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

Given that the triangles are similar, then their corresponding sides are in proportion, that is,

Substituting with data and solving for BX:

According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.

Explanation

The question wants us to obtain the margin of error

A margin of error tells you how many percentages points your results will differ from the real population value.

The formula to be used is

To do so, we will have to list out the parameters to be used

The next step will be to find the z-score value for a confidence level of 80%.

From the statistical table, we have

So, we can input the given data obtained into the formula

So we will have

So the margin of error (M.E.) = 4.163 (To 3 decimal places)

Answer:

125 teachers

Explanation:

We were given that:

20% of teachers teach advanced writing skills = 20/100 = 0.2

Number of writing teachers = 25

The total number of teachers = x

We will obtain the number of teachers in the school as shown below:

Hence, the total number of teachers in the school is 125

we have the system of equations

-4x + 5y =8

6x - y = 11

Using a graphing tool

Remember that

the solution is the intersection point of both lines

We have the next points (1,2) and (3,-6)

The given equation is

The first step is to add 4x to both sides of the equation. We have

3 - 2x = 16x^2

Adding 2x to both sides of the equation, we have

3 - 2x + 2x = 16x^2 + 2x

3 = 16x^2 + 2x

Subtracting 3 from both sides of the equation, we have

3 - 3 = 16x^2 + 2x - 3

0 = 16x^2 + 2x - 3

16x^2 + 2x - 3 = 0

This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have

16x^2 + 8x - 6x - 3 = 0

By factorising, we have

8x(2x + 1) - 3(2x + 1) = 0

Since 2x + 1 is common, we have

(2x + 1)(8x - 3) = 0

2x + 1 = 0 or 8x - 3 = 0

2x = - 1 or 8x = 3

x = - 1/2 or x = 3/8

We would substitute these values in the original equation to check. We have

The solution is x = 3/8

Answer:

-3

Step-by-step explanation:

The slope of a line is the steepness of the line and is given by the formula below:

[tex]\boxed{\text{Slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex], where [tex](x_1,y_1)[/tex] is the 1st coordinate while [tex](x_2,y_2)[/tex] is the 2nd coordinate

The two coordinates given are: (3, 5) and (4, 2)

Slope of line

[tex] = \frac{5 - 2}{3 - 4} [/tex]

[tex] = \frac{3}{ - 1} [/tex]

= -3

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We know that the equation of a line is given by

y = mx + b,

where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.

In order to find the equation we must find m and b.

In all cases, m is given, so we must find b.

We use the equation to find b:

y = mx + b,

↓ taking mx to the left side

y - mx = b

We use this equation to find b.

We have that the line passes through

(x, y) = (-10, 8)

and m = -1/2

Using this information we replace in the equation we found:

y - mx = b

↓ replacing x = -10, y = 8 and m = -1/2

Then, the equation of this line is:

y = mx + b,

↓

y = -1/2x + 3

Equation 1: y = -1/2x + 3

Similarly as before, we have that the line passes through

(x, y) = (-1, -10)

and m = 0

we replace in the equation for b,

y - mx = b

↓ replacing x = -1, y = -10 and m = 0

-10 - 0 · (-1) = b

↓ 0 · (-1) = 0

-10 - 0 = b

-10 = b

Then, the equation of this line is:

y = mx + b,

↓

y = 0x - 10

y = -10

Equation 2: y = -10

Similarly as before, we have that the line passes through

(x, y) = (-6, -9)

and m = 7/6

we replace in the equation for b,

y - mx = b

↓ replacing x = -6, y = -9 and m = 7/6

Then, the equation of this line is:

y = mx + b,

↓

y = 7/6x - 2

Equation 3: y = 7/6x - 2

The line passes through

(x, y) = (6, -4)

and m = does not exist

When m does not exist it means that the line is vertical, and the equation looks like:

x = c

In this case

(x, y) = (6, -4)

then x = 6

Then

Equation 4: x = 6

The line passes through

(x, y) = (6, -6)

and m = 1/6

we replace in the equation for b,

y - mx = b

↓ replacing x = 6, y = -6 and m = 1/6

Then, the equation of this line is:

y = mx + b,

↓

y = 1/6x - 7

Equation 5: y = 1/6x - 7

There is 15% in the premium.

