Simplify 3[tex]\sqrt[/tex]2-√2

The probability of both getting a heart card and a red heart card is 1/4.

Given that there is a deck of 52-cards, we need to find the probability of getting a heart cards,

Probability shows how likely an event will happen.

P(E) = n(E) /n(S).

n(E) = Number of favorable outcomes of E.

n(S) = total number of possible outcomes of E.

No. of heart cards = 13

n(E) = 13

P (getting a card of heart) = no. of favorable outcomes/total no. of possible outcomes of E

= 13/52

= 1/4

Since heart card is red that means there are 13 heart cards which is red in color.

So, the probability of getting a red heart card = 13/52 = 1/4

Hence the probability of both getting a heart card and a red heart card is 1/4.

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The domain of the function from the given graph is [-4, 4]. Therefore, option A is the correct answer.

Domain = the set of all x-coordinates.

From the given graph, the zeros are (-4, 0) and (4, 0),

So, the domain of values are {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Interval notation -4≥x≤4

Therefore, option A is the correct answer.

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Part C is best represents the solution set to the system of inequalities .

Given that;

1st equation is,

⇒  y ≤ x + 1

And, 2nd equation is,

y + x ≤ –1

 y ≤ -x -1

Since, 1st equation represent Part C and Part D region.

And, 2nd equation represent Part B and Part C region.

Thus, Part C is common among those.

So, Part C is best represents the solution set to the system of inequalities .

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Answer:

D

Step-by-step explanation:

The line in option D, y = 3x, does not intersect with any of the other lines.

To see this, we can first note that options A and B have slopes of -3 and 3, respectively, which means they are parallel lines. Therefore, they will never intersect.

Option C has a slope of 3 as well, but its y-intercept is -7, which is different from the y-intercept of line B, which is 7. This means that these two lines are not parallel and will intersect at some point.

On the other hand, line D has a slope of 3 and a y-intercept of 0 (since there is no constant term), which means it passes through the origin. Therefore, it will not intersect with any of the other lines unless one of the other lines also passes through the origin, which is not the case here.

Therefore, the line that does not intersect with any of the other lines is option D, y = 3x.

Answer:  B. y = 3x + 7 and y = -3x + 7 are parallel lines, so they do not intersect.

Step-by-step explanation:

Two lines in a plane may intersect at a point, be parallel, or be coincident (overlapping). To determine which of the given lines do not intersect, we need to find the slope of each line and check for parallelism.

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Therefore, we can write the equations of the given lines in slope-intercept form as follows:

A. y = -3x - 7 (slope m = -3)

B. y = 3x + 7 (slope m = 3)

C. y = 3x - 7 (slope m = 3)

D. y = 3x (slope m = 3)

From the slopes, we can see that lines B and C have the same slope of 3, so they are parallel. Therefore, they do not intersect at any point in the plane. Lines A and D have different slopes, so they are not parallel and will intersect at some point in the plane.

Answer:

6n+30

Step-by-step explanation:

Step 1:

Multiply 6 and n

Step 2:

Multiply 6 and 5

Step 3:

Put together!

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Answer:

the answer is A

Step-by-step explanation:

distributive property states

a(b+c)=ab+ac

therefore

6(n+5)=6n+30

The probability that Ronnie gets a carrot and Sydney gets a green bean is 0.53.

Given that, q bucket contains the following vegetables 1 squash, 2 carrots, 4 heads of broccoli, 2 artichokes and 5 green beans.

Total number of vegetables = 1+2+4+2+5

= 14

The probability that Ronnie gets a carrot = 2/14

= 1/7

The probability that Sydney gets a green bean = 5/13

Here, the probability of a event = 1/7 + 5/13

= (13+35)/91

= 48/91

= 0.53

Therefore, the probability that Ronnie gets a carrot and Sydney gets a green bean is 0.53.

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The volume inside the cube but outside of an inscribed sphere is 231.6 cubic inches

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

Cube volume = 486

This means that the side length of the cube is

l³ = 486

So, we have

l = 7.86

This represents the diameter of the sphere

So, the sphere volume is

V = 4/3πr³

So, we have

V = 4/3 * 22/7 * (7.86/2)³

Evaluate

V = 254.36

So, the required volume is

Volume = 486 - 254.36

Evaluate

Volume = 231.64

Approximate

Volume = 231.6

Hence, the volume inside the cube but outside of an inscribed sphere is 231.6 cubic inches

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The expression that has the greatest value is A) 20-(-20).

