Which of the following represents a function?

Answer:

17 + 123 (4 - 1) + (36 / 18) 52 =

17 + 123 x 3 + 2 x 52 =

17 + 369 + 104 =

17 + 473 =

490

Step-by-step explanation:

hope this helps! i made up everything so i hope its okay!

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 1 \: + \: i \sqrt{6} \:(or) \: \: x = - 1 \: -\: i \sqrt{6} }}}}}}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:2}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \: {x}^{3} + 3x - 14 = 0[/tex]

➺[tex] \: {x}^{2} (x + 1) - x(x + 1) + 4(x + 1) = 18[/tex]

➺[tex] \: (x + 1)( {x}^{2} - x + 4) = 18[/tex]

➺[tex] \: {x}^{2} - x + 4 = \frac{18}{(x + 1)} [/tex]

➺[tex] \: {x}^{2} - x + 4 - 6 = \frac{18}{(x + 1)} - 6[/tex]

➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6(x + 1)}{(x + 1)} [/tex]

➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6x - 6}{(x + 1)} [/tex]

➺[tex] \: (x - 2)(x + 1) = \frac{12 - 6x}{(x + 1)} [/tex]

➺[tex] \: (x - 2)(x + 1) = \frac{ - 6(x - 2)}{(x + 1)} [/tex]

➺[tex] \: (x + 1 )² = \frac{ - 6(x - 2)}{(x + 1)(x - 2)} [/tex]

➺[tex] \: (x + 1)² = \frac{ - 6}{(x + 1)} [/tex]

[tex]\sf\pink{Error\:corrected\:here. }[/tex]

➺[tex] \: {x}^{2} + 2x + 1 = - 6[/tex]

➺[tex] \: {x}^{2} + 2x + 7 = 0[/tex]

By quadratic formula, we have

➺[tex] \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

➺[tex] \: x = \frac{ - 2± \sqrt{ {2}^{2} - 4.1.7} }{2 \times 1} [/tex]

➺[tex]x = \frac{ - 2± \sqrt{ - 24} }{2 } [/tex]

➺[tex] \: x = \frac{ - 2± \sqrt{ - 1 \times 4 \times 6} }{2} [/tex]

➺[tex] \: x = \frac{ - 2± \sqrt{ - 1} \times \sqrt{4} \times \sqrt{6} }{2} [/tex]

➺[tex] \: x = \frac{ - 2 \: ± \: i \times 2 \times \sqrt{6} }{2} [/tex]

➺[tex] \: x = \frac{ - 2 \: ± \:i \: 2 \sqrt{6} }{2} [/tex]

➺[tex] \: x = \frac{ 2 \: ( - 1 \: ± \: i \: \sqrt{6}) }{2} [/tex]

➺[tex] \: x = - 1 \: ± \: i \sqrt{6} [/tex]

Therefore, the two values of [tex]x[/tex] are ([tex] \: - 1 \: + \: i \sqrt{6}[/tex]) and ([tex] \: - 1 \: -\: i \sqrt{6}[/tex]).

[tex]x[/tex]³ + 3 [tex]x[/tex] - 14 = 0

➼ [tex]x[/tex]³ + 3 [tex]x[/tex] = 14

➼ [tex]x[/tex] ( [tex]x[/tex]² + 3 ) = 14

Factors of 14 = 1, 2, 7 and 14.

a) Substituting [tex]x\:=\:1[/tex], we have

➼ 1 ( 1 + 3 ) ≠ 14

➼ 1 x 4 ≠ 14

➼ [tex]\boxed{ 4\: ≠ \:14 }[/tex]

b) Substituting [tex]x\:=\:2[/tex], we have

➼ 2 ( 2² + 3 ) = 14

➼ 2 ( 4 + 3 ) = 14

➼ 2 x 7 = 14

➼ [tex]\boxed{ 14 \:= \:14 }[/tex]

c) Substituting [tex]x\:=\:7[/tex], we have

➼ 7 ( 7² + 3 ) ≠ 14

➼ 7 ( 49 + 3 ) ≠ 14

➼ 7 x 52 ≠ 14

➼ [tex]\boxed{ 364\: ≠ \:14 }[/tex]

d) Substituting [tex]x\:=\:14[/tex], we have

➼ 14 ( 14² + 3 ) ≠ 14

➼ 14 x 199 ≠ 14

➼ [tex]\boxed{ 2786\: ≠ \:14 }[/tex]

Hence, our only real solution is 2.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Step-by-step explanation:

the answer is in the above image

Answer:

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

There are 750 identical plastic chips numbered 1 through 750 in a box

This means that [tex]a = 1, b = 750[/tex]

What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?

[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Answer:

If cars did not exist people could do as the did before they were invented. Such as walk to where they need to go or use a horse and buggy or carriage.

Step-by-step explanation:

Answer:

Area of square = Side²

Step-by-step explanation:

The area of a 2-D region, form, or flattened lamina in the planes is the quantity that represents its extent. On the 2-D surface or 3-D object, surface is its counterpart. A shape's area can be calculated by comparing it to squares of a specific size.

Area of square = Side²

Answer:

7/19

Step-by-step explanation:

7/19=square root of 11=22-3 19

The confidence interval of the true proportion of low income people who will vote for the introduction of the tax is

Yes, we can conclude that at the 5% level of significance, the proportion of high income voters favoring the new security tax is 10% higher than that of low income voters using Test of Significance for Difference of Proportions.

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Proportion of high-income people who will vote for the introduction of the tax = p1 =  [tex]\frac{80}{100} = \frac{4}{5}[/tex][tex]= 0.8[/tex]

Proportion of low-income people who will vote for the introduction of the tax = p2 =  [tex]\frac{55}{80} = \frac{11}{16}[/tex] [tex]= 0.6875[/tex]

95% confidence interval of the true proportion of low income people who will vote for the introduction of the tax -

Upper confidence interval -

[tex]= p + 1.96 \sqrt{pq/n}[/tex]

[tex]=0.6875 + 1.96 \sqrt{(0.6875)(1-0.6875)/80} \\= 0.6875 + 1.96 \sqrt{0.00268} \\=0.789[/tex]

Lower confidence interval -

[tex]= p - 1.96 \sqrt{pq/n}[/tex]

[tex]=0.6875 - 1.96 \sqrt{(0.6875)(1-0.6875)/80} \\= 0.6875 - 1.96 \sqrt{0.00268} \\=0.586[/tex]

Test of Significance for Difference of Proportions is used when we want to compare two distinct populations with respect to the prevalence of a certain attribute, say A, among their members.

n1 = 100

X1 = 80

p1 = 0.8

n2 = 80

X2 = 55

p2 = 0.6875

H0:  the proportion of high-income voters favoring the new security tax is 10% higher than that of low-income voters.(P1 - P2 = 0.1)

H1:  the proportion of high-income voters favoring the new security tax isn't 10% higher than that of low-income voters. (P1 - P2 != 0.1)

[tex]z = \frac{(p1 - p2) - (P1 -P2)}{(\frac{X1+X2}{n1+n2})(1-\frac{X1+X2}{n1+n2})(\frac{1}{n1}+\frac{1}{n2} ) }[/tex]

[tex]z = \frac{(0.8 - 0.6875)- 0.1}{\sqrt{0.75*0.25*0.0225} } \\\\z = \frac{0.0125}{0.0649} \\\\z = 0.1926[/tex]

Since z = 0.1926 < 1.96, null hypothesis cannot be rejected. Thus,  the proportion of high-income voters favoring the new security tax is 10% higher than that of low-income voters.

Learn more about confidence interval here

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Answer:

The correct answer is - 178.

Step-by-step explanation:

The standard deviation is a measure of the amount of dispersion in a set of values.

Given:

Mean of a normal distribution (m) = 154

Standard deviation (s) = 15

z-score = 1.6

Solution:

To find: value (x) that has a z-score of 1.6

z-score is given by = x-u/15

1.6*15 = x-154

=> 154+24 = x

x = 178

Step-by-step explanation:

The given expression is :

[tex]\dfrac{a^3b^{-2}}{ab^{-4}}[/tex]

We need to simplify the above expression.

a³ is in numerator and a is in denominator. It gts cancelled.

[tex]\dfrac{a^3b^{-2}}{ab^{-4}}=\dfrac{a\times a\times a\times b\times b\times b\times b}{a\times b \times b}\\\\=\dfrac{a^2\times b^{-2}\times b^4}{1}\\\\=\dfrac{a^2}{b^{-2}}[/tex]

Hence, this is the required solution.

Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y)  = [tex]$100x-34x^2+5xy+50y+3xy-16y^2$[/tex]

[tex]$R(x,y) = 100x-34x^2+8xy+50y-16y^2$[/tex]

In order to maximize the revenue, set

[tex]$R_x=0, \ \ \ R_y=0$[/tex]

[tex]$R_x=\frac{dR }{dx} = 100-68x+8y$[/tex]

[tex]$R_x=0$[/tex]

[tex]$68x-8y=100$[/tex]  .............(i)

[tex]$R_y=\frac{dR }{dx} = 50-32x+8y$[/tex]

[tex]$R_y=0$[/tex]

[tex]$8x-32y=-50$[/tex]  .............(ii)

Solving (i) and (ii),

4 x (i)    ⇒       272x - 32y = 400

     (ii)   ⇒   (-)     8x - 32y = -50  

                        264x        = 450

∴   [tex]$x=\frac{450}{264}=\frac{75}{44}$[/tex]

     [tex]$y=\frac{175}{88}$[/tex]

So, x ≈  $ 1.70      and    y = $ 1.99

    R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

          1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

Answer:

Exponential Function

Step-by-step explanation:

y values increase by x4

Answer:

exponential function

the ans is b

Answer:

[tex]y = -4x + 2[/tex]

Step-by-step explanation:

Required

Determine the equation

From the question, we understand that, it is parallel to:

[tex]4x + y -10 = 0[/tex]

This means that they have the same slope.

Make y the subject to calculate the slope of: [tex]4x + y -10 = 0[/tex]

[tex]y = -4x + 10[/tex]

The slope of a line with equation [tex]y =mx + c[/tex] is m

By comparison:

[tex]m = -4[/tex]

So, the slope of the required equation is -4.

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where:

[tex](x_1.y_1) = (2,-6)[/tex]

So, we have:

[tex]y = -4(x - 2) -6[/tex]

Open bracket

[tex]y = -4x + 8 -6[/tex]

[tex]y = -4x + 2[/tex]

Step-by-step explanation:

there is something wrong with your question.

there is no parallelogram with 8 and 6 ft side lengths that has an area of 54 ft².

the maximum area of a parallelogram with 8 and 6 ft side lengths is 48 ft². and that is a rectangle 8×6 as a special form of a parallelogram.

the area of any parallelogram is calculated

Ap = base length × height

and height is the length of the line perpendicular to the base line to one of the corners on the opposite side (as long as the base line).

if Ap = 54, and the base length is 8, this means

54 = 8 × height

height = 54/8 = 6.75 ft

but the height can only be the length of a side connected to the base line or less. not longer.

and in our example here, this connected side is 6. so, the height can only be 6 or less. not 6.75.

so, there must be something wrong with your numbers.

once you get the actual numbers, use my approach above with them (replace whatever number is wrong here by the true value).

Answer:

Therefore each suit cost $600 and each jean cost $199

Step-by-step explanation:

Let x represent the price of each suit and let y represent the price of each jeans.

Since 3 suits and 3 pairs of jeans cost $2397, this can be represented by the equation:

3x + 3y = 2397

Dividing through by 3:

3x/3 + 3y.3 = 2397/3

x + y = 799    (1)

Also, 8 suits and 11 pairs of jeans cost $6989, this can be represented by the equation:

8x + 11y = 6989      (2)

To find x and y, solve equation 1 and 2 simultaneously. Multiply equation 1 by 8 and subtract from equation 2 to get y:

3y = 597

y = $199

Put y = $199 in equation 1:

x + 199 = 799

x = $600

Therefore each suit cost $600 and each jean cost $199.

Answer:y=log1x

Step-by-step explanation:

Answer:

$24.00=$21.50+r*$.50

Step-by-step explanation:

total cost= entrance fee + r (number of rides) * $0.50 (cost of rides)

$24.00=$21.50+r*$.50

2.50=r*.50

2.5/.5=r

r=5

Answer:

3

Step-by-step explanation:

(10, 5) and (15,20)

m = rise/run

m = ∆y/∆x

m = (y₂ - y₁) / (x₂ - x₁)

m = (20 - 5) /(15 - 10)

m = 15/5

m = 3

Answer:

$5.5 per pound of meat

Step-by-step explanation:

$20.35 ÷ 3.7 = $5.50

Hope this is helpful

Answer:

5

Step-by-step explanation:

10/2=5

The scale factor of the given case that the distance from D to D' is 10 and the distance from A to D is 2 will be 5.

What is the scale factor?

The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics.

The scale factor is the ratio between two big and small figures and the ratio is called a scale for the given geometry.

For example, if we have a triangle with a side of 10 meters and another triangle with a side of 5 then the scale ratio will be 10/5 = 2.

Given that

distance from D to D' is 10

distance from A to D is 2  

So the scale ratio will be

DD'/AD  = 10/2  = 5 hence scale ratio will be 5 for the given

geometry.

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Answer:

First set: 0.95. Second set: 0.86. Third set: 0.88.

Step-by-step explanation:

Imagine that these are not decimals, they are regular numbers (for example: 0.88 is turned into 88). You would determine which one is the greatest depending on which one is higher (like 44 is higher than 32). Therefor the first set: 0.95 the second set: 0.86 the third set: 0.88.

Answer:

6 and 5 over 6

6 5/6

Step-by-step explanation:

it would be a mixed fraction because 6 can't go into 41 evenly

Answer:

6

Hope that this helps!

Answer:

x = -3

Step-by-step explanation:

2x – 3(x + 8) = -21

Distribute

2x - 3x - 24 = -21

Combine like terms

-x - 24 = -21

Add 24 to both sides

-x = 3

Multiply both sides by -1

x = -3

Answer:

All real number greater than equal to zero.

Step-by-step explanation:

The function is given by

[tex]f(x) = \frac{4}{5}\sqrt x[/tex]

The domain is defined as the input values so that the function is well defined.

here, the values of x should be all real number and zero also.

So, the correct option is  (d).

Answer:

D

Step-by-step explanation:

Answer:

B. The distance of an archer's shots from the center of a target

C. The time it takes for an airliner to fly from Los Angeles to New York

Step-by-step explanation:

According to the Question,

B & C should each have a range of values that cover most occurrences with outlying values that decrease in number as they move further away from the dominant value range, which is the definition of a normal distribution.

Aver si le entiendes bro

Answer:

Step-by-step explanation:

From Left (earliest) to Right (most recent)

First Pharaoh   3100 BC

First Babylon    1830 BC

First Mali            1235 CE

First US President 1789 CE