[PLS HELP WILL GIVE BRAINLIEST!!]
Given that sin θ = – 4/9 and 3π/2 ≤ θ ≤ 2π, find cot θ.

The probability that one of the cards is an ace and another one is either a ten or a jack, and the other one is either a queen or a king is [tex]$\frac{4}{2197}[/tex]  (or) 0.00182

Let:

A: Drawing one ace card

B: Drawing either a ten or a jack card

C: Drawing either a queen or a king card

Probability of drawing one ace card

P(A) = [tex]$\frac{4}{52} \\[/tex]

Probability of drawing one ten-numbered card.

A number of ten cards 4.

= [tex]$\frac{4}{52}[/tex]

Probability of drawing one jack card.

A number of jack cards 4.

= [tex]$\frac{4}{52}[/tex]

[tex]$ P(B)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}[/tex]

Probability of drawing one queen card.

A number of queen cards 4.

= [tex]$\frac{4}{52}[/tex]

Probability of drawing one king card.

A number of king cards 4.

= [tex]$\frac{4}{52}[/tex]

[tex]$P(C)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}[/tex]

Now Probability (one of the cards is an ace and another one is either a ten or a jack and the other one is either a queen or a king

[tex]P(A \cap B \cap C)[/tex] = P(A) P(B) P(C)

[tex]$=\frac{4}{52} \times \frac{8}{52} \times \frac{8}{52}[/tex]

[tex]$=\frac{4}{2197}[/tex] (or)

= 0.00182

Therefore the probability is [tex]$\frac{4}{2197}[/tex]  (or) 0.00182

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The approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].

To find the exact value of the definite integral of 4x over the interval [0,1] we can found using the antiderivative:

[tex]\int_0^1 4x dx = 2x^2 |_0^1 = 2(1)^2 - 2(0)^2 = 2.[/tex]

To approximate the value of the integral using the trapezoidal rule with ten equal subintervals, we can break the interval into ten equal subintervals of length 1/10 and approximate each subinterval using a trapezoid.

The error of the trapezoidal rule is given by:

[tex]|E_T| = -(b-a)^3/(12n^2) * f''(c)[/tex]

where a and b are the limits of the integration, n is the number of subintervals, and f''(c) is the second derivative of the integrand evaluated at some value c in the interval.

The error of this approximation will depend on the value of f''(c) for some value c in the interval [0,1]. The second derivative of 4x is constant and equal to 4, so the error will be a constant value:

[tex]|E_T| = -(1-0)^3/(12*10^2) * 4 = -1/300.[/tex]

Thus, the approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].

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Answer:

Since you are finding FG, FG=3

Step-by-step explanation:

picture above

Replicate measurements of 14 and 33 are necessary to decrease the 95 and 99% confidence limits to +0.19ug Cu/mL respectively.

a) For a 95% confidence limit, N is about 14

b) For a 99% confidence limit, N is about 33

To determine the number of replicate measurements necessary to achieve a desired confidence limit, we can use the formula:

[tex]N = (z * Spooled / d)^2[/tex]

where z is the Z-score associated with the desired confidence level (from the table provided), Spooled is the pooled standard deviation, and d is the desired decrease in the confidence limit.

[tex]N = (1.96 * 0.27 / 0.19)^2 = 14.22 = 14[/tex] (rounded to the nearest integer)

[tex]N = (2.58 * 0.27 / 0.19)^2 = 33.06 = 33[/tex] (rounded to the nearest integer)

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Complete Question:

An atomic absorption method for the determination of copper in fuel samples yielded a pooled standard deviation of Spooled = 0.27ug Cu/mL (s-->Sigma). How many replicate measurements are necessary to decrease the 95 and 99% confidence limits to +0.19ug Cu/mL?

Confidence Level%/z 95%/1.96 99%/2.58

a) For a 95% confidence limit, N is about __?

b) For a 99% confidence limit, N is about __?

Answer:-2.5

Step-by-step explanation:

1. Set up your problem it would be 5x+2y=-5

2. Then you would set your x to be 0 so you can solve for y

5(0)+2y=-5 aka 2y=-5

3. Divide each side by 2

2y (divided by 2) = -5 (divided by 2)

y=-2.5

I hope this helps!

The velocity and acceleration vectors and the equation of the tangent line for the curve = 3i+4tj

What is Velocity?

When an item is moving, its velocity is the rate at which it is changing position as seen from a certain point of view and as measured by a specific unit of time.

What is Acceleartion?

Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.

r(t) = 3cos(t)+sin4(t)j

velocity,V(t) = dr(t)/dt

=3sin(t)i + 4cos4(t)j

and acceleration a(t) = dv(t)/dt

= [tex]d^{2}r(t)/dt^{2}[/tex]

i.e a(t) = -3cos(t)i - 16sin(4t)j

v(0) = 0.i + 4j =4j

and a(0) = -3i -0j

=-3i

now we find the equation of the tangent line for the curve (t) at t=0

r(0) = 3i

r(t) = -3sin(t)i +4 cos 4(t)j

r (0) = 4j

equation target to the curve r(t) at t=0 is

1(t) = r (0) + (t)r(0)

= -3i+(t).4j

= -3i+4tj

The curve's tangent line equation, velocity and acceleration vectors, is -3i+4tj

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(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.

(B) Writing an equation for the relationship in the form of y = mx, we get y = 40x.

What is Proportionate Relationship?

It is given that there is a proportional relationship between hours, x, and number of miles, y, of water in a tank.

Also, the point (2, 80) is on a graph of this relationship.

(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.

(B) We have the given point, (2, 80)

Writing the relationship in the form of equation, y = mx using the point (2, 80), we get

80 = m × 2

⇒ m = 80/2

⇒ m = 40

Thus, writing an equation for the relationship in the form of y = mx when m = 40, we get y = 40x.

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The population of grasshoppers can be estimated by using a formula that takes into account the number of weeks that have passed since the start of the experiment (0 < t < 12).

The population of grasshoppers can be estimated with a formula that takes into account the amount of weeks that have passed since the start of the experiment (0 < t < 12). The first step in this process is to define the variables that will be used. The variable p will represent the population of grasshoppers after t weeks and t will represent the number of weeks that have passed. The next step is to use a formula to estimate the population of grasshoppers. This formula will take into account the amount of weeks that have passed and will likely result in an exponential increase in the population of grasshoppers as the weeks pass. After the formula is applied, the result will be the estimated population of grasshoppers after t weeks.

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Answer:

Step-by-step explanation:

As stated in the question that One vehicle transports 14 tourists and there are 34 tourists

Number of vehicles required = 34/14 = 2 vehicles + 6 people left

So, the remaining 6 people will be transported through 3rd vehicle.

So, there are 3 vehicles needed to transport 34 tourists.

Answer:

Step-by-step explanation:

The sum of the first 20 terms of a linear sequence can be found using the formula for the sum of an arithmetic series:

S = n/2 * (a1 + a20)

where n = number of terms = 20, a1 = first term = 1, and a20 = 20th term = 1 + 4 * (20 - 1) = 77

Substituting these values, we have:

S = 20/2 * (1 + 77) = 20/2 * 78 = 20 * 39 = 780

So, the sum of the first 20 terms of the sequence 1, 5, 9, 13 is 780.

Answer:

First what you want to do is find what fraction is equal to 1/4 and has a denominator of 20.

The way you can find this is by taking 1/4 and seeing how many times the denominator or 4 will go into 20.

4 * 5 = 20

Since 4 times 5 is 20, we will multiply 5 to the numerator of the fraction to.

1 * 5 = 5

So 5/20 is = to 1/4

x = 5

Now the question says, " x less thsn the denominator" so we just need to find how much less is 5 compared to 20.

20 - 5 = 15

The numerator has a value, "15 less than the denominator."

Step-by-step explanation:

Hope this helps! =D

The acorn is 9 meters far from the base of the tree. The solution has been obtained by using Pythagoras theorem.

What is Pythagoras theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

We are given that a flying squirrel's nest is 12 meters high in a tree.

So, the height is 12 meters.

Also, from its nest, the flying squirrel glides 15 meters to reach an acorn that is on the ground.

So, the distance the squirrel flied is 15 meters

Using Pythagoras theorem,        

c² = a² + b²

Here, c = 15 and a = 12

So,

⇒b² = c² - a²

⇒b² = 15² - 12²

⇒b² = 225 - 144

⇒b² = 81

⇒b = 9

Hence, the acorn is 9 meters far from the base of the tree.

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Answer:

3°

Step-by-step explanation:

33 +19x = 90     subtract 33 from both sides of the equation

19x = 57             divide both sides by 19

x = 3°

Answer:

5

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Complementary angles sum to 90 °

x = angle 1

4x = other angle            they sum to 90°

x   +    4x   = 90 °

5x = 90°

x = 18°        then      4x = 72°

The probability of all outcomes must add up to 1. The Expected Value (EV) shows the weighted average of a given choice.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100% and can be denoted as the possible outcomes upon the total number of outcomes.

