Use the quadratic formula to find both solutions to the quadratic equation given below
4x^2+3x-1=0

Check the picture below.

so the center of the circle is the midpoint of that diameter, and its radius is half its length.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ r(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~4 - (-2)~~)^2 + (~~7 - (-1)~~)^2} \implies r=\sqrt{(4 +2)^2 + (7 +1)^2} \\\\\\ r=\sqrt{( 6 )^2 + ( 8 )^2} \implies r=\sqrt{ 36 + 64 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~10^2\implies {\large \begin{array}{llll} (x-1)^2+(y-3)=100 \end{array}}[/tex]

If the cost to fill a gas tank in 1995 is $15 then the cost to fill a gas tank in 2015 is equals to the $31.25.

Price Index is a effective method of comparing relative change in the price of a quantity with respect to its price in a reference year. This year which we use as a reference is called the base year and price index is ratio of the price of a product in a year to its price in the base year ( expressed in percentage ).

The cost to fill a gas tank in 1995 = $15

Price index in 1995 = 100.8%

price index in 2015 = 210.0%

In this case we want to determine the cost to fill a gas tank in 2015. Let the required cost value be x dolars. Using the formula, price index in 1995/price index in 2015 = reference value/ value in 2015

=> 100.8% /210% = 15/x

=> 2015 cost value, x =( 15 × 210 )/100.8

=> x = 3150/100.8

=> x = 31.25

Hence, required value is $31.25.

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Complete question:

If it cost $15 to fill a gas tank in 1995, how much would it cost to fill the same tank in 2015. 1995 index is 100.8%

2015 index is 210.0% round your answer nearest cent.

To display this data on a line plot, we need to create a number line with a range of values from 1.4 to 2.0 with intervals of 0.1.

Then, we can plot each data point by hovering over the corresponding number on the number line and clicking and dragging up to the corresponding value.

The line plot will show a visual representation of the data, with each point representing the average time spent on the computer each day by a different student.

The line connecting the points will show the trend of the data and can be used to make inferences about the overall behavior of the students in terms of their computer usage.

In conclusion, the line plot for the given data on the average number of hours different students spend on the computer each day will show the student's weekly computer time and provide insight into their computer usage patterns.

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We use the product rule and the chain rule to find the derivative of y = e^4x sin 4x.

y = e^4x sin 4x

y' = (e^4x)(4sin 4x + cos 4x(4))

y' = 4e^4x(sin 4x + cos 4x)

Therefore, the first derivative of y=e^4x sin 4x is y' = 4e^4x(sin 4x + cos 4x).

Interpretation: The first derivative gives the instantaneous rate of change of the function at each point. In this case, the derivative represents the rate at which the amount of medicine remaining in a person's bloodstream changes with respect to time x. The function has a maximum or minimum when the first derivative is equal to zero.

Answer:

Step-by-step explanation:

The number of different ways in which no song is liked by all three and there is at least one song liked by those two girls but disliked by the third is (b) 132 ways.

Let the song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), be denoted as : AB, BJ, and AJ.

Similarly, let the letters "A, B, J, and N" denote the song that is liked by only Amy, only Beth, only Jo, and none of them, respectively.

We know that there is at least 1 AB, BJ, and AJ, there must be 3 songs out of 4 songs which Amy, Beth, and Jo listened to.

The fourth song can be of any type : N, A, B, J, AB, BJ, and AJ (there is no ABJ because "no-song" is liked by all three),

So, we must find the number of ways to rearrange AB, BJ, AJ and a song from the set {N, A, B, J, AB, BJ, AJ}.

⇒ Case 1: Fourth song choices = N, A, B, J

All the four of choices for fourth song are different from the first 3 songs.

⇒ Number of ways to rearrange = 4! × 4 choices = 96.

⇒ Case 2: Fourth song choices = AB, BJ, AJ

All 3 of choices for fourth song repeat in the first three songs.

So, Number of ways to rearrange = (4!/2!) × 3 = 36,

So, total number of ways = 96 + 36 = 132.

Therefore, the required number of ways of arrangement is 132 ways, the correct option is (b).

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The given question is incomplete, the complete question is

Amy, Beth, and Jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible?

(a) 108

(b) 132

(c) 671

(d) 846

(e) 1105

The association on the line is a negative linear assosciation and other solutions are shown below

To find the slope of the line passing through the given points, we use the slope formula

slope = (change in y) / (change in x)

Let's use the points (0, 90) and (8, 40) to find the slope:

slope = (40 - 90) / (8 - 0) = -50 / 8 = -6.25

The y-intercept is 90 i,e, when x = 0

The equation is represented as

y = mx + c

Where

m = slope and c = y when x = 0

So, we have

y = -6.25x + 90

The association on the line is a negative linear assosciation

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The total volume of the plant stand is given by the sum of these expressions: (x+1)³ + (x+1) * (x+1) * (x-1) + (2x+3) * (2x-2) * (x+1)

Volume refers to the amount of space occupied by an object or substance. It is typically measured in cubic units (such as cubic centimeters, cubic inches, or liters) and is used to describe the size or capacity of an object or container. Volume can also refer to the loudness or intensity of a sound. In physics, volume is an important measurement in determining the properties and behavior of gases, liquids, and solids.

Here,

Let's calculate the volume of each section based on the given sides.

Cube with sides x+1:

The formula for the volume of a cube is V = side³, where side is the length of one of its sides. In this case, the side length of the cube is x+1, so the volume of this section would be:

V1 = (x+1)³

Cuboid with sides x+1, x+1, and x-1:

The formula for the volume of a cuboid is V = length * width * height. In this case, the length would be x+1, the width would be x+1, and the height would be x-1. So the volume of this section would be:

V2 = (x+1) * (x+1) * (x-1)

Cuboid with sides 2x+3, 2x-2, and x+1:

Similarly, using the formula for the volume of a cuboid, the volume of this section would be:

V3 = (2x+3) * (2x-2) * (x+1)

Now, to find the total volume of the plant stand, we can add up the volumes of all three sections:

Total volume = V1 + V2 + V3

= (x+1)³ + (x+1) * (x+1) * (x-1) + (2x+3) * (2x-2) * (x+1)

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The measure of angle y is 32°.

To find the measure of angle y, follow these steps:
1. Since the exterior angle to angle x is w, and w measures 100°, we can use the fact that the sum of an interior angle and its corresponding exterior angle is 180°.

So, angle x = 180° - 100° = 80°.
2. Now we know that a triangle has angles x, y, and z.

The sum of angles in a triangle is always 180°.

We have x = 80° and z = 68°,

so we can find angle y as follows:

y = 180° - (80° + 68°)

= 180° - 148°

= 32°.

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The solutions in the interval [0, 2) are:

x = 0 and x = 2π/3.

What is the trigonometric ratio?

The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Using the identity cos2θ = cos²θ - sin²θ, we can rewrite the equation as:

cos²x - sin²x = cos x

We can then use the Pythagorean identity sin² x + cos² x = 1 to substitute for sin² x:

cos²x - (1 - cos²x) = cos x

Simplifying this equation gives:

2cos² x - cos x - 1 = 0

We can solve for cos x using the quadratic formula:

cos x = [1 ± √(1 + 8)] / 4

cos x = [1 ± √9] / 4

cos x = (1 ± 3) / 4

cos x = 1 or cos x = -1/2

If cos x = 1, then x = 0.

If cos x = -1/2, then x = 2π/3 or x = 4π/3.

However, we need to check that these solutions are in the interval [0, 2). The solution x = 4π/3 is outside this interval, so we discard it.

Therefore, the solutions in the interval [0, 2) are:

x = 0 and x = 2π/3.

In increasing order, the solutions are:

x = 0 and x = 2π/3.

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48% of the people polled like playing golf.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

The percentage of people polled who like playing golf can be calculated by dividing the number of people who like golf (3,360) by the total number of people polled (3,360 + 3,640 = 7,000) and then multiplying by 100 to express the answer as a percentage:

(3360 ÷ 7000) x 100% = 48%

Therefore, 48% of the people polled like playing golf.

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For any value of x and y, this equation cannot be true. As a result, the equation system has no solution.

0x + 0y = 1

The elimination approach can be used to resolve the system of equations below.

How does elimination work?

The elimination method is a method for algebraically resolving systems of linear equations. Using fundamental arithmetic operations, we can eliminate any one of the variables in the elimination technique, and then we can simplify the equation to determine the value of the remaining variable1.

The elimination procedure involves the following steps:

1. Choose one variable to leave out.

2. In order to make the coefficients of that variable opposite in sign, multiply or divide both equations by a non-zero constant.

3. Adjust the resulting equations such that the selected variable is removed.

4. Simplify and ascertain the other variable's value.

According to the question:

2x - 3y = 6

4x - 6y = 11

The result of multiplying the first equation by two is:

4x - 6y = 12

We can now take the second equation out of this equation:

4x - 6y = 12

(4x - 6y = 11)

—————————

0x + 0y = 1

For any value of x and y, this equation cannot be true.

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This bond has a Current yield of 6.9 percent, a volume of 18, and a net change of negative one-eighth. The correct answer is (a)  101Three-fourths; $101,750.

The bond listing provided is a typical example of how Corporate bonds are displayed. The table consists of 5 columns with 1 row, where each column provides specific information about the bond.

The first column displays the name of the bond, which in this case is NYTel 7 and one-fourth 33, indicating that it is a bond issued by New York Telephone.

The second column shows the current yield of the bond, which is 6.9 percent.

The third column displays the volume of the bond, which is 18.

The fourth column provides the closing price of the bond, which is 101 and three-fourths.

Finally, the fifth column shows the net change of the bond, which is negative one-eighth.

To answer the question, we need to determine the closing price and dollar amount of the bond. According to the bond listing, the closing price of the bond is 101 and three-fourths. To calculate the dollar amount, we need to multiply the closing price by the face value of the bond. Assuming that the face value of the bond is $1,000, the dollar amount of the bond would be $101,750 (101.75 x 1000).

Therefore, the correct answer is (a) 101Three-fourths; $101,750. This bond has a current yield of 6.9 percent, a volume of 18, and a net change of negative one-eighth. Understanding how to read and interpret bond listings is crucial for investors who want to make informed investment decisions.

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Option A is the answer. The system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:

8c + 6v ≤ 70

8c + 6v ≤ 7016c + 20v ≥ 150

The cost of c gallons of chocolate ice cream is $8c, and the cost of v containers of vanilla ice cream is $6v. Krystal wants to spend no more than $70 on ice cream, so the inequality for the total cost of ice cream is:

8c + 6v ≤ 70

Krystal needs at least 150 servings of ice cream, and each gallon of chocolate ice cream provides 16 servings, while each container of vanilla ice cream provides 20 servings. The inequality for the total number of servings of ice cream is:

16c + 20v ≥ 150

Therefore, the system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:

8c + 6v ≤ 70

16c + 20v ≥ 150

Option A is the correct answer.

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Answer:

A) Jeremy has the greater speed.  

B) y = 23x

C)  See graph

D) The slope is 23.  This means that Lauren can travel 23 miles in 1 hour.

Step-by-step explanation:

Part A:

Kevin's rate is 11.5 miles per hour.

Take two points, I used (2,23) and (4,46) to find the rate for Kevin.

Find the change in y over the change in x.  The y values are 46 and 23.  The x values are 4 and 2.  You find the change by subtracting

[tex]\frac{46-23}{4-2}[/tex] = [tex]\frac{23}{2}[/tex] = 11.5

Part B:

If Kevin's rate is 11.5, then Lauren's rate is 23

Part C:

See graph

 Part D :  

  The slope for C is 23.  This means that Lauren can ride 23 miles in one hour.

Helping in the name of Jesus.                                                                                      

The better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.

Everything in surveys revolves around asking the appropriate questions in the right ways since they are meant to elicit feedback. Many polls purposefully and unintentionally ask one-sided questions.

An objective question attempts to avoid using leading language and is fact-based rather than judgmental.

Biased questionnaire items use word choice and sentence structure in a way that affects how respondents react. This is sometimes done on purpose. This usually happens as a result of inadequate survey planning and assessment.

Here are a few advices.

Given query:

Thus, the better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.

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Answer:Radius = 21

Step-by-step explanation:

Volume of a sphere = 4/3 * pie * radius^3

12,348 pie = 4/3 * pie  radius ^3

12,348 = 4/3 * radius^3

(12,348 * 3)/ 4 = radius^3

9261 = radius^3

radius = 21

The calculated value of the surface area of the sphere is  676π

Given that

Radius, r = 13 inches

The formula for the surface area of a sphere is:

Surface area = 4πr^2

where r is the radius of the sphere

Substituting the given value of radius r = 13 inches, we get:

Surface area = 4π * 13^2

So, we have

Surface area = 676π

Hence, the surface area is 676π

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Answer:

1789/30

Step-by-step explanation:

To solve the expression

You have to convert the mixed fraction => improper:

(284/5 + 7/6) + 4/3

After that add:

1749/30 + 4/3

Add:

1789/30

To get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies, you would use a proportional relationship.

Let's say x represents the number of eggs used to make a certain number of cookies, y represents the number of cookies made, and z represents the number of eggs needed to make some other number of cookies.

Then, we can set up the proportion:

x eggs / y cookies = z eggs / (some other number of cookies)

We can then solve for z by cross-multiplying:

z eggs = x eggs * (some other number of cookies) / y cookies

This formula tells us how many eggs are needed to make the specified number of cookies, based on the number of eggs used and the number of cookies originally made.

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The impact on the mode will be insignificant.

When a new student joined the classroom with a height of 51 inches, the statistics that were calculated will be

impacted in the following ways:

Mean: The mean is calculated by adding up all the heights and then dividing the total by the number of heights. Since

the new student is much taller than the rest of the class, the addition of 51 to the data set will increase the sum of the

data set by a significant amount. This will cause the mean to increase.

Median: The median is the middle number when the data set is ordered from lowest to highest. Since the data set has

an odd number of values, the median is 40. When a new student joins the class with a height of 51 inches, this will

cause the median to increase to 40.5.

Mode: The mode is the number that appears most often in the data set. Since the mode of the given data is 40, adding

a new student with a height of 51 will not change the mode. Therefore, the impact on the mode will be insignificant.

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The manufacturer B is calculated to produce, on the average, the fewest number of defective rivets amongst all the manufacturers.

To determine which manufacturer will produce, on average, the fewest number of defective rivets, we need to calculate the proportion of defective rivets for each manufacturer.

Let X be the breaking strength of a rivet from manufacturer A, and let Y be the breaking strength of a rivet from manufacturer B. Then:

P(X < 10000) = P((X - μ_A) / σ_A < (10000 - μ_A) / σ_A) = P(Z_A < -2.5) ≈ 0.0062

where Z_A is a standard normal random variable, and we use the given values μ_A = 14000 psi and σ_A = 2000 psi.

Similarly:

P(Y < 10000) = P(Z_B < -3) ≈ 0.0013

where Z_B is a standard normal random variable, and we use the given values μ_B = 13000 psi and σ_B = 1000 psi.

Therefore, the proportion of defective rivets for manufacturer A is approximately 0.0062, and the proportion of defective rivets for manufacturer B is approximately 0.0013.

Since manufacturer B has a lower proportion of defective rivets, on average, it will produce fewer defective rivets than manufacturer A. So the manufacturer that will produce, on average, the fewest number of defective rivets is manufacturer B.

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If every 2 inches of Yolanda's drawing represents 3 feet of the actual wall, we can use the scale factor to convert the dimensions of the drawing to the dimensions of the actual wall.

Since we are dealing with area, we need to square the scale factor.

2 inches : 3 feet

(2 inches / 3 feet)^2 = (2/36)² = 1/324

This means that every square inch of Yolanda's drawing represents 1/324 square feet of the actual wall.

If the area of the mural in Yolanda's drawing is A square inches, then the area of the actual mural is:

A (square inches) x (1/324) (square feet per square inch) = A/324 square feet

Therefore, to find the area of the actual mural in square feet, we need to first find the area of the mural in Yolanda's drawing and then divide by 324.

If the area of the mural in Yolanda's drawing is, for example, 500 square inches, then the area of the actual mural is:

500 (square inches) / 324 = 1.54 square feet (rounded to two decimal places)

Therefore, the area of the actual mural is 1.54 square feet.

[tex] \: \: [/tex]

I will solve each equation one by one to find the value of the variables:

a + 7 = 20

a = 20 - 7

a = 13

c - 12 = 29

c = 29 + 12

c = 41

46 + 12 = 60

b is not present in the equation. This equation cannot be used to find the value of b.

5x + 2x = 35

7x = 35

x = 35 / 7

x = 5

127 - 57 - 9 = 40

z is not present in the equation. This equation cannot be used to find the value of z.

5y + 3y + 4 = 68

8y = 68 - 4

8y = 64

y = 64 / 8

y = 8

2(x + 4) = 24

2x + 8 = 24

2x = 24 - 8

2x = 16

x = 16 / 2

x = 8

6(5g - 7) = 18

30g - 42 = 18

30g = 18 + 42

30g = 60

g = 60 / 30

g = 2

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The value of the N must be in order of the 31 so that the value of the Sn will get exceeded by 4.

Only when the kind of sequence is known can the sum of n words in a sequence be calculated. Normally, while computing the sum of an n-number of terms, we take into account arithmetic progression.

The common distinction between each following phrase and each preceding term remains unchanged throughout this process. Natural numbers are an illustration of AP, where the common difference is 1. Hence, in order to determine the sum of all natural numbers, we must be aware of the formula.

[tex]S_N = \sum^N_{k=1} \frac{1}{k}[/tex]

= 1 + 1/2 + 1/3 + 1/4 + ..... 1/N

It is a harmonic series,

Therefore, by trial and error method we get N = 31 to exceed Sn = 4

There are some elimination methods,

ln N + 1/N < Sn < ln N+1

we want Sn > 4

ln N+1/N < 4

maximum value of N is ln N+1/N =4

4<ln N+1 → ln N > 3, N > e³

5<ln N+1 → ln 4, N > e⁴

For Sn to exceed it value maybe in between

e³ < N < e⁴.

20.08 < N < 54.5

As I said it is an approximation it won't give exact value.

By taking a value in that range and check for desired value.

for N = 31 Sn willl exceed '4'.

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Complete question:

How large must N be in order for

[tex]S_N = \sum^N_{k=1} \frac{1}{k}[/tex]

to exceed 100 to exceed 4? Note: Computer calculations show that for SN to exceed 20, N = 272, 400, 600 and for Sn to exceed 100, N = 1.5x10⁴³.

N = ?