Answer:
A.) 1508 ; 1870
B.) 2083
C.) 3972
Step-by-step explanation:
General form of an exponential model :
A = A0e^rt
A0 = initial population
A = final population
r = growth rate ; t = time
1)
Using the year 1750 and 1800
Time, t = 1800 - 1750 = 50 years
Initial population = 790
Final population = 980
Let's obtain the growth rate :
980 = 790e^50r
980/790 = e^50r
Take the In of both sides
In(980/790) = 50r
0.2155196 = 50r
r = 0.2155196/50
r = 0.0043103
Using this rate, let predict the population in 1900
t = 1900 - 1750 = 150 years
A = 790e^150*0.0043103
A = 790e^0.6465588
A = 1508.0788 ; 1508 million people
In 1950;
t = 1950 - 1750 = 200
A = 790e^200*0.0043103
A = 790e^0.86206
A = 1870.7467 ; 1870 million people
2.)
Exponential model. For 1800 and 1850
Initial, 1800 = 980
Final, 1850 = 1260
t = 1850 - 1800 = 50
Using the exponential format ; we can obtain the rate :
1260 = 980e^50r
1260/980 = e^50r
Take the In of both sides
In(1260/980) = 50r
0.2513144 = 50r
r = 0.2513144/50
r = 0.0050262
Using the model ; The predicted population in 1950;
In 1950;
t = 1950 - 1800 = 150
A = 980e^150*0.0050262
A = 980e^0.7539432
A = 2082.8571 ; 2083 million people
3.)
1900 1650
1950 2560
t = 1900 - 1950 = 50
Using the exponential format ; we can obtain the rate :
2560 = 1650e^50r
2560/1650 = e^50r
Take the In of both sides
In(2560/1650) = 50r
0.4392319 = 50r
r = 0.4392319/50
r = 0.0087846
Using the model ; The predicted population in 2000;
In 2000;
t = 2000 - 1900 = 100
A = 1650e^100*0.0087846
A = 1650e^0.8784639
A = 3971.8787 ; 3972 million people
What is the following product? Assume x>0 and y>0 v5x^8y^2•v10^3•v12y
Answer:
[tex]10x^{5}y \sqrt{6xy}[/tex]
Step-by-step explanation:
x °
68°
26 °
Find the measure of x (Hint: The sum of the measures
of the angles in a triangle is 180°
Answers:
6 °
86 °
90 °
180 °
Answer:
86°
Step-by-step explanation:
180° is the sum of all angles in a triangle
The two angles given are 68° and 26°
The equation is : 180° - 68° - 26° = x°
180° - 68° - 26° = 86°
x° = 86°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
How do you complete the other two?
I know how to complete the first one but 3D Pythag confuses me so much
For now, I'll focus on the figure in the bottom left.
Mark the point E at the base of the dashed line. So point E is on segment AB.
If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is
a^2+b^2 = c^2
c = sqrt(a^2+b^2)
c = sqrt((8.4)^2+(8.4)^2)
c = 11.879393923934
which is approximate. Squaring both sides gets us to
c^2 = 141.12
So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12
------------------------------------
Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.
EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28
In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56
Applying another round of pythagorean theorem gets us
a^2+b^2 = c^2
b = sqrt(c^2 - a^2)
CE = sqrt( (CB)^2 - (EB)^2 )
CE = sqrt( 70.56 - 35.28 )
CE = 5.939696961967
It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.
Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)
------------------------------------
Now let's focus on triangle CED
We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.
We'll use the pythagorean theorem once more
c = sqrt(a^2 + b^2)
ED = sqrt( (CE)^2 + (CD)^2 )
ED = sqrt( 35.28 + 70.56 )
ED = 10.2878569196893
This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).
Answer: 10.3==============================================================
Now I'm moving onto the figure in the bottom right corner.
Draw a segment connecting B to D. Focus on triangle BCD.
We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.
Like before, we'll turn to the pythagorean theorem.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
BD = sqrt( (BC)^2 + (CD)^2 )
BD = sqrt( (3.7)^2 + (3.7)^2 )
BD = 5.23259018078046
Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE
a^2 + b^2 = c^2
b = sqrt( c^2 - a^2 )
ED = sqrt( (EB)^2 - (BD)^2 )
x = sqrt( (5.9)^2 - (5.23259018078046)^2 )
x = sqrt( 34.81 - 27.38 )
x = sqrt( 7.43 )
x = 2.7258026340878
x = 2.7
--------------------------
As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)
The 3D version of the pythagorean theorem is
a^2 + b^2 + c^2 = d^2
where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9
So we get the following
a^2 + b^2 + c^2 = d^2
c = sqrt( d^2 - a^2 - b^2 )
x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )
x = 2.7258026340878
x = 2.7
Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.
Answer: 2.7Answer:
Qu 2 = 10.3 cm
Qu 3. = 2.7cm
Step-by-step explanation:
Qu 2. Shape corner of a cube
We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.
