Brandon is an amateur marksman. When he takes aim at a particular target on the shooting range, there is a 0.1, point, probability that he will hit it. One day, Brandon decides to attempt to hit 10 such targets in a row.

Assuming that Brandon is equally likely to hit each of the 10 targets, what is the probability that he will hit at least one of them?

Please show me the question and I am gonna answer It

Answer:

Triangles A B C and X Y Z are shown. The length of side A B is 6 and the length of side B C is 5. The length of side X Y is 1.5, the length of side Y Z is 1.25, and the length of X Z is 1. Angles A B C and X Y Z are congruent. Angles B C A and Y Z X are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C. Line m is shown below both triangles.

Which sequence of transformations could map △ABC to △XYZ?

wrong answer a reflection across line m and a dilation  

wrong answer a dilation by One-fourth and a reflection across line m

wrong answer a rotation about C and a dilation

Right answer a dilation by One-fourth and a translation

Step-by-step explanation:

Answer:

a dilation by One-fourth and a translation

Step-by-step explanation:

Answer:

Each person runs 3 miles in a relay race.

Step-by-step explanation:

Given:

Distance of Relay race m = 12 miles.

The expression m divided by 4 is the  distance each person runs in a relay race that is m miles.

Each person runs in relay race = [tex]\frac{m}{4}[/tex]

Now given the total distance of the relay race is 12 miles.

i.e. value of m = 12 miles

Now substituting the value of m in above equation we get;

Each person runs in relay race = [tex]\frac{m}{4} = \frac{12}{4}=3 \ miles[/tex]

Hence each person runs 3 miles in a relay race.

Answer:

the 3rd one (:

Step-by-step explanation:

Answer:

First One:

x { 6, 9, 12, 15, 18 }
y { -14, -4, 8, 22, 38 }

Step-by-step explanation:

Not sure if the other guy is trolling...
The x values constantly rise by 3, so we find the y value change
The differences are 10, 12, 14, 16
If we do it again we get 2, 2, 2. So since we did the reduction 2 times, this is a quadratic function.
Why isn't "the third one"
Constant rise by 2

Change of 9, 9, 9, 9
This is one reduction, so it is not quadratic.

Answer:

[tex]x= +2\sqrt{5} or -2\sqrt{5}[/tex]

Step-by-step explanation:

for the given equation,

[tex]4 - x^{2} = -16[/tex]

using rules of equation and inverse operations as isolating x on one side of equation,

interchanging sides  of equation  we get,

[tex]x^{2} =20[/tex]

[tex]x= +\sqrt{20} or x= -\sqrt{20}[/tex]

[tex]x= +2\sqrt{5}  or x= -2\sqrt{5}[/tex]

Answer:

The population of this country in 11 years will be 76972702.82

Step-by-step explanation:

The population of this country in 11 years can be calculated using the formula

Population in 11 years =  Starting population x [tex](1+growth rate)^{period}[/tex]

Thus

Population in 11 years =50000000×[tex](1+0.04)^{11}[/tex] =76972702.82

The population of this country in 11 years will be 76.97 million.

In order to determine the population of a country in 11 years, this formula would be used:

FV = P (1 + r)^n

50 million x (1 + 0.04)^11

= 50 million x (1.04)^11

= 76.97 million

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Answer:

D = 360

Step-by-step explanation:

Number of monsters that arrive at the theater = 6

Total number of arrangement for the 6 mobsters = 6!

= 6*5*4*3*2*1

= 720

The chance that Frankie will be behind Joey is half while the chance that Joey will be behind Frankie is half.

Since Frankie wants to stand behind joey in the line though not necessarily behind him, the arrangement can be done in 6!/2 ways

= (6!) 1/2

= 720/2

= 360 ways

Answer:

Step-by-step explanation:

You have to assume the the marked lines are parallel.

Alternate exterior angles are congruent, so ...

