The correct option regarding how many times stronger the wave amplitude of the earthquake was than the standard wave Ao is given by:
A = 3981Ao.
Ratio of A and AoTo find the ratio of A and Ao, measuring how many times a earthquake measuring R in the Richter scale was than Ao, we have to solve the following logarithmic function:
R=log(A/Ao)
The power of 10 in inverse to the logarithm, hence it is applied to both sides of the expression, as follows:
10^R = 10^log(A/Ao).
Since they are inverses, we can remove the power and the logarithm as follows:
A/Ao = 10^R
Hence the formula for how many times stronger and earthquake is than Ao is given as follows:
A = 10^R Ao
In this problem, the Richter measure of the earthquake was of:
R = 3.6.
Hence the ratio is:
A = 10^(3.6)Ao
A = 3981Ao.
Missing informationThe problems asks how many times stronger the earthquake was than Ao.
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How do you solve #16?
∠A + ∠B + ∠C = 180°
reason : Sum of all angle of triangle is 180°
72° + 86° + ∠C = 180°
158° + ∠C = 180°
∠C = 180° - 158°
∠C = 22°
hence the value of ∠3 is 22°
Now ,
∠3 =∠4
reason : Being vertically opposite angle
4 = 22°
hence the value of ∠4 is 22°
Again ,
∠C + ∠D + ∠E = 180°
reason : Sum of all angle of triangle is 180°
22° + ∠D + 70° = 180°
92° + ∠D = 180°
∠D = 180° - 92°
∠D = 88°
hence the value of ∠5 is 88°..
[tex]...[/tex]
hope it helps ....☘✨
Given a polyhedron with 6 vertices and 12 edges, how many faces does it have?
SOLUTION
GIVEN
A polyhedron has 6 vertices and 12 edges.
TO DETERMINE
The number of faces
CONCEPT TO BE IMPLEMENTED
Euler’s formula for Polyhedron :
For polyhedron F + V = E + 2
Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .
EVALUATION
Here it is given that a polyhedron has 6 vertices and 12 edges
V = Number of vertices = 6
E = Number of edges = 12
F = Number of faces = ?
By Euler’s formula
F + V = E + 2
⇒ F + 6 = 12 + 2
⇒ F + 6 = 14
⇒ F = 8
FINAL ANSWER
The number of faces = 8
How many ones are between 1 and 1,000,000 (inclusive)?
There are 600,001 ones are between 1 and 1,000,000.
By using the below process we can find the number of ones between 1 and 1,000,000.
The number of times a digit 2 to 9 digit appears in numbers 1 to [tex]10^n = n(10^(^n^-^1^))[/tex].
The number of times the digit 1 appears in numbers in numbers 1 to [tex]10^n = n(10^(^n^-^1^)) + 1[/tex]
Therefore, the number of times a digit 1 appears in numbers 1 to 1,000,000 [tex]= 6(10^(^6^-^1^)) + 1\\= 6(10^5) + 1\\= 600,000 + 1\\= 600,001[/tex]
Therefore, there are 600,001 ones are between 1 and 1,000,000.
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im confused on premtier
we have to calculate the perimeter of the semicircle which radius is 16 mm
[tex]P_{sc}=\frac{2\pi\cdot r}{2}=\pi\cdot r=16\pi\approx50.26\operatorname{mm}[/tex]Now we have to add the outter sides of the triangle
[tex]P=20+20+50.26=90.26\operatorname{mm}[/tex]7) The water park is a popular field trip destination. This year the senior class at High School A and thesenior class at High School B both planned trips there. The senior class at High School A rented andfilled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buseswith 354 students. Each van and each bus carried the same number of students. Find the number ofstudents in each van and in each bus.C) Van: 19 Bus: 29 D) Van: 15, Bus: 21
Given
The water park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buses with 354 students. Each van and each bus carried the same number of students.
Answer
Let students in Van be x
And students in bus be y
A/Q
x + 14y = 309 (1)
4x + 14y = 354 (2)
Subtracting (1) and (2)
3x = 45
x = 15
Put in eq (1)
15 + 14 y = 309
14y = 309 - 15
14 y = 294
y = 21
St
What is the measure of ZTVU shown in the diagram below?VSV12°R120°TO A. 132O B. 66 °C. 54D. 108
The external angle formed by the secants equals one-half the difference of the intercepeted arcs. Therefore:
In the diagram shown, ray CD is perpendicular to ray CE. If the measure of DCF is 115then what is the measure of ECF?
m∠FCE =25º
1) Since the measure of ∠DCF = 115º and ∠DCE = 90º then by the Angle Addition postulate we can state that
∠DCF = ∠DCE +∠FCE Plugging into that the given values
115º = 90º + ∠FCE Subtracting 90º from both sides
115-90=∠FCE
25º =∠FCE
2) Then the measure of ∠FCE is 25º
find the value of X and y if l || m.
The Solution.
Step 1:
We shall find two equations from the given angles.
First, by vertically opposite angle property of angles between two lines, we have that:
[tex]\begin{gathered} 7y-23=23x-16 \\ \text{Collecting the like terms , we get} \\ 7y-23x=23-16 \\ 7y-23x=7\ldots.eqn(1) \end{gathered}[/tex]Similarly, by alternate property of angles between lines, we have that:
[tex]\begin{gathered} 23x-16+8x-21=180 \\ \text{Collecting like terms, we get} \\ 31x-37=180 \\ 31x=180+37 \\ 31x=217 \\ \text{Dividing both sides by 31, we get} \\ x=\frac{217}{31}=7 \end{gathered}[/tex]Step 2:
We shall find the values of y by substituting 7 for x in eqn(1), we get
[tex]\begin{gathered} 7y-23(7)=7 \\ 7y-161=7 \\ 7y=7+161 \\ 7y=168 \\ \text{Collecting the like terms, we get} \\ y=\frac{168}{7}=24 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
The correct answers are; x = 7 , and y = 24
hi I need on this. $6000 invested at 5.5% interest, compounded annually. how how would i have in 6years?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
principal = $6000
rate (interest) = 5.5%
time = 6 years
Step 02:
compound interest:
n = annually
n = 1
r = 5.5 % = 5.5 / 100 = 0.055
A = amount
[tex]A\text{ = P \lparen1 + r/n\rparen}^{nt}[/tex][tex]A\text{ = 6000 * \lparen1 + }\frac{0.055}{1})\placeholder{⬚}^{1*6}[/tex][tex]A\text{ = 6000 * \lparen1.3877\rparen = 8273.06}[/tex]The answer is:
$8273.06
Question 9 of 10 What is the measure of 7 shown in the diagram below? 110- O A. 71• O B. 35.5° X C 32° 39- Z D. 74.50
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Diagram
arc vw = 110 °
angle = 39°
arc xy = ?
Step 02:
We must analyze the diagram to find the solution.
39 = 1/2 ( 110 - arc xy)
39*2 = 110 - arc xy
78 - 110 = - arc xy
- 32 = - arc xy
arc xy = -32 / - 1 = 32
The answer is:
arc xy = 32°
Answer:
Step-by-step explanation:
Answer is C
Tran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family members to sit around for dinner. Below is the floorplan that she drew for the eventStageHow many people can be seated as the tables are arranged right now? (In the box below, type your answer as a number only
Tran has made a plan with 12 tables for 8 people each of them. Then, we have 12 tables * 8 ( amount of chairs each of them) = 96. So 96 people can be seated.
Find the y-intercept of the line represented by the equation: -5x+3y=30
We need to find the y-intercept of the equation.
For this, we need to use the slope-intercept form:
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
Now, to get the form, we need to solve the equation for y:
Then:
[tex]-5x+3y=30[/tex]Solving for y:
Add both sides 5x:
[tex]-5x+5x+3y=30+5x[/tex][tex]3y=30+5x[/tex]Divide both sides by 3
[tex]\frac{3y}{3}=\frac{30+5x}{3}[/tex][tex]\frac{3y}{3}=\frac{30}{3}+\frac{5x}{3}[/tex][tex]y=10+\frac{5}{3}x[/tex]We can rewrite the expression as:
[tex]y=\frac{5}{3}x+10[/tex]Where 5/3x represents the slope and 10 represents the y-intercept.
The y-intercept represents when the graph of the equations intersects with the y-axis, therefore, it can be written as the ordered pair (0,10).
Find the equation of the line passing through points (6,0) and (-1,14)
Answer:
y = -2x + 12
Step-by-step explanation:
Hope this helps!!
Which function, A or B, has a greater rate of change? Be sure to include the values for the rates of change in your answer. Explain your answer.
The function B has a greater rate of change
Explanation:Function A is represented by the table:
Selecting the points (1, 5) and (2, 7)
The rate of change of function A:
[tex]\begin{gathered} m_A=\frac{7-5}{2-1} \\ \\ m_A=2 \end{gathered}[/tex]The rate of change of the function A = 2
Function B is represented by the graph:
(1, 1) and (2, 4)
[tex]\begin{gathered} m_B=\frac{4-1}{2-1} \\ \\ m_B=3 \end{gathered}[/tex]The rate of change of the function B = 3
The function B has a greater rate of change
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table. (a) Make a scatter plot of the data. (b) Find and graph a linear regression equation that models the data. (c) Use the model to predict soft-drink sales if the temperature is 95°F.
ANSWER and EXPLANATION
a) First we have to make a scatter plot. We do this by plotting the calues of High Temperature on the x axis and Number of cans sold on the y axis:
b) We want to find and graph the linear regression equation that models the data.
The linear regression equation will be in the form:
y = a + bx
[tex]\begin{gathered} \text{where} \\ a\text{= }\frac{(\sum ^{}_{}y)(\sum ^{}_{}x^2)\text{ - (}\sum ^{}_{}x)(\sum ^{}_{}xy)}{n(\sum ^{}_{}x^2)\text{ }-\text{ (}\sum ^{}_{}x)^2} \\ \text{and b = }\frac{n(\sum ^{}_{}xy)\text{ - (}\sum ^{}_{}x)(\sum ^{}_{}y)}{n(\sum ^{}_{}x^2)\text{ }-\text{ (}\sum ^{}_{}x)^2} \end{gathered}[/tex]We have from the question that:
x = High Temperature
y = Number of cans added
So, we have to find xy and x^2. We will form a new table:
Now, we will find a and b:
[tex]\begin{gathered} a\text{ = }\frac{(4120)(39090)\text{ - (}554)(297220)}{8(39090)\text{ }-554^2} \\ a\text{ = }\frac{\text{ 161050800 - 164659880}}{312720\text{ - 306916}} \\ a\text{ = }\frac{-3609080}{5804} \\ a\text{ }\cong\text{-62}2 \end{gathered}[/tex][tex]\begin{gathered} b\text{ = }\frac{8(297220)\text{ - (554})(4120)}{5804} \\ b\text{ = }\frac{2377760\text{ - 2282480}}{5804} \\ b\text{ = }\frac{95280}{5804} \\ b\text{ }\cong\text{ 16} \end{gathered}[/tex]Therefore, the linear regression equation is:
y = -622 + 16x
Now, let us graph it using values of x (High Temperature):
That is the Linear Regression Graph.
c) To predict soft drink sales if the temperature is 95 degrees Farenheit, we will put the x value as 95 and find y. That is:
y = -622 + 16(95)
y = 898
The model predicts that 898 cans of soft drinks will be sold when the High Temperature is 95 degrees Farenheit.
suppose that you have a savings account with 8500 in it. it pays 7% interest compound as shown below. find the value for the next 4 years
We want find the compound interest annualy for 4 years, $8500, at 7%'
The formula for the compound amount over one year is;
[tex]A=P(1+\frac{r}{100})[/tex]1st year:
[tex]\begin{gathered} A=8500(1+0.07) \\ A=\text{ \$9095} \end{gathered}[/tex]2nd year:
[tex]\begin{gathered} A=9095(1.07) \\ A=\text{ \$9731.65} \end{gathered}[/tex]3rd year:
[tex]\begin{gathered} A=9731.65(1.07) \\ A=\text{ \$10412.87} \end{gathered}[/tex]4th year:
[tex]\begin{gathered} A=10412.87(1.07) \\ A=\text{ \$11141.77} \end{gathered}[/tex]What is the equation in slope-intercept form of the line that passes through the points (-4,8) and (12,4)?
ANSWER
y = -0.25 + 7
EXPLANATION
The line passes through the points (-4, 8) and (12, 4).
The slope-intercept form of a linear equation is written as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope of the line.
We do that with formula:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{where (x}_1,y_1)\text{ = (-4, 8) } \\ (x_2,y_2)\text{ = (12, 4)} \end{gathered}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m\text{ = }\frac{4\text{ - 8}}{12\text{ - (-4)}}\text{ = }\frac{-4}{12\text{ + 4}}\text{ = }\frac{-4}{16}\text{ = }\frac{-1}{4} \\ m\text{ = -0.25} \end{gathered}[/tex]Now, we use the point-slope method to find the equation:
[tex]\begin{gathered} y-y_{1\text{ }}=m(x-x_1) \\ \Rightarrow\text{ y - 8 = -0.25(x - (-4))} \\ y\text{ - 8 = -0.25(x + 4)} \\ y\text{ - 8 = -0.25x - 1} \\ y\text{ = -0.25x - 1 + 8} \\ y\text{ = -0.25x + 7} \end{gathered}[/tex]That is the equation of the line. It is not among the options.
Two train leave stations 210 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other traves a 70miles per hout. How long will it take for the two trains to meet?___ hours Do not do any rounding
SOLUTION
At the same time t,
Train 1 would have covered a distance of 80t, since distance = average speed x time.
Train 2 would have covered a distance of 70t.
Now both added should give 210 miles
That is 80t + 70t = 210
150t = 210
t = 210/150
t = 1.4 hours
the drop down menus choices are: two imaginary solutionstwo real solutionsone real solution
Given a quadratic equation of the form:
[tex]ax^2+bx+c=0[/tex]The discriminant is:
[tex]D=b^2-4ac[/tex]And we can know the number of solutions with the value of the discriminant:
• If D < 0, the equation has 2 imaginary solutions.
,• If D = 0, the equation has 1 real solution
,• If D > 0, the equation has 2 real solutions.
Equation One:
[tex]x^2-4x+4=0[/tex]Then, we calculate the discriminant:
[tex]D=(-4)^2^-4\cdot1\cdot4=16-16=0[/tex]D = 0
There are 1 real solution.
Equation Two:
[tex]-5x^2+8x-9=0[/tex]
Calculate the discriminant:
[tex]D=8^2-4\cdot(-5)\cdot(-9)=64-20\cdot9=64-180=-116[/tex]D = -116
There are 2 imaginary solutions.
Equation Three:
[tex]7x^2+4x-3=0[/tex]
Calculate the discriminant:
[tex]D=4^2-4\cdot7\cdot(-3)=16+28\cdot3=16+84=100[/tex]D = 100
There are 2 real solutions.
Answers:
Equation 1: D = 0, One real solution.
Equation 2: D = -116, Two imaginary solutions.
Equation 3: D = 100, Two real solutions.
what are three requirements for fully defining a reference point?
1 - reference point should consist of abstract coordinates.
2- it should be stationary
3- it should be related to all the variables in the frame.
5. What is the range of the graph?8all real numbers{y 1-1 sys1)(XI-15x51){x | xs-1 or x 21)
The correct option is option D
For more comprehension,
Option D is :
[tex]undefined[/tex]A circular plot of land has a diameter of 16 yards. What is the area of theland? Use 3.14 for it.O A. 803.84 yd2O B. 50.24 yd2O C. 200.96 yd2O D. 25.12 yd2
The area of the circle can be calculated with the following formula
[tex]A=\pi\cdot r^2[/tex]First let's find the radius
[tex]\begin{gathered} r=\frac{16}{2}\text{yds} \\ r=8\text{yds} \end{gathered}[/tex][tex]\begin{gathered} A=\pi\cdot8^2 \\ A=3.14\cdot64 \\ A=200.96\text{ yd2} \end{gathered}[/tex]The answer would be 200.96 square yards
7.2. I have a question about advanced trig equations that I really need help with picture included
1) Let's start out isolating the cosine by dividing both sides by 2
[tex]\begin{gathered} 2\cos \mleft(\theta\mright)=\sqrt{3} \\ \frac{2\cos\left(θ\right)}{2}=\frac{\sqrt{3}}{2} \\ \cos \mleft(\theta\mright)=\frac{\sqrt{3}}{2} \\ \end{gathered}[/tex]2) From that we can find two general solutions in which the cosine of theta yields the square root of 3 over two:
[tex]\begin{gathered} \cos (30^{\circ})or\cos (\frac{\pi}{6})\text{ and }cos(330^{\circ}or\frac{11}{6}\pi)=\frac{\sqrt[]{3}}{2} \\ \theta=\frac{\pi}{6}+2\pi n,\: \theta=\frac{11\pi}{6}+2\pi n \end{gathered}[/tex]But not that there is a restraint, so we can write out the solution as:
[tex]\theta=\frac{\pi}{6},\: \theta=\frac{11\pi}{6}[/tex]Select the correct answer.Christi is using a display box shaped like a regular pentagonal prism as a gift box. About how much gift wrap does she need to completely coverthe box?A 800 cm²B. 480 cm2C. 1,020 cm²D. 1,600 cm²
Given: A regular pentagonal prism with base edge 8cm and height 20 cm .
Find: wrap need to cover the box.
Explanation: for to find the length of wrap we need to find the area of regular pentagonal prism .
[tex]A=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5)}}a^2[/tex]
where a=base edge=8cm and h =height=20 cm
[tex]\begin{gathered} A=5\times8\times20+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}\times8^2 \\ =1020.2211\text{ cm}^2 \end{gathered}[/tex]Final answer: the required answer is 1020 square centimeter.
Answer:
C. 1,020 [tex]cm^{2}[/tex]
Hope this helps!
Step-by-step explanation:
1 + 3 4 Solve. 3 A 8 B 2 3 1) 1. Illuminate Education TM, Inc.
Given:
[tex]\frac{1}{2}+\frac{3}{4}[/tex]Let's add the fractions above.
To perform the addition, find the Lowest Common Multiple (LCM) of the denominators.
LCM of 2 and 4 = 4
Divide each denominator by the LCM and multiply the result with the numerator.
Thus, we have:
[tex]\begin{gathered} \frac{1}{2}+\frac{3}{4} \\ \\ \frac{2+3}{4}=\frac{5}{4} \\ \\ \frac{5}{4} \end{gathered}[/tex]Convert the improper fraction (5/4) to mixed fraction.
We have:
[tex]\frac{5}{4}=1\frac{1}{4}[/tex]ANSWER:
[tex]1\frac{1}{4}[/tex]V256 rational or irrational
First, in order to get to know if 256 it is a rational or irrational number we have to begin with the definition of what is rational and irrational number.
Rational numbers are all the number that can be represented as fractions, while the irrational numbers are all the numbers that can not be expressed as fractions.
In this case, then we can confirm that the number 256 can be considered as a rational number because it can be expressed as the quotient of the two integers: for example 256/1.
The ratio of girls to
boys in a math club
was 1:7. There were
6 girls. How many
boys
Were there in the
club?
Answer: 42
Step-by-step explanation: If the ratio is 1 girl for 7 boys and there are 6 girls you do 6x7=42
how many term has G.p whose 2nd term is 1/2 and common ratio and the last term are 1/4and1/128respestively
The geometric progression has the form:
[tex]\mleft\lbrace a,ar,ar^2,ar^3,\ldots,ar^n\mright\rbrace[/tex]We have the information about the second term, a*r:
[tex]ar=\frac{1}{2}[/tex]We know that the common ratio is
[tex]r=\frac{1}{4}[/tex]So from this information we can get the coefficient a:
[tex]\begin{gathered} ar=\frac{1}{2} \\ a\cdot\frac{1}{4}=\frac{1}{2} \\ a=\frac{4}{2}=2 \end{gathered}[/tex]And we also know that the last term is 1/128, that is
[tex]ar^n=\frac{1}{128}[/tex]From this one we can find n:
[tex]\begin{gathered} 2\cdot(\frac{1}{4})^n=\frac{1}{128} \\ (\frac{1}{4})^n=\frac{1}{128\cdot2} \end{gathered}[/tex]We can apply the property of the logarithm of power to get n:
[tex]\begin{gathered} \log ((\frac{1}{4})^n)=\log (\frac{1}{256}) \\ n\cdot\log (\frac{1}{4})^{}=\log (\frac{1}{256}) \\ n=\frac{\log (\frac{1}{256})}{\log (\frac{1}{4})} \\ n=4 \end{gathered}[/tex]Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms
Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10min for calls. Find the model of the total cost of company a's plan. using m for minutes.
Based on the monthly fee charged by Company A and the charges per minute for calls, the model for the total cost of Company A's plan is Total cost = 20 + 0.05m.
How to find the model?The model to find the total cost of Company A's plan will incorporate the monthly fee paid as well as the amount paid for each minute of calls.
The model for the cost is therefore:
Total cost = Fixed monthly fee + (Variable fee per minute x Number of minutes)
Fixed monthly fee = $20
Variable fee per minute = $0.05
Number of minutes = m
The model for the total cost of Company A's plan is:
Total cost = 20 + 0.05m
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The required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
As of the given data, Company A has a monthly fee of $20 and charges $.05/min for calls. An equation that represents the total cost of Company a's plan is to be determined.
Here,
Let x be the total cost of the company and m be the number of minutes on a call.
According to the question,
Total charges per minute on call = 0.5m
And a monthly fee = $20
So the total cost of company a is given by the arithmetic sum of the sub-charges,
X = 20 + 0.5m
Thus, the required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
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HELPPPPPP PLEASEEEEEEEEEEEEEE
Answer:
Option C, [tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]
Step-by-step explanation:
Oooo the ol canvas quiz yeesh.
Anyway, for this sort of problem, anywhere in your second equation that you see an x, sub for (x+h).
[tex]f(x)=-3x^{2} +2x+1[/tex]
[tex]f(x)=-3(x+h)^{2} +2(x+h)+1\\[/tex]
You must foil the first part
[tex]f(x)=-3(x^2+h^2+2xh)+2(x+h)+1\\[/tex]
Now distribute to eliminate the parentheses
[tex]f(x)=-3x^2-3h^2-6xh+2x+2h+1[/tex]
As your answer choice has it:
[tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]
