The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closet to the length of this rectangle in feet?

The expression which is equivalent to the given expression is 1 / 5x⁸ y¹³.

Given expression is,

3 x⁻⁶y⁻³ / 15 x² y¹⁰

We have to find the equivalent expression for this, which means that the end value for both expressions will be same.

We can write the given expression as,

3/15 × (x⁻⁶ / x²) × (y⁻³ / y¹⁰)

1/5 × (x⁻⁶ ⁻ ²) × (y⁻³ ⁻ ¹⁰)

= x⁻⁸ y⁻¹³ / 5

When the variables goes in to the denominator sign changes to positive in the exponent.

= 1 / 5x⁸ y¹³

Hence the correct expression is 1 / 5x⁸ y¹³.

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By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).

In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Furthermore, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By adding the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)

[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]

[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]

[tex]\vec a + \vec b[/tex] = (3, -5).

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The diameter of the sphere to the nearest tenth is [tex]5.3\ cm[/tex].

According to the question:

[tex]Volume(V) = 79\ cm^3[/tex]

To find:

[tex]Radius(r)[/tex]

We know that:

[tex]V = \frac{4}{3}\pi r^3[/tex]

⇒ [tex]r = (\frac{3V}{4\pi})^{1/3}[/tex]

Take [tex]\pi[/tex] = [tex]3.1415[/tex] and substitute the given values in the above equation:

[tex]r = (\frac{3\times 79}{4\times 3.1415})^{1/3}[/tex] ...(∵ [tex]\pi = 3.1415[/tex])

[tex]r = 18.8604^{1/3}[/tex]

[tex]r = 2.661\ cm[/tex]

⇒[tex]diameter = 2\times 2.661\ cm[/tex]

⇒[tex]diameter = 5.322\ cm[/tex]

Rounded to the nearest tenth:

[tex]diameter = 5.3\ cm[/tex]

Therefore, the diameter of the sphere to the nearest tenth is [tex]5.3\ cm[/tex].

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Step-by-step explanation:

work he in a department store

1. We can see here that  the initial flounder population will be = [tex]\frac{220}{0.6t + 1}[/tex].

2. The P'(11) in 2 decimal places is: 28.95.

Population refers to the total number of people residing in a given region or area. In most cases, it is expressed as the number of people in relation to a unit of area, like a square kilometer or square mile. A census, which is a count of every person residing in a specific area, can be used to estimate the population of a nation or region.

Many variables, such as birth, mortality, and migration rates, can have an impact on population size.

1. The initial flounder population:

[tex]\frac{4t + 216}{0.6t^{2} + 1 } = \frac{4 + 216}{0.6t + 1} = \frac{220}{0.6t + 1}[/tex]

2. The P'(11) will be:

where t = 11

[tex]\frac{220}{0.6(11) + 1} = \frac{220}{7.6} = 28.9473[/tex]

= 28.95 (2d.p.)

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Check the picture below.

so the part on the left is a template for transformations, and we can look at g(x) like this

[tex]{\Large \begin{array}{llll} g(x)=\stackrel{A}{-3} ~~ (\stackrel{B}{1}x+\stackrel{C}{4})^2 ~~ \stackrel{D}{-3} \end{array}}[/tex]

now, if you look at the template, we do +4 first, then -3 shift down, then 3 vertical shrink, and then the negative of -3, landing at g(x) from our parent f(x).

Answer: passes a horizontal AND vertical line test✅; no repeating x values✅

Step-by-step explanation:

To pass a line test, the function must pass BOTH the horizontal and vertical line test. If it only passes one but not the other, is it NOT a function.

Lastly, it can be a function if it has repeating y values.

The values of

1. DF = 28cm

2. AC = 64 cm

3. CF = 32 cm

It states that the line segment in a triangle joining the segment of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Therefore we can say that;

triangles , BDE, AD ,EFC, DE are congruent.

congruent triangles are triangles with equal sides and equal angles.

D = BE

BE = 56/2 = 28cm

A = DE = 32 cm

AC = 2AF

= 2 × 32 = 64 cm

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The probability that calls last between 4.0 and 4.6 minutes will be around 0.4332.

we have to standardize the values and utilize the standard typical dispersion table or calculator.

To discover the z-scores for 4.0 and 6.0  minutes:

z1 = (4.0 - 6.0  ) / 0.70 = 2.8

z2 = (4.5 - 6.0  ) / 0.70= 2.1

Since Employing a standard ordinary conveyance table, we are able to discover the likelihood of the calls enduring between 4.0 and 4.6 minutes:

P(0 ≤ Z ≤ 2.1) = 0.4332

However the likelihood that calls final between 4.0 and 4.6 minutes is 0.4332, or around 0.4332.

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Step-by-step explanation:

14÷100×1680.00

=$235,20

Answer:187 miles

Step-by-step explanation: 155.33-16.95=138.38/74=187

Answer:

30

Step-by-step explanation:

We can move the triangle on the top to the bottom to form a rectangle.

Then, it is 5x6 = 30.

The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.

To determine the slope of the line tangent to the graph of the given function when x = -6;

Using alternative form of the definition of derivative.

f'(a) = lim (h->0) [f(a+h) - f(a)] / h

Using this formula for the given function;

h'(a) = lim (h->0) [h(a+h) - h(a)] / h

Now, substitute a = -6 into the formula:

h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h

Next, simplify the expression by plugging in the values:

h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h

Simplifying further:

h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h

Now, let's combine the fractions with a common denominator:

h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h

Simplifying the numerator:

h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h

Canceling out the h's:

h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]

Taking the limit as h approaches 0:

h'(-6) = -1 / ((-6)(-6))

Simplifying further:

h'(-6) = -1 / 36

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Answer:

The correct answer is C. Net income refers to your take-home pay after taxes and other deductions have been taken out of your gross income. It is an important financial measure because it represents the actual amount of money you have available to save, invest, or spend on your expenses and bills.

Step-by-step explanation:

Answer:

1 South African Rand is equal to 100 cents. Therefore, 349 South African Rands is equal to 34900 cents.

Answer:

349 South African Rand equals

United States Dollar

17.95

South African Rand

349

The cardinality of set A (n(A)) is 3.

The cardinality of set B (n(B)) is 4.

To find the cardinality of a set, we count the number of elements in that set.

For set A, we need to count the number of integers between -6 and -4 (inclusive).

The integers in this range are -6, -5, and -4.

Therefore, the cardinality of set A (n(A)) is 3.

For set B, we simply count the number of elements given in the set. From the given set B = {-29, 20, 28, 29}, we have 4 elements.

Therefore, the cardinality of set B (n(B)) is 4.

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a. The demand equation is p=−300Q+6000.

b. When the price per unit is Rs 1650, the number of calculators demanded is 2500.

c. When 4500 calculators are demanded, the price per unit is Rs 900.

a. The slope of the demand curve is m = 0.3. We can find the y-intercept by substituting the slope and one of the points into the demand equation. When the price is Rs 1200, the quantity demanded is 4000. Therefore, the y-intercept is b=1200−(−0.3)(4000)=2400.

The demand equation is p=−0.3Q+2400.

1650 = 0.3Q - 2400

b. When the price per unit is Rs 1650, the number of calculators demanded is:

= (1650 - 2400) /-0.3

= 2500.

c. To find the price per unit of calculator when 4500 calculators are demanded, we substitute Q = 4500 into the demand equation and solve for p:

p = 0.3(4500) + 2400

p = 900

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To solve the inequality:

9.5 + 6x ≥ 42.1

We will follow these steps:

Subtract 9.5 from both sides of the inequality:

9.5 + 6x - 9.5 ≥ 42.1 - 9.5

6x ≥ 32.6

Divide both sides of the inequality by 6:

(6x) / 6 ≥ 32.6 / 6

x ≥ 5.433333...

Rounded to two decimal places, the solution to the inequality is:

x ≥ 5.43

To find the first four terms of the infinite sequence u_n = 1/(7n - 2), we substitute the values of n from 1 to 4 into the formula:

For n = 1:

u_1 = 1/(7(1) - 2) = 1/5

For n = 2:

u_2 = 1/(7(2) - 2) = 1/12

For n = 3:

u_3 = 1/(7(3) - 2) = 1/19

For n = 4:

u_4 = 1/(7(4) - 2) = 1/26

Therefore, the first four terms of the infinite sequence are:

u_1 = 1/5

u_2 = 1/12

u_3 = 1/19

u_4 = 1/26

Answer: a. A $100 stock loses 20% of its value.

To find the ending value of the stock after a 20% decrease in value, we can multiply the initial value by (1 - 0.20) or 0.80.

Ending value = $100 x 0.80 = $80

Therefore, the ending value of the stock after a 20% decrease is $80.

b. An $80 stock gains 20% of its value.

To find the ending value of the stock after a 20% increase in value, we can multiply the initial value by (1 + 0.20) or 1.20.

Ending value = $80 x 1.20 = $96

Therefore, the ending value of the stock after a 20% increase is $96.

Step-by-step explanation: :)

Answer:

please see detailed answers below

Step-by-step explanation:

1) circumference = πd = 16π inches.

arc length = (15/360) X πd = (2/3)π inches.

area of circle = πr² = π(8)² = 64π square inches.

area of sector = (15/360) X 64π = (8/3)π square inches.

2) circumference = πd = 30π inches.

minor arc length = (60/360) X 30π = 5π inches.

major arc length = (300/360) X 30π = 25π inches.

area of circle = πr² = π(15)² = 225π square inches.

area of minor sector = (60/360) X πr² = (75/2)π square inches.

area of major sector = (300/360) X πr² = (375/2)π square inches.

3) circumference = πd = 40π inches.

arc length = (125/360) X 40π = (125/9)π inches.

area of circle = πr² = π(20)² = 400π square inches.

area of sector = (125/360) X 400π = (1250/9)π square inches.

Answer:

If the height and radius of a cone are both 9 yards, then you can use the formula for the volume of a cone to calculate its volume. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Plugging in the values for r, h, and π gives us:

V = (1/3)πr^2h

 = (1/3)(3.14)(9 yd)^2(9 yd)

 = (1/3)(3.14)(81 yd^2)(9 yd)

 = (1/3)(254.34 yd^3)

 ≈ 84.78 yd^3

So, the volume of a cone with a height and radius of 9 yards is approximately 84.78 cubic yards, rounded to the nearest hundredth.

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Answer:

x = 4

Step-by-step explanation:

the angle immediately to the left of 20x must be 25x. that's because the two lines with double arrows at the top are parallel lines.

the angle to the left of 20x and the 25x are called alternate angles. they are equal.

also, 20x and the angle to the left of it are on a straight line. angles on a straight line add up to 180°.

so, we now have 20x + 25x = 180.

45x = 180

divide both sides by 45:

x = 180/45

= 4.

x = 4.

Step-by-step explanation:

This graph shows a vertical asymptote at x = 0  

                                           this is where it is not continuous

The greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.

In order to distribute the mangoes equally among children, we first need to determine the total number of mangoes in the bag.

If there are 215% (or 2.15) of 224 mangoes in the bag, we can calculate the total number of mangoes by multiplying these values: 2.15 * 224 = 481.6 mangoes.

Since we cannot have fractional mangoes, we round down to the nearest whole number, which gives us a total of 481 mangoes in the bag.

To distribute these mangoes equally among the children, we divide the total number of mangoes by the number of children. Let's assume there are 'x' children.

Each child will receive 481/x mangoes.

To determine the greatest number of children, we need to find a value for 'x' that evenly divides 481. We can do this by finding the factors of 481. The factors of 481 are 1, 13, 37, and 481.

Therefore, the greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.

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The value of 6(x + 1), given that 6* = 7 is [tex](7/6)x + 7/6.[/tex]

Given that 6* equals 7, we will solve for the value of "" by dividing 7 by 6.

6 = 7

= 7/6

To get value of 6 multiplied by (x + 1), we substitute the value of "*" into the expression:

6 * (x + 1) = (7/6) * (x + 1)

Expanding expression:

6 * (x + 1) = 7/6 * x + 7/6 * 1

6 * (x + 1) = 7/6 * x + 7/6

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Answer:

c) The equation of this line is y = 3x + 12.

Answer:

A= 158

B=158

D=22

Step-by-step explanation:

An isosceles trapezoid has 2 pairs of equal angles.

A=B

C=D

Also A+C=180

So we have that A=158

B=158 and D=22