You bought a magazine for $5 and 20 erasers. If you spent a total of $11, how much did each eraser cost

The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors.

A fraction is a mathematical expression that represents a part of a whole, where a numerator is divided by a denominator. To simplify a fraction, we must divide both the numerator and the denominator by the same number until we cannot divide any further. To simplify a fraction, you must divide both the numerator and denominator by their greatest common factor (GCF).

For example, let's simplify the fraction 24/36. The GCF of 24 and 36 is 12. So, dividing both numbers by 12 will give us the simplified fraction 2/3.

24 ÷ 12 = 2

36 ÷ 12 = 3

Therefore, the simplified fraction of 24/36 is 2/3.

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:670

Step-by-step explanation:

200 + 500 - 30 =

700-30

670

Answer:

150c+40t

Step-by-step explanation:

150 dollars per yearly fee and 40 dollars for each tool bought.

Answer:

false

Step-by-step explanation:

The statement "Construct validity ensures that the measure includes an adequate and representative set of items." is true because researchers can determine the extent to which a measure has construct validity and whether it includes an adequate and representative set of items.

Construct validity is established by accumulating evidence through various means. One way to establish construct validity is by examining the content of the measurement tool. This involves carefully selecting items that represent the construct of interest.

In mathematical terms, we can think of construct validity as a process of creating a mathematical model that accurately reflects the construct being measured. This model should include a comprehensive set of items that adequately represent the construct.

In practice, researchers employ statistical techniques such as factor analysis to examine the relationships between the items and the construct.

Construct validity also involves assessing the convergent and discriminant validity of the measure. Convergent validity refers to the degree to which different items measuring the same construct are positively related to each other.

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The mean, summation of (x - μ), summation of (x - μ)², variance, and standard deviation will be 5, 0, 360, 72, and 8.49, respectively.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation. The standard deviation is given as,

\(\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}\)

The data set is given below.

14, 3, -10, 12, 6

The mean of the data will be

μ = (14 + 3 - 10 + 12 + 6) / 5

μ = 25 / 5

μ = 5

The summation of the (x - μ) will be

∑(x - μ) = (14 - 5) + (3 - 5) + (- 10 - 5) + (12 - 5) + (6 - 5)

∑(x - μ) = 9 - 2 - 15 + 7 + 1

∑(x - μ) = 0

The summation of the (x - μ)² will be

∑(x - μ)² = (14 - 5)² + (3 - 5)² + (- 10 - 5)² + (12 - 5)² + (6 - 5)²

∑(x - μ)² = (9)² + (-2)² + (-15)² + (7)² + (1)²

∑(x - μ)² = 81 + 4 + 225 + 49 + 1

∑(x - μ)² = 360

Then the standard deviation (σ) will be

σ = √(360 / 5)

σ = √72

σ = 8.49

Then the variance (σ²) will be

σ² = 8.49²

σ² = 72

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Answer:

Step-by-step explanation:

A regular octagon shape has eight equal sides and eight equal angles. All the sides are of equal length, and all the angles are of equal measure. The sum of the interior angles is 1080°, and the sum of the exterior angles is 360°. In a regular octagon, the interior angle at each vertex is 135°.

so

3f = 135

f = 135 : 3

f = 45°

There are 2 quart jars can he fill.

There is 4 pint jar can he fill with any leftover sauce.

Fractions are numerical values that are a part of whole.

Julian is making barbecue sauce to the can. He uses 6 cups white vinegar, 1/2 cup honey, and 1/2 cup maple syrup.

We know that

1 quarts = 4 cups

Total number of cups is;

6 + (1/2) + (1/2) = 7

The total number of jars that he can fill is;

= total number of cups/4

=7/4

=1.75

There are 2 quart jars can he fill.

There are pint jars he can fill with any leftover sauce is;

1 quart = 2 pints

So, 2 quart = 2 × 2 = 4 pints.

There is 4 pints jar can he fill with any leftover sauce.

