Given: <5=<16;<2=<4
Prove: <11 and <14 aré supplementary

The percentage discount is 58%

The old price is $50

The new price is $21

The percentage discount can be calculated as follows

old price-new price/old price × 100

= 50-21/50 × 100

= 29/50 × 100

= 0.58 × 100

= 58

Hence the percentage discount is 58%

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If angela uses this schedule for 4 weeks, the total number of hours she will many have practiced in total is 35.6 hours

Week 1:

Total = Monday + Tuesday + Saturday

= 1.4 + 2 1/2 + 5

= 1.4 + 2.5 + 5

= 8.9 hours

Total number of hours she practice for weeks = 8.9 hours × 4

= 35.6 hours

Therefore, if angela uses this schedule for 4 weeks, the total number of hours she will many have practiced in total is 35.6 hours.

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The polynomial is quintic binomial.

The given polynomial is [tex]3r^5-7r[/tex]. The polynomial is given in standard form. i.e., terms are arranged in the decreasing order of its powers.

The degree of the polynomial is the highest power of 'r' in the polynomial.

So degree of the polynomial  [tex]3r^5-7r[/tex] is 5.

Polynomials of degree 5 are called quintic.

The polynomial has 2 terms:  [tex]3r^5, 7r[/tex]

Since the number of terms are two, we can call it binomial.

So the polynomial [tex]3r^5-7r[/tex] is quintic binomial.

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The simplification by combining like terms of 2(h + 2g) - (g - h) is 3(h + g).

According to the given question.

We have an expression 2(h + 2g) - (g - h).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression

2(h + 2g) - (g - h).

Here 2h, and h and 2g and -g are the like terms.

So, we add and subtract coeffcients of h and g to simplify the given expression.

Therefore, the simplification of 2(h + 2g) - (g - h) is given by

= 2(h + 2g) - (g - h)

= 2h + 4g - g + h

= 3h + 3g

= 3(h + g)

Hence, the simplification by combining like terms of 2(h + 2g) - (g - h) is

3( h + g).

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Answer: x=-8   y=7

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{-2x-5y=-19\ \ \ \ (1)} \atop {3x+2y=-10\ \ \ \ \ (2)}} \right.[/tex]

Multiply both parts of the equation (1) by 3 and multiply both parts of the equation (2) by 2:

[tex]\displaystyle\\\left \{ {(-2x)(3)-(5y)(3)=(-19)(3)} \atop {(3x)(2)+(2y)(2)=(-10)(2)}} \right. \\\\\left \{ {{-6x-15y=-57\ \ \ \ (3)} \atop {6x+4y=-20\ \ \ \ (4)}} \right. \\[/tex]

Summarize equations(3) and (4):

[tex]-11y=-77[/tex]

Divide both parts of the equation by -11:

y=7

Hence,

[tex]3x+2*7=-10\\3x+14=-10\\3x+14-14=-10-14\\3x=-24[/tex]

Divide both parts of the equation by 3:

[tex]x=-8[/tex]

Answer:

39.6534

Step-by-step explanation:

You divide 4005 by 101 and find the numbers that repeat as a decimal. In this case, the repeating decimals are 6534.

Using the concepts of subsets and proper subsets, the statements are classified, respectively, as:

Suppose we have a set given by:

A = {a, b, c}.

The subsets will be all possible combinations involving at least one element of A, or the empty subset, hence:

S(A) = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b,c}, {a,b,c}}

In which S(A) is composed by the subsets of A.

The proper subsets are all the subsets, except the empty set, hence:

PS(A) = {{a}, {b}, {c}, {a, b}, {a, c}, {b,c}, {a,b,c}}

In which PS(A) is composed by the proper subsets of A.

Hence:

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Answer: QT = 15

Step-by-step explanation:

RT=9, RS=7, and QS=13

Find QT=QR+RT

find QR=QS-RS

QR=13-7=6

therefore QT=QR+RT=6+9=15

Answer:

Savannah will have 35 pennies after 10 days.

It will take her 49 days to have at least $1.50

Step-by-step explanation:

Start Value = .05

Linear Increase = .03

.05 + .03x = TV

TV = Total Value

10 days = .05 + .03(10)

10 days = $.35

.05 + .03x = 1.50

1.50 - .05 = 1.45

1.45/.03 = 48.33

48 days is not enough for her to have 1.50 as she is not gaining hourly but rather daily so it would take her 49 days to have at least 49

4 significant digit the quotient have.

Significant digit are the important digit in a number which convey the accuracy. all non zero numbers are significant and zero between two non zero is a significant digit and all zeros at the right of decimal is significant digit in number.

Given numbers are 2.058 * 10^9 and 3.0571 * 10^-4

To calculate the division first we have to solve the exponent.

In divide we subtract the powers

10^(9-(-4)) = 10^13

Now do the division

(2.058 ÷ 3.0571)*10^13 = 0.67318*10^13 = 0.6732 *10^13

=6.732 * 10^12

Number of significant digit are 4.

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Step-by-step explanation:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

The equation be I = √W/R  

Where I is the current.

W stands for electrical power.

R stands for resistance in ohms then the value of I = 1.414

A circuit's ability to transport electrical energy is referred to as its electric power. One joule per second, or one watt, is the SI unit of power. Similar to other SI units, watts have standard suffixes that refer to thousands, millions, and billions of watts as kilowatts, megawatts, and gigawatts, respectively.

Let the equation be I = √W/R

Where W and R are both within the square root symbol and 

I is the current.

W stands for electrical power.

R stands for resistance in ohms.

When W = 100, R = 25, to solve for the value of I for each set.

I = √100/25

The square root of I = √4

W = 100, R = 50 and I = 2.

I = √100/25

The square root of I = √2

Therefore, the value of I = 1.414

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Answer:

x= 10 , DEG = 60 , GEF = 40

Step-by-step explanation:

Firstly the angle DEH is 90 degrees because of the red square indicating it.

That means the angle DEF is also 90 degrees.

To find the x you would do:

6x + 4x = 90

now add the 6x and 4x together:

10x = 90

now divide 10 from both sides to isolate the x:

x = 10

now you have your x which is 10.

For angle DEG you plug in the 10 for the x:

DEG = 6(10)

after that you multiply the 6 and 10:

DEG = 60

For angle GEF you plug in the 10 for the x:

GEF = 4(10)

after that you multiply 4 and 10:

GEF = 40

Answer:

Yes

Step-by-step explanation:

9.50=9.5+0.00 ==> The only difference between 9.50 and 9.5 is that it has an extra zero in the right hand side of .5. Hence, you add 0.00 to 9.5 to get 9.50. 0.00=0. Whenever you add 0 to a number, that number won't change. Hence, 9.5=9.50.

The probability for the arrow that land in the odd number is 1/2.

Probability:

Basically, the word probability define the possible way of occurring the event.

Given,

The spinner is divided into 8 equal sections.

Here we need to find if the arrow lands on a number, what is the probability that it will land on an odd number.

Let us consider that the spinner has 8 equal-sized sections numbered 1 to 8.

Since the sections have equal size, each section is equally probable.

The probability of falling on each section is therefore 1/8.

We know that, in the 8 sections,

There are four odd numbered sections.

Hence, probability is

=> 4/8

When we simplify it,

=> 1/2

Therefore, the probability for the arrow that land in the odd number is 1/2.

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The number combinations that fit the criteria will be 25 + 30 + 32 + 38.

It should be noted that the information illustrated that the sum of the four integers in that set must be no less than 118 and no greater than 144.

Therefore, the numbers that fit this will be:

= 25 + 30 + 32 + 38

= 125

Therefore, the number combinations that fit the criteria will be 25 + 30 + 32 + 38.

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The height of the television is 13.268 inches.

The television is in the shape of a rectangle and when we draw an imaginary diagonal line it would become a right-angle triangle in which the diagonal line would become the hypotenuse and the length would become base.

We need to find out the tallness of the television which is the perpendicular of our imaginary right-angle triangle

By applying the Pythagoras theorem [tex]H^{2}[/tex]= [tex]P^{2} + B^{2}[/tex]

As we need perpendicular the formula would become P = [tex]\sqrt{H^{2} -B^{2} }[/tex]

After putting the values in the above equation,

         we get = [tex]\sqrt{(55) – (35.51)}[/tex]

        =[tex]\sqrt{3025-1260.96}[/tex]

                       =[tex]\sqrt{1764.04}[/tex]

            =13.268 inches

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The range of the function f(x) = x + 51 is {y | -∝ < y < ∝}

The range of a function is the set of output values of the function

The function is given as

f(x) = x + 51

The above function is a linear function

The range of any linear function is the set of all real numbers

This is represented as

-∝ < f (x) < ∝

This can also be represented as

-∝ < y < ∝

So, we have

{y | -∝ < y < ∝}

Hence, the range of the function f(x) = x + 51 is {y | -∝ < y < ∝}

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The most commonly used explicit of an arithmetic sequence is given as,

an = a + (n - 1) d

Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,

2nd row seat = 12+ 1x2

3rd row seat = 12 + 2 x2

nth seat = 12 + (n-1) x 2

16th row seat = 12 + (16–1) x2 = 42

Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows,

Average number of seats per row = (12 +42)/2= 27.

So total seats = average per row x number of rows.

= 27 x 16 = 432.

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Answer:

- 4 < n ≤ 4

Step-by-step explanation:

2 < n + 6 ≤ 10 ( subtract 6 from each interval )

- 4 < n ≤ 4

Answer:

only mathematics = 20

only accounting = 10

mathematics and accounting = 16

All = 46

Step-by-step explanation:

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The lengthof the rectangle is 23 cm and width of the rectangle is 25cm.

Consecutive odd integers are odd integers that follow each other and they differ by 2.

Given that Length and width are consecutive odd integers then

Let length be x so width will be x+2.

The [tex]Perimeter \ of \ Rectangle = 2 (Length \ + \ Width)[/tex]

Perimeter of Rectangle= 96cm

[tex]96 = 2 (Length \ + \ Width)\\(Length \ + \ Width) = 48\\x + x + 2 = 48\\2x = 46\\x = 23[/tex]

So, length = x = 23cm

therefore, width = x+2 = 25cm

Therefore, Length of the rectangle is 23 cm and the Width of the rectangle is 25 cm.

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  The binomial expansion of the given expression is:

p⁶ + q⁶ + 8p⁵q + 17p⁴q² + 20p³q³ + 11p²q⁴ + 4pq⁵

   A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.

 Depending on the number of terms it can be :

 We solve first by perfect square trinomial, then we apply the distributive property.

(p + q)⁶ = (p + q)²(p + q)²(p + q)²

(p + q)²= p² + 2pq + q²

p⁴ + 2p³q + p²q² + 2p³q + 4p²q² + 2pq³ + q²p² + 2pq³ + q⁴

p⁴ + 4p³q + 6p²q² + 2p³q + 2pq³ + q⁴

(p⁴ + 4p³q + 6p²q² + 2p³q + 2pq³ + q⁴)(p² + 2pq + q²)

    p⁶ + 4p⁵q + 6p⁴q² + 2p⁵q + 2p³q³ + p²q⁴

+( 2p⁵q + 8p⁴q² + 12p³q³ + 4p⁴q² + 4p²q⁴ + 2q⁵p)

+(p⁴q² + 4p³q³ + 6p²q⁴ + 2p³q³ + 2pq⁵ + q⁶)

p⁶ + q⁶ + 8p⁵q + 17p⁴q² + 20p³q³ + 11p²q⁴ + 4pq⁵

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explantation is at the top :)

The slope of the line is the y-intercept, and 40 caramel apples are required to raise $200.

Students in the math club are supposed to sell enough caramel apples and popcorn balls to generate $200, according to the question. This expression's line equation has the following form:

Expression's slope is 4/5(200) = 4(40) = 160.

40 caramel apples are equal to 200 minus 160.

Thus, 40 caramel apples are required, and the slope of a line is represented by the y-intercept.

The ratio between the y-axis and x-axis values is known as the slope of a line. Depending on the slope's values, it can

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Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Use slope formula.

y2-y1/x2-x1

Plug in the given info.

4-2/0+9

2/9

Hope this helps!

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Using the formula for the distance between two points, the relationship between RA and R'A is given by:

RA = R'A.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

The coordinates of the points of interest to find the segments' lenghts are given as follows:

Applying the formula, the length of RA is given by:

[tex]RA = \sqrt{(1.5 - (-5))^2+(1.5 - (-5))^2} = 9.19[/tex]

Applying the formula, the length of R'A is given by:

[tex]R^{\prime}A = \sqrt{(1.5 - 8)^2+(1.5 - 8)^2} = 9.19[/tex]

Hence the relationship for the length of the segments is:

RA = R'A.

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Using an arithmetic sequence, it is found that the perimeter when 106 triangles are put together is of 108 cm.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

The perimeter of a figure is the sum of the outer sides of the figure. Hence, considering that all sides are 1 cm long, we have that:

Hence the first term and the common difference are given as follows:

[tex]a_1 = 3, d = 1[/tex]

Hence the 106th term of the sequence is:

[tex]a_{106} = 3 + 105 = 108[/tex]

The perimeter when 106 triangles are put together is of 108 cm.

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Answer:

4900

Step-by-step explanation:

70x70=4900

Answer:

1

Step-by-step explanation: