rpapenfuse25
2 hours ago
Mathematics
High School
An ordinary (fair) die is a cube with the 1 numbers through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event 1: The sum is greater than 8 .
Event 2: The sum is divisible by 2 .
Write your answers as fraction

Jimmy's approximate monthly payment over the life of the loan is given as follows:

B. $295.

The monthly payment formula is defined by the equation as follows:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which the parameters are listed as follows:

The parameter values for this problem are given as follows:

P = 17000, r = 0.07, n = 6 x 12 = 72.

Hence:

r/12 = 0.07/12 = 0.005833.

Then the monthly payment is obtained as follows:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(A = 17000\frac{0.005833(1.005833)^{72}}{(1.005833)^{72}-1}\)

A = 290.

Which is approximated to $295.

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The union set for the given sets X and Y are: X∪Y = {0,1,2,4,6,8,9}.

The elements shared by all of the sets are contained in the union of two (maybe three, as well as four, or more) sets.

The given sets are;

X={1,2,8,9}

Y={0,1,2,4,6,8,9}

So, union set contains all the values from both set without repeating the values.

Thus,

X∪Y = {0,1,2,4,6,8,9}.

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Answer:

1600$

Step-by-step explanation:

By using the SI formula,

\(SI={PXRXT}/{100} \\SI=10000X2X8/100\\SI = 1600$\\\\Hence, the interest is 1600$\)$

Option C) 1600$ is correct

Mark me brainliest

The fraction of the carton that was used to make breakfast was ⁷/₁₂.

The fraction refers to a portion or part of a whole number.

The fraction is obtained by having a numerator and a denominator, which is the whole value.

Fractional values can also be expressed as decimals or percentages.

The fraction of a carton of eggs that Craig started the day with = ¹¹/₁₂

The fraction or portion remaining after the breakfast = ¹/₃

The fraction Craig used for breakfast = ⁷/₁₂ (¹¹/₁₂ - ¹/₃)

Thus, we can conclude that Craig used ⁷/₁₂ of a carton of eggs for breakfast.

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Answer:

c

Step-by-step explanation:

Answer:

None of the choices are correct.

Step-by-step explanation:

\( 9x^3 + 9x^2 - 4x - 4 = 0 \)

The polynomial has 4 terms and no common factors. We can try factoring by grouping.

\( 9x^2(x + 1) - 4(x + 1) = 0 \)

\( (x + 1)(9x^2 - 4) = 0 \)

Now we factor the difference of squares.

\( (x + 1)(3x + 2)(3x - 2) = 0 \)

\( x + 1 = 0~~or~~3x + 2 = 0~~or~~3x - 2 = 0 \)

\(x = -1~~or~~x = -\dfrac{2}{3}~~or~~x = \dfrac{2}{3}\)

None of the choices are correct.

Stokes' Theorem is a vector calculus theorem used to evaluate surface integrals of a vector field over a curved surface S by calculating the curl of the vector field over a surface S enclosed by a closed curve C. To use Stokes' Theorem, it is essential to have a vector field F and a closed curve C over a surface S

