Can someone please help me on these four problems. The photo is linked above

Answer:

-1.3

Step-by-step explanation:

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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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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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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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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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 property of equality that was used to solve the equation is the division property of equality

From the question, we are to determine the property of equality that was used to solve the given equation

From the given information,

The equation is

-5x = 4

and

The solution is

(- 5x)/- 5 = 4/- 5

x = - 4/5

From the solution step, we can observe that both sides of the equation were divided by -5.

Thus,

The property of equality that was used is the division property of equality

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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

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.

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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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.

Answer: its -1

Step-by-step explanation:

Answer:

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

[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]

Answer: The missing value is 86

Step-by-step explanation: The mean of a data set is the same as the average. The formula for mean is the sum of the data values/(the number of data values). Right now there are only 6 data values and we are looking for a seventh. If we sum the 6 current values and divide by 6, we get a data set with a mean of 96.5. We need a lower mean. The data set we need has 7 points so the sum of all 7 points should be 7(95) since if we divide 7(95) by the number of points which is 7, we get 95 which is the mean we want. 7(95) is 665. We can subtract the sum of the current 6 points from 665 to find the value we want.

[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]

The quotient when 2x² + 4x – 14 is divided by 2x is [tex]x + 2 - \frac{7}{x}[/tex] .  

When two numbers are divided by each other, the result is known as a quotient. For instance, when we divide 8 by 2, the result will be 2, where 2 is the quotient.

As we know division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). When we divide a number, the result we ultimately get is the quotient.

Here we have

2x² + 4x – 14 is divided by 2x  

=> [tex](2x^{2} + 4x - 14) \div {2x}[/tex]  

=>  [tex]\frac{(2x^{2} + 4x -14)}{2x}[/tex]  

Take 2x as common

=>  [tex]\frac{2x(x + 2 - \frac{7}{x} )}{2x}[/tex]    

=>  [tex]x + 2 - \frac{7}{x}[/tex]    

Therefore,

The quotient when 2x² + 4x – 14 is divided by 2x is [tex]x + 2 - \frac{7}{x}[/tex] .  

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Answer:

Desert city is the largest city.

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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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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Answer:

2.14 rounded ............

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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Answer:

145236 4236. b. fjdjfjfjfjfjdjfjfjfjfjfnfjfjfjfnfjgjfjfnfjf

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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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:

a = 3.31ft.

Step-by-step explanation:

The opposite is 3.31 feet.

Please let me know if this helped!!!

Answer:

Triangle VWX and triangle IGH are congruent

Step-by-step explanation:

Answer:

x=0

y=0

z=0

Step-by-step explanation:

Answer:

6x+7y=2/5

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

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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