Find the exact value of cos using cos( - ): Hint: To calculate π/12, select two fractions that when subtracted from each other will result in π/12.

If no chicken in the flock is infected with the h6n2 virus, the probability that the veterinarian will conclude that the h6n2 virus is not present in the flock

[tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right] * O.O5^2 *0.95^8[/tex]

= 0.98849

Using the answer probability of veterinarian will incorrectly conclude that

h6n2 virus present in the flock

1- 0.98849 =0.1150

veterinarian will incorrectly conclude that h6n2 virus present in the flock least three chicken shows positive result

∑[tex]\left[\begin{array}{ccc}10\\k\\\end{array}\right] 0.90^{k} * 0.10^(10-k)[/tex]

= 1-[tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right] * O.90^0 *0.10^10 +\left[\begin{array}{ccc}10\\1\\\end{array}\right] * O.90^1 *0.10^9 + \left[\begin{array}{ccc}10\\2\\\end{array}\right] * O.90^2 *0.10^8[/tex]

=0.9999996

the probability of randomly selected chicken shows positive result is

P(true positive)*P(infected chicken) +P(false positive)*P(non infected chicken)

= 0.90*0.20 + 0.05*0.80

= 0.22

probability of  three chicken shows positive result

[tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right] * O.22^0 *078^10 +\left[\begin{array}{ccc}10\\1\\\end{array}\right] * O.22^1 *0.78^9 + \left[\begin{array}{ccc}10\\2\\\end{array}\right] * O.22^2 *0.78^8[/tex]

=0.38311

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James gets 140 pounds.

What is a ratio?

A ratio is a mathematical comparison of two or more values. A ratio can be written in various ways, such as "5 to 3" or "5:3", which means that for every 5 parts, there are 3 parts. Ratios can also be simplified to their lowest form, just like fractions.

In this case, Carly and James share money in a ratio of 5:3, meaning that for every 5 parts of the money that Carly gets, James gets 3 parts. If Carly gets £70 more than James, we can set up the equation as:

x + 70 = 5/8 * x

Where x is the amount James gets.

Solving this equation we get:

x = 140

Hence, James gets 140 pounds.

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if the density of the metal cube is 2.3 x 10⁻³ kilograms/micro liters, 2968 cm. is the length of one side of a cube if the mass is 88 milligrams

The amount of digits that contribute to the correctness of a value—often a measurement—are known as significant figures. The first digit that is non-zero is where we begin counting significant figures.

The number of significant single digits (0 through 9 inclusive) in an expression's coefficient is referred to as the significant figures in scientific notation. The amount of accuracy or assurance an expert or scientist uses to state a quantity is indicated by the number of significant figures in a statement.

The given mass of the metal cube is 2.3 × 10⁻³kg/micro-liters or 2300000 gm/liter

The density of the metal cube is 88 mg or 0.088 gm.

Now, we know that density, d = mass/volume.

So, volume of the metal cube,

V = mass/density

V = (2300000/0.088)

V = 26136363.7 L

Now, we know that volume of a cube is a³ where a is the length of a side of the cube. So, a³ = 26136363.7 L or 26136363.7 dm³.

So, a = 296.8 dm or 2968 cm.

So, the length of one side of the cube is 2968 cm.

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The solution to the given exponential equation is 0.791.

What is a logarithm?

The logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be raised to produce x is the logarithm of a number x to the base b.

Given exponential function is

5x⁻² = 8

Divide both sides by 5:

x⁻² = 8/5

x⁻² = 1.6

Taking logarithm of base x:

[tex]log_x(x^{-2})=log_x1.6[/tex]

-2 [tex]=log_x(1.6)[/tex]

Now applying the logarithm of change of base formula:

-2 = log 1.6/log x

Divide both sides by -2:

1 = log 1.6/( -2log x)

Multiply both sides by log x:

log x = log 1.6/-2

log x = -0.1021

Now applying the formula [tex]log_xa = b[/tex] implies [tex]a = x^b[/tex]:

x = 10^(-0.1021)

x = 0.7905

x = 0.791

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23/20 students in barbara's class have both a cat and a dog.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Given that,

The number of students in barbara's class having a pet cat = 2/5

The number of students in barbara's class having a pet dog = 3/4

Thus, the fraction of the students in barbara's class have both a cat and a dog = 2/5+3/4 = 8+15/20= 23/20

Hence, 23/20 students in barbara's class have both a cat and a dog.

