Using the formula for population density, it is found that the approximate area of Puerto Rico is of 3980 square miles.
What is the formula for population density?It is given by the number of habitants divided by the area, that is:
[tex]D = \frac{H}{A}[/tex]
In this problem, we have that:
Puerto Rico has a population of [tex]H = 3.98 \times 10^6[/tex].The density is of about 1000 people per square mile, that is, [tex]D = 10^3[/tex].Hence:
[tex]D = \frac{H}{A}[/tex]
[tex]10^3 = \frac{3.98 \times 10^6}{A}[/tex]
[tex]A = \frac{3.98 \times 10^6}{10^3}[/tex]
A = 3980.
The approximate area of Puerto Rico is of 3980 square miles.
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Write an equation and solve it. Anything goes as long as you address the following points:
a. The equation must start with an 'x' variable in an exponent. B. The equation must require logarithms to solve. C. In the solution you must use the power rule, the product rule and the quotient rule at least once each. D. Explain each step as you solve; which rules are you using and why?
e. What challenges did you face as you were writing your problem? Did you run into any dead ends?
Im having trouble thinking up an equation that uses all three rules. The power rule, the product rule, and the quotient rule. I can create one that uses 2 but i cant quiet imagin 3. Im probably just not thinking about it in the right way but any help would be appreciated.
The equation is 4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where 'a' is a constant and a>1
After following the rules to model the equation.
The equation becomes:
[tex]\rm 4^3^x= 8^{1/x}\times 2^{x+3}[/tex]
After solving, we get:
[tex]2^{6x}= 2^{3/x \ +x+3}[/tex] (power rule)
Taking log on both sides with base 2
[tex]\rm log_2(2^{6x})= log_2(2^{3/x \ +x+3})[/tex]
After solving, we will get a quadratic equation:
[tex]\rm 5x^2-3x-3 = 0[/tex]
After using quadratic formula, we will get,
[tex]\rm x=\dfrac{3+\sqrt{69}}{10}[/tex] or
[tex]\rm x=\dfrac{3-\sqrt{69}}{10}[/tex]
Thus, the equation is 4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)
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a train traveled 162 miles in 3hours. At that rate, how many miles will the train travel in 1/3 hour?
Answer:
18 miles
Step-by-step explanation:
162 ÷ 3 × ⅓ = 18 miles
Hope this helps =)
A book bag was bought on a 45% off sale for $65.87. What was the original price rounded to the nearest cent.
Answer: 119.76 approx to 119.8
Step-by-step explanation:
55 % = 65.87
1% = 65.87/55
100% = 65.87/55 × 100/1
The price of a computer is marked down from $550 to $484 for a sale. The
following week, the computer is marked down again by the same percent as
during the week before. How much lower than the original price is the price after
the second markdown?
A $425.92
C
$124.08
B $132.00
D
$58.08
Answer:
A) $425.92
Step-by-step explanation:
The new price percentage with relation to the previous can be determined by dividing [tex]p = \frac{484}{550}[/tex]. Once we calculate p, we can multiply it by 484, which is equivalent to applying the same discount, thus [tex]\frac{484}{550}484=425.92[/tex]
Help me find X and explain the process please.
Answer:
x=23
Step-by-step explanation:
10*18=9*(x-3)
180=9x-27
207=9x
x=23
I may be wrong its been a long time doing this problem.
Which equation can be used to solve for the measure of angle abc? tan(x) = startfraction 2.4 over 10 endfraction tan(x) = startfraction 10 over 2.4 endfraction sin(x) = startfraction 10 over 10.3 endfraction sin(x) = startfraction 10.3 over 10 endfraction
The equation can be used to solve for the measure of angle abc is sinx = 2.4/10.3
SOH CAH TOA identityThe identity is used to find the measure of sides and acute angles of a right triangle
From the diagram shown, <ABC is the reference abgle hence;
Opposite side = 2,4cm
Hypotenuse .=10.3cm
According to the identity
sin x = opp/hyp
sinx = 2.4/10.3
sinx = 0.233
x = 13.47 degrees
Hence the equation can be used to solve for the measure of angle abc is sinx = 2.4/10.3
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Answer: tan(x) = 2.4/10.3
Step-by-step explanation:
I saw the answers
If the rent of flat is Rs. 3,60,000 for one year, find the monthly rent of the flat.
