Answer:
Step-by-step explanation:
D=4300x /x² + 40.
x = 1
D = 4300 / 41 = 104.88 p / mi²
x = 6
D = 25800 / 76
= 339.47 p / mi²
Population density increases as we go away from city's centre .
b )
x = 10
D=4300x /x² + 40.
D = 307.14 p/ mi²
x = 30
D = 137.23 p / mi²
Population decreases .
c )
when x is very high , density will decrease due to squared denominator whose value increases very fast .
d )
D < 200
4300x /x² + 40 < 200
4300 x < 200 x² + 8000
43 x < 2 x² + 80
2 x² - 43 x + 80 > 0
( x - 19.44 ) ( x - 2.05 ) > 0
Range x < 2.05
x > 19.44
A couch sells for $820. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $400 down and $60 per month for 12 months. How much is saved by paying the total amount at the time of purchase?
Answer:
$300
Step-by-step explanation:
The couch is sold in two ways; outright payment or installment payment.
Outright payment would cost = $820
Installment payment = down payment + monthly charges
Down payment = $400
Monthly charges for a period of one year (12 months) = 12 × $60
= $720
Installment payment would cost = $400 + $720
= $1120
Amount saved by paying total amount at the time of purchase = $1120 - $820
= $300
Thus, the outright buying the couch would save $300.
Please answer this correctly without making mistakes
Answer:
The distance between the art gallery and the office supply store is 42 miles
Step-by-step explanation:
Notice that the segment that joins the office store with the art gallery, has a length that equal the distance between the art gallery and the bank, plus the distance between the bank and the office supply store. That is;
32.1 mi + 9.9 mi = 42 mi
You are dealt two card successively without replacement from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second is a queen. Round to nearest thousandth
Answer:
0.078
Step-by-step explanation:
The probability P(A) of an event A happening is given by;
P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]
From the question;
There are two events;
(i) Drawing a first card which is a king: Let the event be X. The probability is given by;
P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]
Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.
Also, the total number of sample space = 52, since there are 52 cards in total.
P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;
P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]
Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4
But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.
P(Y) = [tex]\frac{4}{51}[/tex]
Therefore, the probability of selecting a first card as king and a second card as queen is;
P(X and Y) = P(X) x P(Y)
= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078
Therefore the probability is 0.078
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?
Answer:
4 boys
Step-by-step explanation:
Let x represent boys and y represent girls
Hence, x : y = 3 : 2
x/y = 3/2
2x = 3y ------ (1)
x/y + 4 = 3/3
3x = 3(y + 4)
3x = 3y + 12 --------- (2)
From (1): x = 3y/2
Substitute x into (2) we have:
9y/2 = 3y + 12
9y = 6y + 24
9y - 6y = 24
3y = 24
∴ y = 8
From (2) : 3x = 24 - 12 = 12
∴ x = 4
Hence there Four boys
2x + 3 + 7x = – 24, what is the value of x?
14x + 3 = - 24
theeeeen I get stuck, HELP!
Answer:
-3
Step-by-step explanation:
2x + 3 +7x = -24
Add the X together
9x +3 = -24
Bring over the +3. [when you bring over change the sign]
9x = -24 -3
9x = -27
-27 divide by 9 to find X
therefore answer is
x= -3.
Hope this helps
Answer:
x = -3
Step-by-step explanation:
question is
2x + 3 + 7x = -24
First you combine the like terms
2x and 7x you can add them so it will be 9x
so it will then it will be like this:
9x + 3 = -24
now you take the 3 and send it to the other side, and right now the 3 is positive so when it goes to the other side it will turn into -3
so
9x = -24 -3
again now you combine the like terms
-24 -3 = - 27
now you have
9x = -27
now just divide each side by 9
x = -27/9
x = -3
Sorry if this doesnt help
For a certain type of tree the diameter D (in feet) depends on the tree's age t (in years) according to the logistic growth model. Find the diameter of a 21-year-old tree. Please give the answer to three decimal places.
