Christian recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 6
Bass 4
Drums 7
Keyboard 2
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 15
Drums 13
Keyboard 6

Based on these results, express the probability that a student chosen at random will play the bass as a fraction in simplest form.

The measure of the apothem is 1.75cm.

What is a regular octagon?

Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.

Here, we have

Given: The area of the regular octagon is 10.15 cm².

We have to find the measure of the apothem.

The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.

Area (triangle AOB) = 10.15/8 = 1.27cm².

Area(triangle AOB) is also 1/2*MO*AB

 1.27 =  1/2*MO*1.45

MO = 1.75cm

Hence, the measure of the apothem is 1.75cm.

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Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:

Distance = √(x2 - x1)^2 + (y2 - y1)^2

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.

For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:

Distance = √((5 - 2)^2 + (8 - 3)^2)

Distance = √(3^2 + 5^2)

Distance = √(9 + 25)

Distance = √(34)

Distance = 5.83

Therefore, the distance between the two points is 5.83 units.

Step-by-step explanation:

The required loan out of 14000 which is on 7% interest is given as $3800.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

Let part of the loaned amount at 7 % interest be x and another part with 17% interest be y,
A bank loaned out ​$14000​, part of it at the rate of 7% per year and the rest at 17% per year, and the interest received in one year totaled ​$​2000,

According to the question,
x + y = 14000
x = 14000 - y - - - - - (1)

and,
0.07x + 0.17y = 2000 - - - - (2)

Put x from equation 1 in equation 2
Gives,
y = 10200

Now,
x = 14000 - 10200
x = 3800

Thus, the required loan out of 14000 which is on 7% interest is given as $3800.

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Answer:

0.65 and 13/20

Step-by-step explanation:

The slope-intercept form of the equation of the given line which passes through the point (2, 7) and has a slope of 8 is:

     y = 8x - 9

What is meant by slope-intercept form of the line equation?

The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.

Given the line passes through a point  (2,7) and the slope is 8.

When a point on the line and slope are given, the equation of the line is:

y - y₁ = m ( x - x₁)

m = slope  = 8

Substituting,

y - 7 = 8 ( x - 2)

y - 7 = 8x -16

y = 8x - 9

Therefore the slope-intercept form of the equation of the given line is:

     y =  8x - 9

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Answer: The probability of not taking a yellow ball can be found by using the formula:

Probability of event A = (Number of favorable outcomes) / (Total number of outcomes)

In this case, the event of not taking a yellow ball is the favorable outcome, and the total number of outcomes is the total number of balls in the bag, which is 10 yellow, 5 orange, and 5 green balls. So, the total number of outcomes is 20.

The number of balls that are not yellow is 5 orange + 5 green = 10.

So, the probability of not taking a yellow ball is

Probability of not taking a yellow ball = (Number of non-yellow balls) / (Total number of balls) = 10/20 = 1/2

So the answer is 1/2.

Step-by-step explanation:

Answer:

---------------------------

The speed limit is 65 mph, the speed of the car is at least 74 mph.

The difference m is the over the speed limit value.

Set an inequality:

Using the mathematical operations of addition and subtraction, the weight of the bag of grapefruit is 3¹¹/₁₆.

The basic mathematical operations we have studied so far include addition, subtraction, division, and multiplication.

In addition operation, two or more addends are added to obtain a result known as the sum or total.

Using subtraction operation, the minuend, subtrahend, and difference are the major parts, including the subtraction operator (-).

There are two ways of solving this problem, we can add the fractional weights of apples and bananas and subtract the sum from the total weight of fruits Lynne bought.

We can also subtract each fractional weight from the total weight of fruits to arrive at the fractional weight of the bag of grapefruit.

The total weight of Lynne's purchases = 7¹/₂ pounds

The weight of apples = 1⁵/₈ pounds

The weight of bananas = 2³/₁₆ pounds

The weight of grapefruit = x

= 7¹/₂ - 1⁵/₈ - 2³/₁₆

= 3¹¹/₁₆

Add fractional weights:

1⁵/₈ + 2³/₁₆ = 3¹³/₁₆

Subtract the sum of the fractional weights from the total weight:

7¹/₂ - 3¹³/₁₆ = 3¹¹/₁₆

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The angles are 36,118,62

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.

Given: m and n are parallel lines with 3 transversals

We can observe that a=36 (vertically opposite angles)

and b =180-(36+26)     ∵  They all lie on a line .

          =118

and c= 180-118               ∵They all lie on a line.

         =62

Hence, The angles are 36,118,62

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Answer:

(a) Law connecting the variables:

[tex]M = \frac{5}{8}Ir^{2}[/tex]

(b) r = 8 and r = -8

Step-by-step explanation:

(a) Equation for a joint variation is:

             [tex]M = KIr^{2}[/tex]   where K is the constant

Substituting the provided values of M, I and r:

        =  [tex]20 = K(8)(2^{2} )[/tex]

        =  [tex]20 = K(8)(4)[/tex]

        = 20 = 32K

        = [tex]K = \frac{20}{32}[/tex]

[Divide the numerator and the denominator by the highest common factor (i.e. 4)]

       = [tex]K = \frac{5}{8}[/tex]

Therefore:

[tex]M = \frac{5}{8}Ir^{2}[/tex]

(b) [tex]M = \frac{5}{8} I r^{2}[/tex]

Substituting the values of M and I:

[tex]400 = \frac{5}{8} (10)r^{2}[/tex]

[tex]400 = \frac{5}{8} (10)r^{2}[/tex]

[tex]400 = \frac{50}{8} r^{2}[/tex]

[tex]\frac{(400)(8)}{500} =r^{2}[/tex]

[tex]\frac{3200}{50} = r^{2}[/tex]

[tex]64 =r^{2}[/tex]

Taking the square root on both sides of the equation:

[tex]r = \sqrt{64}[/tex]

[tex]r = 8[/tex] and [tex]r = -8[/tex]

When the thickness of a textbook is b mm the expressions for:

thickness of 5 stacked textbooks = 5b mm

thickness of each page, if the pages are numbered to 225 = b / 225

The thickness for each of the condition is written as follows

For the thickness of 5 stacked textbooks

= b + b + b + b + b

= 5b

For thickness of each page, if the pages are numbered to 225

In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book

= b / 225

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The compound inequality for the graph given is  -2 < x < 5.

When a compound inequality is graphed such that there is an open circle instead of a filled - in circle over a number, then it means that x is either greater than this value, or less than this value. In other words, x is not equal to this value.

The circles over - 2 and 5 are not filled in which means that x is greater or less than - 2 and 5.

x is less than 5 because the arrow goes from 5 to infinity and x is greater than - 2 for the same reason.

The compound inequality is therefore:

-2 < x < 5

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Answer: (15 + 72) + 19

Explanation: "Associative Law = (a + b) + c = a + (b + c)"

Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...

Step-by-step explanation:

How I've been today? Quite magnificent. Thank thou for your generosity.

The people that have posted the meme after 8 days using the exponential equation y=t^3 will be 512.

What are Exponential Equations?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.

Now,

To find number of people who have re-posted

we need to make a exponential equation

Here, As cindy tags meme to 3 people in starting and they also tag 3 people in subsequent days, then equation will be y=t^3 where t=no of days.

No of people after 8 days,

y=8^3

y=512 (no of people after 8 days)

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This is an example of geometric growth, So after 8 days 6561 people will have re-posted the meme.

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The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.

Here we want to explain why the two ratios:

5:6 and 15:18

Are equivalent, where equivalent means that these two ratios mean the same thing.

Now, if we take any ratio

a:b

and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.

k*a: k*b

Now, let's look to our ratios:

5:6

If we multiply these 2 numbers by 3, we will get.

3*5: 3:6

15: 18

So yes, these are equivalent.

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The requried solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁².

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,

Given the differential equation,

y' = 2 √y . x

y' = dy/dx so,

dy/dx = 2√y.x
dy/√y = 2x dx
[tex]y^{-1/2}dy = 2xdx\\\sqrt{y} /[1/2] = x^2 + c_1[/tex]
y = [1/2(x² + c₁)]²
y = x⁴/4 + c₁x²/2 + c₁²  

Thus, the requried solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁² .

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The value of expression is ,

10) 6

11) 18

12) 2

13) 4

14) [tex]\frac{1}{4}[/tex]

15) [tex]\frac{1}{3}[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression

10) 7+x+(-3)

Put x=2 then

=> 7+2-3

=> 7-1 = 6

11) 4[tex]x^2[/tex]+2

put x=2 then

=> [tex]4*2^2+2[/tex]

=> 4*4+2

=> 16+2=18

12) Ix+10I

put x=-12 then

=> I-12+10I

=> I-2I = 2

13) |2x + 1|

put x= 3/2 then

=> I2*[tex]\frac{3}{2}[/tex]+1I

=> I3+1I

=> I4I = 4

14)(x - 3)/4

put x=4 then

=> [tex]\frac{4-3}{4}[/tex]

=> [tex]\frac{1}{4}[/tex]

15) (5 - x)/6

put x=3 then

=> [tex]\frac{5-3}{6}[/tex]

=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

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Answer:

P = 5c + 11 , c = 3

Step-by-step explanation:

(a)

the perimeter P) is the sum of the sides.

Note that the 2 sides with a ' dash' through them are congruent

summing the 4 sides

P = c + 5 + 3c - 2 + 10 - 2c + 3c - 2 ( collect like terms )

  = 5c + 11

(b)

equate the expression for P from (a) to 26

5c + 11 = 26 ( subtract 11 from both sides )

5c = 15 ( divide both sides by 5 )

c = 3

a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.

b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school

The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.

In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.

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Answer:

Step-by-step explanation:

This is a quadratic function, which is a function of the form f(x) = ax^2 + bx + c, where a, b and c are constants. The function can be written in general form as f(x) = (x-4) / (x^2 +13x + 36).

To find the roots of the function (i.e. the points at which the function intersects the x-axis), we can use the quadratic formula:

x = [-b +/- sqrt(b^2 - 4ac)] / 2a

In this case, a = 1, b = 13 and c = 36.

Substituting these values into the quadratic formula, we get:

x = [-13 +/- sqrt(169 - 4(1)(36))] / 2

x = [-13 +/- sqrt(97)] / 2

x = [-13 +/- 9.8488578] / 2

x1 = -1.1744289

x2 = 11.1744289

Therefore, the roots of the function are x1 = -1.1744289 and x2 = 11.1744289.

After adding the expressions (8.5+ 6.25m) and (12 +3.75m) the value is obtained as (20.5 + 10m).

What is an expression?

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

The first expression is - (8.5+ 6.25m)

The second expression is - (12 +3.75m)

Apply the addition operation on the expressions -

= (8.5+ 6.25m) + (12 +3.75m)

= 8.5 + 6.25m + 12 + 3.75m

= 8.5 + 12 + 6.25m + 3.75m

= (20.5 + 10m)

Therefore, the value is obtained as (20.5 + 10m).

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The algebraic fraction which is equivalent to the given expression in which case, the denominator is 24a³b² as required is; 15b³ / 24a³b².

As evident in the task content; the given algebraic expression whose equivalent is to be determined is; 5b / 8a³.

However, to determine an equivalent expression whose denominator is; 24a³b²; one must determine the quotient of 24a³b² and 8a³.

= 24a³b² / 8a³.

= 3b²

On this note, it follows that the numerator and denominator of the given algebraic fraction can each be multiplied by 3b² in order to determine the equivalent expression.

= ( 5b • 3b² ) / ( 8a³ • 3b² )

= 15b³ / 24a³b².

Ultimately, thee required equivalent algebraic fraction is; 15b³ / 24a³b².

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Answer: 3 x y (2 x + 5 y)

Step-by-step explanation:

im not really sure but i gave it a try

The ratio of Bob's to Ron's to Don's partnership interest is 26.6% : 33.3% : 40.0%.

A partnership interest is the percentage of a partnership that a specific member or individual owns. In this context, partnerships refer to a specific method of organizing business ownership in which each owner is a partner, with equal rights, privileges, and obligations to the company as a whole.

Data

Partnership interests in Maloney Bros:

Don - $78,000

Bob -  $52,000

Ron Maloney’s - $65,000

The total capital contribution is:

= $78,000 + $52,000 + $65,000

= $195,000

Bob's partnership interest is:

= $52,000/$195,000

= 0.266 or 26.6%.

Ron's partnership interest is:

= $65,000/$195,000

= 0.333 or 33.3%.

Don's partnership interest is:

= $78,000/$195,000

= 0.400 or 40.0%.

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Answer: top right

Step-by-step explanation:

It says decrease by 7 which mean subtract (-) and times 3 mean multiply by 3 (x3)

Answer:

>4

Step-by-step explanation:

the answer of the question is >4