The division is one of the four fundamental arithmetic operations. The rent of the flat for each month will be Rs. 30,000.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that the rent of the flat for one year is Rs. 3,60,000. Since a year has 12 months. Therefore, the rent for each month will be,
[tex]\rm \text{Rent for one month} = \dfrac{Rs.\ 3,60,000}{12} = Rs.\ 30,000[/tex]
Hence, the rent of the flat for each month will be Rs. 30,000.
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has the lowest unit price?
A. 20 oz: $9
B. 16 oz: $7.39
ch proportion.
C. 12 oz: $5.29
D. 5 oz: $2.39
PLS HELP ASAP! (show work)
Solve the compound inequality.
3 < 2x − 1 < 9
Answer: x = 2
Step-by-step explanation:
(Pls help ASAP) (Willing to give 15 points for 2 answers) (Pls don't answer if you don't know)
The second one you have to choose GREATER THAN, LESS THAN, OR EQUAL TO
Answer:
what is intercept: intercept simply means a point on the y axis through which a slope passes and also in the equation you were given y = mx + c I mean y = 2x -2 the c is the intercept meaning -2 .
so wherever that straight line meets with with y axis the number at that very point is your intercept.
the y intercept for the first one is -2
and it's "less than" since it's a negative number.
Step-by-step explanation:
Hope this helps.
Good luck✅.
What value of k is the expression x^4+kx^2+36 a perfect square?
[tex]\text{ The discriminant is 0 if the quadratic expression is a perfect square.}\\\\~~~~~b^2 -4ac =0\\\\\implies k^2-4\cdot 1 \cdot 36 = 0\\ \\\implies k^2 - 144 = 0\\\\\implies k^2 = 144\\\\\implies k = \pm\sqrt{144}\\\\\implies k= \pm12\\\\\text{Hence}~ k=12 ~\text{and}~ k=-12.[/tex]
Evaluate the expression when
у = 3 and z = 9.
2
y + (z-7)² x 2
Step-by-step explanation:
[tex]y + (z - 7) {}^{2} \times 2 \\ 3 + (9 - 7) {}^{2} \times 2 \\ 3 + (2) {}^{2} \times 2 \\ 3 + 4 \times 2 \\ 3 + 8 = 11[/tex]
Find the y-intercept of the line: 2x + 4y = 8
Question 2 options:
(2,4)
(0,2)
(4,0)
(4,2)
Answer:
(4, 0)
Step-by-step explanation:
2x + 4y = 8
x-intercept when y = 0
2x = 8
x = 4
so x-intercept (4, 0)
:) hole this helps
Find the standard deviation, correct to 2 decimal places.
Data Set: 10, 12, 12, 16, 24
Mean 14.8
Answer:
5
Step-by-step explanation:
Step 1: Mean
10+12+12+16+24
=74/5
=14.8
Step 2: Standard Deviation
Formula----- square root of varieance
23.04+7.84+7.84+1.44+84.64/5
124.8/5
24.96
[tex]\sqrt{24.96}[/tex]
4.996
5
Tell me the answer please 6*5=
Answer:
6*5=30
Step-by-step explanation:
Answer: 30
Step-by-step explanation: it means multiply 6 by 5
75-90 divided by 6 HELP ME ASAP PLS
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 39
Step-by-step explanation:
all triangles have angle measures that add up to 180°.
This means that to find what x is, you add 102 and 39, and then subtract that from 180, so
180-(102+39) = x
180-141=x
39=x
Answer:
x° = 39°
Step-by-step explanation:
According to the angle sum property of triangles, the 3 angles in a triangle will sum up to 180°.
102° + 39° + x° = 180°
141° + x° = 180°
x° = 180° - 141°
x° = 39°
_________
Hope it helps ⚜
If a wave has a wavelength of 0.5 m and a frequency of 2134 Hz, what is its speed? *SHOW ALL 4 STEPS.
wave length= 0.5 m
frequency= 2134 Hz
to find:the speed
solution:[tex]v = f \gamma [/tex]
[tex]v = velocity[/tex]
[tex]f = frequency[/tex]
[tex] \gamma = wave \: length[/tex]
[tex]v = 2134 \times 0.5[/tex]
[tex]v = 1067s[/tex]
hence, the speed of the wave is 1067s.
