DIMENSIONAL ANALYSIS (MATH) GIVING BRAINILIEST!

Q1: What is the speed of a horsefly in feet per second? Round to the nearest hundredth.

Q2: How many times does a dragonfly's wing beat per minute?

Q3: About how many times can a bumble bee travel in one minute?

The greatest number among the given numbers is= 57

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The distance from the top of the window to the base of the wall is 5.4 m.

According to the question,

We have the following information:

The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. And the window is 1 meter high.

Now, we know that the ladder, wall and base will make a right-angled triangle. We can use Pythagoras theorem to find height of the wall.

(Pythagoras theorem: square of hypotenuse = sum of squares of base and height)

Let's take height of the wall to be h meters.

[tex]h^{2}[/tex] = [tex](5.5)^{2} -(3.3)^{2}[/tex]

[tex]h^{2}[/tex] = 30.25-10.89

19.36

h = √19.36

h = 4.4 m

Now, the distance from the top of the wall window to the base of the wall is:

4.4 + height of the window

4.4+1

5.4 m

Hence, the distance from the top of the window to the base of the wall is 5.4 m.

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When the numerical data (number) 0.000007328 is rounded to the nearest millionth, the number is about 0.000007.

A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:

Based on the numerical data (number) provided above, the place value of seven (7) is millionth and it would be rounded up as seven (7) because the next number on its right (3) is less than five (5) and as such, it can seven (7) rounded up to eight (8).

In this context, we can reasonably infer and logically deduce that 0.000007 is a numerical data (number) that represents millionth based on the place value of seven (7).

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Multiplication of  2.9x and 5x gives 14.5x²

The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants

Given: 2.9x and 5x

To multiply 2.9x and 5x, multiply the numbers and multiply the letters:

2.9x × 5x = 2.9 × 5 × x × x = 14.5x²

Therefore,   2.9x multiplied by 5x is 14.5x²

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Only function (a) is one-to-one.

acc to our question-

If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.

The elements of a function are

A = {a,b,c,d}

Therefore, this function is one-to-one.

(b).f (a) = b, f (b) = b, f (c) = d, f (d) = c.

Here, the value of function is b for x=a and x=b. For two domains the functions has same range.

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Based on an exponential model of the data, the predicted temperature of the water at 7 minutes is 39.7 °C using desmos graphing calculator.

Similar to how you discovered linear and quadratic models in prior chapters, exponential models can be found by fitting data to them. As you may already be aware, exponential functions take the form y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time. Based on an equation like this one, the exponential model represents the degradation failure process: Y = deterioration; T = time; A and B = parameters to be calculated using the regression approach based on historical data. An expansion within a population that happens at the same pace across time is represented by the function of exponential growth. It is reasonable to suppose that data grows exponentially as populations double or triple in size.

Graph all the points on a graph. Then from the graph, we can find that at 7 minutes the temperature is 39.7°C.

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Answer: 38.2 degrees

Step-by-step explanation:

enter into desmos

use y1 ~ abx2

then input numbers provided

(22.9178)1.07564^7

equals 38.18049

round 38.2

Answer:

7x+40=180

Step-by-step explanation:

(5x+40)+(2x)=180

7x+40=180

if you were to solve

subtract 40 from each side

7x=140

divide both sides by 7

x=20

check your answer

5(20)+40+2(20)=180

100+40+40=180

this is correct

hope this helps..and with future questions if you need to solve it

To find BCD

we know that C is 40 degrees and we know that  triangle is also 180

we can also see that B is a right triangle or 90 degree

so 90+40+A=180

130+A=180

subtract 130 from 180

A=50

The given expression is proved by the necessary changes.

cosec 2A + cosec 4A = cot A - cot 4A​

Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Taking LHS  :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2    (  we know:1+ Cot 2 θ =  Cosec 2 θ )

⇒Cosec 2 A +  Cosec 4 A  + 1  - 2 Cosec 2 A

⇒ Cosec 4 A  + 1  - Cosec 2 A

⇒ Cosec 4 A  + 1  - ( 1 + Cot 2 A)

⇒ Cosec 4 A  + 1  -  1 - Cot 2 A

⇒ Cosec 4 A  - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A

Hence Proved.

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Answer:

the additive inverse of 16 5/7 IS 26/7

Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.

Given that,
The coordinate pairs separated by a vertical distance of greater than 6 units is to be determined.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

here,
(A)
Since the x coordinate is the same in all the pairs, distance on the y axis can only be calculated.

(5.1, -3.3) and (5.1, 3.4)
y = 3.4 - (-3.3)
y = 6.7

Similarly distance,
(B) y = 6.8
(C) y = 5.6
(D) y = 3.5

Thus, Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.

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Answer: 16/18 and 10/16

Step-by-step explanation: The least common denominator would be 18 and 16 because you would multiply by 2.

Hoped This Helped!

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

Explanation:

The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.

R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}

R U S = {2, 3, 5, 17, 19, 37,      3, 5, 7, 11, 13, 37}

R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}

This list of values consist of items in set R, set S, or both.

There are 9 items in set R U S.

This is out of 12 items total in the universal set rectangle.

The probability of randomly selecting something from set R U S is 9/12 = 3/4

Answer:

Step-by-step explanation:

You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)

Answer:

D) n<-4

Step-by-step explanation:

The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2

The curve opens downward.

from, the graph, the roots of the equation are -4 and 0

so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y = [tex]x^{2}[/tex] + 4x

the x coordinate of the vertex = -b/2a = axis of symmetry

where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

substitute x = -2 into y =  [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex

y = [tex](-2)^{2}[/tex] + 4(-2)

y = 4 -8

y = -4

vertex is (-2, -4)

The axis of symmetry is -b/2a which is -2

The curve opens downward as the vertex is at -4

In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward

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Answer:

The trigonometric functions, sin, cos and tan for an angle are the primary functions. The value for cos 60 degrees and other trigonometry ratios for all the degrees 0°, 30°, 45°, 90°, 180° are generally used in trigonometry equations. These trigonometric values are easy to memorize with the help trigonometry table.

Cos 60 Degree Value

In a right-angled triangle, the cosine of ∠α is a ratio of the length of the adjacent side (base) to the ∠α and its hypotenuse, where ∠α is the angle formed between the adjacent side and the hypotenuse.

Cos 60 Degree value

Cosine α = Adjacent Side / Hypotenuse

Cos α = AC / AB

Cos α = b / h

Now, to find the value of cos 60 degrees, let us consider, an equilateral triangle ABC as given below:

Cos 60 Degree

Here, AB = BC = AC and AD is perpendicular bisecting BC into two equal parts.

As we know, cos B = BD/AB

Let us consider the length of each side as 2 units, such as AB = BC = AC = 2 units and BD = CD = 1 unit.

Therefore, the value of cos 60° = BD/AB = ½

In the same way, we can write the value of sin 60° and tan 60° by evaluating the required sides.

In right triangle ABD, by Pythagoras theorem:

AB2 = AD2+ BD2

22 = AD2 + 12

AD2 = 22 -12

AD2 = 4 – 1

AD2 = 3

AD = √3

Now, we have got all the sides of triangle ABD.

Sin 60° = AD/AB = √3/2

Tan 60° = AD/BD = √3 / 1 = √3

We can also write the value of cos 60 degrees in decimal form as:

cos 60° = 1/2 = 0.5

Also, we can write the values of sine, cosine and tangent with respect to all the degrees in a table.

Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.

Angle in Degrees 0 30 45 60 90 180 270 360

Angle in Radians 0 π/6 π/4 π/3 π/2 π 3π/2 2π

Sin 0 1/2 1/√2 √3/2 1 0 -1 0

Cos 1 √3/2 1/√2 1/2 0 -1 0 1

Tan 0 1/√3 1 √3 ∞ 0 ∞ 0

Unit Circle in Trigonometry

It is possible to give the values of trigonometric ratios with respect to radians equivalent to degrees, in case of a unit circle, whose radius is equal to one. The radian for a unit circle is denoted by π. In the below figure, the angle values are represented in degrees instead of radians.

Cos 60 Degree graph

You have learned about cos 60 degrees value along with other degree’s values here now. Also, the derived values for sin and tan with respect to degrees and radians. In the same way, we can find the values for other trigonometric ratios like secant, cosecant and cotangent.

Let us see some example where we can use the value of cos 60 degrees.

Example 1: Find the value of cos 60° + sin 30°.

Solution:

cos 60° + sin 30°

= cos 60° + sin (90° – 60°)

= cos 60° + cos 60°

= (1/2) + (1/2)

= (1 + 1)/2

= 2/2

= 1

Alternatively, cos 60° + sin 30° = (1/2) + (1/2) = (1 + 1)/2 = 2/2 = 1

Example 2: Calculate: 2 sin 60° – 4 cos 60°

Solution:

We know that, sin 60° = √3/2 and cos 60° = 1/2

Thus, 2 sin 60° – 4 cos 60° = 2(√3/2) – 4(1/2)

= √3 – 2

therefore it 3/2

Step-by-step explanation: Peace Out.... Have a good day

PLEASE GIVE MARK BRAINIEST I WORK SO HARD IT TOOK  ALL DAY!!!

The largest head diameter that can accommodate the clientele is 8.5743

Mean, u = 6.4

Standard deviation = 0.9

We must utilize the inverse of the common normal table to obtain our values.

the smallest head width possible.

P(Z < z) = 1.4%

P(Z < z) = 0.014

P(Z < -2.0749) = 0.014

z = -2.0749

Using the z-score calculation,

(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]

Let x be the heads' breath.

Making x the focus of the equation,

x = z × σ + μ

We already have:

z = -2.0749

u = 6.5

s.d = 1

Replacing numbers,

x = (-2.0749 × 1) + 6.5

x = 4.4251

The clientele requires a minimum head breadth of 4.4251.

The largest head width that can be accommodated.

P(Z > z) = 1.4%

1 - P(Z < z) = 0.014

P(Z < z) = 1 - 0.014 = 0.981

P(Z < 2.0749) = 0.981

Using the z-score calculation,

(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]

Let x be the heads' breath.

Making x the focus of the equation,

x = z × σ + μ

z = 2.0749

u = 6.5

s.d = 1

Substituting figures,

x = (2.0749 × 1) + 6.5

x = 4.4251

x = 8.5743

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The length of the hypotenuse is 4√3 units.

Given that hypotenuse is 4 times the length of one leg of a triangle. So here we can assume that length to be x. Hence the hypotenuse length is 4x. To calculate hypotenuse we have the formula a²=b² + c², where b and c are two sides of the triangle and a is the hypotenuse. If we put these values in the formula we get,

16x² = x² + (3√5)²

15x² = 45

x² = 3

x = ±√3

Since length cannot be negative, the final value of x = √3, and since the length of the hypotenuse was 4x, the final value of the hypotenuse is 4√3.

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The mean yearly growth rate for this period is 0.0036.

The average annualized return of a portfolio, asset, or cash flow over time is known as the average annual growth rate, or AAGR. The basic arithmetic mean of a set of returns is used to calculate AAGR.

The change in a measurement's value over a year is known as the annual growth rate (AGR).

The sum of the growth rates for each year divided by the total number of years yields the mean growth annual rate.

Where the annual growth rate is calculated as follows: 5.5 + 1.1 - 3.5 - 1.1 + 1.8 = 3.8%

And the total number of years is 5.

Then ,

The average annual growth rate for this time period is = 3.8/5

Over this time span, the average yearly growth rate was 0.76%.

Make a decimal conversion

= 0.76% = 0.0076

Therefore, the mean yearly growth rate for this period is 0.0036.

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The ratio 120/150 represented in the simplest form is 4 : 5 .

The given ratio is 120 /150 .

Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.

The HCF of the number is 30. Hence the ratio in simplest form will be

120÷30 : 150÷30 = 4 : 5 .

By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.

Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.

Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.

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Answer:

Perimeter = 18√3 = 18SQR(3)

Area = 27√3 = 27SQR(3)

Step-by-step explanation:

The sides of a regular polygon are congruent.

Therefore, as the triangle is a regular polygon, it is an equilateral triangle since its sides (and interior angles) are congruent.

The interior angles of a triangle sum to 180°.  Therefore, each interior angle of the equilateral triangle is 60°.  

Therefore, the right triangle formed inside the equilateral triangle by the perpendicular bisectors is a 30-60-90 triangle with hypotenuse of 6 units.

The ratio of the side lengths of a 30-60-90 triangle is b : b√3 : 2b, where:

As the hypotenuse of the 30-60-90 right triangle is 6 units:

[tex]2b = 6 \implies b=3[/tex]

Therefore, the length of the longest leg of the right triangle is 3√3.

As this is half the length of one side of the equilateral triangle:

[tex]\implies \sf Perimeter = 6 \times 3 \sqrt{3}=18\sqrt{3}\; units[/tex]

Heron's Formula allows us to find the area of a triangle in terms of its side lengths.

Heron's Formula

[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where:

Given:

Substitute these values into the Heron's formula to calculate the area of the equilateral triangle:

[tex]\begin{aligned}\implies \sf Area &= \sf \sqrt{9\sqrt{3}(9\sqrt{3}-6\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(3\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(81\sqrt{3})}\\&=\sf \sqrt{2187}\\&=\sf \sqrt{729 \cdot 3}\\&=\sf \sqrt{729}\sqrt{3}\\&=\sf 27\sqrt{3} \;\;units^2\end{aligned}[/tex]

The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]

Calculation

from ( - 3, 2) and (5, 7)

slope(m)  = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

[tex]=\frac{7 - 2}{5 - (-3)}[/tex]

[tex]= \frac{5}{8}[/tex]

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]

⇒[tex]2 = \frac{15}{8} + b[/tex]

⇒[tex]2 - \frac{15}{8} = b[/tex]

⇒[tex]\frac{16+15}{8} = b[/tex]

⇒[tex]\frac{31}{8} = b[/tex]

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]

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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.

When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,

Slope-intercept form

Point slope form

Two-point form

Intercept form

from ( - 3, 2) and (5, 7)

slope(m)  = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]

=7-(-2)/5-(-3)

=5/8

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , 2=5/8*(-3)+b

⇒2=15/8+b

⇒2-15/8=b

⇒16+15/8

31/8=b

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒y=5/8x +31/8

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The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.

It follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.

Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).

However, the possible values of constant, b include all real numbers except 0.

On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.

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Answer:

It should be ≈ 6,6

calculated the angle <CAB and both are 90°. But that would mean BC is wrong

Answer:

10,500 g

Step-by-step explanation:

Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 25 minutes. After 75 minutes, then, the amount of radioactive atoms is halved three times. Therefore:

1st half-life: [tex]84000\text{ g}\div{2}=42000\text{ g}[/tex]

2nd half-life: [tex]42000\text{ g}\div{2}=21000\text{ g}[/tex]

3rd half-life: [tex]21000\text{ g}\div{2}=10500\text{ g}[/tex]

The scientific notation representation is 2.6 x [tex]10^{-2}[/tex].

Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.

Given:

(0. 00032) (5.2 x [tex]10^6[/tex])/ 6.4 x [tex]10^5[/tex]

Now, solving the above expression

= 0.001664 x 10² / 6.4

= 0.00026  x 10²

= 2.6 x [tex]10^{-2}[/tex]

Hence, the scientific notation representation is 2.6 x [tex]10^{-2}[/tex].

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The size of the squares should be 3 inches in order to create a box with the largest possible volume.

If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.

let x = length of square to be cut = height of the box

length of the box = 30 - 2x

width of the box = 14 - 2x

The volume of the box, which is a rectangular prism, is the product of the length, height and width.

V = l x w x h

V = (30 - 2x)(14 - 2x)(x)

V = 420x - 88x² + 4x³

To obtain the largest volume possible, the first derivative of the volume should be equal to zero.

V'(x) = 0

V = 420x - 88x² + 4x³

420 - 176x + 12x² = 0

Simplify and solve for the value of x.

12x² - 176x + 420 = 0

3x² - 44x + 105 = 0

(3x - 35)(x - 3) = 0

x = 35/3   ;   x = 3

Check each value.

When x = 35/3 = h

l = 30 - 2x = 20/3

w = 14 - 2x = -28/3 ( length should be positive)

When x = 3 = h

l = 30 - 2x = 24

w = 14 - 2x = 8

Hence, the length of square to be cut  is 3 in.

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Answer:

3c

3c mean 3xc

but just write 3c

Answer:

c I got you ok answer c

Step-by-step explanation:

bc I got this correct

Answer:

Its D, x+y=-7;x-y=11. Also Part 2 is 2,-9

Step-by-step explanation:

Just did it Pearson 2022

The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest.

To begin, change R from a percentage to a decimal, using the formula:

r = R/100 r = 14/100

r = 0.14 rate per year;

Next, find A by solving

A = P(1 + r/n)nt A = 12,000.00(1 + 0.14/12)(12). (5)

A = 12,000.00(1 + 0.011666666666667)(60) (60)

A = $24,067.32

Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.

The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest. You will then be left with the loan balance plus compound interest.

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Answer:

119days

Step-by-step explanation:

1 week= 7 days

take week as w

so 1w=7 or w=7

now 17 weeks=??

17w=??

w=7 so input in above statement:

17(7)=119days

Answer: 119 days

Step-by-step explanation:

       We can set up a dimensional analysis problem to solve.

               [tex]\displaystyle 17 \;\text{weeks}\;(\frac{7\;\text{days}}{1\;\text{week}} )[/tex]

       The units of [tex]\frac{weeks}{weeks}[/tex] cancel out, leaving us with days. Since we are being asked to find days, this will leave us at the right point.

               [tex]\displaystyle \frac{17*7}{1} =119\;\text{days}[/tex]