Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]

Since, c = 5 so,

[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³  ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

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Answer:

3.75

Step-by-step explanation:

3/4 times 5 =3 3/4

Answer: 38 teachers.

Step-by-step explanation:

Let the share ratio be x.

So, quantity of teachers = 2x, quantity of male students = 17x,

quantity of female students = 18x.

17x+18x=665

35x=665

Divide the left and right sides of the equation by 35:

х=19.

2x=2*19

2x=38.

Answer:

Hey Desmariesin7587, the median of the data set that you gave is  15.9

Step-by-step explanation:

Since the amount of values in the data set was not even, I could not find a middle number. Instead, I added up all of the values and divided the total sum by the amount of values that there were; in this case, 10.

----------------------

Have a great day,

Nish

The 45th term of the arithmetic sequence is 178. Option C

Given the arithmetic sequence formula as;

an = 2 + 4(n − 1)

we have n = 45

Let's substitute the value of 'n' into the formula;

a = 2 + 4( 45 - 1)

expand the bracket

a = 2 + 4(44)

a = 2 + 176

a = 178

The 45th term is 178

Thus, the 45th term of the arithmetic sequence is 178. Option C

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The amount of variance for y that is predicted by its relationship with x is 64%.

Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset. Variance measures the variation of a data set.

Correlation is a statistical measure used to measure the linear relationship that exists between two variables. The greater the correlation coefficient is closer to one, the greater the linear relationship that exists between the two variables. A positive correlation occurs when the two variables move in the same direction.

Variance = (correlation coefficient²) x 100

(0.80²) x 100

0.64 x 100 = 64%

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Answer:

17 hours

Step-by-step explanation:

We first want to figure out how much money shes making per hour.

We can simply divide 176 by 8 getting us 22

Since we know she makes 22 dollars an hour we can divide 374 by 22 getting us 17.

Now we know it would take 17 hours to make 374 dollars

If you want to double check you can simply multiply 17 by 22 which would get you 374

Answer: 17 hours

Step-by-step explanation

The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

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Answer:

[tex] \frac{3}{2} [/tex]

Step-by-step explanation:

From the attached photo, we can deduce:

(2,2) as (x1,y1)

(-2,-4) as (x2,y2)

Slope Formula =

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Now we can substitute these values into the formula to find the slope.

Slope of line =

[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]

The new dimensions of the flower bed are 4√2 and 6√2

The dimensions of the initial rectangular flower bed are given as:

Length = 4ft

Width = 6 ft

The area of the new flower bed is twice the area of the old one.

This means that

New Area = Old Area * 2

Substitute the dimensions of the old area in the above equation

New Area = 4 * 6 * 2

Express 2 as √2 * √2

This gives

New Area = 4 * 6 * √2 * √2

Rewrite the above equation as:

New Area = 4√2 * 6√2

The area of a rectangle is

Area = Length * Width

This means that:

Length = 4√2 ft

Width = 6√2 ft

Hence, the new dimensions of the flower bed are 4√2 and 6√2

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Answer: 6x8

Step-by-step explanation:

(4+x)(6+x)=2*24

x^2+10x+24=48

subtract 48 on both sides

x^2+10x-24=0

Solve using the quadratic formula

-10±√(100+96)÷2

simplifies to

-(10±14)÷2 = 2, -12

-12 doesn't work though because the sides can't be negative.

So x=2

To check, add both sides by 2:

2(4x6)=6x8=48

Answer:

1.2 meters long

Step-by-step explanation:

3(4/5)m=3.8m

5m-3.8m=1.2m

The time it will take for the car to skid for 150 feet is 8.23 seconds.

The function D(t) = 18t² − 130t gives the distance a car going a certain speed will skid in t seconds.

The time the it would take for the car to skid for 150 feet can be calculated as follows:

Therefore,

D(t) = 18t² - 130t

150 =  18t² - 130t

18t² - 130t - 150 = 0

divide by 3

9t² - 65t - 75 = 0

Hence,

t = 65 ± 5√277 / 18

t = 8.23425471586 or -1.01166666667

Hence,

t = 8.23 seconds.

Therefore, the time it will take for the car to skid for 150 feet is 8.23 seconds.

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[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]

So, we need to find

[tex]\sum^{\infty}_{n=1} n(5/6)^n

[/tex]

Let this sum be S.

Then,

[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]

concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.

These numbers go from 1 to 10.

5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.

This means that if the card that we turn up is smaller than 6, we discard it.

If the card has the value 6 or larger, we keep it.

In this case, the probability of losing is if one of the other cards has a value larger than 6.

The probability that a random card has a value larger than 6 is:

p = (number of cards with a value larger than 6)/(total number of cards)

p = (16/39)

(The quotient is 39 instead of 40, because we already know one of the cards)

This means that if keep the 6, the probability of winning is:

1 - 16/39 = 0.59

If instead, we got a 7, obviously we keep it, in that case the probability of winning is:

1 - 12/39 = 0.69

And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

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Given: [tex]2x^2 - 12x + 1 = 0[/tex]

Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]

Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]

Second answer:  [tex]2(x - 3)^2 - 17 = 0[/tex]

Explanation in detail:

The quadratic equation a[tex]x^{2} + bx + c = 0[/tex]'s vertex form is

where a[tex](x - h)^{2} + k[/tex] equals zero

A is the [tex]x^{2}[/tex] coefficient, and h is the vertex's x-coordinate on the equation's graph.

The vertex of the equation's graph, k, has the y-coordinate.

The completing square can be used to determine the vertex form.

[tex]2x^{2} - 12x + 1 = 0[/tex] is the equation.

Put[tex]2x^{2} -12x[/tex] in a bracket and subtract 2 from them as a common component to utilize the completing square.

∵ [tex]2(x^{2} - 6x) + 1 = 0[/tex]

To determine the product of the first and second terms in the binomial, divide the second term by two.

∵ [tex]6x / 2 = 3x[/tex]

∵[tex]3x = 3 * x[/tex]

∴ The binomial's first and second terms are x and 3, respectively.

The phrase in the bracket's middle is (-)

∴ Middle of the binomial's sign is (-)

∴ The binary value is [tex](x - 3)^2[/tex]

Square 3 is nine.

To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.

∴ [tex]2(x^2 - 6x + 9 - 9) + 1 = 0[/tex]

- Remove the brace and multiply -9 by 2.

∵ [tex]2 *-9 = -18[/tex]

∴ [tex]2(x^2- 6x + 9) + 1 - 18 = 0[/tex]

- Construct a square binomial from [tex](x^{2} - 6x + 9)[/tex]

∵ [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]

∴ [tex]2(x - 3)^2 + 1 - 18 = 0[/tex]

Include related terms.

∴[tex]2(x - 3)^2 - 17 = 0[/tex]

∴ The equation's vertex form is[tex]2(x - 3)^2 - 17 = 0.[/tex]

Given that: [tex]2x^2 - 12x + 1 = 0[/tex]

Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]

Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]

Step 3:  [tex]2(x - 3)^2 - 17 = 0[/tex]

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the value of x is -3. Option B

WE have the expression to be;

4^x=(1/8)^x+5

With the knowledge of indices, we have that;

2 = 2 ^1

4 = 2^2

8 = 2^3

16 = 2^4

32 = 2^5

So from this given information,

we can express the expression as;

4^x = 2^2x

1/8^x = 2^-3x

Substitute into the formula

2^2x = 2^-3x - 15

Cancel out the like terms

2x = -3x - 15

collect like terms

2x + 3x = - 15

x = -15/ 5

x = -3

Thus, the value of x is -3. Option B

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The two positive numbers satisfying the given requirements are 15.56 and 15.56

For given question,

Let x and y be  two positive numbers satisfying the given requirements.

⇒ xy = 242             .............(1)

The sum of given two positive numbers is a minimum.

Let the sum of given two positive numbers is S.

⇒ x + y = S             ............(2)

From equation(1),

⇒ y = 242/x

Substitute above value of y in equation (2),

⇒ x + y = S  

⇒ S = x + (242 / x)    

Now, for above equation we find the derivative of x with respect to x.

⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]

⇒ 242/x² = 1

⇒ x² = 242

⇒ x = ±15.56

Since the numbers are positive, x = 15.56

For x = 15.56

⇒ y = 15.56

Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56

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Step-by-step explanation:

4x + 10 = -2 + 4

4x = -2 + 4 - 10

4x = -8

x = -2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{4x + 10 = -2+ 4}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{4x + 10 = 2}[/tex]

[tex]\huge\textbf{Subtract 10 to both sides:}[/tex]

[tex]\mathsf{4x + 10 - 10 = 2 - 10}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{4x = 2 - 10}[/tex]

[tex]\mathsf{4x = -8}[/tex]

[tex]\huge\textbf{Divide 4 to both sides:}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{-8}{4}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{-8}{4}}[/tex]

[tex]\mathsf{x = -2}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The length of the line segment of octagon which is AB equal to 3.4 cm.

Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.

We are required to find the length of the line segment AB.

A regular octagon has eight equal sides.

Area of regular octagon=Perimeter*apothem/2-----------1

We have to put the value of area and apothem in equation 1.

54=perimeter*4/2

Perimeter=(54*2)/4

=27 cm

Perimeter=27 cm.

Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,

Perimeter=8*side

27=8*AB

AB=27/8

=3.375 cm

After rounding off it will be equal to 3.4 cm.

Hence the length of line segment is equal to 3.4 cm.

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Answer:

A

Step-by-step explanation:

Step-by-step explanation:

31) the answer is (98765x9) +3=888888

why if u look at the equation is descending and if u verify the cinjecture u will find out is correct

41)½+¼+⅛+1/16+1/32=1-1/32

just d same reason with (31)

The last one because the other ones only go to the positive side and not the negative too since the cube root

Answer:

89.19

Step-by-step explanation:

           8 9  .  1     9

         79,56 . 00, 00

8    |  64

      |  1556

169 |  1521

      |      3500

1781 |      1781

              1719

17829|        6200

first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.

let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so

[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]

The expression of the equation will be:

x² - 8x = x(x - 8)

x² - 10x = x(x - 10)

x² - 5x = x(x - 5)

x² - 3x = x(x - 3)

It should be noted that an equation simply means the expression of the variables that are given.

In this case, the following can be represented:

x² - 8x = x(x - 8)

x² - 10x = x(x - 10)

x² - 5x = x(x - 5)

x² - 3x = x(x - 3)

This is illustrated above.

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Answer:

the frequency is the number of times a particular value occurs in a given data.

Answer:

3, 7, 14

Step-by-step explanation:

Answer: 60.

Step-by-step explanation:

Let in a right triangle one of the legs is 25, and the hypotenuse is 65.

Hence, the other leg is:  [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]

Answer:

-1

Step-by-step explanation:

n^2+2n = -1

n(n+2) = -1

Answer:

Height = 6m

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] × 36 = 12

72 ÷ 12 = 6