Jim has 1/3 of a box of cereal. He eats 1/3 of the remaining cereal. What fraction of the original whole box of cereal did Jim eat?
Which of the following points lie in the solution set to the following system of inequalities?
y < −3x + 3
y < x + 2
(1, −5)
(1, 5)
(5, 1)
(−1, 5)
Answer:
(1, −5)
Step-by-step explanation:
Because in this case it is less than and the -3x would be cancelled out and I had this question and that correct answer was A(1,-5).
Hope this helps:)
Answer:
the answer is (1,-5)
Step-by-step explanation:
plug in the x and y values and see if they are true
y<-3x+3
(-5)<-3(1)+3
-5<-3+3
-5<0 is true
y<x+2
(-5)<(1)+2
-5<1+2
-5< 3 is true also
The area of a circle is 9π ft What is the circumference, in feet? Express your answer in terms of \piπ. (pi)
Answer:
6×pi ft
Step-by-step explanation:
the area of a circle is
pi × r²
with r being the radius of the circle.
so,
9×pi = r² × pi
9 = r²
r = 3 ft
the circumference of a circle is
2×pi× r
that means in our case it is
2×pi×3 = 6×pi ft
PLEASE HELP ME!!!!
Given that f(x)=x+2 and g(x)=3x^2-1. What is (fg)(x)?
Answer: ???
PLEASE EXPLAIN YOUR REASONING!!
Done!
5. On a test, 85% of the students
scored higher than 70. If there are
40 students in the class, how many
more students scored higher than
70 than students who did not? ?
When computing a correlation coefficient, if you have 55 degrees of freedom, your sample size must be ______. Group of answer choices 56 57 54 58
Considering that you have 55 degrees of freedom, your sample size must be of 56.
What is the amount of a degrees of freedom in a sample?It is given by one less than the sample size.
In this problem, you have 55 degrees of freedom, hence:
n - 1 = 55
n = 56.
Your sample size must be of 56.
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Need help! Its For Khan Academny
Answer:
Your 3 answers are
A) y=0.25xC) GraphE) TableStep-by-step explanation:
If you were to graph them and compare the original graph they are exactly the same.
A) y=0.25x is the same thing as y= 1/4 * x
slope m is 1/4 on the original graph and given decimal form.
C) Is the same graph but the point given is at (4,1)
E) is the points between 6<x<8 and 1.5<y<2 as the original graph.
Thang decided to borrow $7000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 6%. How much interest will Thang pay?
Answer:
$420
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answer:
i odnt know use ur fingers or a calculator
Step-by-step explanation:
A bottle of vitamins has 90 capsules in it. Each capsule has 450 milligrams of the supplement. What is the total number of grams of the supplement in one capsule?
The total number of grams of the supplement in one capsule will be 0.45 grams.
What is unit conversion?The measurement of any quanity is expressed by its unit. Now the units for the same matter can be expressed in different ways for higher quanity or lower quanity so we need to convert the units for the calculations.
Here in the question
Each capsule has 450 miligrams of supplement.
Total grams in one capsule will be calculated by unit conversion
[tex]\rm 1 \ gram=1000\ miligram\\\\\\1 \ Mg=\dfrac{1}{1000}\ gram\\\\\\450\ Mg=\dfrac{450}{1000}\ gram\\\\\\450 Mg=0.45\ gram[/tex]
Hence the total number of grams of the supplement in one capsule will be 0.45 grams.
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I need help, i cant use calculator
Answer: True.
Step-by-step explanation:
This inequality is ALWAYS true.
Hope this helps!
The number of weeds found growing along the side
number
of a new highway each month forms the sequence whose general term is a, = (n + 1)(n +4), where n is the
of the months. Find the number of weeds found in the fifth month, and find the total number found in the first five months.
How many weeds were found in the fifth month? 54
How many weeds were found during the first five months? _
270 = 54 x 4 Hope you have great day!