Price of one pound of mercury is derived as follows;
[tex]\begin{gathered} Price\text{ of 1lb of merc}=\frac{Cost\text{ of flask}}{Pounds\text{ of merc in the flask}} \\ \text{Price of 1 lb}=\frac{150.50}{76} \\ \text{Price of 1 lb}=1.98 \end{gathered}[/tex]This means 1 pound of mercury costs $1.98
1 pound = 453.6 grams
Therefore;
[tex]\begin{gathered} 1lb=453.6gms \\ 76lb=34,473.6gms \end{gathered}[/tex]The price of 1 gram of mercury would be;
[tex]\begin{gathered} Price\text{ of 1 gram}=\frac{Price\text{ per pound}}{\text{grams in 1 lb}} \\ \text{Price of 1 gram}=\frac{1.98}{453.6} \\ \text{Price of 1 gram}=0.004365 \end{gathered}[/tex]This means 1 gram of mercury costs $0.004365
Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;
[tex]\begin{gathered} \text{Price of 1 cubic cm}=grams\text{ per cubic cm x price of 1 gram} \\ \text{price of 1 cubic cm}=13.534\times0.004365 \\ \text{Price of 1 cubic cm}=0.059 \end{gathered}[/tex]This means 1 cubic centimeter of mercury would cost $0.059
Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,
[tex]\begin{gathered} Price\text{ of 1 cubic inch}=16.387\text{ cubic cm x }price\text{ of 1 cubic cm} \\ \text{Price of 1 cubic inch}=16.387\times0.059 \\ \text{Price of 1 cubic inch}=0.9668 \end{gathered}[/tex]This means 1 cubic inch costs $0.9668
It takes 4.800 cubic inches to make 1 manometer.
Therefore, the cost of 4.800 cubic inches would be;
[tex]\begin{gathered} Price\text{ of 4.800 cubic inches}=Price\text{ of 1 cubic inch x 4.800 cubic inches} \\ Price\text{ of 4.800 cubic inches}=0.9668\times4.800 \\ \text{Price of 4.800 cubic inches}=4.64 \end{gathered}[/tex]If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64
Therefore, to make 21 manometers, we would have;
[tex]\begin{gathered} 1\text{ manometer}=4.64 \\ 21\text{ manometers}=21\times4.64 \\ 21\text{ manometers}=97.44 \end{gathered}[/tex]ANSWER:
The price of mercury required to make 21 manometers would be $97.44
Given the figure below, find the values of x and z. (9x + 70). (6x + 80).
( 9x+70)+(9x+70) + (6x + 80) + (6x+ 80 ) = 360
If you solve the equation you get that
x = --44/5
Now, since
z = ( 6x +80 ) = ( 6*(-44/5) + 80 ) = 136 / 5
So, there you have, x,z
to qualify for a police academy, candidates must score in the top 21% on a general abilities test. assume the test scores are normally distributed and the test has a mean of 200 and a standard deviation of 20. find the lowest possible score to qualify
The lowest value that is needed in order to qualify is given as 216.128
What is z score?The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from:
z = (raw score - mean) / standard deviation
Given; mean of 200 and a standard deviation of 20
P(z > c) = 21% = 0.21
1 - P(z < c) = 0.21
P(z < c) = 0.79
we are to find the critical value of z using excel function
=NORM.S.INV(1-0.21)
= 0.806421247
To get the lowest value we would have to put the values in the formula
0.8064 = (x - 200)/20
0.8064 * 20 = (x - 200)
16.128 = (x - 200
take like terms
x = 200 + 16.128
x = 216.128
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Find both the x-intercept and the y-intercept of the line given by this equation 7.2x-9.6y-5.7=0
To find the x intercept of the line we have to replace y for 0 and solve for x:
[tex]\begin{gathered} 7.2x-9.6y-5.7=0 \\ 7.2x-9.6(0)-5.7=0 \\ 7.2x-5.7=0 \\ 7.2x=5.7 \\ x=\frac{5.7}{7.2} \\ x=0.79 \end{gathered}[/tex]To find the y intercept of the line we have to replace x for o and solve for y:
[tex]\begin{gathered} 7.2x-9.6y-5.7=0 \\ 7.2(0)-9.6y-5.7=0 \\ -9.6y-5.7=0 \\ -9.6y=5.7 \\ y=\frac{5.7}{-9.6} \\ y=-0.59 \end{gathered}[/tex]It means that the x intercept is 0.79 and the y intercept is -0.59.
TED BORROWED $1,200 FOR TWO YEARS AND HE MADE MONTHLY PAYMENTS. IF THE TOTAL FINANCE CHARGE IS $175.92 WHAT IS THE APR?
Given: Ted Borrowed $1200 for two years and made monthly payments. The total finance charge is $175.92
Required: To determine the Annual Percentage Rate.
Explanation: The formula for APR is as follows-
[tex]APR=\lbrace\frac{(Fees+Interest)}{\frac{Principal}{n}}\frac{}{}\times365\rbrace\times100[/tex]where n is the total number of days in the loan term.
Here, the total finance charge is $175.92, and the Principal amount is $1200.
Also, n=2 years or 730 days. Substituting these values into the formula as-
[tex]APR=(\frac{175.92}{\frac{1200}{730}}\times365)\times100[/tex]Further solving as-
[tex]APR=7.29\%[/tex]Final Answer: The Annual Percentage Rate is 7.29%
Divide 30.4cm into 8 equal parts.
Find the length of each part.
Answer:
304/10÷8/1
304/10×1/8
38/10
3.8
or
304÷8
=38
reshma is making a necklace using green beads and purple beads in a ratio represented on the following double number line fill in the missing values on the diagram and then answer the following question
From the double number line, we can see that the corresponding number of Green and Purple beads needed in each case are stated.
[tex]\begin{gathered} 4\text{ Gre}en\text{ }\rightarrow5\text{ Purple} \\ 8\text{ Gr}een\text{ }\rightarrow10\text{ Purple} \\ \cdot \\ \cdot \\ 20\text{ Gre}en\text{ }\rightarrow\text{ 25 Purple} \end{gathered}[/tex]Therefore, for 20 Green beads she will need to use 25 Purple Beads.
[tex]25\text{ Purple Beads}[/tex]I need help with this assignment!! I already did A and B! I need help with the rest.
Given:
The roller-coster is moving in the trajectory of this curve
[tex]f(x)=3x^4-18x^3-21x^2+144x-108[/tex]Step by step solution:
To solve this complete problem we need to draw the estimated graph of this function, so that we can answer this question easily.
First of all, we need to find the roots of the given equation,to plot the curve:
let us put the random numbers that may satisfy the equation:
Let us put x = 1:
[tex]\begin{gathered} f(x)=3x^4-18x^3-21x^2+144x-108 \\ \\ f(1)=3-18-21+144-108 \\ \\ f(1)=\text{ 0} \end{gathered}[/tex]From here we can say that 1 is the root of the equation.
We will now divide this function from (x-1), so that we can get the cubic equation:
We will use long division method for division, the result we get after the division is:
[tex]f(x)=(x-1)(3x^3-15x^2-36x+108)[/tex]We will now try to factorize the cubic equations, by putting the random numbers that may satisfy the equation:
let us put x = 2:
[tex]\begin{gathered} f(x)=(x-1)(3x^3-15x^2-36x+108) \\ \\ f(2)=(2-1)(3(2)^3-15(2)^2-36(2)+108) \\ \\ f(2)=(1)(24\text{ }-\text{ 60 - 72 +108}) \\ \\ f(2)=0 \end{gathered}[/tex]From here we can say that f(2) is also the root of this cubic
We will now divide the cubic equation with (x-2), so we can break the cubic into quadratic:
Upon division the cubic equation break into following factors:
[tex]\begin{gathered} =(x-2)(3x^2-9x-54) \\ \\ which\text{ further simplified into:} \\ \\ =(x-2)(x-6)(x+3) \end{gathered}[/tex]From here we have found out four roots of the initial function that are:
x = 1,2,6,-3
Now we can easily plot the curve:
This is estimated curve, there are no sharp edges.
On the basis of this curve, we can easily answer all the questions related to this curve.
what is the density of the oak board? show your work.
I think this is a physics problem.
