verify the identity (cos 2x)/(sin x)=csc x-2sinx

The multiplication of the given fraction 6 × 3/5 is 15 or 3 3/5

Fraction refers to numbers which comprises of a numerator and a denominator. A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.

6 × 3/5

multiply the numerator and denominator separately

= (6 × 3) / (1 × 5)

= 18/5

= 3 3/5

Therefore, 3 3/5 is the solution to the multiplication of the fraction.

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Answer:

A

Step-by-step explanation:

A is correct because 3+4 = 7

B is incorrect because 9/3=3 ,not 3/9

There is no x in C

D is incorrect because 8×3=24

E is incorrect because 3-10= -7 (negative)

hope this helped :)

The given probability distribution for the random variables is valid

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The equation will be

The probability = Number of favorable outcomes / Total number of outcomes

The probability distribution is the probabilities of the each random event

From the table we can see that the probability distribution of each random events are

0.20, 0.15, 0.25, 0.40

Add the probability distributions of each random events

= 0.20 + 0.15 + 0.25 + 0.40

= 1

Here the sum of the probability distribution of the random events is 1

Therefore, the probability distribution is valid

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Hence, It is proved that, Pythagorean theorem, is verified.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

A triangle has sides with lengths 8, 15, and 17.

so, here, 8^2 + 15^2

             =64 +225

             =289

             =17^2

Hence, It is proved that, Pythagorean theorem, is verified.

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The possible values of the number of quarters are at least 14 and more.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

1 dime = $0.10

1 quarter = $0.25

Number of dimes = x

Number of quarters = y

Now,

He has at most 25 coins worth at least $4.60 combined.

This means

we can write two inequalities.

x + y ≤ 25 ____(1)

0.10x + 0.25y ≥ 4.60 _____(2)

Now,

From (1) and (2).

x ≤ 25 - y

Substituting in (2).

0.10x + 0.25y = 4.60

0.10 (25 - y) + 0.25y ≥ 4.60

2.5 - 0.10y + 0.25y ≥ 4.60

2.5 + 0.15y ≥ 4.60

0.15y ≥ 4.60 - 2.5

0.15y ≥ 2.1

y ≥ 2.1/0.15

y ≥ 14

This means,

y is at least 14.

Thus,

The possible values of the number of quarters are at least 14 and more.

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Answer:

3:31

Step-by-step explanation:

The equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number" is 3 – (n – 1) = 1/2(3n – 4)

Let the number be n.

Gven: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"

So,

The expression "three minus the difference of a number and one" represent the equation is;  

3 – (n – 1)

Also,

The expression "one-half of the difference of three times the same number and four" represent the equation  is;

1/2(3n – 4)

Hence,

Complete expression represents the equation is

3 – (n – 1) = 1/2(3n – 4)

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(1 – n) – 3 = (4 – 3n)

3 – (1 – n) = (4 – 3n)

(n – 1) – 3 = (3n – 4)

3 – (n – 1) = (3n – 4)

Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).

Expanding this makes -2x²+3x+2

Each of the quadratic function should be factorized as follows;

x² - 6x + 8 ⇒ (x - 4)(x - 2).

x² - 4x - 32 ⇒ (x - 8)(x + 4).

x² + x - 42 ⇒ (x - 6)(x + 7).

In Mathematics, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Next, we would solve each of the quadratic function by using the factorization method as follows;

x² - 6x + 8 = 0

x² - 4x - 2x + 8 = 0

x(x - 4) - 2(x - 4) = 0

(x - 4)(x - 2) = 0

x² - 4x - 32 = 0

x² - 8x + 4x - 32 = 0

x(x - 8) + 4(x - 8) = 0

(x - 8)(x + 4) = 0

x² + x - 42 = 0

x² - 6x + 7x - 42 = 0

x(x - 6) + 7(x - 6) = 0

(x - 6)(x + 7) = 0

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Answer:

2(t+6)-5

Step-by-step explanation:

The unknown number is t

=> Adding 6 will make it t+6

=> Multiplying 2 will make it 2(t+6)

=> Subtracting 5 will make it 2(t+6)-5

Answer:

[tex]\frac{t+6}{2}[/tex] - 5

Step-by-step explanation:

[tex]\frac{t+6}{2}[/tex] - 5

If a sample of 250 RDNS was randomly selected from a list of all RDNS in the state of California for a California policy study, then the sampling method was simple random sample

Here a sample of 250 RDNS was randomly selected from a list of all RDNS.

