Which of the following is equivalent to

Answer:

3,067,020 = [tex]3.06702\,\,10^6[/tex]

19.507 = [tex]1.9507\,\,10[/tex]

Step-by-step explanation:

3,067,020 = [tex]3.06702\,\,10^6[/tex]

19.507 = [tex]1.9507\,\,10[/tex]

Split up the interval [0, 2] into n equally spaced subintervals:

[tex]\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right][/tex]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

[tex]r_i=\dfrac{2i}n[/tex]

where [tex]1\le i\le n[/tex]. Each interval has length [tex]\Delta x_i=\frac{2-0}n=\frac2n[/tex].

At these sampling points, the function takes on values of

[tex]f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}[/tex]

We approximate the integral with the Riemann sum:

[tex]\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3[/tex]

Recall that

[tex]\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4[/tex]

so that the sum reduces to

[tex]\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}[/tex]

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

[tex]\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}[/tex]

Just to check:

[tex]\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28[/tex]

Hey there! :)

Answer:

-8/27.

Step-by-step explanation:

Begin by converting 2 1/4 to an improper fraction:

2 1/4 -->   [tex]\frac{9}{4}[/tex]

Divide fractions by multiplying by reciprocal:

[tex]\frac{-2}{3}* \frac{4}{9} = \frac{-2*4}{3*9} = \frac{-8}{27}[/tex]

Therefore, -2/3 divided by 3 1/4 = -8/27.

Answer:

- 8/27

Step-by-step explanation:

-2/3 ÷ 2 1/4= - 2/3 ÷ 9/4 = -2/3 × 4/9 = - 2×4/3×9= - 8/27

Answer:

1.  perim is 43.2

2. where are the blanks? dont see any

Step-by-step explanation:

Answer:

The y-intercept is when x = 0 so that means that the y intercept is (0, -8) or -8.

Answer:

64

Step-by-step explanation:

4/7

16x7= 112

4x16=64

Answer:

The cost of one large drink is $1.50.

(13.5-10) + 4 = (7.5 ÷ 5) = $1.50

Step-by-step explanation:

The first step is to minus the $10.00 from the $13.50, which gives us $3.50.

13.5 - 10

We've done this because the pizza is irrelevant to what we're trying to figure out, so we subtract the price of the food, which as we already know is $10, to isolate the price of the 5 drinks to make it easier to find the price of just one.

Once we've done that, we're going to add on the $4.00 they got discounted to the $3.50 in order to find the original price of the drinks without using the gift certificate.

(13.5 - 10) + 4

This gives us $7.50, or the price of 5 large drinks. But we're only looking for the price of one. So we're going to divide the 7.50 by the total number of drinks ordered.

(13.5-10) + 4 = (7.5 ÷ 5)

This gives us 1.5, or $1.50.

(13.5-10) + 4 = (7.5 ÷ 5) = $1.50

Step-by-step explanation:

Refer to the two diagrams, attached

Start with the first set (soccer balls)

Hexagons (six-sides)

5 orange, 5 light green, 5 dark green, 5 light orange

total of 20 hexagons

Pentagons (5 sided black figures)

1+5+5+1 = 12 pentagons.

For the next set:

Triangles (3 sides)

5 orange+5 dark green+5 light green+5 light orange

= 20 triangles

Squares (4 sides)

5 between orange triangles+5 between light orange triangles

+ 5 between orange and green triangles

+ 5 between light orange and light green triangles

+ 10 between green and light green triangles

= 40 squares

Pentagons (5 sides)

1 at north pole + 5 between orange and green triangles

+ 5 between light green and light orange triangles + 1 at south pole

= 12 pentagons.

Summary:

Soccerball: 20 triangles + 12 pentagons + 20 hexagons

GoalScorerBall: 20 triangles + 40 squares + 12 pentagons

Answer:

[tex]S=6600\pi \text{ mm}^2[/tex]

[tex]S\approx 20724 \text{ mm}^2[/tex]

Step-by-step explanation:

A can of fruit is geometrically a cylinder.

We are talking about the surface area of a cylinder:

[tex]S=2\pi rh+2\pi r^2[/tex]

[tex]\pi \approx 3.14[/tex]

[tex]r: \text{radius}[/tex]

[tex]h: \text{height}[/tex]

Factoring, we have:

[tex]S=2\pi r (h+r)[/tex]

Calculating the surface area of the can of fruit:

[tex]S=2\pi (30) (80+30)[/tex]

[tex]S=2\pi (30) (110)[/tex]

[tex]S=6600\pi[/tex]

[tex]S\approx 20724 \text{ mm}^2[/tex]

The question is a True or False question

Answer:

True

Step-by-step explanation:

Given

5 ≤ x ≤ 8

Required

Is [5,8] the interval of the given range?

The interval given shows that the range of x begins at 5 and ends 8.

Start by splitting the interval to different inequalities.

1. 5 ≤ x

This implies that 5 is less than or EQUAL TO x;

The keyword needed here is EQUAL TO;

The fact that the inequality gives room for EQUALITY (=) means that the interval begins exactly at 5

2. x ≤ 8

This implies that x is less than or EQUAL TO 8;

Similarly, the keyword needed here is EQUAL TO;

The fact that this inequality gives room for EQUALITY (=) means that the interval ends exactly at 8

So, this implies that the range of values of 5 ≤ x ≤ 8 is 5, 6, 7, 8

And can be represented with [5,8]

So, the statement is true.

Answer:

B)

Focus = (6,6), directrix is y = 4

Step-by-step explanation:

A parabola is the locus of a point that is equidistant from a fixed line (known as directrix) and a fixed point (known as focus).

The equation of a parabola in vertex form is given as:

[tex]y=a(x-h)^2+k[/tex]

It can be further simplified to:

[tex](x-h)^2=4p(y-k)[/tex]

The directrix of this parabola is given at line y = k - p and the focus is at (h, k + p)

Given that:

[tex]y = \frac{1}{4}(x-6)^2+ 5 \\(y-5)=\frac{1}{4}(x-6)^2\\(x-6)^2=4(y-5)[/tex]

Comparing (x-6)² = 4(y-5) with (x-h)² = 4p(y-k), It can be gotten that h = 6, p =1 and k = 5

The directrix of this parabola is given at line y = k - p = 5 - 1 = 4 and the focus is at (h, k + p) =  (6, 5+1) = (6, 6)

Focus = (6,6), directrix is y = 4

Answer:

x = ±6

y = 10

Step-by-step explanation:

Solve for the top part.

x² + -4 = 32

x² = 32 + 4

x² = 36

x = √36

x = ±6

Solve for bottom part.

y + y - 4 = y + 6

2y - 4 = y + 6

2y - y = 6 + 4

1y = 10

By solving the upper part and the lower part of the matrix equation, the value of x and y are:

[tex]\mathbf{x = \pm6}\\\\\mathbf{y = 10}[/tex]

The given matrix equation can be solved by taking the upperpart to create an equation to solve for x, and also taking the lower part to create an equation to solve for y.

[tex]x^2 + (-4) = 32[/tex] (upper part)

[tex]y + y - 4 = y + 6[/tex] (lower part)

Solve each of the equation in the matrix.

Solve the upper part for x:

[tex]x^2 + (-4) = 32\\\\x^2 - 4 = 32[/tex]

[tex]x^2 - 4 + 4 = 32 + 4\\\\x^2 = 36[/tex]

[tex]x = \sqrt{36} \\\\\mathbf{x = \pm6}[/tex]

Solve the lower part for y:

[tex]y + y - 4 = y + 6\\\\[/tex]

[tex]y + y - 4 = y + 6\\\\2y - 4 = y + 6\\\\2y - y = 4 + 6\\\\\mathbf{y = 10}[/tex]

Thus, by solving the upper part and the lower part of the matrix equation, the value of x and y are:

[tex]\mathbf{x = \pm6}\\\\\mathbf{y = 10}[/tex]

Learn more here:

https://brainly.com/question/13694076

Answer:

x = 4y+28

Step-by-step explanation:

x/4 -7 = y

Solve for x

Add 7 to each side

x/4  -7+7 = y+7

x/4 = (y+7)

Multiply each side by 4

x/4*4 = 4(y+7)

x = 4y+28

Answer: X = 4y + 28

Step-by-step explanation: Our first step will be to solve for x.

To do this, we first add 7 to both sides.

This gives us x/4 = y + 7.

Now we want to multiply each side of the equation by 4.

So we get x/4(4) = 4(y + 7).

On the right, distribute the 4 through the parenthses!

Simplifying from here, we get x = 4y + 28.

So this is our final answer.

Answer:

option c is the correct ans .

because we can easily substitute the value of y in equn 2 to get value of x..

Answer:

To me, the third one is the best.

Note:  y has  been made subject of formula which makes it easy to substitute it into equation 2 and find x .

Step-by-step explanation:

Answer:

1152 minutes

Step-by-step explanation:

$104.64-24.00 = $ 80.64

80.64 ÷ 0.07 = 1152

Answer:

17.5

Step-by-step explanation:

A = [tex]\frac{pq}{2}[/tex]

p = 7

q = 5

7 x 5 = 35

35 ÷ 2 = 17.5

Answer:

The correct answer is 70 square units I took the test and got it right! Good luck! God bless you!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope is increasing by one so your unit rate is 1/1 and your slope is 1

Answer: 125

Step-by-step explanation:

For any number to be divisible by 5 it must end in either 0 or 5, thus for a 4 digit odd number it should end with 5 eg.1005,1015,1055 etc.

The exact number of 4 digit odd nos divisible by 5 can be calculated by using Principle of counting:

Therefore, no of possible numbers are: 5x5x5x1=125 numbers

Answer:

9

Step-by-step explanation:

The distance from the x axis is from the point (8,0)

d = sqrt( (8-8)^2 + (-9-0)^2)

   = sqrt(0+ 81)

   = sqrt( 81)

    =9

Answer:

8

Step-by-step explanation:

8 is how far away it is in square units from the x-axis and the 7 is how far it is from the y-axis

Hope this helps

Answer:

A. x^11 and B. 8x.

Step-by-step explanation:

A monomial is a polynomial with just one term. That would be Options A and B.

Options C and E are trinomials.

Options D and F are binomials.

Hope this helps!

Answer:

A and B

Step-by-step explanation:

Answer:

21.5

Step-by-step explanation:

Arrange numbers from smallest to largest:

56, 65, 69, 77, 79, 82, 88, 89, 90

The interquartile range is the range in the middle of the data set, we can find it by knowing the upper and lower quartiles.

56, 65, 69, 77, 79, 82, 88, 89, 90

(65+69)/2 = 67

(88+89)/2 = 88.5

The interquartile range:

88.5 - 67

= 21.5

Answer:

0.009 mm

Step-by-step explanation:

Find the difference between the two values.

0.03 - 0.021

0.009 mm more gold coating must be added to finish the ring.

Answer:

d) Vessels that are any length

Step-by-step explanation:

MSDs can be defined fully as Marine

Sanitation Devices. Marine Sanitation Devices are devices in the shape of a tank that is used for storing and treating of waste materials when marine vessels e.g. boats are on sea.

It is very inappropriate, unhygienic and illegal to dump waste materials at sea because this could cause harm to the aquatic life forms at sea. This is the reason why a marine sanitation device is required.

There are three types of MSDs

a) Type I

b) Type II

c) Type III

Marine Sanitation Devices are classified into types based on

1) The length of the vessels in which that are installed on.

2. The method for treating or breaking down the waste materials in the devices.

In the question above, the TYPE III MARINE SANITATION DEVICES CAN BE INSTALLED ON VESSELS THAT ARE ANY LENGTH.

This is because the Type III Marine Sanitation Devices are devices that stops the discharge or expelling of waste materials e.g sewage (whether have been treated or untreated) into the sea.

These type III MSDs is consists mainly of a tank used for holding and storing the waste materials. In this tank as well as other types of methods used for treating the waste which the includes incineration, composting e.t.c. may be found in the tank as well. Even after treating the waste in a Type III MSD, it can't be expelled into the sea , it can only be transferred to the Water Treatment Facility when the marine vessel comes to the seaport for more treatment and appropriate disposal.

This question is not correctly written

Correct Question

A sector whose central angle measures 120° has an area of 12 square inches. What is the radius of the circle?

Answer:

Radius of the circle = 3.3851375013 inches

Approximately to one decimal place, radius of the circle = 3.4 inches

Step-by-step explanation:

The formula for the area of a sector is given as:

Area of a sector = θ × π/360 × r²

θ = Central angle in degrees = 120°

Area of a sector = 12 in²

12 = (120° × π)/360 × r²

r² = 12 ÷(120° × π)/360

r² = 12 ÷ 1.0471975512

r² = 11.459178217

r = √11.459178217

r = 3.3851375013 inches

Approximately to one decimal place, radius of the circle = 3.4 inches

Answer:

Irrational

Step-by-step explanation:

Irrational numbers have decimal expansions that neither terminate not repeatable

π = 3.1428.........

-4π =-12.5714..........

Answer:

D. Irrational

Step-by-step explanation:

First, let's calculate what -4π is.

-4π= -4*π= -12.5663706143....

Now, let's analyze the answer choices.

Whole numbers are the numbers 1,2,3,4,5...

Integers are like whole numbers, but negatives are also included.

Rational numbers are numbers that can be written as fractions, or have repeating/terminating decimals.

Irrational numbers cannot be written as fractions, do not repeat and do not terminate.

-12.5663706143... doesn't repeat or terminate, therefore it must be irrational.

Answer:

5/42

Step-by-step explanation:

11/6 - 12/7

Make denominators equal.

77/42 - 72/42

Subtract the fractions.

5/42

Answer:

Answer A

Step-by-step explanation:

Answer A is correct.  Sides 3.6 and 3 form one ratio and sides 5.4 and 4.5 form another ratio of the lengths of corresponding sides.

Answer:

Answer A is the first step

Step-by-step explanation:

Normally, to prove an identity, you start by writing all trig expressions in their most simple forms using the two basic trig functions sin and cos. That is done in option A, with writes tan and cot in terms of sin and cos.

Answer:

p=(0,2) q=(0.5,0)

Step-by-step explanation:

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▹ Answer

The correct answer is C. x = 375 sq ft y = 6,300 sq ft

▹ Step-by-Step Explanation

The ratio is 1:15 so...

x → 5,625

(Divide 5,625 by 15 since we have to find the x value meaning we have to do the inverse operation)

5,625 ÷ 15 = 375

420 → y

(Multiply 420 by 15 since we have to find the y value meaning we have to do multiplication)

420 × 15 = 6,300

Hope this helps!

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