what is the probability that the first card you draw is a heart, the second card is a jack, and you roll the same number twice?

The exact values of trigonometric functions cosine and tangent are 4 / 5 and 3 / 4, respectively.

How to determine the exact value of a trigonometric function

In this question we must determine the exact value of two trigonometric functions on the basis a given value of another trigonometric function, whose quadrant is also known. According to the statement, sine is in the first quadrant, then both cosine and tangent are also positive. The value of cosine can be found by means of following trigonometric formula:

cos θ = √(1 - sin² θ)

cos θ = √[1 - (3 / 5)²]

cos θ = 4 / 5

And the exact value of tangent can be found by this formula:

tan θ = sin θ / cos θ

tan θ = (3 / 5) / (4 / 5)

tan θ = 3 / 4

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The probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.

The probability of rolling a 1 with the first die and a 5 with the second die can be calculated using the joint probability formula. The joint probability formula is P(A ∩ B) = P(A) x P(B|A). In this case, A is rolling a 1 with the first die and B is rolling a 5 with the second die. P(A) is the probability of rolling a 1 with the first die, which is 1/6. P(B|A) is the probability of rolling a 5 with the second die given that a 1 was rolled with the first die, which is also 1/6. Therefore, the probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.

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Answer:

5.18181818182

5.2 (nearest 10th)

Step-by-step explanation:

The third term of this arithmetic sequence is 21.

eleventh term of an arithmetic sequence is 69.

a₁₁ = a + 10 d = 69

also sum of the first three terms is 45

the first three terms are a, a + d, a + 2d

a + a + d + a + 2d = 45

3a + 3d = 45

a + d = 15

a = 15 - d

so, a + 10 d = 69

15 - d + 10d = 69

9d = 69 - 15

9d = 54

d = 6

a = 15 - 6 = 9

a₃ = a + 2d

   = 9 + 2(6)

a₃ = 21

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A plurality of magnitude can represent the property of number or amount, which exhibits both discontinuity and continuity and in the given situation, we would pay a quantitative amount to the seller.

A property called quantity or amount can take the form of a plurality of magnitude, which shows both discontinuity and continuity.

Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.

Among the well-known examples of quantitative qualities are mass, time, distance, heat, and angle.

Along with quality, substance, change, and relationship, quantity is one of the fundamental categories of things.

Some quantities serve as states (properties, dimensions, qualities) of things like heavy and light, long and short, broad and narrow, little and large, or much and little, while others are such by their very nature (as numbers).

Therefore, in the given situation, we would pay a quantitative amount to the seller.

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Correct question:

J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012.

What Price did you pay?

The slope of the situation is 10.20. Answer (a) is correct.

The cost of the breakfast platter of 12 bagels is $10.20 and the cost of a gallon of coffee is $4.65.

The slope represents the rate of change between two variables, typically represented as y and x. In this case, it's not clear which variables we should use to calculate the slope. If we use the number of bagels as x and the cost as y, then the slope would represent the rate of change in cost per bagel.

Alternatively, if we use the gallons of coffee as x and the total cost as y, then we can calculate the slope. The total cost would be the sum of the cost of bagels and the cost of coffee, which is $10.20 + $4.65 = $14.85.

Using the formula for slope, which is (change in y) / (change in x), we can calculate the slope as follows:

slope = (change in cost) / (change in gallons of coffee)

= ($14.85 - $4.65) / (1 - 0)

= $10.20 / 1

= 10.20

Therefore, the slope of the situation is 10.20. Answer (a) is correct.

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Answer:

The weight is 95.53 ounces of bluegill which has a length of 9.5 inches using linear regression.

Step-by-step explanation:

good luck to you

With his average speed of 3mph, Viktor should leave his house by 6:36 am to arrive at the skaring rink on time.

From the case, we know that:

Average speed = 3.0 mph

Distance = 1.2 miles

Arrival time = 7:00 am

Departure time?

Using the average speed concept, we know that average speed can be calculated by dividing the travel distance with the travel time, or it can be formulated as:

Average speed = distance : travel time

3.0 = 1.2 : travel time

travel time = 0.4 hours

After finding the travel time Viktor spend to go from his house to the skating rink, we need to find the departure time for him to arrieve at the skating rink on time. However, we need to convert the travel time into minutes first.

Travel time = 0.4 hours

Travel time = 0.4 x 60 minutes

Travel time = 24 minutes

Arrival time = Departure time + Travel time

7:00 = Departure time + 24 minutes

Departure time = 6:36 am or 24 minutes before 7:00 am

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Step-by-step explanation:

Pythagoras

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

Plugging in numbers

[tex] {4}^{2} + {8}^{2} = {c}^{2} [/tex]

If we do the math given

[tex]16 + 64 = {c}^{2} - - - 80 = {c}^{2} [/tex]

Last but not least, we root both sides

[tex] \sqrt{80} = c[/tex]

Which means C = 8.9

The volume of the resulting solid is 3,280.953 cm3.

The volume of the resulting solid is calculated by subtracting the volume of the inner sphere (the hole) from the volume of the outer sphere (the ball). The volume of a sphere is calculated by the formula V=4/3πr3. Therefore, the volume of the outer sphere is V1=4/3π(13)3=4,714.286 cm3. Similarly, the volume of the inner sphere is V2=4/3π(7)3=1,433.333 cm3. Subtracting V2 from V1 gives the volume of the resulting solid as V3=4,714.286 - 1,433.333=3,280.953 cm3. Therefore, the volume of the resulting solid is 3,280.953 cm3.

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The tangent line is y=x-1 and differentiation of ln(x) is 1/x

What does differentiation in mathematics mean?

Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables.

                            The most prevalent example is velocity, which is the rate at which a distance changes in relation to time.

The ratio of the vertical to the horizontal distance between any two points on it  is called slope of ray or line or line segment in analytical geometry.

y-y1 = m(x-x1)

If the function passes through (1,0)  and the slope equals to 1 is:

y-0 = 1(x-1)

y=x-1

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The complete question is -

Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.

The potential energy of the water in a lake is 57 trillion N × m, which is 57 trillion joules (J).

Gravitational potential energy applies in this situation. G P E = m g h is the formula for gravitational potential energy, where: mg stands for weight or mass times gravity (w). The height to which an object can fall before kinetic energy replaces potential energy is denoted by the symbol h. In the example of the lake, we first determine the amount of water using the equation for the volume of a typical cylinder in order to determine the weight of the cylinder: V cy l = π r²L , The weight density of the water per cubic foot, which is about 62 lb, can then be multiplied by this volume: W(water) = (Volume) (Density)

W (water) = (28,000,000 ft² ⋅ 40ft) ( 62 lb ÷ ft³ )

W (water) = 69,440,000,000 lb

To calculate the potential energy, multiply this weight by the height. GPE=mgh

GPE=Wh=(69,440,000,000lb)(600ft)

GPE=41,644,000,000,000ft⋅lb

matching the level of precision by rounding the response to two significant digits. 4.2X10¹³ft⋅lb , or 42 trillion ft-lb.

Because joules are measured in N × m units, multiply the result by fractional equivalencies. 42trillionft × lb × (4.45N ÷ lb) × (m ÷ 3.28ft)

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Answer:

2(x+2)² - 18

Step-by-step explanation:

Given

2x² +8x-10

express in the form a(x + b)² + c

Take out common factor 2 from 2x² +8x-10 ==> 2(x² + 4x -5)

x² + 4x - 5 can be converted to the form (x + b)² + c as follows using complete the square technique

(x + b)² = x² +2bx + b²

Comparing  x² +2bx + b² and x² + 4x - 5 we can see that b = 2

So the expression becomes
x² + 4x - 5 = (x+2)³ + c
= x² + 4x + 4 + c

Therefore -5 = 4 - c

c = -5 -4 = -9

Therefore
x² + 4x - 5 = (x+2)³ -9

2(x² + 4x -5) = 2[(x+2)³ -9]

=2(x+2)² -18

ANSWER

Verify

2(x+2)² -18 = 2(x² +4x + 4) - 18 = 2x²+8x +8 - 18 = 2x² + 8x - 10
Thus verified

Answer:

  (3, 6)

Step-by-step explanation:

You want the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7).

The orthocenter is the point where the altitudes of the triangle meet. An altitude is the line through a vertex that is perpendicular to the opposite side.

This is an acute triangle, so the orthocenter is within the boundaries of the triangle.

We note that side WY of the triangle is a horizontal line, so the orthocenter will lie on the vertical line through point X. The x-coordinate of point X is 3, so that vertical line has equation x=3.

Side XY can be seen on the graph to have a slope of 1. Or, you can compute it from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -4)/(6 -3) = 3/3 = 1

Then the point-slope equation of the altitude to that line will have the opposite reciprocal slope, and will go through point W(2, 7):

  y -7 = -1(x -2)

The y-value of the point of intersection of the altitude through W with the altitude through X will be the solution to ...

Substituting for x in the second equation, we have ...

  y -7 = -3 +2

  y = 6 . . . . . . . . . . add 7

The orthocenter is (x, y) = (3, 6).

__

Additional comment

The orthocenter of a right triangle is the vertex where the right angle is located. The orthocenter of an obtuse triangle is outside the triangle.

Answer: 1/5

Step-by-step explanation:

Answer:

Answer provided in image May it help you !!!

Step-by-step explanation:

Answer:

A collection of facts, such as numbers, words, measurements, observations.

Step-by-step explanation:

Answer:

8595.4

Step-by-step explanation:

The formula for volume of cylinder is: V = [tex]\pi[/tex][tex]r^{2} h[/tex]

[tex]\pi[/tex] = 3.14

radius = 12

height = 19

plug in the numbers which would give us = 3.14(12)^2(19)

which gives us 8595.4

Answer:

Step-by-step explanation:

can you include a picture please

Answer:

7-isoceles, 8- equilateral 9-scalene

Step-by-step explanation:

isoceles have 2 identical sides unlike scalene, where all sides have different lengths.

is obtuse and acute I think

The simplification of the given expression gives the value 2(a + b) / a(a - b).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is,

[(a + b) / 2a²] ÷ [(a - b) / 4a]

The fractional term in the denominator of the main expression can be written as the multiplication of it's reciprocal.

[tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{d}{c}[/tex]

So the expression becomes,

[tex]\frac{a+b}{2a^2}[/tex] × [tex]\frac{4a}{a-b}[/tex]

= 2(a + b) / a(a - b)

Hence the simplified form of the given expression is 2(a + b) / a(a - b).

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Answer: -165.59

Step-by-step explanation: Search math w ay on the internet :)

The figure with the least surface area is the cube.

The surface area of a 3 dimensional figure or solid figure is the sum of the area of the whole surface.

Therefore,

surface area of the cube = 6a²

where

surface area of the cube = 6 × 6²

surface area of the cube = 6 × 36

surface area of the cube = 216 units²

surface area of the second rectangular prism = 2(lh + lw + hw)

where

Therefore,

surface area of the second rectangular prism = 2(54 + 54 + 16)

surface area of the second rectangular prism = 2(124)

surface area of the second rectangular prism = 248 units²

Therefore,

surface area of the third rectangular prism = 2(13.5 + 216 + 16)

surface area of the third rectangular prism = 2(245.5)

surface area of the third rectangular prism = 491 units²

Therefore, the least surface area is the cube.

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The minimum total cost for the company if all of the order constraints are fulfilled is given as follows:

$25.

The cost function is given as follows:

C = 3x + 2y.

Meaning that:

The relevant restrictions to minimize the costs are given as follows:

Since an item y costs less than an item x, considering the second bullet point above, the cost is minimized with an equal amount of x and y.

From the first restriction, they must have at least 10 amounts, hence the cost is minimized with:

x = 5 and y = 5.

And the cost is of:

C = 3 x 5 + 2 x 5

C = $25.

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Answer:$2.97

Step-by-step explanation: 35 divided by 12 = 2.97

Answer:

E. and F.  (11 and 15).  D. is not correct since the equation says > 8, not >= to 8.

Step-by-step explanation:

3(2x-1)>5(x+1)

6x-3>5x+5

x>8

Even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.

Freelancer, freelancer, or freelance worker are phrases frequently used to describe someone who is self-employed and isn't necessarily long-term dedicated to a certain employer.

Others work independently or use websites or professional associations to find work.

Freelancers are occasionally represented by a business or a temporary agency that resells their services to clients.

Independent contractors must always pay taxes on their wages, regardless of how much they make.

The term "freelancing" is most frequently used in the culture and creative industries, and use of this term may indicate participation in these sectors, even though the term "independent contractor" would be used in a different register of English to designate the tax and employment classes of this type of worker.

Therefore, even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.

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The standard deviation for the given data is 5

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Given that,

the data,

X            Xₙ - X₀            (Xₙ - X₀)²

18            -7                      49

21             -4                      16

24            -1                        1

24            -1                        1

25             0                       0

31              6                      36

32            7                     49  

175                                  152

X₀  = 175/7 = 25

Variance  =    (Xₙ - X₀)²/(n-1)

                 =  152/(7-1)

                 =   25.33

Standard deviation =  √Variance

                                =  √25.33

                                =   5.03

Hence, the standard deviation is 5

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The probability that fund-raising event is a success and total contributors exceeds $5,000 is 0.0351  or 3.51%

Number of family members = 40

Mean of individual contributions for each family is normally distributed is $115 (μ) and standard deviation(σ) is $35. It is also given that the organizers would call this event a success if the total contributions exceed $5,000

Mean = [tex]\frac{5000}{40}[/tex]

Mean = 125

P-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

P(mean > 125) = P( 2 > [tex]\frac{(125 - 115)\sqrt{40} }{35}[/tex] )

                      = P(2 > 1.81)

                      = 1 - P(2 < 1.81)

1.81 has a pvalue of 0.9649

                      ≅ 0.0351

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