Let:
[tex]\begin{gathered} V_1\colon\text{ volume of iceberg below the water line} \\ V_2\colon\text{ volume of iceberg above the waterline} \end{gathered}[/tex]We want to finde some number k such that we can express the volume of the iceberg below the water line as the product of k and the volume of the iceberg above the waterline, this is:
[tex]V_1=k\cdot V_2[/tex]then, solving for k we have the following:
[tex]\begin{gathered} V_1=2^5m^3 \\ V_2=2^2m^3 \\ V_1=k\cdot V_2 \\ \Rightarrow k=\frac{V_1}{V_2}=\frac{2^5}{2^2}=2^{5-2}=2^3^{} \\ k=2^3 \end{gathered}[/tex]we have that k=2^3. This means that the volume of the iceberg above the water line is 2^3 times the volume of the iceberg below the water line
The ratio of the number of adults to the number of students at a field trip has to be 3:8. During a current field trip, there are 190 more students on the trip than there are adults. How many students are attending the field trip? How many adults?
Please put this answer in a easy way (no algebra) use ratios and basic opreations.
The number of students attending the field trip is 304 and the number of adults is 114.
Calculating number of students and adults attending a field tripFrom the question, we are to determine the number of students and adults attending the field trip.
From the given information,
"The ratio of the number of adults to the number of students at a field trip has to be 3:8"
Let the number of students be x and the number of adults be y
Thus,
y/x = 3/8
8y = 3x ------------- (1)
Also,
There are 190 more students on the trip than there are adults
That is,
x - y = 190
Therefore,
x = 190 + y -------------- (2)
Substitute into equation
8y = 3x
8y = 3(190 + y)
8y = 570 + 3y
8y - 3y = 570
5y = 570
y = 570/5
y = 114
Thus, the number of adults is 114
Substitute the value of y into equation (2)
x = 190 + y
x = 190 + 114
x = 304
Hence, the number of students is 304
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Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw $300 automatically every month to pay off his 10-year student loan. Will Rajesh have enough money in the account to cover all of the required loan payments? (Round to the nearest tenth of a year.)
By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.
The Principal Amount(P) = $30,000
Rate of Interest (r) = 2.16 %
Time(t) = 10 years
Number of Times it is Compounded in a year(n) = 12
Now, we have
[tex]A =P(1+\frac{r}{100n}) ^{nt}[/tex]
Putting all the values, we evaluate the amount,
[tex]A =30,000(1+\frac{2.16}{100*12}) ^{12*10}\\\\A = 30,000 * 1.240\\A = 37,225.84[/tex]
Hence, the Amount after Compound Interest = $37,225.87
Now, The loan amount that he pays = 300 *12*10 = $ 36,000
Yes, he will have enough money in the account to cover all of the required loan payments.
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Line l passes through the points, (6,-14) and (2,-4) . If line m is parallel to line l, the slope of the line m is equal to
Determine the slope of line l passes through points (6,-14) and (2,-4).
[tex]\begin{gathered} m=\frac{-4-(-14)}{2-6} \\ =\frac{-4+14}{-4} \\ =-\frac{10}{4} \\ =-\frac{5}{2} \end{gathered}[/tex]The line m is parallel to line l and parallel line have equal slope. So slope of line m is equal to -5/2.
Option 3 is correct.
if f(x) = 1/x and g(x) = x+1/x find(fog)(x).a) x +1/ x squared b) x / x + 1 c) x squared (x + 1)d) x + 1 / x cubed
We have the following:
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ g(x)=\frac{x+1}{x} \end{gathered}[/tex]now, (f(x) o g(x))
[tex]\mleft(f\: (x)\circ\: g(x)\mright)=\frac{1}{\frac{x+1}{x}}=\frac{x}{x+1}[/tex]The answer is the second option
[tex]\frac{x}{x+1}[/tex]This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeAB.CDF3 2Frequency 51015Find the probability that a student earns agrade of A, B, or C.p = [?]Enter a decimal rounded to the nearest hundredth.
The probability of an event is obtained as follows:
[tex]Pr(\text{Event)}=\frac{number\text{ of favourable outcomes}}{number\text{ of sample space}}[/tex][tex]\begin{gathered} Pr(a\text{ student earns a grade of A) = }\frac{number\text{ of students that earn grade A}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of A)=}\frac{5}{35} \\ \\ Pr(a\text{ student earns a grade of B)=}\frac{number\text{ of students that earn grade B}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of B)=}\frac{10}{35} \\ \\ Pr(a\text{ student earns a grade of C)=}\frac{\text{number of students that earn grade C}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of C)=}\frac{15}{35} \end{gathered}[/tex]Therefore, the probability that a student earns a grade of A, B or C=
Pr(a student earns a grade of A) + Pr(a student earns a grade of B) + Pr(a student earns a grade of C).
This becomes;
[tex]\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\text{ }\frac{30}{35}=\frac{6}{7}[/tex]Hence, the probability that a student earns a grade of A, B or C is
[tex]\frac{6}{7}=0.86\text{ (to the nearest hundredth)}[/tex]find (x) 76° 6x-9 47°
There are two degrees, one variable and one number.
use trigaonamets functions as nessary to find the missing parts the triangle
Given a right angle triangle:
As shown on the acute angles is 21
So,
[tex]\begin{gathered} \cos \text{ 21=}\frac{adjacent}{\text{hypotenuse}}=\frac{6.4}{H} \\ \\ H=\frac{6.4}{\cos 21}=6.855 \end{gathered}[/tex]And:
[tex]\begin{gathered} \tan 21=\frac{opposite}{\text{adjacent}}=\frac{y}{6.4} \\ \\ y=6.4\cdot\tan 21=2.457 \end{gathered}[/tex]the third angle of the triangle =
[tex]90-21=69[/tex]Which Problems can be solved by performing this multiplication 1/5 x 30
Answer:
c
Step-by-step explanation:
On March 8, 2017, one U.S. dollar was worth 19.61 Mexican pesos.(a) On that date, how many dollars was 149.23 pesos worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many pesos was 63.64 dollars worth?Round your answer to the nearest hundredth of a peso.OPpesosI need help with these two math problems.
ANSWERS
(a) 7.61 USD
(b) 1247.98 MXN
EXPLANATION
We know that on March 8, 2017, 1 USD was worth 19.61 MXN.
(a) To find how many dollars was 149.23 MXN worth on that date, we have to divide this amount by 19.61,
[tex]149.23\text{ }MXN\cdot\frac{1\text{ }USD}{19.61\text{ }MXN}\approx7.61[/tex]Hence, 149.23 Mexican pesos were worth 7.61 US dollars.
(b) Now, to find how many Mexican pesos were 63.64 USD worth on that date, we have to multiply it by 19.61 instead,
[tex]63.64\text{ }USD\cdot\frac{19.61\text{ }MXN}{1\text{ }USD}\approx1247.98\text{ }MXN[/tex]Hence, 63.64 US dollars were worth 1247.98 Mexican pesos.
What is the difference in elevation between the highest and lowest bodiesof water listed in the table below? Write an equation to show how youfound your answer."Height Above Sea LevelBody ofElevation(in feet)WaterCaspian Sea92Lake Maracaibo0Lake Superior600Lake Victoria3,720
The highest value is the highest positive integer, which is 3720.
The lowest value is the negative value, -92.
To obtain the difference between the two, subtract -92 from 3720. thus we have the following:
[tex]3720-(-92)[/tex]Add the additive inverse of -92 to 3720.
[tex]3720-(-92)=3720+92=3812[/tex]Determine the direction angle (in degrees) for each vector:• Make sure you're using degrees instead of radians.• If you use a decimal approximation, you must be accurate to at least 3 decimal places.a. (5, 3) has direction angle: 0 =b. (-4,5) has direction angle: 0 =c. (8,-8) has direction angle: 0=d. (-12, -3) has direction angle: 0=
Explanation
a vectors makes a rigth angle to the x-positve axis , so
so, the x coordinate is adjacent side and the y-coordinate becomes into the opposite side, then we can use a trigonometric function that relates those values,it is
[tex]\begin{gathered} tan\theta=\frac{opposi\text{te side}}{adjacent\text{ side}} \\ tan\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \end{gathered}[/tex]hence
Step 1
a)
let
[tex]\begin{gathered} \langle5,3\rangle, \\ x=5 \\ y=3 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{3}{5} \\ \theta=\tan^{-1}(\frac{3}{5}) \\ \theta=30.964° \end{gathered}[/tex]so,
a)Blank1: 30.964
Step 2
b)
let
[tex]\begin{gathered} \langle-4,5\rangle, \\ x=-4 \\ y=5 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{5}{-4} \\ \theta=\tan^{-1}(\frac{5}{-4}) \\ \theta=-51.340\~+180(Iquadrant) \\ \theta=128.660 \\ . \end{gathered}[/tex]so,
b)Blank2:128.660
Step 3
c)
[tex]\begin{gathered} \langle8,-8\rangle, \\ x=8 \\ y=-8 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{-8}{8} \\ \theta=\tan^{-1}(-1) \\ \theta=-45 \end{gathered}[/tex]so,
c)Blank3:-45 °
Step 4
d)
[tex]\begin{gathered} \langle-12,-3\rangle, \\ x=-12 \\ y=-3 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{-3}{-12} \\ \theta=\tan^{-1}(\frac{1}{4}) \\ \theta=14.036 \end{gathered}[/tex]so,
direction
[tex]\begin{gathered} direcgtion\text{ =}\theta+180=14.036 \\ angle=194.036 \end{gathered}[/tex]graph
d)Blank4: 194.036
I hope this helps you
Find the equation of the line thatis parallel to y = 2x – 7 andcontains the point (-3,6).y = [ ? ]x + []Enter
Answer:
y = 2x +12
Step-by-step explanation:
You want the line through point (-3, 6) that is parallel to y = 2x -7.
Parallel lineThe given line equation is in slope-intercept form ...
y = mx + b . . . . . line with slope m and y-intercept b
This allows us to see that its slope is 2.
The parallel line will have the same slope. All we need to do is find its y-intercept.
InterceptSolving the above equation for 'b', we get ...
b = y - mx
Using (x, y) = (-3, 6) and m = 2, we find 'b' to be ...
b = 6 -(2)(-3) = 12
EquationUsing the values for m and b that we now know, the desired equation is ...
y = 2x +12
<95141404393>
encuentra la medida de dos angulos complementarios. A=7×+4 y B=4×+9
Complementary angles mean that they add up to 90.
Thus, we can write:
[tex]\begin{gathered} A+B=90 \\ 7x+4+4x+9=90 \end{gathered}[/tex]We can use algebra to find x:
[tex]\begin{gathered} 7x+4+4x+9=90 \\ 11x+13=90 \\ 11x=90-13 \\ 11x=77 \\ x=\frac{77}{11} \\ x=7 \end{gathered}[/tex]To find measure of the individual angles, A and B, we simple plug in 7 into x of the expressions of A and B.
Angle A:
7(7) + 4 = 53 degrees
Angle B:
4(7) + 9 = 37 degrees
Find the area of the composite figure below. Round your answer to the tenths.
Answer:
54 square units
Explanation:
First, divide the composite figure into common plane shapes as shown below:
Thus, we have two plane shapes:
• A triangle with a base of 10 units and a height of 6 units.
,• A rectangle with a length of 6 units and a height of 4 units.
Therefore:
[tex]\begin{gathered} \text{ Area of the composite figure}=\text{ Area of the triangle+Area of the rectangle} \\ =\frac{1}{2}bh+lh \\ =(\frac{1}{2}\times10\times6)+(6\times4) \\ =30+24 \\ =54\text{ square units} \end{gathered}[/tex]The area of the composite figure is 54 square units.
hentIf TR = 11 ft, find the length of PS.IfР P.TentR16d ArcsSnd ArcsRound to 2 decimal places.and Arcs
SOLUTION
This is a length of arc problem.
The formula for finding the length of an arc is:
[tex]\frac{\theta}{360}\times2\pi r[/tex]r=TR=PT=11ft
[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ r=11ft \\ \theta=164^o \end{gathered}[/tex][tex]\begin{gathered} \frac{164}{360}\times2\pi(11) \\ =\frac{164}{360}\times2\times3.14\times11 \\ =31.4698ft \\ =31.47ft(to\text{ 2 decimal places)} \end{gathered}[/tex]The final answer is 31.47ft.
Estimate 52% of 42 right in a whole number
52% of 42 is 21.84 rounded to the nearest whole number is 22.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
We know 52% of 42 can be numerically expressed as,
(52/100)×42.
= 21.84.
Now, 21.84 rounded to the nearest whole number is 22.
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How much do you owe at the end of five weeks ?
First, find the interest percentage. Divide the amount borrowed by the interest amount.
[tex]\frac{100}{10}=10[/tex]Then, divide the result by 100% to express it as a percentage.
[tex]\frac{10}{100}=0.10[/tex]Once we have the interest percentage as a decimal number, multiply it by the new borrowed amount.
[tex]0.10\times1100=110[/tex]Therefore, you owe $110 at the end of the five weeks.The 19% APR is the annual interest rate, but it is compounded monthly. What is the monthly interest rate ?
Answer:
1.583%
Step-by-step explanation:
19% divided by 12% (how many months there are) = 1.583%
I need help if because I’m not sure if I was right or not
A trapezium has only 4 sides. This rules out option A
A trapezium has only one pair of parallel sides.
For option c, it is a parallelogram because it has 2 pairs of parallel sides.
For option d, it has no pair of parallel sides.
Thus, the correct option is B
Rhombus ABCD with vertices A(1,0), B(6,-2), C(8,-7), and D(3,-5); 90° counterclockwise rotation about the origin
Given data:
The given coordinates of Rhombus are A(1,0), B(6,-2), C(8,-7), and D(3,-5).
The coordinate of a point after 90 degrees counterclockwise rotation is,
[tex](x,\text{ y)}\rightarrow(-y,x)[/tex]The final coordinate of Rhombus are,
[tex]\begin{gathered} A(1,0)=A^{\prime}(0,\text{ 1)} \\ B(6,\text{ -2)=B'(2, 6)} \\ C(8,\text{ -7)=C'(7},\text{ 8)} \\ D(3,\text{ -5)=D'(5, 3)} \end{gathered}[/tex]Thus, the final coordinate of Rhombus are A'(0,1), B'(2, 6), C'(7, 8) and D'(5, 3).
ASSUME THAT THE WAITING TIMES FOR CUSTOMERS AT A POPULAR RESTAURANT BEFORE BEING SEATED ARE NORMALLY DISTRIBUTED WITH A MEAN OF 16 MINUTES AND STANDARD DEVIAITON OF 4 MINUTES.1. IN A RANDOM SAMPLE OF 1000 CUSTOMERS, HOW MANY WAIT 18 MINUTES OR MORE BEFORE BEING SEATED.2. IN A RANDOM SAMPLE OF 500 CUSTOMERS, HOW MANY WAIT LESS THAN 9 MINUTES BEFORE BEING SEATED
Solution.
Calculate the z-score
The formula is shown below
[tex]\begin{gathered} \sigma=4 \\ \mu=16 \\ \end{gathered}[/tex][tex]\begin{gathered} Z_{18}=\frac{18-16}{4}=0.5 \\ P\left(x>0.5\right)=0.30854 \\ n=0.30854\text{ x 1000} \\ n=308.54 \\ n=309(nearest\text{ whole number\rparen} \end{gathered}[/tex]Thus, 309 customers (to nearest whole number) wait 18 minutes or more before being seated
(ii)
[tex]\begin{gathered} Z_9=\frac{9-16}{4} \\ Z_9=-1.75 \\ P\left(x<-1.75\right)=0.040059 \\ n=0.040059\text{ x 500} \\ n=20.03 \\ n=20(nearest\text{ whole number\rparen} \end{gathered}[/tex]Thus, 20 customers (to nearest whole number) wait less than 9 minutes before being seated
19. The Millers open a savings account for their newborn son with $430. Find the total amount in the account after 3 years if the simple interest rate is 2.5%.
we get that
[tex]C=430+3\cdot0.025\cdot430=462.25[/tex]100 in it takes 10 pounds of potatoes to make 15 pounds of mashed potatoes at this rate how many pounds of mashed potatoes can they make with 15 pounds of potatoes
The box of cereals will weigh
[tex]undefined[/tex]33 over r =11 over 2
Answer:
r=6
Step-by-step explanation:
33/r = 11/2
r/33 = 2/11 multiply both sides of the equation by 33
r = 33 * 2/11 = 6
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 8z
Answer:
(0, 0)(0.1, 0.005)=====================
Given system2y = x² y = 5x³Substitute the value of y into first equation2*5x³ = x²10x³ - x² = 0x²(10x - 1) = 0x = 0 and 10x - 1 = 0x = 0 and x = 0.1Find the value of yx = 0 ⇒ y = 5*0³ = 0x = 0.1 ⇒ y = 5*(0.1)³ = 0.005Answer:
[tex](x,y)=\left(\; \boxed{0,0} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{\dfrac{1}{10},\dfrac{1}{200}} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}2y=x^2\\ \;\;y=5x^3\end{cases}[/tex]
To solve by the method of substitution, substitute the second equation into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=5x^3 \implies 2(5x^3)&=x^2\\10x^3&=x^2\\10x^3-x^2&=0\\\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}10x^3-x^2&=0\\x^2(10x-1)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]x^2=0 \implies x=0[/tex]
[tex]10x-1=0 \implies x=\dfrac{1}{10}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=0 \implies y&=5(0)^3\\y&=0\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies y&=5\left(\dfrac{1}{10}\right)^3\\y&=5 \cdot \dfrac{1}{1000}\\y&=\dfrac{1}{200}\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{0,0} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{\dfrac{1}{10},\dfrac{1}{200}} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
What is the inverse of the statement "If it is winter, then I am cold"?If it is not winter, then I am not coldIf it is winter, then I am coldIf I am cold, then it is winterIf I am not cold, then it is not winter
ANSWER
If it is not winter, then I am not cold.
EXPLANATION
We want to find the inverse of the statement given:
If it is winter, then I am cold
To do this, we have to negate the if statement and the conclusion of the if statement there.
That is we find the negative of the if part and the then part of the statement.
The if part is:
If it is winter
The negative of this is:
If it is not winter
The then part is:
then I am cold
The negative of this is:
then I am not cold
Therefore, the inverse of the statement is If it is not winter, then I am not cold.
the factor of 26 are
EXPLANATION
Factors are numbers we can multiply together to get another number.
The factor of 26:
26 divides by 2: 26/2=13
13 divides by 13: 13/13 = 1
2,13 are all prime numbers, therefore no further factorization is possible.
Add the primer factors:
2,13
Add 1 and the number 26 itself:
1,26
The factors of 26 are 1,2,13,26.
if (x=5)and y=10 which expression has the greatest value
Let's assume the question was as stated below;
"If x=5 and y=10, which expression has the greatest value?"
a. xy
b. x + y
c. x-y
d. x/y
Answer:
Option A. Expression xy has the greatest value.
Explanation:
To determine which of the given options has the greatest value, let's go ahead and evaluate each of them;
Option A;
[tex]xy=x\ast y=5\ast10=50[/tex]Option B;
[tex]x+y=5+10=15[/tex]Option C;
[tex]x-y=5-10=-5[/tex]Option D;
[tex]\frac{x}{y}=\frac{5}{10}=\frac{1}{2}[/tex]We can see that the expression (xy) gives the greatest value.
Therefore, option A would be our correct answer.
Round 2.8962 to the nearest hundredth. Do not write extra zeros.
To round the number
2.8962 to the nearest hundredth
First check the digit whose place value is hundredth
The digit is 9
You will either round it up or down depending on the next digit immediately after it which is called the decider
If the decider is from 0-4 then we round the number down
If the decider is from 5 -9 then we round the number up
The decider is 6 so we are rounding the number up
2.8962 ≈ 2.90 to the nearest hundredth
When the 9 increases to ten, we can't write 10 down so we write 0 and add 1 to 8 which makes it 9
Answer:
9
Step-by-step explanation:
Solve for V5/6= v-5 /4
Okay, here we have this:
Considering the provided equation, we are going to solve it to find the value of y, so we obtain the following:
5/6= v-5 /4
v-5 /4+ 5 /4=5/6 + 5/4
v= 5/6 + 5/4
v=(20+30)/24
v=50/24
v=25/12
Finally we obtain that v is equal to 25/12.