Activity No. 16
Find the roots of the following radical expressions.
1. √64
2. ⁴√ -1
3. ³√1000
Write each expression in radical form or with a rational exponent, and simplify.
1. (⁴√ 1)⁷
2. ³ √-64
3. (2⁹)¹/³
4. (11²)¹/²

The probability of choosing a box and picking two quarter coins in a row is 1/108

Probability is the branch concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1. 0 indicates impossibility of the event and 1 indicates certainty.

Probability= sample space / total possible outcome

therefore probability of choosing two quarters in a row = 1/6×1/6= 1/36

The probability of choosing the first box =1/3

Therefore the probability of choosing the first box and picking two quarters In a row is 1/36×1/3= 1/108.

Since box two contain no quarter and box three has only one quarter , the probability of choosing two quarters in a row is 0.

Therefore the probability of choosing a box at random and picking two quarters in a row is 1/108.

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Answer:

Unit rate is 2

Step-by-step explanation:

Pick two columns of the ordered pairs. Lets use (2,4) and (3,6)

The x values are 2 and 3 and the y values are 4 and 6

Now you’re going to divide y by x so

4/2 = 2

6/3 = 2

(Always choose two ordered pairs so you know that your answer is right)

Unit rate of the table is 2.

The units of concentration and rate are always going to be molars per second. We now understand that molar per second is equal to k times molar in units. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given,

Choose two columns from the paired ordered columns. Using (2, 4) and (3,6)

The x and y values are 2 and 3, respectively, and the

You will now divide y by x, so

4/2 = 2

6/3 = 2

Unit rate of the table is 2.

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Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A wheat farmer plows 5 acres of land and collects 135 bushels of wheat

The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.

Let us create a equation

Bushels/Acres

For first day:

Number of bushels of wheat=135

Number of acres of land=5

135/5=27

Next day:

Number of bushels of wheat=216

Number of acres of land=8

216/8=27

The proportional relation between 1st day and next day is same. It is proportional because the farmer collected 27 bushels for every 1 acre plowed.  

Hence, Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.

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The equation of a line is written as [tex]y=mx+c[/tex].

What is the equation of a line?

The equation [tex]y = mx + c[/tex] is the general equation of any straight line where [tex]m[/tex] is the gradient of the line and [tex]c[/tex] is the [tex]y -intercept[/tex] .

Here the given equation is

[tex]y=1.5x+20[/tex]       ........[tex](1)[/tex]

when [tex]x=0[/tex]

[tex]y=1.5(0)+20\\y=20[/tex]

when [tex]x=1[/tex]

[tex]y=1.5(1)+20\\y=1.5+20\\y=21.5[/tex]

when [tex]x=-1[/tex]

[tex]y=1.5(-1)+20\\y=-1.5+20\\y=18.5[/tex]

Draw the graph

Hence, by using the values of [tex]x[/tex] and [tex]y[/tex] we formed a straight-line graph.

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The ingredients Rose needs to make 5 short bread fingers are;

Recipe for 30 shortbread fingers.

To determine the recipe needed for 5 short bread fingers ; divide 30 by 5

= 30/5

= 6

This means, each recipe needed for 30 short bread fingers will be divided by 6 to achieve recipe needed for 5 short bread fingers.

Therefore,

Recipe needed for 5 short bread fingers:

Butter = 120 g / 6

= 20 g

Sugar = 60 g / 6

= 10 g

Flour = 180 g / 6

= 30 g

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The pressure that would be required to have a flow rate of 62 gal/min is f=86.25

The velocity of the stream is exactly proportional to nozzle pressure. In the given scenario, instead of a stream moving at 80 mph through the fire's super-heated gases, it moves at 60 mph.

The velocity increases as the pressure decreases in a convergent nozzle, but we know that pressure is inversely related to area.

The following formula can be used to compute the flow rate for a given nozzle. Q represents the flow rate. K = Nozzle K factor. P = Nozzle pressure differential. n = Is a constant that is determined by the type of spray pattern.

Given equation is,

f = √120p

Here p denotes the nozzle pressure in pounds per square inch

Also given that p=62 gal/min

f = √120p

Then,

f= √120(62)

f=√7440

f= 86.25

The pressure that would be required to have a flow rate of 62 gal/min is f=86.25

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The word sentence which is used to represent the given inequality

p ≥ 8.9 is a number is at least as large as 8.9.

As given in the question,

Given inequality is equal to :

p ≥ 8.9

In the given inequality sign of greater than and equals to is used.

Explanation for the given word sentences:

Meaning of at least is minimum this much.

At least as large means ( ≥) greater than or equal to

Option is correct.

It represents the symbol (≤ )less than or equal to.

Incorrect option.

It represents the symbol of > greater than only.

Incorrect option.