Based on the given expressions, we can known the greatest value by testing them one after the other  then any value that have the highest number among the option will be the epression tht posses the greatest value which is the answe we are looking for.

The first option;

20-(-20) = 40

The second option;

-16-17 +31 = -2

The third option;

18-15+27 = 30

The fourth option;

-20+10 +10 = 0

The fifth option;

-4(3)(-2) = 24

Therefore, based on the calculation above we can see that the greatest value is 40, hence option A is correct.

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The volume of the square pyramid is approximately 10 cm³.

Given that a pyramid with a square base, where the perimeter of the base is 8.7 cm and the height of the pyramid is 6.3 cm.  

We need to find the volume of the pyramid,

Since, the perimeter = 8.7

therefore,

4a = 8.7

a = 2.175

So,

The volume of a square pyramid = side² × height / 3

= 2.175²×6.3/3

= 9.93 ≈ 10 cm³

Hence, the volume of the square pyramid is approximately 10 cm³.

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The square pyramid has a volume of around 10 cm3.

Given that the height of the pyramid is 6.3 cm and the base's perimeter is 8.7 cm, a pyramid with a square base is there.  

We must determine the pyramid's volume.

As a result, the perimeter is 8.7.

therefore,

4a = 8.7

a = 2.175

So,

A square pyramid's volume is equal to side2 height / 3.

= 2.175²×6.3/3

= 9.93 ≈ 10 cm³

Consequently, the square pyramid's volume is roughly 10 cm3 in size.

Answer:

The conic section basis of the equation x^2 + xy + y^2 + 2x = -3 can be determined by examining the coefficients of the x^2, xy, and y^2 terms.

To do this, we can start by completing the square for the quadratic terms in the equation:

x^2 + xy + y^2 + 2x = -3

(x^2 + 2x) + xy + y^2 = -3

(x + 1)^2 - 1 + xy + y^2 = -3

(x + 1)^2 + xy + y^2 = -2

Now, we can see that the coefficient of the xy term is positive, which indicates that the conic section is an ellipse. Specifically, this is a rotated ellipse because the x and y terms are not squared separately and have a non-zero coefficient.

Therefore, the conic section basis of the equation x^2 + xy + y^2 + 2x = -3 is a rotated ellipse.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given equation is:

x^2 + xy + y^2 + 2x = -3

To identify the conic basic of the equation, we need to check its discriminant, which is given by:

Δ = B^2 - 4AC

where A, B, and C are the coefficients of x^2, xy, and y^2 terms respectively.

In this case, A = 1, B = 1, and C = 1.

So,

Δ = B^2 - 4AC

= 1^2 - 4(1)(1)

= -3

Since the discriminant is negative, the given equation represents an ellipse.

Answer:

  81, 89, 91

Step-by-step explanation:

You want to know Aura's three exam scores if their average was 87, the second was 8 point higher than the first, and the third was 2 points higher than the second.

Let x represent the first exam score. Then x+8 and x+10 will be the other two scores. Their average is ...

  (x +(x +8) +(x +10))/3 = 87

  x +6 = 87 . . . . . . . . simplify

  x = 81 . . . . . . . . subtract 6

  x +8 = 89

  x +10 = 91

Aura's three exam scores were 81, 89, and 91.

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The fixed cost is $275, and the variable cost for each product is $0.25.

The cost function can be written as: C(x) = 275 + 0.25x

(a) The linear cost function representing the cost C(x) (in $) to the vendor to produce x products can be determined by considering both the fixed cost (booth setup) and the variable cost (cost per product).

The fixed cost is $275, and the variable cost for each product is $0.25.

Therefore, the cost function can be written as:

C(x) = 275 + 0.25x

b. (b) R(x) = 3x, where x is the number of products sold and R(x) is the revenue in dollars.

(c) To break even, the cost must equal the revenue: 0.25x + 275 = 3x. Solving for x, we get x = 137.5. The vendor must produce and sell 138 products to break even.

(d) If 40 products are sold, the cost is C(40) = 0.25(40) + 275 = $285, and revenue is R(40) = 3(40) = $120. The vendor will lose money, as the cost is greater than the revenue.

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Answer:

A. one solution

Step-by-step explanation:

The only solution was negative one half

Answer:

B. Triangle A and B

Step-by-step explanation:

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

ΑΠSШЕЯ®

Step-by-step explanation:

The probability that all three students prefer to take some of their courses fully online can be found by multiplying the probabilities of each event together. Since each student has a 68% chance of preferring fully online courses, the probability that the first student prefers fully online courses is 0.68, the probability that the second student prefers fully online courses given that the first student does is also 0.68, and the probability that the third student prefers fully online courses given that the first two students do is also 0.68. Therefore, the probability that all three students prefer to take some of their courses fully online is 0.68 x 0.68 x 0.68 = 0.314. The probability is approximately 0.314 or 31.4%.

Value of cosθ will be cosθ = (√2)/2 after using Pythagorean Identity.

The Pythagorean Identity states that sin²θ + cos²θ = 1. We can use this identity to find cosθ given that sinθ = (√2)/2 and θ terminates in Quadrant I.

Since sinθ = (√2)/2 and θ terminates in Quadrant I, we can draw a right triangle with angle θ in Quadrant I, opposite side equal to √2, adjacent side equal to 1, and hypotenuse equal to √3.

Using the Pythagorean Theorem, we can find the length of the hypotenuse as:

h² = a² + b²

√3² = 1² + (√2)²

3 = 1 + 2

3 = 3

So, the length of the hypotenuse is √3.

Now, we can use the Pythagorean Identity to find cosθ:

sin²θ + cos²θ = 1

Substituting sinθ = (√2)/2:

(√2/2)² + cos²θ = 1

Simplifying:

2/4 + cos²θ = 1

1/2 + cos²θ = 1

cos²θ = 1 - 1/2

cos²θ = 1/2

Since θ terminates in Quadrant I and sinθ is positive, we know that cosθ is also positive. Therefore, taking the positive square root of both sides, we get:

cosθ = √(1/2) = (√2)/2

So, cosθ = (√2)/2.

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The factored form of the expression 816² - 25c² is 816 + 5c )( 816 - 5c).

Given the expression in the question:

816² - 25c²

To factor 816² - 25c², we the:

a² - b² = (a + b)(a - b)

Written as the product of two factors

Since both terms are perfect squares

a = 816

b = 5c

Hence, plugging into the formula:

a² - b² = (a + b)(a - b)

816² - 25c² = ( 816 + 5c )( 816 - 5c)

Therefore, the factored form is ( 816 + 5c )( 816 - 5c ).

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The sample space for choosing 2 marbles from the bag with replacement

Purple Red Blue

Purple Purple, Purple Purple, Red Red, Blue

Purple Red, Purple Purple, Red Red, Blue

(option c)

To find the sample space, we need to list all possible outcomes. Since we are choosing two marbles, we can have three possible outcomes for the first marble: purple, red, or blue. Similarly, we can also have three possible outcomes for the second marble.

To construct the sample space, we need to list all possible pairs of the first and second marbles. Since we are choosing two marbles, the total number of pairs will be the product of the number of outcomes for each marble. In this case, we have three outcomes for each marble, so the total number of pairs will be:

3 x 3 = 9

Therefore, there are nine possible pairs of marbles that we can select from the bag with replacement. To represent the sample space in a table, we can list all possible pairs of marbles as follows:

Purple Red Blue

Purple Purple Purple

Purple Red Blue

Red Purple Red

Red Red Red

Blue Blue Blue

Blue Red Purple

Blue Red Blue

Purple Blue Red

Purple Blue Blue

Hence the correct option is (c).

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[tex]Ans\ 13: \{(d)\ (f\circ g)(1)=26\}\\\\(f\circ g)(1)=f(g(1))\\\\g(1)=3(1)+2=5\\\\\therefore (f\circ g)(1)=f(g(1))=f(5)\\\\\implies (f\circ g)(1)=26\ (i.e.\ 25+5-4)\\\\\hrule \ \\\\Ans\ Q14: \{(e)\ (f+g)(3) = 20\}\\\\(f+g)(3)=f(3)+g(3)\\\\\implies (f+g)(3)=(9+3)+(9-1)\\\\=20[/tex]

Answer: x = -2.

Step-by-step explanation:

-8x + 44 ≥ 60

Subtracting 44 from both sides, we get:

-8x ≥ 16

Dividing both sides by -8 (and reversing the inequality since we are dividing by a negative number), we get:

x ≤ -2

Next:

-4x + 50 < 58

Subtracting 50 from both sides, we get:

-4x < 8

Dividing both sides by -4 (and reversing the inequality), we get:

x > -2

Putting the two inequalities together, we get:

-2 < x ≤ -2

This means that the solution for x is x = -2.

Answer: y=2+6

Step-by-step explanation:

Using the hypergeometric distribution, it is found that there is a 0.19704% probability that the balls have the same number.

The balls are chosen without replacement, hence, the hypergeometric distribution is used.

Hypergeometric distribution:

P (X = x) = h (x, N, n, k)

              = [tex]\frac{C_{k, x} C_{n - k, n - k} }{C_{N, n} }[/tex]

[tex]C_{n, x} = \frac{n!}{x!(n - x)!}[/tex]

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There are 3 balls, hence .

For each number, there are 3 balls, hence .

3 balls are selected, hence .

For each ball, the probability is P(X = 3). There are 8 balls, hence we have to find 8P(X = 3).

P (X = x) = h (x, N, n, k)

              = [tex]\frac{C_{k, x} C_{n - k, n - k} }{C_{N, n} }[/tex]

P (X = 3) = h (3, 30, 3, 3) = 0.0002463

0.0002463 x 8 = 0.0019704

0.0019704 = 0.19704% probability that the balls have the same number.

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Answer:

60 degrees

Step-by-step explanation:

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The value of 2 digit number has order rotational of 2 is, 16

And, The value of 3 digit number has order rotational of 2 is, 931

Now, For a two-digit number with an order rotational of 2, it means that if you flip the digits, you get a different but still valid number.

Hence, There are a few such numbers, but one example is 16 which becomes 61 when you flip the digits.

And, For a three-digit number with an order rotational of 2, it means that if you rotate the digits, you get a different but still valid number.

And, There are also a few such numbers, but one example is 319 which becomes 931 when you rotate the digits.

Thus, The value of 2 digit number has order rotational of 2 is, 16

And, The value of 3 digit number has order rotational of 2 is, 931

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The excluded points for the function are; x = -2 and x = 9

The excluded values of a function are the values of the independent variable (usually denoted as "x") that would make the function undefined.  In other words, the excluded values are the values that the independent variable cannot take on in order for the function to be well-defined.

We have that;

[tex]x^2 - 9x/x^2 - 7x - 18[/tex]

When we factor the denominator we have that;

[tex]( x + 2) (x - 9)[/tex]

Thus the points of discontinuity are x = -2 and x = 9

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They can improve their graph by doing the following ; Tips:

1. They should show which one represents 100% as a key

2. The height of the books compared to the percentages are not accurate

3. To simplify the graph, their should be a stack of books for each individual year

Answer:

10. -3(y+1)

The coefficients in this polynomial are -3 and 0 (for the constant term). The

sum of these coefficients is -3+0=-3.

11. 5x(3x²-4)

The coefficients in this polynomial are

15, 0, and -20 (for the constant term).

The sum of these coefficients is 15 +0

-20=-5.

12. 7(-2m²+5m+6)

The coefficients in this polynomial are

-14, 35, and 42 (for the constant term). The sum of these coefficients is -14 +

35+ 42 = 63.

13. (x+1)(3x-4)

The coefficients in this polynomial are 3, -1, and 0 (for the constant term). The sum of these coefficients is 3-1+0= 2.

14.

(-2z+5z)(-4x-8)

The coefficients in this polynomial are 8 and 32 (for the constant term). The sum of these coefficients is 8+32= 40.

15. (9x+5)(-4x-8+10x)

The coefficients in this polynomial are -36, 38, and -40 (for the constant term). The sum of these coefficients is -36+38-40 = -38

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]x-2=0\implies x=2\impliedby \textit{vertical line, }\underline{und efined~slope}[/tex]

Check the picture below.