8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm
BD = AB = 11.9 cm Base of cube.
To find height x we split into right angles
formula slant (base/2 )^2 x slope^2 = 11.8920141^2 - 5.94600705^2 = sq rt 106.065
= 10.2987863
height therefore is x = 10.3 cm
EB = 5.9cm
BC = 3.7cm
CE^2 = 5.9^2 - 3.7^2 = sqrt 21.12 = 4.59565012 = 4.6cm
2nd triangle ED = EC- CD
= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264
ED = 2.7cm
x = 2.7cm
Movie genres. The pie chart summarizes the genres of 120 first-run movies released in 2005. a) Is this an appropriate display for the genres
Answer:
Yes, it is appropriate
Step-by-step explanation:
Given
See attachment for pie chart
Required
Is the pie chart appropriate
The attached pie chart displays the distribution of each of the 4 genre. The partition occupied represents the measure of each genre.
rank the three fractions from smallest to largest? and why
2/7, 4/14, 8/11
Answer:
2/7 = 4/14 so from smallest to largest the fractions are:
2/7 4/14 and 8/11
Step-by-step explanation:
A student sees a newspaper ad for an apartment that has 1330. How many square meters of area are there
Answer:
[tex]Area = 123.55 m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 1330ft^2[/tex]
Required
Convert to [tex]m^2[/tex]
To convert from square feet to square meter, we simply divide by 3.281^2
So, we have:
[tex]Area = \frac{1330}{3.281^2}m^2[/tex]
[tex]Area = \frac{1330}{10.765}m^2[/tex]
[tex]Area = 123.55 m^2[/tex]
Evaluate 12 sin 85° correct to two decimal places.
Answer:
12 x sin(85)
12x 0.99619
155.40
Solution:
12 x sin (85) = 11.95 (Since sin85 is 0.996194)
So, the answer is 11.95.
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 5?
Answer:
1/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
probability that the ticket drawn has a number which is a multiple of 5 =
Number of tickets that are a multiple of 5 / total number of tickets
Multiple of 5 = 5, 10, 15, 20
there would be 4 tickets that would be a multiple of 5
= 4/20
To transform to the simplest form. divide both the numerator and the denominator by 4
= 1/5
74. A portion of a board has length x feet. The other part has
length (7x – 9) feet. Express the total length of the board
as a simplified expression in x.
Step-by-step explanation:
Given that,
Length of the one portion of the board = x feetLength of the another portion = (7x – 9) feetAccording to the question,
[tex]\longrightarrow[/tex] Total length = Sum of the length of the two pieces
[tex]\longrightarrow[/tex] Total length = {x + (7x – 9)} feet
[tex]\longrightarrow[/tex] Total length = {x + 7x – 9} feet
[tex]\longrightarrow[/tex] Total length = (8x – 9) feet
Therefore, the total length of the board as a simplified expression in x is (8x – 9) feet.
When P(x) is divided by (x - 1) and (x + 3), the remainders are 4 and 104 respectively. When P(x) is divided by x² - x + 1 the quotient is x² + x + 3 and the remainder is of the form ax + b. Find the remainder.
Answer:
The remainder is 3x - 4
Step-by-step explanation:
[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]
So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]
In this case our dividend is always P(x).
Part 1
When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]
When [tex]x = 1[/tex],
[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]
--------------------------------------------------------------------------------------------------------------
Part 2
When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]
When [tex]x = -3[/tex],
[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]
--------------------------------------------------------------------------------------------------------------
Part 3
When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]
We will call [tex]a + b = -1[/tex] equation 1
From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]
We will call [tex]3a - b = 13[/tex] equation 2
Now we can create a system of equations using equation 1 and equation 2
[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]
By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]
So equation 1 + equation 2:
[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]
Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.
So substituting [tex]a = 3[/tex] into equation 1:
[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]
Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.
So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:
[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]
Therefore, the remainder is [tex]3x - 4[/tex].
5.
Tax: The property taxes on a house were
$1050. What was the tax rate if the house was
valued at $70,000?
Answer:
1.5%
Step-by-step explanation:
house value x property tax rate = property taxes
70,000 x property tax rate = 1050
property tax rate = 1050/70000
property tax rate = .015 0r 1.5%
2 (m+n) +m=9
3m-3n = 24
Answer:
m=5
n=-3
Step-by-step explanation:
3m+2m=9
3m-3n=24
3(5)+2(-3)=9
15-6=9 correct
Find the standard deviation of the following data. Round your answer to one decimal place. x 0 1 2 3 4 5 P(X
Answer:
[tex]\sigma = 1.8[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]
Required
The standard deviation
First, calculate the expected value E(x)
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]
[tex]E(x) = 2.7[/tex]
Next, calculate E(x^2)
[tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]
[tex]E(x^2) = 10.5[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]
[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]
[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]
[tex]\sigma = \sqrt{3.21}[/tex]
[tex]\sigma = 1.8[/tex] --- approximated
How do I find the image after it’s been rotated 270 degrees about the point (-2,-1)?
