A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 500 contains 100 green, one-headed Jolos; 125 purple, two-headed Jolos; and 270 one headed-jolos.How many green Jolos are there in Balan's colony?A. 105B. 170C. 205D. 230

The given polynomial is:

Using the long division method:

The equattion can be written in the form:

Quotient + Remainder / Divisor

1) To add or subtract fractions, let's firstly check the denominators

In this case, the denominator is the same.

The plus before the bracket does not change the sign.

That is why we get to -3/13 as a result.

The price of one adult ticket is $9 and the price of child ticket is $8

First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108

Consider the price of adult ticket as x and child ticket as y

Then the equation will be

4x+9y = 108

Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets

10x+3y = 114

Here we have to use the elimination method

Multiply the first equation by 10 and second equation by 4

40x+90y = 1080

40x+12y = 456

Subtract the equation 2 from equation 1

90y-12y = 1080-456

78y = 624

y = 624/78

y = $8

Substitute the value of y in any equation

10x+3y =114

10x+3×8 =114

10x +24 =114

10x = 90

x = 90/10

x = $9

Hence, the price of one adult ticket is $9 and the price of child ticket is $8

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Solution:

Using the formula;

Thus;

ANSWER: $33

the triangle is ACD is equal to the triangle CBE so let write all the information we have in the figure so:

And for oposit angles we know that then angle BCE = to the angle ACD, so we have two angles and ine side equal so the triangles are similar

by: ASA

Given a quadrilateral ABCD

A cyclic quadrilateral has all its vertices on the circumference of the circle

Also cyclic quadrilateral

has the opposites angles add up to 180°

then

then

Option A

A=90

B=90

C=90

D=90

since A+C= 180

and B+D = 180

measures from Option A could come from a cyclic quadrilateral

Option B

A=80

B=80

C=100

D=100

Since A+C = 80+100 = 180

and B+D = 80 + 100 = 180

measures from Option B could come from a cyclic quadrilateral

Option C

A=70

B=110

C=70

D=110

Since A+C=70+70 = 140

And B+D =110+110=220

measures from Option C could NOT come from a cyclic quadrilateral

Option D

A=60

B=50

C=120

D=130

A+C= 60+120 = 180

B+D= 50+130 = 180

measures from Option D could come from a cyclic quadrilateral

Option E

A=50

B=40

C=120

D=150

A+C=50+120= 170

B+D=40+150 = 190

measures from Option E could NOT come from a cyclic quadrilateral

Then correct options are

Options

A,B and D

Allison must score 280 on Exam B to do equivalently well as she did on Exam A

Note that:

Since we want Allison to perform similarly in Exam A and Exam B, their z-scores will be the same

Therefore for exam B:

Allison must score 280 on Exam B to do equivalently well as she did on Exam A

Solution:

Given the graph;

The axis of symmetry and vertex of the graph are;

Also, the x-intercepts are;

And the y-intercep is;

Thus, the function that best represents the graph is;

CORRECT OPTION: C

Given the function

The graph of the function is as shown below:

Answer:

The correct statements are:

C. If Joan uses no electricity, her total cost for the month is $12.

F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.

G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.

Step-by-step explanation:

Notice that the given function is the equation of a line in the slope-intercept form:

From this interpretation, we'll have that the correct statements are:

C. If Joan uses no electricity, her total cost for the month is $12.

F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.

G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.

The inequality is:

now we solve the inequality for x

This means that all the number, from -1 to infinit are solution of the inequality, and the only option that is not a solution is a) -2

The smallest degree of rotation is achieved through the division of the full circumference over the total number of sides

The answer would be 3.75°

Answer:

Step-by-step explanation:

At the beginning of the day, the temperature was of x.

It dropped 21 degrees to -9C. So

x - 21 = -9

x =

The vertex-form equation of the parabola is given as follows:

y = 1/10(y - 3)² - 3/2.

An horizontal parabola of vertex (h,k) is modeled as follows:

x = (1/4p)(y - k)² + h.

In which:

In the context of this problem, we have that:

A system of equations is built for h and p as follows:

Hence:

2h = -3

h = -3/2.

p = 1 + 3/2 = 2.5.

Then the equation is:

y = 1/10(y - 3)² - 3/2. (first option).

The graph is given by the image at the end of the answer.

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ANSWER:

0.475

STEP-BY-STEP EXPLANATION:

The probability of a person has disease given the test is positive:

P (disease) = 3.8% = 0.038

P (positive | disease) = 93.9% = 0.939

P (positive | no disease) = 4.1% = 0.041

P (no disease) = 100% - 3.8% = 96.2% = 0.962

The probability that the person has the disease given that the test result is positive is calculated as follows:

The correct answer is the first option: 0.475

Answer: I = $ 1,102.50

Step-by-step explanation: First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year,

then, solving our equation

I = 4500 × 0.07 × 3.5 = 1102.5

I = $ 1,102.50

The simple interest accumulated

on a principal of $ 4,500.00

at a rate of 7% per year

for 3.5 years is $ 1,102.50.

We have to calculate the perimeter of a triangle of which we know the vertices.

The perimeter is the sum of the length of the three sides, which can be calculated as the distance between the vertices.

The vertices are V1=(-10,-3), V2=(2,-3), and V3=(2,2).

We then calculate the distance between each of the vertices.

We start with V1 and V2:

We know calculate the distance between V1 and V3:

Finally, we calculate the distance between V1 and V3:

Then, the perimeter can be calcualted as:

Answer: the perimeter is 30 units.

The system of equation are:

to solve this problem we can solve the second equation for x so:

Now we can replace x in the firt equation so:

and we can solve for y so:

Now we replace the value of y in the secon equation so:

So the solution as a ordered pair is:

The correlation could be positive, meaning both variables move in the same direction,

If it is negative, meaning that when one variable's value increases, the other variables' values decrease.

Since the correlation between the 2 variables is -16

Since -16 is a negative value

Then The answer should be

There is a weak negative association between variables

The strong negative correlation should be between 0 and -1

Let be "n" Irene's height (in inches), "t" Theresa's height (in inches) and "j" Jane's height (in inches).

You know Irene's height:

You can write the Mixed number as an Improper fraction as following:

- Multiply the Whole number by the denominator.

- Add the product to the numerator.

- Use the same denominator.

Then:

Now convert the other Mixed numbers to Improper fractions:

Based on the information given in the exercise, you can set up the following equation that represents Theresa's height:

Adding the fractions, you get:

Now you can set up this equation for Jane's height:

Answer: 3/8

Step-by-step explanation:

Given:

[tex]B-(-\frac{1}{8} )+c[/tex]

replace variables with their given values: b = 2 and C = 7/4

[tex]2-(-\frac{1}{8})+\frac{-7}{4}[/tex]

to make subtracting and addition easier, make each number has the same common denominator.

[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})[/tex]

Finally, solve equation.

***remember that subtracting a negative is the same as just adding and adding by a negative is the same as simply subtracting.

[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})=\frac{16}{8} +\frac{1}{8}-\frac{14}{8}[/tex]

= 3/8

Answer:

3/8

Step-by-step explanation:

2 - (-1/8) + (-7/4)

= 17/8 - 7/4

= 17/8 + -7/4

= 3/8

Let's define:

x: pairs of shoes of Shanice

y: pairs of shoes of Ron

Shanice has 4 times as much many pairs of shoes as does her brother Ron, means:

x = 4y (eq. 1)

If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does, means:

x - 12 = 2y (eq. 2)

Replacing equation 1 into equation 2:

4y - 12 = 2y

4y - 2y = 12

2y = 12

y = 12/2

y = 6

and

x = 4*6 = 24

After she gives Ron the shoes, she will have left 24-12 = 12 pairs of shoes

According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.

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Reflexive Property

In Math, especially in geometry, but also in other fiels.

What we have here is the Reflexive Property, that states that

If a= b+c then b+c=a

Multiplicative Identity

The multiplicative identity is the number 1, so every number times 1 is equal to itself and this property is called multiplicative identity.

It is to be noted that the slope of the line is 5/2. This means that 5 mm of rain falls every 2 hours. See the calculation below.

In general, the slope of a line indicates its gradient and direction. The slope of a straight line between two locations, say (x₁,y₁) and (x₂,y₂), may be simply calculated by subtracting the coordinates of the places. The slope is often denoted by the letter 'm.'

To find the slope of the line in the graph, we use the following equation:

m = [y₂ - y₁]/[x₂-x₁]

Where (x1,y1) = coordinates of the first point in the line; and

(x₂,y₂) = coordinates of the second point in the line

Given that the points (2, 5) from the graph is (x₁, y₁) and the point on graph (4, 10) are (x₂,y₂) Hence,

m = [10-5]/[4-2]

The slope (m) = 5/2

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Full Question:

This is the complete question and the described graph is attached

This graph shows the amount of rain that falls in a given amount of time.

What is the slope of the line and what does it mean in this situation?

Select from the drop-down menus to correctly complete each statement

The slope of the line is ___

This means that ___ mm of rain falls every ___

1) Given these line segments, let's find the slope of them. Let's begin with AB

2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:

Thus, x=-1

A.

This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.

Hence, the answer that better represent the resulting vector is answer A.

A.

This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.

Hence, the answer that better represent the resulting vector is answer A.

ThereforeGiven the image, we can find the missing angle using the sum of angles at a point rule.

The sum of angles at a point is known to be 360 degrees.

Therfore,

Therefore, the measure of "a" is

Answer:

The situation forms a right triangle:

Where x is the distance traveled.

We can apply the Pythagorean theorem:

c^2 =a^2 + b^2

Where:

c= hypotenuse = x

a & b= the other 2 sides = 5 ,12

Replacing:

x^2 = 5^2 + 12^2

x^2 = 25+144

x^2 = 169

x= √169

x= 13

Distance traveled = 13 miles

The Solution To Question Number 10:

The question says what operations would the set of quadratics be closed under.

Let the sets of quadratics be

The set of two quadratics (polynomials) is closed under Addition.

Explanation:

The set of two quadratics is closed under Subtraction.

The set of quadratics is not closed under Multiplication.

The set of quadratics is not closed under Division.