calculus help needed!

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.

Answer:

The slope 7/5 and the y intercept is -3

Step-by-step explanation:

Y=7/5x-3

This equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope 7/5 and the y intercept is -3

Answer:

7/19

Step-by-step explanation:

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

Answer:

3x-2x+7=-9

We simplify the equation to the form, which is simple to understand  

3x-2x+7=-9

We move all terms containing x to the left and all other terms to the right.  

+3x-2x=-9-7

We simplify left and right side of the equation.  

+1x=-16

We divide both sides of the equation by 1 to get x.  

x=-16

Answer:

$53.07

Step-by-step explanation:

Delta Math

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

[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]

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➺[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]

Answer:y=log1x

Step-by-step explanation:

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

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:

$5.5 per pound of meat

Step-by-step explanation:

$20.35 ÷ 3.7 = $5.50

Hope this is helpful

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:

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.

For more about scale ratio,

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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:

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.

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:

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:

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:

False.

Step-by-step explanation:

Equivalent systems of equations are those that have the same solutions or roots, although they have different numbers of equations. Equivalent systems of equations must have the same number of unknowns.

In other words, two systems of equations are said to be equivalent when they have the same solutions. Equivalent systems of equations do not have to have the same number of equations, although they do have to have the same number of unknowns.

So, the sentence is false.

Step-by-step explanation:

You can't expect to get exactly 2500 out of 5000 tosses more than a few times . You will come pretty close, but that's only good in horseshoes.

Of course I'm answering this on the basis of a computer language and not actually performinig this a million tmes, each part of a million consisting of 5000 tosses.

Simulations and not completely unbiased, but based on experience, 5000 is a very small number and getting 2500 more than a couple of times is unlikely

The probability of flipping a coin

coming up heads and tails is 1/2.

So, toss 5000 times 5000/2= 2500

heads: 2500

tails : 2500

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.

Answer:

m(arc CD) = 112°

Step-by-step explanation:

Use the property of intersecting chords and angles between these chords,

m∠CED = [tex]\frac{1}{2}(\text{arc CD}+\text{arc}AB)[/tex]

m∠CED + m∠AED = 180°

80° + m∠CED = 180°

m∠CED = 100°

Now substitute the measure of angle CED and arc AB in the expression,

100° = [tex]\frac{1}{2}(88^{\circ}+\text{arc CD})[/tex]

200° = 88° + m(arc CD)

m(arc CD) = 112°

Aver si le entiendes bro

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

9514 1404 393

Answer:

  3.8 radians

Step-by-step explanation:

The length of an arc is given by ...

  s = rθ . . . . . where r is the radius and θ is in radians

so the angle is ...

  θ = s/r

  θ = 29.6/7.7 ≈ 3.8

The angle is about 3.8 radians.

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:

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.

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