Sum of the ages of a father and the son is 40 years. If father's age is 3 times that of his son, then father's age is ________ * 2 points 35 40 30 45

The coordinates of the vertices after the reflection across x = 1 are:

⇒ X'(2,-3),  W(1,0),  V'(2,1)

Now First, let's visualize the reflection across x = 1.

This means that all points will have the same x-coordinate but their y-coordinate will be mirrored across the line x = 1.

So, X(0,-3) will reflect to X'(2,-3),

Since, the distance between X and the line x = 1 is 1 unit,

and the y-coordinate of X' will be the same as that of X.

Similarly, W(1,0) will remain unchanged, as it lies on the line of reflection.

And, Lastly, V(4,1) will reflect to V'(2,1),

Since, the distance between V and the line x = 1 is 3 units, and the y-coordinate of V' will be the same as that of V.

Therefore, the coordinates of the vertices after the reflection across x = 1 are:

⇒ X'(2,-3),  W(1,0),  V'(2,1)

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Answer:

Step-by-step explanation:

Take the log of both sides:

log (5^2) = log 25, or

2 log 5 = log 25 or 2 log 5

Note that 5^2 = 25 is always true.

Answer:

Question 1: 6

Question 2: 15

Sorry I dont know the last one but the other ones are correct

Step-by-step explanation:

To find the volume of the solid enclosed by the paraboloids z=25(x^2+y^2) and z=8-25(x^2+y^2), you can use the triple integral method. In this case, the volume can be found by integrating the difference of the functions over the specified region.

Volume = ∬∬ (8 - 25(x^2 + y^2) - 25(x^2 + y^2)) dx dy

Since the problem is symmetric, you can convert this to polar coordinates:

Volume = ∬∬ (8 - 50r^2) rdrdθ

Now, find the limits of integration for r and θ by setting the two functions equal to each other:

25(x^2 + y^2) = 8 - 25(x^2 + y^2)
50(x^2 + y^2) = 8
r^2 = 8/50
r = sqrt(8/50)

For θ, the limits will be from 0 to 2π because the solid is symmetric about the z-axis.

With these limits, the volume integral becomes:

Volume = ∫(from 0 to 2π) ∫(from 0 to sqrt(8/50)) (8 - 50r^2) rdrdθ

Compute the integral to get the volume of the solid enclosed by the given paraboloids.

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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If the terminal point p(x, y) determined by a real number t is given then sin(t) = 13/sqrt(205), cos(t) = -6/sqrt(205), and tan(t) = -13/6.

To find sin(t), cos(t), and tan(t), we first need to determine the values of x and y. The terminal point p(x, y) is given as (−6/7, 13/7), which means that x = -6/7 and y = 13/7.

Next, we can use the Pythagorean theorem to find the length of the hypotenuse r:

r² = x² + y²

r² = (-6/7)² + (13/7)²

r² = 36/49 + 169/49

r² = 205/49

r = sqrt(205)/7

Now we can find sin(t), cos(t), and tan(t):

sin(t) = y/r = (13/7) / (sqrt(205)/7) = 13/sqrt(205)

cos(t) = x/r = (-6/7) / (sqrt(205)/7) = -6/sqrt(205)

tan(t) = y/x = (13/7) / (-6/7) = -13/6

Therefore, sin(t) = 13/sqrt(205), cos(t) = -6/sqrt(205), and tan(t) = -13/6.

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The terminal point determined by t is (-6/7, 13/7).

To find sin(t), we need to find the y-coordinate of the point on the unit circle that corresponds to t. Since the y-coordinate of the point is 13/7, and the radius of the unit circle is 1, we can use the Pythagorean theorem to find that the x-coordinate of the point is -√(1 - (13/7)²) = -√(48/49) = -4/7.

Therefore, sin(t) = y-coordinate / radius = 13/7. To find cos(t), we can use the same method to find that the x-coordinate of the point is -4/7, so cos(t) = x-coordinate / radius = -4/7. Finally, tan(t) = sin(t) / cos(t) = -(13/7)/(4/7) = -13/4.

In summary, for the terminal point determined by t (-6/7, 13/7), sin(t) = 13/7, cos(t) = -4/7, and tan(t) = -13/4. These values represent the ratios of the sides of a right triangle in standard position with hypotenuse of length 1 and one of the acute angles t.

These trigonometric functions are useful in solving various problems involving angles and distances, as well as in modeling real-world phenomena.

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There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.

To choose a president, a vice-president, and a secretary from a committee of 20 members,

We will use the formula for combinations,

which is: C(n, k) = n! / (k! (n - k)!)

where n is the total number of members and k is the number of members being chosen.

So, for n = 20 and k = 1, we have:

C(20, 1) = 20! / (1! (20 - 1)!) = 20

This gives us 20 choices for the president.

For the vice president,

We need to choose 1 member from the remaining 19 members.

So, for n = 19 and k = 1,

we have:

C(19, 1) = 19! / (1! (19 - 1)!) = 19

This gives us 19 choices for the vice president.

Finally, for the secretary,

We need to choose 1 member from the remaining 18 members.

So, for n = 18 and k = 1,

we have:

C(18, 1) = 18! / (1! (18 - 1)!) = 18

This gives us 18 choices for the secretary.

Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:

So, the required number of ways will be 20 * 19 * 18 = 6840

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Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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When a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.

The binomial distribution's PMF is;

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

Following are the results of a calculation using a binomial distribution to determine the likelihood of receiving at least 9 heads.

P(X ≥ 9) = P(X = 9) + P(X = 10)

P(X ≥ 9) = ¹⁰C₉. (0.6)⁹ (1 - 0.6)¹ + ¹⁰C₁₀. (0.6)¹⁰ (1 - 0.6)⁹

P(X ≥ 9) = 0.0403 + 0.0060

P(X ≥ 9) = 0.0463

Thus, when a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.

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The complete question is-

A biased coin is tossed 10 times and the probability of obtaining heads is 0.6.

Find the probability of obtaining at least 9 heads. Round answer to the nearest ten-thousandth.

Answer:

5 yds

Step-by-step explanation:

Answer:

10 because 11*5*10=550

Step-by-step explanation:

mrk me brainliest plzzzzzz

No, molar mass is a constant and does not depend on pressure or temperature.

Molar mass is a physical property of a substance and is the mass of one mole of a given substance. It is a constant value that represents the amount of grams of a substance that contains 022 x 1023 atoms or molecules. Since molar mass is a constant, it does not depend on pressure or temperature. Pressure and temperature can affect the physical and chemical properties of a substance, but they do not have an effect on the molar mass. The molar mass of a substance can be useful in determining molecular and empirical formulas, as well as calculating densities and molar concentrations.

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

To find the moles of gas remaining in the bag, we can use the initial and final volumes and the initial moles of gas. Since the temperature and pressure remain constant, we can use the formula:

Initial moles × Initial volume = Final moles × Final volume
0.80 mol × 18 L = Final moles × 16 L

Solve for the final moles:
(0.80 mol × 18 L) / 16 L = Final moles

14.4 mol / 16 L = Final moles
Final moles = 0.9 mol

So, 0.9 moles of gas remain in the bag after the leak. The closest answer is 0.91 mol, so the correct option is:
0.91 moles of gas remain in the bag.

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Answer:

3x + 5

Step-by-step explanation:

3x + 5 is common factor.

The answer is option A.

A common factor is an entire wide variety which is a thing of or greater numbers. The highest common factor (HCF) is the finest issue to be able to divide into greater numbers. The lowest common multiple (LCM) is the smallest multiple that is common to 2 or greater numbers.

Common factors of two or more numbers are a number that divides each of the given numbers exactly. The common factors above are shown below.

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The area of triangle ABC with vertices is 22 square units

The vertices are given as:

A(4, -3) B(9,-3) , and C(10, −11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

This gives

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Evaluate the sum of products

Area = 0.5 * |44|

Remove the absolute bracket

Area = 0.5 * 44

Evaluate

Area = 22

Hence, the area of ABC with vertices is 22 square units

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The linear approximation for the expression indicated as per the attached question is given by:

\(L\left ( x \right );\)

\(L\left ( x \right )=f\left ( a \right )+f{}'\left ( a \right )\left ( x-a \right )\).

\(f\left ( x \right )=\sin ^{2}x,\, \, a=2\pi\)

\(f\left ( 2\pi \right )=\sin ^{2}2\pi =0\)

\(f{}'\left ( x \right )=\frac{\mathrm{d} }{\mathrm{d} x}\left [\sin ^{2}x \right ]\)

\(=2\sin x\times \frac{\mathrm{d} }{\mathrm{d} x}\left [\sin x \right ]\)

\(=2\sin x\times \cos x\)

\(=\sin 2x\)

\(f{}'\left ( 2\pi \right )=\sin \left (2\times 2\pi \right ) =0\)

\(L\left ( x \right )=f\left ( 2\pi \right )+f{}'\left ( 2\pi \right )\left ( x-2\pi \right )\)

\(=0+0\left ( x-2\pi \right )\)

= 0

Step 2 : \(f\left ( x \right )=x+x^{4},\, \, a=0\)

f (0) = - + 0⁴ = 0

\(f{}'\left ( x \right )=\frac{\mathrm{d} }{\mathrm{d} x}\left [x+x^{4} \right ]\)

\(=\frac{\mathrm{d} x}{\mathrm{d} x}+\frac{\mathrm{d} }{\mathrm{d} x}\left [x^{4} \right ]\)

= 1 + 4x³

f' (0) = 1 + 4 x 0³

= 1

L (x) = f(0) + f' (0) (x-0)

= 0 + 1 * x

= x

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Answer:

630

Step-by-step explanation:

350+4000(0.07)

350+280

=630

I think this is right

A natural logarithm is a logarithm with a base of e, where e is a mathematical constant approximately equal to 2.71828.

The notation for a natural logarithm is ln(x), where x is the argument of the function.

The natural logarithm has a special relationship with logarithms with base b.

Specifically, the relationship is:
ln(x) = logb(x) / logb(e)

In other words, to convert a natural logarithm to a logarithm with base b, you divide by the logarithm of e with base b.

Similarly, to convert a logarithm with base b to a natural logarithm, you multiply by the logarithm of e with base b. The notation for a logarithm with base b is logb(x).

The difference in notation between a natural logarithm and a logarithm with base b is the inclusion of the base in the latter.

The natural logarithm is used in many areas of mathematics, especially in calculus and differential equations. It also has applications in physics, engineering, and finance.

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ya man it's kinda hard I don't really know

Therefore, the indefinite integral of f(x) = x - \(tan^{(-1)}(x)\) / x as a power series is:

F(x) = \((1/2)x^2 - (x - x^3/9 + x^5/25 - x^7/49 + ...)\)+ C, where C is the constant of integration.

To evaluate the indefinite integral of f(x) = x -\(tan^{(-1)}(\)x) / x, we can expand tan^(-1)(x) as a power series and then integrate each term.

The power series expansion of tan^(-1)(x) is:

\(tan^{(-1)}(x) = x - x^{3/3} + x^{5/5} - x^{7/7} + ...\)

So, we have:

f(x) = x - (\(x - x^{3/3} + x^{5/5} - x^{7/7} + ...)\) / x

    = x - (x/x - \(x^{3/3}x + x^{5/5}x - x^{7/7}\)x + ...)

    = x - (1 - \(x^{2/3} + x^{4/5} - x^{6/7 }\)+ ...)

Now, we can integrate each term of the power series:

∫ (x - (1 - \(x^{2/3} + x^{4/5} - x^{6/7}\) + ...)) dx

= ∫ x dx - ∫ (1 - \(x^{2/3} + x^{4/5} - x^{6/7}\) + ...) dx

= (1/2)x^2 - (x - \(x^{3/9} + x^{5/25} - x^{7/49}\) + ...) + C

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Answer:

x = 14

Z = 60°

Step-by-step explanation:

9x - 6 = 12x - 48      (because these are congruent vertical angles)

-3x = -42

x = -42/-3 = 14

Find the measure of the vertical angles:

9(14) - 6 = 120   (this angle is supplementary to angle Z)

180 - 120 = 60 = m∠Z

The probability that a randomly selected x-value from the distribution is in the given interval is 68.27%.

The area under the normal curve is calculated using the cumulative normal distribution.

Step 1: Calculate z-score for lower boundary (25):

z = (25-28)/3

= -1

Step 2: Calculate z-score for upper boundary (31):

z = (31-28)/3

= 1

Step 3: Calculate the area under the normal curve between the two z-scores using the cumulative normal distribution:

Area = 0.6827

Step 4: Calculate the probability that a randomly selected x-value from the distribution is in the given interval:

Probability = Area

= 0.6827

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Answer:

Dan is correct

Step-by-step explanation:

Mean = the sum of all data values divided by the total number of data values

Number of adults in Sample A:

= 70 + 90 + 135 + 140 + 65 = 500

Mean of Sample A:

= [ (1 × 70) + (2 × 90) + (3 × 135) + (4 × 140) + (5 × 65) ] ÷ 500

= 1540 ÷ 500

= 3.08

Number of adults in Sample B:

= 80 + 80 + 130 + 135 + 75 = 500

Mean of Sample A:

= [ (1 × 80) + (2 × 80) + (3 × 130) + (4 × 135) + (5 × 75) ] ÷ 500

= 1545 ÷ 500

= 3.09

Mean of the two samples:

= (3.08 + 3.09) ÷ 2

= 3.085 hours

= 3 hours (nearest hour)

The mean of Sample A is 3.08 hours and the mean of Sample B is 3.09 hours, so the mean of the entire sample is 3.085 hours.  If we round this to the nearest hour, then the mean is 3 hours.  Therefore, Dan is correct in concluding that the adults spend a mean of 3 hours each day doing leisure and sports activities.  

(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Answer:

y = -2

Step-by-step explanation:

The equation is y = mx + b

But this line has no slope, but it has a y-intercept at (0,-2), so the equation is

y = -2

Question d:

(D) Find the probability of F'nA'

Answer:

0.4140

0.7619

0.2381

0.9576

Step-by-step explanation:

Given that :

Female in fatal accident P(F) = 0.2805

Driver is 24 years or less P(A) = 0.1759

Driver is female and 24 years or less P(FnA) = 0.0424

A.) Find the probability of FUA.

P(FUA) = P(F) + P(A) - P(FnA)

= 0.2805 + 0.1759 - 0.0424

= 0.4140

(b) Find the probability of F'UA.

P(F'UA) = 1 - P(F) + P(FnA)

= 1 - 0.2805 + 0.0424

= 0.7619

C.) P(FnA') = 1 - P(F'UA)

= 1 - 0.7619

= 0.2381

(d) Find the probability of F'nA'

P(F'nA') = (FnA)' = 1 - (FnA)

= 1 - 0.0424

= 0.9576

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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