Therefore, the word sentence which is used to represent the given inequality p ≥ 8.9 is a number is at least as large as 8.9.

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The third graph passing through the points (-2,4) and (2,-2) represents the equation y = 3/2x + 1.

Given:

y = 3/2 x + 1

m = 3/2

the graph whose m value is equal to 3/2 is correct.

First graph:

Take any two points (-2,-2) and (0,2)

slope m = 2-(-2) / 0-(-2)

= 2+2 / 0+2

= 4/2

= 2

This graph is incorrect

Second graph:

Two points(-2,2) and (2,-4)

slope m = -4-2 / 2-(-2)

= -6/2+2

= -6/4

= -3/2

This graph is incorrect.

Third graph:

Two points (-2,4) and (2,-2)

slope m = -2-4 / 2-4

= -6/-2

= 3/2

This graph is correct.

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He has to climb UP 40 feet

Step-by-step explanation:

Answer:

slope = 16/13, increasing

Step-by-step explanation:

solve for the slope

-1.2-(-2.8)/(6.4-5.1)

= 16/13

it's positive meaning it's increasing

Using the proportion rule, the ratios 1/3 and 2/5 does not form a proportion.

In the given equation,

We have to check the ratios 1/3 and 2/5 form a proportion or not.

As we know that proportion is a ratio in which both ratios are equal to each other.

So to check whether the given statement is proportion or not we put both equation equal to each other.

So the ratios are 1/3 and 2/5.

Now checking the proportion.

1/3=2/5

Multiply by 15 on both side.

1/3 ×15=2/5 ×15

Simplifying

1×5=2×3

5=6

As we can see that both side is not equal so the given ratio is not proportion.

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The value of  ∇r^n = n(r^n-2)r​ is [tex]-n r^{n-2} \bar{r}[/tex]

A quantity in mathematics known as a vector that lacks position but has both magnitude and direction

The movement of an object between two points is described by a vector. The directed line segment can be used to geometrically represent vector math. The magnitude of a vector is the length of the directed line segment, and the vector's direction is indicated by the angle at which it is inclined.

Given ,

[tex]$&\nabla r^n=n r^{n-2} \bar{r} \\[/tex]

[tex]$&\text { let } \bar{r}=x \hat{i}+y \hat{j}+z \hat{k} \\[/tex]

[tex]$&r=|\bar{r}|=\sqrt{x^2+y^2+z^2} \\[/tex]

[tex]$&\frac{\partial r}{\delta x}=\frac{-x}{r} ; \frac{\delta r}{\delta y}=-\frac{y}{r}, \frac{\delta r}{\delta z}=-\frac{z}{r} \\[/tex]

[tex]$&\because \nabla r^n=\frac{\delta}{\delta x}\left(r^n\right) \hat{i}+\frac{\delta}{\delta y}\left(r^n\right) \hat{j}+\frac{\delta}{\delta z}\left(r^n\right) \hat{k} \\[/tex]

[tex]$&\left.=n r^{n-1} \frac{\delta r}{\delta x} \hat{i}+n r^{n-1} \frac{\delta r}{\delta y} \hat{j}+\frac{\delta}{\delta z} x r^n{ } \hat{k} \\[/tex]

[tex]$&=n r^{n-1}\left[\frac{\delta r}{\delta x} \hat{i}+\frac{\delta r}{\delta y} \hat{j}+\frac{\delta r}{\delta z} \hat{k}\right] \\[/tex]

[tex]$&=n r^{n-1}\left[\frac{\delta r}{\delta x} \hat{i}+\frac{\delta r}{\delta y} \hat{j}+\frac{\delta r}{\delta z} \hat{k}\right] \\[/tex]

[tex]$&=n r^{n-1}\left[-\frac{x}{r} \hat{i}- \frac{y}{r} \hat{j}-\frac{z}{r} \hat{k}\right] \\[/tex]

[tex]$&=\frac{n r^{n-1}}{r}[-x \hat{i}-y \hat{j}-z \hat{k}]=-n r^{n-2} \bar{r} \\[/tex]

Therefore the value of ∇r^n = n(r^n-2)r is [tex]-n r^{n-2} \bar{r}[/tex]

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Answer:

Take a look at the attachment...

Hope this helps! :)

If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.

As per the question statement, The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, and the total value of the coins in this piggy bank is at least $4.35,

Then, we are required to determine the smallest possible number of individual coins in the bank.

To answer this question, first we will need to know the monetary values of nickels and dimes, that is,

(1 dime = 10 cents = $0.1), and (1 Nickel = 5 cents = $0.05).

