The distance between a 16 feet long chord and the center of a circle is 15 feet. Compute the diameter of the circle

The constant of proportionality is 9 and equation of the proportion.

is y= 10x.

If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.

Given:

As, we know using the Constant of Proportionality

y = kx

or,  k = y/x  where k is Constant of Proportionality.

Then, from the table we have

k = 90/9

k= 10

Thus, y = kx

or, y= 10x

Hence, the equation of the proportion is y= 10x.

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The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .

To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.

The multiples of 4 and 7 are:

Multiples of 4 :

4, 8, 12, 26, 20, 24, 28, 32, 36, 40,

Multiples of 7 :

7 , 14 , 21 , 28 , 35 , 42 , 49

The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.

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We calculated   volume of pyramid = 160 cubic inches and surface area = 214.59 square inches.

A three-dimensional geometrical figure having flat polygon base along with a number of lateral triangular shaped faces.

The given pyramid is a rectangular pyramid having length 10 inch and width 8 inch. The height of pyramid is 6 inches.

length, l = 10 inch

width, w = 8 inch

height, h = 6 inch

Now the volume will be, V = 1/3 × l × w ×h

                                       V = 1/3 × 10 × 8× 6

hence, the volume = 160 cubic inches

We calculate the surface area of the given pyramid,

formula for surface area, SA = l × w + 1/2 × w ×√(4h²+l²) + 1/2 × l ×√(4h²+w²)

SA = 10 × 8 + 1/2 × 8 ×√(4×6²+10²) + 1/2 ×10×√(4×16²+8²)

Surface area = 214.593 square inches

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The volume of the cone is one third the volume of the cylinder.

The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter

Similar to a prism, a cylinder has two bases, but they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a figure in space with equal distances between each of its points and the center.

The cone's volume is one-third that of the cylinder. A sphere's volume is 2/3 that of a cylinder with the same radius, and its height is equal to its diameter.

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The answer is 11, 12, 13

83.2 square feet is the area of the figure.

A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given figure is a cone with radius 3 ft and height 5 ft.

We need to find the area of cone=A=πrl+πr²

where l is √r²+h²

A=πr(r+√r²+h²)

=π×3(3+√3²+5²)

=3π(3+√34)

=3×3.14(3+5.83)

=3×3.14(8.83)

=83.2 square feet

Hence, 83.2 square feet is the area of the figure.

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Answer:

AROC = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

the average rate of change of g(x) in the closed interval [ a, b ] is

[tex]\frac{g(b)-g(a)}{b-a}[/tex]

here [ a, b ] = [ - 4, 5 ] , then

g(b) = g(5) = - 1 ← point (5, 1 ) on graph

g(a) = g(- 4) = 5 ← point (- 4, 5 ) on graph

average rate of change = [tex]\frac{-1-5}{5-(-4)}[/tex] = [tex]\frac{-6}{5+4}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]

The description for the problem involving the linear function is given as follows:

The time it will take to make a total of 20 parts is of 6 minutes.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In this problem, the function is defined as follows:

y = 2x + 8.

In which the variables are given as follows:

Hence the time needed to make 20 pieces is given as follows:

20 = 2x + 8

2x = 12

x = 12/2

x = 6 minutes.

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Since, Kim works on commission and her trend of monthly earnings are not constant, Calculate the average from the data and estimate for the whole year , The answer is C) $15,720

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It helps to make sense of large amount of data and use it to draw conclusions and make informed decisions. It provides methods to summarize, describe and analyze data, as well as techniques to infer characteristics of a population from a sample.

The mean is a measure of central tendency and a way to describe the average value of a dataset. It is calculated by adding up all the values in a dataset and then dividing by the number of values. The resulting value is the mean of the dataset, also known as the arithmetic average. Mean is commonly used to describe a large data set, while median is used to describe data with values have outliers.

salary for four months = $1625, $960, $1235, and $1420.

Average = ($1625 + $960+ $1235+$1420) /4 = $1310

for whole year = $1310 * 12 = $15,720

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Answer:1000000

Step-by-step explanation:

Sixth grade math class can be difficult, even for students who have done well in math previously. In sixth grade you begin to learn more advanced topics such as ratios and rates.

You also work more with fractions. Sixth grade is also when you begin building the foundations of algebra, geometry, and statistics.

example

given problem in maths

- x + 8 > 6 ( isolate the term in x by subtracting 8 from both sides )

- x > - 2 ( multiply both sides by - 1 )

Remembering to reverse the inequality symbol when multiplying/dividing by a negative quantity

x < 2 ← reverse symbol

From the given list the only value less than 2 is 1, hence

x = 1 ← is the only possible solution

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The probability is 0.4444.

Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.

The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.

For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.

Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.

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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).

The original price of the case of candles before markup was $8.50.

Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:

Original price = Marked up price / (1 + markup percentage)

In this case, the original price would be:

$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50

So the original price of the case of candles before markup was $8.50.

Thus, Original price is $8.5

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a) The greatest number of students who will get the refreshment is 210.

b) Each student will get 0.5 hot dogs.

c) Each student will get 0.6 cans of fruit juice.

a) To find the greatest number of students who will get the refreshment , we need to find the least common multiple of hot dogs and fruit juice.

The least common multiple is 210, which is the multiple of 105, and 126 is the least.

So the greatest number of students who will get the refreshment is 210.

b) To find the number of hot dogs each student will receive, we need to divide the total number of hot dogs (105) by the greatest number of students who will get the refreshment (210)

105/210 = 0.5

So each student will get 0.5 hot dogs.

c) To find the number of fruit juices each student will receive, we need to divide the total number of fruit juice (126) by the greatest number of students who will get the refreshment (210)

126/210 = 0.6

So each student will get 0.6 cans of fruit juice.

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The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.

An algebraic equation is formed by comparing two algebraic expressions to one another.

In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8

If G-H-I is a line and GH, HI and GT lies between G to I

To find G to I ⇒ GI = GH + HI = GT

GI = 2x - 9 + 14 = 3x - 8

2x + 5 = 3x - 8

2x - 3x = -8 - 5

-x = -13

x = 13

Substituting x in GT = 3x - 8; GI = GT

GI = 3(13) - 8

GI = 39 - 8

GI = 31

Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31

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To find the slope of two points on a graph, use the formula:

[tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]

Substitute the coordinates of the two points into the formula and solve for the slope.

The slope of two points on a graph is a measure of how steep the line connecting the two points is. To find the slope, you can use the slope formula: [tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]

This formula requires the coordinates of the two points, which can be found on the graph. Once you have the coordinates, you can substitute them into the formula and solve for the slope. This will give you the slope of the line connecting the two points.

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The equation on how to find the volume is πr²h = 24

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

Volume = 24 cubic feet

The volume of a cylinder can be calculated as

Volume = πr²h

Where

r = radius

h = height

Substitute the known values in the above equation, so, we have the following representation

πr²h = 24

Hence, the equation is πr²h = 24

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Answer:

11 pounds

Step-by-step explanation:

The ratio of the amount of money Rachel spent on food to clothes is 1/3
She spent: 44 : (1 + 3) x 1 = 11 pounds

Answer:11

Step-by-step explanation:

11 times 3 equals 33(for the clothing)

so 11 is left

In 35 differnt ways (Combination) the 4 players can be selected from a team of 7.

Combinations are decisions that are made by choosing some or all of a group of things, regardless of how they are arranged.

Utilizing the combinations formula, it is simple to determine how many distinct groups of r items each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.

A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. In order to determine the number of configurations for seating 3 people in 5 seats, we thus multiply the alternatives at our disposal.

Permutations are several ways to arrange things in a certain sequence. It may alternatively be stated as the linear reordering of elements in an already ordered collection.

Here we have to select 4 people from a team of 7, so its a combination

So the number of ways are = [tex]\x^{7}C\x_{4} = \frac{7!}{4!\ 3!} = 35[/tex].

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In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.  

Diagonal of a rhombus bisects the angles of the rhombus at the vertex.

So as m∠MNL is 120°,

∠MNO = ∠LNO = 120/2 = 60°

The diagonals intersect each other at a 90 degree angle, therefore

m∠MON = 90°

Considering ΔMNO, right angled at O.

cos(∠MNO) = NO/ MN

cos(60) = NO/ 8

NO = 0.5×8 = 4

NP = NO + OP

NP = 2NO

NP = 2×4

NP = 8 in

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ln() is a function in Excel that calculates the natural logarithm of a number. The natural logarithm is the logarithm to the base e, where e is an irrational number approximately equal to 2.718281828.

1. Enter the number for which you want to calculate the natural logarithm in a cell.

2. Click on the cell and enter "=ln()" function (without the quotation marks) in the formula bar.

3. Within the parentheses, enter the cell reference or the number for which you want to calculate the natural logarithm.

4. Press the Enter key and the natural logarithm of the number will be calculated and displayed in the cell.

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The domain of x=4 is (−∞,∞) and range is {y|y=4} .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

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The most probable prediction( according to biogeography theory of islands) for this situation would be continued colonization of large species population( due to balance between immigration and extinction of species) through time on the island.

A species is a unit of biodiversity as well as the fundamental classification and taxonomic rank of an organism in biology.

Given:

Consider a species that occupies a large, but fixed, number of islands.

The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events.

According to island biogeography theory the population of an island is maintained constant through time when the immigration rate of new species to the island and extinction rate of species in the island is constant.

In a model for the relationship between the fraction of islands occupied by species and time, if the number of new species immigrating to the island will be equal to the number of species that become extinct in the island species population and will thrive continuously through time( will never become extinct) as the island species population will be maintained due to the existence of a dynamic equilibrium of species in the island.

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Answer:

8.2 × 10⁻³

Step-by-step explanation:

1.64 × 10⁰      1.64 × 1         1.64

-------------- = -------------- = ---------- = 0.0082

2.0 × 10²        2 × 100        200

Scientific notation: 8.2 × 10⁻³

I hope this helps!

Answer:

Step-by-step explanation:

A unit rate means a rate for one of something. You should write it as a ratio with a denominator of one.

For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate

IT's  0.80 per serving i think

x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement  best describes the end behavior.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

First, we need to analyze the plotting of the graph. When it is on the negative axis of x, as the values of x increase (x values increasing in the negative axis means it's decreasing in value), the y values also increase. So as x decreases, y increases.

On the positive axis of x, as the x values increase, the corresponding values of y also increase with x. So as x increases, y values also increase with it.

Hence, x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this  statement  best describes the end behavior.

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Answer: Five Days

Step-by-step explanation:

Isabella can hike 8 miles per day. So:

[tex]\frac{30miles}{8miles} = 3.75 days[/tex]

It will take:

[tex]\frac{70 miles}{8 miles} = 8.75 days[/tex]

..in total to hike 70 miles.

So, subtracting the two values:

[tex]8.75 - 3.75 = 5[/tex]

She still needs to hike five days in order to finish the trail.

The coefficient of expression 5x^2 in 5x^2 5x is 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.

The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.

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There are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.

We know that the company uses the same ratio of different types of nuts in each container. Therefore, we can use the ratio of peanuts to the total weight in the 20-ounce container to find the weight of almonds in the 42-ounce container.

In the 20-ounce container, 11 ounces of the nuts are peanuts. Therefore, 20-11 = 9 ounces of the nuts are not peanuts.

To find the weight of almonds in the 42-ounce container, we can use the same proportion of non-peanut nuts to the total weight. So,

9 ounces / 20 ounces = x / 42 ounces

Cross-multiplying we get:

9 × 42 ounces = 20 × x

x = 37.8 ounces

So, there are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.

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