Two consecutive whole numbers that lie between 101?

The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

Learn more on indices here:

brainly.com/question/10339517

#SPJ1

a) In the long run, he makes 53.2 $ per hour

b) He spends 46% of the time in a day driving to and from the airport

a)

The amount of the expected money he will earn in airport trips per minute will be = (Probability that he gets an airport drop) * ((Total Earnings)/(Total time taken in minutes))

So, the value of the amount of expected money he will earn in airport trips per minute will be

\(= (\frac{1}{3}) \times (\frac{(28 \times 2)}{(20+20+35)})\\=\frac{56}{225}=0.249\)

Then, the Expected money he earns in airport trips per hour will be =0.249*60=$14.93

The expected money he earns within city trips per minute will be

=(Probability that he gets a within-city fare) * (Avg. money he earns in within-city fares)

So, the value of the amount of the expected money he earns within city trips per minute will be= (2/3) * 1.33 = 0.886

Expected money he earns within city trips per hour = 0.886*60 = 53.2$

b)

Fraction of time spent going to and from the airport (excluding the time spent in line there)

=((Probability of airport trip) * (Time taken to and fro airport))/

((Probability of airport trip) * (Avg. time taken in airport trips))+((Probability of city trip) *(Avg. time taken in city trips))

= (1/3)*(20+20)/(((1/3)*(20+35+20))+((2/3)*((2+10)/2))))

=40/(12+20+35+20)

=40/87

=0.46

For more questions on Probability

https://brainly.com/question/25870256

#SPJ4

In order to write log10(0.001) = -3 in index form, we have \(10^{-3} = 0.001\).

The logarithm of a number refers to the power to which a given base is raised to give the number. In this case, the base is 10 and the index is 3. Our task is to write log10(0.001) = -3 in index form.

Recall that;

Hence, to write  log10(0.001) = -3 in index form we have to write, \(10^{-3} = 0.001\)

Learn more about logarithm: https://brainly.com/question/7302008

Answer:

C. = 69.5

Step-by-step explanation:

The median or the average between 80 and 59 is 69.5

Hope this helps! :)

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer: 2x2 + 1000 x 1000 = 1000004

Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also

Answer:

1000004

Step-by-step explanation:

First we do can separate it into the parentheses: (2*2) + (1000*1000)

= 4 + 1000000

= 1000004

Answer:

x=11

y=-7

z=-6

Step-by-step explanation:

y=11+3z

x-33-5z=8

11+8z=-37

z=-6

x-3=8

y=-7

x=11

Answer:x-(2 7/8)=1/2

Step-by-step explanation:

Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.

1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.

Learn more about Shapes:

https://brainly.com/question/28636956

#SPJ4

Answer:

4

Step-by-step explanation:

subtract negative 4 by negative 8

The inverse of the function will be f⁻¹(y) = y + 1.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

The given function is y = x - 1.

To find the inverse of this function, we need to solve for x in terms of y.

y = x - 1

Adding 1 to both sides, we get:

y + 1 = x

Therefore, the inverse function is:

x = y + 1

f⁻¹(y) = y + 1

Note that the inverse function represents the reflection of the original function across the line y = x.

To know more about an inverse of the function follow

https://brainly.com/question/19425567

#SPJ1

Answer:

X could be equal to both -7 and 7

Step-by-step explanation:

a negative times a negative equals a positive.

she didn't notice that x could also be x = -7

1. The standard equation of the circle is x² + y² = 4. 2. The standard equation of the circle is (x - 3)² + (y - 2)² = 4.

The points in a plane that are equally spaced apart from a fixed point known as the centre make up a circle, which is a two-dimensional geometric object. The radius of a circle is the separation between its centre and any other point on the circle. The circle is one of the most fundamental and significant geometric forms. It is used in many fields of science, mathematics, and engineering, including calculus, coordinate geometry, and trigonometry. The design of wheels, gears, and lenses as well as the simulation of scientific events like the motion of planets and electrons are other common practical uses for circles.

The standard equation of a circle is

(x - h)² + (y - k)² = r²,

where (h,k) is the center of the circle and r is its radius.