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Answer:

y = -1/2x - 1/2

Step-by-step explanation:

lmk if you want an explanation

a. The tree diagram that summarizes the given probabilities is attached.

b.  The probability that the individual does not participate in sports, given that he graduate sis  0.2 =  20%.

We apply Bayes' theorem to calculate:

Probability (Does not participate in sports if graduates)  = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)

The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating  = 0.18

Probability (Does not participate in sports if graduates)  = (0.02 * 0.82) / 0.18 = 0.036 / 0.18=  0.2

| Sports | No Sports |

                          |-------|--------|

Student participates | 0.18  | 0.62  |

                          |-------|--------|

Student does not participate | 0.02  | 0.78  |

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Answer:

5.123 × 10-3

m × 10n, where m is a number between 1 and 10 ( 1 ≤ |m| < 10 ) and the exponent n is a positive or negative integer.

I hope this helps.. :D

It is true that the indexed variables (members) of an array must be integers.

The indexed variables or members of an array must be integers. This is because arrays are data structures that store elements in a contiguous block of memory, and each element is accessed using an index. Indexing allows us to uniquely identify and retrieve specific elements within the array. In most programming languages, including C, C++, Java, and Python, array indices are integers and must be whole numbers (positive or negative) without any fractions or decimals. Attempting to use non-integer values as indices would result in a compilation error or unexpected behavior.

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The formula for determining the area of a rectangle is expressed as

Area = length * width

From the diagram,

Length = 3x + 6

Width = 4x - 1

The expression for the area of the room would be

In standard polynomial form, the terms are arranged in decreasing order of exponents. Therefore, the expression in standard form is

Answer:

  (d)  x = 4

Step-by-step explanation:

You want the solution to the system of equations using the given graph.

The solution to the equation f(x) = g(x) is the x-coordinate of the point(s) on their graphs where the curves intersect.

The graph shows the point of intersection of the two functions is (4, 1). This is the solution you have marked in the supplied image.

  x = 4

<95141404393>

A function in mathematics is a relation between two sets such that each element of the first set is matched to exactly one of the second set element

The correct option for the maximum velocity of the object is the option;

13 cm/s

The reason for the selection is as follows:

The known parameters of the motion of the vehicle are:

The type motion of the vehicle = Repetitive back and forth

The path of the motion of the object = Along a straight line

The function that gives the velocity in centimeters per second (cm/s) is given as follows;

\(v(t) = \mathbf{13 \cdot sin \left(\dfrac{\pi}{45} \cdot t \right)}\)

Where;

t = The time in seconds (a set of the input variables of the function)

v(t) = The velocity of the object (the output variables of the function)

The velocity of the object, v(t), depends (is given by) on the time t, therefore;

The maximum velocity is given at a particular value of t, which together with \(\dfrac{\pi}{45}\) is operated by the sine function

The maximum output value of the sine function = 1, therefore;

\(\mathbf{Maximum \ value \ of \ sin \left(\dfrac{\pi}{45} \cdot t \right)_{max}} = 1\)

\(The \ maximum \ velocity \ v(t)_{max}} = 13 \times sin \left(\dfrac{\pi}{45} \cdot t \right)_{max} = 13 \times 1 = \mathbf{ 13}\)

The units of the of the function is cm/s

Therefore, the maximum velocity of the object is 13 cm/s

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Answer: B. 13 cm/s

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number to the previous term

The first term of an arithmetic sequence is denoted by 'a₁', the second term by 'a₂', and so on.

Given that;

Un = a + (n - 1)d

U50 = 4 + (50 - 1) 2

U50 = 102

Then;

Un = ar^n-1

U10 = 1000(1/2)^9

U10 = 1.95

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9514 1404 393

Answer:

  1 solution

Step-by-step explanation:

The ratios of x- and y-coefficients are different, so the lines have different slopes. Lines with different slopes intersect at exactly one point. That point is the solution to the system of equations.

There is exactly one solution.

The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.

Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

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Answer:

2245

Step-by-step explanation:

2282-37=2245

2245 students are girls

Answer:

1304

Step-by-step explanation:

3/7 of students are boys

total students= 2282

girls are 1-3/7= 4/7 of all students

girls= 2282*4/7= 1304

Radius of a circle is the distance from the center of the circle to any point on its circumference. The radius of the circle is 3.2 x 10^8.

The diameter of a circle is twice the length of its radius. So, to find the radius, we divide the diameter by 2.

Given that the diameter is 6.4 x 10^8, we divide it by 2 to get the radius: (6.4 x 10^8) / 2 = 3.2 x 10^8.

To calculate the radius of a circle, you need to know either the diameter or the circumference. If you have the diameter (the distance across the circle passing through the center), you can divide it by 2 to find the radius. If you have the circumference (the distance around the circle), you can use the formula: radius = circumference / (2 * π), where π is a mathematical constant approximately equal to 3.14159.

The radius of the circle is 3.2 x 10^8.

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Answer:

Vertical

Step-by-step explanation:

Vertical angles are two nonadjacent angles formed by two intersecting lines.

Answer: Vertical

Step-by-step explanation:

Thus, we get a total of 210 + 90 + 6 + 60 = 366 number of ways to distribute the 7 apples among the 4 lecturers.

To solve this problem, we can use a combination of techniques from combinatorics and basic arithmetic. Since each lecturer can receive at most two apples, we can break down the problem into several cases:

1. Each lecturer receives 2 apples: In this case, we simply need to distribute the 7 apples among the 4 lecturers in a way that each receives 2. This can be done in (7 choose 2) * (5 choose 2) * (3 choose 2) * (1 choose 2) = 210 ways.

2. Three lecturers receive 2 apples and one receives 1 apple: In this case, we need to choose one of the lecturers to receive 1 apple, and then distribute the remaining 6 apples among the other three in pairs. There are 4 ways to choose the lecturer who receives 1 apple, and then (6 choose 2) * (4 choose 2) * (2 choose 2) = 90 ways to distribute the remaining apples.

3. Two lecturers receive 2 apples each, and two receive 1 apple each: In this case, we need to choose two of the lecturers to receive 2 apples each, and then distribute the remaining 3 apples among the other two in a way that each receives 1. There are (4 choose 2) = 6 ways to choose the two lecturers who receive 2 apples, and then (3 choose 1) * (2 choose 1) = 6 ways to distribute the remaining apples.

4. One lecturer receives 2 apples, and three receive 1 apple each: In this case, we need to choose one of the lecturers to receive 2 apples, and then distribute the remaining 5 apples among the other three in a way that each receives 1. There are 4 ways to choose the lecturer who receives 2 apples, and then (5 choose 1) * (4 choose 1) * (3 choose 1) = 60 ways to distribute the remaining apples.

Adding up the results from each case, we get a total of 210 + 90 + 6 + 60 = 366 ways to distribute the 7 apples among the 4 lecturers.

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Answer:

7.79

Step-by-step explanation:

19 percent of 41 is the same as 19 per hundred of 41. We can therefore make the following equation:

19/100 = X/41

To solve the equation above for X, you first switch the sides to get the X on the left side, then multiply each side by 41, and then finally divide the numerator by the denominator on the right side to get the answer. Here is the work to illustrate:

19/100 = X/41

X/41 = 19/100

X*41/41 = 19*41/100

X = 779/100

X = 7.79

The work above shows the long way to explain how to calculate 19 percent of 41 in order to give you a foundation and better understanding of how to calculate the percentage. In the future, you could use this simplified formula:

(Y * P)/100

In our problem "What is 19 percent of 41?", Y is 41 and P is 19:

(41 * 19)/100 = 7.79

And once again you see that the answer is 7.79.

Window dressing refers to the practice of making something appear more attractive, impressive, or favorable than it actually is, typically for the purpose of deceiving or misleading others. In a management context, window dressing can involve manipulating financial statements or presenting a superficially positive image to stakeholders.

Window dressing is a term commonly used in business and finance to describe actions taken to enhance the appearance or presentation of something, often to create a favorable impression. In the context of management, window dressing is commonly associated with financial reporting. It involves manipulating financial statements, such as income statements or balance sheets, to make a company's financial performance or position appear better than it actually is.
One example of how management might use window dressing is by delaying the recognition of expenses or accelerating the recognition of revenues to improve the company's financial ratios temporarily. For instance, a company might defer the recording of certain expenses until the next reporting period or engage in aggressive revenue recognition practices. By doing so, the company can create the illusion of higher profits or healthier financial stability, which may attract investors or lenders.
Another way management can engage in window dressing is by selectively disclosing information to stakeholders. They may highlight positive aspects of the company's operations while downplaying or omitting negative factors. This can create a false impression of the company's overall performance and mask underlying issues or challenges.
In conclusion, window dressing refers to the practice of enhancing the appearance of something to deceive or mislead others. In a management context, it can involve manipulating financial statements or selectively disclosing information to present a more favorable image of a company's financial performance or position.

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Answer:

Step-by-step explanation:

Given triangle ACD

Perimeter is sum of the side lengths:

AD = CD because D is vertex and the triangle is isosceles

AC = AB + BC because B is midpoint of AC

Then P is:

Find the value of x from the AB = BC:

Then find the value of P:

By comparing the responses across the three groups, the researcher can identify potential variations in opinions based on educational background. This information can provide valuable insights into how different types of schooling may shape perspectives on civic policies like curfews.

That's an interesting research approach!  By gathering opinions from different groups of children, specifically home-schooled, private school attendees, and public school attendees, the researcher can gain insights into how various educational backgrounds might influence their opinions on the new town curfew.

Collecting a simple random sample from each group ensures that every child within the respective groups has an equal chance of being selected for the survey. This helps in minimizing bias and increasing the generalizability of the findings to the larger population of home-schooled, private school, and public school children.

Once the samples are obtained, the researcher can administer a survey or questionnaire to collect the children's opinions on the new town curfew. The survey may include questions related to their awareness of the curfew, their understanding of its purpose, and their personal opinions on whether they support or oppose it.

By comparing the responses across the three groups, the researcher can identify potential variations in opinions based on educational background. This information can provide valuable insights into how different types of schooling may shape perspectives on civic policies like curfews.

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The standard form of the equation is (x' - 8x) + (y - 3)^2 = 48

To write the equation in standard form and identify the related conic, let's rearrange the given equation:

x' + y^2 - 8x - 6y - 39 = 0

Rearranging the terms, we have:

x' - 8x + y^2 - 6y - 39 = 0

Now, let's complete the square for both the x and y terms:

(x' - 8x) + (y^2 - 6y) = 39

To complete the square for the x terms, we need to add half the coefficient of x (-8) squared, which is (-8/2)^2 = 16, inside the parentheses. Similarly, for the y terms, we need to add half the coefficient of y (-6) squared, which is (-6/2)^2 = 9, inside the parentheses:

(x' - 8x + 16) + (y^2 - 6y + 9) = 39 + 16 + 9

(x' - 8x + 16) + (y^2 - 6y + 9) = 64

Now, let's simplify further:

(x' - 8x + 16) + (y^2 - 6y + 9) = 8^2

(x' - 8x + 16) + (y - 3)^2 = 8^2

(x' - 8x + 16) + (y - 3)^2 = 64

Now, we can rewrite this equation in standard form by rearranging the terms:

(x' - 8x) + (y - 3)^2 = 64 - 16

(x' - 8x) + (y - 3)^2 = 48

The equation is now in standard form. From this form, we can identify the related conic. Since we have a squared term for y and a constant term for x (x' is just another variable name for x), this equation represents a parabola opening horizontally.

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