I) if y varies directly as x and inversely as the square root of z, and y = 1/6 when x = 20 and z = 6, determine y when x = 14 and z = 5

The value of x and y in the diagram are 26° and 9° respectively.

Two adjacent angles formed a linear pair.

The linear pair property:

The sum of the angle measure of both the angles is 180°.

Given:

Using linear pair theorem,

(5x - 17)° + (3x - 11)° = 180°.

8x - 28°= 180°

8x = 180° + 28°

8x = 208°

x = 208/8

x = 26°

The value of x is 26°.

Now,

3x - 11° = 3×26°-11°

           = 67°

Linear pair theorem,

67° + 90° + (2y+5)° = 180°

157°+2y+5° = 180°

2y + 162° = 180°

2y = 180° - 162°

2y = 18°

y = 9°

The value of y is 9°.

Therefore, the value of x is 26° and y is 9°.

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The complete question is given in the attached image.

a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram

b) For this one the class width is given to be the following: class with = 10 .  See the attachment for table

c)  See the attachment for the graph

What is histogram ?

A histogram is a collection of rectangles with bases and the gaps between class boundaries. All of the rectangles are contiguous, and each rectangle bar represents some kind of data. Rectangles have heights that are proportionate to the corresponding frequencies for both related and dissimilar classes.

a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram

b) For this one the class width is given to be the following: class with = 10 .  See the attachment for table

c)  See the attachment for the graph

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The lower bound for the number of minutes that it takes for all people to leave is of:

70 minutes.

At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:

29,750.

(as 29749 would be rounded to 29,700).

At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:

424 people per minute.

(as 425 people would be rounded to 450).

Hence the time it would take is obtained applying the proportion as follows:

29750/424 = 70 minutes.

(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).

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On solving the provided question we can say that here in null hypothesis a negative relationship; as anxiety rises less items are remembered

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

here,

in null hypothesis a negative relationship; as anxiety rises less items are remembered

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Therefore , the solution of the given problem of fraction comes out to be 4((2x)³ + (3y)³) /xy.

To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the fraction to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the exponent or population of a complicated fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces. For instance, 12 is used to denote half of a total number or item.

Here,

Given : 32x²/y + 108y²/x

=> (32x³+ 108y³ ) /xy

=>  4(8x³ + 27y³) /xy

=> 4((2x)³ + (3y)³) /xy

Therefore , the solution of the given problem of fraction comes out to be

4((2x)³ + (3y)³) /xy.

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Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.

You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.

Finding the distance and the time is necessary to calculate speed.

In this situation, you must deduct mile marker 88 from 121 to determine the distance.

121 - 88 = 33mile

Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.

The next step is to divide the distance by the time: 33/0.5 = 66 mph.

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Answer: c = P - a - 5

Step-by-step explanation:

P= a + 5 + c

P - a - 5= c

The information you gave was presented as a table with three columns: value, x-coordinate, and y-coordinate.

You would need to make a graph with the x-coordinate acting as the horizontal axis and the y-coordinate acting as the vertical axis in order to plot this data point. The size or colour of the data point would serve as a representation of the value.

Here is an illustration of a data point plot:

[tex]x | 12 | 14 | 14 | 34 \\ y | 1 | 1 | 3 | 3 \\ v | 1 | 1 | 3 | 3[/tex]

The value at the position (12,1) will be 1, the value at the point (14,1) will be 1, the value at the point (14,3) will be 3, and the value at the point (34,3) will be 3. It's vital to remember that the values on the graph can be depicted by many colours or shapes.

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Answer:

48 units.

Step-by-step explanation:

Since the triangles are similar (proportional), their dimensions are increased at the same ratio at any point, which means their perimeter too. So the base of the larger triangle is twice as long as the base of the smaller triangle.

The perimeter of the smaller triangle is 10 + 6 + 8 = 24 units.

24 * 2 = 48. Because the ratio of increase is 2:1 from the bigger triangle to the smaller triangle.

Hope you could understand this,

The Boolean dual are created by replacing AND operator with OR operator and the complement is defined as the negation of the statement .

What is Boolean Expression ?

The Boolean Expression is defined as a logical statement that is either TRUE or FALSE . It compares data of any type as long as both the parts of  expression have same basic data type.

The Dual of Boolean Expression are calculated by simply replacing AND operator with OR and OR operator with AND .

The Compliment of Boolean Expression  is defined as negation of  variables with replacement .

For Example : if the statement is [tex]A+B[/tex] ,

then the dual will be [tex]AB[/tex] and the compliment will be [tex]A'B'[/tex] .

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Answer:

x = 60

Step-by-step explanation:

Let the two opposite angles be equal and let's call them y.

Because of the theory of angles on a straight line 120 +y = 180

y = 60

Because of the theory of angles on a straight line 2x + y = 180

2x + 60 = 180

2x =  120

x = 60

Alternatively. (also a lot easier)

120 and 2x are opposite angles so they are equal and so;

2x = 120

x = 60

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Answer: 23

Step-by-step explanation:

Answer: $49

Step-by-step explanation:

2.5% of 40 = 1, 9x1= 9, 40+9 = $49

Answer:

$35.97

Step-by-step explanation:

33 × .09 = 2.97

33 + 2.97 = $ 35.97

For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm

In general, the term proportion refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal.

The length of the house on the map is calculated using equality in proportions as follows

The required proportion is

= height of the house / length of the house

= 6 / 4.5

= 4/3

Using this proportion, the length of the house in the drawing is

= 30 mm / 4/3

= 22.5

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On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, the equation is -

1200=300+5x

900 = 5x

x=180

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The scale factor 5/2 takes hexagon J to hexagon K.

From the given two Hexagon's K and L, the Hexagon K is copy to Hexagon K.

The scale factor = the ratio of edges

Scale factor = 20/8 = 30/12 = 5/2

Hence, the scale factor 5/2 takes hexagon J to hexagon K.

Complete question:

Complete question is attached below.

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N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.

An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.

Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.

Now we solve

3n+4 <19

3n+4-4<19-4

3n<15

n<5

so n is less than and equal to 5 it will be {3, 4, 5].

10n/[tex]n^{2}[/tex]+16  >1

10n> [tex]n^{2}[/tex] +16

0> [tex]n^{2}[/tex]-10n +16

0>[tex]n^{2}[/tex] -8n -2n +16

0> n(n-8)-2(n-8)

0> (n-8) (n-2)

So         n-2<0          n-8<0

             n<2              n<8

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By using the triangular inequality, we will get the possible lengths:

a) 6km < x < 16km

b) 0mi < x < 24mi

c) 15yd < x < 30yd

If A, C, and D are the lengths of the sides of a triangle, then the triangular inequality says that:

A + C > D

A + D > C

C + D > a

Now, if the two sides are 5km and 11 km, and the other side is x, then we can write:

x + 5km > 11km

x + 11km > 5km

11 km + 5 km > x

From these inequalities we can get:

16km > x

x > 11km - 5km

x > 6km

Then the possible lengths of the third side are:

6km < x < 16km

b) Now the sides are 12 mi and 12mi, then the inequalities are:

x + 12mi  > 12mi

12mi + 12mi > x

The first one gives:

x > 0mi

The second:

24mi > x

The possible lenghts are 0mi < x < 24mi

c) 25 yd and 10 yd

Here we will get:

25yd + 10yd > x  ----- >  30yd > x

x + 10 yd > 25yd -------> x > 15yd

The possible lengths are:

15yd < x < 30yd

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On solving the provided question we can say that - and a lines need only two points to drawn; so, yes we can draw a line

A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line (Casey 1893)

here we have,

2 points

(1,5) and (4,5)

and a lines need only two points to drawn,

so, yes we can draw a line

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The length of the sides of ΔABC are; AB = 2√5, BC = √13, and AC = √17

The length of the sides of ΔDEF are; DE = 2√5, EF = √13, and DF = √17

By the SSS Congruence Theorem, ΔABC ≅ ΔDEF

We are given the coordinates of Triangles ABC and DEF as;

A(5, 3), B(7, 7), C(9, 4)

D(-8, 6), E(-12, 8), F(-9, 10)

The formula for distance between two coordinates is;

Distance = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

AB = √[(7 - 3)² + (7 - 5)²]

AB = √20

AB = 2√5

Similarly;

BC = √[(4 - 7)² + (9 - 7)²]

BC = √13

AC = √[(4 - 3)² + (9 - 5)²]

AC = √17

Likewise;

DE = √[(8 - 6)² + (-12 + 8)²]

DE = √20

DE = 2√5

Similarly;

EF = √[(10 - 8)² + (-9 + 12)²]

EF = √13

DF = √[(10 - 6)² + (-9 + 8)²]

DF = √17

Since the corresponding sides of the two triangles are equal and as such they can be said to congruent by SSS Congruency.