  (15x -26)° = (12x +1)°

  3x = 27 . . . . . . divide by °, add 26-12x

  x = 9 . . . . . . . . .divide by 3

Then the alternate exterior angles are ...

  (12·9 +1)° = 109°

___

The angle at upper right is vertical with the obtuse interior angle of the triangle whose other interior angles are marked. The sum of them is 180°, so we have ...

  28° +109° +(4y -9)° = 180°

  4y = 52 . . . . . . divide by °, subtract 128

  y = 13 . . . . . . . . divide by 4

Then the third interior angle of the triangle is ...

  (4·13 -9)° = 43°

Answer:

Step-by-step explanation

so the probability of not getting 2 first is 5/6, and this happens six times so we do (5/6)^6 and this is 0.33489797668 , or 33%, so A.

The formula for the expected value would be:

Expected Value = (Probability of Winning)*(Prize if won) + (Probability of not winning)*(Prize if not won)

The price you get if you don't win is 0, so we can ignore the 2nd term. Now, the probability of winning is 1/1000, because you bought 1 ticket out of 1000. Since the prize is $500:

Exp. Value = (1/1000)*500 = $0.50 , so its D

I hope this helps!

Answer:

1). A 33%

2). D $-0.50

Step-by-step explanation:

1).  The probability of not getting a 2 first is 5/6 that is 1-1/6=5/6 = 0.8333

number of occurrence is 6

probability = (5/6)^6

= 0.8333^6

= 0.33489797668 ,

= approximately 0.33 to two decimal place

= 33%

The formula for the expected value would be:

Expected Value = (Probability of Winning)*(Prize if won) + (Probability of not winning)*(Prize if not won)

The price you get if you don't win is 0,

so expected value = (probability of winning)*(prize if won)

So, the probability of winning is 1/1000, because you bought 1 ticket out of 1000.

Since the prize is $500:

Exp. Value = (1/1000)*500 = $0.50 , so its D

Answer:

Step-by-step explanation:

Alice borrowed 16700 from the bank at a simple interest rate of 9% to purchase a used car. It means that the interest is not compounded. Simple interest is usually expressed per annum. The formula for simple is

I = PRT/100

Where

I = interest

P = principal(amount borrowed from the bank)

R = 9% ( rate at which the interest is charged

T = number of years

At the end of the loan,she had paid a total of 24215. This means that the interest + the principal = 24215

Therefore,

The interest = 24215 - 16700 = 7515

Therefore

7517 = (16700 × 9 × t)/100

751700 = 150300t

T = 751700/150300

T = 5 years

Converting 5 years to months,

1 year 12 months

5 months = 12 × 5 = 60 months

Final answer:

Alice's car loan was for 60 months. This was calculated using the simple interest formula and the total interest paid, which was the difference between the total amount paid and the principal amount borrowed.

Explanation:

To determine how many months the car loan was, we can use the simple interest formula, I = PRT, where:

Alice borrowed $16,700 at a rate of 9%, and the total amount paid was $24,215. The total interest paid is the total amount minus the principal, which is $24,215 - $16,700 = $7,515.

Using the formula, we get:

Thus, Alice's car loan was for 60 months.

Answer: Choice B) -5.2 degrees

=====================

Work Shown:

Add up the given temperatures

-42 + (-17) + 14 + (-4) + 23 = -26

Then divide by 5 since there are 5 values we're given

-26/5 = -5.2

Answer:

The true statement is that the expression is satisfied for n = -2.

Step-by-step explanation:

Given:

[tex]4n = \frac{1}{2}\times (2n-12)[/tex]

To check:

Left hand side = Right-hand side ( for n = -2)

Proof :

For n = -2

Consider  Left hand side of the equation given above.

