64c³ +1

Factoring polynomials

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Ur answer is

(x+8)(x-3)

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Therefore , the solution of the given problem of probability comes out to be  a) P(X=5) = 0.2465 , (b) P(X>=6) = 0.3204 and (c) P(X<4) = 0.2448.

The main objective of an procedure's criteria-based approaches is to estimate the likelihood that a claim is accurate or that a particular event will take place. Any number between 0 and 1, where 0 commonly denotes the possibility of something occurring and 1 typically denotes a degree of trust, can be utilized to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

P(X=k) is equal to (n choose k) * p*k*1-p.(n-k)

We need to determine the following when n = 10 and p = 0.51 (the probability of having very little trust in newspapers):

(a) P(X=5)

(b) X>equals6 = X=6 + X=7 +... + X=10

(c) The equation P(X4) equals P(X=0), P(X=1), P(X=2), and P(X=3)

Using the equation:

(a) P(X=5) = (10 choose 5) * 0.51⁵ * 0.49⁵ = 0.2465

(b) The equation P(X>=6) = P(X=6) + P(X=7) +... + P(X=10) = (10 choose 6) * 0.51⁶ * 0.49⁴

+ (10 choose 7) * 0.51⁷* 0.49^3

+ (10 choose 8) * 0.51⁸ * 0.49^2

+ (10 choose 9) * 0.51⁹ * 0.49^1

+ (10 choose 10) * 0.51¹⁰ * 0.49^0

= 0.3204

(c) If P(X4) = P(X=0), P(X=1), P(X=2), and P(X=3), then (10 choose 0) * 0.51^0 * 0.49^10

+ (10 choose 1) * 0.51¹* 0.49^9

+ (10 choose 2) * 0.51² * 0.49^8

+ (10 choose 3) * 0.51³ * 0.49^7

= 0.2448

The odds are as follows: a) P(X=5) = 0.2465

(b) P(X>=6) = 0.3204

(c) P(X<4) = 0.2448

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Answer:

Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484

Standard deviation = √(0.1484/6

s = 0.16

Standard error = s/√n = 0.16/√6 = 0.065

Part B

Confidence interval is written as sample mean ± margin of error

Margin of error = z × s/√n

Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5

Therefore, z = 3.365

Margin of error = 3.365 × 0.16/√6 = 0.22

Confidence interval is 2.48 ± 0.22

Part C

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 2.3

For the alternative hypothesis,

H1: µ > 2.3

This is a right tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 6

Degrees of freedom, df = n - 1 = 6 - 1 = 5

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.48

µ = population mean = 2.3

s = samples standard deviation = 0.16

t = (2.48 - 2.3)/(0.16/√6) = 2.76

We would determine the p value using the t test calculator. It becomes

p = 0.02

Assuming significance level, alpha = 0.05.

Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.

Step-by-step explanation:

Answer:

A. I Think False

B. True

C.True

Step-by-step explanation:

Answer:

f(x)= x^2+x-12

Step-by-step explanation:

FOIL

First= (x)(x)=x^2

Outer=(x)(4)=4x

Inner=(-3)(x)=-3x

Last=(-3)(4)=-12

x^2+4x-3x-12

x^2+x-12

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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Answer:

the probability that the first groupmate you meet has studied some statistics is 0.45

Step-by-step explanation:

From the information given :

A professor divided the students in her business class into three groups

Let consider then to be :

Group            Statistics Class

A                    Never taken a statistics class

B                    Taken one statistics class

C                     Taken two or more statistics class.

