? Question
Select the graph of the transformation.
The graph f(x)=√√ is transformed to form
shows g(x).

Answer:

P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

Step-by-step explanation:

As we know that, if A and B are two events then

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.

The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

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

4 toppings are chosen from a set of 12, hence the number of ways is given by:

[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]

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Answer:

9

Step-by-step explanation:

a^2+b^2=c^2

a^2+12^2=15^2

a^2=225-144

a=sqrt(81)

a=9

Answer:

Step-by-step explanation:

Comment

If you know this formula

tn = t1 + (n - 1)*d then you don't even have  to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.

Givens

1 = t1

25 = tn

d = 2

Solution

25 = 1 + (n - 1)*2                 Subtract 1 from both sides?

25-1 = 1-1 + (n - 1)*2            Combine

24 = (n  -  1) * 2                   Divide by 2

24/2 = (n - 1)*2/2                

12 = n - 1                               Add 1 to both sides

12 + 1 = n - 1 + 1                     Combine

13 = n

Answer

So you have 13 cards that  will bring success.

In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.

The missing table is given below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Shawn is collecting money from students at his school for a charity.

The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.

Since 30 is 1/3 of 90, we know the ratio is 1:3.

In order of blank boxes going from left to right then down

1, 9, 5, 75, 35

The complete table is attached below.

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The solution of the given equation (x + 5) - ( 2x - 3) = 6 is 2.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

(x + 5) - ( 2x - 3) = 6

To solve;

(x + 5) - ( 2x - 3) = 6

Distribute the negative;

(x + 5) - 2x + 3 = 6

we need to get the like terms together;

x - 2x + 5+ 3 = 6

-x + 8 = 6

Subtract 8 from both sides, we get;

-x = -2

x = 2

Hence, the solution of the given equation is 2.

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Answer:

4 inches

Step-by-step explanation:

Given information:

Let y = height of snow on the lawn

Let t = time in hours

⇒ y = 2 + 0.5t

To find how much snow is on the lawn after 4 hours of snowing, substitute t = 4 into the found equation and solve for y:

⇒ y = 2 + 0.5(4)

⇒ y = 2 + 2

⇒ y = 4 inches

Therefore, Amadou will have 4 inches of snow on his lawn after 4 hours of snow falling.

After 4 hours of continuous snowfall at a rate of 0.5 inches per hour, Amadou would have 4 inches of snow on his lawn. After t hours of snow falling at the same rate, he would have 2 + 0.5t inches of snow on his lawn.

After 4 hours of snow falling at a constant rate of 0.5 inches per hour, Amadou would have:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × 4 hours)

Snow accumulation = 2 inches + 2 inches

Snow accumulation = 4 inches of snow.

After t hours of snow falling, the amount of snow on Amadou's lawn would be:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × t hours)

Snow accumulation = 2 + 0.5t inches of snow.

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The correct option is Option D: Yes, the graph passes the vertical line test.

The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.

The vertical line test states that

If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.

So here in this function shown in the graph.

If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.

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The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

y = x³ - 5x + 2

The maximum is at dy/dx = 0, hence:

3x² - 5 = 0

x = -1.29 or x = 1.29

y = (-1.29)³ - 5(-1.29) + 2 = 6.3

The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29

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Answer:

14N+5

Step-by-step explanation:

Five years ago; Rose Nx

Amanda x

Now; Rose Nx+5

Amanda x+5=19

x=19-5=14years

Rose(NOW) =14N+5

The expected number of M&M's in the bag is 308

The parameters that complete the question are:

Number of blue pieces = 4

Total = 15

From the question, the number of blue pieces is:

Blue = 82

Let the total number of M&M be M.

So, we have:

Blue = Number of blue/Total * M

This gives

82 = 4/15 * M

Multiply both sides by 15/4

15/4 * 82 = M

Evaluate

M = 307.5

Approximate

M = 308

Hence, the expected number of M&M's in the bag is 308

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Answer:

n = [tex]\frac{1}{36}[/tex]

Step-by-step explanation:

n × 18 = [tex]\frac{1}{2}[/tex]

To find the value of n we have to divide both sides by 18.

Let us solve it now.

18n = [tex]\frac{1}{2}[/tex]

[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18

n =  [tex]\frac{1}{2}[/tex] ÷ 18

n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]

n =  [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]

n = [tex]\frac{1}{36}[/tex]

Answer: x=0

Step-by-step explanation:

[tex]x=4+(4x-4)\\\\x=4+4x-4\\\\x=4x\\\\3x=0\\\\\boxed{x=0}[/tex]

The solution to the equation x = 4 + (x + 4) is 0.

