14a) Kevin asked a random group of students what theirfavorite class was, and the results are below.If Kevin were to randomly select a boy to explain whichclass was his favorite, what is the probability that he willpick a boy who likes History?A. 19.6%BoysGirlsMath810B. 29.3%English1517C. 35.3%Science105History 189D. 52.9%

We have the following inequality:

x > - 0.75

This is the same as state "x is greater than -0.75". Therefore, any value greater than -0.75 is a solution to this inequality

Considering this rule, we can answer each item:

a) The statement "-0.75 is a solution to the inequality" is FALSE, because, or rule states that x must be greater than -0.75.

b) The statement "There are many solutions to this inequality" is TRUE. Actually, there is an infinite number of solutions to this inequality (some of them can be expressed by -0.74, -0.73, -0.72...)

c) The statement "All the solutions to the inequality are negative" is FALSE, since any positive (or null) number is also greater than -0.75.

d) The statement "The inequality -0.75 < x is equivalent to the given inequality" is TRUE, since this inequality is tha same as the statement "-0.75 is less than x", which is a different form of express the original statement "x is greater than -0.75".

e) The statement "-4.5 is a solution to the inequality" is FALSE, because -4.5 is less than -0.75, which contradicts or rule.

The required three options accurately represent the statement are options b, c, and e.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
According to the question,
A negative 3 less than 4.9 times a number, x, is the same as 12.8.
12.8 = 4.9x -(-3)
which matched with options b, c, and e.

Thus, the required three options that accurately represent the statement are options b, c, and e.

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The initial equation is:

so we can move all term with x to the left and the constants to the right so:

Now we divide by 8 bout side of the equation so:

Answer: y=3x+5

Step-by-step explanation:

Answer:

Explanation:

Using the graph of both equations, we want to get the correct option

We start by making a plot of the two on same axes

We have the plot of the functions as follows:

Now, let us take a look at the options:

a) This is wrong. The functions have two intersection points

b) This is incorrect. They have equal y-intercepts at y = 2

c) This is correct. The quadratic function have a greater maximum

Standard form by definition of standard form of polynomials

The slope is define as the rate of y coordinate with respect to the x coordinate.

In the line D which is parallel to x axis has the constant y coordinate i.e

y = -3

So, for the numerator of the slop for line D is ( -3) - ( -3) = 0

Thus the slope will be express as :

Thus the slope of line is 0

Now, for the line A :

The line A is parallel to y axis, that is only y coorsinates are changes x is at contant position.

i.e. x = -5

So, substitute the value in the expression for the slope :

Slope of line A is not define

In the line B and C, the coordinates of x and y aixs are changes countinously

thus thier slopes will be well define.

Answer : Slope of line A is not define.

Answer: n = 42

Step-by-step explanation:

3 (42 - 6)= 126 - 18

= 108

2(42+12) = 84+24

= 108

In overall, the second equation is not greater than the first equation

The first thing we have to know is that pi= 180º

From this value of 1035 we must subtract 360 for each turn of the circumference until it gives us a value less than 360

So the first answer would be

Using the same methodology the following angles would give

Using midpoint of a line, the point at which E is located on the coordinates is (-4, -10)

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

The formula of midpoint is given as

(x, y) = (x₂ + x₁) / 2 , (y₂ + y₁) / 2

Taking x-coordinate

x = (x₂ + x₁) / 2

2 = (8 + x₁) / 2

x₁ = -4

Taking the y - coordinate

y =  (y₂ + y₁) / 2

-4 = (2 + y₁) /2

y₁ = -10

The coordinate of E is (-4, -10)

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EXPLANATION

Given the system of equations:

(1) 60x + 110y = 265

(2) 120x + 90y = 270

We can apply the substraction method as shown as follows:

Multiply 60x + 110y = 265 by 2:

----> (60x + 110y = 265)*2 -------> 120x + 220y = 530

Subtract the equations:

120x + 220y = 530

- (120x + 90y = 270)

--------------------------------

130y = 260

Divide both sides by 130:

y= 260/130

Simplifying:

y= 2

Replacing on the first equation:

60x + 110(2) = 265

Applying the distributive property:

60x + 220 = 265

Subtracting 220 to both sides:

60x = 265 - 220

Subtracting like terms:

60x = 45

Dividing both sides by 60:

x = 45/60

Simplifying:

x= 3/4

The solutions to the system of equations are:

x=3/4 y=2

1. replace f(x) with y:

2. Replace every x with a y and replace every y with an x:

3. Solve for y:

4. replace y with f-1(x):

In order to determine the amount of money Rain, Kevin and Eric have, write the given situation as an algebraic equation.

If x is the money of Raina, y the money of Kevin and z the money of Eric, you have, based on the given problem, the following equations:

x + y + z = 66 All of them have a total of $66

y = 3z Kevin has 3 times what Eric has

x = z - 9 Raina has $9 less than Eric

Replace the expressions for x and y into the first equation and solve for z, as follow:

(z - 9) + (3z) + z = 66

z - 9 + 3z + z = 66

3z = 66 + 9

3z = 75

z = 75/3

z = 25

Next, replace the previous value of z into the expressions for x and y:

y = 3(25)

y = 75

x = 25 - 9

x = 16

Hence, the amount of money each of them has is:

Raina: $16

Kevin: $75

Eric: $75

The area of a parallelogram is given by the equation:

Where b is the base of the parallelogram and h is the height.