Answer:
[tex]D(21) = 1.612\ ft[/tex]
Step-by-step explanation:
The question has missing details;
[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex]
Given that t = 21
Solve for Diameter, D
To do this, we simply substitute 21 for t in the above function
[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex] becomes
[tex]D(21) = \frac{5.4}{1+2.9e^{-0.01 * 21}}[/tex]
[tex]D(21) = \frac{5.4}{1+2.9e^{-0.21 }}[/tex]
Solve for [tex]e^{-0.21}[/tex]
[tex]D(21) = \frac{5.4}{1+2.9* 0.81058424597}[/tex]
Simplify the denominator
[tex]D(21) = \frac{5.4}{1+2.35069431331}[/tex]
[tex]D(21) = \frac{5.4}{3.35069431331}[/tex]
[tex]D(21) = 1.61160628069[/tex]
[tex]D(21) = 1.612\ ft[/tex] (Approximated)
Hence, the diameter of the 21 year old tree is 1.612 feet
If ABCD is dilated by a factor of 2, the
coordinate of C'would be:
Answer:
(4, 4)
Step-by-step explanation:
All you really need to do is multiply C's original coordinates with the scale factor. So (2, 2), becomes (4, 4).
Answer:
( 4 , 4 )
Step-by-step explanation:
original C coordinates : ( 2 , 2 )
since the problem is telling us to dilate by the factor of 2 we multiply both 2's by 2.
( 2 ‧ 2 ) ( 2 ‧ 2 )
= ( 4 , 4 )
Proving the sum of the Interior Angle Measures of a Triangle is 180
Answer:
theres the screenshot of it
The solution to prove the sum of the interior angles of a triangle is 180° is
∠1 + ∠2 + ∠3 = 180° ( angles in a straight line )
∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the angles inside the triangle are ∠2 , ∠5 and ∠6
Now , the lines l₁ and l₂ are two parallel lines
From the figure ,
The measure of ∠1 = The measure of ∠5 ( alternate interior angles )
The measure of ∠3 = The measure of ∠6 ( alternate interior angles )
Now , for a straight line , the measure of angle = 180°
So , ∠1 + ∠2 + ∠3 = 180° ( angles in a straight line ) ( angle addition )
And , the sum interior angles of a triangle is 180°
So , ∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle ) ( substitution )
Hence , the sum of the angles inside a triangle is 180°
To learn more about triangles click :
https://brainly.com/question/16739377
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You have a spool of ribbon that is 279 inches long. How many 4 1/2-inch pieces can
you cut? Write your answer as a mixed number
Answer:
62
Step-by-step explanation:
Turn 4 and 1/2 into a decimal.
4.5
Divide 279 by 4.5
279/4.5=62
You can cut 62 4 and 1/2 inch pieces.
if the discrimant of a equation is equal to -8, which statement describes the roots? A. there are two complex roots B. there are two real roots C. there is one real root D. there is one complex root
Answer:
Option A
Step-by-step explanation:
If Discriminant < 0 , (Just as -8) the roots are imaginary (Complex) and there are two complex roots.
A cream is sold in a 34-gram container. The average amount of cream used per application is 1 and two ninths grams. How many applications can be made with the container?
Answer:
Total cream = 34g
One application = 1 8/9 =(9+8)/9 = 17/9
Total applications = total cream/one application = 34/(17/9) = 34*9/17 = 18 applications
Step-by-step explanation:
Using the information above regarding the proportion of agenda-less meetings, choose the correct conclusion for this hypothesis test.
H0:p=0.45 ; Ha:p>0.45
The p-value for this hypothesis test is 0.025.
The level of significance is α=0.05
Select the correct answer below:
There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%.
There is NOT sufficient evidence to conclude that the proportion of agenda-less meetings isgreater than 45%.
There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 55%.
There is NOT sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 55%.
Answer: There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%.
Step-by-step explanation:
Given: [tex]H_0:p=0.45 \\ H_a:p>0.45[/tex]
The p-value for this hypothesis test is 0.025.
The level of significance is α=0.05
As p-value< α ∵0.025< 0.05
[if p-value< α , we reject [tex]H_0[/tex]]
then, we reject the null hypothesis.
i.e. We have sufficient evidence to support the alternative hypothesis.
Hence, the correct statement is : There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%.
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 56 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. What should the lengths of the wires be so that the total area of the circle and square combined is as small as possible
Answer:
Step-by-step explanation:
Let the length of first piece be L .