If 55% of the students have never taken a statistics class,

Then ;

P(A) = 0.55

25% have taken only one semester of a statistics class

Then P(B) = 0.25

and the rest have taken two or more semesters of statistics

Then P(C) = 1 - 0.55 -0.25

P(C) = 1 - 0.80

P(C) = 0.20

The objective is to determine the probability that the first groupmate you meet has studied some statistics

The probability of the first groupmate you meet has studied some statistics = 1 - P(never taken a statistics course)

Let the  probability of the first groupmate you meet that  has studied some statistics be P(D)

Then P(D) = 1 -  P(A)

P(D) = 1 - 0.55

P(D) = 0.45

the probability that the first groupmate you meet has studied some statistics is 0.45

i) Xi(f) = 5rect(f/2007)e^(-j2πft) | ii) Xz(f) = 5rect((f-400)/2007) | iii) X3(f) = 1 - 3*5rect(f/2007) + 1400(X(f) * X(f)) | iv) X(f) = 5rect(f/5)

we'll use properties of the Fourier transform and the given function x(t) = 5sinc(2007).

i) For xi(t) = -4x(t-4):

Using the time shifting property of the Fourier transform, we have:

Xi(f) = X(f)e^(-j2πft)

Since x(t) = 5sinc(2007), the Fourier transform X(f) of x(t) is given by:

X(f) = 5rect(f/2007)

Thus, substituting the values, we have:

Xi(f) = 5rect(f/2007)e^(-j2πft)

ii) For xz(t) = e^(j400)lx(t):

Using the frequency shifting property of the Fourier transform, we have:

Xz(f) = X(f - f0)

Since x(t) = 5sinc(2007), the Fourier transform X(f) of x(t) is given by:

X(f) = 5rect(f/2007)

Substituting the value f0 = 400, we have:

Xz(f) = 5rect((f-400)/2007)

iii) For X3(t) = 1 - 3x(t) + 1400xlx(t):

Using the linearity property of the Fourier transform, we have:

X3(f) = F{1} - 3F{x(t)} + 1400F{x(t)x(t)}

Since x(t) = 5sinc(2007), the Fourier transform X(f) of x(t) is given by:

X(f) = 5rect(f/2007)

Using the Fourier transform properties, we have:

F{x(t)x(t)} = X(f) * X(f)

Substituting the values, we have:

X3(f) = 1 - 3*5rect(f/2007) + 1400(X(f) * X(f))

iv) For X(t) = cos(400ft)x(t):

Using the modulation property of the Fourier transform, we have:

X(f) = (1/2)(X(f - 400f) + X(f + 400f))

Since x(t) = 5sinc(2007), the Fourier transform X(f) of x(t) is given by:

X(f) = 5rect(f/2007)

Substituting the value f = 400f, we have:

X(f) = 5rect((400f)/2007)

Simplifying, we have:

X(f) = 5rect(f/5)

To sketch the magnitude spectrum, Xo(f), we plot the magnitude of the Fourier transform for each case using the given formulas and the properties of the Fourier transform.

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The difference between the Lagrangian and Eulerian descriptions of a flow field lies in the perspective they take to analyze the motion of fluid particles.


1. Lagrangian description: Focuses on tracking individual fluid particles as they move through the flow field.
2. Eulerian description: Analyzes fluid properties at fixed points in space, disregarding individual particle motion.
3. Both descriptions represent the same physical phenomenon - fluid flow.
4. Material derivative: Connects the Lagrangian and Eulerian descriptions by relating the rate of change of a property in the Lagrangian frame to the rate of change in the Eulerian frame.

The two descriptions are related in the sense that they both represent the same physical phenomenon, i.e., the flow of fluid. However, they use different approaches to study the flow. To connect the Lagrangian and Eulerian descriptions, we can use the material derivative, which relates the rate of change of a property in the Lagrangian frame to the rate of change in the Eulerian frame.

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Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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Answer:

Step-by-step explanation:

Answer is in the pic I promise nothing bad.

Answer:

Since PQRS is a rectangle and the area of PQRS is 84 cm², then:

PQ x PS = 84

Since PQRS is a rectangle, PS = QR, so we can substitute PS for QR:

PQ x QR = 84

We also know that XY is parallel to PS, so triangle RXY is similar to triangle RQS:

RY/QS = XY/PS

9/QS = XY/PS

QS = 9XY/PS

The area of PXYS is 21 cm², so:

XY x PS = 21

Substitute QS for 9XY/PS:

XY x (9XY/QS) = 21

Simplify:

9XY²/QS = 21

XY² = 21QS/9

Substitute QS for PQ, since PQ = QS:

XY² = 21PQ/9

Substitute 84/PQ for PQ in the above equation:

XY² = 21(84/PQ)/9

XY² = 196/PQ

Now we can substitute PQ for 84/XY in the equation PQ x QR = 84:

(84/XY) x QR = 84

QR = XY

Substitute QR for PS in the equation XY x PS = 21:

XY² = 21/XY

Multiply both sides by XY:

XY³ = 21

XY = ∛21

Since RY = 9 cm, we can find QS:

9/QS = ∛21/PS

QS = 9PS/∛21

Now we can substitute QS and XY into the equation XY x PS = 21 and solve for PS:

(∛21) x PS = 21/((9/∛21))

PS = (21/((9/∛21)))/∛21

PS = 7∛21

Finally, we can solve for a and b:

a = PQ - XY = (84/PQ) - (∛21)

Substitute PQ for 84/XY:

a = (XY²/84) - ∛21

Substitute XY for ∛21:

a = (∛21²/84) - ∛21

a = 1/4 - ∛21

b = RY - QS = 9 - (9PS/∛21)

Substitute PS for 7∛21:

b = 9 - (9(7∛21)/∛21)

b = -54/∛21 + 9∛21

Step-by-step explanation:

Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Using this property in our product

we're going to have

Comparing this expression to the expression given, we have the value of a.

Answer: x = 78°

opposite angles have the same value

Answer:

78 degree

Step-by-step explanation:

x = 78 degree (being vertically opposite angle)

Answer:

16 cm

Step-by-step explanation:

C = Circumference of circle

   = 80 cm

A = Angle of minor sector

  = \(72^{o}\)

Length of minor arc = \(\frac{A}{360^{o}}\) × \(C\)

∴Length of arc AB = \(\frac{72^{o}}{360^{o}}\) × \((80 cm)\)

                               = \(16\) cm

Answer:

SAS, because vertical angles are congruent.

Answer:

26 metres

Step-by-step explanation:

(Assuming this is for the whole shape)

5 + 5 + 4 + 8 + 4

= 26 m

The function model will be -

Divide the cost by the number of pupils to split it, and you'll get the function C=1200 / n.

1200/N ≤ 7.50

1200 / 7.50 ≤ N

N ≥ 1200/7.5

N ≥ 160

To keep the price per kid to no more than $7.50, there must be more than 160 participants.

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The standard error of the distribution of sample proportions is 0.032.

option C is the correct answer.

The standard error of the distribution of sample proportions is calculated as follows;

S.E = √(p (1 - p)) / n)

where;

The standard error of the distribution of sample proportions is calculated as;

S.E = √ ( 0.1 (1 - 0.1 ) / 90 )

S.E = 0.032

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The value of x is 50 degrees.

What is the angle sum property of a triangle?

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.

The sum of angles in a triangle is 180 degrees. Let's consider the triangle with angles x, x, and y:

x + x + y = 180

2x + y = 180

y = 180 - 2x

Now let's consider the triangle with angles 43 and 57:

43 + 57 + z = 180

z = 180 - 43 - 57

z = 80

As vertically opposite angles, the third angle in the first triangle is also 80, so:

x + x + 80 = 180

2x + 80 = 180

2x = 180-80

2x  = 100

x=100/2

x=50

Therefore, the value of x is 50 degrees.

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Answer:

The answer is D. A clockwise rotation of 144 degrees about the origin.

Step-by-step explanation:

In most cases; when an object is transformed, the position of the object changes. A clockwise rotation of 144 degrees about the origin will map the pentagon onto itself.

Given:

The attached pentagon

The number of sides (n) in a pentagon is:

\(n = 5\)

The pentagon will not be mapped onto itself when reflected across line m because m is not at the center of the polygon

The pentagon will not be mapped onto itself when reflected across the x-axis because the pentagon has 5 sides (odd number of sides)

To map the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

\(\theta = \frac{360}n\)

\(\theta = \frac{360}5\)

\(\theta = 72\)

Other possible angles of rotation must be a multiple of 72. i.e.

\(\theta = 72, 144, 216, 288....\)

This means that: option (d) is correct because 144 is a multiple of 72

Hence, a clockwise rotation of 144 degrees about the origin will map the pentagon onto itself.

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Answer:

2c + 15 = 25

Step-by-step explanation:

The total he wants to earn is $25, so we know the equation must be an expression that equals 25.

____ = 25

He earns a fixed $15. He also earns $2 per customer.

The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.

fixed amount + amount per customer = 25

15 + 2c = 25

2c + 15 = 25

Answer: 2c + 15 = 25

Answer:

fifth option is the correct ans

sin(thita) = -sqare root 2 / 2

The statements which are true are,

The measure of reference angle is 45° and tan (θ) = -1.

Reference number associated with t is defined as the shortest distance from the x axis to the terminal point t, along a unit circle.

Reference angle is shortest angle measure from the X axis to the terminal side of the angle.

Reference angle = 2π - 7π/4 = π/4 = 45°

We have,

7π/4 = 2π - π/4

We also know that,

cos(2π - x) = cos x,

sin (2π - x) = -sin x

tan (2π - x) = -tan x

So, using theses identities,

cos (7π/4) = cos (2π - π/4) = cos(π/4) = 1/√2

sin (7π/4) = sin (2π - π/4) = -sin (π/4) = -1/√2

tan (7π/4) = tan (2π - π/4) = -tan (π/4) = -1

Hence the true statements are The measure of reference angle is 45° and tan (θ) = -1.

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Answer:

5.8 x 10 -4

Step-by-step explanation:

move decimal to 5.8 then find out how many times the decimal is moved from the final 5.8 to initial .00058

The correct Option for this question is option C i.e. x= 4tan34°. The other options which are given in the question are incorrect.

The Right angled triangle along with the base angle of 34°. The base is equal to 4.

θ= 34°

To find the value of x which is equal to the perpendicular of the right-angled triangle

According to the trigonometric ratio

tanθ = Perpendicular ÷ base

According to the above formula

tan 34 = x ÷ 4

Now, we have to multiply each side by 4.

x= 4× tan34° which means x= 4tan34°

tan 34° = 0.6745

x= 4× 0.6745

X=2.70

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Answer:

7 units

Step-by-step explanation:

(Background info, skip if not interested or needed for you)

The equation for distance on a cartesian plane coordinate system is based off the pythagorean theorem.

\(a^2 + b^2 = c^2\)

a and b being sides of a right triangle, c being the hypotenuse.

When we are solving for distance we are solving for c essentially.

\(c\) = \(\sqrt{a^2 + b^2}\)

Because a and b are side lengths of the right triangle, we need to find a way to find that in terms of coordinates. So here we might say that a is equal to the horizontal distance between the 2 points or Δx, and we would say that b is the vertical distance between the 2 points Δy.

(solutions)

So essentially distance is:

\(d = \sqrt{(x_2 - x_1)^2+ (y_2-y_1)^2 }\)

Now we just use the values given to us, and sub in the x and y values respectively.

(-2,4) \(x_1 = -2, y_1 = 4\)

(5,4)\(x_2 = 5, y_2 = 4\)

plug these values in:

\(d = \sqrt{((5) - (-2))^2+ (4-4)^2 } = \sqrt{(7)^2+ (0)^2 } = \sqrt{7^2 } = 7\)

Therefore the distance is 7 units.