Owen earns a base salary plus a commission that is a percent of his total sales. His total weekly pay is described by f(x)=0.15x+325, where x is his total sales in dollars. What is the change in Owen's salary plan if his total weekly pay function changes to g(x)=0.20+325?

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:

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:

Step-by-step explanation:

The price of the 8 ounce box is $2.48, we will determine the price per ounce for the 8 ounce box

If 8 ounce = $2.48

1 ounce will be 2.48/8 = $0.31

The price of the 14 ounce box is $3.36

we will also determine the price per ounce for the 14 ounce box

If 14 ounce = $3.36

1 ounce will be 3.36/14 = $0.24

To determine how much greater is the cost per ounce of cereal in the 8 ounce box than in the 14 ounce box, we will subtract the unit cost of the 14 ounce box from the 8 ounce box. It becomes

$0.31 - $0.24= $0.07

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:

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:

  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:

2√26

Step-by-step explanation:

First, let's label side AB as y and side BP as h.

Then, using the Pythagorean Theorem, we can determine that for ΔABP,

5²+h²=y², which is equal to h² = y²- 25.

For ΔBPC, 8²+ h² = x², which is equal to h² = x²- 64.

Because both equations are equal to h², you can determine that y²- 25 = x²- 64. You can rewrite this equation as x²- y² = 39.

Then, for ΔABC, x²+ y² = (5+8)², which is equal to x²+ y² = 169.

Now, you can see that we have a system of equations. Using elimination, we can add the equations, getting:

2x² = 208

x² = 104

x = ±√104 which simplifies into ±2√26, but since x is a distance, and distance is always positive, the answer has to be 2√26.

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.

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:

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.

Total sales are 200 tickets

Step-by-step explanation:

the formula for percentage will be used for this situation

Given

Sold tickets on first day = 44

Percentage = 22%

Let x be the total sales

Then

[tex]Tckets\ sold\ on\ first\ day = 22\%\ of\ x\\44=0.22*x\\x=\frac{44}{0.22}\\x=200[/tex]

Total sales are 200 tickets

Keywords: Percentage

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Answer:

200 (tickets)

Please show me the question and I am gonna answer It

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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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:

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:

Final answer:

The average speed of the flock of birds over 5 hours is 9 miles per hour, calculated by dividing the distance function f(x) by the time function g(x) at x equal to 5.

Explanation:

The student asked to solve f divided by g of 5 for the given functions f(x) = 2x + 26 and g(x) = x − 1. This will give us the average speed of the flock of birds over the time interval when x equals 5.

First, we substitute x with 5 in both functions:

f(5) = 2(5) + 26 = 10 + 26 = 36 miles

g(5) = 5 − 1 = 4 hours

Next, we divide the outcome of function f by the outcome of function g:

\(\frac{f(5)}{g(5)} = \frac{36}{4} = 9 \) miles per hour

This result represents the average speed of the flock of birds over the time interval when x equals 5 hours.

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:

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:

answer is 90 for first term

Step-by-step explanation:

Let the terms be  

First term x

We will use the formula s∞=x/1−r to find the sum of an infinite geometric series, where −1<r<1.  

We know the sum and the common ratio, so we'll be solving for x where r =4/5

s∞=x/1−r

450=x/1−4/5

450=x/1/5

450=5x

x=90

this is the first term x1 = 90

we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term  

90 x 4/5=   72 second term  

Answer:

C) 90

Step-by-step explanation:

The sum of an infinite geometric series is:

S = a₁ / (1 − r)

where a₁ is the first term and r is the common ratio.

450 = a₁ / (1 − 4/5)

450 = a₁ / (1/5)

450 = 5a₁

a₁ = 90

Answer:

Step-by-step explanation:

In order to buy the new car, Nancy

paid $1,500 up front and took out a loan for the rest of the amount.

Let x = The amount of loan that she took.

The interest rate on the loan is 5%.

This means that she paid interest of 5/100 × x = 0.05 × x

= 0.05x

If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02,

It means that

1,500 + x + 0.05x is greater than 16,213.02

1500 + 1.05x = 16213.02

1.05x = 16,213.02 - 1500

1.05x = 114713.02

x = 114713.02/1.05

x = $109250 .49524

The amount that Nancy borrowed is greater than $109250 .49524

Answer:

amount borrowed + interest = x+5% of x

                                               = x + 5/100x

                                               = x + 0.05x

                                               = 1.05x

The expression 1.05x represents the sum of the amount Nancy borrowed and the interest she owes on that amount.

Step-by-step explanation:

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:

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:yes

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

5x-3/3x+2 = 60/40

=> x = 12

Hope it's helpful ;)

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.

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:

$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:

1)[tex]\mu=\frac{1}{2}(7.5+20) =13.75[/tex]

[tex]\sigma^2 = \frac{1}{12}(20-7.5)^2 =13.02[/tex]

2) [tex]F(x)=\big\{0, x<a[/tex]

[tex]F(x) =\big\{ \frac{x-a}{b-a}=\frac{x-7.5}{20-7.5}, a\leq x<b[/tex]

[tex]F(x)=\big\{1, x\geq b[/tex]

3) [tex]P(X<10)=F(10)=\frac{10-7.5}{20-7.5}=0.2[/tex]

[tex]P(10\leq X \leq 15)=F(15)-F(10)=\frac{15-7.5}{20-7.5} -\frac{10-7.5}{20-7.5}=0.6-0.2=0.4[/tex]

4) [tex]P(10.142\leq X \leq 17.358)=F(17.358)-F(10.142)=\frac{17.358-7.5}{20-7.5} -\frac{10.142-7.5}{20-7.5}=0.789-0.211=0.578[/tex]

[tex]P(6.534\leqX\leq 20.966)=P(6.534\leq X<7.5)+P(7.5\leq X \leq 20)+P(20<X\leq 20.966)=0+1+0=1[/tex]

Step-by-step explanation:

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability.

Part 1

If X is a random variable that follows an uniform distribution [tex]x\sim U(a,b)[/tex]. The mean for an uniform distribution is given by : [tex]\mu=\frac{1}{2}(a+b)[/tex]

On this case a=7.5 and b=20 so if we replace we got:

[tex]\mu=\frac{1}{2}(7.5+20) =13.75[/tex]

The variance for the uniform distribution is given by this formula:

[tex]\sigma^2 = \frac{1}{12}(b-a)^2 [/tex]

And replacing we have:

[tex]\sigma^2 = \frac{1}{12}(20-7.5)^2 =13.02[/tex]

Part 2

The cumulative distribution function is given by:

[tex]F(x)=\big\{0, x<a[/tex]

[tex]F(x) =\big\{ \frac{x-a}{b-a}=\frac{x-7.5}{20-7.5}, a\leq x<b[/tex]

[tex]F(x)=\big\{1, x\geq b[/tex]

Part 3

What is the probability that observed depth is at most 10?

We are interested on this probability:

[tex]P(X<10)=F(10)=\frac{10-7.5}{20-7.5}=0.2[/tex]

What is the probability that observed depth is between 10 and 15?

On this case we want this probability:

[tex]P(10\leq X \leq 15)=F(15)-F(10)=\frac{15-7.5}{20-7.5} -\frac{10-7.5}{20-7.5}=0.6-0.2=0.4[/tex]

Part 4

What is the probability that the observed depth is within one standard deviation of the mean value? within 2 standard deviations?

First we find the limits within one deviation from the mean:

[tex]\mu-\sigma= 13.75-3.608=10.142[/tex]

[tex]\mu-\sigma= 13.75+3.608=17.358[/tex]

And we want this probability:

[tex]P(10.142\leq X \leq 17.358)=F(17.358)-F(10.142)=\frac{17.358-7.5}{20-7.5} -\frac{10.142-7.5}{20-7.5}=0.789-0.211=0.578[/tex]

Now we find the limits within two deviation's from the mean:

[tex]\mu-2*\sigma= 13.75-2*3.608=6.534[/tex]

[tex]\mu-2*\sigma= 13.75+2*3.608=20.966[/tex]

But since the random variable is defined just between (7.5 and 20) so we can find just the probability on these limits.

[tex]P(6.534\leqX\leq 20.966)=P(6.534\leq X<7.5)+P(7.5\leq X \leq 20)+P(20<X\leq 20.966)=0+1+0=1[/tex]

The probability of the observed depth being at most 10 is 0.295 and between 10 and 15 is 0.295. The probability that the observed depth is within one standard deviation of the mean is 0.525.

To find the mean and variance of the depth, we use the formula:

Mean = (a + b) / 2 = (7.5 + 20) / 2 = 13.75 cm

To find the variance, we use the formula:

Variance = (b - a)^2 / 12 = (20 - 7.5)^2 / 12 ≈ 12.1875 cm^2

The cumulative distribution function (CDF) of depth can be calculated by finding the probability that the observed depth is less than or equal to a certain value. In this case, since the depth follows a uniform distribution, the CDF is:

CDF(x) = (x - a) / (b - a)

To find the probability that the observed depth is at most 10, we substitute x=10 into the CDF formula:

CDF(10) = (10 - 7.5) / (20 - 7.5) = 0.295

To find the probability that the observed depth is between 10 and 15, we subtract the CDF of 10 from the CDF of 15:

Probability = CDF(15) - CDF(10) = (15 - 7.5) / (20 - 7.5) - (10 - 7.5) / (20 - 7.5) = 0.59 - 0.295 = 0.295

To find the probability that the observed depth is within one standard deviation of the mean value, we need to find the range between Mean - Standard Deviation to Mean + Standard Deviation. Since the variance is the square of the standard deviation, we take the square root of the variance to find the standard deviation:

Standard Deviation = √Variance = √12.1875 ≈ 3.49 cm

Hence, the range is (Mean - Standard Deviation, Mean + Standard Deviation):

Range = (13.75 - 3.49, 13.75 + 3.49) = (10.26, 17.24) cm

To find the probability within this range, we calculate the difference between the CDF of 17.24 and the CDF of 10.26:

Probability = CDF(17.24) - CDF(10.26) = (17.24 - 7.5) / (20 - 7.5) - (10.26 - 7.5) / (20 - 7.5) ≈ 0.82 - 0.295 ≈ 0.525

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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:

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.