Decide whether the given orderd pair is a solution to the stystem of equations?I don’t know how to to the bottom equation.

The median is defined as the sum of all the values divided by the total number of data, then in this case:

To find the median we need to order the data:

The median is the number that divides all the data in half, since we have an even number of data we need to take the mean between the middle data, that is, the median is:

The mode is the number that repeats itself more on the data set, then in this case we the mode is 98.

The range is the difference between the lowest and highest data, then:

Summing up we have:

mean: 90.7

median: 89.5

mode: 98

Range: 16

Solution

We have the following info given:

P(A) = 4/5

P(B)= 1/7

P(A and B) = 1/9

We want to find this probability:

P(A|B)= P(A and B)/P(B)

Replacing we got:

The following observation are derived from the graph shown relating number of guesses against the number of trials

+) Guessed 6 correctly on 2% of the trials

+) Guessed 7 correctly on 8% of the trials

+) Guessed 8 correctly on 25% of the trials

+) Guessed 9 correctly on 30% of the trials

+) Guessed 10 correctly on 19% of the trials

+) Guessed 11 correctly on 12% 0f the trials

+) Guessed 12 correctly on 3% of the trials

+) Guessed 13 correctly on 1% of the trials

From the options provided, it can be concluded that:

He guessed 9 correctly on 30% of the trials. The first option is the correct option

Answer:

Step-by-step explanation:

find "q'

first take 2 as common

solution .

2(-9q+9q+q+7)=4

Now divided 2 by both sides.

2(-9q+9q+q+7) ÷2

=4÷2

-9q+9q+q+7 =2

q+7=2

q=2-7

q=-5 Answer.

First let us define the theorem that would help us solve the problem

The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.

Next, applying the theorem:

Solving for x:

Answer:

x = 6

Step 1

Analyze the Sampling method

In stratified sampling, the population is divided into two or more groups called strata according to some criterion such as geographic location, grade level, age, income, etc. Subsamples are randomly selected from each stratum. Elements within each stratum are homogenous but are heterogeneous across the strata. For example;

From this question, the general study is on the use of antidepressants. This is the strata, each stratum of 50 participants each based on age cuts across. They are homogenous in their individual stratum of age grades( 20-29), (30-39), (40-49) but are homogenous in the sense that 50 participants were chosen across all stratum and the study is generally about antidepressants.

Hence, the right answer is stratified sampling.

Hello

For the first expression, we have

This have a 2 significant value

This have a 1 significant value.

This have a 3 significant value

We can find the point with help of the end points and the ratio so:

now for y:

So now we can graph it so:

plane flies 390 miles with the wind

or 325 miles against the wind

The speed of the wind is 10 miles per hour

find the speed of the plane

In this case, we can see that

hence the answer is

Find the 0.125% of 7.92x10^10: Multiply the amount by 0.125 and then divide into 100 or multiply the amount by 0.125/100

Given

The polynomial function,

To find: The x-intercepts.

Explanation:

It is given that,

That implies,

The x-intercept is determined by setting f(x)=0.

Then,

Hence, the x-ntercepts are (-2,0), (4,0), (3,0).

Answer:

Explanation:

Here, we want to get the distance the snail can go in the given time

Mathematically, we have it that:

speed = 3/25 mph

Time = 1 2/3 hours = 5/3 hours

Thus, we have it that:

The equation given is,

Since the boundary line is thick bold line and from the graph we can observe that the line (shaded portion) moves from the right to the left hand side.

Then the inequality of the shaded region is,

Answer:

(a)The slope of f(x) is greater than the slope of g(x).

(b)g(x) has a greater y-intercept.

Explanation:

Part A

From the table of f(x), we have the pairs:

(-1,-12),(0,-6) and (1,0).

First, we find the slope of f(x).

Given the function g(x) defined as follows:

Comparing g(x) with the slope-intercept form (y=mx+b), the slope of g(x) is m=2.

Sentence: The slope of f(x) is greater than the slope of g(x).

Part B

The y-intercept is the point in a function where x=0.

In f(x), When x=0, f(x)=-6

• The y-intercept of f(x) is -6.

Comparing g(x) with the slope-intercept form (y=mx+b), the y-intercept of g(x), b=6.

Therefore, g(x) has a greater y-intercept.

First, let's convert the mixed numbers to fractions:

5 1/4 = 21/4 = 5.25

3 3/8 = 27/8 = 3.375

2 5/6 = 17/6 = 2.83333

5.25 + 3.375 + 2.83333 = 11.45833333

Therefore he made a low estimate

The food for both gorilla and grizzly bear in the bucket is 9.972 kg.

Given, at the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears.

The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food.

Let the weight of the grizzly bear food be x,

According to the question,

weight of gorilla food = weight of grizzly bear food + 0.796 kg

5.384 = x + 0.796

x = 5.384 - 0.796

x = 4.588

So, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.

Hence, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.

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ANSWER

9

EXPLANATION

A perfect square is a number that can be expressed as the product of two equal integers.

For example, 9 is a perfect square because it can be expressed as the product 3 x 3 = 3² - which are two equal integers.

EXPLANATION:

Given;

We are told that a forest covers an area of 2300 square kilometers.

Next we are told that this forest area decreases by 7.75% each year.

Required:

We are required to calculate the area remaining after 8 years.

Step-by-step solution:

To solve this math problem, take note that what we have is an exponential decay problem. The initial size decreases (decays) at a constant rate every year.

The formula for an exponential growth/decay is given as shown below;

Where the variables are as follows;

With the values given, we can substitute and we'll have the following;

Rounded to the nearest square kilometer, we would now have;

ANSWER:

33,200 sq units (option A)

Surface area of triangular prism = base × height + length ×perimeter of triangle

base = j = 150 units

height = h = 40 units

length = k = 85 units

m = 85 units

Perimeter of triangle = j + m + m

Perimeter of triangle = 150 + 85 + 85 = 320 units

Surface area of triangular prism = 150(40) + 85(320)

Surface area of triangular prism = 6000 + 27200

Surface area of triangular prism = 33,200 sq units (option A)

Given:

There are given the decimal number:

Explanation:

According to the question:

We need to write the given decimal number in the form of scientific notation.

Then,

To write into the scientific notation, we will use their properties.

So,

From the given decimal number,

Then,

The scientific notation is:

Final answer:

Hence, the answer is shown below:

A trinomial square has two possible forms:

So, for us to check if

Is a trinomial square, we first check if the first and thrid terms are positive, because both options has positive first and thrid terms, even if a or b are negative, because they are squared in the process.

Both are positive, x² and 64.

Now, by comparison, we see that, in thi case we would have:

If it is a trinomial square, than the middle term has to be:

We use the negative form because we have a negative middle term.

So, let's see if it checks out:

We got -16x, but the middle term is -8x, they don't match.

Since they don't match, the given expression is not a trinomial square. The answer is No.

Given the follow:

Root96 - root54 + root24

We are to find the expression that is equivalent.

root96 = root16 x root6

root54 = root9 x root6

root24 = root4 x root6

(root16 x root6) - (root9 x root6) + (root4 x root6)

= 4root6 - 3root6 + 2root6

= (4 - 3 + 2)root6

= (1 + 2)root6

= 3root6

Therefore, the correct option is C which is 3root6

ANSWER

Subtraction property of equality

EXPLANATION

In this problem they subtracted 14 from both sides of the equation. On the left side we can see that subtraction clearly, but on the right side, we have (19-5). If we solve this: 19 - 5 = 14, we can see that 14 has been subtracted from the right side too.

The simple interest after 2, 5 and 8 years on a principal of $3400 at 0.2% are $3413.6, $3434 and $3454.4 respectively

Simple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r(%) and is to be written as r/100.

Using the data given;

S.I = P × R × T

When T = 2 years

S.I = 3400 * 0.002 * 2

S.I = 13.6

The amount after 2 years = 3400 + 13. 6 = $3413.6

When T = 5 years

S.I = 3400 * 0.002 * 5

S.I = 34

The amount after 5 years = 34 + 3400 = $3434

When T = 8 years

S.I = $3454.4

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Given:

EF = 2

m∠FEG = 144 degrees.

Let's fid the length of arc FG.

To find the length of arc FG, apply the formula:

Where:

r is the radius = 2

θ is the central angle = 144 degrees.

Thus, we have:

Therefore, the length of arc FG as a fraction times pi is:

ANSWER:

Hello there. To solve this question, we have to remember some properties about triangles.

Given a triangle ABC as follows:

We can show for each point what it is on this triangle.

1. Midsegment. This is the segment that is parallel to the base, in this case BC and has half its length. Another property: it divides the sides AB and AC into proportional parts. See the drawing.

2. Circumcenter. Take the triangle and inscribe it in a circumference (all its vertices are in the circumference. Now take the perpendicular bisector of each sides. The point in which at least two of them intersects is the circumcenter. See the drawing.

3. Incenter. Take the bisectors of the angles of ABC. The point in which they intersect is the incenter. Another property: It is the center of the inscribed circumference that is tangent to all sides of the triangle.

To solve this expression we need to solve the parenthesis first:

One of the properties of a parallelogram is that its diagonals bisect each other. This means that one diagonal cuts the second diagonal in equal length.

This means that AP = PC. If AP = PC, then 45 = 3x + 15.

We can now find the value of x using the equation above.

First, subtract 15 on both sides of the equation.

Then, divide both sides of the equation by 3 to isolate x.

Therefore, the value of x is 10. (Option B)