Hal sold a box of 30 books at a yard sale for a total of $62.16. He sold the paperback books for $1.78 each and sold the hardcover books for $2.51 each.
Which system of equations can be used to determine the number of $1.78 paperback books, x, and the number of $2.51 hardcover books, y, that were
sold at the yard sale?

In the given figure , the measure of angle p is 41 degrees.

A quadrilateral is a closed figure that has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

It is given that the kite is shares a side with an equilateral triangle to form a new quadrilateral.

The side of kite which is attatched to triangle contains an angle of 79 degree.

the other end of side which is attatched to the triangle contains angle of 120 degree because it is attatched to the side of triangle which makes a straight line and the triangle is having each angle of 60 degrees.

So, the angle opposite to it will also be of 120 degrees.

Now in the kite, the angles are,

79+120+p+120=360

p=360-319

p=41 degrees

Hence, the measure of angle p is 41 degrees.

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The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Let 'x' be the number of people and 'y' be the total cost.

From the table, the two points are (6, 52) and (9, 58). Then the equation of the line is given as,

(y - 52) = [(58 - 52) / (9 - 6)](x - 6)

y - 52 = 2x - 12

y = 2x + 40

The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.

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According to hing theorem, the following inequalities describe each triangle:

According to Euclidean geometry, the hing theorem states that if two triangles with two pairs of congruent sides and the former triangle has larger internal angle, then the third side of the former triangle is longer than the third side of the latter triangle.

Mathematically speaking, the relationship between the third can be expressed in terms of inequalities. Now we proceed to express the inequalities in terms of variable x for each case below:

The letter e has been eliminated from hing[e] due to profanity detector.

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The Probability that all four of the light bulbs work is 0.004 approx.

The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:

P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)

P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25

P(all 4 bulbs) = 0.25^4

P(all 4 bulbs) = 0.00390625

So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.

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Answer:

B.y=(x+2)

Step-by-step explanation

Multistage sampling is a probability sampling technique that involves sampling in stages or multiple steps. In this technique, a large population is divided into smaller subgroups, and then a random sample is selected from each subgroup.

Here is an example of multistage sampling:

Suppose we want to conduct a study on the prevalence of a certain disease among high school students in a particular country. The population of high school students in the country is very large, so it is not feasible to sample all of them. Instead, we can use multistage sampling to select a representative sample.

In the first stage, we randomly select a certain number of schools from different regions of the country. Let's say we select 20 schools.

In the second stage, we randomly select a certain number of classes from each of the selected schools. Let's say we select 2 classes from each of the 20 schools, resulting in a total of 40 classes.

In the third stage, we randomly select a certain number of students from each of the selected classes. Let's say we select 10 students from each of the 40 classes, resulting in a total of 400 students.

This process of selecting a sample in stages is an example of multistage sampling. By selecting schools, classes, and students in a random and systematic way, we can obtain a representative sample of high school students in the country, which can be used to estimate the prevalence of the disease.

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The required probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.

Normal distributions can be altered to standard normal distributions by the formula:

Z = (X - μ)/σ

The difference in diameter between the lid and cup, D = L - C, is also a normal distribution with mean μ(D) = μ(L) - μ(C) = 3.98 - 3.96 = 0.02 inches and standard deviation σ(D) = √(σ² (L)+ σ²(C)) = 0.03 inches.

The probability that a randomly selected lid will fit on a randomly selected cup is the probability that D is between 0 and 0.06 inches. To find this probability, we can standardize D using the z-score formula and find the corresponding area under the standard normal curve.

Let z = (D - μ) / σ.
Then, the required probability is,
P(0 < D < 0.06) = P(0 < z < (0.06 - 0.02) / 0.03) = P(0 < z < 2).

We can use a standard normal table or a calculator to find the area under the standard normal curve between 0 and 2. This area represents the required probability. For example, using a standard normal table, we can find that P(0 < Z < 2) = 0.9772.

Therefore, the probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.

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Answer:

10y - 3

Step-by-step explanation:

(y + 9y) + (-10 - 3)

(1 + 9) x y + (-10 - 3)

10y - 13

Answer:is this real

Step-by-step explanation:

1 =727

The difference between a right circular cylinder and a cylinder is that a right circular cylinder has a circular base and is perpendicular to the base, whereas a cylinder can have any shaped base and the sides do not have to be perpendicular to the base.

