The magnitude, M, of an earthquake is represented by the equation M=2/3logE/E0 where E is the amount of energy released by the earthquake in joules and E0=10^4.4 is the assigned minimal measure released by an earthquake. Which shows a valid step in the process of calculating the magnitude of an earthquake releasing 2.5 • 10^15 joules of energy?
2.5•10^15 = 2/3logE/10^4.4
10^4.4=2/3logE/2.5•10^15
M=2/3log(9.95•10^9)
M=2/3log(2.55•10^10)
M=2/3log(9.95•10^10)
The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
M = (2/3) * log (E/E₀)
Where M is the magnitude, E is the amount of energy and E₀ = 10^4..4
For E = 2.5 * 10¹⁵:
M = (2/3) * log (2.5 * 10¹⁵/10^4.4)
M = 7.33
The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33
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Which equation represents the vertex form of the equation y = x² + 2x - 6?
y = (x + 2)² -
y = (x + 1)2 - 6
y = (x + 2)²-7
y = (x + 1)²-7
Answer:
Step-by-step explanation:
Steps
1] On the right, put brackets around the 1st 2 terms.
y = (x^2 + 2x) - 6
2] Divide the second term's coefficient by 2 and square the result.
2/2 = 1
3] Square the result
1^2 = 1
4] Add that inside the brackets
y = (x^2 + 2x + 1) - 6
5] Subtract 1 outside the brackets. The original equation is still there.
y = (x^2 + 2x + 1) - 6 - 1
y = (x^2 + 2x + 1) - 7
6] What is inside the brackets is a perfect square.
y = (x + 1)^2 - 7
Answer D
!!HELP! 1-8 PLEASE ANSWERS ONLY PLEASE
Distributive Property :
[tex]\boxed {a(bx + c) = a(bx) + a(c)}[/tex] or
[tex]\boxed {(ax + b)(cx + d) = acx^{2} + bcx + adx + bd}[/tex]
Question 1 :
6(4v + 1)6(4v) + 6(1)24v + 6Question 2 :
5(8r² - r + 6)5(8r²) - 5(r) + 5(6)40r² - 5r + 30Question 3 :
(2x - 2)(7x - 4)2x(7x) - 2(7x) - 2x(4) - 2(-4)14x² - 14x - 8x + 814x² - 22x + 8Question 4 :
(6a - 7)(3a - 8)(6a)(3a) - 7(3a) + (6a)(-8) - 7(-8)18a² - 21a - 48a + 5618a² - 69a + 56p(m) = 2m² − 4m + 3, find p(1/3)
Answer:
17/9
Step-by-step explanation:
Plug in 1/3 as m.
2*(1/3)^2 - 4(1/3) + 3 = 17/9
Check the box labeled Show Segment Parallel to BC. Notice that intersects two sides of creating a smaller triangle, . How is related to ? How do you know?
The graph of the discrete probability to the right represents
the number of live births by a mother 40 to 44 years old
who had a live birth in 2015. Complete parts (a) through (d)
below.
0.30-
0.25-
0.20
0.15
0.10
0.05
0.00
0
0.235
1
0.270
2
0784
113 0101
-4426-0004 0.045
3
6
Number of Live Births
(a) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth live birth in that year?
(Type an integer or a decimal)
(b) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year?
(Type an integer or a decimal.)
(c) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year?
(Type an integer or a decimal)
(d) If a 40-to 44-year-old mother who had a live birth in 2015 is randomly selected, how many live births would you expect the mother to have had?
The values of the probabilities are
The probabilities are 0.109, 0.202, 0.106The expected number of births is 3How to determine the probabilities?The image that completes the question is added as an attachment
The probability of having her fourth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
Hence, the probability is 0.109
The probability of having a live birth in her fourth or fifth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
P(x) = 0.093 when x = 5
So, we have:
P(4 or 5) = 0.109 + 0.093
Evaluate
P(4 or 5) = 0.202
Hence, the probability is 0.202
The probability of having a live birth in her sixth or more live birth in that year?This is represented as:
P(x >= 6)
From the attached graph, we have:
P(x) = 0.022 when x = 6
P(x) = 0.036 when x = 7
P(x) = 0.048 when x = 8
So, we have:
P(x >= 6) = 0.022 + 0.036 + 0.048
Evaluate
P(x >= 6) = 0.106
Hence, the probability is 0.106
How many live births would you expect the mother to have had?This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = 0.234 * 1 + 0.291 * 2 + 0.167 * 3 + 0.109 * 4 + 0.093 * 5 + 0.022 * 6 + 0.036 * 7 + 0.048 * 8
Evaluate
E(x) = 2.986
Approximate
E(x) = 3
Hence, the expected number of births is 3
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A total of $5000 is invested: part at 7% and the remainder at 12%. How much is invested at each rate if the annual interest is $400?
The amount invested in the account that yields 7% interest is $4000.
The amount invested in the account that yields 12% interest is $1000.
What are the linear equations that represent the question?a + b = 5000 equation 1
0.07a + 0.12b = 400 equation 2
Where:
a = amount invested in the account that yields 7% interest.
b = amount invested in the account that yields 12% interest.
How much is invested at each rate?
Multiply equation 1 by 0.07
0.07a + 0.07b = 350 equation 3
Subtract equation 3 from equation 2
0.05b = 50
b = 50 / 0.05
b = 1000
Subtract 1000 from 5000: 5000 - 1000 = 4000
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wwqrwqretertertreterterter
Answer:
answer: no spam please
oly questions
5x6-3x²+7-2x6-3x6+4x² for x = -10
Answer:
Hope you like it. I have just wrote answers
Census Bureau data shows that the mean household income in the area served by a shopping mall is $64,500 per year with the standard deviation of $8,000. A market research gathers a random sample of 100 shoppers at the mall to find out whether the mean household income of mall shoppers of $61,000 is different than the general population.
Q: What is the null hypothesis ?
Considering the situation described, the null hypothesis is given as follows:
[tex]H_0: \mu = 64,000[/tex].
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is the same as in the Census, of $64,000, hence:
[tex]H_0: \mu = 64,000[/tex].
At the alternative hypothesis, it is tested if the mean is different from the Census, hence:
[tex]H_1: \mu \neq 64,000[/tex].
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PLS ANSWER THESE QUESTIONS
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The linear function y = 3 · w - 1 represents the number of sea shells found in each week.
The speed of the driven gear is 180 rounds per minute.
How to use direct and inverse relationships to analyze situations
In the first problem we have an example of linear progression, in which the number of sea shells is increased linearly every week. After a quick analysis, we conclude that the linear function y = 3 · w - 1, a kind of direct relationship.
In the second problem, we must an inverse relationship to determine the speed of the driven gear. Please notice that the speed of the gear is inversely proportional to the number of teeths. Then, we proceed to calculate the speed:
[tex]\frac{v_{1}}{v_{2}} = \frac{N_{2}}{N_{1}}[/tex]
If we know that [tex]v_{2} = 60\,rpm[/tex], [tex]N_{2} = 60[/tex] and [tex]N_{1} = 20[/tex], then the speed of the driven gear is:
[tex]v_{1} = v_{2}\times \frac{N_{2}}{N_{1}}[/tex]
[tex]v_{1} = 60\,rpm \times \frac{60}{20}[/tex]
[tex]v_{1} = 180\,rpm[/tex]
The speed of the driven gear is 180 rounds per minute.
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What is the best approximation of the solution to the system to the nearest integer values?
Answer:
(-2, 6)
Step-by-step explanation:
3x - 4y = -32
3x + 5y = 24
-9y = -56
y = [tex]\frac{56}{9}[/tex] = 6
3x - 4*[tex]\frac{56}{9}[/tex] = -32
3x - [tex]\frac{224}{9}[/tex] = -32
3x = -32 + [tex]\frac{224}{9}[/tex]
3x = -[tex]\frac{288}{9}[/tex]+ [tex]\frac{224}{9}[/tex]
3x = -[tex]\frac{64}{9}[/tex]
x = -[tex]\frac{64}{27}[/tex] = -2
Two sides of a four-sided figure have negative slopes. Which are the endpoints of the sides of this figure?
(–4, –4), (–4, –1), (–1, –4), (–1, –1)
(–2, –4), (–1, –1), (1, –1), (2, –4)
(1, 1), (2, 4), (5, 4), (4, 1)
(1, 4), (2, 1), (5, 1), (4, 4)
The endpoints of the sides of the quadrilateral are; (1, 4), (2, 1), (5, 1), (4, 4)
How to calculate the slope of sides of a quadrilateral?To get the endpoints of the quadrilateral that has 2 sides with negative slope, we will use the formula for slope;
m = (y2 - y1)/(x2 - x1)
Option A; Coordinates are (–4, –4), (–4, –1), (–1, –4), (–1, –1). Slopes are;
m1 = (-1 + 4)/(-4 + 4) = undefined
m2 = (-4 + 1)/(-1 + 4) = -1
m3 = (-1 + 4)/(-1 + 1) = undefined
m4 = (-4 + 1)/(-4 + 1) = 1
No two slopes are negative and this is not correct.
Option B; Coordinates are (–2, –4), (–1, –1), (1, –1), (2, –4). Slopes are;
m1 = (-1 + 4)/(-1 + 2) = 3
m2 = (-1 + 1)/(1 + 1) = 0
m3 = (-4 + 1)/(2 - 1) = -3
m4 = (-4 + 4)/(-2 - 2) = 0
No two slopes are negative and this is not correct.
Option C; Coordinates are (1, 1), (2, 4), (5, 4), (4, 1). Slopes are;
m1 = (4 - 1)/(2 - 1) = 3
m2 = (4 - 4)/(5 - 2) = 0
m3 = (1 - 4)/(4 - 5) = 3
m4 = (1 - 1)/(1 - 4) = 0
No two slopes are negative and this is not correct.
Option D; Coordinates are (1, 4), (2, 1), (5, 1), (4, 4). Slopes are;
m1 = (1 - 4)/(2 - 1) = -3
m2 = (1 - 1)/(5 - 2) = -0
m3 = (4 - 1)/(4 - 5) = -3
m4 = (4 - 4)/(1 - 4) = -0
Two slopes are negative and this is correct.
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ION 10
answered
out of 1.00
Flag
n
What is the likelihood of Jada investing with Bank JNC if the following holds under the following conditions?
..
there is a 75% chance Jada will invest if the economic conditions remain stable;
there is a 25% chance investing if economic conditions suffer a decline;
there is a 55% chance of investing if the economic conditions improve.
the chance the economic conditions remaining stable (S), declining (D) and improving (1) are 0.20, 0.40
and 0.40, respectively.
Select one:
O.a. 0.135
O b. 0.103
OC. 0.400
O d. 0.470
Answer:
a
Step-by-step explanation:
A line graph titled Meals per Day has number of days on the x-axis, and number of meals prepared on the y-axis. At 5 days there are 30 meals prepared; at 10 days, 60 meals; at 15 days, 90 meals; at 20 days, 120 meals.
Use proportional reasoning to find the constant of proportionality for the relationship shown on the graph.
What is the value of y when the value of x is 1?
The constant of proportionality is 6.
How to calculate the constant?From the information given, the constant will be:
30 meals ÷ 5 days = 6
60 meals ÷ 10 days = 6
90 meals ÷ 15 days = 6
120 meals ÷ 20 days = 6
The constant of proportionality is 6. Therefore, the function will be:
y = kx
y = 6x
The value of y when x is 1 will be:
y = kx
y = 6 × 1 = 6
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Answer:
what they said
Step-by-step explanation:
The sum of two integers is 250.If one of them is -87,find the others integers
About % of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9 and z = 0.9 z = 0.9 (or within 0.9 standard deviations of the mean).
Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The area within 0.9 standard deviations of the mean is the p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841), hence:
0.8159 - 0.1841 = 0.6318 = 63.18%.
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order the decimales from leaste to gratest: 72.5, 73.943, 72.1, 73.77,
43.2 43.219 42.1 42.59
38.507 38.507 38.4 28.23 39.5
71.743 71.3 71.3 72.43 72.5
The decimals would be ordered as:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
How to Order Decimals?To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.
The decimals will be ordered as shown below:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
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Heights of men on a baseball team have a bell-shaped distribution with a mean of 176cm and a standard deviation of 5cm .Using the empirical rule,what is the approximate percentage of men between the following values?
% of the men are between 165cm and 186cm
95% men are between 165 cm and 186 cm.
What is the empirical rule?
The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule.
z-score = (raw-score minus mean) / standard deviation.
z1 = (165-176)/5 = -2.2
z2 = (186-176)/5 = 2
The empirical rule tells us that about 95% of all values are within standard deviations of the mean,
so, 95% men are between 165 cm and 186 cm.
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95% of men are between 165 cm and 186 cm.
What is the approximate percentage of men between the following values?Given:
The heights of men on a baseball team have a bell-shaped distribution a mean of 176cm and a standard deviation of 5cm.Find:
What is the approximate percentage of men between the following values?Solution:
The empirical rule is also referred to as the three sigma rule or the 68-95-99.7
Rule:
z - score = (raw - score minus mean) / standard deviation.
z1 = (165-176)/5 = -2.2
z2 = (186-176)/5 = 2
The empirical rule tells us that about 95% of all values are within standard deviations of the mean.
So, 95% of men are between 165 cm and 186 cm.
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A 28-metrelong guy wire is attched to a point 24 m up the side of a tower. How far from the base of the tower is the guy wire attached
The distance between the guy and the wire attached is 14.42m
Pythagoras theoremThe square of the longest side is equal to the sum of the square of other two sides.
In order to determine the length of base of the tower, we will use the expression below:
b² = 28² - 24²
b² = 208
b = 14.42
Hence the distance between the guy and the wire attached is 14.42m
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The function g(x) = 10x2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. Which statements are true about g(x)? Select three options. The axis of symmetry is the line x = –5. The vertex of the graph is (5, –37). The parabola has a minimum. The parabola opens up. The value of a, when the equation is written in vertex form, is negative.
Answer:
The vertex of the graph is (5, -37) [see attached image]The parabola has a minimum [the coefficient of x² is positive]The parabola opens up [the coefficient of x² is positive]All the correct statements are,
The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function g(x) = 10x² - 100x + 213 written in vertex form is,
⇒ g(x) = 10(x – 5)² – 37.
Since, General equation is,
y = a (x - h)² + k
Where, (h, k) is vertex of parabola.
Hence, We get;
The vertex of the graph is (5, -37)
Since, the coefficient of x² is positive
Hence, The parabola has a minimum
And, The parabola opens up.
Thus, All the correct statements are,
The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
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100 Points! Which shorts should I get?
Find and sketch the domain of f(X,y) = 1/√x^2-y
Answer:
Step-by-step explanation:
The definition of a Domain in math is all the possible input values that go into the function, so we will have to find all the valid values that can go into the function
The function given is [tex]F(x, y)=\frac{1}{\sqrt{x^2-y} }[/tex] , the denominator cannot be 0.
So we set up the equation
[tex]\sqrt{x^2-y} \neq 0[/tex]
[tex]\sqrt{x^2-y}^{2} \neq 0x^2-y\neq 0x^2\neq y[/tex]
And that the the square root needs to be more than 0.
[tex]\sqrt{x^2-y}\geq 0[/tex]
[tex]x^2-y\geq 0[/tex]
[tex]x^2\geq y[/tex]
So we can conclude that all values of [tex]x^{2}[/tex] must be greater y
That means that our domain is all X values greater than[tex]\sqrt{y}[/tex]
help this is affecting my grade i need help pls i beg of you
Select the correct answer from each drop-down menu. The options are: The ratio of the heights is 1 : 2.5 1 : 5 1 : 10 1 : 25 The ratio of the surface areas is 1 : 5 1 : 10 1 : 25 1 : 125 The ratio of the volumes is 1 : 5 1 : 10 1 : 25 1 : 125.
Using proportions, it is found that:
The ratio of heights is of 1:5.The ratio of surface areas is of 1:25.The ratio of volumes is of 1:125.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The heights are measured in units, hence the ratio is:
[tex]r = \frac{5}{25} = \frac{1}{5}[/tex]
The surface areas are measured in units squared, hence the ratio is:
(1:5)² = 1:25.
The volumes are measured in cubic units, hence the ratio is:
(1:5)³ = 1:125.
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Solve. −4 3/4=x−1 1/5 What is the solution to the equation? Enter your answer as a simplified mixed number in the box.
plssssss helppp
Answer: x= -3 11/20 Decimal form: x=-3.55
Step-by-step explanation:
I need help determining how many roots
By graphing the polynomial, we conclude that there is only one real root, so the correct option is A.
How many roots has the given polynomial?
We have the polynomial:
[tex]y = -3x^2 + 12x - 12[/tex]
To see how many real roots this polynomial has, we can graph it and see how many times the graph intercepts the x-axis.
The graph can be seen below:
There we can see that there is only one intercept, so there is only one real root.
So the correct option is A.
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Given: F(x) = 3xˆ2+ 1, G(x) = 2x-3, H(x) = x F(-2) =
heeeelp
Answer:
firstly,need to know domain and range
Which of the following functions has an initial value of -1/2 and a rate of change of 0?
A.
2
x
B. y=−12x
y
=
−
1
2
x
C. y=−12x
y
=
−
1
2
x
D. y=−12
The function that has the given initial value and rate of change is: D. y = -1/2.
What is the Initial Value and Rate of Change of a Function?A function is given as, y = mx + b, where, m is the rate of change, and b, which is a constant is the initial value.
Given the following:
b = -1/2
m = 0
Plug in the values into y = mx + b
y = 0(x) + (-1/2)
y = -1/2
Therefore, the function is: D. y = -1/2.
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please no scam please answer ASAP 30 points need steps
QUE :
75 - [5 + 3 of (25 - 2 × 10)]
= 75 - [5 + 3 of ( 25 - 20)]
= 75 - [5 + 3 of 5]
= 75 - [5 + 15]
= 75 - 20
= 55
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