Determine the number of solutions:
36 - 7x = -7(x - 5)

The value of the percent increase in the value of W is 50%.

How can I determine the ratio between two quantities?

When the ratio of each of the two quantities' values is equal, the two quantities are said to be proportionate. It comes in two varieties: direct and indirect. The ratio is more than one for direct relations whereas it is less than one for indirect relations.

The relationship provided in the issue can be expressed as,

W ∝ X

X now has a new value when it is increased by 50%:

X + 50% × X

⇒ X + 50/100 × X = 3X/2

Assume that X and W now have values of X1 and W1, respectively.

Consequently, they are related in the following ways:

W ∝ X

⇒ 3/2W ∝ 3/2X

⇒ 3/2W ∝ X₁

W's value is increased by 3/2W - W, which equals 1/2W.

The percentage growth

⇒ (1/2W)/W × 100%  = 50%

Hence, the percent increase is obtained as 50%.

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The heights of the two legs (a and b) of a right triangle are equal. Ha = b and hb = an as a result. The height of the hypotenuse is hc. The intersection of a triangle's three altitudes occurs at the orthocenter H, which for a right triangle is located on the vertex C of the right angle.

A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.

The extended base of the altitude is the name given to this line that contains the opposing side.

The foot of the altitude is the point at which the extended base and the height converge.

Each leg (a and b) of a right triangle has the same altitude as its opposite leg.

As a result, ha = b and hb = a.

The hypotenuse rises to an altitude of hc.

The orthocenter H, which for a right triangle lies on the vertex C of the right angle, is where the three altitudes of a triangle intersect.

Therefore, the heights of the two legs (a and b) of a right triangle are equal. Ha = b and hb = an as a result. The height of the hypotenuse is hc. The intersection of a triangle's three altitudes occurs at the orthocenter H, which for a right triangle is located on the vertex C of the right angle.

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The Side-Side-Side (SSS) criterion states that two triangles are similar if "sides of one triangle in two triangles are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and so the two triangles are comparable."

Look at the triangles in the picture below. We can observe that the triangles' three sets of side pairs are all congruent. "SSS" or "side-side-side" are other names for this. Two triangles are congruent if they have three pairs of congruent sides, according to the SSS requirements for triangle congruence.

Congruence Rule Theorem for SSS

Two triangles are said to be congruent if the corresponding three sides of one triangle match the corresponding three sides of the other triangle exactly.

We shall now demonstrate the aforementioned theorem.

Given: [tex]\triangle A B C[/tex] and [tex]\triangle P Q R[/tex] such that AB=PQ, BC=QR and AC=PR.

To prove: [tex]\triangle A B C \cong \triangle PQR[/tex]

Construction: Let BC be the longest side of [tex]\triangle A B C[/tex] and so QR is the longest side of [tex]\triangle P Q R.[/tex]

Draw PS so that [tex]\angle R Q S=\angle C B A[/tex] and [tex]\angle Q R S=\angle B C A[/tex].

Join SQ and SR.

In [tex]\triangle ABC[/tex] and [tex]\triangle SQR[/tex],

BC=QR Given

[tex]\angle C B A=\angle R Q S[/tex] By construction

[tex]\angle B C A=\angle Q R S[/tex] By construction

[tex]\triangle A B C \cong \triangle SQR[/tex] By ASA congruence

[tex]\angle A=\angle S[/tex] By CPCTC

AB=SQ By CPCTC

AC=SR

Now, AB=PQ and AB=SQ => PQ=SQ

Similarly, AC=PR and AC=SR => PR=SR

Hence, [tex]\triangle ABC \cong \triangle PQR,[/tex]

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Answer:

13

Step-by-step explanation:

Divide 500 by 40 to find the amount of buses you need

500 ÷ 40 = 12.5

BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people

you'll need 13 buses

Answer:

13 buses

Step-by-step explanation:

12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.

The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.