I'll read it
a) A rectangular prism and a cylinder
b) Volume of the log = pi*r^2 x h
Volume of the log = 3.14*5^2* 30
Volume of the log = 2355 in^3
density = weight / volume
density = 4263 / 2355
density = 1.81 lb/in^3 This is the result
finding the vertex, intercepts, and axis of symmetry from the graph of a parabola
Solution
Explanation:
Given:
(b) Equation of the axis of symmetry
[tex]\begin{gathered} x=-8 \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} x=-8,x=4 \\ (x+8)(x-4)=0 \\ x^2-4x+8x-32=0 \\ x^2+4x-32=0 \\ y=x^2+4x-32 \end{gathered}[/tex]where
[tex]\begin{gathered} y=ax^2+bx+c \\ a=1,b=4,c=-32 \end{gathered}[/tex]The formula for the axis of symmetry and the x value of the vertex
[tex]x=-\frac{b^2}{2a}[/tex]Plug in the value
[tex]x=\frac{-(4)^}{2}=-2[/tex](d) To find the y value of the vertex, substitute 1 for x in the equation.
[tex]\begin{gathered} y=x^2+4x-32 \\ y=(-2)+4(-2)-32 \\ y=-2-8-32 \\ y=-42 \end{gathered}[/tex]The vertex is (-2 , -42) Since a > 0 the vertex is the minimum point and the parabola opens upward.
Hence the vertex = (-2 , -42)
Analyze the diagram below and complete the instructions that follow.F45E28DSolve AEFD. Round the answers to the nearest hundredth.
Since this is a right triangle we can use trig functions
First we can find the length of the hypotenuse using the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
28^2 + 45^2 = c^2
784+2025 = c^2
2809 = c^2
Taking the square root of each side
sqrt(2809) = sqrt(c^2)
53 = c
The hypotenuse, DR = 53
Then we can find the measurements of the angles
sin F = opp/ hyp
sin F = 28/53
Taking the inverse sin of each side
sin D = opp/ hyp
sin D = 45/53
Taking the inverse sin of each side
To solve for x, you divide each side by what number?(4.5)x = 264.5456
Answer
4.5
Step-by-step explanation
Given the equation:
[tex]4.5x=26[/tex]Dividing at both sides by 4.5, we get:
[tex]\begin{gathered} \frac{4.5x}{4.5}=\frac{26}{4.5} \\ x=\frac{52}{9} \end{gathered}[/tex]Answer:
Divide each side by 4.5
Step-by-step explanation:
(4.5)x = 264.5456
We want to isolate x
Divide each side by 4.5
(4.5)x / 4.5 = 264.5456/ 4.5
x =58.78791
Please help me this question I couldn’t understand it please.
Given:
Length of a rectangle is a+1
width of a rectangle is a
[tex]\begin{gathered} \text{Perimeter}=2(a+1+a) \\ =2(2a+1) \\ =4a+2 \end{gathered}[/tex]Write the point-slope form of the equation of the line that passes through the point (-1, 5) and has a slope of -1.
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies {\large \begin{array}{llll} y -5= -(x +1) \end{array}}[/tex]
Solve 3x2 + 18x + 15 = 0 by completing the square
Step 1
Given;
[tex]3x^2+18x+15=0[/tex]Required; To solve by completing the square method.
Step 2
Subtract 15 from both sides of the equation.
[tex]\begin{gathered} 3x^2+18x+15-15=0-15 \\ 3x^2+18x=-15 \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ all terms by 3} \\ x^2+6x=-5 \end{gathered}[/tex]Find half of the coefficient of x (i.e 6) and square it
[tex](\frac{6}{2})^2=3^2[/tex]Add it to both sides
[tex]\begin{gathered} x^2+6x+3^2=-5+3^2 \\ Use\text{ perfect square} \\ (x+3)^2=-5+9 \\ (x+3)^2=4 \\ x+3=\pm\sqrt{4} \\ x=\operatorname{\pm}\sqrt{4}-3 \end{gathered}[/tex][tex]\begin{gathered} x=\pm2-3 \\ x=-1\text{ or -5} \end{gathered}[/tex]Answer;
[tex]x=-1,-5[/tex]help me; its all explained in the picture thank you
The mean, mode, and mid-range of the given numbers are 13,13,16 respectively.
What are the mean, mode, and range?The total of all the numbers is represented by the mean. The median is the number in the center of an ordered list. The most frequent number is the mode. The highest number less the smallest number is the range.
