, while a smaller value indicates less variability within the dataset.

To calculate the mean, we multiply the probability of selecting a rotten apple (4/10) by the total number of apples chosen (3). Mean = (4/10) * 3 = 1.2.

To calculate the standard deviation, we need to find the variance first. The variance is the sum of the probabilities of each possible outcome multiplied by the square of the difference between that outcome and the mean.

The possible outcomes are 0, 1, 2, or 3 rotten apples chosen. The probabilities for each outcome are:

P(x=0) = (6/10) * (5/9) * (4/8) = 0.3333

P(x=1) = (4/10) * (6/9) * (5/8) = 0.3333

P(x=2) = (4/10) * (3/9) * (6/8) = 0.2000

P(x=3) = (4/10) * (3/9) * (2/8) = 0.0667

Now, we calculate the variance:

Variance = (0² * 0.3333) + (1² * 0.3333) + (2² * 0.2000) + (3² * 0.0667) - mean²

= (0 * 0.3333) + (1 * 0.3333) + (4 * 0.2000) + (9 * 0.0667) - 1.2^2

= 0.6666 + 0.3333 + 0.8000 + 0.6003 - 1.44

= 1.4 - 1.44

= -0.04

Finally, the standard deviation is the square root of the variance:

Standard deviation = sqrt(-0.04) = approximately 0.979

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Simple random sampling is a frequently chosen for its simplicity and periodicity.

What is frequently ?

Frequently refers to something that happens or occurs often or many times. It is an adverb that describes the regularity of an action or event, indicating that it happens with a high frequency or on a regular basis.

Simple random sampling is a random sampling technique that is frequently chosen by researchers for its simplicity and its periodic quality. This technique involves randomly selecting a sample from a larger population, with each individual in the population having an equal chance of being selected. Simple random sampling is considered to be an unbiased and efficient method for selecting a representative sample, and it is often used as a benchmark for comparing other sampling methods.

Simple random sampling is a frequently chosen for its simplicity and periodicity.

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Answer:

C

Step-by-step explanation:

Fractions cant be integers

The equation of the line through the point (-6,5) and parallel to the line is    y=\(\frac{1}{2}\)x-7 is y=\(\frac{1}{2}\)x+8.

What is equation of line ?

Any location with an x and y axis can have a line equation constructed using the slope of the line. To build a line with a certain point, one uses the equation for a straight line. Any two points can be used to find the slope. Slope is the part of a straight line that is steep.

Here the given equation is y=\(\frac{1}{2}\)x-7

We know that equation of line is y=mx+c , where m = slope.

Then slope of given line is m= 1/2 . Now the line is parallel to given line so slope of the equation is also equal.

=> slope m=1/2.

Now the given point \((x_1,y_1)=(-6,5)\) .

Using equation of the line is ,

=> \(y-y_1=m(x-x_1)\)

=> y-5 = 1/2(x+6)

=> 2y-10=x+6

=>2y=x+16

=>y=\(\frac{1}{2}\)x+8

Hence the equation of the line is y=\(\frac{1}{2}\)x+8.

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Randy should begin his homework by 07:10 in order to sleep by 10:00

The given parameters are:

If the above activities are done, the time spent would be:

Time = 45 minutes + 40 minutes + 1 hour and 15 minutes + 10 minutes

Add the time

Time =  2 hour and 50 minutes

He wants to go to bed by 10:00.

So, the time to begin his homework is:

Begin = 10:00 - 2 hour and 50 minutes

Evaluate the difference

Begin = 07:10

Hence, Randy should begin his homework by 07:10

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Answer:

I thank it is 12 4/5

Step-by-step explanation:

hope this helps if not please let me now and dont worry about  brainliest my main focus is just helping people.