∴ Left hand side = 4n

                            = 4×(-2)   ......................for n = -2

                            = -8

Consider Right-hand side of the equation given above

∴ Right-hand side = [tex]\frac{1}{2}\times (2n-12)[/tex]

                              [tex]=\frac{1}{2}\times (2\times(-2) - 12) \\= \frac{1}{2}\times (-4 - 12)\\ =\frac{1}{2}\times (-16)\\ =-8[/tex]

Now we get Left hand side equal to Right hand side

i.e. Left hand side = Right hand side

i.e. [tex]4n = \frac{1}{2}\times (2n-12)[/tex] is true for n = -2

Answer:

The probability of cured people in who took the remedy is 8/9.

Step-by-step explanation:

Success rate of the cold remedy = 88%

The number of people who took the remedy = 45

Now, 88% of 45 = [tex]\frac{88}{100}  \times 45 = 39.6[/tex]

and 39.6 ≈ 40

So, out of 45 people, the remedy worked on total 40 people.

Now, let E: Event of people being cured by cold remedy

Favorable outcomes = 40

[tex]\textrm{Probability of Event E}  = \frac{\textrm{Total number of favorable outcomes}}{\textrm{Total outcomes}}[/tex]

or, [tex]\textrm{Probability of people getting cured}  = \frac{\textrm{40}}{\textrm{45}}[/tex]  = [tex]\frac{8}{9}[/tex]

Hence, the probability of cured people in who took the remedy is 8/9.

Final answer:

To find the probability of at least four patients out of 25 actually having the flu, the binomial probability formula is used. For the expected number of flu cases, the probability (4%) is multiplied by the number of patients (25).

Explanation:

The question pertains to the calculation of probabilities regarding how many patients actually have the flu given a certain success rate of 4% for flu diagnosis among those reporting symptoms. Specifically, we are asked to find the probability that at least four out of the next 25 patients calling in actually have the flu. To solve this, we would use the binomial probability formula:

P(X ≥ k) = 1 - ∑ [ P(X = i) where i goes from 0 to k-1 ]

In this case, X represents the number of patients who actually have the flu, k is the number we are interested in (at least four), and P(X = i) is the probability that exactly i patients have the flu. To express the distribution of X, we use a binomial distribution as we are dealing with a fixed number of independent trials, each with two possible outcomes (having the flu or not).

To determine the expected number of patients with the flu, we would multiply the probability of an individual having the flu (4%) by the number of patients calling in, which is 25.

Expected number of patients with the flu = 25 * 0.04 = 1

The projectile will be back at ground level at t = 0 (initially fired) and t = 8 seconds after being fired.

To find when the height of the projectile is less than 128 feet, we set s < 128 and solve for t using the given position equation:

[tex]\[ -16t^2 + v_0t + s_0 < 128 \][/tex]

Given:

- [tex]\( v_0 = 128 \)[/tex]  feet per second

- [tex]\( s_0 = 0 \)[/tex] (since the object is fired upward from ground level)

Substitute these values into the equation:

[tex]\[ -16t^2 + 128t < 128 \][/tex]

Now, let's solve this inequality for t. First, let's rewrite it in standard quadratic form:

[tex]\[ -16t^2 + 128t - 128 < 0 \][/tex]

Divide all terms by -16 to simplify:

[tex]\[ t^2 - 8t + 8 > 0 \][/tex]

Now, we need to find the values of t for which this inequality holds true.

To solve quadratic inequalities, we can find the roots of the corresponding quadratic equation [tex]\( t^2 - 8t + 8 = 0 \)[/tex], and then determine the intervals where the quadratic expression [tex]\( t^2 - 8t + 8 \)[/tex] is positive.

