Task 3: Solve the following quadratic equation by extracting the square root.

Given :

1)

Set t=1 we get

There are 20 numbers to choose from. Thus, the total sample space is 20.

If you choose one number, the probability of choosing that number is:

Now, if after choosing one number in the first round, you proceed to choose another number in the second round.

The probability of choosing a number for this second round will be:

Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.

For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:

The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.

Thus the final answer:

Therefore, the final answer is:

ok

AC = 7

AD = 6

BC = 18

It must be 12, because the sum of two sides of a triangle is higher than the other side.

And 6 + 5 = 11

AB + AC = 11 + 7 = 18

SOLUTION

Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.

The problem can be modeled using the figure below

Notice that the triangle formed is a right triangle:

Therefore using Pythagorean theorem it follows:

Solve for x

Therefore the other leg no miss

Answer: Yes

Step-by-step explanation:

Yes, the numbers in the table are a function. The equation for the equation would be

y = 2x

The most appropriate choice for annular region will be given by

This graph represents an annular region shown in the figure

What is annular region?

Annular region represents the space between two concentric circles of different radii.

Equation of annular region centered at (0, 0) is

[tex]a^2 \leq x^2+y^2\leq b^2[/tex]

Here,

[tex]x^2 + y^2\geq 16\\x^2 + y^2 \geq 4^2\\[/tex]

It denotes the outside of a circle of radius 4 centered at (0, 0)

[tex]x^2 + y^2\leq 25\\x^2 + y^2 \leq 5^2\\[/tex]

It denotes the inside of a circle of radius 5 centered at (0, 0)

So the complete graph is being attached here.

This region is known as annular region

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It is given that,

The length of a rectangle is 5 cm more than three times the width.

That is, l=3w+5

Put width, w=12.

Therefore, the length becomes,

l=3(12)+5

l=36+5

l=41 cm.

Hence, the length of the rectangle is 41 cm.

Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:

[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]

Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:

[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]

Then substitute f(3) down to f(1):

[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]

Therefore, f(5) = 7.5

Answer:

x=6

Step-by-step explanation:

3 (x+1) -22 +13=12

3x+3 -22+13=12

3x+3-9=12

3x-6= 12

3x= 12+6

3x= 18

x= 18/3

x= 6

We have two functions for the sales of popcorn:

being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.

We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.

We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.

Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).

Then, we can calculate the difference in sales as:

Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.

An observation is considered an outlier if it is below -16.75

An observation is considered an outlier if it is above 33.25

Extremely low or high values in a data set are considered outliers. Outliers are a product of statistical observational errors and variability. They frequently produce significant statistical issues, hence they are frequently left out of the study.

We must think about if it meets the following criteria in order to identify an outlier:

Q₁ - 1.5 (IQQ) ⇒ for lower value

Q₃ + 1.5 (IQR) ⇒ for higher value

Q₁ stands for the lower quantile, Q₃ for the higher quantile, and IQR for the inter-quantile range. Using the previous data,

Q₁ and Q₃ come from:

Q₁ = (0 + 4) / 2 = 4 / 2 = 2

Q₃ = (12 + 17) / 2 = 29 / 2 = 14.5

IQR = Q₃ - Q₁ = 14.5 - 2 = 12.5

(a)  An observation is considered an outlier if it is below:

Q₁ - 1.5 (IQR) = 2 - 1.5 (12.5) = 2 -  18.75 = -16.75

An outlier is a number that is less than -16.75

(b) An observation is considered an outlier if it is above:

Q₃ + 1.5 (IQR) = 14.5 + 1.5 (12.5) = 14.5 + 18.75 = 33.25

An outlier is a number that is greater than 33.25

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The graph that can be used to model the correct amount on the Richter scale is r = log(a/4) + 2.

It should be noted that the magnitude of an earthquake is gotten by using the equation:

r = log(a / t) + d.

where

r = magnitude of an earthquake

a = amplitude

t = time

d = distance.

In this case, the earthquake occurred for 4 seconds and D = 2. We'll substitute the value into the equation and this will be r = log(a/4) + 2.

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Answer:

122

Step-by-step explanation:

43 * (100/25) - 50

43 * 4 - 50

172 - 50

122

Hope this helps! :)

Answer:

1 ÷ [tex]\sqrt{n\\}[/tex] = x

Step-by-step explanation:

For the given, "the quotient of 1 and the square of a number", the expression is 1+√n

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.

The phrase "The quotient of 1 and the square of an integer" is presented.

The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.

If n is the number the expression can be written as,

=1+√n

Thus, for the given expression the expression is 1+√n.

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From the calculations below, we can tell that quadrilateral ABCD is not a rectangle because AB is not parallel to CD

We are given that the quadrilateral is ABCD with the vertices as;

A(-6,-2)

B(-4,4)

C(8,1)

D(6,-6)

We are further told that Angle A is a right angle. Thus;

AB must be perpendicular to AD.

Secondly, for ABCD to be a rectangle, AB must be parallel to CD. Thus;

By slope formula, for AB and CD are gotten from the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope of CD = (-6 - 1)/(6 - 8)

Slope of CD = -7/-2 = 7/2

Slope of AB = (4 - (-2))/(-4 - (-6))

Slope of AB = 6/2

Slope of AB = 3

Since Slope of AB and AC are not equal then ABCD is not a rectangle.

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(3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5.

1.) For the first expression with exponents:

(3/5)to the power of 3 can be written as , where the number 3/5 is called the base, and 3 is the power or exponent of the expression. So (3/5) times 3 .

Where, Side of the cube (a) = 3/5

⇒ (3/5)^3  

⇒ 0.216 cube.units

2.) For the second expression without exponents:

The formula of volume of the cube is given by volume(side) =a*a*a, where a is the length of its sides or edges.

Cube ⇒ ( 3/5 × 3/5 × 3/5)

Cube ⇒  0.216 cube.units

Cube of having side (3/5) = 0.216 cube.units

Hence, (3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5 .

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Given an expression:

We have to simplify the expression, if it does not result in a real number then the answer is NONE.

Let:

Then,

There is no real number whose power 4 is a negative number.

Thus, the answer is not a real number. The answer is NONE.

The crate's density in pounds per cubic foot = 137.28 lb/ft³

Density is defined as the quantity that shows the relationship between the mass and volume of an object which is measured in kilograms per cubic meter or in pounds per cubic foot.

The density of the given crate of medicine = 2,200 kg / m³

To convert to pounds per cubic foot;

1 kg/m³ = 0.0624 lb/ft³

2,200 kg/m³ = X

Make X the subject of formula;

X = 2,200 × 0.0624/1

X = 137.28 lb/ft³

Therefore, when converter to pounds per cubic foot the density of the crate of the medicine= 137.28 lb/ft³.

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Given:

Initial deposit = $8500

rate of interest = 5% compounded annuallly

time (t) = 6 years

If Ao is invested at an annual interest rate r and compounded semiannually, the amount At after t years is given by the formula:

The compound amount in 6 years:

Simplifying we have:

Answer:

$11431.56

The probability that it is not yellow candies will be 119/139.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

A bag contains;

Number of red candies = 42

Number of green candies = 45

Number of yellow candies = 20

Number of purple candies = 32

Now,

Total number of candies in a bag = 42 + 45 + 20 + 32

                                                   = 139

And, The number of candies in a bag not contain yellow candy

= 139 - 20

= 119

Thus, The probability that it is not yellow candies will be;

Probability = Number of not yellow candies / Total candies

                = 109 / 139

Therefore, The probability that it is not yellow candies will be 119/139.

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The sum of angles of a triangle is equal to 180 degree.

Determine the value of x, by using angle sum for the triangle.

The value of x is 24

6x - 3y = -30 -------------------------------(1)

3x - 6y = 12 ---------------------------------(2)

Multiply through equation(1) by 3 and then multiply through equation (2) by 6

18x - 9y = - 90 ---------------------------------(3)

18x - 36y = 72 ----------------------------------(4)

subtract equation (4) from equation (3)

f(n+1) is

Therefore, substitutig, we get, option c.

First, from the formula given we solve the equation for D:

Now, substituting the given data:

(a) PD=405 cu in, L=4.7 in, and N=7,

in the above equation we get:

(b) PD=399.4 cu in, L=2 in, and N=6,

in the above equation we get:

Answer:

(a) 3.96 in.

(b) 6.51 in.

Answer: 0.64 ...........

Relation 1 and Relation 3 are functions while Relation 2 and Relation 4 are not functions.

Function is a relation which maps a set to another set with some criteria.

It includes a property that one element of the domain set should only be related to exactly one element in the range set. That is, same element from the domain cannot be related to different elements in the range. Also all elements in the domain should have images in the range also.

Now we will check all the relations given one-by-one.

In relation 1, the relations are:

Chair ---------> 0

Pencil --------> 0

Paper ---------> 4

Star ------------> 1

Here All the domain elements are mapped only once to one element from the range. So it is a function.

In relation 2, the relations are:

4 ----------------> 5

4 ----------------> 9

0 ----------------> -9

1 -----------------> 4

8 -----------------> -4

Here 4 is mapped to both 5 and 9. So it does not satisfy the definition of a function and hence is not an function.

In relation 3, the relations are:

z -----------------> c

k -----------------> a

a -----------------> k

c ------------------> c

Here also all elements in the domain are mapped only once to an element from the range. So it is a function.

In relation 4, the relations are:

-4 -----------------> m

-4 -----------------> d

-4 -----------------> c

9 -----------------> s

Here, -4 is mapped to m, d and s. So it cannot be a function as it has more than one images.

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Answer:

C -9, -4

E -8, 4

G-4, 0

I-6, -8

B0, 0

D-16, 4

F-2, 9

H0, 7

J9,-2

Step-by-step explanation:

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