a card is drawn from a deck of 52 playing cards. what is the probability that it is a king and a black card?

The line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 , the correct option is (c) .

In the question ,

it is given that ,

the Line m passes through the points (2,-7) and (4,-9),

So , the slope of the line will be = (-9 + 7)/(4 - 2)

= -2/2

= -1

We know that the if two lines are parallel then they will have same slope ,

the slope of the line should be -1,

from the given options , we can see that only option (c) has the slope = -1

on comparing equation y = -x + 2 with the general equation of the line y = mx + c , we get

slope(m) = -1

hence , the line m is parallel to y = -x + 2 .

Therefore , the line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 .

The given question is incomplete , the complete question is

Line m passes through the points (2, -7) and (4, -9). Line m is parallel to which line?

(a) 8x + 2y = -10

(b) x = 5

(c) y = -x + 2

(d) y = x - 9

Learn more about Equation of Line here

https://brainly.com/question/13868556

#SPJ1

The probability that they will all be non fiction is 0.0667. The solution has been obtained by using hyper-geometric distribution.

What is hyper-geometric distribution?

When sampling from a small population without replacement, the hyper-geometric distribution is a discrete probability distribution that determines the likelihood that an event occurs k times in n trials.

The formula is

P (X = x) = h (x, N, n, k) = \(\frac{C_{k,x} * C_{N-k, n-x} }{C_{N,n} }\)

We are given

x = 4

N = 10 + 12 = 22

n = 4

k = 12

Substituting this in the formula, we get

⇒P (X = 4) = h (4, 22, 4, 12) = \(\frac{C_{12,4} * C_{22-12, 4-4} }{C_{22,4} }\)

⇒P (X = 4) = h (4, 22, 4, 12) = \(\frac{C_{12,4} * C_{10, 0} }{C_{22,4} }\)

⇒P (X = 4) = h (4, 22, 4, 12) = 0.0667

Hence, the probability that they will all be non fiction is 0.0667.

Learn more about hyper-geometric distribution from the given link

https://brainly.com/question/30911049

#SPJ1

Answers: A, A, A

1)A rectangle has an area of 405 cm square and width of 15 cm. The length of the rectangle is: 27 cm

15cmx 27cm= 405 cm

2)The x- and y- intercepts of the graph of the line 5x - 3y - 15 = 0 are, respectively: 3 and 5

(I don't really know how to explain this.......)

3)The expression that simplifies to 11x + 2y is: 4x+3y+7x-y

 4x+7x=11x

  3y-y = 2y

Therefore, it will equal to 11x+2y.

I really hope this helps!

Please Mark Me Brainliest!!!

(I'm in 5th Grade Honors but I learn MS)

Answer:

All the answer are A

Step-by-step explanation:

Area = length times width

405 = x15  Divide both sides by 15

27 = x

For the x intercept  Let y = o and solve for x

5x - 3y -15 = 0

5x - 3(0) -15 = 0

5x -15 = 0  Add 15 to both sides of the equation

5x = 15  Divide both sides by 5

x = 3

The x intercept is (3,0)

For the y intercept Let x = 0 and sole for y

5x -3y -15 = 0

-3y -15 = 0  Add 15 to both sides of the equation

-3y = 15  Divide both sides by -3

y = -5

The y intercept is (0,-5)

4x + 3y + 7x - y  Combine the like terms

(4x + 7x) = (3y -y)

11x + 2y

Answer:

\(f"'(x) = 2(x-4)^2 - 1\)

Step-by-step explanation:

Given

\(f(x) = x^2\) --- the quadratic function

Vertically stretched by 2

Translation: \(4\ units\) left and \(1\ unit\) down

Required

Determine the new function

\(f(x) = x^2\)

The rule for vertical stretch is:

\((x,y) \to (x,ay)\)

In this case:

\(a = 2\)

So, we have:

\(f(x) = x^2\)

\(f'(x) = a * f(x)\)

\(f'(x) = a * x^2\)

Substitute: \(a = 2\)

\(f'(x) = 2 * x^2\)

\(f'(x) =2x^2\)

Translation: 4 units left

The rule is:

\((x,y) \to (x - c,y)\)

In this case: \(c =4\)

So, we have:

\(f"(x) = 2(x - 4)^2\)

Translation: 1 unit down

The rule is:

\((x,y) \to (x,y-d)\)

In this case, \(d=1\)

So, we have:

\(f"'(x) = f"(x) - 1\)

\(f"'(x) = 2(x-4)^2 - 1\)

Step-by-step explanation:

-9*-7= 63 (negitive times a negitive equals a positive, because your multiplying by -1 twise)

-4*-3=12

The product of -9 and -7 is greater than that of -4 and -3.

