H(x)=(x+5)^9 can be be expressed into the form f(g(x)) where f(x)=x^9, and g(x) is defined below
G(x)=?

Answer:

m = -2 and n = -3

Explanation

Given the polynomial

x^2 - 5x + 6

Rewrite as x^2 +mx + nx + 6

x^2 - 2x - 3x + 6

Compare

mx = -2x

m = -2

Similarly;

nx = -3x

n = -3

Hence m = -2 and n = -3

Probability of red or green card = 3/5

Number of red cards = 3

Number of blue cards = 6

Number of green cards = 6

Total number of cards = 6 + 6 + 3 = 15

Probability of red or green card = Probability of red card + Probability of green card

Probability of red card = number of red cards/total number of cards

Probability of red card = 3/15

Probability of green card = number of green cards/total number of cards

Probability of green card = 6/15

Probability of red or green card = 3/15 + 6/15

Probability of red or green card = 9/15

In simplest term:

Probability of red or green card = 3/5

Answer:

85% but in a fraction 17/20

Step-by-step explanation:

a)Total different number plates will be 45697600

b) Total different number plates will be 32292000

What is permutation and combination?

In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order.

Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations

We are given that license plate allows 2 digits and 4 upper case letters

a) repetition is allowed

hence for 2 numbers we have 10*10=100 choices

Also letter are allowed 26*26*26*26=456976 choices

And Hence total choices are 456976*100=45697600 ways

b) Repetition is not allowed

hence for 2 numbers we have 10*9=90 choices

Also letter are not allowed 26*25*24*23= 358800 choices

And Hence total choices are 456976*100=32292000 ways

Hence

a)Total different number plates will be 45697600

b) Total different number plates will be 32292000

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We are given the following two vectors

We are asked to find the following

First, multiply the vector a with the scaler -2 to get -2a

Now, multiply the vector b with the scaler 5 to get 5b

Finally, add -2a and 5b to get -2a+5b

Therefore, the resultant vector in component form is

A) Simplification of the given Algebraic Expression is; [-⁴³/₂₄j + (-1)]/12

B) The equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9

A) We want to simplify negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths. This would be expressed as;

-1/8j + 2/3 - (5/3j + 9/12)

= -1/8j + 2/3 - 5/3j - 9/12

= -1/8j - 5/3j + (2/3 - 9/12)

= (-3j-40j / 24 + (8-9) / 12

= [-⁴³/₂₄j + (-1)]/12

B) The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)

Expand the brackets to get;

-13.5b - 6.3 - 6b - 0.6

= -13.5b - 6b - 6.3 - 0.6

= - 19.5b - 6.9

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To simplify the expression (x-2) +(x+6), you have to follow these steps:

1.Get rid of the parentheses:

(x-2) +(x+6)

x -2 + x + 6

2. Combine like terms:

x + x - 2 + 6

2x + 4

So the answer is 2x + 4

SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?​

we know that

The total numbers in the spinner are 10

The numbers that are greater than 6 are (7,8,9 and 10)------> 4 numbers

so

To find out the probability, divide the total numbers that are greater than 6 by the total number

therefore

P=4/10

Percent

P=4/10(100)

the answer is

The given expression is

Solving for a means that we need to isolate that variable.

First, we need to multiply the equation by 4

Second, we divide the equation by x

Therefore, the answer is

The y-intercept of the line graphed by the equation [tex]\frac{1}{2} x+y=7[/tex] is (0,7)

Option (D) is correct.

The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

The given equation is [tex]\frac{1}{2} x+y=7[/tex]

Converting the equation in Slope-intercept form, we get

[tex]y=-\frac{1}{2} x+7[/tex]                   ...(1)

Now, to find the y-intercept, substitute x = 0 in the equation and solve for the value of y

Putting x = 0 in equation (1), we get

[tex]y=-\frac{1}{2} (0)+7[/tex]

[tex]y=7[/tex]

Therefore, the y-intercept of the line will be (0,y) i.e., (0,7)

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There are various types of equation systems, including linear, non-linear, and multiple or single-variable systems.

