Q3 The grade-point averages of 20 college seniors selected at random from the graduating class are as follows:
3.2 1.9 2.7 2.4 2.8 2.9 3.8 3.0 2.5 3.3
1.8 2.5 3.7 2.8 2.0 3.2 2.3 2.1 2.5 1.9
a) Evaluate the Median of grade point
b) Calculate the highest marks of bottom 30% students
d) Calculate Q1 & Q3.

Answer:

(115 x 5) / 100 = 0.575 grams of the pure drug.

Step-by-step explanation:

To make a 5% solution, the concentration of the pure drug is 5 grams per 100 mL of solution.

To find the amount of pure drug needed for a specific volume, such as 115 mL, you can use the formula:

(volume of solution x concentration of pure drug) / 100

So in this case:

(115 x 5) / 100 = 0.575 grams of the pure drug.

This calculation shows that 0.575 grams of the pure drug would be needed to make 115 mL of a 5% solution.

Answer:

5.75 g

Step-by-step explanation:

First calculate 5% of the total amount of solution, 115 ml:

[tex]\implies \sf 5\%\;of\;115\;ml=\dfrac{5}{100} \times 115=5.75\;ml[/tex]

As we have not been told any information about the drug, assume the standard equivalent that 1 ml equals 1 gram.  Therefore, the amount of pure drug needed to make 115 ml of solution at the 5% strength is 5.75 g.

The common ratio for the sequence is 1/2.

Sets of numbers that adhere to a pattern or norm are known as number sequences. A geometric sequence is one where the rule is to multiply or divide by the same number each time.

Formula : [tex]a_n[/tex] = a[tex]r^{n-1[/tex]

where a is the first term, r is the common ratio.

Given:

Sequence: 14, 7, 7/2, 7/4

To calculate the common ratio = [tex]a_1/ a_2[/tex]

Now, the common ratio

= 7/14

= 1/2

Hence, the common ratio is 1/2.

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Answer:108-8 1/4=89 3/4 Jaden has 89 3/4 measures they still need to learn

Step-by-step explanation:

Answer: 89 3/4

Step-by-step explanation: Jaden played 18 1/4 of the measures and the total of Fur Elise is 108 measures. If you do 108 - 18 1/4 it would be 89 3/4. We did this because the total was 108 and we wanted to know how much of fur elise is left after we played 18 1/4.

Answer:

I believe it is -2a⁶b¹² (the first option)

Answer: y = 3x - 8

Step-by-step explanation: Given slope m = 3, and point x = 3, y = 1
y -1 = 3(x-3)
y = 3x - 9 + 1
y = 3x - 8

Answer:

x=0

y=0

z=0

Step-by-step explanation:

The solution to the inequality is z > 14

Mathematical expressions with inequalities include those in which the two sides are not equivalent. Contrary to equations, we assess and contrast two values in inequality. The inequality signs that are used in place of the equal signs are:

Given:

-6 > z/-2 + 1

Rewrite so "z" is on the left side of the inequality.

z/-2 + 1 <  -6

Move the negative in front of the fraction.

-z/2 + 1 < -6

Move all terms not containing z to the right side of the inequality.

-z/2 < - 6 - 1

-z/2 < - 7

Multiply both sides by 2

z < -14

Interchange the sign since z cannot be negative;

z > 14

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Answer:

6x+7y=2/5

im not entirely sure if its correct sorry if u get it wrong-

The sign that makes the following statement  -1/5 _____ -1/2 true is <. Option 1

Inequalities are simply described as a relation that makes a non-equal comparison between two numbers mathematical expressions.

Inequalities are mostly used in comparing two numbers on the number line based on their size.

Mathematically signs used for the representation are;

From the information given, we have that;

-1/5 is not equal to -1/2

Thjs is so because smaller numbers on the negative side of the number line are greater than the larger numbers.