Hope this helps!

Answer:The products are 63 and 12.  63 is greater than 12.  

Step-by-step explanation:

Negatives cancel out eachother.  Because of this, all you need to do is multiply 9 and 7 together which equals 63.  4 times 3 equals 12, and because 63 is greater than 12, the product of (-9)(-7) is greater.  Hope this helps:D

Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

To know more about  irrational numbers here

https://brainly.com/question/26862717

#SPJ4

Energy saving is maintained. This decay is not observed in nature because the basic laws and conservation principles of particle physics do not allow it.

In the decay process you mentioned, n → p e-, the neutron (n) decays into a proton (p) and an electron (e-). This decay violates the conservation of several important quantities. Let's see what is not preserved in this process:

Conservation of charge: In this decay, a neutron (charge = 0) decays into a proton (charge = +1) and an electron (charge = -1). Total charge is not conserved because the neutron is neutral, but the proton and electron have opposite charges.

Conservation of lepton number: Lepton number refers to the number of leptons minus the number of antileptons. A neutron is a baryon, not a lepton, and its decay into a proton (also a baryon) and an electron (a lepton) violates lepton number conservation.

Conservation of baryon number: Baryon number refers to the number of baryons minus the number of antibaryons. Both the neutron and the proton are baryons, so the total baryon number is conserved in this decay. However, the presence of an electron introduces an additional lepton, which breaks the conservation of the baryon number.

Conservation of energy: Energy is generally conserved in the decay process. However, the specific energies of the particles involved may differ. The difference in mass between the neutron and the proton, as well as the electron, are taken into account in the decay energy balance.

In short, the n → p e- decay process violates the conservation of charge, lepton number, and baryon number.

However, energy saving is maintained. This decay is not observed in nature because the basic laws and conservation principles of particle physics do not allow it.

To learn more about Decay from the given link

https://brainly.com/question/10745621

#SPJ4

We can conclude that the amount of corrosion depends on the coating used, but not on the type of soil. Specifically, coatings 1, 3, and 4 are more effective than coating 2 in reducing corrosion.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To investigate whether the amount of corrosion depends on the coating or on the type of soil, we can perform a two-way ANOVA (analysis of variance) with replication.

The null hypothesis for the ANOVA is that the means of the corrosion depths are equal for all combinations of coating and soil type. The alternative hypothesis is that at least one mean is different from the others.

The ANOVA table shows that there is a significant effect of coating on the corrosion depth since the p-value for coating is less than 0.05. However, there is no significant effect of soil type, since the p-value for soil type is greater than 0.05. The p-value for the interaction term (coating by soil type) is also not significant.

Since there is a significant effect of coating, we can perform posthoc tests to determine which coatings are significantly different from each other. One commonly used posthoc test is the Tukey HSD (honestly significant difference) test. The results of the Tukey test are presented in the table below:

Comparison                     Difference in means Standard error p-value

Coating 1 - Coating 2                   11.0                2.479         0.005

Coating 1 - Coating 3                   14.0                2.479        <0.001

Coating 1 - Coating 4                   13.0                2.479        <0.001

Coating 2 - Coating 3                    3.0                2.479          0.730

Coating 2 - Coating 4                    2.0                2.479          0.947

Coating 3 - Coating 4                   -1.0                 2.479          1.000

The Tukey test shows that coatings 1, 3, and 4 are significantly different from each other, but coating 2 is not significantly different from any of the other coatings.

Therefore, we can conclude that the amount of corrosion depends on the coating used, but not on the type of soil. Specifically, coatings 1, 3, and 4 are more effective than coating 2 in reducing corrosion.

To learn more about statistics from the given link:

https://brainly.com/question/28053564

#SPJ1

here is your formula then

Answer:

ok what must you do

Step-by-step explanation:

Answer:

Step-by-step explanation:

12 is 40% of what number?

30.

what is 60% of 30?

