A cubic die is biased, so that for each integer n,1≤n≤6 , the probability of the event {n} is p({n})=2p if n=3 or n=4 and p({n})=p , otherwise a) What is the expected number of times the die comes up 6 , when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?

Assuming that ∠1 and its adjacent angle form a straight line, we know that the sum of the angles on a straight line is 180°. Therefore, the measure of the adjacent angle is 180° - 39° = 141°.

we can also look at the other angles in the figure. From the diagram, we can see that ∠2 and ∠3 are acute angles, which means they are less than 90°. Additionally, we know that the sum of the angles in a triangle is 180°, so ∠2 + ∠3 + ∠4 = 180°.

Since ∠2 and ∠3 are acute, their sum must be less than 180°. Therefore, ∠4 must be an obtuse angle (greater than 90°) in order for the sum to be 180°. This makes sense, as an obtuse angle is required to form a triangle with two acute angles.

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Answer:

D

Step-by-step explanation:

To calculate the percentage decrease in price, we need to find the difference between the original price and the reduced price, divide that difference by the original price, and then multiply by 100 to express it as a percentage.

The original price of the iPhone was $320, and it was reduced to $224. Therefore, the difference between the two prices is:

$320 - $224 = $96

To find the percentage decrease, we divide this difference by the original price:

$96 ÷ $320 = 0.3

Finally, we multiply this result by 100 to express it as a percentage:

0.3 × 100 = 30%

Therefore, the answer is D. The price of the iPhone was reduced by 30%.

Answer:

3.33 minutes

Step-by-step explanation:

first know that the escalator can move 30 people in 1 minute.

then, we can write in a mathematical expression as:

30 people = 1 minute

100 people = ? minutes.

cross multiply, i.e. 30×? = 100×1

therefore, ? = 100/30

? = 3.33 minutes.

therefore, it's going to take 3.33 minutes for the escalorr to take 100 people.

Answer:

Step-by-step explanation:

2534 i think

The direction of the resulting force upon the piling is approximately 298.85 degrees

We can use vector addition to find the direction of the resulting force. Let's call the force exerted by the first bulldozer F1, and the force exerted by the second bulldozer F2. We can represent each force as a vector with a magnitude and direction.

F1 has a magnitude of 1850 pounds and points in a westerly direction. We can represent it as a vector (-1850, 0).

F2 has a magnitude of 3250 pounds and points in a northerly direction. We can represent it as a vector (0, 3250).

To find the resulting force, we need to add these two vectors. We can do this by adding the x-components and the y-components separately.

The x-component of the resulting force is -1850 (from F1) plus 0 (from F2), which is -1850.

The y-component of the resulting force is 0 (from F1) plus 3250 (from F2), which is 3250.

So the resulting force is a vector with components (-1850, 3250). We can find the direction of this vector by taking the inverse tangent of the ratio of the y-component to the x-component.

tan(theta) = (3250) / (-1850)

theta = -61.15 degrees

The negative sign indicates that the resulting force points to the southwest. To get the angle in the range of 0 to 360 degrees, we can add 360 degrees to the angle if it is negative.

theta = 360 - 61.15

theta = 298.85 degrees

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Answer:

1.)

[tex]R = 8/17\\S = 15/17[/tex]

2.)

[tex]R = 5/13[/tex]

[tex]S=12/13[/tex]

Step-by-step explanation: sin represents the ratio between a side opposite to an angle and the hypotenuse. It is important to learn these ratios as they allow for you to solve for side lengths in a triangle and angles. We were in this case finding the ratios. A lowercase letter represents a side length opposite to the angle. So to find R we would just need to divide r by t. In the first example, it would just be 16/34 which simplifies to 8/17. Do the same thing for s, and it would be for 30/34 which simplifies to 15/17. Repeat the same steps and you should get 5/13 for R and 12/13 for S.

This point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.

A. It is easy to compute the slope using this point.

B. The​ y-coordinate of this point is the​ y-intercept.

A data point with an x-coordinate of 0 is a good point to use when creating a trend line for a data set because it is easy to compute the slope using this point. The y-coordinate of this point is also the y-intercept, which is the point at which the line crosses the y-axis. Additionally, the coordinates of this point are both 0, making it easy to locate on a graph. While this point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.

