The brass section of a middle school jazz band has 4 trumpets and 3 trombones.
What is the ratio of trombones to all the brass section members?

A. 7/3, 7:3, or 7 to 3
B. 4/7, 4:7, or 4 to 7
C. 4/3, 4:3, or 4 to 3
D. 3/7 , 3:7, or 3 to 7

Answer:

16 visitors per hour

Step-by-step explanation:

96/6 = 16

Answer:

2/3 cups

Step-by-step explanation:

The recipe calls for 2/4 cup of onion and 1/6 cup of celery. To find the total, we need to add the two fractions together; the amount of onions(2/4 cup or 1/2 a cup if simplified), and the amount of celery(1/6). To do this, we need to find a common denominator. We can do this buy finding a common multiple between 2 and 6.

Multiples of 2: 2, 4, 6, 8, 10, 12...

Multiples of 6: 6, 12, 18, 24, 30...

A common multiple is 6. 1/2x3/3=3/6 <--- an equivalent fraction of 1/2

Now both fractions have the same denominator:

Onions: 3/6

Celery: 1/6

3/6+1/6 = 4/6

4/6 simplifies to 2/3.

The total amount of celery and onion need for the soup is 2/3 cup

Answer:

2/3 cups

Step-by-step explanation:

There are 840 ways for the person to get 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die.

To calculate the number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die, we can use the formula for combinations with repetition.

The number of ways to choose 6 rolls to be fives out of 10 is given by the combination formula:

C(10, 6) = 10! / (6! * (10 - 6)!) = 210

Similarly, the number of ways to choose 3 rolls to be ones out of the remaining 4 rolls is:

C(4, 3) = 4! / (3! * (4 - 3)!) = 4

Finally, there is only one way to choose the remaining roll to be a two.

Therefore, the total number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die is:

210 * 4 * 1 = 840.

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It will take 50 seconds for the person to travel from one end to the other at the current speed.

We know that the person travels 28 feet in 7 seconds, remember that speed is defined as the quotient between distance and time, then the person's speed is:

s = 28ft/7s = 4ft/s

Now we want to find the time T that it takes for the person to travel the 200 feet of the sidewalk, then we need to solve:

(4ft/s)*T = 200ft

T= 200ft/(4 ft/s) = 50s

It takes 50 seconds.

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a) The probability that the second person chosen is also a boy is; 13/28

b) The probability that both students chosen are girls is; 5/18

The parameters given in the question are;

Total number of students in the class = 28 students

Number of boys in class = 13 students

Number of girls = 28 - 13 = 15 students

a) Probability of the first student being selected as a boy is;

P(First is boy) = 13/28

b) The probability that both students chosen are girls is;

P(both girls) = (15/28) * (14/27) = 5/18

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To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.

In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.

To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.

Let's consider a graph:

     A

    / \

   B---C

  / \ / \

 D---E---F

In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.

    A

    / \

   B---C

  / \ / \

 D---E---F

Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.

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By examining the shape and degree of association on the scatter plot, we can gain insights into the nature of the relationship between the variables and make predictions about their behavior in the future.

A scatter plot is a graphical representation of a set of data that shows the relationship between two variables.

The type of association between the two variables can be identified by the shape of the scatter plot. If the points on the plot form a linear pattern, then the association is said to be linear. If the points on the plot form a curved pattern, then the association is said to be nonlinear.

The degree of association between the two variables can be determined by the strength of the correlation coefficient, which is a measure of how closely the points on the scatter plot follow a linear pattern. The correlation coefficient ranges from -1 to 1, where a correlation coefficient of 1 indicates a perfect positive linear association, a correlation coefficient of -1 indicates a perfect negative linear association, and a correlation coefficient of 0 indicates no association between the two variables.

In this scenario, if the scatter plot shows a linear pattern and the correlation coefficient is positive, it means that there is a positive association between the amount of time the player spent practicing and the number of points he scored in the game.

On the other hand, if the correlation coefficient is negative, it means that there is a negative association between the two variables, which implies that the more time the player spent practicing, the lower the number of points he scored in the game.

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Answer: No

Step-by-step explanation:

Valid only for numbers less than 40.

P(40) = 412 which is not a prime number

Answer:

2

Step-by-step explanation:

the prime factorization of the number 90 is

2, 3, 3, 5

The probability of getting both the marbles to be red will be 4/25.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.

Probability = Number of favorable outcomes / Number of samples

Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.

The probability of getting red in the first draw,

P = 2 / 5

Now the marble is returned and again the probability of getting the red marble is,

P = 2 / 5

The probability of getting both the marbles red will be,

Pb = ( 2/ 5 ) x ( 2 / 5 )

Pb = 4 / 25

Therefore, there is a 4/25 chance that both marbles will be red.

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The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.

5/8 - 3/8 = x

5/8 = 5 ÷ 8

= 0.625

3/8 = 3 ÷ 8

= 0.375

0.625 - 0.375 = x

= 0.25

Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.

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The angle corresponding to each other of the different triangles are equal. The correct option is D.

"Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion ".

Here given, ΔJGR is similar to a triangle ΔMST

So, from the definition of a similar triangle,

angle J ≅ angle M

angle G ≅ angle S

angle R ≅ angle T

Hence, option D is correct.

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The simplified expression after factoring numerator and denominator is (x + 7) / x.

We can start by factoring the numerator and denominator of the first fraction:

x^2 - 49 = (x + 7)(x - 7)

The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:

x^2 - 4x - 21 = (x - 7)(x + 3)

So, the first fraction can be simplified as:

(x + 7)(x - 7)/[(x - 7)(x + 3)]

We can cancel out the (x - 7) factor in the numerator and denominator, leaving:

(x + 7)/(x + 3)

Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:

(x + 3)/x

Putting it all together, we get:

[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x

Therefore, the simplified expression is (x + 7) / x.

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____The given question is incorrect, the correct question is given below:

The numerator should be expanded and simplified. The denominator should be either expanded or factored.

Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x

Answer:

alternate exterior angles

Step-by-step explanation:

congruent alternete exterior angles

The x has a value of 36. The line's two points are (-12, 1) and (36, 7).

The slope of a line frequently represents the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.

We can apply the slope formula to determine the value of x:

m is the slope and (x1, y1) and (x2, y2) are two points on the line, with m = (y2 - y1) / (x2 - x1).

We are given the point (x1, y1) = (-12, 1) and the slope m = 1/8. We are also given the y-coordinate of the other point as y2 = 7.

Plugging in the known values, we get:

1/8 = (7 - 1) / (x - (-12))

Simplifying and solving for x, we get:

1/8 = 6 / (x + 12)

1 = 48 / (x + 12)

x + 12 = 48

x = 36

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The algebraic expression is h - 21 = 62

If we let "h" be Holly's original height,

The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:

h - 21 = 62

This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.

We can solve for h by adding 21 to both sides of the equation:

h - 21 + 21 = 62 + 21

h = 83

Hence, Holly's original height was 83 units.

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The above expression in terms of 8n can be written as 8(0).

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.

We are given a an expression (8-8)(8³)

Now the first bracket after simplifying we get an answer is 0.

Hence the expression can be given in the form of 8(n) as 8(0)

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answer:     12          

explanation:

The cost of 600 copies is  $90.10

The cost of 900 copies is $137.80.

The equation that expresses cost is y = 1.06 x ($10 + $15x)

The equation that represents the information in the question is:

Total cost = 1 + sales tax x [cost of the first 100 copies + (x x cost of every additional 100 copies)]

y = 1.06 x ($10 + $15x)

Cost of 600 copies:

x = (600 - 100) / 100 = 500 / 100 = 5

y = (1 + 6/100) x [$10 + (5 x $15)]

y = 1.06 x [$10 + $75)

y = 1.06 x $85

y = $90.10

Cost of 900 copies:

x = (900 - 100) / 100 = 800 / 100 = 8

y = (1 + 6/100) x [$10 + (8 x $15)]

y = 1.06 x [$10 + $120)

y = 1.06 x $130

y = $137.80

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The systems of equations in slope intercept form is

y = -6x + 110

y = 9x + 54

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

As, We know Slope-intercept form is

y = mx + b

where b is the starting value and m is the change per day.

Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.

So, the Equation to show the Situation

y = -6x + 110

and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.

So, the Equation to show the Situation

y = 9x + 54

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The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².

From the given figure, side of the equilateral triangle is 8 m.

Now, area of an equilateral triangle is

√3/4 ×8²

= √3/4 ×64

= 16√3 m²

The perimeter of an equilateral triangle is 3a.

Now, the perimeter is 3×8

= 24 m

Therefore, the area of an equilateral triangle is 16√3 m².

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The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
From the given data,
Name Number of Cards

Chris      7

Mike       8

Sally       10

Susan     25
Total cards = 50

Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%

Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.

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In all together, Clara ate 20 nuts.

A system of equations is a set of one or more equations involving a number of variables.

The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.

Let the number of pecans be x and the number of almonds is y.

We can write the system of equations as:

y = 3x

y = x + 10

Equating the value of {y}, we get -

3x = x + 10

2x = 10

x = 5          ...(1)

y = x + 10 = 15

y = 15         ...(2)

x + y = 15 + 5 = 20

Therefore, in together, Clara ate 20 nuts.

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The value of the right triangle cos d = 15/17 and cos c = 8/17.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given that, the value of tan c = 15/8 and the value of sin d = 8/17.

From the trigonometric functions we can conclude that:

Opposite side to c = 15

Adjacent side to c = 8

Hypotenuse = 17

Opposite side to d = 8

Adjacent side to d = 15

The values of cos d is:

cos d = Adjacent side to d / Hypotenuse = 15/17

cos c = Adjacent side to c / Hypotenuse = 8/17

Hence the value of the right triangle cos d = 15/17 and cos c = 8/17.

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Answer:

  36 bottles

Step-by-step explanation:

You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.

The profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.

  profit = selling price - purchase price

  profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle

To make a profit of $120, you need n bottles such that ...

  (10/3)n = 120

  n = 36 . . . . . . . . . multiply by 3/10

The club needs to buy, paint, and sell 36 bottles to raise $120.

For four variables the required number of system of linear equations are at least option d. 4 equations.

Therefore, if there are four variables in the system of linear equations then we should have option d. 4 equations.

The above question is incomplete , the complete question is:

If we have four variables, then how many equations will we have in our system of linear equations?

a. 5       b. 2      c. 3     d. 4

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After solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.

A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3.

The number on top denotes the component of the unit under consideration, while the number at the bottom indicates the total number of parts that make up one unit.

An element of a whole is a fraction.

The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

So, we have the operations:

7/3a - 8/5 + 4/15a

Now, solve as follows:

7/3a - 8/5 + 4/15a

7/3a + 4/15a - 8/5

7*5 + 4 /15a - 8/5

39/15a - 8/5

Therefore, after solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.

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Answer:

the iqr is the best measure of variability

The IQR is the best measure of variability, and it equals 4.

Option C is the correct answer.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

The appropriate measure of variability for the data is the interquartile range (IQR), which is the range of the middle 50% of the data.

In other words, it is the difference between the third quartile (Q3) and the first quartile (Q1).

From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.

This means that Q1 is 17 and Q3 is 21.

The IQR is:

IQR = Q3 - Q1 = 21 - 17 = 4

Thus,

The IQR is the best measure of variability, and it equals 4.

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The values of x, y and z are;

x. x = 60° y = 55°

xi. x = 68° y = 56° z = 56°

xiii. x = 40° y = 50°

xiv. x = 40° y = 50°

A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.

x. x = 60° (corresponding angles are equal)

y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)

y + 125° = 180°

y = 180° - 125°

y = 55°

xi. y = 56° (corresponding angles are equal)

y = z = 56° (angles in equal sides of a triangle are equal)

x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)

x + 112° = 180°

x = 180° - 112°

x = 68°

xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)

x = 180° - 140°

x = 40°

y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)

y + 130° = 180°

y = 180° - 130°

y = 50°

xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)

y = 180° - 130°

y = 50°

x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)

x + 140° = 180°

x = 180° - 140°

x = 40°

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