The side of a square lot is (5×-3) meters. How many meters of fencing materials are needed to enclose the square lot?

Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24​

we have 2/3

Multiply by 8/8

(2/3)(8/8)=16/24

therefore

Let us solve the equation to arrange the steps

In the first step, we must multiply the bracket by -3 (distributive property)

Then the equation is

Now add the like terms on the left side

Next step, add 12 to both sides

The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.

Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We can model the equation for Madeline's total pay as follows -

P = base pay + (number of sold computer) × (cost of 1 computer)

P = 80 + 20x

Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x

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Explanation:

mu = 500 = mean

sigma = 100 = standard deviation

We'll need the z score for x = 620

z = (x - mu)/sigma

z = (620-500)/100

z = 1.20

The task of finding P(x > 620) is equivalent to P(z > 1.20)

Use a Z table or a Z calculator to find that

P(Z < 1.20) = 0.88493

which leads to

P(Z > 1.20) = 1 - P(Z < 1.20)

P(Z > 1.20) = 1 - 0.88493

P(Z > 1.20) = 0.11507

This converts to 11.507% and rounds to 11.5%

About 11.5% of the students score higher than a 620 on the SAT.

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Another approach:

Open your favorite spreadsheet program. The command we'll be using is called NORMDIST. The template is this

NORMDIST(x, mu, sigma, 1)

If you were to type in [tex]\text{=NORMDIST(620,500,100,1)}[/tex] then you'll get the area under the normal distribution to the left of x = 620

This means [tex]\text{=1-NORMDIST(620,500,100,1)}[/tex] will get us the area to the right of 620. The result of that calculation is approximately 0.11507 which leads to the same answer of 11.5% as found earlier.

When using a spreadsheet, don't forget about the equal sign up front. Otherwise, the spreadsheet will treat the input as text and won't evaluate the command.

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Another option is to use a TI83 or TI84 calculator.

Press the button labeled "2nd" in the top left corner. Then press the VARS key. Scroll down to "normalcdf"

The template is

normalcdf(L, U, mu, sigma)

The mu and sigma values aren't anything new here. But the L and U are. In this case L = 620 is the lower boundary and technically there isn't an upper boundary since it's infinity. Unfortunately the calculator wants a number here, so we just pick something very large. You could go for U = 99999 as the stand in for "infinity". The key is to make sure it's more than 3 standard deviations away from the mean.  

So if you were to type in [tex]\text{normalcdf(620,99999,500,100)}[/tex] then the calculator will display roughly 0.11507, which is in line with the other answers mentioned earlier.

As you can see, there are many options to pick from. Searching out "normal distribution calculator" or "z calculator" will yield many free options. Feel free to pick your favorite.

When the price of bananas goes from $0.39 per pound to $1.06 per pound, the likely effect of quantity demanded is that it will reduce.

The quantity of a commodity or service that consumers are willing and able to acquire at a particular price within a specific time period is referred to as demand. The quantity required is the amount of an item or service that customers will purchase at a certain price and period.

Quantity desired in economics refers to the total amount of an item or service that consumers demand over a given time period. It is decided by the market price of an item or service, regardless of whether or not the market is in equilibrium.

A price increase nearly invariably leads to an increase in the quantity supplied of that commodity or service, whereas a price decrease leads to a decrease in the quantity supplied. When the price of good rises, so does the quantity requested for that good. When the price of a thing declines, the demand for that good rises.

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Given:

Simplify:

Apply the properties of fractions:

Simplify:

Eliminate common terms:

Answer:

Solution:

The modulus of a complex number;

is denoted by;

Thus, given the complex number;

The modulus is;

ANSWER:

Given:

David had $350. After shopping, he was left with $235.

Required:

If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.

Explanation:

We know c is the amount spent

So,

Available amount = Total amount - spent amount

235 = 350 - c

c= 350 - 235

c = 115

Answer:

Hence, David spent $115.

Question:

Solution:

An equation of the circle with center (h,k) and radius r is:

This is called the center-radius form of the circle equation.

Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:

To obtain the general form, we must solve the squares of the previous equation:

this is equivalent to:

this is equivalent to

this is equivalent to:

so that, the general form equation of the circle would be:

thus, the correct answer is:

CENTER - RADIUS FORM:

GENERAL FORM:

We copy the first number, change the division sign to multiplication, then flip the second fraction

Cancel the three's

If you want to simplify the improper fraction, divide the numerator by the denominator

5/4 = 1 1/4

Answer:

P(2 or odd)=1

Explanation:

The spinner has 3 parts.

The probability of spinning a 2:

The probability of spinning an odd number (1, 3):

Therefore:

Answer:

[tex]y=-3(x+7)+2[/tex]

Step-by-step explanation:

Alright, so the first mistake people make is to try to visualize this graph.  For the sake of the problem, it does not matter in the slightest.

To start, we have y=f(x).

The first change is a vertical stretch.  These are represented outside the parentheses.  Meaning, the new stretched equation would be y=3(x).  The three does not replace the "f", just no one would write the f into the equation as it is implied.

Next, the graph is reflected across the x-axis.  This means that there is a negative outside of the parentheses.  The new equation would be -3(x).  As stretches are always greater than 1 and shrinks are between 0 and 1, it is clear the negative denotes a reflection.

Translations to the left are denoted as positives inside parentheses.  In this case, left 7 would be -3(x+7).

Finally, upwards translations are positive numbers shown following the parentheses.  Up two would make your final equation -3(x+7)+2.

S={1/15}

1) Solving that expression

4-10x = 3+5x Subtract 4 from both sides

4-4-10x=3-4+5x

-10x =-1+5x Subtract 5x from both sides, to isolate x on the left side

-10x -5x = -1 +5x -5x

-15x=-1 Divide both sides by -15 to get the value of x, not -15x

x=1/15

S={1/15}

Answer:

D.

Explanation

We know that g(x) = f(1/2x)

Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).

It means that f(-2) = 0 and f(2) = 0

Then, g(-4) = 0 and g(4) = 0 because

Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.

Solution

If A die is rolled one time find the probability of getting an even number

The total number in a die rolled once = 6

number of even number = 3

Probability = number of required outcome / number of possible outcome

Therefore the probability of getting an even number = 1/2

Answer:

\sqrt[29]

Explanation:

Given the coordinate (5,10) and (10, 12). The formula for calculating the distance between two points is expressed as;

Given that;

x1 = 5

y1 = 10

x2 = 10

y2 = 12

Substitute:

Hence the distance between the points is \sqrt[29]

To solve this problem, first, let's remember the definitions of even and odd functions.

• A function f is ,even, if the graph of f is ,symmetric about the y-axis,.

• A function f is ,odd, if the graph of f is ,symmetric about the origin.

a) To make the function even, we must complete the graph such the graph result is symmetric about the y-axis (the vertical axis). Doing that we get:

b) To make the function odd, we must complete the graph such the graph result is symmetric about the origin (the horizontal axis). Doing that we get:

SSS, or Side Side Side

SAS, or Side Angle Side

ASA, or Angle Side Side

AAS, or Angle Angle Side

HL, or Hypotenuse Leg, for right triangles only

Side Side Side Postulate

A postulate is a statement taken to be true without proof. The SSS Postulate tells us,

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles, sides may be marked with one, two, and three hatch marks.

If △ACE has sides identical in measure to the three sides of △HUM, then the two triangles are congruent by SSS:

Side Angle Side Postulate

The SAS Postulate tells us,

If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

△HUG and △LAB each have one angle measuring exactly 63°. Corresponding sides g and b are congruent. Sides h and l are congruent.

A side, an included angle, and a side on △HUG and on △LAB are congruent. So, by SAS, the two triangles are congruent.

Angle Side Angle Postulate

This postulate says,

If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

We have △MAC and △CHZ, with side m congruent to side c. ∠A is congruent to ∠H, while ∠C is congruent to ∠Z. By the ASA Postulate these two triangles are congruent.

Angle Angle Side Theorem

We are given two angles and the non-included side, the side opposite one of the angles. The Angle Angle Side Theorem says,

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Here are congruent △POT and △LID, with two measured angles of 56° and 52°, and a non-included side of 13 centimeters:

[construct as described]

By the AAS Theorem, these two triangles are congruent.

HL Postulate

Exclusively for right triangles, the HL Postulate tells us,

Two right triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent.