Now let us assume that, there are "x" nickels and "y" dimes in that bank, Then as per the condition that, the number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, we can write an equation with the above assumed two variables, which is, [x = (2y - 1)]...(i)

And as per the other condition that, the total value of the coins in this piggy bank is at least $4.35, we can write another equation, which is,

[(0.1y + 0.05x) = 4.35]

Or, [100(0.1y + 0.05x) = (100 * 4.35)]

Or, [(10y + 5x) = 435]...(ii)

Now substituting eqn (i) in eqn (ii), we get,

[{10y + 5(2y - 1)} = 435]

Or, [(10y + 10y - 5) = 435]

Or, [(10y + 10y) = (435 + 5)]

Or, (20y = 440)

Or, [y = (440/20)]

Or, (y = 22)

Therefore, [x = {(2 * 22) - 1}]

Or, [x = (44 - 1)]

Or, [x = 43]

That is, If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.

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It will take 12 hours for 15 men to do same job.

How to determine this?

When amount of hour ∝ 1/number of men

When H represent Hour

And M represent the number of men

k to represent the constant

H = k/M as it is inversely proportional

It takes 10 men 18 hours to repair a road

18 = k/10

k = 18 × 10

k = 180

How long will it take 15 men?

When k = 180

H = k/M

H = 180/15

H = 12 hours

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1

Step-by-step explanation:

28-28=1 11111111111111111111111111

The actual price of an item is $1371.49.

Given that, the discount percentage is 12.5% and the selling price is $1200.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Let the actual price be x.

Now, x-12.5% of x =1200

⇒ x- 12.5/100 ×x=1200

⇒ x- 0.125x=1200

⇒ 0.875x=1200

⇒ x=1200/0.875

⇒ x=$1371.49

Therefore, the actual price of an item is $1371.49.

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Answer:

BC = 7.9 cm

Step-by-step explanation:

To construct triangle ABC:

Answer:

Dinner should cost 250 today.

Step-by-step explanation:

The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

The decimal that represents the number 4×1+1×1/100+9×1/1000 is given as follows:

4.0119.

A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:

Fraction = x/y.

The terms that represent x and y are listed as follows:

In this problem, we are given two fractions, and their decimal equivalents are given as follows:

Hence the numeric value of the expression is given as follows:

4×1+1×1/100+9×1/1000 = 4 + 0.01 + 0.0019 = 4.0119.

Which is the decimal number represented by the fraction.

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The value of (fоg)(3) = 134.

What is composition of functions?

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

Consider, the given functions

f(x) = 3x - 1, g(x) = 4x^2 + 9

First to find f(g(x)).

Let,

f(g(x)) = 3(4x^2 + 9) - 1

         = 12x^2 + 27 - 1

f(g(x)) = 12x^2 + 26

Now, to find f(g(3)).

Plug x = 3 in the above equation,

f(g(3)) = 12(3)^2 + 26

         = 12(9) + 26

f(g(3)) = 134

Hence, (fоg)(3) = 134.

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The required expression 16m + 6n - 8 represents the perimeter of the triangle. which is the correct answer would be option (D).

A triangle has side lengths of (7m - 2) centimeters, (9m - 5) centimeters, and (6n - 1) centimeters.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

The perimeter of the triangle = (7m - 2) + (9m - 5) + (6n - 1)

Rearrange the terms likewise in the above equation,

The perimeter of the triangle = 7m + 9m + 6n - 2 - 5 - 1

Apply the arithmetic operation to get the required expression

The perimeter of the triangle = 16m + 6n - 8

Therefore, the required expression 16m + 6n - 8 represents the perimeter of the triangle.

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The additive inverse of the matrix A is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

From the question, the matrix is given as

[tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]

This matrix is given as matrix A

So, we have the following representation

A = [tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]

Next, we calculate the required matrix operation

The matrix operation is given as additive inverse of the matrix

This additive inverse of the matrix is calculated by negating each element present in the matrix

i.e. if an element in the matrix is a, the inverse would be -a

Using the above highlights as a guide, we have the following representations

Additive inverse = [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

Hence, the additive inverse is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

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Graph will shift from(0,0) to (3,4) after the shifting happens due to change in expressions of the parent function.

Graph transformation is the process by which an parent graph, or graphed equation, is changed to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification in algebraic equations.

The deduced parent function is [tex]\sqrt{x}[/tex]

So, Domain= (0 , ∞)

     Range= (0 , ∞)

Let us take (0,0) as the point and see the shifting of the point with respect to (0,0).

So when function is transformed to √x+3

Function shift from (0,0) to (3,0)

and when function is transformed to [tex]\sqrt{x+3} +4[/tex]

then point shifts to (3,4).

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Answer: D

Step-by-step explanation:

I dont gotta explain it, here you go bro :) its -10

Answer:

x=12

Step-by-step explanation:

2x+4=6x

x-6=6x

6x=6x

x=6+6

Answer:

b: x=66 degrees

Step-by-step explanation:

132 degrees and 2x are corresponding angles since of the transversal.

So 132=2x and x=66 degrees