The roots of the quadratic equation [tex]\( t^2 - 8t + 8 = 0 \)[/tex] can be found using the quadratic formula:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where [tex]\( a = 1 \), \( b = -8 \), and \( c = 8 \).[/tex]

[tex]\[ t = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 1 \cdot 8}}{2 \cdot 1} \][/tex]

[tex]\[ t = \frac{8 \pm \sqrt{64 - 32}}{2} \][/tex]

[tex]\[ t = \frac{8 \pm \sqrt{32}}{2} \][/tex]

[tex]\[ t = \frac{8 \pm 4\sqrt{2}}{2} \][/tex]

[tex]\[ t = 4 \pm 2\sqrt{2} \][/tex]

So, the roots of the equation are [tex]\( t = 4 - 2\sqrt{2} \) and \( t = 4 + 2\sqrt{2} \).[/tex]

Now, we can test the intervals [tex]\( (-\infty, 4 - 2\sqrt{2}) \), \( (4 - 2\sqrt{2}, 4 + 2\sqrt{2}) \), and \( (4 + 2\sqrt{2}, \infty) \)[/tex] to determine where the inequality [tex]\( t^2 - 8t + 8 > 0 \)[/tex] holds true.

However, it seems there might be an error in the equation. Let's reassess the situation. If the projectile is fired straight upward from ground level, it will reach its maximum height and then fall back to the ground. The time at which it returns to the ground can be found by setting \( s = 0 \) in the position equation:

[tex]\[ -16t^2 + 128t = 0 \][/tex]

Factor out -16t:

-16t(t - 8) = 0

This equation will be true when either -16t = 0 or t - 8 = 0.

Solving each equation:

1.  -16t = 0

t = 0

2. t - 8 = 0

t = 8

So, the projectile will be back at ground level at t = 0 (when it's initially fired) and at t = 8 seconds after being fired.

Answer:

Step-by-step explanation:

Having drawn the line, Kendall must verify that the point P belongs to the line y = 2x-1 and then calculate the distance between A-P  and verify if it is the closest to A or there is another one of the line

Having the point P(3,5) substitue x to verify y

y=2*(3)-1=6-1=5 (3,5)

Now if the angle formed by A and P is 90º it means that it is the closest point, otherwise that point must be found

[tex]d_{AP}=\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}=\sqrt{(5-7)^{2}+(3-(-2}))^{2}}=\\\sqrt{(-2)^{2}+(5)^{2}}=\sqrt{29}[/tex]

and we found the distance PQ and QA

; [tex]d_{PQ}=\sqrt{125}[/tex], [tex]d_{QA}=12[/tex]

be the APQ triangle we must find <APQ through the cosine law (graph 2).

Answer:

8923 years

Step-by-step explanation:

Half life of C-14 = 5730yrs

decay rate= 34%

Halt life (t^1/2) = (ln2) / k

5730 = (ln2) /k

k = (ln2) / 5730

k = 1.209 * 10^-4

For first order reaction in radioactivity,

ln(initial amount) = -kt

ln(34/100) = -(1.209*10^-4)t

-1.0788 = -(1.209*10^-4)t

t = -1.7088/ -1.209*10^-4

t = 8923 years

It would take 8918 years for the tree to decay to 34%.

The half life is the time taken for a substance to decay to half of its value. It is given by:

[tex]N(t) = N_0(\frac{1}{2} )^\frac{t}{t_\frac{1}{2} } \\\\where\ t=period, N(t)=value\ after\ t\ years, N_o=original\ amount, t_\frac{1}{2} =half\ life\\\\Given\ t_\frac{1}{2} =5730,N(t)=0.34N_o, hence:\\\\0.34N_o=N_o(\frac{1}{2} )^\frac{t}{5730} \\\\t=8918\ years[/tex]

It would take 8918 years for the tree to decay to 34%.

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Answer:

10.44

Step-by-step explanation:

The weighted average cost per unit method seeks to get the cost of goods sold as an average of all cost of goods in the inventory as at the time of sales.

Part of its objective is to strike a balance between the (FIFO and LIFO) inventory valuation methods.

Beginning inventory ( Jan) = 10 units

Cost of beginning inventory per unit = $10

Total cost of beginning inventory = Cost * Number of units

In this case (10*$10) = $100

Additional purchase (Jan 5) = 8 units

Cost of additional purchase per unit = $11

Total cost of additional purchase = 8 * $11 = $88

Weighted average cost per unit at the time 11 units are sold on January 7 = Total cost of units at that time / number of units available at that time.