To calculate this expected values multiply the probability of each given outcome by its expected value and add them together. And the net expected values can be found out by summing up all the possible expected values.

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The  number should replace A to give the best scale for the vertical axis of this data is 15.75

From the given parameters and graphs, we notice that we should find the mean of the set of data.

The scale should be chose in a way that the center shows the the mean of the frequencies

Recall that mean is the average of all the frequencies, then we have to find the mean of the means of the two frequencies.

(30+12+10)/2  52/3 = 17.3

Also, (27+6+13)/3  = 14.2

Then we find the average of the two averages to have

(17.3+14.2)/2 = 31.5/215.75

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates (2,4) and (-2,-8) into the formula:

m = (-8 - 4) / (-2 - 2) = -12/ -4 = 3

We can use one of the coordinates to find the y-intercept.

Plugging in the point (2,4) and the slope 3 into the equation y = mx + b, we get:

4 = 3*2 + b

so b = -2

Therefore, the equation of the line is y = 3x - 2.

The length of the rectangle is 23 km and the width of the rectangle is 15 km.

A rectangle is 8 km longer than it is wide.

Its area is 345 sq-km.

Let the width of the rectangle is x.

The length is 8 km longer than the width.

So the width of the rectangle is x + 8 km.

The formula of the area of rectangle is:

A = length × width

We know A = 345 sq-km.

Now putting the value

x × (x + 8) = 345

Now simplifying

x^2 + 8x = 345

Subtract 345 on both side, we get

x^2 + 8x - 345 = 0

Now factor the equation

x^2 + (23 - 15)x - 345 = 0

x^2 + 23x - 15x - 345 = 0

x(x + 23) - 15(x + 23) = 0

(x - 15)(x + 23) = 0

Now equation the factor equal to zero.

x - 15 = 0           or             x + 23 = 0

x = 15                or              x = -23

Since the dimension of the rectangle can't be negative. So

The width of the rectangle is 15 km.

Now we determine the value of length

x + 8 = 15 + 8 = 23

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Total 13,608,000 has length of eight are there containing exactly six distinct characters.

Total number of string = 10

The length of the string should be = 8

The distinct characters = 6

So the same character should be = 2

There are total 10 numbers in which 6 are distinct, so

[tex]^{10}P_{6}=\frac{10!}{(10-6)!}[/tex]

[tex]^{10}P_{6}=\frac{10!}{4!}[/tex]

[tex]^{10}P_{6}[/tex] = 3,628,800/24

[tex]^{10}P_{6}[/tex] = 151,200

Hence, strings of length eight are there containing exactly six distinct characters = 151,200 × 10 × 9

Strings of length eight are there containing exactly six distinct characters = 13,608,000

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The solution to the equation is x = 2

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

|x^3-1|-7=0

Add 7 to both sides

So, we have

|x^3-1| = 7

Remove the absolute bracket

x^3 - 1  = 7

So, we have

x^3 = 8

Take tge cube roots of both sides

x = 2

Hence, the solution is 2

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The dot product of two free vectors is independent of the choice of frames, as it relies only on the inner product of their transposed coordinate vectors.

The dot product of two free vectors, v1 and v2, can be expressed as the inner product of their transposed coordinate vectors, v1t and v2. This inner product is invariant under changes of frames, i.e. the same result will be obtained regardless of the choice of frames in which the coordinates are defined. This is because the transpose of a vector only changes the order of the coordinates, and the inner product of two vectors is unaffected by this reordering. Therefore, the dot product of two free vectors does not depend on the choice of frames in which their coordinates are defined.

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Answer:12.405 would be correct

Step-by-step explanation:

In probability theory and statistics, variance is the squared deviation from the mean of a random variable. The variance is also often defined as the square of the standard deviation. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value

The variance is a measure of variability

Therefore c is your answer!

Answer: The size of angle x in a regular pentagon is 72 degrees.

To find the size of angle x in a regular pentagon, you need to divide the total number of degrees in a full circle (360) by the number of sides in a pentagon (5).

A full circle has 360 degrees, so each interior angle of a regular pentagon must measure 360/5 = 72 degrees.

Therefore, he size of angle x in a regular pentagon is 72 degrees.

If Canister contained [tex]6\frac{1}{8}[/tex] cup of flour when Karina started making cookie and used [tex]2\frac{1}{2}[/tex] cup then number of cup left in Canister is 29/8 cups   .

the number of cups of floor in the canister initially is = [tex]6\frac{1}{8}[/tex] = 49/8 ;

the amount of floor that she used is =   [tex]2\frac{1}{2}[/tex] = 5/2 cups ,

To find out how much flour is left in the canister, we need to subtract the amount used from the total amount.

We can start by converting the mixed fractional cups to improper form ,

we get ;

number of cups left in the canister is = 49/8 - 5/2 = 49/8 - 20/8 = 29/8 .

Therefore , 29/8 cups were left in the canister .

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The Simplified values are

1. 7∛3 + 2∛192 = 15∛3.

2. 10√7 - √28- 6√180 = 8√7 - 36√5

3. 8[tex]\sqrt[4]{48}[/tex] - 5√90 + 9[tex]\sqrt[4]{3}[/tex] = 25[tex]\sqrt[4]{3}[/tex] - 15√10

4. 5∛32x³[tex]y^4[/tex] - 3xy∛4y = 7xy ∛4y

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.

Given:

1. 7∛3 + 2∛192

= 7∛3 + 2 ∛ 2 x 2 x 2 x 2 x 2 x 2 x 3

= 7∛3 + 2 x 2 x 2 ∛3

= 7∛3 + 8∛3

= 15∛3.

2. 10√7 - √28- 6√180

= 10√7 - √2 x 2 x 7 - 6√2 x 2 x 3 x 3 x 5

= 10√7 - 2√7 - 36√5

= 8√7 - 36√5

3. 8[tex]\sqrt[4]{48}[/tex] - 5√90 + 9[tex]\sqrt[4]{3}[/tex]

=  8 x 2 [tex]\sqrt[4]{3}[/tex] - 5 x 3 √10 + 9[tex]\sqrt[4]{3}[/tex]

= 25[tex]\sqrt[4]{3}[/tex] - 15√10

4. 5∛32x³[tex]y^4[/tex] - 3xy∛4y

= 10xy ∛4y - 3xy∛4y

= 7xy ∛4y

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In the line of symetry for this parabola is x = -1.

The maxima or minima of the parabola is [tex]-\frac{21}{4}[/tex]

Estimate the gradient of the curve at x = 4 is 5.

The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.

The gradient of the curve at the point (-1, 1) is -1.

The steps are as follows:

The function of parabola y = x² - 3x - 3

(i) In the line of symetry for this parabola.

Symetry of the parabola:

x =  [tex]-\frac{b}{2a}[/tex]    → for y = ax² + bx + c

x =  [tex]-\frac{-3}{-3}[/tex]

x = -1

(ii) The maxima or minima of the parabola.

The maximum or minimum parabola can be found when the derivative is 0

y = x² - 3x - 3

y' = 2x - 3

0 = 2x - 3

2x = 3

x =  [tex]\frac{3}{2}[/tex]

The maxima or minima of the parabola

y = x² - 3x - 3

  = ( [tex]\frac{3}{2}[/tex] )² - 3 (  [tex]\frac{3}{2}[/tex] ) - 3

  =  [tex]\frac{9}{4}[/tex]  -   [tex]\frac{9}{2}[/tex]  - 3

  =   [tex]\frac{9}{4}[/tex]  -  [tex]\frac{18}{4}[/tex]  -  [tex]\frac{12}{4}[/tex]

  = [tex]-\frac{21}{4}[/tex]

(iii) Estimate the gradient of the curve at x = 4

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(4) - 3

          = 8 - 3

          = 5

y = x² - 3x - 3

y = 4² - 3(4) - 3

  = 16 - 12 - 3

  = 1

(iv) The equation of the tangent of the point (4, 1)

(y - b)² = m (x - a)²

(y - 1)² = 5 (x - 4)²

y² - 2y + 1 = 5 (x² - 8x + 16)

y² - 2y + 1 = 5x² - 40x + 90

5x² - y² - 40x + 2y + 90 - 1 = 0

5x² - y² - 40x + 2y + 89 = 0

(v) The gradient of the curve at the point (-1, 1)

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(1) - 3

          = 2 - 3

          = -1

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Answer:

y=x+3

Step-by-step explanation:

Answer:  A=4.5m²

Step-by-step explanation:  length: 1.5 Width: 300

Unit Conversion:l=1.5mw

A=wl=3·1.5=4.5m²