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Check the picture below.

Answer:

-1233

Step-by-step explanation:

Step 1.) Plug in the orresponding number to letter

- |135+ -2| 2- -7.

Step 2.) Find absolute value

-| 137 | 2- -7

Step 3.) Solve

-137 × 9

= -1233

The required inequality describes for the given problem is  x < 8.5.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

she used 3.5 pounds of the wax to make vanilla-scented candles and has less than 5 pounds of wax left to make orange-scented candles.

let x represent the weight of the block of wax originally

then,inequality can be written as,

x - 3.5 < 5

x < 8.5

Thus, required inequality is x < 8.5.

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Answer:

Manuel worked 40 hours * $15.00/hour = $<<40*15=600>>600 for his regular hours.

For his overtime hours, he worked 5.75 hours * $15.00/hour = $86.25

For overtime, he is paid time and a half, which is $15.00/hour * 1.5 = $22.50/hour.

So he was paid 5.75 hours * $22.50/hour = $128.44 for his overtime hours

Therefore, his gross pay for the week is $600 + $128.44 = $728.44

Answer:

Step-by-step explanation:

You need to know trigonometry for this.\

You can't solve this without a scientific calculator.

TOA means Tan x = Opposite/Adjacent or in this case, 5.1/4.2

tan x = 5.1/4.2

arctant(tanx) = arctan(5.1/4.2)

x = arctan(5.1/4.2)

≈ 50.5°

arctan x is also known as tan inverse x

The only value that is a solution of the inequality -9> -4+5x is the first one, x = -5.

Here we have the inequality:

-9> -4+5x

And we want to see which of the given values is a solution for that inequality.

The first option is x = -5

Replacing that value we will get:

-9 > -4 + 5*-5

-9 > - 4 - 25

-9 > -29

This is true.

The second option is x = 2

-9> -4+5*2

-9 > -4 + 10

-9 > 6

This is false.

The last option is x = -1

-9 > -4 + 5*-1

-9 > -9

This is false.

Then the only solution is the first one, x = -5.

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Most accurate statement is "The plane clears the tower with about 6 yards to spare". So the option c is correct.

In the given question, a plane travels 1500 yard before lifting off the ground.

If the plane continues on the runway, it is 600 more yard to the control tower, which is 198 feet high.

Instead, the plane takes flight and travels 603 yards.

Initial distance traveled = 1500

Yards to control tower = 600

Height of control tower = 198 feet

Height of control tower = 198×3 yards

Height of control tower = 594 yards

If the airplane's rate of ascent is proportionate to the distance flown, then 1 yard of length equals 1 yard of height achieved.

The height of the plane would be 600 yards after flying 600 yards to the location of the control tower.

So, Difference in height = Height of plane - Height of tower

Difference in height = 600 yards - 594 yards

Difference in height = 6 yards

Hence, most accurate statement is "The plane clears the tower with about 6 yards to spare". So the option c is correct.

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The vertex form of equation is discussed below,

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants. of the parabola is at (h, k).

As, A parabola has a lowest point if it opens upward.

Additionally, a parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Now, the parent function f(x) = x² has its vertex at the origin.

Also, The vertex form of a quadratic function is

f(x) = a(x – h)² + k, where a, h, and k are constants.

For example, The parent function f(x) = x² is vertically stretched by a

factor of 4/3 and then translated 2 units left and 5 units down.

So, the vertex form : g(x) = 4/3 (x+2)² - 5.

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Answer:

The angle in radians is 4.6.

Note that it is expressed in radians, to convert it to degrees you need to multiply it by 180/π, but it is already rounded to the nearest 10th.