Mean = sum of the number/ total no. of observations
Mean = 117/ 9
Mean = 13
Mode: The unique number that repeatedly comes
Given,
9, 9, 10, 11, 13, 13, 13, 14, 25
Mode = 13
Range: Deduct the smaller number from the greater one.
Range = 25-9
Range = 16
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The length of a rectangle is 5 inches more than the width. The perimeter is 42 inches. Find the length and the width of the rectangle.The width of the rectangle is ___ cubit inches, square inches or inches ? and the length of the rectangle is ____ cubit inches, square inches or inches?
Given
perimeter = 42 inches
length of a rectangle is 5 inches more than the width.
Find
width, length
Explanation
Let width of rectangle = x inches
length = 5 + x
Perimeter of rectangle = 2 (l + b) = 2(5+x+x) = 42
[tex]\begin{gathered} 2\times(5+x+x)=42 \\ 5+2x=21 \\ 2x=16 \\ x=8 \end{gathered}[/tex]width = 8 inches
Length = 5 + 8 = 13 inches
Final Answer
The width of the rectangle is 8 inches.
The length of the rectangle is 13 inches.
I could use some help on math I’m really struggling
We need to find how much will be left after 6 half-lives of a radioactive isotope starting with 130g.
One way to write the amount N of radioactive isotope left after a time t, with an initial amount N₀ and a half-life τ is:
[tex]N=N_0\left(\frac{1}{2}\right)^{t\text{ /}\tau}[/tex]Notice that when t = τ, we have:
[tex]N=\frac{N_0}{2}[/tex]In this problem, we have:
[tex]\begin{gathered} N_0=130g \\ \\ t=6\tau \end{gathered}[/tex]Then, we obtain:
[tex]N=130g\left(\frac{1}{2}\right)^{6\tau\text{ /}\tau}=130g\left(\frac{1}{2}\right)^6=\frac{130g}{64}\cong2\text{ g}[/tex]Therefore, rounding to the nearest gram, the answer is 2 grams.
you are in a hot air balloon that is 600 feet above the ground. if the angle from your line of sight to your friend is 20°, how far is he from the point on the ground.
Answer
x = 164.9 ft
Explanation:
Given the following figures
To find the distance from the point on the ground, we need to apply the SOH CAH TOA
[tex]\begin{gathered} \text{Height = 600 ft} \\ \text{Horizontal distance x} \\ \theta\text{ = 20} \\ \text{ }\tan \theta\text{ =}\frac{opposite}{\text{adjacent}} \\ \text{opposite = 600 ft} \\ \text{adjacent = x ft} \\ \tan \text{ 20 = }\frac{600}{x} \\ \text{Cross multiply} \\ x\cdot\text{ tan 20 = 600} \\ \text{x = }\frac{600}{\tan \text{ 20}} \\ \tan \text{ 20 = }0.3639 \\ \text{x = }\frac{60}{0.3639} \\ \text{x = }164\text{ .9 ft} \end{gathered}[/tex]Therefore, the distance is 164.9 ft
This table shows how many sophomores and juniors attended two school events.What is the probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert?Round your answer to two decimal places.
Given:
Number of sophomores attended jazz band concert = 35
Total number of students = 137
Required: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert.
Explanation:
The formula to find probability is
[tex]p=\frac{\text{Number of favorable outcomes}}{\text{ Total number of outcomes}}[/tex]Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert
[tex]\begin{gathered} =\frac{\text{Number of sophomores attended jazz band concert}}{\text{ Total number of students in this group}} \\ =\frac{35}{137} \\ =0.26 \end{gathered}[/tex]Option D is correct.
Final Answer: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert is 0.26.
Leave K in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredth.
By definition, an equation of a Combined Variation has the following form:
[tex]z=k(\frac{x}{y})[/tex]Where "k" is the Constant of Variation.
In this case, you know that the resistance "R" of a wire varies directly as its length and inversely as the square of its diameter.
Then, let be "R" the resistance of the wire (in ohms), "l" its length of the wire (in feet), and "d" its diameter (in inches).
Therefore, you can set up that the equation has this form:
[tex]R=k(\frac{l}{d^2})[/tex]According to the information given in the exercise, when:
[tex]\begin{gathered} l=3300 \\ d=0.16 \end{gathered}[/tex]The resistance is:
[tex]R=10357[/tex]Then, you can substitute values into the equation and solve for "k":
[tex]\begin{gathered} 10357=k(\frac{3300}{(0.16)^2}) \\ \\ (10357)(\frac{(0.16)^2}{3300})=k \end{gathered}[/tex][tex]k\approx0.080[/tex]Therefore, you can set up the following equation that represents this situation (using the value of "k"):
[tex]R=0.080\cdot\frac{l}{d^2}[/tex]Hence, if:
[tex]\begin{gathered} l=2900 \\ d=0.15 \end{gathered}[/tex]You can substitute these values into the equation and then evaluate, in order to find the corresponding resistance. This is:
[tex]\begin{gathered} R=0.080\cdot\frac{(2900)}{(0.15)^2} \\ \\ R\approx10311.11 \end{gathered}[/tex]Therefore, the answer is:
[tex]10311.11\text{ }ohms[/tex]
hello) i need some help with b) include an explanation if not a problem, thanks in advance)
What would happen if X doesn't lie on OM? If it is true that X lies on OM, if we suppose the opposite then we should have a contradiction, so the only way the contradiction doesn't happen is that it is true
Statements1. We know that BX:XA = 1:2
2. We know that M is the middle point between B and P
We need to prove that X lies on OM
Let's suppose X doesn't lie on OM
By 2, we know that 2BM = BP
If X doesn't lie on OM then the intersection between OM and BA is not X
Let's say the line that goes from O to the line BP and intersects BA on X is OX', where X'≠M
Frank has a circular Garden the area of the garden is 100 ft Square what is the approximate distance from the edge of Frank's garden to the center of the garden (A= 3.14r ² )
ANSWER
[tex]5.64ft[/tex]EXPLANATION
The approximate distance from the edge of the garden to the center is the radius of the garden.
The area of a circle is given as:
[tex]A=\pi\cdot r^2[/tex]We can find the radius by making r the subject of the formula:
[tex]\begin{gathered} \frac{A}{\pi}=\frac{\pi\cdot r^2}{\pi} \\ r^2=\frac{A}{\pi} \\ r=\sqrt[]{\frac{A}{\pi}} \end{gathered}[/tex]Therefore, the approximate distance from the edge of the garden to the center (radius) is:
[tex]\begin{gathered} r=\sqrt[]{\frac{100}{3.14}} \\ r=\sqrt[]{31.85} \\ r\approx5.64ft \end{gathered}[/tex]That is the answer.
is this left continuous at x=2?from those intervals pleases answer the part of the question asking if left or right continuous and where
Not, the left graph is discontinuous in x=2, the kind of discontinuity is removable discontinuity. It is not continuous because in x=2 there us a abrupt change in the function value.
To determine if the function is left or right continuous you identify if the function in a jump discontionuity has the defined point on the left or on the right.
The function given in number 11 has a jump discontinuity at x=3, as the defined point is on the part of the graph on the left, you say the function is left continuous at x=3.
Answer: left continuous at endpoint x=3Write a simplified expression for the model below. 1 1 -1 -1 х X X х х -X -X 1 1 ו-ווו-| 1 1 1 -1 ||-1
we have the following:
[tex]\begin{gathered} 4\cdot(x)+2\cdot(-x)+6\cdot(1)+6\cdot(-1) \\ 4x-2x+6-6 \\ 2x \end{gathered}[/tex]therefore, the answer is 2x
what is the common difference in the sequence 25,20,15,10...?
We have a arithmetic sequence: 25, 20, 15, 10...
Tipically, arithmetic sequences can be written in recursive form as:
[tex]a_n=a_{n-1}+d[/tex]where a(n) and a(n-1) are consecutive terms and d is the common difference.
In this case, we can see that each term decreases by 5 units.
Then, we can describe this sequence as:
[tex]a_n=a_{n-1}-5[/tex]which means that d = -5.
Answer: the common difference is d = -5.
y varies directly as x. y =84 when x=6. Find y when x=12y= ?
If y varies directly as x, we have that
[tex]y\propto x[/tex]Then
[tex]y=kx(where\text{ k is a constant\rparen}[/tex][tex]\begin{gathered} When\text{ y=84 , x= 6} \\ y=kx \\ 84=6k \\ k=\frac{84}{6}=14 \end{gathered}[/tex]The relationship between x and y is given as
[tex]\begin{gathered} y=kx \\ y=14x \end{gathered}[/tex]Therefore when x= 12, y=?
[tex]\begin{gathered} y=14x \\ y=14\times12=168 \end{gathered}[/tex]Hence, the value of y when x = 12 is 168
Final answer: y = 168
The radius of a quarter circle is 3 millimeters. What is the quarter circle's perimete r=3 mm ude 3.14 for .. millimeters Submit can you explain
Given:
The radius of the quarter circle is given 3 mm.
To find:
The perimeter of the quarter circle.
Solution:
It is known that the perimeter of the quarter circle is given by:
[tex]2r+\frac{\pi r}{2}[/tex]So, the perimeter of the quarter circle:
[tex]\begin{gathered} P=2r+\frac{\pi r}{2} \\ =2(3)+\frac{3.14\times3}{2} \\ =6+4.71 \\ =10.71 \end{gathered}[/tex]Thus, the perimeter of the quarter circle is 10.71 mm.
Pls help now You play a game that requires rolling a 6 sided die then randomly choosing a colored card from a deck containing 5 red cards,4blue cards, and 8 yellow cards find the probability that you will roll 3 on the die and choose a yellow card
Find the probability that you will get a 3 on a roll of a die. Since there is only one 3 in a die and there are 6 sides in a die, divide 1 by 6.
[tex]P(3)=\frac{1}{3}[/tex]Find the probability that you will get a yellow card. Divide the number of yellow cards by the total number of cards.
[tex]\begin{gathered} P(y)=\frac{8}{5+4+8} \\ =\frac{8}{17} \end{gathered}[/tex]Since the two events are independent, multiply the obtained probabilities.
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Two boats leave the same marina. One heads north, and the other heads
east. After some time, the northbound boat has traveled 39 kilometers, and
the eastbound boat has traveled 52 kilometers. How far apart are the two
boats
The distance travelled by the two boats forms a right triangle. Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.
It is given to us that -
There are two boats
One boat heads north while the other heads east
The boat travelling north has traveled 39 kilometers
The boat travelling south has traveled 52 kilometers
We have to find out the distance between the two boats after they have travelled the respective distances.
It is known to us that one boat heads north while the other heads east. We can see that the trajectory formed between the two boats resembles a right triangle as they start from the same point.
One leg of the right triangle formed equals to the distance travelled by the boat travelling north.
Let us say the distance travelled by the boat travelling north be "a".
=> a = 39 kilometers ----- (1)
Other leg of the right triangle formed equals to the distance travelled by the boat travelling east.
Let us say the distance travelled by the boat travelling east be "b".
=> b = 52 kilometers ------ (2)
Now, the distance between the two boats after they have travelled the respective distances is equal to the value of the hypotenuse of the right triangle formed.
Let us say the hypotenuse of the right triangle formed be "h".
According to the Pythagorean Theorem for a right triangle,
[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (3)
where, a, b = legs of the right triangle
and, h = hypotenuse of the right triangle
Substituting the values of a and b from equations (1) and (2) respectively in equation (3), we have
[tex]a^{2} +b^{2} =h^{2}\\= > 39^{2} +52^{2} =h^{2}\\= > h^{2}=1521+2704\\= > h^{2}=4225\\= > h=65[/tex]
So, the value of the hypotenuse of the right triangle formed is 65 kilometers.
Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.
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a bank account principal is $1,000 and accumulate yearly interest at 6%. assuming that no withdrawals are made, use the compound interest formula to compute the amount in the account after 10 yearsIf interest is compounded yearly, what is the amount of money after t = 10 years?
The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the rate in decimal
n is the number of periods per year
t is the time in years
Since the principal is $1000, then
P = 1000
Since the yearly interest rate is 6%, then change it to decimal by dividing it by 100
r = 6/100 = 0.06
Since the interest is compounded yearly, then
n = 1
Since the time is 10 years, then
t = 10
Substitute them in the rule above
[tex]\begin{gathered} A=1000(1+\frac{0.06}{1})^{(1)(10)} \\ A=1000(1.06)^{10} \\ A=1790.847697 \end{gathered}[/tex]The amount of money in the account after 10 years is $1790.847697