= ($100+ $88) / (10+8)

= 188/18

=10.44 (approximated to 2 decimal places)

I hope this helps make the concept clear.

Final answer:

Using the principle of inclusion-exclusion, it's calculated that 25% of the teachers surveyed had neither high blood pressure nor heart trouble.

Explanation:

To find the percentage of teachers who had neither high blood pressure nor heart trouble, we can use the principle of inclusion-exclusion in set theory. We begin by adding the number of teachers with each condition, then subtract those counted twice because they have both conditions.

The formula we will use is:

Total surveyed - (High blood pressure + Heart trouble - Both) = Neither condition

Substituting the numbers from the survey, we get:

120 - (70 + 40 - 20) = 120 - (90) = 30

So, 30 teachers had neither high blood pressure nor heart trouble.

To find the percentage, we divide the number of teachers with neither condition by the total surveyed and then multiply by 100:

(30 / 120) * 100 = 25%

Therefore, 25% of the teachers surveyed had neither high blood pressure nor heart trouble.

Answer:

7 years old

Step-by-step explanation:

Robert's mother pours a cup of milk for him and realizes that cup has a small crack so she pour the milk into another cup. Robert is not upset because he knows that the amount of milk has remained same.

As Robert is 7 year old . He can groups the milk in the cup according to size , shape and color. He has a better understanding of numbers and can understand problems easily.

Robert's recognition of the conservation of volume implies he is at least 7 years old, the age at which children typically enter the concrete operational stage and understand this concept.

The question asks us to determine Robert's age based on his understanding of the concept of conservation of volume. According to developmental psychology, children gain the ability to understand that a change in the form of an object does not necessarily imply a change in the volume or quantity after a certain age. This concept is typically acquired during the concrete operational stage of development, which is from about 7 to 11 years old. Since Robert recognizes that the same amount of milk remains constant despite being poured into cups of different shapes, we can infer that Robert is at least in the concrete operational stage of development. Thus, Robert is at least 7 years old.

Answer:

Option C

Step-by-step explanation:

As you can see in the graph the shaded region is in 1st quadrant which means that both x and y are greater than or less than equal to zero. From this statement only option A and B get eliminated. But still we will look further...

The equation of the yellow line should be determined in order to know the complete answer. If you don't know how to write equation of line in intercept form then just assume the line's equation to be :

y=mx + c    ; where m and c are constants.

Now you just need to find two points satisfying the line's equation. As you can see in the graph (2,0) and (0,-2) are the points lying on the line. Now put them in the assumed line's equation to determine the constants.

0 = m × 2 + c  .........equation (1)

-2 = m × 0 + c .........equation (2)

solving equation (2) gives c = -2

put the value of c in equation (1) then solve it to get the value of m

0 = m × 2 - 2

m=1

Therefore line's equation is y = x - 2

Since the value of y is greater than and equal to the value of y which we get from the line's equation so

y ≥ x - 2

rearrange the above inequality

x - y ≤ 2

So these three conditions are there

x ≥ 0

y ≥ 0

x - y ≤ 2

which gives the shaded region

Answer:yes

Step-by-step explanation:

Answer:

8x + 29 < 17

Step-by-step explanation:

Let the unknown number be x .

According to the question ,

8 times x when added to 29 will give a sum less than 17 .

So , we can write

8x + 29 < 17.

We can also solve it

so we will get

8x < -12

x<-1.5.

Answer:

 2115751

Step-by-step explanation:

Count the number length of string of lowercase letter. one String has 26 letter.

26 letters in the lowercase.

Same as in the next string.So number of length of 5 string is = 26^5

Lets count the length of string that does not have x then string of lowercase is containing 25 letters.

