: Given the following P(A)-0.3 P(B) = 0.2 PA and B) 0.06 A and B are disjoint and independent. A and B are disjoint. A and B are independent A and B are neither disjoint nor independent.

Answer:

4am, it's 4 am.

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

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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9,900 codes that are available for reckha.

There are a total of 10,000 possible three-digit codes when each digit is in the set {0,1,2,3,4,5,6,7,8,9}. Since each digit can take 10 different values, we can use the formula 10^3 = 1000 to calculate the total number of codes.

However, since reckha cannot choose a code that is the same as yours or one that is the same as yours except for switching the positions of two digits, we have to subtract these possibilities from the total. We can calculate the number of codes forbidden by subtracting the number of codes with the same digits in all three positions (10) and the number of codes with the same digits but different positions (90) from the total. This leaves us with 10,000 - (10 + 90) = 9,900 codes that are available for reckha.

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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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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 approximate percentage of daily phone calls numbering between 46 and 82 is 95%.

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

In this case, the mean is 64 and the standard deviation is 9. Therefore, approximately 68% of the daily phone calls answered by each receptionist fall between 64 - 9 = 55 and 64 + 9 = 73.

Additionally, approximately 95% of the data falls between 64-18 = 46 and 64 + 18 = 82.

So, the approximate percentage of daily phone calls numbering between 46 and 82 is 95%.

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The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.

What is a triangle ?

triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.

Given ,

The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.

the length of side p is 4 cm

Let the lengths of q and r are x and y respectively.

The perimeter of an isosceles triangle  =  (p+2q)

So,

p+2q = 9

4+2q = 9

2q = 9-4

2q = 5

q = 5/2

q = 2.5 cm

Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .

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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.

Answer: 7.4

Step-by-step explanation:

[tex]\frac{x}{\sin 46^{\circ}}=\frac{5}{\sin 29^{\circ}}\\\\x=\frac{5\sin 46^{\circ}}{\sin 29^{\circ}}\\\\x \approx 7.4[/tex]

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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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 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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The peak, the largest deposit, made in July

It's the tallest one in the plot.

Let's arrange the number from smallest to greatest:

50<80=80<95<100<110<250<300<320

Jan<Feb=Sep<May<Apr<Mar<June<Aug<July

So, the greatest amount of deposit was in July.

These trades took place between June and August 2020. June 1 After giving it some deliberation, Natalie decides to offer Curtis a mixer for $1,150 (mixer cost: $620) on credit with terms of n/30. 30 Curtis gives Natalie a call. He signs a one-month, 8.35% note payable since he won't be able to pay the sum due for another month. Curtis calls on July 31.

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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.

If a fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit of water. The value of n that will maximize the total fish weight per unit of water is 125 fish . The weight is 31,250g.

a. Value of n that will maximize the total fish weight per unit of water?

W(n) = 500 -2n

W=n(500 -2n)

W = 500n -2n

0=500 -4n

n =500/4

n = 125 fish

b. Weight

Weight = Number of fish/ Average weight of fish

Weight = 125 × (500/2)

Weight = 125 × 250

Weight = 31,250g

Therefore the value of n that will maximize the total fish weight per unit of water is 125 fish . The weight is 31,250.

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Check the picture below.

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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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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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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Answer:

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Find the distance between the given point (-3, 2) and the center of circle (4, 0) using distance formula:

As we see the distance is greater than radius, hence it is outside circle.

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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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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Answer:

50

Step-by-step explanation:

An equation Dividing 4x^2+6x by 4x+2 gives : Therefore , the expression ... 4x + 2, as follows: 4x^2 + 2x + 4x + 2 − 2, or x(4x + 2) + (4x + 2) − 2.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the given equation is

this above equation is equivalent to

2X - 10/2X+2,

as root of both equation are same

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Answer:

To solve this problem, we will use the following steps:

Step 1: We know that the amount of time it takes Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. So we can use this information to calculate the proportion of Susan's trips to class that would take less than 40 minutes.

Step 2: To calculate the proportion of Susan's trips to class that would take less than 40 minutes, we need to find the z-score for the value of 40 minutes. We can use the following formula to find the z-score:

z = (x - μ) / σ

Where x is the value we are interested in (40 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).

z = (40 - 50) / 5 = -2

Step 3: We can use a standard normal table or a calculator to find the proportion of Susan's trips to class that would take less than 40 minutes.

The proportion of Susan's trips to class that would take less than 40 minutes is 0.0228 or 2.28%.

Step 4: To calculate the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes, we need to find the proportion of Susan's trips to class that would take more than 50 minutes and add it to the proportion of Susan's trips to class that would take less than 40 minutes.

Step 5: To find the proportion of Susan's trips to class that would take more than 50 minutes, we need to find the z-score for the value of 50 minutes.

z = (50 - 50) / 5 = 0

Using a standard normal table or a calculator, the proportion of Susan's trips to class that would take more than 50 minutes is 0.5 or 50%.

Step 6: Finally, we can add the proportion of Susan's trips to class that would take more than 50 minutes and the proportion of Susan's trips to class that would take less than 40 minutes to find the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes.

0.50 + 0.0228 = 0.5228 or 52.28%

Final Answer: The proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes is 0.5228 or 52.28%.

If the point (3√5,d+3) is 3d Units away from the origin , then the smallest possible value of d is 3 .

The point (3√5,d+3) is 3d Units away from the origin , that means ,

the distance between the points (0,0) and (3√5,d+3) is 3d units ;

By using the distance formula , the given situation can be represented as

⇒ [tex](3d)^{2} =(3\sqrt{5} -0)^{2} + (d+3)^{2}[/tex] ;

On simplifying the equation ,

we get ;

⇒ [tex]9d^{2} = 45+d^{2} +6d+9[/tex] ;

⇒ [tex]4d^{2} -3d--27 = 0[/tex] ;

Writing in factor form ,

we get ;

⇒ [tex](4d+9)(d-3)= 0[/tex] ;

On solving we have [tex]d=-\frac{9}{4}[/tex] and [tex]d=3[/tex] .

Since the distance is only positive , So we can write d = 3 ;

Therefore , the smallest possible value of d is 3 .

The given question is incomplete , the complete question is

A point (3√5,d+3) is 3d Units away from the origin. What is the smallest possible value of d ?

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The likelihood that a student chosen at random has any siblings is 0.777. This is determined by deducting from 1 the probability of having no siblings (0.223).

1. Get the probability of 0 siblings : 0.223

2. Subtract the probability of 0 siblings from 1 :

1 - 0.223

= 0.777

3. Round the result to 3 decimal places :

0.777

The probability of a student not having 0 siblings can be calculated by subtracting the probability of having 0 siblings from 1. The probability model created from the survey results is a 2-column table with 5 rows. Column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. Column 2 is labeled probability with entries

0.223, 0.532, 0.121, 0.085, 0.039.

The probability of having 0 siblings is 0.223. To calculate the probability of not having 0 siblings, we subtract 0.223 from 1. This gives us 0.777, which is the probability of not having 0 siblings. This result should be rounded to 3 decimal places, giving us 0.777 as the final answer.

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