The size of the array is N – 1. So the sum of n elements, that is the sum of numbers from 1 to N can be calculated by using the formula N * (N + 1) / 2. Now find the summation of all elements in the array and subtract it from the summation of first N natural numbers, the value obtained will be the value of the missing element.

The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.

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The number of oranges needed to make 3quarts of oranges juice is 20oranges

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 4 girls you could write the ratio as: 1 : 4(for every one boy there are 3 girls). This also means that for 2 boys there will be 6 girls.

Similarly 5 oranges is needed to make 3 cups of juice. it can also be put in like 5:3

to make 3quarts,

2cups = 1pint

2pints = 1quart

therefore 4 cups = 1quart

3 quart = 3×4=12cups

if 3 cups is from 5 oranges

then 1 cup = 5/3

12cups = 5/3× 12= 20 oranges

Therefore 20oranges will be needed to make 12 cups of juice

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We can reduce the margin of error in an interval estimate of p by doing any of the following except using a planning value p* closer to 0.5.

The breadth of the confidence interval is affected by the following features:

Correct Question:

We can reduce the margin of error in an interval estimate of p by doing any of the following except ____.

increasing the sample size

using a planning value p* closer to 0.5

increasing the level of significance

reducing the confidence coefficient

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The 3 consecutive odd numbers whose sum will be 51 are  16, 17, 18.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Let the numbers be x, x+1 and x+2.

Then the sum is : x + x+1+ x+2 = 3x + 3

3x + 3 = 51 (given)

3x = 51 – 3 = 48

x = 48 ÷ 3

x = 16

∴

Hence , the 3 consecutive odd numbers whose sum will be 51 are  16, 17, 18.

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The value of the following expression is true.

Expressions include operators and can consist of any set of variables and constants that can be evaluated to produce a result. Relational expressions are used in decision-making to compare operands and evaluate to 1 (true) or 0. (false).

If a logical expression is true when it is evaluated by C++, it returns an integer value of 1; if it is false, it returns an integer value of 0. Any value other than zero is treated as true in C++, while a value of zero is considered false.

Correct Question :

Suppose x is 5 and y is 7. Choose the value of the following expression: (x ! = 7) & & (x <= y)

a. false

b. true

c. 0

d. null

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Whole Numbers are the numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}.

Whole Numbers

Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.

Addition , Subtraction , Division and multiplication are also possible with the whole numbers as they are also numbers . Addition and Multiplication are closed which means the sum and multiplication of two numbers is also a whole number whereas Subtraction and Division are unclosed.

We know that natural numbers refer to a set of counting numbers starting from 1, 2, 3, 4 and so on. In simple words, whole numbers are a set of numbers without fractions, decimals, or even negative integers.

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Equiangular triangle or Equilateral triangle have  all the sides equal and all the angles are also equal.

A triangle that has equal-length sides is known as an equilateral triangle in geometry. The three angles that lie across the three equal sides are also equal in size since the three sides are also equal.

With each angle measuring 60 degrees, it is also known as an equiangular triangle.

An equilateral triangle has three interior angles that are all equivalent to one another and each measure 60 degrees in the basic Euclidean geometry. The term "regular triangle" is also used to describe this polygon because it is a regular polygon. The exceptional case of an isosceles triangle with three equal sides and angles is an equilateral triangle.

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Answer:

[tex]\frac{2}{15} (3+\sqrt[3]{3})[/tex]

or

[tex]\frac{6+2\sqrt[3]{3} }{15}[/tex]

You can rationalize the denominator to simplify the answer so many different ways.

Step-by-step explanation:

Simplify the radicals.

A dilation is a type of transformation that enlarges or reduces a figure.It is also called pre image.To create new figure is called image.For this purpose we can use scale factor ,r how much bigger or smaller the dilation image will be compared to pre-image.

It is a transformation which is used to resize the image.It is used to make objects smaller or greater.But there is no difference in the size of the shape.The pre -image and image is not congruent.

For this purposes we use scale factor.

When you dilates a image the scale factor find that how much image will be smaller or larger.

.If the scale factor is between o0 and 1 .Then image is smaller than preimage.Dilation with a scale factor between 0 and 1 i called transformation.

.if the scale factor is greater than 1.Then image will be larger than the preimage.

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(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial. A degree three polynomial might be referred to as a cubic polynomial.

A degree three polynomial might be referred to as a cubic polynomial. In other words, the number three will be the largest exponent of the variable in a cubic polynomial. A cubic polynomial would therefore have the generic form ax3+bx2+cx+d, where a ≠0.

here

Let p(x)=[tex]x^{3}[/tex]−7x+6

From figure, we have p(1)=0

Thus, (x−1) is a factor of p(x)

The other factor is [tex]x^{2}[/tex]+x−6

=(x+3)(x−2)

Therefore, [tex]x^{3}[/tex]−7x+6 =(x−1)(x+3)(x−2)

(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial.

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The Median of the following sample 3 4 6 7 8 9 10 12 13 15 is 8.5.

One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.

When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:

sort the data in ascending or descending order.

If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.

The average of the top two observations is the same as the median of the data given (as determined in step 2).

Median = [tex]\frac{1}{2} [(\frac{n}{2} ) + (\frac{n}{2}+1 )][/tex].

Here n = 10, So [(10/2) + (10/2 + 1)]/2.

=> Median = 8.5.

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Yes, the equation has real roots. By completing the square, we can make the equation in the form of ax^2+bx+c=0. Then, we can use the quadratic formula to solve for x. The discriminant of this equation is b^2-4ac = 10-60 = -50, which is negative, so the equation has two real roots.

Yes, the equation 3x^2+2√5x has real roots. By expanding the equation, we get 3x^2+2x√5=0. We can use the quadratic formula to solve for x. First, we need to make the equation in the form of ax^2+bx+c=0. To do this, we complete the square. We divide both sides of the equation by 3, giving us x^2+2/3*√5x=0. Then, we add (2/3*√5/2)^2 to both sides, giving us x^2+2/3*√5x+(2/3*√5/2)^2= (2/3*√5/2)^2. Simplifying, we get x^2+2/3*√5x+5/12=0. This is now in the form of ax^2+bx+c=0, with a=1, b=2/3*√5, and c=5/12.

Now, we can use the quadratic formula to solve for x

x = [-2/3*√5 + √(-50/3)]/2

x = [-2/3*√5 - √(-50/3)]/2

Therefore, the two real roots of the equation are

x = [-2/3*√5 + √(-50/3)]/2 and

x = [-2/3*√5 - √(-50/3)]/2.

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The relationship between the volume of a sphere and the volume of a cylinder is said to be that the volume of any sphere is 2/3rd of the volume of any with equal radius and height which is equal to the diameter.

Assuming a cylinder with radius r, height h.

We are aware that the cylinder-volume formula is,

V₁ = π * r² * h

Consider a sphere with radius r₁.

We know that the formula for the volume of sphere is,

V₂ = 4/3 * π * r₁³

If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r₁ = r and h = 2r

V₂ = 4/3 * π * r³

And V₁ = π * r² * (2r)

V₁ = 2 * π * r³

V₁ = 2 * 3/4 * V₂

V₁ = 3/2 * V₂

Volume of cylinder = (3 / 2) *  Volume of sphere

Therefore, the Volume of a sphere = 2/3 * Volume of a cylinder

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The option that would not be a lurking variable in the above scenario is c.) the day of the week that stephanie attends service

a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.

When researching the relationship between two or more variables, we occasionally neglect the influences on the relationship that exist outside of these two variables. These are also known as lurking variables or extraneous variables. These significantly impact the relationship. Lurking variables are those that were not taken into consideration for the study but have an impact on the two studied variables.

The day of the week will not be a lurking variable since we are talking about the number of churches and bars. Hence, Option c is correct.

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Answer:

Step-by-step explanation:

a.) Correct.

A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely street name length is related to the number of bars in a given area.

The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = CA / sin B

The measure of the third angle is given as,

∠A + ∠B + ∠C = 180°

35° + 90° + ∠C = 180°

∠C = 55°

Then the measure of the side c (AB) is calculated as,

AB / sin C = BC / sin A

c / sin 55° = 10 / sin 90°

c = 8.2

Then the measure of the side b (AB) is calculated as,

AC / sin B = BC / sin A

b / sin 35° = 10 / sin 90°

b = 5.7

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Answer:

30 inches

Step-by-step explanation:

The longest piece (15 in) is represented as 5 in the ratio, so we can find what one unit is. We can do 15÷5=3, so one unit is 3 inches. We could multiply each of them by 3 and add them up, but there's a simpler way. We can find the total of the ratio, 2+3+5=10. So, we can do 3x10=30 inches. Therefore, the length of the stick is 30 inches.

95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

What is proportional limit?

The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.

To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:

lower confidence bound = sample mean - (t-value * standard error)

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

              [tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]

To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.

Substituting these values into the formula for the lower confidence bound, we get:

lower confidence bound = 8.52 - (1.725 * 0.19)

= 8.52 - 0.327

= 8.19

So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.

Hence,  95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

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Answer:

May be minus

Step-by-step explanation:

minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32

The four parts of a line graph is Tittle, Legend, Data, Y-axis, X-axis and Line.

A line graph—also called a line plot or a line chart—is a graph that makes use of lines to connect individual data points. A line graph presentations quantitative values over a distinctive time of language. In finance, line graphs are normally used to depict the ancient rate action of an asset or security. Line graphs may be compared with different visualizations of facts which includes bar charts, pie charts, and (in buying and selling) candlestick charts, amongst others.

Line graphs might also vary relying non-obligatory capabilities or formatting. the very best-excellent, easiest to understand line graphs have the subsequent characteristics:

Line graphs may additionally have a name above the graph to succinctly provide an explanation for what the graph is depicting except we provide a user with written context, the user will regularly depend on the title to better understand what information is being pulled in. The title can also mainly name out a time frame or limits to the information.

The legend explains what every based variable is and the way to distinguish extraordinary units of data. In the instance above, every dependent variable is marked with its own coloration. The field that explains what each coloration method is the legend.

Each object of facts on a line graph is a reference to a distinctive supply that ties the structured variable to an unbiased variable. that is the records on our graph; it is the item that creates the dots that get linked to form the lines to our chart. There may be a couple of units of statistics blended into a single graph. To make sure statistics is blanketed and correct, companies might also have precise information integrity analyst or similar positions to screen database hobby.

The x-axis is the set of records that runs along the horizontal, flat component at the bottom of the road graph. In most line graphs, the x-axis could be related to time, whether it's far the distinctive months in a year or the wide variety of weeks which have exceeded considering that a product launch.

The y-axis is the set of data that runs alongside the vertical, left-aspect of the graph. some iterations of line graphs have this set of data on the proper. In any case, these numbers count number the items being measured. The graph might also begin at 0, even though there are instances wherein it makes more experience to begin at a higher variety.

Finally, the line. the road connects all statistics points within a single structured variable. This line's motion shows the growth and reduce of information throughout time. it may also easily be as compared towards different strains so long as all facts units are being measured over similar periods of time. Although overly simplified, this line can speak to management what actions need to be taken to enhance operations or strategic planning.

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To find the interest rate, we can use the formula for simple interest:

I = P * r * t

Where I is the interest, P is the principal (the amount of money in the account), r is the interest rate, and t is the time (in years).

We know that I = $480, P = $2,000, and t = 2 years.