Step-by-step explanation:

To find the angle in radians to the nearest 10th, you need to use the relationship between the length of an arc, the radius of the circle, and the angle of the arc:

arc length = (angle in radians) * (radius)

In this case, the radius of the circle is 8.5 and the arc length is 38.9, so you can substitute these values into the equation:

38.9 = (angle in radians) * (8.5)

To solve for the angle in radians, you need to divide both sides of the equation by the radius:

angle in radians = 38.9 / 8.5

The angle in radians is 4.6.

Note that it is expressed in radians, to convert it to degrees you need to multiply it by 180/π, but it is already rounded to the nearest 10th.

The general solution of  dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

The given differential equation is  dy over dx equals x times y plus 3 times x question

dy/dx=xy+3x

dy/dx=x(y+3)

dy/dx-x(y+3)=0

Solve seperable ODE

[tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]

Hence, the general solution of dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]

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The value(s) of x will make x² = 16 true are 4 and -4.

B. is the answer

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included

The values of x that will make x² = 16 true are -4 and 4.

x² = 16 can be written as follows:

x² = 16

x = ±√16

x = ± 4

x = 4 or -4

This because the square of 4 is 16 i.e. 4² = 16. Likewise the square of -4 is 16 i.e. (-4)².

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R-squared is an important statistic in regression, it measures how well the model fits the data.

What is regression ?

Regression is a statistical method used to analyze the relationship between one or more independent variables and a dependent variable. It is used to predict the value of the dependent variable based on the values of the independent variables.

One important statistic from the regression outputs is R-squared, it measures how well the model fits the data. It ranges from 0 to 1, and a higher R-squared value indicates a better fit. In other words, it represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It can provide an overall measure of how well the model is able to explain the variation in the dependent variable based on the independent variable(s).

The statistic that can be hardest to interpret and why can vary depending on the complexity of the model and the user's level of understanding of statistics. But one statistic that can be challenging for some people to interpret is the p-value, which is used to determine the statistical significance of the coefficients of the model.

R-squared is an important statistic in regression, it measures how well the model fits the data.

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Answer:

y-1=2/3(x+9)

Step-by-step explanation:

Sorry cant really explain well but I am positive this is the right answer.

The direct relantionship model indicates that variable q is equal to 225 / 19 when r is 45.

In this problem we must derive an equation based on following relationship:

Variable q is directly proportional to r.

In other words, we have the following direct relationship model that describes well the situation:

q = k · r

Where:

First, determine the constant of proportionality:

k = q / r

k = 76 / 20

k = 19 / 5

Second, calculate the variable r is:

q = r / k

q = 45 / (19 / 5)

q = 225 / 19

The statement presents several typing mistakes, correct form is introduced below:

q is directly proportional to r is 76 when r is 20.

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e6z = xyz,  implicit differentiation of the following equation-

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. 

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. 

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. 

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

According to our question-

Given e6z = xyz

To find ∂z/∂x → consider z as a function of x and take y to be a constant

So differentiating with respect to x, we get

e6z × 6 × ∂z/∂x = z × y + xy × 1 × ∂z/∂x

[using the chain rule on the LHS and the product rule on the RHS]

Factor out the ∂z/∂x:

∂z/∂x [6e6z - xy] = yz

∂z/∂x = yz / [6e6z - xy]

Do the same thing to find ∂z/∂y except consider z to be a function of y and take x to be a constant

Differentiating with respect to y:

e6z × 6 × ∂z/∂y = z × x + xy × 1 × ∂z/∂y

∂z/∂y [6e6z - xy] = xz

∂z/∂y = xz / [6e6z - xy]

Therefore, ∂z/∂x = yz / [6e6z - xy] and ∂z/∂y = xz / [6e6z - xy]

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The solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and            k = 1,3,5,7,9...

Let d = [tex](2a^{2} +29a + 65, a+ 13)[/tex]

Now, we can split [tex]2a^{2} + 29a + 65[/tex] in the following way, so that it becomes easier to factorise.

[tex]2a^{2} + 29a + 65 = (2a^{2} + 29a + 39) + 26[/tex]

From this, we can quantify and notice that -13 is one root of this equation, while the other root is -3/2.