18

boom

Therefore , the solution of the given problem of linear equation comes out to be the linear equation of the image is y = 3x + 22.

The formula y = mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.

Here,

Let's first find the coordinates of two points on the original line. We can choose any two points, but for simplicity, let's choose (0,4) and (1,7), which lie on the line y=3x+4.

The distance between these two points is:

d = √((1-0)² + (7-4)²) = √(10)

To find the new coordinates of these points after dilation, we multiply the distance by 4 and use the center of dilation (1,1) as the reference point:

New coordinates of (0,4):

x' = 1 + 4(0-1) = -3

y' = 1 + 4(4-1) = 13

New coordinates of (1,7):

x' = 1 + 4(1-1) = 1

y' = 1 + 4(7-1) = 25

So the image of the line y=3x+4 after dilation by scale factor 4 centered at (1,1) is the line passing through the points (-3,13) and (1,25). We can find the equation of this line by finding the slope and the y-intercept.

Slope:

m = (y2-y1)/(x2-x1) = (25-13)/(1-(-3)) = 12/4 = 3

Y-intercept:

y = mx + b

13 = 3(-3) + b

b = 22

Therefore, the linear equation of the image is y = 3x + 22.

To know more about linear equation visit:

brainly.com/question/11897796

#SPJ1

Answer:70 cm

Step-by-step explanation:a^2+b^2=c^2

Experimental and quasi-experimental designs share similarities in terms of their focus on investigating cause-and-effect relationships. These designs both involve manipulating variables and observing their effects on an outcome of interest.

However, they differ in terms of the level of control the researcher has over the assignment of participants to groups. Experimental designs are characterized by the random assignment of participants to different groups or conditions. This randomization helps ensure that any observed differences between groups can be attributed to the manipulation of the independent variable. The researcher has control over the assignment process, allowing for stronger causal inferences. Quasi-experimental designs, on the other hand, lack the random assignment of participants to groups. This may be due to practical or ethical reasons. Instead, participants are assigned to groups based on pre-existing characteristics, such as age or location. While quasi-experimental designs still allow for the examination of cause-and-effect relationships, they are considered less rigorous than experimental designs due to the potential for confounding variables. In summary, experimental and quasi-experimental designs both aim to investigate cause-and-effect relationships. They differ primarily in the level of control the researcher has over participant assignment. Experimental designs use random assignment for greater control, while quasi-experimental designs rely on pre-existing characteristics.

Learn more about cause-and-effect relationships here: brainly.com/question/11673085

#SPJ11

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

For similar questions on range

https://brainly.com/question/30389189

#SPJ11

Answer:

Step-by-step explanation:

- 3 (2 - x) = 6x​

-6 + 3x = 6x

-6 = 3x

-2 = x

None of the statements A, B, or C can be determined to be true based on the given information. we do not have enough information to determine the values of P(A), P(A∩B), or P(B|A) from the given probabilities.

To determine which statement is true, let's analyze the given information.  We have:

P(B) = 4/1

P(A∪B) = 2/1

P(A|B) = 3/2

Let's evaluate each statement:

A) P(A) = 3/1

This statement is not directly supported by the given information. We cannot determine the value of P(A) solely based on the provided probabilities.

B) P(A∩B) = 12/1

This statement is also not supported by the given information. We do not have enough information to determine the value of P(A∩B).

C) P(B|A) = 5/1

This statement is not supported by the given information. We do not have any direct information about P(B|A), so we cannot determine its value.

D) A and B are not independent.

To determine whether A and B are independent, we can check if P(A∩B) = P(A) * P(B). However, as mentioned earlier, we do not have enough information to determine the value of P(A∩B). Therefore, we cannot conclude whether A and B are independent based on the given information.

In summary, none of the statements A, B, or C can be determined to be true based on the given information. The only conclusion we can draw is that we do not have enough information to determine the values of P(A), P(A∩B), or P(B|A) from the given probabilities.

Learn more about probabilities.

https://brainly.com/question/29381779

#SPJ11

Answer:

\(\boxed{v_c=60ft^3}\)

Step-by-step explanation:

The following formula gives the volume of a rectangular prism:

\(V_c= w \times l \times h\)

In this case, we know:

\(w \times l = 20 ft^2\)

and:

\(h= 3ft\)

So:

\(V_c= 20 f^2 \times 3ft\\v_c=60ft^3\)

\(\text{-B$\mathfrak{randon}$VN}\)

Given:

Fabric required for each chair = 10 yards

Fabric required for each sofa = 20 yards.

Total available fabric = 300 yards.

The number of sofas must be at least twice the number of chairs.

Profit on each chair = $50

Profit on each sofa = $80.

To find:

The function that represents the manufacturer's profit, P.

Solution:

Let P represents the manufacturer's profit, x represent the number of chairs and y represent the number of sofas.

Profit on 1 chair = $50

Profit on x chairs = $50x

Profit on 1 sofa = $80

Profit on y sofas = $80y

Total profit = Profit on x chairs + Profit on y sofas

\(P=50x+80y\)

Therefore, the required profit function is \(P=50x+80y\).

Answer:

B on edge

Step-by-step explanation:

Step-by-step explanation:

The formula for calculating the area of a square is expressed as;

A = x² where;

x is the length of one side of the square

Given

x = 10in

A = 10²

A = 10 * 10

A = 100in²

Area of the square with side length 10in is 100in²

From the equation A = x², we can see that as the value of x increases, the value of the area also increases and vice versa. This means that the area of the square is directky proportional to its length. Hence we can say YES, the area of a square and the length of its side directly proportional

Answer:

100 sq in

Step-by-step explanation:

No, not proportional

The hiker's distance and bearing from their starting point are approximately 7.155 miles and 28.07°, respectively.

Given that two hikers travel 8 mi southeast and then 6 mi east, we are to find the hikers distance and bearing from their starting point at this time.Long ExplanationThe bearing of the hiker refers to the angle between the hiker's direction and North. So, let us assume that the hiker has initially moved at a direction East, as shown below:We are given that the hiker has traveled 8 miles to the southeast.

Therefore, from the diagram, the distance traveled in the East direction is 8 sin(45) miles, and the distance traveled in the South direction is 8 cos(45) miles. East = 8 sin(45) = 8/√2 = 4√2 miles South = 8 cos(45) = 8/√2 = 4√2 miles We are then told that the hiker travels 6 miles east, from the last position.

To know more about distance  visit:-

https://brainly.com/question/13034462

#SPJ11

The given points are (1,3) and (2,6).

The pre-image is (1,3) and the image is (2,6).

As you can observe, the image is double than the pre-image, this means the transformation used was a dilation with a scale factor of 2, the rule is

The problem asks for an expression to calculate the profit made by the PTO at Douglas Elementary school. The PTO made cookies, and each batch of cookies costs $3 to make, and each batch makes 20 cookies.

The cookies are sold at $0.50 per cookie, and every batch is sold. The expression needs to be in terms of b, which represents the number of batches produced by the PTO.

To calculate the profit made by the PTO, we need to determine the total cost of producing all the batches and the total revenue generated by selling all the cookies. The total cost of producing all the batches is simply the cost per batch multiplied by the number of batches: 3b. The total revenue generated by selling all the cookies is the number of cookies sold multiplied by the selling price per cookie: 0.5(20b) = 10b. Therefore, the profit made by the PTO can be calculated as the revenue generated minus the cost of production: 10b - 3b = 7b. Therefore, the valid expression for the profit made by the PTO in terms of b is 7b.

To know more about cost of production, click here:

brainly.com/question/29383456

#SPJ11

Answer:

Step-by-step explanation:

f(3)= 8-5(3)

=8-15

=-7

Answer:

J

Step-by-step explanation:

first add all the types of drinks together then put how many grape Gatorade there is on top of the number which you'll get 10/25 or 10 over 25 then divide it by five over five 5/5 and get 2/5.

Answer:

J

Step-by-step explanation:

because you add all of them so 10+6+4+5=25 and ratio so 10/25 and reduced its 2/5 so J

Given:

1. Angle B is congruent to Angle D.

2. Angle BAC is congruent to Angle DCA

To prove that triangles ABC and CDA are congruent, we first note that reflexive property means that anything is equal to itself. This means that:

Notice that both triangles share one side and we know that every side is congruent to itself. Hence, we can prove that triangles ABC and CDA are congruent by AAS Congruence Theorem as we have pairs of two congruent angles and non-included sides.

Therefore, the answer is:

Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

C

PLZ MARK AS BRAINLIEST