What is the rage of the function graphed below?

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The dimensions of the original sandbox was 2 ft X 2 ft..

Let, The original has a length of Xft and a width of Xft

The area of original sandbox is X^2 ft^2

As per given statement,

The new sandbox would have a length of (X+4)ft and a width of (X+5)ft

So, the area of new sand box would be: (X+4)(X+5) ft^2

Given, the area of new sandbox will be 38 square feet greater than the area of the original sandbox.

so,

X^2+38 = (X+4)(X+5)

or, X^2+38 = X^2 + 9X + 20

Eliminating X^2 from both side

0r, 9X+ 20 = 38

0r, 9X = 18

0r, X = 18/9 = 2

So, we assumes that the original has a length of Xft and a width of Xft

then the dimensions of the original sandbox was 2 ft by 2 ft.

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Step-by-step explanation:

Regular decagons have two additional identifying properties: 10 exterior angles of 36° , summing to 360° 10 interior angles of 144° , summing to 1,440°

Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°. 30×12= 360

On solving the provided question, we can say that - sequence (0.67,3-√4,√8,0.14) are the  rational, real, integer, irrational, irrational.

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

here,

the given sequence is (0.67,3-√4,√8,0.14)

as we can see that in the sequence we have a rational number, integer, real number and a irrational so,

the answer is  rational, real, integer, irrational, irrational.

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Answer:

55

Step-by-step explanation:

The paper is folded into 5 folds before the area is less than 1 square inches.

What is area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Here the area of the folded paper after n folds is,

A = 90[tex](\frac{1}{3})^n[/tex]

Now put n=0 into given formula,

A = 90[tex](\frac{1}{3})^0[/tex]=90×1 = 90 square inches.

Here Area of the paper before being fold is 90 square inches.

Now area is less than 1 square inches then

=> 90[tex](\frac{1}{3}) ^n[/tex] < 1

=> [tex](\frac{1}{3}) ^n < \frac{1}{90}[/tex]

Here if n= 4 then  [tex](\frac{1}{3}) ^4 > \frac{1}{90} = \frac{1}{81} > \frac{1}{90}[/tex] then n=5.

Hence the paper is folded into 5 folds before the area is less than 1 square inches.

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Answer: Kaitlyn can run the triangular route represented by HEDF. This route is the same distance as Lucy's route, ABDF, because it is composed of three sides of the same length. H is the starting point, E is the midpoint, and F is the endpoint. The route starts at point H, travels to point E, then to point D, and finally to point F, completing the triangle.



As per the given points in the question, the slope in the simplest form will be equal to 0

Using two of the points on the line you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise and the horizontal change is called the run. The slope equals the rise divided by the run.

Here the given points are (−5,8) and (−11,8)

Hence the required slope of the line is

=   8     -       8

     11 -  [ - 5 ]

=      0      

 - 11 + 5

=        0    

        - 6

= 0

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The time taken by Wendy after she learned flying is m/4 minutes or 0.25m minutes.

We will solve this problem with the help of Percentages.

In the concept of percentages, we know that:

100% = 100/100 = 1

75% = 75/100 = 3/4

50% = 50/100 = 1/2

25% = 25/100 = 1/4

In our question, it is given that previously wendy took ‘m’ minutes to commute.

Now she reduced her daily commute by 75% after learning how to fly.

So, our new time = (100-75)% of previous time

= 25% of m minutes

= 25/100 of m minutes = ¼ of m minutes = m/4

So our final answer will be m/4 minutes or 0.25m minutes taken by wendy to commute now.

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Answer:

[tex] \sf \: 6 + 3b + 8 = 32[/tex]

Step-by-step explanation:

Given expression,

→ 6 + 3b + 8

Now we have to use,

→ b = 6

Let's solve the expression,

→ 6 + 3b + 8

→ 6 + 3(6) + 8

→ 6 + 18 + 8

→ 24 + 8

→ 32 => final value

Hence, the answer is 32.

The probability that a sequence will contain exactly one 0 as calculated from the data given is found to be 3/8.

Taking into consideration the sequences where the digit 0 occurs , we will get the possibilities of getting 0 and 1 as 2 .

The number of sample points in the  sample space will be ,

2 x 2 x 2 = 8 sample points.

These sample space are, S = {111, 110, 101, 011, 100, 010, 001, 000},

Now , the sequence having all three 0 as seen from the sample space is found to be 3.

So the  probability becomes , P(0) = no of favorable outcomes / total number of outcomes =3/8.

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Answer:

no

Step-by-step explanation:

the one equation has variables and numbers go in for the variable and the other equation just equals 11

When a polynomial has four or more terms, the easiest way to factor it is to use grouping.

Grouping can be understand more better with an example:

for eg:  factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:

However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).

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i thinj the answer is 2-1

We can solve the given linear equation 7x = 5y by plotting the graph of x and y on the coordinate plane.

An equation is known to be a linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b and c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

First, solve for x

7x = 5y

Divide both sides by 7

7/7 x = 5/7 y

Dividing by 7 undergoes the multiplication by 7

x = 5/7 y

Similarly, solve for y

7x = 5y

Divide both sides by 5

7/5 x = 5/5 y

Dividing by 5 undergoes the multiplication by 5

y = 7/5 x

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Answer: original price: £400

Step-by-step explanation:

20/100 × original price = £80

Original price = £80 ÷ 20/100

                      = £400

The Binomial Expression is defined as the type of algebraic expression that consists of exactly two terms .

What is Binomial Expression ?

The algebraic expression which contains exactly only two terms is termed as  binomial expression . It is called a two term polynomial.

the binomial is also called a sum or a difference between two or more monomials. Binomial is the simplest form of a polynomial.

Some Examples of Binomial Expression are ⇒ [tex]4x^{2} +6y^{2}[/tex] , [tex]xy^{3} +xy[/tex] ;

Various Mathematical Operations can be performed on Binomial Expression such as Addition , Subtraction , Multiplication and Division .

and The  Equation that contains one or more binomial expression is called as a Binomial Equation.

The given question is incomplete , the complete question is

What is a Binomial Expression ?

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We can use the Z-score formula to determine what percent of patients have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

The Z-score formula is:

Z = (X - M) / SD

Where:

X = Patient's score (45)

M = Mean score (52)

SD = Standard deviation (5)

Plugging in the given values:

Z = (45 - 52) / 5

Z = -7 / 5

Z = -1.4

This Z-score of -1.4 corresponds to a percentage of approximately 9.1% of patients who have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

It is important to note that this percentage is approximate, as it's calculated based on the standard normal distribution table which provides approximate values, and it assumes the scores of the test are normally distributed, in case this assumption is not met the result may not be accurate.

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Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Adam earns $186 for 8 hours of work, so his hourly rate is $186/8 = $23.25 per hour

Kim earns $54 for 3 hours of work, so her hourly rate is $54/3 = $18.00 per hour

Kim earns $125 for 7 hours of work, so her hourly rate is $125/7 = $17.86 per hour

Kim earns $216 for 12 hours of work, so her hourly rate is $216/12 = $18.00 per hour

Adam earns $23.25 per hour and Kim earns $18.00 per hour on average.

Adam earns $23.25 - $18.00 = $5.25 more per hour than Kim.

Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.

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simplest form of  equation V= 60

Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1.

A 'Simplest Form Calculator' is a free online tool that reduces a fraction to its simplest form. In this calculator, you can enter value and find its simplest form within a few seconds.

V=S3

S = 20

Give your answer in simplest form.

V = S3

V = S× 3

S = 20

Therefor

V = 20 × 3

V= 60

simplest form V= 60

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The exponential function to model the predicted value of Bruce's investment account is

y = 6225 * 2^x.

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

here, we have,

we know that,

An exponential function is written in the form - y=a*(b)^x

Here, y is the function, a is the base value b is the rate and x is time period.

now, we have,

from the given information, we get,

This equation uses the initial value of the account (6225)

and the base of the exponent (2) representing the account will double in value every decade.

if, we have,

the predicted value of Bruce's investment account is y.

time period is, x decades after starting the account.

So, the exponential equation will be -

y = 6225 * 2^x.

Therefore, the exponential equation is .

y = 6225 * 2^x.

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Answer: No, -0.0022 is not less that -0.022

Step-by-step explanation:

1. We know that the bigger the negative number the lesser it is ( 0.022 is a bigger number than 0.0022) but since it's a negative number it's less in value.

Answer:

$5,775

Step-by-step explanation:

The equation is:

A = P( 1 + rt)

We know

P = $5,500

r = 5% = 0.05

t = 1 month

Let's solve

A = 5,500( 1 + 0.05 x 1)

A = 5,500( 1.05)

A = $5,775

So, his account will be at $5,775 after one month.

The value of x is 10.66

Complementary angles  is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.

If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

Collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Therefore, the value of x is 10.66

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Answer:

x = -4 or x = -1

Step-by-step explanation:

Let's check

x = -4

(-4 + 4)(-4 + 1) = 0

(0)(-3) = 0

0 = 0

Let's check x = -1

(-1 + 4)(-1 + 1) = 0

(-3)(0) = 0

0 = 0

So, x = -4 or x = -1 is correct answer!

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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Answer:

2nd choice:  -3x - 5 = 10

Step-by-step explanation:

10 - x = -5

-x = -5 - 10 = -15

-3x - 5 = 10

-3x = 10 + 5

x = 15/-3 = -5

Answer:

1.5 ft

Step-by-step explanation:

The area of a parallelogram is base times height.

So to find the height, you will need to use area/base

Small: 16.25/6.5=2.5 ft

Large: 34/8.5=4ft

4-2.5=1.5ft

Answer:

11√12

Step-by-step explanation:

√12 = 2√3

2√12

= 2 * 2√3

= 4√3

√48 = 4√3

3√48

= 3 * 4√12

= 12√12

√75 = 5√3

2√12 + 3√48 - √75

= 4√3 + 12√12 - 5√12

= 16√12 - 5√12

= 11√12

Answer: My answer is 11√3

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers.

Exact Form:

11√3

Decimal Form:

19.05255888…

Bar charts display categorical variables, whereas histograms display numerical or quantitative data.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.

Therefore, the correct answer is option C. 6 or fewer.

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Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

p(x)=6x+2

for p(-2)

p(-2) = 6(-2) + 2

p(-2) = -12 + 2

p(-2) = -10

for p(4)

p(4) = 6(4) + 2

p(4) = 24 + 2

p(4) = 26

p(-2) < p(4)

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Answer:

(B) "The value of p(-2) is smaller then the value of p(4)" is True

Step-by-step explanation:

p(x)=6x+2

p(-2) = 6*(-2)+2

p(-2) = -12+2

p(-2) = -10

p(4) = 6*(4)+2

p(4) = 26

====

p(-2) = -10

p(4) = 26

===

(A) The value of p(-2) is larger then the value of p(4).   False

(B) The value of p(-2) is smaller then the value of p(4).  True

(C) The value of p(-2) is the same as the value of p(4).  False

(D) The values of p(-2) and p(4) cannot be compared.   False