Sampling is defined as the selecting the individual members or the group that you will actually collect data from in your research. There are five types of sampling method. They are Random, Systematic, Convenience, Cluster, and Stratified.

In the simple random sampling the researchers select the random samples from the population. Here a sample of 250 RDNS was randomly selected from a list of all RDNS.

Therefore, the sampling method that used is simple random sample

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The equation of the trend line in the graph can be found to be y = 5 x + 15

The equation of the trend line takes the form :

y = Slope ( x ) + y intercept

From the diagram, we know the y - intercept is 15 as this is where the line intercepts the y - axis.

The slope can be found by picking a point and using the formula. We will pick ( 1, 20 ).

The slope is:

20 = Slope ( 1 ) + 15

Slope = 20 - 15

Slope = 5

The equation is:

y = 5 x + 15

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The regression analysis provides important insights into the relationship between single-parent households and student math performance.

To begin our analysis, we will run a simple linear regression of math4 on pctsgle. This will help us understand the relationship between the percentage of single-parent households in a school's ZIP code and the math performance of the students in that school.

Mathematically, the simple linear regression model can be written as:

math4 = β₀ + β₁pctsgle + ε

where math4 represents the average math score for a given school, pctsgle represents the percentage of single-parent households in the school's ZIP code, β₀ and β₁ are the intercept and slope coefficients respectively, and ε represents the error term.

After running the regression, we will obtain the following results:

math4 = 63.91 - 0.52pctsgle

Interpreting the results, we can see that for every one percent increase in the percentage of single-parent households in a school's ZIP code, the average math score of the students in that school decreases by 0.52 points.

The effect of single parenthood may seem small based on the slope coefficient of -0.52. However, it is important to note that this is just one variable and there may be other factors that could be contributing to the decrease in math performance.

Therefore, further analysis may be needed to fully understand the impact of single-parent households on student math performance.

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Complete Question:

Use the data in MEAPSINGLE to study the effects of single-parent households on student math performance. These data are for a subset of schools in southeast Michigan for the year 2000. The socioeconomic variables are obtained at the ZIP code level (where ZIP code is assigned to schools based on their mailing addresses).

Run the simple regression of math4 on pctsgle and report the results in the usual format. Interpret the slope coefficient. Does the effect of single parenthood seem large or small?

The coordinates of point P are (12, 12.5).

to put different elements or individuals in a coordinated effort.

To find the coordinates of point P, we can use the fact that P divides NO into two segments in the ratio of 4:3.

First, we can find the distance between points N and O using the distance formula:

d(NO) = sqrt((19-5)^2 + (9-16)^2) = sqrt(196 + 49) = sqrt(245)

Next, we can use the ratio of 4:3 to determine the distance between P and O:

d(OP) = (3/7) * d(NO) = (3/7) * sqrt(245)

Similarly, we can find the distance between P and N:

d(NP) = (4/7) * d(NO) = (4/7) * sqrt(245)

Now, we can use the midpoint formula to find the coordinates of P:

x-coordinate of P = (x-coordinate of N + x-coordinate of O) / 2 = (5 + 19) / 2 = 12

y-coordinate of P = (y-coordinate of N + y-coordinate of O) / 2 = (16 + 9) / 2 = 12.5

So the coordinates of point P are (12, 12.5).

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The length of AC is √(4x⁴+ 16x³ + 76x² - 16x + 64). In order to find the unit length of AC you have to get more measurement and solve for x in the equation.

We can use the fact that the diagonal of a rectangle is the square root of the sum of the squares of its sides. If the sides of the rectangle are "a" and "b", then the length of the diagonal is given by: √(a² + b²)

Let's call the length of AC "d". Then, from the information given, we have: d = √((2x² + 4x - 6)² + (x² - x + 8)²)

Expanding and simplifying the squares, we get:

d = √(4x⁴ + 16x³ + 12x² + 64x² - 16x + 64)

d = √(4x⁴+ 16x³ + 76x² - 16x + 64)

So, the length of AC is √(4x⁴ + 16x³ + 76x² - 16x + 64).

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In order to determine whether a critical point of a loss function is a global minimum, it is necessary to consider the second derivative of the function.

If the second derivative is positive at the critical point, then we can say with certainty that the critical point is a local minimum. However, this does not necessarily mean that it is a function function. This is because there may be other local minima at points which the second derivative is negative, and in this case, the critical point must be compared to these points to determine if it is indeed the global minimum.

In order to assess whether a local minimum is a global minimum, we must first identify any other local minima. This can be done by locating the points at which the first derivative of the function is equal to zero and then evaluating the second derivative of the function at these points. If the second derivative is negative at any of the points, then we have identified a local minimum. Then, we can compare the value of the loss function at the points function as local minima to the value of the loss function at the critical point. If the value of the loss function at the critical point is lower than the value of the loss function at the other local minima, then the critical point is the global minimum. If the values are equal, then the critical point is a global minimum if and only if it is the only local minimum.Overall, identifying whether a critical point of a loss function is a global minimum requires both sufficiency and necessity. It is necessary to evaluate the second derivative of the function at the critical point in order to determine whether it is a local minimum, and it is also necessary to identify any other local minima and compare the value of the loss function at the critical point to the value of the function at the other local minima in order to determine whether the critical point is the global minimum.

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Answer:

1/9 buckets of fish

---------------

The dolphins are fed 1/3 of a bucket of fish and the sea otters are fed 1/3 as much as the dolphins.

That is 1/3 of 1/3 buckets:

The image of the point after the dilation of scale factor k = -1/2 is:

(-1, -1/3)

If we have a point (x, y), and we dilate it by a scale factor k with the center of dilation on the origin, then the new coordinates of the point are (k*x, k*y).

Here the original point is (3, 1)

And the scale factor is k = -1/3

Then the image of the point after the dilation is:

( -1/3*3, -1/3*1)

(-1, -1/3)

That is the image.

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Answer: Jack made $898.25 in commission

Step-by-step explanation:

Jack made $898.25 in commission. ($2,000 x 15%) + ($3,975 x 5%) = $898.25

[tex]5975-2000=3975[/tex] this is the amount jack earns 5% commission on

Answer:La masse d'un atome de cuivre est de 1,05 x 10^-25 kg. Un atome de cuivre comporte 29 électrons. Ces electrons constituent le nuage electronique de l'atome. chaque electron a une masse de 9,11 x 10^-311.

Step-by-step explanation:

The area occupied by the ship is 10 inches².

The area of a parallelogram is -

A{||gm} = base x height

Given is that Ships in a first generation video game were modeled like the one shown in the image.

We can write the area occupied by the ship as -

Area = A{||gm} + A{triangle}

Area = {b x h} + {L x B}

Area = [tex]$(3\frac{2}{5}\times 2)\;+\; (3\frac{2}{5}-1)\times1\frac{1}{3}[/tex]

Area = (17/5 x 2) + (17/5 - 1) x (4/3)

Area = 34/5 + 12/5 x 4/3

Area = 34/5 + 16/5

Area = 50/5

Area = 10 inches²

Therefore, the area occupied by the ship is 10 inches².

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The value of 33.4 meters to centimeters is 3340 centimeters

Conversion of units is described as the  conversion between different units of measurement for the same quantity, and it is done mostly through multiplicative conversion factors.

It also involves multiple steps of multiplication or division by a numerical factor or, a conversion factor.

From the information given, we have to convert meters to centimeters

Note that;

100 centimeter = 1 meter

Then x centimeters = 33.4 meters

cross multiply

x = 100(33.4)

multiply the values

x = 3340 centimeters

Hence, the value is 3340 centimeters

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The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.

To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:

In this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

where X is the random variable representing the number of seeds that germinate.

Using the binomial distribution formula, we can calculate the probability of each outcome:

P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]

where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].

Plugging in the values, we get:

P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057

P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205

P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324

Therefore,

[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586

So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.

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In the given right angle triangle the measure of tanL, sinL, and cosL is 73.74°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

Given, A right-angled triangle has side lengths 7, 24, and 25.

Here, Hypotenuse is 25, Adjacent is 7 and opposite is 24.

Now, tan = opposite/adjacent.

tanL = 24/7.

L = tan⁻¹(24/7).

L = 73.74°.

Similarly,

sinL = 24/25.

L = sin⁻¹(24/25).

L = 73.74°.

And,

cosL = 7/25.

L = cos⁻¹(7/25).

L = 73.74°.

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The number of pet-owners that are in the union of cat owners and other pet owners is given as follows:

20 pet-owners.

The set representing the union of two sets is composed by all the elements that belong to at least one of the sets.

Hence the union of pet-owners that are in the union of cat owners and other owners is composed as follows:

Hence the total number is given as follows:

11 + 9 = 20.

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Answer:

alternate exterior angles

Step-by-step explanation:

congruent alternete exterior angles

Answer:

[tex]104 ft^2[/tex]

Step-by-step explanation:

The answer is [tex]104 ft^2[/tex].

Divide the shape into 3 different rectangles. Now we have 2 rectangles that are 5 by 4.

The last rectangle is 16 by 4. (8-4 =4)

This is because 6+5+5=16.

Then you add up the area to get the whole figure.

The two smaller rectangles are 20 each or 40 altogether and the larger rectangle is 64.

When you add it up you get an area of [tex]104 ft^2[/tex]

Equivalence means to be same, whether it be value, temperature, size, etc.

Let's take a look at shape 1.

Shape 1 has a base of 3, and a height of 4, but there is a gap with a width of 1 and a height of 2. So, we can use this equation to figure out the area:

So, shape 1 has an area of 10 units.

Let's look at shape 2.

Shape 2 has a base of 2, and a height of 4, but there is also a gap, with a width of 1 and a height of 3. So, we can use this equation to figure out the area:

So, shape 2 has an area of 5 units.

Let's look at shape 3.

Shape 3 consists of 4 right triangles, put together to form an arrowhead. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:

So, shape 3 has an area of 4 units.

Let's look at shape 4.

Shape 4 consists of 4 right triangles, put together to form a diamond. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:

So, shape 4 has an area of 4 units.

Looking to the final shape (5), we can see it consists of a long rectangle and 2 right triangles. Instead of calculating the base and height of the entire shape, we can break it into pieces, making a rectangle that has a base of 3, and a height of 1. Then we are left a shape that has a base of 2, and a height of 3. So, we can use this equation to figure out the area:

So, shape 5 has an area of 6 units.

Let's compare the area of all of the shapes.

Therefore, the two figures that have equal areas are shapes 3 and 4.

a) The probability that no one reports the loss or theft of their credit cards is 0.0498.

b) The probability that every credit card is lost or stolen is practically zero.

c) The probability that exactly six people report the loss or theft of their cards is 0.1042

d) The probability that at least nine people report the loss or theft of their cards is 0.2142

a. To calculate the probability that no one reports the loss or theft of their credit cards, we can use the Poisson distribution with an average of λ = 0.02% * 15,000 = 3.

The probability that no one reports the loss or theft of their credit cards is:

P(X = 0) = e^(-λ) * (λ^0 / 0!) = e^(-3) * (1 / 1) = 0.0498 or approximately 5%.

b. The probability that every credit card is lost or stolen is:

P(X = 15000) = e^(-λ) * (λ^15000 / 15000!)

Since λ is very small, the probability of all 15000 credit cards being lost or stolen in a month is practically zero.

c. To calculate the probability that six people report the loss or theft of their cards, we again use the Poisson distribution with an average of λ = 3.

The probability that exactly six people report the loss or theft of their cards is:

P(X = 6) = e^(-λ) * (λ^6 / 6!) = e^(-3) * (3^6 / 720) = 0.1042 or approximately 10.4%.

d. To calculate the probability that at least nine people report the loss or theft of their cards, we need to sum the probabilities for X = 9, 10, 11, ..., 15, since there are only 15,000 credit cards in total.

The probability that at least nine people report the loss or theft of their cards is:

P(X >= 9) = Σ(i=9 to 15) P(X = i) = Σ(i=9 to 15) e^(-λ) * (λ^i / i!)

This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(X >= 9) is approximately 0.2142 or 21.42%.

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