The hypotenuse of a right triangle is the longest side. The other two sides are legs. Either leg can be congruent between the two triangles.

Here are right triangles △COW and △PIG, with hypotenuses of sides w and i congruent. Legs o and g are also congruent:

[insert congruent right triangles left-facing △COW and right facing △PIG]

So, by the HL Postulate, these two triangles are congruent, even if they are facing in different directions.

Proof Using Congruence

Proving Congruent Triangles 5

Given: △MAG and △ICG

MC ≅ AI

AG ≅ GI

Prove: △MAG ≅ △ICG

Statement Reason

MC ≅ AI Given

AG ≅ GI

∠MGA ≅ ∠ IGC Vertical Angles are Congruent

△MAG ≅ △ICG Side Angle Side

If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

The circumcenter of a triangle is the center of a circumference where the three vertex are included. So basically we must find the circumference that passes through points O, V and W. The equation of a circumference of a radius r and a central point (a,b) is:

We have three points which give us three pairs of (x,y) values that we can use to build three equations for a, b and r. Using point O=(6,5) we get:

Using V=(0,13) we get:

And using W=(-3,0) we get:

So we have a system of three equations and we must find three variables: a, b and r. All equations have r^2 at their right side. This means that we can take the left sides and equalize them. Let's do this with the second and third equation:

If we develop the squared terms:

Then we substract a^2 and b^2 from both sides:

We substract 9 from both sides:

And we divide by 6:

Now we can replace a with this expression in the first equation:

We develop the squares:

So this expression is equal to r^2. This means that is equal

30pq=3p×5q=15pq×2=30pq

twelve and two hundred six thousandths

In a function, any x-value is related to at most 1 y-value.

In the first table, x = 20 and x = 17 are related to 2 different y-values. Then, it is not a function.

In the second table, x = 9 is related to 2 different y-values. Then, it is not a function.

The third and fourth tables are functions

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

Answer:

32.2 feet

Explanation:

The diagram given is a right angled triangle

Using the SOH CAH TOA identity

Given the following

Hypotenuse = 38

Opposite = x

Sin theta = opposite/hypotenuse

Sin 58 = x/38

x = 38sin58

x = 38(0.8480)

x = 32.23

Hence the length of VT to the nearest tenth of a foot. is 32.2feet

Answer:

[tex](y+6)=\frac{2}{8} (x+2)[/tex]

Step-by-step explanation:

First, find the slope

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

-4+6=2

6+2=8

m=2/8

With the slop, you have everything you need to stick one of your points in point-slope form.  I chose (-2,-6)

[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]

Really, that's all you need as it is not an equation of a line.  Not the most useful form, but works as an answer.

The 5 number summary of the data given is:

Minimum = 59

Q1 = 66.50

Median = 78

Q3 = 90

Maximum = 99

A stem and leaf plot is a table that is used to display a dataset. A stem and leaf plot divides a number into a stem and a leaf. The stem is the first digit in a number while the leaf is the second digit in the number.

The minimum is the smallest number in the stem and leaf plot. This is 59. Q1 is the first quartile.

Q1 = 1/4 x (n + 1)

Where n is the total number in the dataset

1/4 x 19 = 4.75 term

(64 + 69) / 2 = 66.50

Q3 is the third quartile.

Q1 = 3/4 x (n + 1)

Where n is the total number in the dataset

3/4 x 19 = 14.25 term = 90

The median is the number that is at the center of the dataset.

Median = 1/2(n + 1)

1/2 x 19 = 8.5 term

(76 + 80) / 2  = 78

The maximum is the largest number in the dataset. This number is 99.

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Answer:

Concept:

If you flip a coin once, there are

Using the binomial probability formula below, we will have

Where

By substituting the values, we will have

Hence,

The final answer is

EXPLANATION

Given that two angles form a linear pair, we can assevere that the postulate that applies is the Linear Pair Postulate.

From 1 to 10, there are 3, 6, and 9 are divisible by 3

Then we have 3 choices out of 10 numbers

Since the probability = an event/outcomes

Since the event is 3

Since the outcomes are 10, then

This is the probability for spinning the spinner one time

But we need to spin it 70 times

We will multiply 3/10 by itself 70 times, which means make it to the power of 70

The answer is (3/10)^70 OR (0.3)^70

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.