1. Center (0, 0) and radius = 2:

(x - 0)² + (y - 0)² = 2²

x² + y² = 4

Therefore, the standard equation of the circle is x² + y² = 4.

2, Center (3, 2) and radius = 2:

(x - 3)² + (y - 2)² = 2²

(x - 3)² + (y - 2)² = 4

Therefore, the standard equation of the circle is (x - 3)² + (y - 2)² = 4.

Learn more about circle here:

https://brainly.com/question/11833983

#SPJ1

Answer:

u = -3

Step-by-step explanation:

[Given]

7 = 10 + u

[Subtract 10 from both sides of the equation]

-3 = u

[Reflexive Property]

u = -3

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

e) Finding how many students answered at most 4 questions.

The number of students that answered at most 4 questions correctly is:

Students answered 0 questions correctly + Students answered 1 question correctly + Students answered 2 questions correctly + Students answered 3 questions correctly + Students answered 4 questions correctly

So, the number of students is:

4 + 8 + 6 + 2 + 15 = 35

35 students answered at most 4 questions correctly.

f) Finding the sum of relative frequency.

The sum of relative frequency is:

0.08 + 0.16 + 0.12 + 0.04 + 0.3 + 0.3

Sum = 1.

The sum of the relative frequency in a distribution is always 1.

g) Creating a histrogram

To create a histogram, create a bar for each result correct. The values of the frequency will be used in the y-axis.

Given =

n=6,

r=1/4

a=2

Sn = a+ar+ar²+ar³+ar⁴+ar⁵= 2+0.5+0.125+0.03125+0.0078125+0.00195~ 2.67

hope you will like it

Answer:

one of the things that helps is to study at certain times, because trying to do it for a while at once, you will feel burnt out. try to study for a half hour, then go do something else for a half hour to an hour, and just keep doing that until you feel more comfortable and motivated to start studying for a longer time. There are many different things you can do to help, but hopefully you find this useful

Answer:

a. geometric series

b. r_n = 100 × (0.75)^n ft

c. 400

Step-by-step explanation:

a.

Start: 100 ft

After 1 hour: 75% of 100ft = 100 ft × 0.75

After 2 hours: 75% of 100ft × 0.75 = 100 ft × 0.75²

After 3 hours: 75% of 100 ft × 0.75² = 100 ft × 0.75³

Notice what is happening to the radius as the hours pass.

With each passing hour, the radius is 0.75 times the previous radius.

Since each new term is the previous term multiplied by a constant, 0.75, this is a geometric series.

b.

At each hour, multiply 100 ft by 0.75 raised to the number of the hour.

a_n = 100 × (0.75)^n ft

The nth term is 100 times 0.75 to the nth power.

c.

The sum of all the radii is the sum of a series that has 100 as its first term, and each subsequent term is 0.75 times the previous term.

r_n = 100(0.75)^n

Since the constant ratio has an absolute value less than 1, the series has a sum.

S = a_1/(1 - r)

S = sum of infinite series

a_1 = first term

r = constant ratio

S = 100/(1 - 0.75)

S = 100/0.25

S = 400

The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

To know more about Surface area, visit:

https://brainly.com/question/29298005

#SPJ1

Answer:

A=43

B=32

C=105

Answer:

Step-by-step explanation:

Surface area of a cylinder:

Substitute values:

Matching choice is C

Answer:

y= -12

Step-by-step explanation:

3y+18+10=-8

Basically just used the distributive property

Combine like terms:

3y+28=-8

   -28.  -28

3y=-36

y=-12

Answer:

y = -11

Step-by-step explanation:

3(y+6) + 10 = -8

3y + 18 + 10 = -8

3y = -8 - 18 - 10

/3      /3

y = -12

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

Step-by-step explanation:

Let the trapezium be B.

Draw a line from the top of the trapezium to it's base and call the triangle formed B.

The base of is 2cm (8cm - 6cm

The area of the triangle = 40cm² ( 5cm x 4cm x 2cm)

Area of the trapezium =. ½ (base x height)

. = 18cm²

Add area of trapezium and triangle.

 = 40cm² + 18cm² = 58cm²

.