Thus, the sign is <

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(6 + 3)9}\leftarrow\text{Your given equation}\\\mathsf{= 9(6 + 3)}\leftarrow\text{Convert your equation to this to make it easier to solve}\\\mathsf{= 9(6) + 9(3)}\leftarrow\text{What you are looking for because it is your answer to this question}\\\mathsf{= 54 + 27}\leftarrow\text{Making it more easier to solve for the overall answer} \\\mathsf{= 81}\leftarrow\text{This is your overall answer to the whole equation}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D. \ 6(9) + 3(9)}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]30 + 60[/tex]

I am pretty sure I'm wrong

[tex]30 \div 60[/tex]

[tex]30 \times 60[/tex]

[tex]30 - 60[/tex]

Answer:

Triangle VWX and triangle IGH are congruent

Step-by-step explanation:

The width of the base is __57.625__ feet

The length of the base is __57.625__ feet

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given,

Perimeter of the rectangular base of a monument is 230.5 feet.

width is equal to its​ length

Perimeter of rectangle = 2 (length + width)

230.5 = 2 (length + length)

4 length = 230.5

length = 230.5/4

length = 57.625 feet

thus, width = 57.625 feet

Hence,

57.625 feet is the length of rectangular base.

57.625 feet is the width of rectangular base.

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Answer:

-79

Step-by-step explanation:

First Identify the sequence

-28 to -45 is -17

-45 to -62 is -17

This is an Arithmetic Sequence because it is constant

(Constant ; same throughout)

Two Formulas:

a60=28 -45 -62

or

an= -17(60)-11

The solution to the equation -9 = 6m + 15 is m = -4.

Given the equation in the question;

-9 = 6m + 15

Rewrite the equation as 6m + 15 = -9

Move all terms not containing m to the right side of the equation by subtracting 15 from both sides

6m + 15 - 15 = -9 - 15

6m = -9 - 15

Add -9 and -15

6m = -24

Divide both sides by 6

6m/6 = -24/6

m = -24/6

m = -4

Solution check

Plug m = -4 into the equation and check

-9 = 6m + 15

-9 = 6( -4 ) + 15

-9 = -24 + 15

-9 = -9

Correct.

Therefore, the numerical value of m is -4.

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1)  A sequence of real numbers is an ordered list of real numbers where each number in the list is assigned a specific position or index, usually denoted by n. The sequence is denoted by {xn} n>n0, where xn represents the nth term of the sequence and n ranges from 0 to infinity.

2)An example of a sequence of rational numbers is {2, 1.5, -0.5, -1.25, ...}, where each term in the sequence is a rational number.

3) The recursive definition of the summation of ai is a mathematical formula that defines the nth term of the summation in terms of the previous terms. It is typically denoted as:

∑(i=1)^ni = a1 + (a2 + (a3 + ....(an-1 + an)...)),

Where a1 is the first term of the summation, a2 is the second term, and so on and so forth. This recursive definition is used to calculate the nth term of the summation by adding the previous term to the current term. It is generally used in mathematical induction and recursion.

4)The associative property of summation notation states that the order in which the summation is performed does not affect the final result. In other words, for any three indices a, b, and c, and any sequence of numbers {xn}, the following equation holds:

∑(a=b)c xn = ∑(a=c)b xn = ∑(a=b)c xn

This property allows us to group the terms in a summation in different ways without changing the final result.

5) The translation invariance property of summation notation states that the value of a summation is unchanged when the index of summation is translated (shifted) by a constant value. In other words, for any indices a and b, any constant k, and any sequence of numbers {xn}, the following equation holds:

∑(a=b)xn = ∑(a+k=b+k)xn

This property allows us to shift the index of summation without affecting the final result of the summation.

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Answer:

145236 4236. b. fjdjfjfjfjfjdjfjfjfjfjfnfjfjfjfnfjgjfjfnfjf

Nya's average speed was 10 miles per hour.

What is the speed, distance, and time?

Speed, distance, and time are related concepts in physics that are used to measure and describe motion.

Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed can be calculated using the formula:

Speed = Distance / Time

To find Nya's average speed in miles per hour, we need to divide the distance she traveled by the time it took her to travel that distance.

Average speed = distance/time

We know that Nya rode her bike 2 ½ miles in ¼ hour. To use these measurements in the formula, we need to convert the units to the same unit of measurement. In this case, we need to convert the distance to miles and the time to hours.