From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

First six-month auto insurance = $658

Renewal premium = $756

Change in the insurance = $98

percentage of $98 from $658

= 15%

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Given data:

The given point is (a,b)=(-5,1).

The given line is 2y=2x-4.

The given line can be written as,

2y=2(x-2)

y=x-2

The standard equation of the line is,

y=mx+c

comapre the given line with the standard form.

m=1

The slope of two parallel lines are always equal.

m'=m

=1

The expression of the line which is parallel to the given line is,

y-b=m'(x-a)

Substitue the given values in the expression.

y-1=1(x-(-5))

y-1=x+5

y=x+6.

Thus, the equation of the line parallel to the given line is y=x+6.

Given:

The dimension of square shape floor is 200 feet by 200 feet.

The area of the square is calculated as,

Now, given that the 1/2 bottle will cover approximately 2000 quare feet.

It gives,

So, the number of bottles required are,

Answer: option B)

Therefore, the solution is t > -7.

Answer:

Part A:

The volume of a cylinder is given below as

By substituting the values , we will have

Hence,

The volume = 628.3in³

Part B:

To determine the weight of the flour in ounces, we will use the relation below

Hence,

The weight = 81.7 ounces

Answer

a) V (3) = 7.2 thousand dollars.

In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.

b) t = 4years.

The resale value will be 6.1 thousand dollars in the year 2015.

c) t = 9.545 - 0.909V

d) t = 7 years.

7 years after the start of 2011 = 2018.

Explanation

We are given that the resale value (V), in thousands of dollar, of a boat is given as

V = 10.5 - 1.1t

where t = number of years since the start of 2011.

a) We are told to calculate V(3).

V = 10.5 - 1.1t

t = 3

V = 10.5 - 1.1 (3)

V = 10.5 - 3.3

V = 7.2 thousand dollars.

In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.

b) In what year will the resale value be 6.1 thousand dollars.

V = 10.5 - 1.1t

what is t when V = 6.1

6.1 = 10.5 - 1.1t

1.1t = 10.5 - 6.1

1.1t = 4.4

Divide both sides by 1.1

(1.1t/1.1) = (4.4/1.1)

t = 4 years.

4 years afther the start of 2011 = 2015.

c) We are asked to solve for t and obtain a formula expressing t as a function of V.

V = 10.5 - 1.1t

1.1t = 10.5 - V

Divide through by 1.1

t, expressed in terms of V, is t = 9.545 - 0.909V

d) We are now asked to calculate in what year will the resale value be 2.8 thousand dollars.

t = 9.545 - 0.909V

t = 9.545 - 0.909 (2.8)

t = 9.545 - 2.545

t = 7 years.

7 years after the start of 2011 = 2018.

Hope this Helps!!!

Answer:

Step-by-step explanation

Correct option is A)

C.I. for the third year = Rs. 1,452.

C.I. for the second year = Rs. 1,320

∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.

Rate of interest =

1,320

132×100

​

=10%.

Let the original money be Rs. P.

Amount after 2 year − amount after one year =C.I. for second year.

P(1+

100

10

​

)

2

−P(1+

100

10

​

)=1,320

P[(

100

110

​

)

2

−

100

110

​

]=1,320

⇒P[(

10

11

​

)

2

−

10

11

​

]=1,320⇒P(

100

121

​

−

10

11

​

)= Rs. 1,320

⇒P×

100

11

​

=Rs.1,320⇒P=

11

1,320×100

​

= Rs. 12,000

∴ Rate of interest =10%

and Original sum of money = Rs. 12,000

Answer:

x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]

Step-by-step explanation:

y = a - bx² ( subtract a from both sides )

y - a = - bx² ( multiply through by - 1 )

bx² = a - y ( divide both sides by b )

x² = [tex]\frac{a-y}{b}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]

We know that Ava is paying $2 dollars per week so if L is the money that she owes and t is the number of weeks, and I is the initial debt so we can write an equation like:

Now we can replace the info we have to find the value of I so:

and we solve for I

So the final equation will be:

Answer:

Yes.  r = 3 + 3sin θ is symmetrical along the y axis

Step-by-step explanation:

Original polar equation is

r = 3 + 3sinθ

If this plot is to be symmetrical about the y axis then replacing Θ with (π-θ) in the original equation should not change the equation and thereby should not change the plot

r = 3 + 3sinθ

Replace θ with π-θ:

==>  3 + 3sin(π-θ)

But sin(π-θ) = sinθ

So the equation is unchanged at 3 + 3sin(π-θ) from the original equation r = 3 + 3sinθ

Hence the equation is symmetrical along the y-axis

This can be also be clearly seen if you plot both the equations, you will see the plot does not change

We will determine the height of the building as follows:

First, we determine the height above her window, that is:

Now, we calculate the height below her window:

Then, we will have that:

So, the height of the building is approximately 316.1 ft tall.

anywhere you see x, input the value in the brackets.

eg f(-2) = 2(-2)+8

= -4+8

=4

Answer:

if x= -2

then f(x) = 2×(-2)+8

= -4+8

= 4

if x=0

then f(x)=2×0+8

=0+8

=8

if x=5

then f(x)=2×5+8

=10+8

=18

First, remember that:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this problem, notice that:

2 + 3 is not greater than 5.

3 + 5 is not greater than 2.

2 + 5 is not greater than 3.

So, the statement is false. A triangle can't have sides 2

Given:

A bee produce 0.05 ml of honey per day

We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days

Let it produces x ml

So, using the ratio and proportions

Solve for x:

Convert ml to liters

1 liter = 1000 ml

So, 1.4 ml = 0.0014 liters

So, the answer will be

The bee can produce honey in its lifetime = 0.0014 liters

Answer:

The number that comes next is;

Explanation:

Given the series;

From the series, if we observe the series closely we can see a relationship between the difference between consecutive terms.

We can see that the difference follows the same pattern.

So, the next term would be the sum of the last term and the square of 6;

Therefore, the number that comes next is;

Answer:

From the image below we will bring out two coordinates we are going to use to calculate the rate of change of the graph

The coordinates are given below as

Concept:

The rate of change will be calculated using the formula below

By substituting the values, we will have

Hence,

The rate of change = 1

The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then

Then, the measure of angle CDB is 32 degrees.

We have the next formula to find the volume of a triangular prism-

where

B= area of the base

h= height

in our case

B=18 square inches

H= 5 inches

the volume of the triangular prism is 90 cubic inches

Hi there. To solve this question, we have to remember some properties about similar triangle and congruency.

Given the triangles ADH and ECK,

We know that

That is, the angle at D is congruent to the angle at C in the respective triangles.

In this case, we can think of the congruency between the triangles in the following diagram:

Notice that ADCB is a parallelogram and the angles given show that the angles at D and at C are congruent, hence the other angles in the parallelogram must be congruent as well.

This means that opposite sides are parallel and have the same measure (length).

The opposite sides are AD and CB and DC and AB.

In this case, we find that only AD and CB are an option to this question, therefore the correct answer.

In fact, AC is the diagonal of the parallelogram and is not parallel to any segment of the figure.

AE isn't a segment drawn and hence not parallel to any other segment.

The correct answer is the option A).

Data

Milk drank = 1 1/2 twice a day

Volume in a container = 15 cups

Number of days the contaier will be empty = ?

Procedure

To solve this problem just divide the volume of the container by the milk drank by the child.

As the child drinks 1 1/2 twice a day, the total milk drank in a day will be = 2 x 1 1/2 = 3

Division 15/3 = 5

Solution: The container will be empty in 5 days

Answer:

B

Step-by-step explanation:

[tex]m_{\overline{AB}}=\frac{4-0}{-2-2}=-1 \\ \\ m_{\overline{CD}}=\frac{-2-4}{-3-3}=1 [/tex]

Since the slopes are negative reciprocals of each other, and since they intersect, they are parallel.