A right circular cylinder has a circular base and its sides are perpendicular to the base, forming a right angle. This means that the axis of the cylinder is at a right angle to the base.

On the other hand, a cylinder can have any shaped base, such as a rectangle or an ellipse, and the sides do not have to be perpendicular to the base. This means that the axis of the cylinder can be at any angle to the base.

In summary, the main difference between a right circular cylinder and a cylinder is the shape of the base and the angle of the sides to the base. A right circular cylinder has a circular base and perpendicular sides, while a cylinder can have any shaped base and the sides can be at any angle to the base.

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Nul(A) = Nul(B) , Col(A) = Col(B) in integer matrices.

Describe matrix using an example?

A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements.

                                 In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics.

The null space of any matrix A consists of all the vectors

 X  such that Ax = 0

And the column space of a matrix A is the span of its column vectors.

Let  A = [tex]\left[\begin{array}{ccc}1&0&0 \\0&1&0\\0&0&1\end{array}\right][/tex]

Therefore, Nul(A) = {(0,0,0,w ) w∈ Z }

 Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }

By using definition of Null space of matrix and column space of matrix.

 Let B = [tex]\left[\begin{array}{ccc}1&1&0\\0&1&0\\0&0&1\end{array}\right][/tex]        

Nul(A) = {(0,0,0,w ) w∈ Z }

 Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }

Hence Nul(A) = Nul(B) , Col(A) = Col(B)

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Answer:

h = 10.0708 cm

Area of shaded region = 8.1841 [tex]cm^{2}[/tex]

Step-by-step explanation:

r = radius of circle

 = 14 cm

h = perpendicular height of triangle

Use SinФ trigonometric function to determine h

SinФ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

Sin46° = [tex]\frac{h}{14}[/tex]

Cross-multiplication is applied:

∴h = (14)(Sin46°)

   h = 10.0708 cm (Rounded to four decimal places)

Area of sector = [tex]\frac{AngleOfSector}{360^{o}}[/tex] × ([tex]\pi r^{2}[/tex])

                         = [tex]\frac{46}{360}[/tex] × [tex]\pi (14^{2})[/tex]

                         = [tex]\frac{9016}{360} \pi[/tex] [tex]cm^{2}[/tex]
                         = 78.68 [tex]cm^{2}[/tex]

Area of triangle = [tex]\frac{1}{2}[/tex] × (Base of triangle) × h

                           = [tex]\frac{1}{2}[/tex] × (14 cm) × [(14)(sin46°)]
                           = (98)(sin46°)

                           = 70.50 [tex]cm^{2}[/tex]

∴Area of yellow shaded region = Area of sector - Area of triangle

           = {[[tex]\frac{9016}{360} \pi[/tex]] - [(98)(sin46°)]} [tex]cm^{2}[/tex]

           = 8.1841 [tex]cm^{2}[/tex]  (Rounded to four decimal places)

A unit of measurement which is equal to one thousands meters is known as one kilometers.

Therefore, the given units of measurement equal to one thousand meters is called one - kilometers.

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The side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:

sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

QR² = 16² + 30²

QR = √(256 + 900) {take square root of both sides}

QR = √1156

QR = 34

since we have QR = 34, RS = 30, and SQ = 16, then:

Considering the angle Q for the right triangle;

sin Q = 30/34 {opposite/hypotenuse}

cos Q = 16/34 {adjacent/hypotenuse}

tan Q = 30/16 {opposite/adjacent}

Considering the angle R for the right triangle;

sin R = 16/34 {opposite/hypotenuse}

cos R = 30/34 {adjacent/hypotenuse}

tan R = 16/30 {opposite/adjacent}

Therefore, the side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:

sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16.

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[tex]\dfrac{2}{3}x=6[/tex]

[tex]\dfrac{\frac{2}{3}x}{\frac{2}{3}}=\dfrac{6}{\frac{2}{3}}\\\\x=\dfrac{6}{\frac{2}{3}}\\\\x=6\div\dfrac{2}{3}[/tex]

[tex]x=6\times\dfrac{3}{2}\\\\x=\dfrac{18}{2}\\\\x=9[/tex]

x = 9

The statements that are not characteristics of a normal curve are III, IV, and VI. The answer is B.

A normal curve is a bell-shaped probability distribution that is commonly used in statistics. It has several key characteristics that make it useful in modeling real-world data. These include the fact that the mode and median occur at the mean, the curve is symmetric about the mean, and the total area under the curve and above the horizontal axis is equal to 1.

In addition, the normal curve is asymptotic to the horizontal axis on both sides. However, not all normal curves are asymptotic to the horizontal axis on both sides, as this is only true for curves with a finite standard deviation.

Finally, the probability that a normal random variable is equal to a specific discrete value is always zero, since the normal variable is continuous, and the probability that the variable is between two values is given by the area under the curve between those values and the horizontal axis.

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164 pounds is equal to 74.389 kilograms (kg). To convert pounds to kilograms, you can use the conversion factor of 0.45359237, which is the number of kilograms in one pound.

To convert 164 pounds to kilograms, you can use the conversion factor of 0.45359237, which represents the number of kilograms in one pound. Multiplying 164 pounds by this conversion factor gives the result in kilograms. Using this method, 164 pounds is equivalent to 74.389 kilograms. This conversion is useful in many situations, such as when traveling to countries that use the metric system, or when working with scientific measurements that use metric units. Understanding the relationship between pounds and kilograms can help to make conversions easier, and allow for more accurate and consistent measurements across different systems of measurement.

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A yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.

To convert a yearly salary to an hourly rate, you need to divide the annual salary by the number of working hours in a year.

Assuming a typical workweek of 40 hours and 52 weeks in a year, the total number of working hours in a year is:

40 hours/week x 52 weeks/year = 2,080 hours/year

To calculate the hourly rate for a yearly salary of $47,000, you can divide the annual salary by the total number of working hours in a year:

$47,000 / 2,080 hours = $22.60 per hour

Therefore, a yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.

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The value of x from the right triangle is x = 3√11

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDBC

Now , BD is perpendicular to AC

So , the triangles ΔABC and ΔDBC are similar

The measure of BD = x

The measure of AD = 9

The measure of DC = 20

Now , AD / AB = AB / DC

Substituting the values in the equation , we get

9/a = a/20

On simplifying the equation , we get

a² = 180

So , a = 3√20

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Now , the measure of x = √ ( 3√20 )² - ( 9 )²

So , the measure of x = √ ( ( 180 ) - 81 )

The measure of x = √ 99

The measure of x = 3√11

Hence , the measure of x of triangle is 3√11

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Given piecewise function has a jump discontinuity at 0 or x=0 i.e. B.

What exactly is a piecewise function?

A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x≥0 ,

     -x  if x><0)

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

As jump discontinuity is defined as where the endpoint of one segment and the start of the following segment may have the same x coordinate but have different values of f(x). In the piecewise linear function, such a difference is known as a jump discontinuity.

and in the given graph that happened at x=0 or 0.

Hence,

         Given piecewise function has a jump discontinuity at 0.

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The equation of the circle that models the circumference of the circular area the bees were foraging in is given as follows:

(x - 3)² + (y - 7)² = 41.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

A beehive is located at (3, 7), hence the center is located at (3,7), thus:

(x - 3)² + (y - 7)² = r².

The farthest patched was located at (-1,2), hence the radius is obtained as follows:

(-1 - 3)² + (2 - 7)² = r²

r² = 41.

Hence the equation is:

(x - 3)² + (y - 7)² = 41.

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Answer: To compare the costs between the two suppliers, we need to find the total cost of 83 bushes and 22 trees from each supplier.

For Pinedale Plants:

The first order was for 10 bushes and 5 trees, so the cost per bush is $393.6 / 10 = $39.36.

The second order was for 5 bushes and 2 trees, so the cost per bush is $177.32 / 5 = $35.464.

To find the average cost per bush from Pinedale Plants, we can take the average of the two costs: ($39.36 + $35.464) / 2 = $37.412

The total cost from Pinedale Plants for 83 bushes would be 83 * $37.412 = $3108.976

The total cost from Pinedale Plants for 22 trees would be 22 * $35.464 (since the cost per tree was not specified), which is $777.75

The total cost from Pinedale Plants for 83 bushes and 22 trees would be $3108.976 + $777.75 = $3886.726

For Sierra Shrubs:

The cost per bush from Sierra Shrubs is $18.27

The total cost from Sierra Shrubs for 83 bushes would be 83 * $18.27 = $1510.01

The cost per tree from Sierra Shrubs is $41.96

The total cost from Sierra Shrubs for 22 trees would be 22 * $41.96 = $923.12

The total cost from Sierra Shrubs for 83 bushes and 22 trees would be $1510.01 + $923.12 = $2433.13

So, we can see that the total cost from Sierra Shrubs for 83 bushes and 22 trees is lower than the total cost from Pinedale Plants. The company would save $3886.726 - $2433.13 = $1453.596 by ordering from Sierra Shrubs.

Step-by-step explanation:

The circumcenter of the triangle is (-3, -4), units.

The circumcenter is the intersection point of the perpendicular bisectors of sides of a triangle. It is the Centre of a triangle's circumcircle.

For a right-angled triangle, the circumcenter lies on the hypotenuse.

The middle of the horizontal length of the triangle = - 3

The  middle of the vertical length of the triangle = - 4

The circumcenter of the triangle is located at (x, y ) = ( -3, -4 )

Thus, the circumcenter of the triangle is determined from the interception point of the horizontal length and vertical length.

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Based on degree, polynomials can be classified as follows:

Then for number of terms, there are monomials with a single term, binomials with two terms, trinomials with three terms and multinomials with more than three terms.

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The values of x is 13.42, y is 12 and z is 26.83 for right angle triangle ABC shown below.

The Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, is a fundamental property of right triangles.

By the figure apply Pythagorean theorem in right angle ΔABC;

x² + z² = (24+6)² = 30²

x² + z² = 900         (eq. 1)

Apply Pythagorean theorem in right angle ΔAEB;

y² + 24² = z²

z² - y² = 576          (eq. 2)

Apply Pythagorean theorem in right angle ΔAEC;

y² + 6² = x²

x² - y² = 36            (eq. 3)

subtract eq. 2 and 3; then we get,

z² - x² = 540      (add this eq. with eq. 1)

2z² = 1440

z = √720  = 26.83

put in eq. 1

x² + 720 = 900

x = √180 = 13.42  

put x value in eq. 3

180 - y² = 36

y = 12

Therefore, the values of x is 13.42, y is 12 and z is 26.83

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The area of the rectangle is 200 square centimeters

The area of a rectangle can be found by multiplying its length and width. In this case, the width is given as w and the length is given as 2w.

Therefore, the area of the rectangle can be found using the expression 2w^2.

If the width of the rectangle is 10 centimeters, we can substitute this value into the expression for the area to find the area in square centimeters.

Area = 2w^2

= 2(10)^2

= 2(100)

= 200 square centimeters

Therefore, the area of the rectangle is 200 square centimeters

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The prime factorization of 35 is 5 * 7

From the question, we have the following parameters that can be used in our computation:

Number = 35

Express 35 as the product of its factors

So, we have the following representation

Number = 5 * 7

None of the factors 5 and 7 can be further simplified

This means that the prime factorization of 35 is 5 * 7

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Answer:

B isa the answer for me it might be wrong for you or switch them

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the information given, we can calculate the change in the depth of the river between the years 1846, 1847, and 1848.

Change in depth between 1846 and 1847:

The depth of the river dropped from 5 feet in 1846 to 4.9 feet in 1847. The change in depth can be calculated as:

Change in depth = 4.9 - 5 = -0.1 feet

So, the depth of the river dropped by 0.1 feet between 1846 and 1847.

Change in depth between 1847 and 1848:

The depth of the river rose from 4.9 feet in 1847 to 6.4 feet in 1848. The change in depth can be calculated as:

Change in depth = 6.4 - 4.9 = 1.5 feet

So, the depth of the river increased by 1.5 feet between 1847 and 1848.