Average speed = (2.5 miles) / (0.25 hour)

To find out the speed in miles per hour, you need to multiply by the conversion factor 1 hour/60 minutes, so

Average speed = (2.5 miles) / (0.25 hour) * (1 hour/60 minutes)

Average speed = (2.5 miles) / (0.25 hour) * (4)

Average speed = 10 miles per hour.

Hence, Nya's average speed was 10 miles per hour.

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Answer:

Desert city is the largest city.

PSI stands for Pounds per Square Inch, and it's the unit of measurement that reflects the air pressure inside your tire.

Given the data representation of the strength of nine randomly selected casts​ (in psi) as 3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780.

Mean is the average of the samples

[tex]x={3960+4050+3170+3080+2940+3830+ 4050+4060+3810}[/tex]

x=32950/9

x=3661

is thw sum of the given data

N is the sample size

is the mean

Hence the mean of the data is 3,670psi

MEDIAN

Median is the value at the middle of the data after rearrangement.

On rearranging in ascending order

2940, 3100, 3200, 3,780) 3,830 (3,960, 4040, 4090, 4090

It can be seen that the middle value is 3860. Hence the median of the data is 3860psi.

MODE

Mode is the most occurring data in the dataset. It is the data with the highest frequency. From the data, it can be seen that the only data occurring most (twice) is 4090, hence the modal value is 4090psi

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The factor z-8 is less than zero when z<8. Similarly, the factor z-3 is less than zero when z>3. Combining the two solutions,[tex]$z \in(3,8)$[/tex]

.

Given inequality:

[tex]$$z^2-11 z+24 < 0$$[/tex]

Factor the left-hand side.

[tex]z^2-11 z+24 & < 0 \\[/tex]

[tex]z^2-8 z-3 z+24 & < 0 \\[/tex]

[tex]z(z-8)-3(z-8) & < 0 \\[/tex]

[tex](z-8)(z-3) & < 0[/tex]

The factor z-8 is less than zero when z<8. Similarly, the factor z-3 is less than zero when z>3. Combining the two solutions,[tex]$z \in(3,8)$[/tex].

The complete question is,

Solve the following inequality:

[tex]$$z^2-11 z+24 < 0$$[/tex]

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Using substitution method to solve the system of linear equations, the granola and drinks cost $1.25 and $2.5 respectively while the modelled system of linear equation is attached below

A grouping of two or more linear equations that share the same set of variables is known as a system of linear equations. When a, b, and c are constants and x and y are variables, the equations can be written as ax + by = c. Elimination, substitution, and graphing are just a few of the techniques that can be used to solve these problems.

In this given problem, we have to define our variables and then set our system of equations.

a)

Let;

2x + 5y = 15 ...eq(i)

4x + 3y = 12.50 ...eq(ii)

b)

Using substitution method;

From equ(i)

2x + 5y = 15

2x = 15 - 5y

x = (15 - 5y) / 2 ...eq(iii)

Put eq(iii) into eq(ii)

4x + 3y = 12.50

4(15 - 5y) /2 + 3y = 12.50

y = 2.5

Put y = 2.5 into eq(i)

2x + 5(2.5) = 15

x = 1.25

c)

Granola = 1.0

drinks = 3.0

The system of linear equations will be

x + y = 4

2x + 3y = 11

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Answer:

-1.3

Step-by-step explanation:

There are 6 goats and 17 ducks present in the farmhouse

Let x represent the number of goats

Let y represent the number of ducks

x + y= 23....equation1

Goats have 4 legs and ducks have 2 legs

4x + 2y= 58.......equation 2

From equation 1

x + y= 23

x= 23-y

Substitute 23-y for x in equation 2

4(23-y) + 2y = 58

92- 4y + 2y= 58

92-2y= 58

-2y= 58-92

-2y= -34

y- 34/2

y= 17

Substitute 17 for y in equation 1

x + y= 23

x + 17= 23

x= 23-17

x= 6

Hence there are 6 goats and 17 ducks in the farmhouse shelter

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The value of x is 14.957.

An equation is the statement of two expressions located on two sides connected with an equal to sign.