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Zero is the middle point of a number line.

On the number line, all positive (natural numbers) numbers are on the right side of zero, while all negative numbers are on the left. A number's value lowers as we turn to the left. As an illustration, 1 is greater than -2.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point. [1]

The integers are frequently represented as specially designated, uniformly spaced dots on a line. It is frequently employed as a teaching tool for basic addition and subtraction, particularly when negative numbers are involved.

The number line may also be referred to as a real line or real number line in advanced mathematics.

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Answer:

7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.

Answer: 907.46 inches squared

Step-by-step explanation:

The formula for the area of the circle is:

[tex]A = \pi r^{2}[/tex]

In this question, pi is 3.14. The radius of a circle is half of its diameter. So:

[tex]\frac{34}{2} =17[/tex]

Plug these values into the equation:

[tex]A = (3.14)(17)^2[/tex]

Simplify:

[tex]A = 907.46[/tex]

The area of the circle is 907.46 inches squared.

'x' is the only variable in the provided polynomial. As a result, the polynomial  4x² - 3x + 7  has one variable.

A polynomial is an expression in mathematics made up of variables (sometimes referred to as indeterminates) and coefficients that only employs the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that combines variables, constants, and exponents utilizing addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

given

'x' is the only variable in the provided polynomial. As a result, the polynomial  4x² - 3x + 7  has one variable.

The following list includes a few examples of polynomials with one variable: x+2. x2+3x+2.

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The value of y from the equation is y = 5

The measure of RS = 38

The measure of ST = 18

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , on the number line , the measures of the sides are

The measure of RS = 7y + 3   be equation (1)

The measure of ST = 2y + 8   be equation (2)

The measure of RT = 56

Now , from the line segment ,

RT = RS + ST   be equation (3)

Substituting the values in the equation , we get

7y + 3 + 2y + 8 = 56

On simplifying the equation , we get

9y + 11 = 56

Subtracting 11 on both sides of the equation , we get

9y = 45

Divide by 9 on both sides of the equation , we get

y = 5

Substitute the value of y in equations (1) and equation (2) , we get

The measure of RS = 7 ( 5 ) + 3 = 38

The measure of ST = 2 ( 5 ) + 8 = 18

Hence , the equations are solved and the value of y = 5

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Answer:

Step-by-step explanation:

Let angle A = w - 15 degree , angle B = -w + 1 degree and angle X = w + 34 degrees then:

We know that the exterior angle of a triangle is equal to the sum of two interior opposite angles.

therefore, w + 34 = w - 15 + (-w +1)

w + 34 = w - 15 - w + 1

w = -15 - 34 = - 49 degrees

since angle cannot be negative

therefore w = 49 degrees

The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.

What is a differential equation?

A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.

The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Given,

    [tex]\frac{dy}{dx} = xy^{4}[/tex]

a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]

In quadrant II, the values of x < 0 and the values of y >0.

So  [tex]\frac{d^{2} y}{dx^{2} }[/tex] =  [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.

Therefore the concavity is up for of all solution curves of the given differential equation.

b)

         [tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]

      Now it is given that initial condition is f(4) = -1

   So substituting x =4 and y = -1 is the above equation to find c, we get

        [tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]

Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.

  [tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]

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well, let's take a looksie, hmm the sector is really a sector with a central angle of 90°, wait a second!! a circle has a total of 360°, so 90°+90°+90°+90° = 360°, so 90°is really just one quarter that of a circle.

Now, if we just get the whole area of the circle, then grab only one quarter of that, we'll be set, yeahhhh!!

[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies A=\pi (9)^2 \\\\\\ \stackrel{\textit{one quarter of that}}{\cfrac{1}{4}\cdot \pi (9)^2}\implies \cfrac{81\pi }{4}\implies \cfrac{81(3.14)}{4} ~~ \approx ~~ \text{\LARGE 63.6}[/tex]

The original amount placed in the account is $320.

What is simple interest ?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.

Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.

The interest earned is calculated as follows:

I = P*r*t

Where:

I = Interest

P = initial principal balance

r = interest rate

t = time

Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.

Substituting in the formula:

288 = P*0.075*12

Calculating:

288 = 0.9P

Dividing by 0.9:

P = $320

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