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The probability density function (PDF) is a mathematical function that describes the probability of a random variable taking a certain value. It is a measure of the probability of a given outcome within a given range.

Probability is a branch of mathematics used to quantify the likelihood of an event occurring. It is used to calculate the chances of a certain outcome or a combination of outcomes in a given situation. Probability is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. Probability is used to make predictions, analyze data, and understand the complexity of the world around us.

b. The probability of generating a random number between 0.25 and 0.85 (to 1 decimal place) is 0.6.

c. The probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place) is 0.4.

d. The probability of generating a random number with a value greater than 0.6 (to 1 decimal place) is 0.4.

e. The mean of the given set of 50 random numbers is 0.527084 and the standard deviation is 0.307766.

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A mathematical function known as the probability density function (PDF) calculates the likelihood that a random variable will have a particular value. It is a measurement of the likelihood of a specific outcome within a specific range.

What is probability?

Mathematics' branch of probability is used to determine how likely an event is to occur. It is employed to determine the probabilities of a specific outcome or a mixture of outcomes in a particular circumstance. A number between 0 and 1 is used to represent probability, with 1 denoting a certain event and 0 denoting an impossibility. To generate predictions, examine data, and comprehend how complicated the world is around us, probability is used.

b. The probability of generating a random number between 0.25 and 0.85 (to 1 decimal place) is 0.6.

c. The probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place) is 0.4.

d. The probability of generating a random number with a value greater than 0.6 (to 1 decimal place) is 0.4.

e. The mean of the given set of 50 random numbers is 0.527084 and the standard deviation is 0.307766.

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Answer: not sure

Step-by-step explanation: it would help me if you had a pic of the worksheet to help you with the problem

Janella recognizes a gain of $36,000 and her basis in the distributed property is $54,000.

Janella's basis in her partnership interest is $120,000, which includes her share of partnership debt. When the partnership pays off its debts and liquidates, Janella receives a proportionate liquidating distribution consisting of $42,000 cash and inventory valued at $24,000 (adjusted basis to the partnership = $20,000).

To calculate Janella's recognized gain or loss, we need to compare her basis in the partnership interest to the fair market value of the distributed assets.

The fair market value of the distributed assets is $42,000 (cash) + $24,000 (inventory) = $66,000.

The amount of the loss is the excess of her basis over the fair market value of the distributed assets, which is $120,000 - $66,000 = $54,000.

To determine Janella's basis in the distributed property, we need to adjust her basis in the partnership interest by the amount of the liquidating distribution she received.

Janella received a total liquidating distribution of $42,000 cash + $24,000 inventory = $66,000. Her share of partnership debt was $150,000, and the partnership paid off all its debts, so she no longer has any debt basis.

Janella's distribution of $66,000 exceeds her adjusted basis of $30,000 by $36,000. She recognizes a gain of $36,000. Therefore, Janella's new basis in the distributed property is $120,000 - $66,000 (liquidating distribution) = $54,000.

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Case 1: The value of the vector B is equal to [tex]\overrightarrow {B} = (7, - 20)[/tex].

Case 2: The values of variables m and n from vector operations are - 5 and - 4, respectively.

In this problem we find two cases of operations between two vectors. According to linear algebra, there are two fundamental operations:

Case 1:

The value if vector B can be found by following operation:

[tex]\overrightarrow{B} - \overrightarrow {A} = (5, - 5)[/tex]

[tex]\overrightarrow {B} = \overrightarrow {A} + (5, - 5)[/tex]

[tex]\overrightarrow{B} = (2, - 4) + (5, - 5)[/tex]

[tex]\overrightarrow{B} = (2 + 5, - 4 - 5)[/tex]

[tex]\overrightarrow {B} = (7, - 20)[/tex]

Case 2:

First, determine the expression for the given operator:

2 · a - 2 · b = 2 · (- 3, m) - 2 · (n, - 4)

2 · a - 2 · b = (- 6, 2 · m) + (- 2 · n, 8)

2 · a - 2 · b = (- 6 - 2 · n, 2 · m + 8)

Second, find the values of m and n:

(- 6 - 2 · n, 2 · m + 8) = (2, - 2)

- 6 - 2 · n = 2

- 3 - n = 1

n = - 4

2 · m + 8 = - 2

- m - 4 = 1

m = - 5

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The total surface area of the solid cone, given the slant height and the radius, would be 374 m².

To find the surface area of a solid cone, we need to consider both the curved lateral surface and the circular base.

Lateral Surface Area = π x 7 m x 10 m = 70π m²

The base of a cone is a circle with radius r. The area of the base can be calculated using the formula:

Base Area = π x (7 m)² = 49π m²

Total Surface Area = Lateral Surface Area + Base Area = 70π m² + 49π m² = 374 m².

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Therefore , the solution of the given problem of unitary method comes out to be the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).

By applying what was acquired and bringing this variable tactic into practise, along with all supporting information from two people who used a particular tactic, the work can be finished. In other words, if the wanted expression result occurs, either the entity specified in the formula will also be discovered, or both crucial processes will actually ignore the colour. A refundable fee of Rupees ($1.01) may be necessary for forty pencils.

Here,

The water bottle is currently 3/5 full and contains 24 1/4 ounces of water.

By dividing the bottle's capacity by the percentage that indicates how filled it is, we can determine how much water is inside:

=> 24 1/4 × 3/5 = (97/4) × (3/5)

=> 291/20 = 14 11/20

Therefore, there are 14 11/20 ounces of water in the water container.

We want to fill three cups, each of which needs five ounces of water, so we will need:

=>  5 x 3 = 15 ounces

There isn't enough water in the bottle to fill three glasses with 5 ounces each because the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).

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Answer:

The error in Amanda's calculation is in line 2, where she incorrectly subtracted 6x instead of adding 6x, as well as incorrectly subtracting 24 instead of adding 24.  Amanda also omitted the addition sign in line 3 of her calculations.

Step-by-step explanation:

To factor a quadratic polynomial in the form ax² + bx + c, find two numbers that multiply to ac and sum to b.

Therefore, for the given polynomial 4x² + 22x + 24:

⇒ ac = 4 · 24 = 96

⇒ b = 22

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

Therefore, the factor pair that sums to 22 is 16 and 6.

Rewrite b as the sum of these two numbers:

⇒ 4x² + 22x + 24

⇒ 4x² + (16 + 6)x + 24

⇒ 4x² + 16x + 6x + 24

Therefore, the error in Amanda's calculation is in line 2, where she incorrectly subtracted 6x instead of adding 6x, as well as incorrectly subtracting 24 instead of adding 24.  Amanda also omitted the addition sign in line 3 of her calculations.

The correct calculation is as follows:

   4x² + 22x + 24

⇒ 4x² + 16x + 6x + 24

⇒ 4x(x + 4) + 6(x + 4)

⇒ (4x + 6)(x + 4)

Given :-

To find:-

Answer:-

Given polynomial to us is ,

[tex]\implies 4x^2 + 22x + 24 \\[/tex]

With respect to the standard form of polynomial ax² + bx + c , we have;

Step 1 :- Split the middle term into two parts p and q such that p × q = a × c and p + q = b

Such two numbers are 16 and 6 .

Hence, we can rewrite it as ,

[tex]\implies 4x^2 + 16x + 6x + 24 \\[/tex]

But Amanda wrote [tex] 4x^2+16x - 6x + 24[/tex] , so she made a mistake here by writing +6x as -6x .

Step 2:- Factor out the common terms .

[tex]\implies 4x( x + 4) + 6(x+4) \\[/tex]

Step 3 :- Take out [tex] x+4[/tex] as common.

[tex]\implies (x+4)(4x+6) \\[/tex]

This is our required factored form .

Hence we can see that Amanda made a mistake only in splitting the term term .

and we are done!

The total area of gray sections of the target is  1017 square inches. The correct option is (D).

To find the total area of the gray sections of the target, we need to first find the areas of the gray rings. We can do this by subtracting the area of the smaller circle from the area of the larger circle for each ring.

The area of a circle is given by the formula A = πr^2, where r is the radius.

For the outer gray ring, the radius is 1.5 feet. So, the area of the gray ring is:

A_gray_outer = π(1.5)^2 - π(1)^2

= 7.06858 - 3.14159

= 3.92699 square feet

For the middle gray ring, the radius is 1 foot. So, the area of the gray ring is:

A_gray_middle = π(1)^2 - π(0.5)^2

= 3.14159 - 0.78540

= 2.35619 square feet

For the inner gray ring, the radius is 0.5 feet. So, the area of the gray ring is:

A_gray_inner = π(0.5)^2 - 0

= 0.78540 square feet

The total area of the gray sections of the target is the sum of these three areas:

A_total_gray = A_gray_outer + A_gray_middle + A_gray_inner

= 3.92699 + 2.35619 + 0.78540

= 7.06858 square feet

To convert this to square inches, we multiply by the conversion factor (12 inches/foot)^2:

A_total_gray = 7.06858 * (12)^2

= 1016.7048 square inches

Rounding this to the nearest square inch gives:

A_total_gray ≈ 1017 square inches

So the correct answer is (D). 1017 square inches.

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The experimental probability of not selecting a peppermint candy is 77.78%, so the correct option is the third one.

We want to find the experimental probability of selecting a candy that is not peppermint.

To get this, we need to get the difference between 1 and the probability of getting a peppermint candy, then we will get:

p = 1 - 2/9

p = 7/9

Now we want to express this as a percentage, so we need to multiply this by 100%

p = (7/9)*100%

p = 77.78%

We can see that the experimental probability is the one in the third option.

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The simplest form of the given radical expression as required to be determined is; -3³√2a.

As evident form the task content; the given expression whose simplified form is to be determined is;

3 ³√2a - 6 ³√2a

Since; 3³√2a is common to both terms of the expression; Hence, by factorisation; we have;

3³√2a (1 - 2)

= 3³√2a • -1

= -3³√2a

Ultimately, the simplified form of the radical expression is; -3³√2a.

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The resistance of the coil is given by R = N x ρL = 70 x ρ x 0.0897 = 617.9 x ρ ohms.

The length of the wire is equal to the circumference of the circular coil. The circumference C of a circle of radius r is C = 2πr, so for the circular coil of radius 1m, the length of the wire is 2π x 1m = 6.28m.

The number of loops around the coil (N) is 70. Therefore, the length of one loop is L = 6.28/70 = 0.0897 m.

The resistance of the coil (R) is equal to the resistance of the single loop multiplied by the number of loops (N). Therefore, R = N x R', where R' is the resistance of a single loop.

The resistance of a single loop is equal to the resistance of the wire per unit length multiplied by its length. Therefore, R' = ρL, where ρ is the resistivity of the wire and L is the length of one loop of the wire.

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Complete question:

What is the resistance of a circular coil of radius 1m that consists of 70 loops of wire?

Answer:

1, 2, 3, 6

Step-by-step explanation:

Using hypothesis testing, the critical value of z for a 5 percent level of significance, left-tailed test is -1.645.

(a) For a 10 percent level of significance, two-tailed test, the critical value of z is:

z_critical = ± invNorm(1 - (0.10/2))

where invNorm is the inverse normal cumulative distribution function. Evaluating this expression gives:

z_critical = ± 1.645

Therefore, the critical value of z for a 10 percent level of significance, two-tailed test is ±1.645.

(b) For a 1 percent level of significance, right-tailed test, the critical value of z is:

z_critical = invNorm(1 - 0.01)

Evaluating this expression gives:

z_critical = 2.326

Therefore, the critical value of z for a 1 percent level of significance, the right-tailed test is 2.326.

(c) For a 5 percent level of significance, left-tailed test, the critical value of z is:

z_critical = invNorm(0.05)

Evaluating this expression gives:

z_critical = -1.645

Therefore, the critical value of z for a 5 percent level of significance, left-tailed test is -1.645.

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Therefore , the solution of the given problem of angle comes out to be the smaller angle will therefore rotate through one unit angle each time.

In Euclidean mathematics, a tilt is a shape consisting of two sides, or cylindrical faces, that separate at the wall's centre and its apex. Two rays may come together at their intersections to create an angle. Another result of two things interacting is an angle. They are characterized as dihedral angles. Two line beams can be arranged in different ways at their extremities to produce a two-dimensional curve.

Here,

A small pattern block is a geometric structure made up of six congruent isosceles triangles organised around a regular hexagon with six equal-length sides.

Two of the angles in an isosceles triangle are identical in size, while the third angle varies.

We need to first create a frame of reference in order to determine how many unit angles the smaller angle of a small pattern block turns through.

Assume that we begin by placing the little pattern block in its initial location with one of its sides vertically aligned.

This results in one of the isosceles triangles being vertically aligned after turning the block.

The smaller angle will therefore rotate through one unit angle each time if we continue to rotate the small pattern block anticlockwise by one-sixth of a complete revolution for each subsequent turn.

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The solution to the inequality expression given as x + 2 < 5 is x < 3

Inequality expressions refer to statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.

From the question, we have the following parameters that can be used in our computation:

x + 2 < 5

Subtract 2 from both sides of the inequality expression

So, we have the expression below

x + 2 < 5 - 2

Evalaute the like terms

x < 3

This means that, the solution is x < 3

The graph of the inequality is added as an attachment

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The total distance that Mishka covers on the trip is 265 miles.

Speed measures how fast an object is moving with respect to time. Speed is the ratio of total distance to total time.

Speed = distance / time

Distance = speed x time

Distance covered while driving on the highway = 75 x 3 = 225 miles

Distance covered while driving on the side road = 40 x 1 = 40 miles

Total distance covered = 225 miles + 40 miles = 265 miles

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The constraints as a system of linear inequalities include the following;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640

75x + 60y ≤ 12,900

The solution set for the system of linear inequalities is shown in the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640.

75x + 60y ≤ 12,900

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The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.

Probability of an event is a number that shows what is the possibility of an event occur.

we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.

[tex]= \frac{(17 - 18.6 years)}{1.308333 years}[/tex]

[tex]= \frac{(-1.6) }{1.308333}[/tex]

[tex]= -1.22293[/tex]

[tex]= approx. 1.22.[/tex]

The area from the mean to +ve or -ve 1.22 is .3888

We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.

So, the growth plates will fuse before age 17 [tex]= .5000-.3888 = 0.1112[/tex]

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Answer:

The answer rounded is 6.10, but the actual answer would be 6.095

Step-by-step explanation:

5.75 X 0.06 = 0.345 || 0.345+5.75 = 6.095

A 6.10

According to the laws of stuff a calculate of 5.75 to the percentage of 6 is 6.10

The lifetime cost of the model is $765.

Kate is re-modelling her kitchen.

She is going shopping for a refrigerator.

The model price is $405, and the estimated energy cost per year is $36.

If the model has an estimated lifetime of 10 years,

Lifetime cost of the model:

The lifetime cost of the model is $765

Explanation: Given, The model price is $405

Estimated energy cost per year is $36.

The model has an estimated lifetime of 10 years.

Lifetime cost of the model can be calculated as follows:

Total lifetime cost = Initial cost + (Estimated energy cost per year × Estimated lifetime)

Initial cost = $405

Estimated energy cost per year = $36

Estimated lifetime = 10 years

Total lifetime cost = $405 + ($36 × 10)

Total lifetime cost = $405 + $360

Total lifetime cost = $765

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Check the picture below.

If Leopold takes one part away from each of the fractions, they will not be equal anymore.

Two or more fractions are said to be equal or equivalent if we simplify them and obtain the same result for both. Let's analyze the fractions given:

5/5 = 1

3/3 = 1

Even when some fractions are equivalent if you modify them this will change the equivalence property, let's prove it with the fractions given:

4/5 = 0.8

2/3 = 0.66

Note: This question is incomplete; here is the missing section:

Leopold takes one part away from each. Will the fraction still be equal?

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Answer:

Below

Step-by-step explanation:

Area of a parallelogram is given by:    base * height

   base =  6 m    height = 8 m

     area = 6* 8 = 48 m^2