The equation is given as,

-12x - (12x + 4) + 12 = 17x - 6(3x + 56)

Since the sign is negative outside the bracket on the left hand side, the signs of terms inside the bracket becomes the opposite of what it has.

-12x - 12x - 4 + 12 = 17x - 6(3x + 56)

Applying the distributive property for the term 6(3x + 56), we get,

-12x - 12x - 4 + 12 = 17x - [(6 × 3x) + (6 × 56)]

-12x - 12x - 4 + 12 = 17x - (18x + 336)

Removing brackets,

-12x - 12x - 4 + 12 = 17x - 18x - 336

Taking all the like terms to separate sides,

-12x - 12x - 17x + 18x = 4 - 12 - 336

-23x = -344

x = -344 / -23

x = 14.957

Hence the value of x for the given equation is 14.957.

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The cost of the class would be $740 x 3 = $2220. If you were to work instead, at $10 per hour for 10 hours per week for 15 weeks, you would earn $1500. So, the net cost of the class would be $2220 - $1500 = $720.

In general, a college degree can lead to higher earning potential and greater career opportunities, so in most cases, it can be considered a worthwhile investment. However, the decision to take a particular class should be based on individual circumstances and goals. If the class is relevant to your future career aspirations and you can afford the cost, it may be a good investment. However, if the class is not directly related to your career goals, or you are not able to afford the cost, it may not be worth it.

To the nearest hundredth of a year (period), it will take Olivia's money 0.54 years more to triple than Aria's money to triple.

The additional period it will take Olivia's money to triple than Aria's is determined as the difference between the two investment periods.

The investment periods are computed using an online finance calculator as follows:

I/Y (Interest per year) = 8.375%

PV (Present Value) = $40,000

PMT (Periodic Payment) = $0

FV (Future Value) = $-120000

Results:

Number of Periods (N) = 4,788.531

= 13.119 years (4,788.531/365) or 13 years and 1 month

Total Interest = $80,000.00

I/Y (Interest per year) = 8.125%

PV (Present Value) = $40,000

PMT (Periodic Payment) = $0

FV (Future Value) = $-120000

Results:

N = 54.633

= 13.65825 years (54.633 quarters/4) or 13 years and 8 months

Total Interest $80,000.00

The difference in investment period:

13.66 - 13.12

= 0.54 years

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We have discussed the general strategy for solving an equation of the form x/a = b.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. An equation is composed of two sides, separated by an equal sign (=), with each side containing one or more variables, numbers, and/or mathematical operations.

The general strategy for solving an equation of the form x/a = b is to:

Multiply both sides of the equation by a, in order to cancel out the fraction on the left side. This will isolate the variable x on one side of the equation.

Simplify the equation by combining like terms if necessary.

Check the solution by substituting it back into the original equation and verifying that it makes the equation true.

For example, consider the equation x/2 = 4

Multiply both sides by 2: x/2 * 2 = 4 * 2

x = 8

To check the solution, substitute it back into the original equation: x/2 = 4, 8/2 = 4. The equation is true, so x = 8 is the correct solution.

It's important to keep in mind that when solving equations, it is important to follow the order of operations, and also to be careful when dividing or multiplying by zero.

Hence, we have discussed the general strategy for solving the equation.

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The solution of the function is as follows:

(f o g)(x) = 16x² + 17x + 1

(g o f)(x) = 4x² + 36x + 1

Composite functions are when the output of one function is used as the input of another.

Therefore, let's solve the composite functions as follows:

f(x) = x² + 9x

g(x) = 4x + 1

Therefore,

(f o g)(x) = f(g(x))

Therefore,

f(g(x)) = (4x + 1)² + 9x = (4x + 1)(4x + 1) + 9x = 16x² + 4x + 4x + 1 + 9x = 16x² + 17x + 1

(g o f)(x) = g(f(x))

g(f(x)) = 4(x² + 9x) + 1 = 4x² + 36x + 1

Therefore,

(f o g)(x) = 16x² + 17x + 1

(g o f)(x) = 4x² + 36x + 1

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Answer: its -1

Step-by-step explanation: