Two cards are each individually drawn.
What is the probability of drawing two blue cards
if the first blue card is NOT placed back into the
deck before the second draw?
Reduce your answer to simplest terms.
?
Hint: Multiply the probability of the 1st draw by the
probability of the 2nd draw to get your answer.
Enter

The equation is  \(g(x) = -\frac{1}{16} (x - 1)^2 + 2\)  Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:

\(g(x) = -\frac{1}{16} (x - 1)^2 + 2\)

Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

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Answer:

a)  (-∞, -1) ∪ (-1, ∞)

b)  (-∞, -4) ∪ (-4, ∞)

c)  Vertical asymptote: x = -1

    Horizontal asymptote:  y = -4

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{1}{x+1}-4\)

The domain of a function is the set of all possible input values (x-values).

When the denominator of a rational function is zero, the function is undefined.  

Rewrite the function as one fraction:

\(\implies f(x)=\dfrac{1}{x+1}-\dfrac{4(x+1)}{x+1}\)

\(\implies f(x)=\dfrac{1-4(x+1)}{x+1}\)

\(\implies f(x)=\dfrac{-4x-3}{x+1}\)

Set the denominator to zero and solve for x:

\(\implies x+1=0\)

\(\implies x=-1\)

Therefore, the given function is undefined when x = -1, so its domain in interval notation is:

The range of a function is the set of all possible output values (y-values).

As the domain is restricted to (-∞, -1) ∪ (-1, ∞), the range is also restricted.

To find the range of a rational function, first solve the equation for x:

\(\implies y=\dfrac{1}{x+1}-4\)

\(\implies y+4=\dfrac{1}{x+1}\)

\(\implies (y+4)(x+1)=1\)

\(\implies x+1=\dfrac{1}{y+4}\)

\(\implies x=\dfrac{1}{y+4}-1\)

\(\implies x=\dfrac{1-(y+4)}{y+4}\)

Set the denominator of the resultant equation ≠ 0 and solve for y:

\(\implies y+4 \neq 0\)

\(\implies y \neq -4\)

Therefore, the range is the set of all real numbers other than y = -4:

A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.

Therefore, there is a vertical asymptote at x = -1.

As the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.

\(\implies f(x)=\dfrac{-4x-3}{x+1}\)

Therefore, there is a horizontal asymptote at:

There are no slant asymptotes as there is a horizontal asymptote.

Answer:

The area of the triangle is 9 and the area of the regtangle is 54 so when you add them you will get 63 i hope it will help!

The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

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Answer:

Given

A

Find the inverse of f(x):

B

C

Answer:

Step-by-step explanation:

(x + 4)^2 - 2 = 7 simplifies to

(x + 4)^2 = 5

We must isolate x.  To do this, take the square root of both sides, obtaining:

x + 4 = ±√5

There are two roots/solutions.  They are:

x = -4 + √5 and x = -4 - √5            

You must include the square root operator (√).  Use "  ^  " to denote exponentiation.

The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7

We are given the equation as;

(x + 4)² - 2 = 7

Add 2 to both sides to get;

(x + 4)² = 9

Find the square root of both sides to get;

x + 4 = ±3

Thus;

x = 3 + 4 and x = -3 + 4

x = 1 and 7

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£6219 will Brian  have after 6 years when he receives 0.6% per year compound interest.

What is Compound interest?

Emulsion interest means that the every time interest is paid on an quantum, that added interest will also admit interest later. emulsion interest is calculated on the star( original) quantum and the interest formerly accumulated on former ages.

Emulsion interest, can be calculated using the formula FV = P *( 1 R/ N)( N * T), where FV is the unborn value of the loan or investment, P is the original star quantum, R is the periodic interest rate, N represents the number of times interest is compounded per time, and T represents time in times.

We are given £6600 into his bank account.

He receives 0.6% per year compound interest.

So, formula we use here as follow;

C.A=P(1+r/100)^n

=6000(1+0.6/100)^6

=6000(1+0.006)^6

=6000(1.006)^6

=6000(1.0365)

=6219£

£6219 will Brian  have after 6 years when he receives 0.6% per year compound interest.

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The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

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The equation of the line in the standard form exists 3x - y = 2.

The equation of a line is a representation of a line on an x-y plane that illustrates the relationship between x and y for each point on the specific line. When x and y are variables and a, b, and c are constants, a line has the standard form ax + by = c.

Y = mx + b is the slope-intercept form of a line, where x and y are variables, m is the line's slope, and b is the line's y-intercept.

The one-point formula reads: y - y₁ = m(x - x₁). to describe the equation of a line traveling through the point (x1, y1) and having a slope of m.

We are asked to graph a line with a slope = -3, passing through the point (1, -5).

We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (1, -5).

Substituting these values in the equation y - y₁ = m(x - x₁), we get

Let the equation be y - -5 = -3(x - 1)

simplifying the equation, we get

y = -3x + 3 - 5

y = -3x - 2

3x - y = 2

The equation of the line in the slope-intercept form exists y = -3x - 2

The equation of the line in the standard form exists 3x - y = 2.

We draw the locations (1,-5) (because it is obvious that the line goes through this location) and (0, 2) (since the y-intercept is at 2 and the line passes through the point (0, 2)) in order to graph this line. We draw a line connecting these places, then we expand it on both sides to create the necessary line.

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The proportion of the variation in the head circumference that can be explained by the variation in the values of height is 0.813 squared, which is 0.659.

The proportion of the variation in head circumference that can be explained by the variation in the values of height is 0.659. This can be calculated using Pearson's correlation coefficient formula. The formula is r2 = r2, where r is the correlation coefficient, which in this case was 0.813.

Thus, the proportion of the variation in the head circumference that can be explained by the variation in the values of height is 0.813 squared, which is 0.659.

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1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Answer:

area = 132 cm²

Step-by-step explanation:

area of rectangle = 7 x 12 = 84

area of one triangle = 8 x 6 x 0.5 = 24

total area = 84 + 24 + 24 = 132 cm²

The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.

From the information, I have have $100 in a savings accoun and save an additional $40 each week.

Let the number of weeks be represented by w. The expression to represent this will be:

= 100 + 40w

My friend has $80 in a savings account and saves and addtional $10 each week. This will be:

= 80 + 10w

The sum will be:

= 100 + 40w + 80 + 10w

= 180 + 50w

The difference in the amount will be:

= 100 + 40w - (80 + 10w)

= 20 + 30w

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Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

24:
6 of 4
or

8 of 3

Step-by-step explanation:

6x4=24
8x3=24

a) On Monday, the total number of muffins that the baker makes is, proportionately, 90.

b) On Tuesday, the number of blueberry muffins that the baker makes is 24, which is 40% of 60.

Proportion is the equation of two ratios.

Proportional values are depicted as fractions, decimals, or percentages.

Monday:

The percentage of blueberry muffins to the total number of muffins made daily = 40%

The number of blueberry muffins the baker makes = 36

40% = 36

Proportionately, 100% = 90 (36 ÷ 0.4)

Thus, the total number of muffins that the baker makes on Monday = 90.

Tuesday:

The total number of muffins made = 60

The number of blueberry muffins = 24 (60 x 0.4)

Thus, proportionately, on Tuesday, the number of blueberry muffins, which represents 40% of 60, is 24.

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The number of blueberry muffins that a baker makes each day is 40% of the total number of muffins she makes.

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer:

(1/8x)-(5/6)

Step-by-step explanation:

-3/4x-1/3+7/8x-1/2

-6/8x-2/6+7/8x-3/6

-6/8x+7/8x-2/6-3/6

1/8x-5/6

Answer:

impulse bullying.

Step-by-step explanation:

Impulse bullying is like he is less likely to be a gang member. His bullying is more impulsive and may appear to be more random. Even when authorities are likely to impose penalties, he finds it impossible to prevent himself from engaging in the activity. He might be suffering from ADHD. Medication, behavioral therapy, and social skills training may help him. He will also most likely be bullied.

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

222 people were influenced by brand.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To determine how many people were influenced by brand, we need to add up the number of people who said "brand" as one of their influencing factors. However, we need to be careful not to double-count those who selected multiple factors.

Let's start by creating a diagram of the data:

         | Color | Size | Brand | Total

Only      |   5   |  8   |   16  |   29

Color/Size|  20   |  0   |   42  |   62

Size/Brand|   0   |  53  |   42  |   95

All Three |   0   |  0   |  102  |  102

None      |  20   |  20  |   20  |   60

Total     |  45   |  81  |  222  |  348

From this table, we can see that 222 people said that brand influenced their choice of cell phone.

Therefore, 222 people were influenced by brand.

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Answer:

\(\frac{5}{2}\) or 2.5

Hope that this helps!

Answer: 1,760

Step-by-step explanation:

60m per hr =

1m per min=

1,760yd per min

Answer:

1045 ft³ of water

Step-by-step explanation:

Given :

Length = 20 feets

Width = 9 1/2 feets

Height = 5 1/2 feets

The maximum of water the pool can hold is equivalent to the volume of the pool ;

Hence, Volume = Length * width * height

Volume = 20 * 9 1/2 * 5 1/2

Volume = 1045 ft³ of water

Answer:

X=85°....

Step-by-step explanation:

you do this by first acknowledging that in any triangle 180° will be present... so 40 + 45° equals 85°..this means that the other angle in the triangle will equal 95 degrees... now, in a line there's 180° present... that means 180 minus the 95 from the angle of c equals 85.

The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).

An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.

Workers who complete the computer security course will each receive a reimbursement of $350.

We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.

Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.  

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Answer:

\(x=3\text{ or } x=-15\)

Step-by-step explanation:

So we have the equation:

\(|2x+12|=18\)

Definition of Absolute Value:

\(2x+12=18\text{ or } 2x+12=-18\)

Subtract 12 from both sides for both equations:

\(2x=6\text{ or } 2x=-30\)

Divide both sides by 2 for both equations:

\(x=3\text{ or } x=-15\)

And we're done!