In this case, b=1/2 in and h=8in, then:

Therefore, the area of the described parallelogram, is:

Given: 0.6 divided by 30

We will find the result as follows:

So, the answer will be 0.02

6The mean number of children each team member will bring

Here, we want to get the mean number of students that each team member willl bring

From the histogram, we can deduce the following;

a) 4 team members will bring no (0) children

b) 3 team members will bring 1 children each

c) 5 team members will bring 2 children each

d) 2 team members will bring 3 children each

e) 1 team member will bring 5 children

So the totla number of children at the party will be;

4(0) + 3(1) + 5(2) + 2(3) + 1(5)

= 0 + 3 + 10 + 6 + 5 = 24 children

The number of team members is 4 + 3 + 5+2 + 1 = 15

So, the mean number each will bring is; the number of children attending the party divided by the number of team members

The recipe yields:

8400 calories in total.

Those 8400 calories are equally divided into 40 mini-cupcakes. Then, each mini-cupcake has

210 calories for each mini-cupcake.

Therefore, 4 mini-cupcakes contain:

The answer is 840 calories

Solution:

Given:

From the table, the probability that Michiko will hava a quiz on Wednesday is 0.070.

This is the probability of success.

Hence, the probability that Michiko will not have a quiz on Wednesday is the probability of failure.

Thus,

Hence, the probability of failure (the probability that Michiko will not have a quiz on Wednesday is 0.93.

As a percent,

Therefore, the probability that Michiko will not have a quiz on Wednesday is 93%

Given:

f(x) = x^2 + 4x + 4 and g(x) = x^2 - 2x - 8.

we are to find the domain of (f/g) (x)

before we find the domain of the function, its best we know what a domain is.

The Domain of a function is the set of all possible inputs for the function. it can also be seen as the set of input or arguement values for which the function is real and defined.

recall that we have x + 2 as our the simplest form

x - 4

so the domain we wil be looking for is x + 2

x - 4

so we have to take t denominator of the above and compare to zero

x - 4 = 0

x = 4

so this is undefined

the function domain

x < 4 or x > 4

so the domain is:

(- infinity, 4) U (4, infinity)

The correct option is A.

the initial function is:

now we replace the values in x that gives the table so:

for -2:

for 0:

for 2:

for 4:

Answer:

Subtract 4

Explanation:

In the number pattern:

We subtract the next term from the previous term below:

We see that each one gives a subtraction of 4.

Therefore, the rule of the pattern is 'Subtract 4'.

Explanation:

Question:

What statements are true regarding undefine terms in geometry

A point has no length or width.

This is true because a point cannot have a dimension

A plane consists of an infinite set of lines.

This is not true because from the definition of a plane, it must have an infinite set of lines or points.

A plane has one dimension, length

This statement is not true because a line is a one dimensional object and as such can only have one dimension which is its' length.

A point indicates a location in a coordinate plane.

This statement is true because any point located on a plane must have an ordered pair of an x and y coordinate

A line has a define begging and end

This is not true because A distance along a line must have no beginning or end.

A line consists of an infinite set of points

This is not true becaue a plane consists of an infinite set of points

Hence,

The final answers are

A point indicates a location in a coordinate plane.

A point has no length or width.

Given function:

The minimum value of the function can be found by setting the first derivative of the function to zero.

Solving for x:

Substituting the value of x into the original function:

Hence, the minimum value in the given range is (-1, -0.368)

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.

In radians this are

To find the complement of 3π/4, subtract it by π/2

To find the supplement of 3π/4, subtract it by π.

Let 'x' be the amount of nickels Anna has, and 'y' the amount of dimes.

If she has '4 more nickels than dimes' this is:

And the total amount is $1.25, that can be written as:

If we replace the equivalence between y and x here we get:

The correct answer is option C

The required value of the x is given as 8.66 for the given triangle.

Given that,
A figure of the triangle is shown, with the help of trigonometric operators we have to determine x.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
Tan60 = x/ 5
x = tan60 × 5
x = 1.732 × 5
x = 8.66

Thus, the required value of the x is given as 8.66 for the given triangle.

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Using the function  f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg

The salinity s calculated using the logarithmic function model

f(x) = 28.7 + 1.2log (x + 1)

given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters

for x = 797 meters

f(x) = 28.7 + 1.2log (x + 1)

f(x) = 28.7 + 1.2log (797 + 1)

f(x) = 28.7 + 1.2log (798)

f(x) = 28.7 + 1.2 * 2.902

f(x) = 28.7 + 3.4824

f(x) = 32.1824

f(x) = 32.18  (to the nearest hundredth)

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Solution

The function is written in factored form

Using vertical asymptote at x = 3 opposite end behaviour

vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2

Therefore the numerator is : -6(x-1)²

The denominator is : (x+3)(x-2)²