Plugging these values into the formula, we get:

$480 = $2,000 * r * 2

Dividing both sides by $2,000 * 2, we get:

r = $480 / $2,000 * 2

r = 0.12

So, the interest rate is 0.12, or 12%.

The coefficient of  y² in the expression 3y²+ 4x is 3.

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.

Firstly,

The given equation is 3y²+ 4x

To find : The coefficient of y²

The coefficient is nothing but the number beside the variable.

In the equation 3y²+ 4x, the number beside the variable y² is 3 and it is termed as coefficient of y² which is 3.

As we can see that the term that is in multiplication with y² is 3. Similarly, the term that is coefficient of  x is 4.

Hence, the coefficient of y² in the equation is 3.

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The end behavior of a polynomial function can be determined by examining the leading coefficient and degree of the polynomial. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. If the leading coefficient is negative, the graph will decrease without bound as the x-values increase.

The end behavior of a polynomial function depends on the equation of the function. The degree of a polynomial is the highest power of the variable, and the leading coefficient is the coefficient of the term with the highest degree. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. This is because the terms in the equation with positive coefficients will become increasingly larger than the terms with negative coefficients as the x-values increase. On the other hand, if the leading coefficient is negative, the graph will decrease without bound as the x-values increase. This is because the terms in the equation with negative coefficients will become increasingly larger than the terms with positive coefficients as the x-values increase. In addition, the degree of the polynomial can also affect the end behavior of the graph. If the degree is even, the graph will not have an extreme point. However, if the degree is odd, the graph will have an extreme point. The extreme point will be a maximum or a minimum depending on the sign of the leading coefficient.

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Answer:

Bookcase A

Step-by-step explanation:

Bookcase A

1 half = 35 book

4 half = 140 books

So, bookcase A can hold 140 books

Bookcase B

1 half = 26 books

5 half = 130 books

So, bookcase B can hold 130 books

So, Mary should buy bookcase A

Answer:

Bookcase A is the answer

Step-by-step explanation:

Mary has 138 books

Bookcase A = 4 shelves holds 35 books per shelf

= 4 * 35=140

Bookcase B = 5 shelves holds 26 books per shelf

= 5 * 26=130

He should buy Bookcase A, it has enough space for his books

An example of continuous data is the temperature of a room over time. It can change gradually, or even rapidly, but the data is always changing.

Continuous data is data that can take on any value within a given range. It can be measured on an infinite scale and can have an infinite number of values. An example of continuous data is the temperature of a room over time. This data can change gradually or rapidly, but it is always changing. Continuous data can be measured directly, such as measuring the temperature of a room with a thermometer, or indirectly, such as measuring the temperature of a room through observation. Continuous data can also be used to describe physical or psychological phenomena, such as measuring a person’s heart rate over time or measuring the concentration of a chemical in a solution. Continuous data is often used in scientific research, as it allows researchers to observe trends and correlations over time.

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Multiplicity is a mathematical concept related to the roots of a polynomial equation.

It is defined as the number of times a given root is repeated in the polynomial equation.

The formula for calculating the multiplicity of a root is :

Multiplicity = n-(degree of the polynomial equation)

where n is the order of the root and the degree of the polynomial equation is the highest exponent in the equation.

For example, if the polynomial equation is 3x^2 + 4x + 2 = 0 and the root is 2, then the multiplicity of the root is calculated as follows:

Multiplicity = n - (degree of the polynomial equation)

Multiplicity = 2 - 2

Multiplicity = 0

This means that the root 2 is not repeated in the polynomial equation and therefore has a multiplicity of 0.

In another example, if the polynomial equation is 4x^3 + x^2 + 6x + 12 = 0 and the root is 2, then the multiplicity of the root is calculated as follows:

Multiplicity = n - (degree of the polynomial equation)

Multiplicity = 2 - 3

Multiplicity = -1

This means that the root 2 is repeated in the polynomial equation and therefore has a multiplicity of -1.

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Answer:

Step-by-step explanation: