What complex number is represented by the polar coordinates (4, negative StartFraction pi Over 4 EndFraction).?

Their present ages are Option d. 14yrs, 38yrs​

Note that algebraic expressions are described as expressions that are made up of terms, variables, constants, factors and coefficients

From the information given, we have that;

Let son's age = x

Two years ago son's age= x-2.

His Father's age at that time = 3(x-2).

Present age of Father = 3x-6+2

collect like terms, we have that;

Present age of father =3x-4

Two years hence father's age=3x-4+2=3x-2.

Two years hence son's age = x+2.

Given that;

-5×(x+2)=2 ×(3x-2)

expand the bracket, we get;

5x + 10= 6x - 4

collect like terms

10+4=6x-5x

14=x

Son's age=  14 years.

Father's age: 38 years.

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Answer: The radius of the circle rounded to the nearest integer is 11 cm

Step-by-step explanation:

To resolve this issue we can utilize the properties inherent to circles along with Pythagoras' theorem while denoting our circle's radius as "r".

Given that we know of a chord of length equaling up to 18 cm placed at a distance measuring exactly 6.3 cm away from the center of our circle sketching out a diagram would make it easier for us to visualize such a situation. Once visualizing this problem statement through our aforementioned diagram we may approach it using Pythagoras' theorem and examine the components regarding the right-angled triangle formed by half-length chord radius "r" and distance between center and chord respectively.

Our calculations factor in measurements representing half of our chords length (which is equal to precisely 9cm) alongside distances measuring up to exactly 6.3cm while possessing "r" on one end as shown below:

r^2 = (6.3cm)^2 + (9cm)^2

Simplifying said equation leads us to have:

r^2 =39.69cm^2+81cm^2

r²=120.69cm²

Calculating square roots on both sides leads us towards the approximation of r equaling around:

r ≈ √120.69cm²

r ≈10.99cm

Therefore rounding off R towards its nearest whole number would give us R=11cm in this case scenario.

The surface area of the sphere is 50.3 yard².

The volume of the rectangular prism is 245 inches³.

The volume of the pyramid is 149.3 m³.

The volume and surface area of the figures can be found as follows:

surface area of the sphere = 4πr²

where

Therefore,

surface area of the sphere = 4 × 3.14 × 2²

surface area of the sphere = 50.3 yard²

Volume of the rectangular prism = lwh

where

Therefore,

Volume of the rectangular prism = 7 × 7 × 5

Volume of the rectangular prism = 245 inches³

Volume of the pyramid = 1 / 3 Bh

where

Therefore,

B = 8² = 64 m²

h = 7 m

Therefore,

Volume of the pyramid = 1 / 3 × 64 × 7

Volume of the pyramid = 149.3 m³

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The equation line is y= 1/50x.

We have a graph from which we can take two points as

(100, 2) and (200, 4).

So, the slope of line

= (change in y)/ (change in x)

= (4-2)/ (200- 100)

= 2/ 100

= 1/50

Now, the equation line is

(y - 2)= 1/50 (x - 100)

y-2 = 1/50 x - 2

y= 1/50x

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Answer:

30/.06 =500

Step-by-step explanation:

30÷6/100

==>

30*100/6

=500

The solution to all parts is shown below.

First, let's filter out all non-valid responses, such as "IAP" (Inapplicable), "NA" (Not Applicable), or "Blank."

Frequency distribution table for the variable "can trust":

| Response                | Frequency |

| Always trusted        |     x     |

| Usually trusted        |     y     |

| Usually not trusted  |    z    |

| Always not trusted  |     w     |

Relative frequency distribution table for the variable "cantrust":

| Response                | Relative Frequency |

| Always trusted        |         x/n        |

| Usually trusted        |         y/n        |

| Usually not trusted |       z/n       |

| Always not trusted  |         w/n        |

Pie chart with the distribution of responses:

To find the percentage of respondents who say strangers can be "always trusted," we calculate the relative frequency or proportion for the "Always trusted" category.

Percentage of respondents who say strangers can be "always trusted"

= (x/n) x 100%

Now, let's calculate the 95% confidence margin of error for the proportion of Americans who answer strangers can "always be trusted":

Margin of error = (z-score) (standard error)

The z-score depends on the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

The standard error can be calculated as:

Standard error = √[(p (1 - p)) / n]

Once we have the margin of error, we can calculate the 95% confidence interval as follows:

Confidence interval = p ± margin of error

The confidence interval provides a range within which the true proportion of Americans who say strangers can be "always trusted" is likely to fall.

By interpreting margin of errors and confidence intervals is essential because survey data is collected from a sample rather than the entire population.

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Answer:

1)  x - 3y = -16

2)  4x - y = -17

Step-by-step explanation:

To determine the equation of a line that is parallel to x - 3y = 9 and passes through the point (2, 6), we first need to find the slope of x - 3y = 9.

To do this, rearrange the equation so that it is in slope-intercept form.

Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.

[tex]\begin{aligned}x-3y&=9\\x-3y+3y-9&=9+3y-9\\x-9&=3y\\3y&=x-9\\y&=\dfrac{1}{3}x-3\end{aligned}[/tex]

Therefore, the slope of the given line is 1/3.

Parallel lines have the same slope.

Therefore, to find the equation of the parallel line that passes through point (2, 6), substitute m = 1/3 and the point (2, 6) into the point-slope formula:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\\implies y-6&=\dfrac{1}{3}(x-2)\end{aligned}[/tex]

Rearrange to standard form Ax + By = C (where A is positive):

[tex]\begin{aligned}y-6&=\dfrac{1}{3}(x-2)\\3y-18&=x-2\\-18&=x-3y-2\\x-3y&=-16\end{aligned}[/tex]

Therefore, the equation of the line in standard form that is parallel to x - 3y = 9 and passes through the point (2, 6) is:

[tex]\boxed{x-3y=-16}[/tex]

[tex]\hrulefill[/tex]

To determine the equation of a line that is perpendicular to y + 1/4x - 5 = 0 and passes through the point (-3, 5), we first need to find the slope of y + 1/4x - 5 = 0.

To do this, rearrange the equation so that it is in slope-intercept form.

Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.

[tex]\begin{aligned}y + \dfrac{1}{4}x - 5 &= 0\\y&=-\dfrac{1}{4}x+5 \end{aligned}[/tex]

Therefore, the slope of the given line is -1/4.

The slopes of perpendicular lines are negative reciprocals.

Therefore, the slope of the perpendicular line is 4.

Therefore, to find the equation of the perpendicular line that passes through point (-3, 5), substitute m = 4 and the point (-3, 5) into the point-slope formula:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\\implies y-5&=4(x-(-3))\end{aligned}[/tex]

Rearrange to standard form Ax + By = C (where A is positive):

[tex]\begin{aligned}y-5&=4(x-(-3))\\y-5&=4(x+3)\\y-5&=4x+12\\-5-12&=4x-y\\4x-y&=-17\end{aligned}[/tex]

Therefore, the equation of the line in standard form that is perpendicular to y + 1/4x - 5 = 0 and passes though point (-3, 5) is:

[tex]\boxed{4x-y=-17}[/tex]

The arc angle  WVY in the circle is 250 degrees.

The theorem of intersecting tangent angles states that the measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's use this theorem to find the arc angle WVY.

Hence,

70 = 1 / 2 (10a - (4a + 10))

70 = 1 / 2 (6a - 10)

70 = 3a - 5

70 + 5 = 3a

3a = 75

divide both sides of the equation by 3

a = 75 / 3

a = 25

Therefore,

arc angle WVY = 10(25)

arc angle WVY = 250 degrees

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Step-by-step explanation:

A: If there are 2 modes, x can be either 1 or 2.

B: To find the mode of the data set, we need to count how many times each number appears.

- 0 appears 2 times

- 1 appears 4 times

- 2 appears 4 times

- 3 appears 3 times

- 4 appears 1 time

Since both 1 and 2 appear 4 times in the data set, there are two modes.

For x, if we add it to the data set, then the mode must be x plus either 1 or 2.

If we choose x to be 2, then the mode would be 2, since 1 and 2 each appear 4 times, and adding another 2 would make it the mode.

So a possible value for x could be 2, and the mode would be 2.

The value of x from the given similar triangles is 10 units.

The given triangles are similar.

Here, 3x/(4x+2) = 20/28

3x/(4x+2) = 5/7

7×3x = 5(4x+2)

21x=20x+10

21x-20x=10

x=10 units

Therefore, the value of x from the given similar triangles is 10 units.

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For the expression  [tex]x^2^/^4x^3^/^6[/tex] the value of exponent of x is 1.

8ab²√5a is the simplified form of the expression 4√20a³b⁴ .

The given expression is [tex]x^2^/^4x^3^/^6[/tex]

x is the variable in the expression.

We know that when bases are same in the product then the powers will be added.

[tex]x^1^/^2^+^1^/^2[/tex]

When 1/2 and 1/2 are added we get 1.

So the value of r is 1.

Now 4√20a³b⁴ is the expression.

4√4×5a².a.b².b²

4.2.ab²√5a

8ab²√5a is the simplified form of the expression.

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The fraction of the cans in George’s pantry which are either soup or vegetables is 11/24.

Fraction of cans in George‘s pantry that are vegetables = 1/8

Fraction of cans in George‘s pantry that are soups = 1/3

Fraction of the cans in George’s pantry which are either soup or vegetables = 1/3 + 1/8

= (8+3) /24

= 11/24

Hence, 11/24 is the fraction of the cans in George’s pantry that are either soup or vegetables.

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Answer:

140

If that's wrong, try 147

Step-by-step explanation:

With this brief sequence of numbers, we can see that the function is linear, and increases by 7 each term, with the first term at -21, and therefore, the "0th" term, or the y-intercept, at -28. With this information we can create a function in slope intercept form (y=mx+b):

[tex]y=7x-28\\[/tex],

where our m (slope) is 7, and our b (y-intercept) is -28.

If this doesn't make sense, then the easiest way is to just keep adding seven to the previous number until you get to the 24th term.

Hope this helps!

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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a. You will find the gallons of gas consumed by the old car in one year when you divide [tex]\frac{18,000}{old\;miles\;per\;gallon}[/tex].

b. The amount of dollars you would save in the first year by switching to the 27 mpg car is $1,150.

c. The amount of dollars you would save after 5 years is $5,750.

d. Yes, the additional savings in gas be worth the extra $3000 over a 5 year loan.

e. The gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car is 23.4 mpg.

Based on the information provided about the car that would provide maximum savings, the following rational equation models the situation:

[tex]g(x)=3.45(\frac{18,000}{old\;miles\;per\;gallon})-3.45(\frac{18,000}{new\;miles\;per\;gallon})[/tex]

Note: "g(x) is used for calculating the amount of dollar savings for one year for driving a car that gets higher miles per gallon rate."

Part a.

Based on the rational equation, we can logically deduce that the expression [tex]\frac{18,000}{old\;miles\;per\;gallon}[/tex] would help to determine the gallons of gas consumed by the old car in one year.

Part b.

The amount of dollars you would save in the first year by switching to the 27 mpg car can be calculated as follows:

[tex]g(x)=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{27})[/tex]

g(x) = 3,450 - 2,300

g(x) = $1,150.

Part c.

The amount of dollars you would save after five years can be calculated as follows:

f(5) = 5g(x)

f(5) = 5 × $1,150

f(5) = $5,750

Part d.

[tex]g(x)=3.45(\frac{18,000}{27})-3.45(\frac{18,000}{33})[/tex]

g(x) = 2,300 - 1,881.82

g(x) = $418.18.

f(5) = 5g(x)

f(5) = 5 × $418.18

f(5) = $2,090.9

Next, we would subtract the cost in 5 years as follows;

Difference = $5,750 - $2,090.9

Difference = $3,659.1.

Therefore, $3,659.1 is greater than $3,000, so an additional savings is worth it.

Part e.

Lastly, we would determine the gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car;

[tex]800=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{y})[/tex]

800 = 3,450 - 62,100/y

62,100/y = 3,450 - 800

62,100/y = 2,650

y = 62,100/2,650

y = 23.4 mpg.

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Answer:

-84x^7

Step-by-step explanation:

The product of (4x)(-3x³)(-7x³) is -84x^8.

To calculate the product, we multiply the coefficients together and add the exponents of the variables:

4 * (-3) * (-7) = 84

x^1 * x^3 * x^3 = x^(1+3+3) = x^7

Combining the coefficient and the variable, we get -84x^7.

1. The percentage of data items below a z-score of 1.8 is 96.41%.

2. The percentage of data items above a z-score of 1.8, is 3.59%.

To find these percentages, we can look up the  z-score of 1.8 is located in the row labeled "1.8" and the column labeled "Percentile."

The value in this cell is 96.41. This means that 96.41% of the data items in the normal distribution table will have a z-score that is less than or equal to 1.8.

P(z = 1.8) = 96.41%.

To find the percentage above 1.8

100 - 96.41 = 3.59%.

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The period of the sound wave created by the tuba is approximately 0.0134 seconds.

The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:

v = λ × f

Where:

v = speed of sound (343 m/s)

λ = wavelength (4.61 m)

f = frequency (unknown)

To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:

v = λ / T

Rearranging the equation to solve for the period (T), we get:

T = λ / v

Substituting the given values, we have:

T = 4.61 m / 343 m/s

Calculating the value, we find:

T ≈ 0.0134 seconds

Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.

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Answer:

28.21°

Step-by-step explanation:

use the Cosine rule (Cos A = (b² + c² - a²) / 2bc)

let's call our angle A.

then Cos A = (12² + 20² - 11²) / (2 X 12 X 20)

= 141/160.

A = Cos^-1 (141/160)

= 28.21° to nearest hundredth

Answer:

Step-by-step explanation:

To determine the amount by which Norah’s taxable income and federal tax payable would increase, we need to calculate the following:

The amount of foreign source income that will be included in Norah’s taxable income.

The federal tax payable on the foreign source income.

For non-business income:

The amount of foreign source income that will be included in Norah’s taxable income is $30,000.

The federal tax payable on the foreign source income is $6,525.

For business income:

The amount of foreign source income that will be included in Norah’s taxable income is $30,000.

The federal tax payable on the foreign source income is $8,700.

The units that each student used, given the measurement that they got and all of them being right was:

The height of a bookshelf is typically measured in inches, feet, or yards .

Student A measured 72 units, which is equal to 6 feet. Student B measured 2 units, which is equal to 24 inches .

Student C measured 6 units, which is equal to 18 yards. All three students are correct, as they all used different units to measure the same height .

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Full question is:

Three students measure the height of a bookshelf. Student A measures 72 units, Student B measures 2 units, and Student C measures 6 units. The teacher says all three students are correct. What units did each student use?

a) The slope of the tangent to the curve is,

⇒ dy/dx = 18x + 9

b)  the instantaneous rate of change of the function at point x = 7 is

⇒ dy/dx = 135

We have to given that;

Function is,

⇒ y = 9x² + 9x + 3

Now, We know that;

The slope of function is defined by derivative of function with respect to x.

Here, Function is,

⇒ y = 9x² + 9x + 3

Hence, the slope of the tangent to the curve is,

⇒ dy/dx = 18x + 9

And, the instantaneous rate of change of the function at point x = 7 is

⇒ dy/dx = 18x + 9

⇒ dy/dx = 18 x 7 + 9

⇒ dy/dx = 126 + 9

⇒ dy/dx = 135

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If the difference between the same side interior angles of two parallel lines is 50 degrees, we know that those angles must sum up to 180 degrees (because they are opposite each other).are supplementary angles. As a result, each of the four angles is 65 degrees, 115 degrees, 65 degrees, and 115 degrees..

Let's call one of the angles "x". Then, the other angle must be (x+50).

Now, let's look at the angles formed by a transversal intersecting those two parallel lines. There are eight angles in total, but we only need to find four of them since the other four are congruent (due to alternate interior angles being congruent).

The angles we need to find are:

1. x (one of the same side interior angles)

2. (x+50) (the other same side interior angle)

3. the corresponding angle to x (opposite x, on the other side of the transversal)

4. the corresponding angle to (x+50) (opposite (x+50), on the other side of the transversal)

Since corresponding angles are congruent when two parallel lines are intersected by a transversal, we know that angles 3 and 4 are equal to angles 1 and 2, respectively.

To determine all four angles, we just solve for x:

x + (x+50) = 180

2x + 50 = 180

2x = 130

x = 65

Therefore, our four angles are:

1. x = 65 degrees

2. (x+50) = 115 degrees

3. the angle corresponding to x = 65 degrees

4. the corresponding angle to (x+50) = 115 degrees

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Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=7\\ b=3\\ h=3 \end{cases}\implies A=\cfrac{3(7+3)}{2}\implies A=15[/tex]

Answer:

The answer is 53

Step-by-step explanation:

50+48+59+39+58=294

360-294=106

106/2=53

Answer:

53

Step-by-step explanation:

The sum of exterior angles of any polygon is 360 degrees

x + x + 59 + 48 + 50 + 39 + 58 = 360

2x + 254 = 360

x = (360 - 254)/2 = 53

Answer:

Step-by-step explanation:

You want to solve the system of equations ...

We can eliminate y by subtracting the first equation from 4 times the second:

  4(3x +y) -(x +4y) = 4(-2) -(25)

  11x = -33

  x = -3

Using the second equation, we have ...

  y = -2 -3x = -2 -3(-3) = 7

The values of x and y that make the equation true are ...

__

Additional comment

The sum of matrices is the sum of corresponding terms. The constant terms on the diagonals are irrelevant to the values of x and y. The off-diagonal sums give the two equations solved here.

<95141404393)

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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The total students participated in in track-and-field day is 485.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have:

Total number of students combined = 584

5/8 of are seventh graders and 3/8 of are eighth graders

If 4/5 if the seventh graders participated in track-and-field day. Thus, the of number seventh graders participated in track-and-field day will be:

5/8 * 4/5 * 584 = 294

If 7/8 of the eighth graders participated.  Thus, the of number eighth graders that participated will be:

3/8 * 7/8 * 584 = 191

total students participated = 294 + 191 = 485

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Complete Question

The event coordinator asks you to determine how many students participated in the track-and-field day. The total number of students in seventh and eighth grade combined is 584. 5/8 of them are seventh graders and 3/8 of them are eighth graders. If 4/5 if the seventh graders participated in tack-and-field day and 7/8 of the eight graders participated, about how many total students participated? Describe the process you used.