The diameter of a proton is about 1.9 cross times 10 to the power of short dash 15 end exponent meters. A hydrogen atom has an overall length of 100,000 times (or 1 cross times 10 to the power of 5 times) the diameter of a proton.
What is the length of the hydrogen atom, in meters, if it were written in scientific notation?

A. 1.9 x 10 (15 exponent)
B. 1.9 x 10 (-15 exponent)
C. 1.9 x 10 (-8 exponent)
D. 1.9 x 10 (-12 exponent)

[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]

[tex]f(3) = 25[/tex]

The volume of the cone to nearest tenth is 247. 12 cm ^3

Note that the shape is a cone

Volume for a cone =

[tex]\pi \: { {r}^{2} \frac{h}{3} } [/tex]

Given that radius = 5.3cm

height = 8.4cm

Substitute into the formula, we have

Volume = 3.142 × 5.3 × 5.3 × (8.4/3)

Volume = 3. 142× 28.09 × 2.8

Volume = 247. 12 cm ^3

Thus, the volume of the cone to nearest tenth is 247. 12 cm ^3

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The amount of wrapping paper he need to cover the shoebox is 190 square inches

The formula for calculating the surface area of a box is expressed as:

SA = 2(lw + wh + lh)

where

l is the length

w is the width

h is the height

Given the following parameters

l = 10in

w = 5in

h =3in

Substitute

S = 2(10*5 + 5*3 + 10*3)

S = 2(50+15+30)

S = 2(95)

S = 190 square inches

Hence the amount of wrapping paper he need to cover the shoebox is 190 square inches

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An equation is formed of two equal expressions. The value of 'a' in the given equation is 6.452.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved for 'a' as shown below,

[tex]\dfrac{(3-0)}{4a} = (10-0.8a)\\\\\dfrac{3}{4a} = (10-0.8a)\\\\[/tex]

0.75a = 10 - 0.8a

0.75a + 0.8a = 10

1.55a = 10

a = 6.452

Hence, the value of 'a' in the given equation is 6.452.

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Answer:

1.090909090909091

Step-by-step explanation:

12/11 = 1.090909090909091

W = 1.090909090909091

Answer:

w = [tex]\frac{12}{11}[/tex]

Step-by-step explanation:

11w = 12 ( isolate w by dividing both sides by 11 )

w = [tex]\frac{12}{11}[/tex]

Answer:

76 sqcm.

Step-by-step explanation:

2(5 x 2) + 2(5 x 4) + 2(4 x 2) = 2(10) + 2(20) + 2(8)
                                             =  20 + 40 + 16
                                             =  76

The measure of the exterior angle x is 90°.

We need to find the measure of the exterior angle x.

An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Now, x°=∠A+∠B

⇒x°=30°+60°=90°

Therefore, the measure of the exterior angle x is 90°.

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Answer:

x = 35.537677791974°

y = 63.434948822922°

Step-by-step explanation:

let x be the measure of the angle of elevation of the sun.

tan(x) = 10/14

Then

x = tan⁻¹ (10÷14) = 35.537677791974°

………………………………………………

let y be the measure of the angle of elevation of the sun

where the shadow decreases to 5m.

tan(y) = 10/5 = 2

Then

y = tan⁻¹ (2) = 63.434948822922°

Answer:

a) 35.54°

b) 63.43°

Given following:

Determining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.

(a)

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(x) = \dfrac{10}{14}[/tex]

[tex]\sf x = tan^{-1}(\dfrac{10}{14} )[/tex]

[tex]\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )[/tex]

(b) If the shadow decreases to 5 meter.

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(x) = \dfrac{10}{5}[/tex]

[tex]\sf x = tan^{-1} (\dfrac{10}{5})[/tex]

[tex]\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)[/tex]

Answer:

a = -17/30

Step-by-step explanation:

So the first step is to distribute the negative sign, if that's a bit confusing think of the negative sign as a -1 instead of just a negative sign, and then think of distributing that negative 1 to the 23a and -13.

Original Equation:

-(23a - 13) + 53a

Distribute negative sign

-23a + 13 + 53a

Group like terms:

(-23a + 53a) + 13

Simplify

30a + 13 = -4

Subtract 13 from both sides

30a = -17

Divide both sides by 30

a = -17/30

There are 7,315 different combinations, thus, the correct option is c

If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:

[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]

In this case we have K = 4 and N = 22, replacing that, we get:

[tex]C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315[/tex]

So there are 7,315 different combinations, thus, the correct option is c.

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Answer: -211/76

Step-by-step explanation:

to solve this word problem equation, we need to first convert the words to numbers and variables we can solve for:

we can replace "a number" for a variable such as x

this gives:

-76·x-61=x+89

now all you have to do is solve the equation and you're done!

The equation which is a function of x is x²=y.

Given an equation that is a function of x.

A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.

If we input a value of x then we get the output f(x) = y, which is the function of x.

We are given four options out of which we are to pick the one which may be a function of 'x'.

The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.

The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.

The third option is x²=y in which y contains power 1. So, option 3 is correct.

The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.

Hence, the equation which is a function of x is x²=y.

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Answer:

-42

Step-by-step explanation:

You have to To subtract the fractions, then find the Least common denominator (LCD) and then combine.

pls brainliest Hope this helps have a nice day :>

[tex]\boldsymbol{(-1-3^{2})-\dfrac{4^{3} }{2} }[/tex]

Calculates 3 to the power of 2 and gets 9.

[tex]\boldsymbol{-1-9-\dfrac{4^{3} }{2} }[/tex]

Subtract 9 from −1 to get −10.

[tex]\boldsymbol{-10-\dfrac{4^{3} }{2} }[/tex]

Calculates 4 to the power of 3 and gets 64.

[tex]\boldsymbol{-10-\dfrac{64}{2} }[/tex]

Divide 64 by 2 to get 32.

[tex]\bf{-10-32 }[/tex]

Subtract 32 from −10 to get −42.

[tex]\bf{-42 \ \ \to \ \ \ Answer}[/tex]

Two more examples of relationship patterns found in mathematics are Geometric sequences and Fibonacci numbers.

Mathematical patterns are a sequence of repeated arrangements of numbers, shapes, colors, letters, etc.

Mathematical patterns are usually abstract.

A geometric sequence is a sequence of non-zero numbers.  The first number is the product of multiplying a previous number by a fixed, non-zero number, called the common ratio.

A Geometric sequence may look like: 2, 4, 8, 16, 32, 64, 128, ..., where the common ratio is 2.

A Fibonacci number starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers.

The rule of the Fibonacci sequence is that each number is equal to the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13.

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The equivalent fraction of 12/25 is 24/50

The fraction is given as:

Fraction = 12/25

Multiply the fraction by 1

Fraction = 12/25 * 1

Express 1 as 2/2

Fraction = 12/25 * 2/2

Evaluate the product

Fraction = 24/50

Hence, the equivalent fraction of 12/25 is 24/50

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The area of the shaded region is 29.5 square yards.

The following calculations are to be done:

Area of the triangle:

Base of the triangle is

= 5 + 4

= 9 yard.

Height of the triangle = 6 + 5  

Height of the triangle= 11 yards.

The area of the triangle is,

[tex]\ Area \ of \ the\ rectangle=\frac{1}{2} \times height\times base[/tex]

[tex]\ Area \ of \ the\ rectangle=\frac{1}{2}\times 9\times 11[/tex]

= 49.5 square yards.

Area of the rectangle:

[tex]=Length\times width[/tex]

[tex]=4\times 5[/tex]

= 20 square yards.

Now finally the shaded region should be

= 49.5 square yards - 20 square yards

= 29.5 square yard

Therefore we can conclude that the area of the shaded region is 29.5 square yards.

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Probability sampling simply illustrates a scenario where the subjects of the population have an equal opportunity.

Probability simply means the likelihood of the occurence of an event.

In this case, in probability sampling, the subjects of the population have an equal opportunity.

In non-sampling, an equal opportunity isn't given.

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Using the Empirical Rule, the percentages are given as follows:

a) 99.7%.

b) 32%.

c) 16%.

It states that, for a normally distributed random variable:

Item a:

61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.

Item b:

87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.

Item c:

Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.

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Answer:

The distance is √17.

Step-by-step explanation:

the step is provided in the image....

I hope it was helpful

Answer:

A) 10

Step-by-step explanation:

Votes for Marcus: 420/2 = 210 votes

Votes for Mary: 420/3 = 140 votes

Votes for Edward: 420/7 = 60 votes

Total number of votes: 210+140+60 = 410 votes

people who didn't vote: 420-410 = 10 people

Answer:

there 32 students and 20 have pets so you take 20 over 30 divide by 2 to get 10/16 then divide by 2 to get 5/8and that is the answer

The table represents an exponential function given by:

[tex]f(x) = 24*(1/2)^x[/tex]

Here we have the table:

x    f(x)

0    24

1      12

2      6

3       3

First, notice that for each unit that x increases, the value of f(x) decreases by its half.

This is clearly an exponential equation, whose base must be equal to (1/2).

And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.

Then the exponential function is:

[tex]f(x) = 24*(1/2)^x[/tex]

Such that:

[tex]f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3[/tex]

Concluding, the table represents an exponential function.

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Answer:

a) $74.62

Step-by-step explanation:

Cost of both clothes = 28+35 = $63

Tax = 0.08*63 = $5.04

Shipping: $6.54

Add: 63+5.04+6.58 = 74.62

The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.

The given statement is "The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx".

The point where the reference axes in a coordinate system meet. The values of coordinates are normally defined as zero.

The equation of the line is y = mx + b.

If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.

The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.

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[tex]\huge\boxed{\textsf{D.}\ 57^\circ}[/tex]

We know that angles 1 and 2 are supplementary angles that add up to 180 degrees.

Solve for angle 2:

[tex]\begin{aligned}\angle1+\angle2&=180^\circ\\123^\circ+\angle2&=180^\circ\\123^\circ-123^\circ+\angle2&=180^\circ-123^\circ\\\angle2&=57^\circ\end{aligned}[/tex]

We also know that angles 2 and 6 are corresponding angles, so they are equal to each other. This means that angle 6 is also 57 degrees.

For more information on this topic, search the Internet. There are many great resources on transversal lines and angles out there that expand on the few details I shared here.

Answer:

19

Step-by-step explanation:

fx=16+4

fx=20

gx= 20-1

gx=19

19

The measure of both the interior angles are 70 and 110 degree.

Lines they never intersect with each other and the distance between them always remains same are called parallel lines.

It is given that

Line l and m are parallel lines and are intersected by a transversal ,n

Interior angles of the same side are (2x−8) degree and (3x−7) degree

Applying the property of interior angles of parallel lines

2x -8 + 3x - 7 = 180 degree

5x -15 = 180

5x = 195

x = 39 degree

Both the angles have measure of

2 * 39 - 8 = 70 degree

3 * 39 -7 = 110 degree

Therefore the measure of both the angles are 70 and 110 degree.

The complete question is

Two parallel lines l and m are cut by a transversal  n . If the interior angles of the same side of n are (2x−8) degree and (3x−7) degree  , find the measure of each of these angles.

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Answer:

?

Step-by-step explanation:

Please explain-WHAT TRACKS?

Answer:

5.275

Step-by-step explanation:

Got the answer from Emma on Gauth Math