The number of students at the start of the week that had a late library book was 200 students. By the end of the week there were only 80 students with a late library book? Is it a increase or decrease in by what percentage? 

The measure of angle B is 107°.

What do similar triangles mean?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given a triangle, NPZ is similar to triangle HBZ.

Which can also be written as ΔNPZ ≈ ΔHBZ

So, by equating the corresponding angles that are angle P = angle B:

8x-37°=180-(2x-5+42)°

10x=180

x=18°

So, H=36-5=31°

Since the sum of all angles in a triangle is 180°, angle B can be calculated  as

B= 180°-(42+31)°

B=107°

Therefore the measure of angle B is 107 degrees

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1.  Convert lb./acre to grams/acre

2. Use the TKW to calculate seeds per acre.

The imperial system and US customary systems both use acres as a measure of land area.

According to traditional definitions, it is the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1640 of a square mile, 4,840 square yards, or 43,560 square feet, and roughly 4,047 m2, or roughly 40% of an acre.

A declared acre is equal to 4,046.8564224 square metres according to the 1959 international yard and pound agreement. Although the word "acre" is typically spelled out, the abbreviation "ac" is sometimes used instead.

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The linear function that passes through (3,1) and has a slope of -1/2 is defined as follows:

y = -0.5x + 2.5.

The graph of the linear function is given by the image presented at the end of the answer.

The linear function for this problem is defined in slope-intercept format, as follows:

y = mx + b.

In which the coefficients of the function are given as follows:

The slope of the function in this problem is given as follows:

m = -1/2 = -0.5

Hence:

y = -0.5x + b.

The line passing through point (3,1) means that when x = 3, y = 1, and thus the intercept b is obtained as follows:

1 = -0.5(3) + b

1 = -1.5 + b

b = 2.5.

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Christian Mansell (born 9 February 2005) is an Australian racing driver set to compete in the 2023 FIA Formula 3 Championship with Campos Racing. He previously competed in the 2022 Neuroforamina Open Championship for Crypto Tower Racing, finishing in third overall in the standings.

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Answer:

8.25cm²

Step-by-step explanation:

the area of the triangle = (half x base x height )=

(1.5x3)÷2= 2.25cm²

the area of the rectangle= length x width = 3x2= 6cm²

total = 2.25+6= 8.25cm²

The value of the missing length LN of the similar triangles is; LN = 18

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.

In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;

LN/LK = MN/JK

We are told that;

MN is 12 more than LN. Thus; MN = 12 + LN

LK = 33

JK = 55

Thus;

LN/33 = (12 + LN)/55

55LN = 33(12 + LN)

55LN = 396 + 33LN

22LN = 396

LN = 396/22

LN = 18

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The Diwali occurred on 0.408 or 40.8% of the year in 2017.

To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.

Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.

There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.

So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408

So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.

Therefore, Diwali occurred on 0.408 or 40.8%

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The term given to us is 4 , this is a constant number therefore this cannot be regarded as a polynomial.

An expression is said to be a polynomial if it also contains a variable along with constants which are joined with each other through various mathematical operations. These expressions usually have more than one terms.

A polynomial can be of various degrees such as one degree , two degree based upon that they are known as linear , quadratic , cubic polynomial etc. Unlike terms are polynomial terms in which the variables are different and also the same variables with different powers. Contrary terms are two or more terms that are not synonymous.

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Answer:

the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.

Answer:

4 sweets each

Step-by-step explanation:

50 sweets to begin with and eats 10 , so 50 - 10 = 40 left

she then gives 8 to her brother , leaving 40 - 8 = 32 sweets

she then shares 32 equally among her 8 friends , so

32 ÷ 8 = 4

that is each friend got 4 sweets

Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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Answer:

6.2 < x < 26.6

Step-by-step explanation:

The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.

16.4 - 10.2 = 6.2

16.4 + 10.2 = 26.6

Let x = length of third side.

6.2 < x < 26.6

Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.

The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.

Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.

The first $8000 of Bob's taxable income is taxed at 15%:

Tax on first $8000 = $8000 * 0.15 = $1200

The remaining $7000 of Bob's taxable income is taxed at 19%:

Tax on remaining income = $7000 * 0.19 = $1330

Total tax = $1200 + $1330 = $2530

So Bob must pay $2530 in income tax for last year.

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According to the solving by  using substitution method the  x and y are x = 6/5 and y = -8/5 respectively.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.

given equations are 2x+4y = 4 and -2x+ y = -4

Now, simplifying -2x+y = -4

-2x+y = -4

∴ y = -4 + 2x

i.e. y = 2x - 4

By substitution method,

y = 2x - 4 in other given equation 2x+4y = 4,

 2x+4y = 4

 2x+4(2x - 4) = 4

∴ 2x + 8x - 8 = 4

∴ 10x = 4 + 8

∴10x = 12

∴ x = 12/10

∴ x = 6/5

Now ,

substituting x = 6/5 in y = 2x - 4,

 y = 2(6/5) - 4

∴ y = - 8/5

∴ x = 6/5  &  y = - 8/5.

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By using systems of linear equations by elimination, it can be determined that x = 0.5 y +2 and 2.2x-1.8y-1.6=0 are equivalent to x=0.818182 and y+0.727273.

Using elimination, let's fix your system. 0.6 x=1.2+0.3 y, 2.2 x-1.8 y-1.6=0 in the graph, and y=2 x-4, y=1.222222 x-0.88888

Step 1: Divide both sides by 0.6 to find the solution for x = 0.6 x=1.2 + 0.3 y.

[tex]$$\begin{aligned}& \frac{0.6 x}{0.6}=\frac{0.3 y+1.2}{0.6} \\& x=0.5 y+2\end{aligned}$$[/tex]

Let's figure out what x is, 2.2 x-1.8 y-1.6=0.

First, multiply both sides by 1.8 y.

[tex]$$\begin{aligned}& 2.2 x-1.8 y-1.6+1.8 y=0+1.8 y \\& 2.2 x-1.6=1.8 y\end{aligned}$$[/tex]

Add 1.6 to both sides in step two.

[tex]$$\begin{aligned}& 2.2 x-1.6+1.6=1.8 y+1.6 \\& 2.2 x=1.8 y+1.6\end{aligned}$$[/tex]

3. Multiply both sides by 2.2.

[tex]$\frac{2.2 x}{2.2}=\frac{1.8 y+1.6}{2.2}$[/tex]

x=0.818182 y+0.727273

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Length of arc EG = 5.446 degrees and EG = 0.05446 degrees while written in hundredth.

Arc length is defined as the distance of two points along the boundary of a circle or a section of a curve. Arc length is not a straight line.

Arc length is calculated by the following formula.

arc length in radians

s = r Ф

where, r is radius of circle or curve

Ф is the central angle in radians

arc length is degrees

s = Ф×π/180 × r

r is the radius of circle

Ф is the central angle in degrees

π = 3.142

given, central angle EFG = 78 degrees.

EF = 4 units

EF is the radius of the given circle

as per the rules of a circle FG is also a radius

FG = FE = 4 units

Now arc length EG = ∠EFG × π/180 × EF

  Arc length = 78 × 3.142/180 × 4

                    =5.446 units

hence, arc length EG = 5.446 units or 5.446 degrees

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The height of the flag is 18 feets.

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Length is equal to 2 (2 + 3) the sum of the side lengths.

The sum of side length divided by (12) equals (2/5)

12 = 0.4(sum of side length) (sum of side length)

divide both sides by 0.4.

The height of the flag is calculated as side lengths plus length.

Height of flag: (30 – 12) = 18 feet

Therefore, the height of the flag is 18 feets.

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The graph of the given line 2x+3y=6 intersects the Y-axis at (0,2).

For the graph of linear equation to intersect the Y-axis, its X-co-ordinate should be zero or the abscissa is zero as Y-axis as the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

According to the first condition the x-coordinate of the equation should be zero so in equation 2x+3y=6 substituting the value of x as zero  2(0)+3y=6

3y=6  

y=6/3=2

So at point (0,2), the graph of the given line 2x+3y=6 intersects the Y-axis.

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Answer:

When solving an inequality:  you can add the same quantity to each side •you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.

you can add subtract multiply and divide the quantity to each side

But if you’re doing any of those with a negative quantity, the inequality symbol must be reversed

3 x -8> 29

3 x -8 < 29

This expression has no defined meaning. It is not a valid mathematical expression.

− [infinity] [infinity] is not a valid mathematical expression so it has no defined meaning.

The expression − [infinity] [infinity] is not a valid mathematical expression, and thus it has no defined meaning. It is not a valid mathematical expression because it contains two symbols, infinity and negative infinity, which do not interact with each other in any meaningful way. Infinity is a concept that is used to represent an unbounded or infinitely large value, while negative infinity is a concept used to represent a value that is infinitely small. When combined, these two symbols do not represent any meaningful mathematical quantity. Therefore, the expression − [infinity] [infinity] has no defined meaning.

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Quantitative variable are - 2,3,5,7 and Qualitative are 1, 4 ,6

1. Marital status of nurses in a hospital-qualitative

2. Time it takes to run a marathon-quantitative

3. Weights of lobsters in a tank in a restaurant- quantitative

4. Colors of automobiles in a shopping center parking lot- qualitative

5. Ounces of ice cream in a large milkshake- quantitative

6. Capacity of the NFL football stadiums -qualitative

7. Ages of people living in a personal care home- quantitative

Qualitative variables are categorized or labelled to belong to a certain category or group.

There are two types of qualitative variables, Categorical and ordinal.

Categorical variable are those variables that are labelled in non-numeric or numeric form, where the numbers have no value. The order also does not matters. For example, the number on the jerseys of football players. It is not necessary that the player number 1 is actually the best player.

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Use the coordinate plane to graph points, lines, and geometric forms in the different quadrants, and then use the absolute value to determine the distances between them.

What does ordinate math entail?

An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Meaning of a Coordinate Plane. The intersection of the x-axis and y-axis, two perpendicular lines that form a 2D plane known as a coordinate plane.

Which three coordinate systems are there?

Cartesian, cylindrical, and spherical are the three most often used coordinate systems. We'll discuss a cylinder-based coordinate system as well as a cartesian-based one in this chapter.

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Exponential growth on a logarithmic graph looks like a straight line. On a regular graph, the line would appear to be curved, but when plotted on a logarithmic graph, the line appears to be a straight line.

Exponential growth on a logarithmic graph appears as a straight line. This is because the logarithmic scale is a compressed scale, meaning that it takes a large range of values and compresses them into a smaller range. This makes the data easier to read and understand. The straight line occurs because the logarithmic scale is designed to fit the data points more closely, making the line appear linear. This is in contrast to the regular scale, where the line appears curved due to the large range of values being plotted. Thus, exponential growth appears as a straight line on a logarithmic graph.

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Let l be the length of the classroom in feet, and w be the width of the classroom in feet. We know that l + 5 = w and l * w = 84.

We can use these two equations to solve for the length and width of the classroom.

First, we can solve the second equation for l:

l = 84 / w

Substituting this expression for l into the first equation gives us:

84 / w + 5 = w

Expanding the left side of the equation gives us:

84 / w + 5 = w

84 / w = w - 5

84 = w^2 - 5w

w^2 - 5w - 84 = 0

This is a quadratic equation that we can solve using the quadratic formula:

w = (5 + sqrt(5^2 - 4 * 1 * -84)) / 2 * 1

= (5 + sqrt(25 + 336)) / 2

= (5 + sqrt(361)) / 2

= (5 + 19) / 2

= 24 / 2

= 12

Now that we know the value of w, we can substitute it back into the equation l = 84 / w to find the value of l:

l = 84 / 12

= 7

Therefore, the dimensions of the classroom are 7 feet by 12 feet.

The place with the highest temperature is Oslo.

The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .

The new temperature in Moscow is 11 degrees Celsius .

When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.

The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:

= - 4 . 3 - ( - 9 . 5 )

= - 4.3 + 9 .5

= 5. 2 degrees Celsius

The new temperature in Moscow is:

= - 7.9 - 3.1

= 11 degrees Celsius

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Answer:

120

Step-by-step explanation:

First, divide 115 by 6:

115/6 =

(114 + 1)/6 =  ==> 114 is a multiple of 6

114/6 + 1/6 = ==> distribution property

19 + 1/6 =  ==> simplify

19 1/6 ==> the smallest integer greater than 19 1/6 is 20

Hence, multiply 20 by 6 to get 120.

Answer:

if its for factor, we have (x+1)(x+5), if its for formula, its x=-1, -5

Step-by-step explanation:

A  range of values which is not a possible for scale factor (k): k = 0

We know that the scale factor is the number (also called the conversion factor) which is used to change the size of a figure without changing its shape.

It is used to expand or compress the size of an object.

The scale factor formula is:

Scale factor = Dimensions of the transformed shape ÷ Dimensions of the original shape

If the scale factor k > 1, the object is enlarged.

If the scale factor is 0< k <1, the object is compressed.

If the scale factor is k = 1, the shape of object remains the same.

And the scale factor cannot be zero.

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