The correct option is "one real solution".

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Expanding the expression on the right-hand side, we have:

x = 4 + (4x - 4)

x = 4x

Subtracting 4x from both sides, we get:

x - 4x = 0

-3x = 0

Dividing both sides by -3, we get:

x = 0

Therefore, there is one solution to the equation x = 4 + (4x - 4) as the equation simplifies to 0.

So the correct answer is 0, "one real solution".

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The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

Length of the arc of a circle:

s = 7.34 units

The measure of central angle:

θ = 81 degrees =  1.413 radians

s = rθ

r is the radius of the circle

7.34 = r(1.413)

r = 5.19 ≈ 5.2 units

Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

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Answer:

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

Step-by-step explanation:

The dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

We can think of this as a right triangle, where the hypotenuse measures 30 inches, and the angles of the triangle are 30°, 60° and 90°.

If we step on the 30° angle, the length will be the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opposite cathetus)/(hypotenuse).

Replacing what we know:

sin(30°) = length/30 in

length = sin(30°)*30in = (1/2)*30 in = 15in

And the adjacent cathetus will be the width, then we can use:

cos(θ) = (adjacent cathetus)/(hypotenuse).

Replacing what we know:

cos(30°) = width/(30 in)

width = cos(30°)*30in = (√3/2)*30in = (√3)*15in

Then the dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

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The correct answer is the fourth option.

Answer:

Answer:

A,B,D

Step-by-step explanation:

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

the slope is always the ratio of

y coordinate change / x coordinate change

in our case, x is the time (minutes), and y is the water height (inches).

we see, the longer the pool get filled, the higher the water gets. logical, right ?

by checking the data points we see :

with every 2 minutes passing the water height increases by 4 inches.

so, the slope is +4/+2 = 2/1 = 2

and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.

every 2 minutes 4 inches more.

so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.

and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.

The sign of the leading coefficient can be found using the graph of a polynomial function.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given the graph of polynomial functions:

In the first graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → -∞

Degree of a function = 3

In the second graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → -∞

Degree of a function = 4

In the third graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → ∞

Degree of a function = 4

In the fourth graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → ∞

Degree of a function = 3

Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.

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The value of cos(A+B) is 36/325.

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

cos(A)=−5/13

sin(B)=7/25

Now Using identity,

sin²A + cos² A= 1

sin A= √1 - cos² A

sin A = √1- 25/169

sin A= √144/169

sin A= 12/13

Again,

sin²B + cos² B= 1

cos B= √1 - sin² B

cos B = √1- 49/625

cos B= √576/625

cos B= -24/25

Now,

cos (A +B) = cos A cos B - sin A sin B.

= -5/13* (-24/25) - 12/13* 7/25

=  120/325 - 84/325

= 36/325

Hence, the value of cos (A + B) is 36/325.

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0.21094 is the probability that the surgery is successful on exactly 3 patients.

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

According to the given question,

Let Y = The number of patients who respond yes: [tex]Y - Bin (n,p)[/tex]

Given , [tex]n = 4 , p = 0.75 , q = 1 - p = 0.25[/tex]

[tex]P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094\\\\[/tex]

The probability that the surgery is successful on exactly 3 patients is 0.21094

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Answer:

4

Step-by-step explanation:

We know that [tex]a = 4[/tex] and [tex]b = -1[/tex], as they are given in the problem. All we have to do is plug them into the equation and solve it.

[tex]5 - 2(a + 3b)/2\\ = 5 - 2(4 -3)/2\\= 5 - 1\\= 4[/tex]

Answer:

Morgan

Step-by-step explanation:

because the pythagoras theorem is

H

[tex] {h1}^{2} = {b}^{2} + {h2}^{2} [/tex]

where h1=hypotenuse

h2=height

b=base

The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.

The quadratic function is given as ax² + bx + c = f(x).

For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0

The given function is f(x) = 6x² + 12x – 7

Then the zeroes of the quadratic function will be

[tex]roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\[/tex]

Here a =6 , b = 12 ,c = -7

Therefore the zeroes are

[tex]\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\[/tex]

[tex]\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}[/tex]

Therefore the correct option is A.

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Answer:

22-3d=x

Step-by-step explanation:

where d is the days that it melts and the amount of snow x is the snow that is left.

Answer:

21 girls.

Step-by-step explanation:

50% of 42 students are girls.

So 42/2 = 21.

Therefore 21 of the students are girls.

Hope I helped

Answer:

X = ABC+ AB+ ABC

X = AB(C+1+C)

X = AB(2C+1)