Which of the fallowing expressions represents the distance between -4 and 1

Answer:x2−7x−8=0

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Step-by-step explanation:

The number with the given characteristics is 17

Let the tens be x and the units be y.

So, the number is 10x + y

The relationship between the digits is

y = x + 6

The relationship between the number and the reverse is

2(10x + y + 10y + x) = 6 + 10 * (10x + y)

Simplify the second equation

2(11x + 11y) = 6 + 100x + 10y

Open the brackets

22x + 22y = 6 + 100x + 10y

Substitute y = x + 6

22x + 22(x + 6) = 6 + 100x + 10(x + 6)

Expand

22x + 22x + 132 = 6 + 100x + 10x + 60

Collect like terms

22x + 22x - 100x - 10x = 6 + 60 - 132

Evaluate the like terms

-66x = -66

Divide by -66

x = 1

Substitute x = 1 in y = x + 6

y = 1 + 6

y = 7

Recall that the number is 10x + y

So, we have

Number = 10 * 1 + 7

Evaluate

Number = 17

Hence, the number is 17

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The speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

It should be noted that the speed is calculated as:

= Distance/Time

Based on the information, the DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr.

Therefore, (v + w) = 3000/3

v + w = 1000 .... I

(v - w) = 3000/4

v - w = 750 .... ii

We'll then add both equations together. Therefore, the speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

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The y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

The y-intercept of a function is the point where the value of x is zero. Given the function below;

4x-9y=36

when the value of x is zero, hence;

4(0) - 9y = 36

Simplify to have:

0 - 9y = 36

-9y = 36

Divide both sides by -9 to have:

-9y/-9 = 36/-9

y = -4

Hence the y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

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The price at which equilibrium is achieved is $20.

The equilibrium point is the point where the lines of the demand and supply functions meet.

From the question, we understand that price is plotted on the vertical axis (i.e. the y-axis).

Also from the question, the lines intersect at point (15, 20).

The y-coordinate of the intersection point is 20 in this scenario.

Hence, the price at which equilibrium is achieved is $20.

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Answer:

b

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think you are trying to use synthetic division for

[tex]x^{4} -2x^{3} -2x^{2} +3x-5[/tex] divided by x-3

First  

x -3 = 0 , make it equal to 0 and add 3 to both sides

x = 3

Then we write all the coefficients and continue with

a pattern of multiply by 3 and add to the next coefficient.

See attachment.

Answer:

  4.346%

Step-by-step explanation:

The points and origination fee are assumed to be capitalized, so the loan payment amount is based on the total of the original loan amount and those fees. The APR is calculated as the rate that would be charged on the original loan value to produce that payment.

The loaned amount is the sum of the original loan value and the added points.

  P = $513,000×(1 +1.4% +0.65%) = $523,516.50

The monthly payment on this amount is given by the amortization formula ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where r=0.04175, the annual interest rate, t=30, the period in years

  A = $523,516.50(0.04175/12)/(1 -(1 +0.04175/12)^-360)) ≈ $2552.45

There is no formula for calculating the APR. It must be developed iteratively or graphically. The attached calculator images show a couple of different ways the value can be found.

The payment of $2552.45 on a loan value of $513,000 represents an APR of 4.346%.

The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

The function is given as:

f(x)=−2x3+x2−4x+1 is divided by x+3.

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Calculate f(-3)

f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1

Evaluate the expression

f(-3)= 76

Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = a, GH = b and GJ = c

put the value of a from equation 1 in equation 2

now, put the value of a and c in equation 3

Now, we need to find HJ (a)

[tex]{ \qquad \large \sf {Conclusion} :} [/tex]

Answer:

assume the formula is true for n is equal to k prove that result is true for n is equal to k + 1 hence result proves since the thorum is true for n is equal to 1 and n k + 1 is unit through a and

If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.

Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.

We are required to find the database whose standard deviation is lower.

Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.

Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.

Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.

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The dosage needed for this in an  order for morphine sulfate 1/4 gr IM stat is 1.5 ml.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

One grain =  60mg, hence:

1/4 gr = 1/4 gr * 60 mg per gr = 15 mg

Hence, for 10 mg per ml:

Dosage = 15 mg /  10 mg per ml = 1.5 ml

The dosage needed for this in an  order for morphine sulfate 1/4 gr IM stat is 1.5 ml.

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The volume of the solids are 240 cubic yards and 125.6 cubic cm

The complete question is added as an attachment

Solid 1

The shape is a rectangular prism.

The volume of a rectangular prism is

Volume = Length * Width * Height

So, we have

Volume = 8 yd * 5 yd * 6 yd

Evaluate

Volume = 240 cubic yards

Hence, the volume of the solid is 240 cubic yards

Solid 2

The shape is a cylinder.

The volume of a rectangular prism is

Volume = πr²h

So, we have

Volume = 3.14 * 2^2 * 10

Evaluate

Volume = 125.6 cubic cm

Hence, the volume of the solid is 125.6 cubic cm

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The two quadrilateral with the listed properties are kite and rhombus respectively.

Thus, the two quadrilateral with the listed properties are kite and rhombus respectively.

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Answer:

your welcome

Step-by-step explanation:

The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.

Number of days =  1       2     3      4      5       6            Total = 6
                              1.72  1.8    1.86 1.88  1.74   1.86                  

The average of the values is the ratio of the total sum of values to the number of values.

Since the mean of the heights of the tides,
= sum of heights / number of heights observation
=  (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters

Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

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The number of $1, $5 and $10 are 49, 44 and 22 respectively.

There are 3 denominations of bills in a wallet: $1, $5, and $10.

There are 5 fewer $5-bills than $1-bills.

let

x = number of $1 bills

Hence,

number of $5 bills = x - 5

There are half as many $10-bills as $5-bills.

number of $10 bills = 1 / 2 (x - 5)

Therefore,

x + x - 5 + 1 / 2 (x - 5) = 115

2x - 5  + 1 / 2 x - 5 / 2 = 115

2x + 1 / 2 x - 5 - 5 / 2 = 115

5 / 2 x  - 7.5 = 115

2.5x  = 115 + 7.5

x = 122.5 / 2.5

x = 49

Number of $1 bills = 49

Number of $5 bills = 49 - 5 = 44

Number of $10 bills = 1 / 2 (49 - 5) = 22

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Answer:

If the question asked mixed fraction:

7/3 = 2 1/3

4/2 = 2

Step-by-step explanation:

I converted it to mixed fraction because it is already improper fraction.

a. By replacing [tex]x[/tex] with [tex]-x^2[/tex] in the power series, we get

[tex]\displaystyle \frac1{1+x^2} = \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n}[/tex]

Integrate both sides to recover [tex]\arctan(x)[/tex] on the left.

[tex]\displaystyle \int \frac{dx}{1+x^2} = \int \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n} \, dx[/tex]

[tex]\displaystyle \arctan(x) = C + \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

By letting [tex]x=0[/tex] on both sides, we find [tex]C=0[/tex], so that

[tex]\displaystyle \arctan(x) = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

Then dividing both sides by [tex]x[/tex] gives

[tex]\displaystyle \boxed{\frac{\arctan(x)}x = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n} \, dx}[/tex]

b. Let [tex]x=\frac1{\sqrt3}[/tex]. Then

[tex]\displaystyle \frac{\arctan\left(\frac1{\sqrt3}\right)}{\frac1{\sqrt3}} = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} \left(\dfrac1\sqrt3\right)^{2n}[/tex]

[tex]\displaystyle \sqrt3 \arctan\left(\frac1{\sqrt3}\right) = \sum_{n=0}^\infty \frac1{2n+1} \left(-\frac13\right)^n[/tex]

Taking the first few terms from the infinite series, we can approximate

[tex]n=0 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1[/tex]

[tex]0\le n\le1 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1+\dfrac13\left(-\dfrac13\right) = \dfrac89[/tex]

which together suggest the value we want is bounded between 8/9 and 9/9 = 1, hence [tex]\boxed{p=8}[/tex].

Since the series is alternating and converges on [tex]-1<x<0\cup0<x<1[/tex],

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^0 a_n \right| < |a_1| = \left|\frac13 \left(-\frac13\right)^1\right| = \frac19[/tex]

and

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^1 a_n \right| < |a_2| = \left|\frac15 \left(-\frac13\right)^2\right| = \frac1{45}[/tex]

which tells us the first approximation is off by at most 1/9 from the actual value of [tex]\frac\pi{2\sqrt3}[/tex], whereas the second approximation is off by at most 1/45 from the actual value. In other words, the second approximation is closer, so [tex]\frac\pi{2\sqrt3}[/tex] is closer to [tex]\frac p9[/tex] :

[tex]\dfrac89 \approx 0.8889[/tex]

[tex]\dfrac{\pi}{2\sqrt3}\approx0.9069[/tex]

[tex]\dfrac99 = 1[/tex]

a. The value of cos2θ = -119/169

b. The value of cosθ = -5/13

The question involves trigonometric identities

Trigonometric identities show the relationship between trigonometric ratios.

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cos2θ = 1 - 2sin²θ

Substituting sinθ = 12/13  into the equation, we have

cos2θ = 1 - 2sin²θ

cos2θ = 1 - 2(12/13)²

cos2θ = 1 - 2(144/169)

cos2θ = 1 - 288/169

cos2θ = (169 - 288)/169

cos2θ = -119/169

So, the value of cos2θ = -119/169

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cosθ = √(1 - sin²θ)

Substituting sinθ = 12/13  into the equation, we have

cosθ = √(1 - sin²θ)

cosθ = √[1 - (12/13)²]

cosθ = √[1 - (144/169)]

cosθ = ±√(169 - 144)/169

cosθ = ±√25/169

cosθ = ±5/13

θ is the quadrant II, it means that 90° ≤ θ ≤180° it means that cosθ is negative.

So, cosθ = -5/13

So, the value of cosθ = -5/13

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Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

Exponential Function can be used for increase rate and also for decay rate.  The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³

If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.

Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation

y = 5000(0.98)^x  represents the value, y, of one account that was left inactive for a period of x years.

According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

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Answer:

The area of windowpane is answer.

Answer:

The area of the window pane

Step-by-step explanation:

The area of an object is the width x length of said object.

Ex: A  4 x 4 sized square has an area of 16 ( 4 x 4 = 4 by 4)

P.S. The area of Andrea´s windowpane is 648.

Using translation concepts, it is found that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The translation y -> y + k represents:

Hence:

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The conclusion regarding the publisher's claim regarding the hypothesis is that have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.

The null hypothesis is a statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

Since we reject the null hypothesis , we have sufficient evidence to support the claim. In this case, we have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.

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Complete question:

A newsletter publisher believes that less than 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

The mean, median, and mode are;

median=77

Mean=73.33

Mode= 78, 67

This is further explained below.

Generally, The middle number in a list that is arranged from smallest to greatest is referred to as the median. On the list, the value that occurs most often is known as the mode. Therefore

median=77

Generally, In mathematics, particularly statistics, the term "mean" may refer to a number of different concepts. The purpose of each mean is to summarize a certain collection of data, often for the purpose of gaining a better understanding of the overall value of a specific data set.

A dataset's mean (also known as the arithmetic mean, which is distinct from the geometric mean) is calculated by dividing the sum of all of the values in the dataset by the total number of values in the dataset. It is the measure of central tendency that is used the most often, and it is sometimes referred to as the "average."

[tex]mean=\frac{\sum x}{n}\\\\Mean=\frac{78+67+98+50+67+78+67+77+78}{9}[/tex]

Mean=73.33

Mean=73.3 in one dp

In conclusion, The mode is the number that appears the most often, or the number that stands out as having the most occurrences overall. The number 2 is the mode of the sequence 4, 2, 4, 3, 2, 2 because it appears three times, which is more than any other number in the sequence.

The mode of 78, 67, 98, 50, 67, 78, 67, 77, 78  is

Mode= 78, 67

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Answer:

fully factored form = 3(x-4)(x+8)

Step-by-step explanation:

first you factor 3 out

3(x^2+4x-32)

then factor it

3(x-4)(x+8)

Answer:

3(x-4)(x+8) This is the answer :)

Step-by-step explanation:

3x^2+12x - 96

3(x^2+4x-32)

3(x^2+4x--32)

3(x^2+8x-4x-32)

3(x^2+8x-4x-32)

3(x(x+8)-4(x+8))

3(x(x+8)-4(x+8))

3(x-4)(x+8)

3(x=4)(x+8)

Part 1)  [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.

Part 2)  The series converges

======================================================

Work Shown:

[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]

[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]

Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series  

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]  

either converge together or diverge together due to the Limit Comparison Test.

But the simpler series is known to converge (p-series test).

Therefore, the original series converges as well.

The two series likely don't converge to the same value, but they both converge nonetheless.

Answer:

a) A = 3, B = 8.

b) C = 2, D = 25

Step-by-step explanation:

See the image below.

The new curriculum significantly affects the earning potential.

According to the question, Eight kids were chosen at random to take part in a brand-new educational program that emphasizes both academics and mental health education between middle school and high school. The average annual income is $29432. The standard deviation is unknown.

The probability level is given to be 5%.

When the p-value is less than or equal to your significance level, reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data.

A probability level of 0.05 means that the new curriculum significantly affects the earning potential.

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The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D

9√4.000

= 4.000/9

= 0.444

Approximately,

= 0.4

Fraction

This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.

Decimal

This is a number expressed in the decimal system (base 10).

Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.

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