Find the arc length of AB. Round your answer to the nearest hundredth.
!no absurd answers, please! : (

The time for the fastest 10 % is less than 89.4 seconds

Here's how to find the qualifying task times:

Calculate the z-score for the 10th percentile:

A z-score represents the number of standard deviations a specific point is away from the mean. In this case, we want the z-score for the lower 10th percentile, which can be found using a z-score table or online calculators. The approximate z-score for the 10th percentile is -1.28.

Translate the z-score to task time:

We know the z-score for the 10th percentile (-1.28) and the standard deviation (20 seconds). We can use the formula to find the corresponding task time (t):

t = mean + (z-score) * standard deviation

t = 115 seconds + (-1.28) * 20 seconds

t ≈ 89.4 seconds

Therefore, task times less than 89.4 seconds qualify individuals for advanced training, as they fall within the lower 10th percentile of the normal distribution.

Complete question:

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 115 sec and a standard deviation of 20 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)

Answer:

[tex]\frac{9}{4}[/tex]

Step-by-step explanation:

Given

x² + 3x - 13 = 0 ( add 13 to both sides )

x² + 3x = 13

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2([tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 13 + ([tex]\frac{3}{2}[/tex] )², that is

x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] = 13 + [tex]\frac{9}{4}[/tex]

(x + [tex]\frac{3}{2}[/tex] )² = [tex]\frac{61}{4}[/tex]

The required number to be added to complete the square is [tex]\frac{9}{4}[/tex]

Hence, required number to be added to complete the square is 9/4

A quadratic equation is any equation that can be rewritten in standard form as ax2+bx+c=0 in algebra. When x is an unknown and a, b, and c are known numbers, and an is less than 0. Because there is no ax2 term when a = 0, the equation is linear rather than quadratic.

Given equation =x² + 3x - 13 = 0 ( add 13 to both sides )

=x² + 3x = 13

using complete the square and add ( half the coefficient of the x- term )² to both sides

=x² + 2(3/2 )x + ( 3/2)² = 13 + (3/2 )², that is

=x² + 2(3/2 )x +  = 13 + 9/4

=(x + 3/2 )² = 61/4

The required number to be added to complete the square is 9/4

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Answer:

Supply curve vs Aggregate Supply

Step-by-step explanation:

- Supply express a direct relationship between what producers supply and how that relationship affects the price of a specific product or service. Hence, expresses a linear increase - or a constant slope

- Aggregate supply are the total supply in an economy at a particular period of time and a particular price threshold. Aggregate supply is an economy's gross domestic product (GDP), the total amount a nation produces and sells.

-  Aggregate supply convey how much firms are willing to produce at a specific price point.

- Aggregate supply is a response to increasing prices that drive firms to utilize more inputs to produce more output. The incentive is that if the price of inputs remains the same but if the price of outputs increase, the firm will generate larger profits and margins by producing and selling more. The aggregate supply curve is represented by a curve that slopes upward, which indicates that as the price per unit goes up, a firm will supply more. Increasing slope - Not constant.

- The supply curve eventually becomes vertical, indicating that at a certain price point a firm cannot produce anymore, as they are limited by certain inputs, e.g. number of employees and number of factories.

Answer: 27.3 degrees

cos x = 16/18

x = arccos(16/18)

x = 27.3 degrees

Value of x is 30°

Step-by-step explanation:

cos x° = adjacent side/hypotenuse = 16/18 = 8/9

x° = cos inverse(8/9) = 27.12° = 30° (Rounded off to nearest ten)

Answer:

13 Minutes

Step-by-step explanation:

If it took 28 minutes total to wait in line and be in the haunted house, then the equation would be 15+x=28

x=13

Answer:

13 Minutes

Step-by-step explanation:

Answer:

Total length of the Nylon rope will be 5.8 feet.

Step-by-step explanation:

Given:

Height of the tent = 5 ft

ground Distance from stake to tent = 3 ft

We need to find the Total length of the nylon rope.

Solution:

Now we can say that the total length of the nylon rope, the height of the tent, the ground distance from the stake to the tent, forms a right angle triangle.

From above we can see that;

the height of the tent, the ground distance from the stake to the tent are the two legs of the right angled triangle.

While the Total length of the nylon rope is the hypotenuse.

Now using Pythagoras theorem we get;

[tex]h^2=l_1^2+l_2^2[/tex]

[tex]l_1[/tex] ⇒ the height of the tent

[tex]l_2[/tex] ⇒  the ground distance from the stake to the tent

[tex]h[/tex] ⇒ the Total length of the nylon rope

substituting the values we get;

[tex]h^2=5^2+3^2\\\\h^2=25+9\\\\h^2=34[/tex]

Taking square root on both side we get;

[tex]\sqrt{h^2} =\sqrt{34} \\\\h=5.8\ ft[/tex]

Hence Total length of the Nylon rope will be 5.8 feet.

Answer:

Just find the hypotenuse by doing a^2 + B^2 = C^2

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

According to fisher equation

Nominal rate = Real rate + Inflation

N = R + I

N is calculated when there is no inflation and for the current year = 8%

The Real rate is calculated from the base year

Real rate is consider "Inflation factor" and R is unknown

Inflation rate (I) = 3%

Hence, N = R + I

8 = R + 3

R = 8 - 3

R = 5%

Answer:

Part 1) [tex]A=28.96^o[/tex]

Part 2) [tex]B=46.57^o[/tex]

Part 3) [tex]C=104.47^o[/tex]

Step-by-step explanation:

step 1

Find the measure of angle A

Applying the law of cosines

[tex]a^2=b^2+c^2-2(b)(c)cos(A)[/tex]

we have

[tex]a=10\ cm\\b=15\ cm\\c=20\ cm[/tex]

substitute

[tex]10^2=15^2+20^2-2(15)(20)cos(A)[/tex]

Solve for A

[tex]2(15)(20)cos(A)=15^2+20^2-10^2[/tex]

[tex]600cos(A)=525[/tex]

[tex]cos(A)=(525/600)[/tex]

using a calculator

[tex]A=cos^{-1}(525/600)=28.96^o[/tex]

step 2

Find the measure of angle B

Applying the law of cosines

[tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]

we have

[tex]a=10\ cm\\b=15\ cm\\c=20\ cm[/tex]

substitute

[tex]15^2=10^2+20^2-2(10)(20)cos(B)[/tex]

Solve for A

[tex]2(10)(20)cos(B)=10^2+20^2-15^2[/tex]

[tex]400cos(B)=275[/tex]

[tex]cos(B)=(275/400)[/tex]

using a calculator

[tex]B=cos^{-1}(275/400)=46.57^o[/tex]

step 3

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]A+B+C=180^o[/tex]

we have

[tex]A=28.96^o[/tex]

[tex]B=46.57^o[/tex]

substitute

[tex]28.96^o+46.57^o+C=180^o[/tex]

[tex]C=180^o-75.53^o[/tex]

[tex]C=104.47^o[/tex]

Answer:

756 is a reasonable estimate because the proportion of the sample whose favorite pizza is pepperoni is about 27 %

Step-by-step explanation:

given data

random sample = 150 people

favorite pepperoni pizza = 40

total of residents = 2800

number of residents favorite pizza = 750

solution

we get here first Proportion favorite pizza that is

Proportion = [tex]\frac{40}{150}[/tex]

Proportion = 0.27 = 27%

and now we get 27% of total of residents that is = 27% × 2800  

= 756

so we can say  756 is a reasonable estimate because here proportion of an sample whose favorite pizza are pepperoni pizza about 27 %

Among the sets given, ∅ is not a power set while {∅,{a}}, {∅,{a},{∅,a}}, and {∅,{a},{b},{a,b}} can be considered power sets of the sets {a}, {a}, and {a,b} respectively according to the definition of power set.

In mathematics, a power set of any set S is the set of all subsets of S, including the empty set and S itself. We can use this definition to examine the four sets provided and determine if they qualify as power sets.

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Answer:

[tex]t=\frac{2.64-2.5}{\frac{1.02}{\sqrt{15}}}=0.532[/tex]    

[tex]p_v =P(t_{(14)}>0.532)=0.302[/tex]  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis at 5% of significance

Step-by-step explanation:

Data given and notation  

[tex]\bar X=2.64[/tex] represent the sample mean

[tex]s=1.02[/tex] represent the sample standard deviation for the sample  

[tex]n=15[/tex] sample size  

[tex]\mu_o =2.5[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is greater than 2.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 2.5[/tex]  

Alternative hypothesis:[tex]\mu > 2.5[/tex]  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{2.64-2.5}{\frac{1.02}{\sqrt{15}}}=0.532[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=15-1=14[/tex]  

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(t_{(14)}>0.532)=0.302[/tex]  

Conclusion  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis at 5% of significance

Question:

A certain vibrating system satisfies the equation u''+γu'+u=0. Find the value of the damping coefficientγfor which the quasi period of the damped motion is 50% greater than the period of the corresponding undamped motion.

Answer: y = √(20/9) = √20/3 = 1.49071

Step-by-step explanation:

u''+γu'+u=0

m =1, k =1, w• = √ (k/m) = 1

The period of undamped motion T, is given by T = 2π/w•, T = 2π/1 = 2π

The quasi period Tq = 2π/quasi frequency

Quasi frequency = ((4km - y^2)^1/2)/2m

Therefore the quasi period Tq = 4πm/((4km - y^2)^1/2)

From the question the quasi period is 50% greater than the period of undamped motion

Therefore Tq = T + (1/2)T = (3/2)T

Thus,

4πm/((4km - y^2)^1/2) = (3/2)(2π)

Where, k =1, m=1,

4π/((4 - y^2)^1/2) = 3π,

(4 - y^2)^1/2 = 4π/3π,

(4 - y^2) = (4/3)^2,

4 - y^2 = 16/9,

y^2 =4 - 16/9,

y^2 = 20/9,

y = √(20/9)

Answer:

Answer is 1.49071

Step-by-step explanation:

See the picture for the complete details

Answer: the speed of the current is 6 mph

Step-by-step explanation:

Let x represent the speed of the current.

Logan is driving a boat that has a speed of 18 mph in standing water.

Assuming the current slowed down the boat while she was going up(upstream), it means that his total speed was (18 - x) mph

Also, if the current helped the boat while she was going down(downstream), it means that his total speed was (18 + x) mph

Time = distance/speed

The boat travels 4 miles each way. The time taken to travel upstream is

4/(18 - x)

Time taken to travel downstream is

4/(18 + x)

The round trip took 0.5 hour. It means that

4/(18 - x) + 4/(18 + x) = 0.5

Multiplying through by (18 - x)(18 + x), it becomes

4/(18 - x) + 4/(18 + x) = 0.5(18 - x)(18 + x)

4(18 + x) + 4(18 - x) = 0.5(18 - x)(18 + x)

72 + 4x + 72 - 4x = 0.5(324 + 18x -

18x - x²)

144 = 0.5(324 - x²)

144 = 162 - 0.5x²

0.5x² = 162 - 144

0.5x² = 18

x² = 18/0.5 = 36

x = √36

x = 6

Answer:

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^t

Where

y represents the population, t years after 2010.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 2.13 × 10^6

r = 2.4% = 2.4/100 = 0.024

Therefore, the equation that you can use to predict the population for the number of years after 2010 is

y = 2.13 × 10^6(1 + 0.024)^t

y = 2.13 × 10^6(1.024)^t

To estimate the percentage of seniors attending college with a 4% margin of error and 90% confidence, a sample size of 424 is needed. For constructing a confidence interval and hypothesis testing about military enlistment, various statistical formulas are applied, including adjustments for undecided responses.

To estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 4% and 90% confidence, we use the formula for determining sample size for a proportion, which is n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score corresponding to the confidence level, p is the estimated proportion, and E is the margin of error. With a 90% confidence level, the Z-score is approximately 1.645, and assuming we don't have a preliminary estimate, we use p = 0.5 for maximum variability, thus maximizing the required sample size.

To calculate: n = (1.645^2 * 0.5 * 0.5) / 0.04^2 = 423.3. Therefore, a sample size of 424 is required to achieve the desired margin of error and confidence level.

For the second question regarding the confidence interval for the percentage of seniors planning to go to college this year, the total sample size is the sum of students from all categories, which is 500. The proportion planning to go to college is 289/500. Using a formula for constructing a confidence interval for a proportion, C.I. = p ± (Z*sqrt(p(1-p)/n)), we can find our interval.

Testing the hypothesis regarding military enlistment involves setting up a null hypothesis (H0: p = 0.045) and an alternative hypothesis (H1: p ≠ 0.045), where p is the proportion of high school seniors enlisting in the military. The test statistic is calculated using a formula, and the P-value associated with this statistic is compared against the alpha level to decide whether to reject H0.

If considering undecided or no response students as potential enlistees changes this calculation significantly, we reassess by including an adjusted number of potential enlistees.

Answer:

D

Step-by-step explanation:

Depending on the number of defects in 6th car,  we have 3 cases:

To find mean we can use the sum of numbers given (= 36) and add either 3, 7, or 12 to it and then divide by 6 (number of cars).

(36 + 3) /6 = 39/6 = 6.5 (== median above)

(36 + 7) /6 = 43/6 = 7.1 (does not equal median above)

(36 + 12) /6 = 48/6 = 8 (== median above)

Answer: D (I and III only).

Final answer:

The set of ordered pairs that correctly satisfies the equation y = 1/8x + 11 is (0,11) (8,12) (16,13). This is determined by substituting the x-values into the equation to check if the y-values correspond.

Explanation:

The question is asking which set of ordered pairs satisfies the equation y = 1/8x + 11. To determine the correct set, we will plug in the x-values from each ordered pair into the equation and see if the resulting y-value matches the one provided in the ordered pair. Let's examine each set:

(0,11) - If we plug in x=0, we get y=1/8*0+11=11. This matches the ordered pair, so (0,11) is correct.

(5,12) - With x=5, y becomes 1/8*5+11=11.625. This does not match the ordered pair (5,12), so this set is incorrect.

(7,13) - With x=7, y is 1/8*7+11=11.875. This does not match the ordered pair (7,13), so this set is also incorrect.

(8,12) - With x=8, y is 1/8*8+11=12. This matches the ordered pair, so (8,12) is correct.

(16,13) - With x=16, y is 1/8*16+11=13. This matches the ordered pair, so (16,13) is correct.

(6,12) - With x=6, y is 1/8*6+11=11.75. This does not match the ordered pair (6,12), so this set is incorrect.

(8,13) - Again, with x=8, y should be 12, not 13, so the ordered pair (8,13) is incorrect.

The only set with all matching ordered pairs for the equation y = 1/8x + 11 is (0,11) (8,12) (16,13).

Answer:

$118,791.2985

Step-by-step explanation:

Given that,

A = 160,000

T = 18 - 8 = 10 years

Rate = 3%

since it is semi annual, n = 2

A = P ( 1 + R/2) ∧ 2T

160000 = P ( 1 + 3/2*100) ∧ 2 * 10

160000 = P ( 1 + 3/200) ∧20

160000 = P( 1 + 0.015) ∧20

160000 = P(1.015)∧20

P= 160000/ (1.015)∧20

P = 160000/ 1.3469

= $118,791.2985

Answer:

3x-7y=-6

Step-by-step explanation:

The accumulator pattern for calculating the sum of numbers using variables number and total in programming is correctly represented by 'total = total + number'. This demonstrates the commutative property of addition, indicating that 'total += number' updates the running total with the new number.

The correct representation of an accumulator to calculate the sum of numbers in a programming context, when the current number is stored in a variable number and the total is stored in a variable total, would be to update the total by adding the number to it. This would look like total = total + number or in a more simplified form as total += number.

Addition in programming is similar to addition in mathematics; it's commutative and associative. This means that the order of adding numbers does not change the sum, as represented by A + B = B + A. Whether we are dealing with numbers, such as integers or real numbers, or other structures like vectors, the concept of addition remains fundamentally the same.

The accumulator pattern is commonly used to build a sum or total by updating a running total each time a new value is added, which is also illustrated by the expression total += number. This pattern is essential in various programming tasks, such as summing a series of numbers in a loop.

Answer:

sampling error i think

Step-by-step explanation:

Answer:

it was B

Step-by-step explanation:

The algorithm employing "Nearest Neighbour" to determine one of the cheaper routes to visit every city and get back home again would be:

B). ATL-CHI-BOS-DEN-ATL

Thus, option B is the correct answer.

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Answer:

Part 1) [tex]m\angle 1=39^o[/tex]

Part 2) [tex]m\angle 3=51^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) Find the measure of angle 1

we know that

The longer diagonal of a kite bisects the kite into two equal parts

That means

[tex]m\angle 1=39^o[/tex]

In this problem the longer diagonal is the segment AC

Part 2) Find the measure of angle 3

we know that

The intersection of the diagonals of a kite form 90 degrees.

That means ----> The triangle ADO (O is the intersection point both diagonals) is a right triangle

so

[tex]39^o+m\angle 3=90^o[/tex] ----> by complementary angles in a right triangle

[tex]m\angle 3=90^o-39^o=51^o[/tex]

Option b: The solution to the system of equations is (2,0)

Explanation:

Given that the graph that contains the system of equations.

We need to determine the solution to the system of equations.

The solution to the system of equations is the points of intersection of these two lines.

The two lines intersect at x - axis at 2 and y - axis 0.

This can be written in coordinates as (2,0)

Thus, the point of intersection of the two lines is the point (2,0)

Hence, Option b is the correct answer.

Answer:

[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x,

and x: >0, <50 is the domain of the function.

Step-by-step explanation:

Draw an appropriate figure and then express the area of the rectangle as a function of x.

We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 50 feet

let w = the width of the rectangle

therefore

[tex]x^2 + w^2 = 50^2\\w^2 = 2500 - x^2\\w = \sqrt{2500-x^{2} }[/tex]

recall

Area = x*w

replace w

[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x

b)state the domain of the function

x: >0, <50

To find the area of the rectangle inscribed in a circle, we can use the Pythagorean theorem to find the length of the rectangle. Then, we can calculate the area by multiplying the width and length. The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2), and the domain is x >= 0 and x <= 50.

To find the area of the rectangle, we need to consider that the diagonal of the rectangle is equal to the diameter of the circle, which is twice the radius. Therefore, the diagonal measures 50 feet.

We can use the Pythagorean theorem to find the length of the rectangle. Let's denote the length as y. We have:

x^2 + y^2 = 50^2

This equation represents the relationship between the width and length of the rectangle. By solving for y, we can express the length as a function of x.

Once we have the width and length of the rectangle, we can calculate the area by multiplying them:

A = x * y = x * sqrt(50^2 - x^2)

The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2). The domain of this function is x >= 0 and x <= 50.

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Answer:

[tex]\sqrt{29}\ units[/tex]

Step-by-step explanation:

we know that

In a right triangle

Applying the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (the greater side)

a and b are the legs (perpendicular sides)

In this problem we have

[tex]a=2\ units\\b=5\ units[/tex]

substitute

[tex]c^2=2^2+5^2[/tex]

[tex]c^2=29[/tex]

[tex]c=\sqrt{29}\ units[/tex]

Answer:

(1) 3628800

(2) 0.00000028

Step-by-step explanation:

We are given that a puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column.

(1) If we make the matches randomly, number of possible matches are given by = 10!

Because after making each match the number will decrease so,

Number of possible matches = 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 .

(2) The probability all 10 of your matches are correct is given by;

      Number of outcomes in favor ÷ Total number of matches

So, there will be only 1 case when all 10 of the matches are correct.

Therefore, required probability = [tex]\frac{1}{10!}[/tex] = [tex]\frac{1}{3628800}[/tex] = 0.00000028 .

Answer:

2 workers

Step-by-step explanation:

Here is additional information for your question:

The questions below deal with the Gizmo Company, which has the following production function.

# Workers # Produce

0 0

1 10

2 19

3 26

4 31

5 34

If the real wage is equal to 8 widgets and only an integer number of workers can be hired the Gizmo company should hire?

My answer:

2 workers. (where MPL is less than real wage)

Answer:

22 rows and 22 flags are needed

Step-by-step explanation:

Total number of vendors = 88

Existing number of rows and flags= 4

Number of rows and flags needed= 88/4 =22

Answer:

4rows and 16flags

Step-by-step explanation:

Since there were 88 vendors at the craft fair and 4flags on each rows. To set up equal number of vendors on each row, we will use the expression;

Number of vendors per row = Total number of vendors/total number of flags per row = 88/4 = 22 vendors

If there are 22 vendors in a rows and there are 88vendors in total, the total of rows will be;

Total number of vendors/number of vendors per row

= 88/22

= 4 rows

If there are four rows in total and 4flags in each row, the total of flags needed will be;

Total number of row × total flag per row

= 4×4

= 16flags

This shows that there are 4rows and 16flags were needed.

Answer:

Pamela = 30

Jiri = 40

Step-by-step explanation:

Two equations needed:

J-10 = P

P+J = 70

Plug and solve:

(J-10) + J = 70

2J - 10 =70

2J = 80

J = 40

40 - 10 = P

P=30

Answer:

30

Step-by-step explanation:

Let Jiri's age be x

Let Pamela's age be (x - 10)

The sum of their ages becomes

x + (x - 10) = 70

x + x - 10 = 70

2x - 10 = 70

2x =70+10

2x = 80

x = 40

Therefore, it means that Jiri's age is 40

Pamela's age is 40-10= 30