25 letters and same is in the next string. So length of 5 string is = 25^5

Hence

The string of 5 lowercase letters are with at least one x = 26^5 -25^5

                                                                                             =   2115751

To find the number of strings of 5 lower case English letters that have the letter x in them, we can subtract the number of strings that don't have an x from the total number of strings. The total number of strings of length 5 is 26^5, and the number of strings that don't have an x is 25^5. Therefore, the number of strings that have the letter x is 26^5 - 25^5 = 45,651.

To find the number of strings of 5 lower case English letters that have the letter x in them somewhere, we can first count the number of strings that don't have an x in them and subtract it from the total number of strings of length 5.

The total number of strings of length 5 is 26^5 since each letter can be any of the 26 lower case English letters.

Now, to count the number of strings that don't have an x in them, we can consider each position in the string. For the first position, we have 25 options (all the letters except x). Similarly, for the second position, we also have 25 options, and so on. Therefore, the total number of strings that don't have an x in them is 25^5.

Finally, we can find the number of strings that have the letter x in them by subtracting the number of strings that don't have an x from the total number of strings: 26^5 - 25^5 = 45,651.

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Answer:

C) 6 square inches.

Step-by-step explanation:

The length of the logo = 3 inches

The width of the logo = 2 inches.

It is rectangle shape.

The area of a rectangle = length × width

So, the space needed to work on the logo = 3 × 2 = 6 square inches.

The answer is C) 6 square inches.

Answer:

50 kg water.

Step-by-step explanation:

We have been given that the number of kilograms of water in a human body varies directly as the mass of the body.

We know that two directly proportional quantities are in form [tex]y=kx[/tex], where y varies directly with x and k is constant of variation.

We are told that an 87​-kg person contains 58 kg of water. We can represent this information in an equation as:

[tex]58=k\cdot 87[/tex]

Let us find the constant of variation as:

[tex]\frac{58}{87}=\frac{k\cdot 87}{87}[/tex]

[tex]\frac{29*2}{29*3}=k[/tex]

[tex]\frac{2}{3}=k[/tex]

The equation [tex]y=\frac{2}{3}x[/tex] represents the relation between water (y) in a human body with respect to mass of the body (x).

To find the amount of water in a 75-kg person, we will substitute [tex]x=75[/tex] in our given equation and solve for y.

[tex]y=\frac{2}{3}(75)[/tex]

[tex]y=2(25)[/tex]

[tex]y=50[/tex]

Therefore, there are 50 kg of water in a 75​-kg person.

To find out how many kilograms of water are in a 75 kg person, we can set up a proportion and solve for x. The number of kilograms of water is directly proportional to the mass of the body.

To solve this problem, we can use the concept of direct variation. Direct variation states that two variables are directly proportional to each other. In this case, the number of kilograms of water is directly proportional to the mass of the body.

We are given that an 87 kg person contains 58 kg of water. To find out how many kilograms of water are in a 75 kg person, we can set up a proportion:

(87 kg) / (58 kg) = (75 kg) / (x kg)

Cross multiplying, we get:

87 kg * x kg = 58 kg * 75 kg

Simplifying, we find that x = 39 kg.

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Answer:

$1.00

Step-by-step explanation:

Total Budget = $35

Cake Spent = $18

Remaining Money = 35 - 18 = $17

Since, each balloon is worth $4, to find how many balloons he will get with remaining money ($17), we divide the the remaining money by price of each balloon:

17/4 = 4.25

We can't have fractional balloons, so Abit can get 4 balloons, MAXIMUM.