A set of two linear equations with two variables is a system of linear equations.

ax + by = C

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. A nonlinear equation can be written as ax+by+C≠0 or ax + b y + C ≠0.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.

Ex: ax+b = 0

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Given a quadratic equation in vertex form

In our case,

h = -10, and k= 2

Therefore the vertex is (-10, 2)

Answer:

Explanation:

From the information given,

mean = 101

standard deviations = 14

We need to find the number of standard deviations between 73 and the mean.

Number of standard deviations = (73 - 101)/14 = - 28/14 = - 2

It is 2 standard deviations from the mean. According to the empirical rule, 95% of the population lies between 2 standard deviations of the mean. The required area is to the right of 2 standard deviations since we want to find the least score. Thus, the probability of having IQ scores are at least 73 is

We would convert to percentage by multiplying by 100

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]

Add 3/4 to both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]

Convert 4 to the fraction 16/4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]

Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]

Multiply both sides by 8/5, the reciprocal of 5/8.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]

Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]

We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]

The ratio of the new scale that we are to be having is going to be 1/2

we have the ratio to be 1 grid unit / 2 ft

the new scale ratio is given as 1 grid unit / 4 ft

We have to divide the ratio of the original scale to the new scale that we have here

This would be ( 1 grid unit / 4 ft ) / ( 1 grid unit / 2 ft)

This can be written as

1/4 * 2/1

when we rewrite it we would have 2/4

= 1/2

This is 1 unit 2 feet

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Answer:

f(1)= -3

Step-by-step explanation:

what f(1) means is when x is 1 what is y. I dont see the graph labeled so im just assuming that the graph is going by ones. So what i did was i found where x is one and then i checked at what point did the line match with the y axis which was 3 points below 0 on y axis ( disclaimer if the graph isnt going by ones then its going to be a different answer, but you can use the same process to find it.

The cost of the the 17 feet by 23 feet Turkish cloth given the constant of variation is  TL14,467.

A variable varies jointly if the value of one variable depends on the value of two or more variables. In this question, if the length and width of the cloth increases, the cost of the cloth increases. Also,  if the length and width of the cloth decreases, the cost of the cloth decreases.

The equation that represents joint variation is:

y = kab

Where:

TL3848 = k(13 x 8)

k = TL3848 / (13 x 8)

k = $37

The cost of 17 feet by 23 feet cloth :

37 x 17 x 23 = TL14,467

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Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph

both the parent graph and the transformed graph on the grid provided. Plot at least

three distinct points for each.

we have that

the parent function is

y=x^2

Is a vertical parabola open upward with the vertex at (0,0)

the transformed function

is

y-4=-2(x-3)^2

y=-2(x-3)^2+4

Is a vertical parabola open downward with vertex at (3,4)

so

The transformations are

1) Reflection over x-axis

Rule is

(x,y) ------> (x,-y)

y=x^2 ------------------> y=-x^2

2) Vertical Dilation with a scale factor of 2

Rule

(x,y) --------> (x,2y)

y=-x^2 ----------> y=-2x^2

3) Translation 3 units at right and 4 units up

Rule is

(x,y) --------> (x+3,y+4)

y=-2x^2 --------> y=-2(x-3)^2+4

see the graph to better understand the problem

Answer:

14.7

Step-by-step explanation:

Let's say the width is x

So volume would be 24 × 2x × x = 10368

24 × 2x² = 10368

2x² = 10368 / 24 = 432

x² = 216 , width can't be negative so

x = 14.6969... ~~ 14.7

Robert will paint 310.5 square ft

The side of Robert's barn contains a triangle and a rectangle of which the dimensions are given in the diagram.

If Robert paint one side of the barn, then he needs to paint the triangle as well as the rectangle. So we need to find the area of the triangle and rectangle first.

For the triangle, base = 23 ft

height = 7 ft

Area of the triangle = 1/2 bh

                                 = 1/2 x 7 x 23

                                 = 80.5 square ft.

For the rectangle, length = 23 ft

width = 10 ft

Area of the rectangle = length x width

                                    = 23 x 10

                                    = 230 square ft.

Area Robert needs to paint = Area of the triangle + Area of the rectangel

                                              = 80.5 + 230

                                              = 310.5 square ft.

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A relationship is a function if and only if for each input, there exists only one output i.e an input cannot have two or more outputs.

We can determine which of the relationship is a function by plotting a graph of the relationship.

The only correct option is the relationship:

The graph of the function is shown below:

Answer:

98 small drinks and 57 large drinks.

Explanation:

Let's call x the number of small drinks and y the number of large drinks.

If they sold 155 drinks, we can write the following equation:

x + y = 155

In the same way, they made $265, so

1.25x + 2.50y = 265

Because each small drink cost $1.25 and each large drink cost $2.50.

Now, we can have the following system of equations

x + y = 155

1.25x + 2.50y = 265

Solving the firs equation for y, we get:

x + y - x = 155 - x

y = 155 - x

Replacing this on the second equation:

1.25x + 2.50y = 265

1.25x + 2.50(155 - x) = 265

Then, solving for x, we ge:

1.25x + 2.50(155) - 2.50(x) = 265

1.25x + 387.5 - 2.50x = 265

-1.25x + 387.5 = 265

-1.25x + 387.5 - 387.5 = 265 - 387.5

-1.25x = -122.5

-1.25x/(-1.25) = -122.5/(-1.25)

x = 98

Finally, we can find the value of y replacing x = 98

y = 155 - x

y = 155 - 98

y = 57

Therefore, they sell 98 small drinks and 57 large drinks.

|u|=c is equivalent to u = c or u = -c.

Given that c > 0.

i.e., c is a positive number.

Then |u| = c. That is, absolute value of u = c, a positive number.

An absolute value function is defined by,

 |u| = { u   ; if u ≥ 0

        { -u   ; if u < 0

The absolute value of any number, Positive or negative, is always a positive number.

So here |u| = c, with c > 0.

Comparing with the definition of absolute value function, c is either u or -u.

More clearly, c = u, when u ≥ 0 or c = -u , when u < 0.

Hence the value of c depends on u.

Thus,  |u|=c is equivalent to u = c or u = -c.

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Given data:

The expression for the age of the girl after two year is,

x+2

The age of girl 5 year ago is,

x-5

According to the given statement of the question.

x+2=2(x-5)

x+2=2x-10

x=12

Thus, the present age of the girls is 12 years old.

Using the binomial distribution, the probability of no one having done a one time fling is of 0.735 = 73.5%.

The mass density formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

The parameters of the formula are given as follows:

In the context of this problem, the values of the parameters are as follows:

The probability that no one has done a one time fling is P(X = 0), hence the probability is calculated as follows:

P(X = 0) = (0.95)^6 = 0.735 = 73.5%.

The problem asks for the probability that no one has done a one time fling.

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Answer:

5

Step-by-step explanation:

negetive two minus negative seven equal to five

Step-by-step explanation:

Chance to roll even number on one dice is 1/2 so

[tex] \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} [/tex]

Answer:

Explanation:

• Car 1 leaves point A at 5:30 p.m., driving due south at an average speed of 35 mph.

• Car 2 leaves point A at 6:30 p.m., driving due north at an average speed of 45 mph.

At 9:30 pm, the time taken by the cars is:

The distance covered by each car is:

Since car 1 drives due South and Car 2 due North of point A:

Therefore, the distance between the drivers at 9:30 p.m. will be:

The two drivers are 275 miles apart at 9:30 pm.

The given system of equations is

We will substitute y in equation (2) by equation (1)

Now, add 4x to both sides

Subtract 9 from both sides

Divide both sides by 5

Substitute x by -3 in equation (1) to find y

The solution of the system is (-3, 6)