. Here, the surface S is the triangle with vertices (9, 0, 0), (0, 9, 0), and (0, 0, 9).The closed curve C is the boundary of the surface S, which is a triangle with vertices (9, 0, 0), (0, 9, 0), and (0, 0, 9).The given vector field is F(x, y, z) = (x + y^2)i + (y + z^2)j + (z + x^2)k.The curl of F is curl(F) = (∂Q/∂y - ∂P/∂z)i + (∂R/∂z - ∂Q/∂x)j + (∂P/∂x - ∂R/∂y)k= (2y - 2z)i + (2z - 2x)j + (2x - 2y)k.Using Stokes' Theorem, we can evaluate the line integral of vector field F over a closed curve C as follows:∫C F · dr = ∫∫S curl(F) · dS= ∫∫S (2y - 2z)i + (2z - 2x)j + (2x - 2y)k · dS.Now, we need to find the normal vector of the given surface S, which is given by N = ±((9, 0, 0) × (0, 9, 0)) ± ((0, 9, 0) × (0, 0, 9)) ± ((0, 0, 9) × (9, 0, 0)))= ±(-81i - 81j - 81k) = ±(-81, -81, -81).We know that C is oriented counterclockwise as viewed from above. Therefore, the outward normal vector is N = (81, 81, 81).Let us consider the projection of the triangle S on the xy plane. We can see that the projection is a right triangle with legs 9. Therefore, the area of the triangle S is A = 1/2 (9)(9) = 40.5.So, ∫∫S (2y - 2z)i + (2z - 2x)j + (2x - 2y)k · dS = ∫∫S (2y - 2z)i + (2z - 2x)j + (2x - 2y)k · N dA= ∫∫S (2y - 2z, 2z - 2x, 2x - 2y) · (81, 81, 81) dA= 81 ∫∫S (2y - 2z + 2z - 2x + 2x - 2y) dA= 81 ∫∫S 0 dA= 0.the value of the line integral of vector field F over the closed curve C is 0. To find the value of the line integral of vector field F over the closed curve C using Stokes' Theorem, we first found the curl of F, which is (2y - 2z)i + (2z - 2x)j + (2x - 2y)k. Then, we found the normal vector of the surface S, which is (81, 81, 81), since the curve C is oriented counterclockwise as viewed from above. Next, we found the area of the surface S, which is 40.5. Finally, we used the formula of Stokes' Theorem to find the value of the line integral of vector field F over the closed curve C, which is 0.

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Random numbers are frequently used in computing and are invaluable tools for applications requiring random outcomes. Random numbers can be used to give random outcomes, such as in a game of chance, where each player has an unpredictable chance of winning. They can also be used to describe the uncertainty of input values, such as when making decisions using probabilistic models.

Random numbers can also be used to assign values to the parameters of a problem, such as in genetic algorithms, where random initial values are used to explore the potential solutions.

Finally, random numbers can also be used to change the problem solution, as in simulated annealing, where a series of random changes is used to find the optimal solution. In conclusion, random numbers can serve many useful and important purposes in computing and are a key part of many problem-solving algorithms.

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The equation of the red graph, whereby the quadratic function, represented by the blue graph and the red graph have the same shape is g(x) = 2 - x², therefore;

C. g(x) = 2 - x²

The sign of the leading coefficient (the coefficient of the variable with the highest index) determines the shape of a quadratic function.

The graph is concave downward, ∩ shaped, which indicates that the leading coefficient has a negative value.

The coordinates of the x- and y-intercepts and the shape of the functions f(x) and g(x) indicates;

The difference between the y-intercept of the function f(x) and g(x) is 3, which indicates that the g(x) = f(x) - 3

The x-intercepts of the red graph g(x) are located at about √2 and -√2, and the peak of the function is located on the y-axis which indicates the function g(x) is symmetrical about the y-axis, and the form of the function is therefore; g(x) = a - b·x², where, a is the y-intercept.

The y-intercept of the function g(x) is (0, 2)

Therefore, the possible equation of the function g(x) = 5 - x² - 3 = 2 - x²

g(x) = 2 - x²

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Answer:

198

Step-by-step explanation:

rectangular side (9,3)

9x3=27

27x2= 54 (because there's rectangular sides)

Square end(6,3)

6x3=18

18x2=36(two square sides)

top&bottom sides

6x9=54

54xsquared2=108(two sides)

add all together

54+36+108=198cm(squared)

The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.

What is Pythagorean theorem?

The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.

The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.

The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.

The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.

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Answer:

AC = 9

Step-by-step explanation:

\( \frac{3}{1} = \frac{ac}{3} \\ ac = 3 \times 3 \\ 9\)

Answer:

  3.75 miles

Step-by-step explanation:

You want to know the number of miles represented by 6 km, when the relationship is 1.6 km = 1 mile.

Anytime measures are related by a constant conversion factor, the values of the measures in one unit are proportional to the values expressed in a different unit. That is, the ratio of km to miles is a constant.

We can let d represent the distance between the school and the park.

  miles / km = (1 mi)/(1.6 km) = d/(6 km) . . . . miles and km are proportional

Multiplying by 6 km, we get ...

  d = (6 km)(1 mi)/(1.6 km) = (6/1.6) mi ≈ 3.75 mi

The school and the park are 3.75 miles apart.