Length of second piece = 56 - L
radius of circle made from first piece
R = L / 2π
Area of circle = π R²
= L² / 4π
side of square made fro second piece
= (56 - L) / 4
area of square = ( 56-L)² / 16
Total area
A = L² / 4π + ( 56-L)² / 16
For smallest possible combined area
dA / dL = 0
dA / dL = 2L / 4π - 2( 56-L)/16 =0
2L / 4π = 2( 56-L)/16
.159 L = 7 - .125 L
.284 L = 7
L = 24.65 inch
other part = 56 - 24.65
= 31.35 inch .
Which is the graph of x – y = 1?
Answer:
Step-by-step explanation:
Hope you can see it.
CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars. Assume the standard deviation is 282 dollars. You take a simple random sample of 55 auto insurance policies. Find the probability that a sample of size n =55 is randomly selected with a mean less than 997 dollars.
Answer: 0.0899.
Step-by-step explanation:
Given: CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars, the standard deviation is 282 dollars.
Sample size : n= 55
Let [tex]\overline{X}[/tex] be the sample mean.
The probability that a sample of size n =55 is randomly selected with a mean less than 997 dollars:
[tex]P(\overline{X}<997)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{997-1048}{\dfrac{282}{\sqrt{55}}})[/tex]
[tex]=P(Z<-1.3412)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(Z<1.3412)\\\\=1-0.9101\ \ \ \ [\text{By z-table}]\\\\ =0.0899[/tex]
Hence, the required probability = 0.0899 .
hi there help me please
Hello!
Answer:
Choice 1.
Step-by-step explanation:
We can go through each answer choice and examine whether it represents the question:
1) This does not represent the question because 10% of 6 is 0.6. The question is asking to find a number that 6 = 10% of, not finding 10% of 6.
2) Correct because a number multiplied by 10%, or 0.1, should be equal to 6 to answer the question.
3) Correct because 6 is equivalent to 10% of the answer, which is stated in this answer choice.
4) Correct because 6 should be 10% of the answer.
Therefore, the incorrect choice would be Choice 1.
I need to know if the following questions are true or false
Answer:
False
Step-by-step explanation:
To find <A, we can do 5x - 80 = 3x + 20.
As we simplify, we will get 2x = 100, which is x = 50
Therefore, <A will be 50 degrees and not 45 degrees.
Also, if you need y, you can do:
3y - 7 = y + 7
2y = 14
y = 7
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 205 yards due west from your position and takes a bearing on the cabin of N 23.9°E. How far are you from the cabin? asap would be great also running out of points srry
Answer:
462.61 yards.
Step-by-step explanation:
To solve, you need to find the measurement of the angle that forms a 90 degree angle with the 23.9 degree angle.
90 - 23.9 = 66.1 degrees.
Now that you have the angle, you can use TOA to solve for x (TOA = Tangent; Opposite over Adjacent).
tan(66.1) = x / 205
x / 205 = tan(66.1)
x = tan(66.1) * 205
x = 2.256628263 * 205
x = 462.6087939
So, you are about 462.61 yards from the cabin.
Hope this helps!
A pile of 55 coins consisting of nickels and dimes is worth $3.90 . Find the number of each. PLZ ANSWER IN 1 MIN
Answer:
23 dimes; 32 nickel
Step-by-step explanation:
Let n = number of nickels.
Let d = number of dimes.
A nickel is worth $0.05; n nickels are worth 0.05n.
A dime is worth $0.10; d dimes are worth 0.1d.
Number of coins:
d + n = 55
Value of the coins:
0.1d + 0.05n = 3.9
Solve d + n = 55 for d:
d = 55 - n
Substitute 55 - n for d in second equation.
0.1(55 - n) + 0.05n = 3.9
5.5 - 0.1n + 0.05n = 3.9
-0.05n = -1.6
n = 32
Substitute 32 for n in d + n = 55 and solve for d.
d + 32 = 55
d = 23
Answer: 23 dimes; 32 nickel
There will be a circular patio with a diameter of 7 metres. Greg is going to put a tiled edge around the patio. What is the circumference of the patio? m Circumference of a circle = 2πr Use π = 3.14
Answer:
[tex]Circumference = 21.99 \ m[/tex]
Step-by-step explanation:
Circumference = [tex]\pi d[/tex]
Given that d = 7 m
[tex]Circumference = (3.14)(7)\\[/tex]
[tex]Circumference = 21.99 \ m[/tex]
Answer:
[tex]\boxed{21.98 \: \mathrm{meters}}[/tex]
Step-by-step explanation:
Apply formula for circumference of a circle.
[tex]C=\pi d[/tex]
[tex]d:diameter[/tex]
Take [tex]\pi =3.14[/tex]
Plug [tex]d=7[/tex]
[tex]C=3.14 \times 7[/tex]
[tex]C= 21.98[/tex]
PLEASE HELP Which ordered pair is a solution to the system of inequalities?
y< 3x
y< 5
Answer:
I am pretty sure that it is C
Step-by-step explanation:
A 1,3 so 3 < 3 no not true
x,y
B -12,50 50< -36 Also not true
x , y
C 9 , 4 4<27 Yes 4< 5 YEPPP
D 4,10 10<12 Yes 10<5 NOOPPPPPEEEE
For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets
Answer:
Step-by-step explanation:
cool
An important proportion that the ancient Greeks used was the
the ancient Greek used the golden ratio
Answer:
An important proportion that the Ancient Greeks used was the Golden Mean, the a0
Step-by-step explanation:
Also known as Golden Ratio, Divine Proportion, or Golden Section
An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 99% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy?
Answer: n = 2401
Step-by-step explanation:
Given;
Confidence level = 2% - 99%
n = ? ( which is the sample size is unknown ).
Solution:
Where;
n = [z/E]^2*pq
Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2
Substituting the given data into the formula.
n = [1.96/0.02]^2(1/2)(1/2)
n = 2401
The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401
how to simplify this expression ?
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }[/tex]
Step-by-step explanation:
Hello,
This is the same method as computing for instance:
[tex]\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}[/tex]
We need to find the same denominator.
Let's do it !
For any x real different from 0, we can write:
[tex]\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
odd function definition
In parallelogram ABCD, the coordinates of A are (4,3) and the coordinates of the midpoint of diagonal AC
are (2,5). What are the coordinates of C?
Answer:
D. (0, 7).
Step-by-step explanation:
Moving from (4,3) to (2, 5) we move 2 to the left; 2 - 4 = 2 then 2 up 3 + 5 = +2.
So the point C is 2-2, 5+2 = (0, 7).
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 109 in. and the height is 198 in.
Answer:
[tex]79591.8872 in^3/s[/tex]
Step-by-step explanation:
we know that the volume of a right circular cone is give as
[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]
Therefore differentiating partially with respect to r and h we have
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]
[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]
[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]
F(x)=8*(1/2)^x table
Answer:
Show the table or make ur question a little more clear so I can help
Step-by-step explanation:
A catering service offers 11 appetizers, 8 main courses, and 4 desserts. A customer is to select 9 appetizers, 3 main courses, and 2 desserts for a banquet. In how many ways can this be done?
Answer:
Total number of required ways = 18480
Step-by-step explanation:
Given that
Total appetizers = 11
Total main courses = 8
Total desserts = 4
To be selected 9 appetizers
3 main courses and
2 desserts.
To find:
Number of ways of selecting them.
Solution:
Number of ways to select 'r' number of items out of 'n' number of items is given as:
[tex]_nC_r = \dfrac{n!}{(n-r)!r!}[/tex]
One important property:
[tex]_nC_r = _nC_{n-r}[/tex]
Here we have 3 items, we will find each items' number of ways of selecting and then will multiply all of them.
Number of ways to select 9 appetizers out of 11 appetizers:
[tex]_{11}C_9\ or\ _{11}C_2 = \dfrac{11 \times 10}{2} = 55[/tex]
Number of ways to select 3 out of 8 main courses:
[tex]_{8}C_3= \dfrac{8 \times 7 \times 6}{6} = 56[/tex]
Number of ways to select 2 desserts out of 4:
[tex]_{4}C_2= \dfrac{4 \times 3}{2} = 6[/tex]
Total number of ways = [tex]55 \times 56 \times 6[/tex] = 18480