The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, .



Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?

Answer:

15ft

Step-by-step explanation:

By Pythagorean theorem

[tex] {a}^{2} + {b}^{2} = {c}^{2}\\ {a}^{2} + {8}^{2} = {17}^{2} \\ {a}^{2} + 64 = 289 \\ {a}^{2} = 289 - 64 \\ {a}^{2} = 225 \\ \sqrt{ {a}^{2} } = \sqrt{225} \\ a = 15ft \\ [/tex]

Answer:-1

Step-by-step explanation:

The slope would be negative one due the fact that every horizontal box, the line also goes down one vertical box. You can also figure this out by using the slope equation which is slope=y2-y1/x2-x1. Just take the xy coordinates of two different points and plug it into the equation if you would like to use a formula.

Answer:

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.

This means that [tex]\mu = 2000, \sigma = 100[/tex]

A sample of 20 cables is selected and tested.

This means that [tex]n = 20, s = \frac{100}{\sqrt{20}} = 22.361[/tex]

Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.

This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-1.645 = \frac{X - 2000}{22.361}[/tex]

[tex]X - 2000 = -1.645*22.361[/tex]

[tex]X = 1963.2[/tex]

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

Answer:

[tex]f(x) = x^4 + 9x^3 + 27x^2 + 27x[/tex]

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

- 3 as a zero of multiplicity 3

So

[tex]f(x) = (x - (-3))^3 = (x + 3)^3 = x^3 + 9x^2 + 27x + 27[/tex]

0 as a zero of multiplicity 1.

So

[tex]f(x) = x(x^3 + 9x^2 + 27x + 27) = x^4 + 9x^3 + 27x^2 + 27x[/tex]

(Use 1 for the leading coefficient.)

Multiply the polynomial by 1, so it stays the same. The polynomial in expanded form is:

[tex]f(x) = x^4 + 9x^3 + 27x^2 + 27x[/tex]

Answer:

The correct answer is the letter C.

Step-by-step explanation:

We can use the following trigonometric identity:

[tex]cos(60)=\frac{6}{b}[/tex] (1)

[tex]cos(45)=\frac{c}{b}[/tex] (2)

Solving each equation by b and equaling we have:

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

Let's recall that:

[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]

[tex]cos(60)=\frac{1}{2}[/tex]

Then we have:

[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]

[tex]c=\frac{2*6}{\sqrt{2}}[/tex]

[tex]c=\frac{12}{\sqrt{2}}[/tex]

[tex]c=6\sqrt{2}[/tex]

Using equation (1) we can find b.

[tex]cos(60)=\frac{6}{b}[/tex]  

[tex]b=12[/tex]      

Finally, we can find a using the next equation:

[tex]tan(60)=\frac{a}{6}[/tex]

[tex]a=6*tan(60)[/tex]

[tex]a=6\sqrt{3}[/tex]

Therefore, the correct answer is the letter C.

I hope it helps you!

I think its A) (f+g)(z)=|2x+4|-2

Step-by-step explanation:

Answer:

18

thả 5 sao nha.....

Step-by-step explanation:

..................

Step-by-step explanation:

Fractions represent equal parts of a whole or a collection. 

Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole. 

a fraction has 2 parts

The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.  It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection. 

There are different types of fraction

Answer:

e. 1.6π cm²

Step-by-step explanation:

Since the window is in a semi-circular shape, its area A = πD²/4 ÷ 2 = πD²/8 where D = diameter of window = 64 cm

Now, the error in the area dA = dA/dD × dD where dD = error in the diameter = 0.1 cm and dA/dD = derivative of A with respect to D.

So, dA/dD = d(πD²/8)/dD = 2 × πD/8 = πD/4

So, the differential dA = dA/dD × dD

dA =  πD/4 × dD

Substituting D = 64 cm and dD = 0.1 cm into the equation, we have

dA =  πD/4 × dD

dA =  π × 64 cm/4 × 0.1 cm

dA =  π × 16 cm × 0.1 cm

dA =  π × 1.6 cm²

dA = 1.6π cm²

So, the maximum error in computing the area of the window is 1.6π cm²

Answer:

There is no difference between the two groups.

Step-by-step explanation:

The test hypothesis (null and alternative) are usually employed in evaluating if there is a statistical significance in a claim about the mean, standard deviation or variance of a sample and it's population parameter.

When comparing two independent variables, The null hypothesis usually establish that there is no difference between the mean value of samples, while the alternative hypothesis is the opposite.

The data given shows values for two independent groups ; Male and Female.

The null hypothesis will be:

H0 : There is no difference between the two groups.

H0 : μ1 - μ2 = 0

Answer:

[tex]b =6[/tex]

Step-by-step explanation:

Given

[tex]f(x) =3x + b[/tex]

[tex]f(2) = 12[/tex]

Required

Find b

[tex]f(2) = 12[/tex] implies that:

[tex]12 = 3 * 2 + b[/tex]

[tex]12 = 6 + b[/tex]

Collect like terms

[tex]b = 12 - 6[/tex]

[tex]b =6[/tex]

Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.

To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81

The formula for calculating the z-score is expressed as;

[tex]z=\frac{x-\overline x}{s}[/tex] where:

[tex]\overline x[/tex] is the mean

s is the standard deviation

z is the z-scores

Given the following

[tex]\overline x[/tex]=2.7 in

s = 0.25

if z = -2.81

[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]

Similarly:

[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]

Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.

Learn more on normal distribution here: https://brainly.com/question/23418254

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

yes it does

Step-by-step explanation:

because the equation y=9x does not have a y-intercept (all slopes come in the form y=mx+b -- it can be written differently though) and since there is no 'b' that means the y-intercept is 0. So whenever there is no y-intercept, the slope starts at 0.

Answer:

(-5, 0) and (5, 0)

Step-by-step explanation:

This equation fits the form for a hyperbola with x-intercepts.  The standard form for such an equation is

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

To get the equation in the question into this standard form, divide each term by 400.

[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]

To find the x-intercepts, make y = 0.

[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]

The vertices are located at the points (-5, 0) and (5, 0).

Note: There are no y-intercepts; making x = 0 produces no real solutions for y.

Answer:

from one point to another, it increases by 1 and right by 2

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Pick two points on the line

(0,1) and (2,2)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = (2-1)/(2-0)

  = 1/2

Answer:

-5/2, 1/6

Step-by-step explanation:

|6n+7|=8

6n+7=8

n=1/6

6n+7=-8

n=-5/2

Answer:

[tex]n=-\frac{5}{2}[/tex] and [tex]n=\frac{1}{6}[/tex]

Step-by-step explanation:

There is no x variable present in the question, but if you are asking for the value of n, I can help with that.

The absolute value function always results in a positive number, so that means 6n+7 can equal 8 or negative 8, and the absolute value function takes care of the rest. First, we will solve for 6n + 7 equaling 8.

[tex]6n+7=8[/tex]

Subtracting 7 from both sides gets us

[tex]6n=1[/tex]

Dividing by 6 from both sides is equal to

[tex]n=\frac{1}{6}[/tex]

Now we will solve for 6n + 7 equaling negative 8.

[tex]6n+7=-8[/tex]

Subtracting 7 from both sides is equal to

[tex]6n=-15[/tex]

Dividing by 6 from both sides gets us

[tex]n=-\frac{15}{6}[/tex]

Simplifying, we have

[tex]n=-\frac{5}{2}[/tex]

Answer:

5765865876+5737555586=11503421462

Answer:

Step-by-step explanation:

From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.

Thus, from the diagram

the length = 8 - 2x   the width = 10 - 2x  and the height = x

So, the volume V = L*w*h

Volume (V) = (8 - 2x) (10 - 2x) x

V = (80 - 16x - 20x +4x²)x

V = 80x -36x² + 4x³

By rearrangement:

V = 4x³ - 36x² + 80x

Answer:

$26,179.82  

Step-by-step explanation:

FVA = PMT * n * (1 + i) ^ (n - 1)

FVA = 440 * 48* (1.00458)^(47)

Answer:

x=0,-3

Step-by-step explanation:

x(x+3)(x+3)=0

Using the zero product property

x=0  x+3=0 x+3 =0

x=0  x=-3  x=-3

Answer:

15 more were sold on friday then thursday

Step-by-step explanation:

Answer

its uhhhhh i dont know

Step-by-step explanation:

Answer:

this is the chapter of linear equations in one variable?

Answer:

3.3km

Step-by-step explanation:

200m on first day

Increase 200 by 100 = 300 (200+100)

From 2nd day to 11th day

300×11

3300m

If 1000m = 1km

3300m =?

3300/1000

3.3km

I hope it helps

9514 1404 393

Answer:

  2.244

Step-by-step explanation:

Your answer looks like it may have a transcription error.

The period is reasonably computed as the difference of the x-values of the given points:

  period = 4.114 -1.870 = 2.244 . . . seconds

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

3x - 5 = 37

Step 2: Solve for x

Answer:

[tex]y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Plug in the slope (m)

We're given that the slope is [tex]\displaystyle-\frac{1}{2}[/tex]. In [tex]y=mx+b[/tex], replace m with [tex]\displaystyle-\frac{1}{2}[/tex]:

[tex]y=\displaystyle-\frac{1}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\displaystyle-\frac{1}{2}x+b[/tex]

We're given the point (-9,4). Plug this point into the equation as [tex](x,y)[/tex] and solve for b:

[tex]4=\displaystyle-\frac{1}{2}(-9)+b\\\\4=\displaystyle\frac{9}{2}+b[/tex]

Subtract [tex]\displaystyle\frac{9}{2}[/tex] from both sides to isolate b:

[tex]4-\displaystyle\frac{9}{2}=\displaystyle\frac{9}{2}+b- \displaystyle\frac{9}{2}\\\\\displaystyle-\frac{1}{2} = b[/tex]

Therefore, the y-intercept is [tex]\displaystyle-\frac{1}{2}[/tex]. Plug this back into [tex]y=\displaystyle-\frac{1}{2}x+b[/tex] as b:

[tex]y=\displaystyle-\frac{1}{2}x+(\displaystyle-\frac{1}{2})\\\\y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}[/tex]

I hope this helps!

Complete question is;

The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?

Answer:

dC/dt = 49.45

Step-by-step explanation:

Since C(x) = ⅔x² + 6x + 45

And x(t) = 0.3t² + 0.04t

This means that;

C(x) = C(x(t))

The rate at what cost is changing with respect to time is given as;

dC/dt

Thus, from chain rule;

dC/dt = (dC/dx) × (dx/dt)

dC/dx = (4/3)x + 6

dx/dt = 0.6t + 0.04

Now, when t = 5, then;

x(5) = 0.3(5)² + 0.04(5)

x = 7.7

Thus;

dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267

At 5 hours,

dx/dt = 0.6(5) + 0.04 = 3.04

Thus;

dC/dt = 16.267 × 3.04

dC/dt = 49.45