Answer:

2 days: 1 week

Step-by-step explanation:

4 days : 2 weeks

2 2

2:1

Answer:

Step-by-step explanation:

So we Have 4 days to 2 weeks

In order to simplify this, we need to turn weeks into days

2 x 7 = 14

so 4 days to 14 days

Now we divide and fnd a common multiple

4/2 = 2

and 14/2 = 7

so, 2 days to 7 days, or 2/7

We can leave it at that, or turn it into a decimal

4/14 =0.2857

Hope this helps!^^

A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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It would be 1 by 3

Since [4 -1 0] and [2 1 0] are both 1 by 3, the result should be the same since they match up.

also im learning the same thing right now lol

Answer:

210 ways

Step-by-step explanation:

In the question, the combination should be computed.

Number of ways of selection 6 flowers = nCr =10C6

                                           \(\frac{n!}{r!(n-r)!}\)  =\(\frac{10!}{ 6!(10-6)!}\)

                                                        =3628800/17280

                                                       =210

Therefore, there are 210 ways in which 6 flowers can be selected from the available 10 flowers.

Answer:

Therefore, there are 210 ways in which 6 flowers can be selected from the available 10 flowers.

Step-by-step explanation:

explanation

Answer:

  50 ft by 25 ft . . . . . 50 ft parallel to the barn

Step-by-step explanation:

You want the dimensions of the largest rectangular area that can be enclosed using 100 ft of fence for three sides.

If the dimensions of the space are L feet in length and W feet in width, where L is parallel to the barn, the length of the perimeter fence is ...

  P = L +2W

Solving for W gives ...

  W = (P -L)/2

The area of the enclosed space is ...

  A = LW

  A = L(P -L)/2 . . . . . substitute for W

The area formula is the equation for a parabola that opens downward. It has zeros at L=0 and at L=P. The vertex (maximum) is found at the value of L that lies on the line of symmetry, halfway between these zeros. If we call that length M, then we have ...

  M = (0 +P)/2 = P/2

The length of enclosure that maximizes the area is 1/2 the length of the available fence.

The width is ...

  W = (P -P/2)/2 = P/4

The width of the enclosure that maximizes the area is 1/4 the length of the available fence.

Using 100 feet of fence, the dimensions are ...

__

Additional comment

Note that we have solved this in a generic way. The solution given is the general solution to the 3-sided enclosure problem.

This is a special case of the general rectangular enclosure problem which has the solution that the total cost in one direction is equal to the total cost in the orthogonal direction. This rule applies even when costs are different for the different sides or for any partitions that might divide the enclosure.

Here the "cost" is simply the length of the fence. The 50 ft of fence parallel to the barn is equal in length to the 25 +25 ft of fence perpendicular to the barn.

The dimensions that give the maximum area inside the rectangle are x = 50 feet (parallel to the barn wall) and y = 25 feet (perpendicular to the barn wall).

To maximize the area of the rectangular fence, follow these steps:

1. Let's assign variables to the dimensions: let the length of the rectangle parallel to the barn wall be x feet, and the length perpendicular to the barn wall be y feet.

2. We are given that 100 feet of fence will be used for the other three sides. This means the fencing equation is:

x + 2y = 100.

3. Solve for x:  x = 100 - 2y.

4. The area A of the rectangle is given by the product of its dimensions: A = xy.

5. Substitute the expression for x from step 3 into the area formula:  A = (100 - 2y)y.

6. Expand the expression: A = 100y - 2y^2.

7. To maximize the area, we need to find the maximum value of the quadratic function A(y). Since the coefficient of the y^2 term is negative, the graph of A(y) is a downward-opening parabola, which means it has a maximum value.

8. To find the maximum, we'll use the vertex formula for parabolas: y_vertex = -b/(2a), where a = -2 and b = 100. Plugging in these values, we get y_vertex = -100/(2 * -2) = 25.

9. Substitute the value of y_vertex back into the equation for x: x = 100 - 2(25) = 50.

10. So the dimensions that give the maximum area inside the rectangle are x = 50 feet (parallel to the barn wall) and y = 25 feet (perpendicular to the barn wall).

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Answer:

B

Step-by-step explanation:

Now, the total amount of discount eligible by Jamie to be applied will be the percentage on the hardcover books plus the percentage on the fiction books

Mathematically, that would be 20% + 15% = 35%

So what this means is that , Jamie is entitled to a total of 35% off

So applying this to the price of the book, we have;

32.99 -(35/100 * 32.99)

= 32.99-(0.35 * 32.99)

= 32.99-(11.5465) = $21.4435

So if she is paying 21.4435 for the book, the amount saved will be 32-21.4435 = $11.5465 which is approximately $11.55

Answer:

A. $10.56

Step-by-step explanation:

20% of $32.99 equals $6.60

$32.99-$6.60 = $26.39

$26.39 x 15%= $3.96

$6.60 +$3.96 = $10.56

The lower bound of the 95% confidence interval is given as follows:

7.981 mm.

The level of confidence of the statement is of 95%.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.

The parameters for this problem are given as follows:

\(\overline{x} = 8.1, s = 0.6, n = 100\)

Hence the lower bound of the interval is given as follows:

8.1 - 1.9842 x 0.6/10 = 7.981 mm.

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Answer:

This means that 1cm on the map means 10miles on actual land so is it the same for 30miles

That is 1cm on map 30 cm on land

Answer:

\({ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} \)

520 x 12 months x 4 years = 24960

24960 + 3000 deposit = 27,960 total paid.

27,960 - 13,000 = 14,960 total interest paid

Answer:

If the family has $800 for sit-down restaurant meals and fast food and they budgeted all of it for fast food, then they can buy $800/$20 = 40 fast food meals.

Step-by-step explanation:

yw;)

Answer:

40

Step-by-step explanation:

No. Of Meal=Budget/price of Meal

=800/ 20

=40

Your answer is A!

Step-by-step explanation:

Your answer is A!

The coordinate point from the given graph is (3, -5). Therefore, option A is the correct answer.

A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.

From the given coordinate plane, the coordinate point lies in fourth quadrant.

Where, x-coordinate is positive and y-coordinate is is negative.

The coordinate point correspond to x-axis is 3 and coordinate point correspond to y-axis is 5.

So, the coordinate point is (3, -5)

Therefore, option A is the correct answer.

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Answer:

17

Step-by-step explanation:

You would make the 10.01 a 10 and the 7.07 a 7.

Answer:

False

Step-by-step explanation:

If you connect it, it won't make sense.

y>x - 2

Now plug it in

2 > -3 -2

2 > -5

That's true, but look at the next one

x >= 1

Plug it in

-3 >= 1

-3 isn't greater OR equal to 1, therefore it's false. I know for a fact, if one system isn't true for the point, then NONE of them are. It asked if the point was a solution to the whole system not just one. Trust me, it's false, whether you already "took the test" or not.

Answer:

£3.96

Step-by-step explanation:

Data obtained from the question include:

Isaac's ratio = 2

Victoria's ratio = 5

Total ratio = 2 + 5 = 7

Amount Victoria recieve = £6.60.

Next, we shall determine the total amount of money shared by Isaac and Victoria. This is illustrated below:

Let T be the total amount of money shared.

Victoria received = £6.60

Victoria's share =

Victoria's ratio/total ratio x total amount

£6.60 = 5/7 x T

£6.60 = 5T/7

Cross multiply

5T = £6.60 x 7

5T = £46.2

Divide both side by 5

T = £46.2/5

T = £9.24

Therefore, the total amount shared is £9.24.

Next, we shall determine the amount received by Isaac. This is illustrated below:

Victoria's share = £6.60

Total amount shared = £9.24.

Isaac's share =?

Isaac's share = Total amount shared – Victoria's share

Isaac's share = £9.24 – £6.60

Isaac's share = £2.64

Therefore, Isaac received £2.64

Finally, we shall determine the difference between how much money Isaac and Victoria receive. This is illustrated below:

Victoria recieve = £6.60

Isaac receive = £2.64

Difference = £6.60 – £2.64

Difference = £3.96

Therefore, the difference in the amount received by Victoria and Isaac is £3.96