how would you write the fraction 5/2 as a division expression?
a. 5÷ 1/2
b. 2÷5
c. 1/2 ÷5
d. 5÷2​

Answer:

  24√3 square units

Step-by-step explanation:

The side length of a regular hexagon is 2/√3 times the length of the apothem. For an apothem of 2√3, the side length is ...

  s = (2/√3)(2√3) = 4

The perimeter P of the hexagon is 6 times the side length, so is 6×4 = 24.

The area is given by ...

  A = 1/2Pa

where P is the perimeter and 'a' is the apothem.

  A = 1/2(24)(2√3) = 24√3

The area of the hexagon is 24√3 square units.

_____

A hexagon can be divided into 6 congruent equilateral triangles. The apothem will be the altitude of one of those, so will divide the triangle into two triangles with angles 30°, 60°, and 90°. The ratios of the side lengths of such a triangle is something you might want to remember: 1 : √3 : 2. The altitude corresponds to the "√3" side, and the side length of the equilateral triangle corresponds to the "2" side. That is, we have the proportion ...

  apothem : hexagon side = √3 : 2

Multiplying by 2 gives the actual values in the hexagon of this problem:

  apothem : hexagon side = 2√3 : 4

Answer: 5/20

Step-by-step explanation: So first, we need to find the total number of people that ordered drinks. We can do this by adding the frequencies: 7 + 5 + 8, which is 20. That will be the total amount of people.

Next, we need to find the number on top, which is the number of people that ordered that certain drink. In this case, 5 people ordered hot cocoa, so the result would be 5/20.

If we could, we can simplify this to 1/4, which is 25%. So there is a 25% chance that people will order hot cocoa. But that answer choice isn't on there. So it would 5/20.

Answer:

Step-by-step explanation:

If we were talking about Spanish or French or Italian, would you be asking the question in the same way you have?

Or would languages make the answer just slightly easier to deal with?

My answer is that Mathematics is a language as well. It has it's own grammar and it's own curious set of rules. It in some form is logical but there is room for it to be not susceptible to any kind of logic.

It is beautiful in the same way that poetry or art is beautiful. Those who love it, find that mathematics is a demanding discipline. I used to tell my physics classes that God spoke Mathematics and Physics and Chemistry long before Hebrew. Sometimes they even laughed politely.

The value of the z-score for the number 15  in a data set is 0.93.

Define z-score.

A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.

You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.

                     ∴  z = (x – μ) / σ

Given:

σ = 4.32

x = 15

Data set: 5, 7, 9, 11, 13, 15, 17

So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7

                = 77/7

            μ = 11

z = (x – μ) / σ

  = (15 - 11)/4.32

   = 4/4.32

z  = 0.93

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Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Answer:

The two answers on the first row are correct

Step-by-step explanation:

PLATO

Answer:

See below for answers and explanations (along with a graph for #3)

Step-by-step explanation:

Problem #1

Applying scalar multiplication, \(-4w=-4\langle-96,-180\rangle=\langle384,720\rangle\).

Its magnitude would be \(||-4w||=\sqrt{384^2+720^2}=816\).

Its direction would be \(\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ\).

Thus, B) 816; 62° is the correct answer

Problem #2

Find the time it takes for the ball to cover 13ft:

\(x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095\)

Find the height of the ball at the time it takes for the ball to cover 13ft:

\(y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053\)

Thus, A) 10.053 is the correct answer

Problem #3

We have \(u=\langle0,-8\rangle\) and \(v=\langle6,0\rangle\) as our vectors. Thus, \(u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle\). Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.

Problem 4 (#7)

\(\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46\)

Thus, C) -46 is the correct answer

Problem 5 (#8)

Find \(r\) and \(\theta\):

\(r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246\)

\(\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ\)

Find the true direction angle accounting for Quadrant IV:

\(\theta=360^\circ-75.964^\circ=284.036^\circ\)

Write the complex number in polar/trigonometric form:

\(z=8.246(\cos284.036^\circ+i\sin284.036^\circ)\)

Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer

Problem 6 (#12)

Eliminate the parameter and find the rectangular equation:

\(x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0\)

Thus, D) x^2-9y+45=0 is the correct answer

Problem 7 (#13)

Find the magnitude of the vector:

\(||v||=\sqrt{(-77)^2+36^2}=85\)

Find the true direction of the vector accounting for Quadrant II:

\(\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ\)

Write the vector in trigonometric form:

\(w=85\cos155^\circ i+85\sin155^\circ j\)

Thus, D) w=85cos155°i+85sin155°j is the corrwect answer

Problem 8 (#15)

\(\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)\)

Thus, C) (-3,-13) is the correct answer

Problem 9 (#16)

Treat the golf ball and wind as vectors:

\(u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle\) <-- Golf Ball

\(v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle\) <-- Wind

Add the vectors:

\(u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle\)

Find the magnitude of the resultant vector:

\(||u+v||=\sqrt{(-0.225)^2+1.755^2}\approx1.769\)

Find the true direction of the resultant vector accounting for Quadrant II:

\(\displaystyle \theta=\tan^{-1}\biggr(\frac{1.755}{-0.225}\biggr)\approx-82.694^\circ\approx-83^\circ=180^\circ-83^\circ=97^\circ\)

Thus, B) 1.769 m/s; 97° is the correct answer

Problem 10 (#17)

Identify the vectors and add them:

\(u+v+w=\langle50\cos20^\circ,50\sin20^\circ\rangle+\langle13\cos90^\circ,13\sin90^\circ\rangle+\langle35\cos280^\circ,35\sin280^\circ\rangle=\langle50\cos20^\circ+13\cos90^\circ+35\cos280^\circ,50\sin20^\circ+13\sin90^\circ+35\sin280^\circ\rangle=\langle53.062,-4.367\rangle\)

Find the magnitude of the resultant vector:

\(||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241\)

Find the true direction of the resultant vector accounting for Quadrant IV:

\(\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ\)

Thus, A) 53.241, 355° is the correct answer

Problem 11 (#18)

We observe that \(z_1=-8-6i\) and \(z_2=4-4i\), hence, \(z_1+z_2=(-8-6i)+(4-4i)=-4-10i\)

Thus, Q is the correct answer

Problem 12 (#19)

Find the dot product of the vectors:

\(F_1\cdot F_2=(12000*14500)+(7000*-5000)=174000000+(-35000000)=139000000\)

Find the magnitude of each vector:

\(||F_1||=\sqrt{12000^2+7000^2}=1000\sqrt{193}\\||F_2||=\sqrt{14500^2+(-5000)^2}=500\sqrt{941}\)

Find the angle between the two vectors:

\(\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ\)

Thus, C) 49° is the correct answer

Problem 13 (#20)

Using scalar multiplication, \(7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j\)

Thus, A) -80i - 29j is the correct answer

Answer:

a)  "Like terms" are terms whose variables (and their exponents such as the 2 in x²) are the same

8y, -3y and y are all likes terms because the variables are all y

b)

\((-2x+8y-11)+(-3y-y+5)\\\\=-2x+8y-11-3y-y+5\\\\=-2x+(8y-3y-y)+(5-11)\\\\=-2x+4y-6\\\\=2(-x+2y-3)\\\\=-2(x-2y+3)\)

Answer:

7 pieces

Step-by-step explanation:

change 4 5/6 into an irregular fraction. 29/6

divide 29/6 by 2/3. to do this, flip and multiply

29/6 * 3/2 = 87/12 = 7.25 or 7 whole pieces

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Answer: Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.

Step-by-step explanation:

The equation of a line can be written in slope intercept form:  

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

You can use the two points to find the slope m:

m = (y2 - y1 ) / ( x2 - x1 )

Given that points (6,-5) and (-4,1)

It represents the values are,

x1 = 6

y1 = -5

x2 = -4

y2 = 1

so,

Replace with x1, x2, y1, y2 values in this equation,

we can write,

m=(1-(-5)) / (-4-(6))

m = (1+5) / (-4-6)

m= 6/-10

m = 3/-5

Now you can select either point and substitute the coordinates in the equation to determine b, the y intercept.  Let's us (-4, 1):

y= mx + b

so, x = -4 and y = 1 and m = 3/-5

Replace with the values in this equation,

y= mx +b

1 = (-3/5)(-4) + b

1 = (0.6)(4) +b

1 = 2.4 +b

1-2.4 = b

-1.4 = b

b = -1.4

The equation will be:

y = mx +b

substitute m and b values,

Then,

y = (-3/5)x + (-1.4)

y = (-3/5)x -1.4

In standard form, the equation would be transformed as:

y = (-3x-7) / 5

5y = -3x-7

3x+5y = -7

3x+5y+7 = 0

In standard form, the equation would be transformed as: 3x+5y+7 = 0

Therefore,

Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.

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The rate of change of the simple index over one day is approximately 12.78%.

To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.

On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:

Total value of Stock A on Monday = 5000 * $2.75 = $13,750

Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:

Total value of Stock B on Monday = 3000 * $4.30 = $12,900

The total value of the index on Monday is the sum of the values of Stock A and Stock B:

Total value of the index on Monday = $13,750 + $12,900 = $26,650

On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.

The total value of Stock A on Tuesday is:

Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500

The total value of Stock B on Tuesday is:

Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550

The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:

Total value of the index on Tuesday = $15,500 + $14,550 = $30,050

To calculate the percent change in the index, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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Answer:

6(x - 3)

Step-by-step explanation:

18(x−3)−6(x−3)2 =>

18x - 54 - 12 (x - 3 ) =>

18x - 54 - 12x + 36 =>

18x - 12x - 54 + 36 =>

6x - 18 or 6(x - 3)

both answers are good, althoguth this second one 6 (x - 3) should be the one that you are looking for

The value of distance AB is 187.5 units

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

sine rule can be expressed as;

a/sinA = b/sinB = c/sinC

The opposite side to angle A is BC

the opposite side to angle C is AB

therefore;

A = 180-( 117 +24)

A = 180- 141

A = 39°

290/sin 39 = x/ sin24

xsin39 = 290 × sin24

0.629x = 117.95

x = 117.95/0.629

x = 187.5

therefore the distance AB is 187.5

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Answer:

-1.3

Step-by-step explanation:

The probability of the first name selected is yours and the second name selected is your friend's name is 1/100 or in ratio 1:100.

Probability is the branch of mathematics that studies how random events turn out. In mathematics, the term "probability" is used to describe chance or potential outcomes. It makes it clear how likely it is that a certain outcome will occur. The phrases "It will likely rain today," "He'll mostly pass the test,"

"There's not much chance of getting a storm tonight," & "The price of onions will probably go up again" are common phrases. Instead of words like possibility, uncertainty, perhaps, likely, etc., the word probability is used in each of these sentences.

Probability, in its simplest form, can be defined as the capacity to forecast an outcome based on the variety and quantity of possible outcomes or by examining historical data.

The probability of first name selected is yours is = 1/10

The probability of 2nd name selected is yours is = 1/10

The probability of selecting your name and your friend name consecutively

= 1/10 * 1/10

= 1/100

Thus, the probability of the first name selected is yours and the second name selected is your friend's name is 1/100.

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Answer:

Definitely 3 hmmm..

Step-by-step explanation:

6/2=3 so 9/z=3

tfo 9/3=3

The missing variables have values of 12, 5, 9, and 3, respectively, for x, y, w and z.

Given that there are two similar polygons with dimension:

Larger polygon = 9, 6, w, 15, x.

Smaller polygon = z, 2, 3, y, 4.

We need to find the missing value of the side length.

According to the definition of the similar polygons, the corresponding sides shows proportionality.

9/z = 6/2 = w/3 = 15/y = x/4

Solving for each variable =

i) Solve for z:

9/z = 6/2

Cross-multiplying:

6z = 9 × 2

6z = 18

Dividing both sides by 6:

z = 18/6

z = 3

ii) Solve for w:

6/2 = w/3

Cross-multiplying:

2w = 6 × 3

2w = 18

Dividing both sides by 2:

w = 18/2

w = 9

iii) Solve for y:

6/2 = 15/y

Cross-multiplying:

6y = 30

Dividing both sides by 6:

y = 5

iv) Solve for x:

6/2 = x/4

Cross-multiplying:

2x = 24

Dividing both sides by 2:

x = 12

Hence the values of the missing variables are x = 12, y = 5, w = 9 and z = 3.

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Answer:

3 miles in 24 minutes

Step-by-step explanation:

The name of shape ABCDE is regular pentagon and the length of line AE is 5 cm

The complete question is added as an attachment

From the question, we can see that

The shape ABCDE has 5 equal sides

This means that ABCDE is a regular pentagon

In (a), we have

5 equal sides

Given that

BC = 5 cm

We have

AE = 5 cm

Hence, the length is 5 cm

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Answer:

I think it may be B (d-$5 )

f(x) = x^3 - 6x^2 + 12x the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. The critical value that will give you a relative maximum is x = 4. The critical value that will give you a relative minimum is x = -2.

The derivative of the given function is f'(x) = 3x^2 - 12x + 12. Setting this equal to 0 gives us x = 0 and x = 4. By the first derivative test, we can determine that the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. Therefore, the critical value that will give us a relative maximum is x = 4 and the critical value that will give us a relative minimum is x = -2. This can be verified by finding the second derivative of the function, which is f''(x) = 6x -12. Setting this equal to 0 gives us x = 2, which is between the two critical values. Since the second derivative is negative for x < 2, the critical value at x = -2 will give us a relative minimum and since it is positive for x > 2, the critical value at x = 4 will give us a relative maximum.

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Answer:

C

Step-by-step explanation:

6/9 simplified is 2/3 they're equal to each other so they're proportional

Hope this helps :)

           If we use a simple example, the additive inverse of 5 is -5. This is because -5 + 5 = 0.

           It is the same with fractions, if we take one half, \(-\frac{1}{2}\) + \(\frac{1}{2}\) = 0

           A rational number is a number that can be written as an integer or a fraction without having a 0 in the denominator.

("In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. ")

           Basically, the sum of a fraction / rational number and its additive inverse is equal to 0 because you are adding together "opposites" with regards to negative / positive. They are the same number, just different sides of the number line.

The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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The length in each circle is:

(a) CD = 19.5 units

(b) UZ = 12.8 units

(a) The Intersecting Secant-Tangent Theorem states that "if two secant lines intersect outside a circle, and a tangent line is drawn from the point of intersection to the circle, then the product of the lengths of the two secant segments is equal to the square of the length of the tangent segment".

Using the theorem, we have:

EC * ED = EG²

6.5 * ED = 13²

6.5ED = 169

ED = 169/6.5

ED = 26 units

ED = EC + CD

26 = 6.5 + CD

CD = 26 - 6.5

CD = 19.5 units

(b) The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

UZ * UW = UX * UY

UZ * 40 = 8 * 64

40UZ = 512

UZ = 512/40

UZ = 12.8 units

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