Plsss help right now

\(( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2=\cfrac{1-\cos(\theta )}{1+\cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2\implies \csc^2(\theta )-2\csc(\theta )\cot(\theta )+\cot^2(\theta ) \\\\\\ \cfrac{1^2}{\sin^2(\theta )}-2\cdot \cfrac{1}{\sin(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\implies \cfrac{1}{\sin^2(\theta )}-\cfrac{2\cos(\theta )}{\sin^2(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\)

\(\cfrac{\cos^2(\theta )-2\cos(\theta )+1}{\sin^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{\sin^2(\theta )} \\\\\\ \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{1-\cos^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1]}\)

\(\cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1^2]}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos(\theta )-1][\cos(\theta )+1]} \\\\\\ \cfrac{\cos(\theta )-1}{-[\cos(\theta )+1]}\implies \cfrac{-[\cos(\theta )-1]}{\cos(\theta )+1}\implies \cfrac{1-\cos(\theta )}{1+\cos(\theta )}\)

The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:

f(x) = 1 / (b - a)

where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.

To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.

Therefore, the probability that the commuting time will be between 50 and 60 minutes is:

P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.

Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.

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Answer:

6/91

Step-by-step explanation:

Total number of fruits = 4 + 2 + 3 + 5 = 14

Apple: 4/14

One of the fruits have been taken from the total. 14 thus becomes 13.

There are 3 oranges

Orange: 3/13

Combine probability: 4/14 * 3/13 = 12/182 = 6/91

Two is a common factor in both 12 and 182

To ensure that the function f(x) is continuous at every 'x', we need to make sure it's continuous at the point x = 3. For a function to be continuous, the left-hand limit, right-hand limit, and the function value at the point should all be equal. Let's evaluate the limits:

1. Left-hand limit (x < 3): lim(x->3-) f(x) = lim(x->3-) x^2 = 3^2 = 9
2. Right-hand limit (x ≥ 3): lim(x->3+) f(x) = lim(x->3+) 2ax = 2a(3) = 6a
3. Function value at x = 3: f(3) = 2a(3) = 6a

For f(x) to be continuous, the left-hand limit, right-hand limit, and function value at x = 3 must be equal:

9 = 6a

To solve for 'a', divide both sides by 6:

a = 9/6 = 3/2

So, the value of 'a' that makes f(x) continuous at every 'x' is 3/2.

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Answer:

D. To increase its number of cells

Explanation:

Mitosis help in increasing the number of cells in a living organism thereby playing a significant role in the growth of a living organism. It helps in the production of identical copies of cells and thus helps in repairing the damaged tissue or replacing the worn-out cells.

Answer:

Step-by-step explanation:

20:50

akeeeeeeeeeeeeeeeeeeetseeeeeeeeeeebe

Answer:

180° is the accurate correct answer

Step-by-step explanation:

mark me as brainliest

Answer:

401.063063063

Step-by-step explanation:

Answer:

Rotation of 180° about the origin,

Followed by a translation (x, y) → (x + 1, y + 1)

Step-by-step explanation:

Given

\(R = (-2,4)\)

\(S = (-4,-1)\)

\(R" = (3,-3)\)

\(S" = (5,2)\)

Required

Determine the transformations

From the list of given options (B) answers the question.

Rotation of 180° about the origin,

When a point (x,y) is rotated 180 about the origin, the new point becomes (-x,y)

So:

\(R = (-2,4)\)

\(S = (-4,-1)\)

becomes

\(R' = (2,-4)\)

\(S' = (4,1)\)

A translation (x, y) → (x + 1, y + 1)

This implies that 1 is added to the x and y coordinates

So:

\(R' = (2,-4)\)

\(S' = (4,1)\)

becomes

\(R" = (2 + 1,-4 + 1)\)

\(R" = (3,-3)\)

\(S"=(4 +1,1+1)\)

\(S" = (5,2)\)

Answer:

Step-by-step explanation:

Let the speed of the car is x, then the speed of motorcycle is x + 20

The distance = 120 km

Time:

Speed of the car is 40 km/h

Speed of the motorcycle is 60 km/h

Answer:

Speed of the car is 40 km/h

Speed of the motorcycle is 60 km/h

Answer:

Option D [\(y=6.61\,*\,1.55^x\)] in the list of possible answers

Step-by-step explanation:

For this problem you are supposed to use a calculator that allows you to do an exponential regression. There are many tools that can help you with that, depending on what your instructors has assigned for your class.

I am showing you the results of a graphing tool I use, and which after entering the x-values and the y-values in independent "List" forms, when I request the exponential regression to fit the data, I get what you can see in the attached image.

Notice that the exponential of best fit with my calculator comes in the form:

\(y=A\,e^{k\, x}\)

with optimized parameters:

\(A \approx 6.6114\,\,\,and\,\,\, k=0.4378321\)

Notice as well that since:

\(e^{0.4378321} \approx 1.5490\)

the exponential best fit can also be written:

\(y=6.611403\,\,*\,e^{0.4378321\, x}=6.611403\,*\,1.549^{\,x}\)

and this expression is very close to the last option shown in your list of possible answers

The given statement mathematical and statistical tools give us many ways to rate the overall performance of a system and its components is True.

Mathematical and statistical tools provide various methods to assess and evaluate the performance of a system and its individual components. These tools enable quantitative analysis , modeling , prediction , and inference , allowing us to measure and interpret the effectiveness , efficiency, reliability, and other relevant characteristics of systems and their components.

Examples of such tools include statistical analysis, regression analysis, hypothesis testing, optimization techniques, control charts, simulation, and more.

Therefore, the given statement is true.

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Complete question is below

Mathematical and statistical tools give us many ways to rate the overall performance of a system and its components.

true or false

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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There is a total of 15 yes/no questions on the test. Hence, 15 is the correct answer.

Let's assume the number of yes/no questions on the test is represented by 'x'. The number of multiple-choice questions would then be '20 - x' since the test consists of a total of 20 questions.

The points obtained from yes/no questions can be calculated as 3 times the number of yes/no questions, which is 3x.

Similarly, the points obtained from multiple-choice questions can be calculated as 11 times the number of multiple-choice questions, which is 11(20 - x).

Since the total points for the test are 100, we can set up the equation:

     \(3x + 11(20 - x) = 100\)

or, \(3x + 220 - 20x = 100\)

or, \(8x = 120\)

or, \(x = 15\)

Therefore, the total number of yes/no questions on the test is 15.

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For this problem, we are given a certain function and we need to determine its range.

The function is:

This quadratic function has a minimum value in its range, which is represented by its vertex. The best way to determine the range is to find the coordinates of the vertex of this function, therefore we have:

The minimum value in the range is -16, which means that the range is:

The correct option is the second one.

Hi!

I'm assuming the question means what integers, so let's figure it out.

Starting from 12, 12 squared is 144, or the square root of 144 is 12.

13 squared is 169, or the square root of 169 is 13.

14 squared is 196, or the square root of 196 is 14.

15 squared is 225, or the square root of 225 is 15.

Based on that list of numbers, we can determine that the square root of 199 lies between the square root of 196 and the square root of 225 -- aka 14 and 15.

Vial contains 0.96g powder.

Proportion is used to show how quantities and amounts are related to each other. The amount that quantities change in relation to each other is governed by proportion rules.

A direct and inverse proportion are used to show how the quantities and amount are related to each other. They are also mentioned as directly proportional or inversely proportional. The symbol used to denote the proportionality is ‘∝‘.  For example, if we say, a is proportional to b, then it is represented as “a ∝ b” and if we say, a is inversely proportional to b, then it is denoted as ‘a∝1/b’

The given question is the example of direct variation.

Powder volume ∝ Liquid volume

∴ We can apply cross multiplication method

Let powder volume be x

1g→ 10ml

x→ 9.6ml

cross multiplying

1 x 9.6 = 10 x \(x\)

x = 0.96 g

Thus Vial contains 0.96g powder.

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We can write the equivalence class of m as [m] = {n ∈ Z : m + n is even}.

(a) To show that ∼ is an Equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer m, we have |m - 3| = |m - 3|, so m ∼ m. Therefore, ∼ is reflexive.

Symmetry: For any integers m and n, if |m - 3| = |n - 3|, then |n - 3| = |m - 3|, so n ∼ m. Therefore, ∼ is symmetric.

Transitivity: For any integers m, n, and p, if |m - 3| = |n - 3| and |n - 3| = |p - 3|, then |m - 3| = |p - 3|, so m ∼ p. Therefore, ∼ is transitive.

To find the equivalence classes of ∼, we need to determine the sets of integers that are related to each other. For any integer m, the equivalence class of m is the set of all integers n such that |m - 3| = |n - 3|. In other words, the equivalence class of m is the set of integers that are the same distance from 3 as m. We can write the equivalence class of m as [m] = {n ∈ Z : |m - 3| = |n - 3|}.

(b) To show that ∼ is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer m, we have m + m = 2m, which is even. Therefore, m ∼ m. Therefore, ∼ is reflexive.

Symmetry: For any integers m and n, if m + n is even, then n + m is also even, so n ∼ m. Therefore, ∼ is symmetric.

Transitivity: For any integers m, n, and p, if m + n is even and n + p is even, then m + p is even, so m ∼ p. Therefore, ∼ is transitive.

To find the equivalence classes of ∼, we need to determine the sets of integers that are related to each other. For any integer m, the equivalence class of m is the set of all integers n such that m + n is even.

In other words, the equivalence class of m is the set of integers that differ from m by an even amount. We can write the equivalence class of m as [m] = {n ∈ Z : m + n is even}.

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The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since the aspect ratio of 4:6 is closer to that of an 11-inch by 14-inch frame (which is approximately 1:1.5) than the aspect ratio of 3.5:5 (which is approximately 7:10).

By minimizing the difference in aspect ratio between the photo and the frame, you will minimize the loss of the edges of the picture when trying to fit it into the frame.

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize the loss of the edges of the picture when trying to fit it into an 11-inch by 14-inch frame.

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The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

Assuming AB = BC = AC = x units, we get:

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

so you write 16 but i don't speak English very good i want help you 2(6+3)-2 ok you you going multiplying 2×6=12+6=18-2=16 so 16

Answer:

first option x = 7

Step-by-step explanation:

"x" is the cathetus opposite the angle of 30°

14 is the hypotenuse

use the sine function

\(sin30^{0} =\frac{x}{14}\)

\(x=14sen30^{0} =14(0.5)=7\)

Hope this helps

Answer:

5/8

Step-by-step explanation:

1/5 x 5

1

1/8 x 5

5/8

The expression represents the time she spent driving is       \(\frac{228.95}{x}\)

The expression represent the time she spent driving can be calculated as follows:

We know that

Time = \(\frac{distance}{ speed}\)

Let x be her speed on the first half of the trip.

Then for first half , the tiime she takes is

T1= \(\frac{150}{x}\)

while in a second half the time taken by her is

T2= \(\frac{150}{1.9x}\)

T2= \(\frac{78.95}{x}\)

the total time she spent on driving is

T1 + T2 =    \(\frac{150}{x}\) + \(\frac{78.95}{x}\) =    \(\frac{228.95}{x}\)

Hence, the expression represents the time she spent driving is       \(\frac{228.95}{x}\)

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The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

We have,

To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:

Mean of rt:

E(rt) = E(0.02 + 0.5rt-2 + et)

= 0.02 + 0.5E(rt-2) + E(et)

= 0.02 + 0.5 * 0 + 0

= 0.02

The variance of rt:

Var(rt) = Var(0.02 + 0.5rt-2 + et)

= Var(et) (since the term 0.5rt-2 does not contribute to the variance)

= 0.02

The mean of the return series rt is 0.02, and the variance is 0.02.

To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

= Cov(r100, r99) / (σ(r100) * σ(r99))

= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

= Cov(r100, r98) / (σ(r100) * σ(r98))

To compute the 1- and 2-step-ahead forecasts of the return series at

t = 100, we use the given model:

1-step ahead forecast:

E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)

= 0.02 + 0.5r100

2-step ahead forecast:

E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)

= 0.02 + 0.5E(rt | r100, r99)

= 0.02 + 0.5(0.02 + 0.5r100)

The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.

Thus,

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

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Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.

We want the total amount to by 25 gal, then we have:

We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:

Hence we have the system of equations:

To solve the system we solve the first equation for y:

then we plug this value of y in the second equation:

Once we have the value of x we plug it in the expression we found for y:

Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.