4 balloons cost = $4 per balloon * 4 = $16

So, from $17 if he spends $16 for balloons, he will have left:

$17 - $16 = $1.00

Answer:

Sometime between the third and fourth year (3.5 years)

Step-by-step explanation:

According to the data provided, we know the initial enrollment in the Spanish class is 555. The trend shows 33 more students will enroll each year. So, being y the time in years, the equation for the number of students in the Spanish class is

[tex]S=555+33y[/tex]

As for the French class, since we lose 2 students each year the equation is

[tex]F=230-2y[/tex]

We require to know the value of y in the exact moment when S=3F

[tex]555+33y=3(230-2y)[/tex]

Operating

[tex]555+33y=690-6y[/tex]

Reducing

[tex]39y=690-555[/tex]

[tex]39y=135[/tex]

[tex]y=135/39=3.5\ years[/tex]

It means that sometime between the third and fourth year, there will be 3 times as many students taking Spanish as French

According to the data provided, we know the initial enrollment in the Spanish class is 555. The trend shows 33 more students will enroll each year. So, being y the time in years, the equation for the number of students in the Spanish class is

According to the data provided, we know the initial enrollment in the Spanish class is 555. The trend shows 33 more students will enroll each year. So, being y the time in years, the equation for the number of students in the Spanish class is

According to the data provided, we know the initial enrollment in the Spanish class is 555. The trend shows 33 more students will enroll each year. So, being y the time in years, the equation for the number of students in the Spanish class is

Answer:

[tex]V_{total} = \displaystyle\int_0^{60} A e^{-k t}~dt[/tex]

Step-by-step explanation:

We are given the following in the question:

Oil leaks out of a tanker at a rate of r = f(t) liters per minute, where t is in minutes.

[tex]f(t) = A e^{-k t}[/tex]

Let V be the volume, then we are given that rate of leakage is:

[tex]\displaystyle\frac{dV}{dt} = f(t) = A e^{-k t}[/tex]

Thus, we can write:

[tex]dV = f(t).dt = A e^{-k t}~dt[/tex]

We have to find the  a definite integral expressing the total quantity of oil which leaks out of the tanker in the first hour.

Thus, total amount of oil leaked will be the definite integral from 0 minutes to 60 minutes.

[tex]dV =A e^{-k t}~dt\\V_{total} = \displaystyle\int_a^b f(t)~dt\\\\a = 0\text{ minutes}\\b = 60\text{ minutes}\\\\V_{total} = \displaystyle\int_0^{60} A e^{-k t}~dt[/tex]

The units of integral will be liters.

The total amount of oil leaked in the first hour can be expressed as the definite integral [tex]\int_{0}^{60} A e^{-k t}[/tex] dt. The unit of this integral is liters, as the rate of oil leak is given in liters per minute and the time is in minutes.

The rate of the oil leak is given by [tex]f(t)=Ae^{-kt}[/tex], where A represents the initial rate of the leak, k is a constant, t is time in minutes, and e is the base of the natural logarithm. To express the total amount of oil leaked in the first hour in the form of a definite integral, we need to integrate this rate function from t=0 (the start of the leak) to t=60 (the end of the first hour).

So, the required integral would be expressed as: [tex]\int_{0}^{60} A e^{-k t} dt[/tex]. This integral calculates the total quantity of oil leaked in the first 60 minutes. The units of this integral would be liters, as the rate of the leak is given in liters per minute and the time is in minutes. Integrating a rate over time gives us a total quantity in the original unit of the rate, in this case liters.

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Answer:

  41,055

Step-by-step explanation:

If there are 805 students in each of 51 schools, the total number of students is ...

  (805 students/school) × (51 schools) = 41,055 students

_____

We have to assume that all of the students in the county go to county schools. Apparently, we are to ignore the students that are dropouts or homeschooled, or that go to schools not in the county.

Answer: 41055

Step-by-step explanation:

51 schools, each has 805 kids

51*805=41055

Answer:

A

Step-by-step explanation:

(kop)(x)=k{p(x)}

=k(x-4)

=2(x-4)²-8

=2(x²-8x+16)-8

=2x²-16x+32-8

=2x²-16x+24

Answer:

a.  2x^2 - 16x + 24.

Step-by-step explanation:

k(x) = 2x^2 − 8

p(x) = x − 4

To find ( k o p)(x) we replace the x in k(x) by x - 4:

= 2(x - 4)^2 - 8

= 2x^2 - 16x + 32 - 8

= 2x^2 - 16x + 24.