In a special triathlon, Betty swam 1 mile in 25 minutes, biked 30 miles in 45 minutes, and then ran 6 miles in 40 minutes. What was her "average" speed for the race? (Round your answer to the nearest whole number. )

Answer:

If you want them at the same exact point then since the theif is 9 steps ahead it

will take 3 seconds

Step-by-step explanation:

Robber:

starts at 9

starts at 9add on 5 and you get 14

starts at 9add on 5 and you get 14add 5 more you get 19

starts at 9add on 5 and you get 14add 5 more you get 19and another 5 would give you 24

Police:

is at 0 meters

add 8 any you get 8

add 8 more and you get 16

and another 8 would get you to 24

Yes, the integral test can be applied to the series [∞] \(1/4^n\) n = 1 because the terms of the series are positive, decreasing, and approaching zero as n approaches infinity.

To use the integral test, we need to find a function f(x) that is continuous, positive, and decreasing such that f(n) = \(1/4^n\) for all n ≥ 1. A good choice for f(x) is f(x) = \(1/4^x\).
Then, we can evaluate the integral from 1 to infinity of f(x) dx:
∫1 to infinity (\(1/4^x\)) dx = [(\(1/4^x\)) / ln(4)] evaluated from 1 to infinity
= [0 - (\(1/4^1\))] / ln(4)
= (1/4) / ln(4)
Since this integral converges, by the integral test, we can conclude that the series [infinity] \(1/4^n\) n = 1 also converges.
Therefore, we can say that the series [∞] \(1/4^n\) n = 1 is a convergent series.

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a) To find the probability that the mouse weighs less than 332 grams is calculated using the z-score formula which is: z= (x-μ)/σ where, x=332μ=409σ=24z= (332−409)/24z=−3.21

Hence, P (x < 332) = P (z < -3.21)

The probability that the mouse weighs less than 332 grams is approximately equal to 0.0007. Therefore, the answer is 0.0007 (rounded to four decimal places).

b) To find the probability that the mouse weighs more than 480 grams is calculated using the z-score formula which is: z= (x-μ)/σwhere,x=480μ=409σ=24z= (480−409)/24z=2.96

Hence, P (x > 480) = P (z > 2.96)

The probability that the mouse weighs more than 480 grams is approximately equal to 0.0015. Therefore, the answer is 0.0015 (rounded to four decimal places).

c) To find the probability that the mouse weighs between 332 and 480 grams is calculated using the z-score formula which is: P (332 < x < 480) = P (-3.21 < z < 2.96)

Hence, the probability that the mouse weighs between 332 and 480 grams is approximately equal to 0.9980. Therefore, the answer is 0.9980 (rounded to four decimal places).

d) The probability of a randomly chosen mouse weighing less than 332 grams is found to be P (x < 332) = 0.0007 which is less than 5%. Therefore, it is unlikely that a randomly chosen mouse would weigh less than 332 grams. Hence, the answer is "Yes, the likelihood is less than 5%".

e) To find the cutoff for the heaviest 6% of this type of mouse can be done by using the Z-table, that gives the z-score for any given probability. For the heaviest 6%, we need to find the z-score corresponding to a probability of 0.94 (100% - 6%). Hence, the Z-score for 0.94 probability is 1.55. Cutoff weight = μ + Z-score * σ= 409 + 1.55 * 24 = 447.2 ≈ 447 (rounded to the nearest whole gram). Therefore, the answer is 447 (rounded to the nearest whole gram).

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To send the frequency distribution data to Excel, you can follow these steps:

1. Open Excel on your computer.

2. Create a new worksheet or open an existing one where you want to import the data.

3. Label the first column as "Number of Tests Performed" and the second column as "Number of Patients".

4. In the first column, enter the values 0, 1, 2, 3, and 4 or more in separate cells, corresponding to the number of tests performed.

5. In the second column, enter the corresponding values 14, 8, 4, 4, and 2, which represent the number of patients for each category of tests.

6. Select both columns by clicking and dragging over the cells.

7. Go to the "Copy" option in the Excel toolbar or use the Ctrl+C keyboard shortcut to copy the selected data.

8. Switch to the Excel worksheet where you want to paste the data.

9. Select the first cell where you want to paste the data.

10. Right-click on the cell and choose the "Paste" option or use the Ctrl+V keyboard shortcut to paste the data.

Now, the frequency distribution data from the emergency room tests should be successfully transferred to Excel.

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By applying Fermat's Little Theorem, we have proven that for any integer a and prime number p, p divides both a^p + (p−1)!a and (p−1)!a^p + a. This result provides a proof based on the properties of prime numbers and modular arithmetic.

To prove that for a∈Z, p∣a^p + (p−1)!a and p∣(p−1)!a^p + a, where p is a prime number, we can use Fermat's Little Theorem.

First, let's consider the expression a^p + (p−1)!a. We know that p is a prime number, so (p−1)! is divisible by p. This means that we can write (p−1)! as p⋅k, where k is an integer.

Now, substituting this value into the expression, we have a^p + p⋅ka. Factoring out an 'a' from both terms, we get a(a^(p−1) + pk).

According to Fermat's Little Theorem, if p is a prime number and a is any integer not divisible by p, then a^(p−1) is congruent to 1 modulo p. In other words, a^(p−1) ≡ 1 (mod p).

Therefore, we can rewrite the expression as a(1 + pk). Since p divides pk, it also divides a(1 + pk).

Hence, we have shown that p∣a^p + (p−1)!a.

Now, let's consider the expression (p−1)!a^p + a. Similar to the previous step, we can rewrite (p−1)! as p⋅k, where k is an integer.

Substituting this value into the expression, we have p⋅ka^p + a. Factoring out an 'a' from both terms, we get a(p⋅ka^(p−1) + 1).

Using Fermat's Little Theorem again, we know that a^(p−1) ≡ 1 (mod p). So, we can rewrite the expression as a(1 + p⋅ka).

Since p divides p⋅ka, it also divides a(1 + p⋅ka).

Therefore, we have shown that p∣(p−1)!a^p + a.

In conclusion, using Fermat's Little Theorem, we have proven that for any integer a and prime number p, p divides both a^p + (p−1)!a and (p−1)!a^p + a.

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Answer:

C

Step-by-step explanation:

It is the easiest to simplify

Answer: It’s D I but C but it was wrong.

Answer:

Step-by-step explanation:

The rule for a rotation by 270° about the origin is:

Coordinates of ABCD:

Coordinates of the image:

Answer:

A'(1,-1)  , B'(3,-2)  , C'(3,-4)  , D'(1,-5)

These are correct answers hope this helps. :)

Step-by-step explanation:

The cost of storing the particles on the fourth day is approximately $232.50.

The decay of 200 particles of a particular radioactive substance is given by y = 200(0.93)ˣ

To find the cost of storing the particles on the fourth day, we first need to calculate how many particles are left on the fourth day.

Substituting x = 4 into the equation y = 200(0.93)ˣ, we get

y = 200(0.93)⁴ ≈ 154.98

So, approximately 155 particles are left on the fourth day.

Now, we can calculate the cost of storing the particles on the fourth day by multiplying the number of particles by the cost per particle

155 particles × $1.50/particle/day = $232.50

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The given question is incomplete, the complete question is:

The decay of 200 particles of a particular radioactive substance is given by y = 200(0.93)ˣ, where x is the number of days and y is the number of particles remaining. It costs the laboratory $1.50 per day to store each particle. What is the cost of storing the particles on the fourth day?

Answer:

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

Distance = √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2

Substitute the actual values of the points into the distance formula.

√ ( ( − 1 ) − 2 ) 2 + ( 4 − ( − 9 ) ) 2

Simplify.

√ 178

The result can be shown in multiple forms.

Exact Form:

√ 178

Decimal Form:

13.34166406 …

:) Hope this helped!! :)

Answer:

The millimeter.

Step-by-step explanation:

The best choice here is the millimeter (mm).

To solve the indefinite integral ∫(e²x + 2)² dx, we can perform a substitution by letting U = e²x + 2. This transforms the integral into ∫U² du, which can be integrated using the power rule of integration.

Let's start by performing the substitution:

Let U = e²x + 2, then du = 2e²x dx.

The integral becomes ∫(e²x + 2)² dx = ∫U² du.

Now we can integrate ∫U² du using the power rule of integration. The power rule states that the integral of xⁿ dx is (xⁿ⁺¹ / (n + 1)) + C, where C is the constant of integration.

Applying the power rule, we have:

∫U² du = (U³ / 3) + C.

Substituting back U = e²x + 2, we get:

∫(e²x + 2)² dx = ((e²x + 2)³ / 3) + C.

Therefore, the indefinite integral of (e²x + 2)² dx is ((e²x + 2)³ / 3) + C, where C is the constant of integration.

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Santiago used 185 cell phone minutes over the course of a month.

To determine the total number of cell phone minutes that Santiago used over the course of a month, you would use the operation of addition.

You would add up the number of minutes that Santiago spoke with his mom, dad, and friends:

Total cell phone minutes = 45 minutes + 30 minutes + 110 minutes

Total cell phone minutes = 185 minutes

Therefore, Santiago used 185 cell phone minutes over the course of a month.

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hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

Therefore, the probability of rolling at least one 3 is11/ 36.

Probability is a branch of mathematics that deals with the study of arbitrary events and their liability of circumstance. It involves the dimension and analysis of the liability of various events being. The probability of an event is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In other words, probability is the measure of the liability of an event being. It's calculated as the rate of the number of favorable issues to the total number of possible issues. Probability plays an important part in various fields analogous as wisdom, engineering, finance, and statistics, and is used to model and predict issues of uncertain events.

a) The sample space of rolling two six- sided bones can be listed as follows, where each ordered brace represents the outgrowth of the two rolls

\({(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),\)

\((2,1), (2,2), (2,3), (2,4), (2,5), (2,6),\)

\((3,1), (3,2), (3,3), (3,4), (3,5), (3,6),\)

\((4,1), (4,2), (4,3), (4,4), (4,5), (4,6),\)

\((5,1), (5,2), (5,3), (5,4), (5,5), (5,6),\)

\((6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}\)

b) There are 6 possible issues where Lydia rolls couple of the same number (,1), (,2), (,3), (,4), (,5), and (,6). Since there are 36 total possible issues, the probability of rolling a brace of the same number is6/36, which simplifies to1/6.

c) To calculate the probability that at least one number will be a 3, we need to count the number of issues in which at least one bones shows a 3, and peak by the total number of issues. There are 11 issues in which at least one bones shows a 3(,1), (,2), (,4), (,5), (,6), (,3), (,3), (,3), (,3), (,3), and(,3). therefore, the probability of rolling at least one 3 is11/36.

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Answer:

Step-by-step explanation:

domain = x

range = y

when the domain is -1

y = 2(-1) - 3

y = -2 - 3

y = -5

range is -5

When the domain is 0

y = 2(0) - 3

y = 0 - 3

y = -3

range is -3

when the domain is 5

y = 2(5) - 3

y = 10 - 3

y = 7

range is 7

The range is { -5, -3, 7 }

Answer:

1/7

Step-by-step explanation:

6 + 5 + 4 = 15

There are 15 marbles to start with.

p(event) = (number of desired outcomes)/(total number of outcomes)

First pick (there are 6 desired outcomes out of a total of 15 possible outcomes):

p(r) = 6/15

Now there are 5 red marbles left and a total of 14 marbles left.

Second pick (there are 5 desired outcomes out of a total of 14 possible outcomes):

p(r) = 5/14

These events are independent, so we multiply the two probabilities.

p(r, r) = 6/15 × 5/14

p(r, r) = 3/7 × 1/3

p(r, r) = 1/7

Answer:

m∠8 = 45°

Step-by-step explanation:

Answer:

2 + 2x = 262x = 24x=12 3.

Step-by-step explanation:

i think its right

We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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Answer:

28 is the total surface area!!

Step-by-step explanation:

A = 2(wl + hl + hw)

Answer:

1/-2

Step-by-step explanation:

To find the slope:

rise/run

From point to point

So....

From (-1,0)

you go up 2(2)

then left 4(-4)

to get to (-5,2)

so 2/-4 reduced is 1/-2

The equivalent value of sin{D} is -

sin{D} = √13/10.

Given is a right angled triangle.

In the given right angle triangle, we can use the Pythagoras theorem as -

{FD}² = {√13}² + {√87}²

{FD}² = 13 + 87

{FD}² = 100

FD = 10

So, we can write that -

sin{D} = √13/10

Therefore, the equivalent value of sin{D} is -

sin{D} = √13/10.

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Answer:

1.01 teaspoons is equal to 5 ml

Step-by-step explanation:

it goes up by ( 0.202884 )

1 ml 0.202884 tsp

2 ml 0.405768 tsp

3 ml 0.608653 tsp

4 ml 0.811537 tsp

5 ml 1.0144 tsp

6 ml 1.2173 tsp

7 ml 1.4202 tsp

Hope This Helped

Answer: $10

Step-by-step explanation:

Angie buys = 1 software package and 1month of gameplay.

Kenny buys = 1 software package and 2 months of game play.

Cost of each software package = $30. Total cost = ​$90​

The total cost is the addition of what Kenny and Angie bought. This will be:

(1 SF + 1 G) + (1 SF + 2 G) = 90

where,

SF = software package = 30

G = game

(1 SF + 1 G) + (1 SF + 2 G) = 90

30 + 1G + 30 + 2G = 90

60 + 3G = 90

3G = 90 - 60

3G = 30

G = 30/3

G = 10

One month of game play cost $10

Answer: 6 liters

Step-by-step explanation:

24 liters

He sells 75%

24 x 0.75 = 18 liters

24 - 18 = 6

He still has 6 liters left

Hello !

Answer:

\(\Large \boxed{\sf x=-11}\)

Step-by-step explanation:

We want to find the value of x that satisfies the following equation :

\(\sf 5x+2=4x-9\)

Let's isolate x !

First, substract 4x from both sides :

\(\sf 5x+2-4x=4x-9-4x\\x+2=-9\)

Now let's substract 2 from both sides :

\(\sf x+2-2=-9-2\\\boxed{\sf x=-11}\)

Have a nice day ;)

Hello!

5x + 2 = 4x - 9

5x - 4x = - 9 - 2

x = -11

Answer:17/3 or 5 and 2/3

Answer:

volume of a cylinder = π r^2 *h

108π=π*r^2*h

108=r^2*h

12=r^2

3.464=r

radius =3.464

Step-by-step explanation:

Brainliest would be appreciated

Ask for questions!

Answer:

The length of the cylinder's radius is 3

Step-by-step explanation:

A cylinders radius is found by the formula, r= √ v/πh

So, 108π/πh.

Because there is pi in both the numerator and denominator, we can cancel them out. This leaves the equation to be : r = √ 108/12.

r = √ 108/12

108/12 is 9.

r = √9

r = 3