Therefore, [tex]2a^{2} + 29a + 39 = (a+13)(2a+3)+26[/tex]

Thus, [tex]d = ((a+13)(2a+3)+26, a+ 13)[/tex]

The greatest common divisor (GCD) of two or more numbers is the greatest common factor number that divides them, exactly. It is also called the highest common factor (HCF).

Now, we can use Euclid's Algorithm.

[tex]= gcd (2a^{2} + 29a + 65, a + 13)\\= gcd (2a^{2} + 29a + 65 - 2a(a+13), a+13)\\= gcd (3a + 65, a + 13)\\= gcd (3a + 65 - 3a(a+13), a+13)\\= gcd (26, a + 13)[/tex]

This is necessarily 1, 2, 13, or 26, which we can see by just looking at the first term. By factoring 1183 and considering that [tex]a[/tex] is an odd multiple, then we should be able to conclude the answer.

Hence, the conclusion is that the solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...

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Answer:

14/3

Step-by-step explanation:

Cross Multiply 6/7 by 4

6/7 x 4/1

= 28/6

Simplify

=14/3

Answer:

4am, it's 4 am.

A triangle with the lengths of the sides 6cm , 8cm , and 10cm is a right angled triangle using Pythagoras theorem.

As given in the question,

In the given triangle,

lengths of the sides of the triangle is given by :

6cm , 8cm , and 10cm

In the given measurement longest side is 10cm.

Using Pythagoras theorem :

( Hypotenuse ) ² = (Base)² + ( Altitude)²

Here

( 6 )² + ( 8 )²

= 36 + 64

= 100

= 10²

It satisfy the condition of Pythagoras theorem.

It is a right angled triangle with hypotenuse = 6cm.

Therefore, the given lengths of the sides of the triangle represents it is a right angled triangle.

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Answer:

the answer is 20 my guy hope this helps

2^8, 4^4 and 16^2 are equivalent to 256. We can find this out by using the concept of Factors.

Factors are numbers or algebraic expressions that divide another number of expression without leaving a remainder.

In the question, the number given is 256.

Options are: 2^8, 4^4, 16^2, and 128^2

We will break down all the numbers into the product of their factors and using multiplication, we will verify if they are equivalent to 256 or not.

2^8 = 2*2*2*2*2*2*2*2 = 256

4^4= 4*4*4*4 = 256

16^2= 16*16 = 256

128^2 = 128*128 = 16384

As we can observe, only 128^2 is not equivalent to 256.

Therefore, 2^8, 4^4 and 16^2  are equivalent to 256.

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The mean and standard deviation of the sampling distribution of the difference in sample means for 8 female and 8 male students who participated in the 2-mile run is -1.5 minutes and 2.413 minutes, respectively.

The mean of the sampling distribution of the difference in sample means is calculated by subtracting the mean of the female students from the mean of the male students, which is 7.3 - 8.8 = -1.5 minutes.

The standard deviation of the sampling distribution of the difference in sample means is calculated by taking the square root of the sum of the squares of the standard deviations of the two populations, which is sqrt(3.3^2 + 2.9^2) = 2.413 minutes.

Therefore, the mean and standard deviation of the sampling distribution of the difference in sample means is -1.5 minutes and 2.413 minutes, respectively.

The mean and standard deviation of the sampling distribution of the difference in sample means for 8 female and 8 male students who participated in the 2-mile run is -1.5 minutes and 2.413 minutes, respectively.

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The residuals for the two points representing companies that have been in business for 3 years, (3, 0.42) and (3, 0.3) are 0.087 and -0.033 respectively.

Given:

The line of best fit is y = 0.091x+0.060.

The two points representing companies that have been in business for 3 years are (3, 0.42) and (3, 0.3).

The predicted value for the point (3, 0.42) can be calculated as:

= (0.091 × 3) + 0.060

= 0.0273 + 0.060

= 0.333

So, the residual will be:

= 0.42 - 0.333 = 0.087

The predicted value for the point (3, 0.3) is calculated as:

y = 0.091x + 0.060.

  = (0.091 × 3) + 0.060.

   = 0.333

So, the residual will be:

= 0.3 - 0.333 = -0.033

Hence, the residual for the two points will be 0.087 and -0.333 respectively.

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