Answer: (-1, 2)
Step-by-step explanation:
It's a counter-clockwise rotation, that means (x, y) changes to (y, -x).
(-2, -1) ⇒ (-1, -(-2)) ⇒ (-1, 2)
If it's a clockwise rotation, then (x, y) will change to (-y, x)
(-2, -1) ⇒ (-(-1), -2) ⇒ (1, -2)
I didn't understand this to be honest I thought I had to find what jm and lm were together and then subtract from the whole total...but ended up being wrong. whats the correct answer?
Answer:
The correct answer is 3x-2
Step-by-step explanation:
It gives you the expression for JM and LM, and it asks for JL. Therefore, if you take away LM from JM, you are left with JL. You must subtract 2x-6 from 5x-8.
∴5x-8-(2x-6)
Do not forget to distribute the negative since you are subtracting, so instead of subtracting 6 from 8, you will be adding 6 to 8 because two negatives make a positive.
round 6.8 to nearest hundredth
Answer:
6.8
Step-by-step explanation:
The number is already rounded to the nearest tenth and hundredth.
The square root of the variance is called the: standard deviation beta covariance coefficient of variation
Answer:
standard deviation
Step-by-step explanation:
When Claire chooses a piece of fruit from a fruit bowl, there is a 22% chance that it will be a plum, an 18%
chance that it will be an orange, and a 60% chance that it will be an apple. Which type of fruit is she least likely
to choose?
Answer:
Orange
Step-by-step explanation:
As the chance of choosing orange is 18% which is the least.
PLEASE ANSWER ILL MARK !!
Step-by-step explanation:
a) Use sine law:
[tex]\dfrac{g}{\sin 60} = \dfrac{17\:m}{\sin 49}[/tex]
Solving for g,
[tex]g = \left(\dfrac{\sin 60}{\sin 49}\right)(17\:m)=19.5\:m[/tex]
b) Use the cosine law here:
[tex]q^2 = (11\:\text{cm})^2 + (16\:\text{cm})^2 \\ - 2(11\:\text{cm})(16\:\text{cm})\cos 29[/tex]
Solving for q,
[tex]q = 8.3\:\text{cm}[/tex]
Which number is located to the right of on the horizontal number line?
A. -1 1/3
B. -2 1/3
C. -2 2/3
D. -3 1/3
Please help me
Answer:
A
Step-by-step explanation:
since it's negative so it will get smaller
The slope of diagonal OA IS__,
and its equation is__
Answer:
[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA
[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation
Step-by-step explanation:
Given
The attached graph
Solving (a): Slope of OA
First, we identify two points on OA
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
So, the slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4-0}{3-0}[/tex]
[tex]m = \frac{4}{3}[/tex]
Solving (b): The equation
This is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Recall that:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]m = \frac{4}{3}[/tex]
So, we have:
[tex]y = \frac{4}{3}(x - 0) + 0[/tex]
[tex]y = \frac{4}{3}(x)[/tex]
[tex]y = \frac{4}{3}x[/tex]
help pls i don't get the question
Answer:
pretty sure it could
Step-by-step explanation:
Answer:
What it's asking is for 2 angles at different angles of attack, are parallel
Step-by-step explanation:
for example, // these two slashes are parallel because they wont ever touch, it wants you to find if the angles are parallel or not.
Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews a simple random sample of 50 students living in the dormitory. She finds that 14 think the dorm food is good. Find a 90% confidence interval for the true proportion of students that think the dorm food is good.
a. 0.176 to 0.384
b. 28%
c. 0.28 +/- 0.03
d. 0.156 to 0.404
Answer:
Step-by-step explanation:
The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.
Please I need help!!!!!!!!
Answer:
10 is the correct answer
Answer:
Go with the third option 10!
i hope this helped!
answer please I’m dying from math
Answer:
B
substract the variables
Solve the following inequality.
- 202-16
Which graph shows the correct solution?
Which one is the correct answer? help pls!!
Answer:
(2k, k)
Step-by-step explanation:
x + y = 3k
x - y = k
Add the equations.
2x = 4k
x = 2k
2k + y = 3k
y = k
Answer: (2k, k)
please help!! What is the equation of the line that passes through (0, 3) and (7, 0)?
Answer: y= -3/7x + 3
Step-by-step explanation:
I used some graph paper for this, mark the two points and use a ruler to connect the lines. y=-3/7x is slope, and 3 is the y intercept.
Answer:
3x + 7y -2=0
Step-by-step explanation:
Two points are given to us and we need to find the Equation of the line passing through the two points . The points are (0,3) and (7,0) . We can use here two point form of the line as ,
[tex]\implies y-y_1 = \dfrac{y_2-y_1 }{x_2-x_1} ( x - x_1) \\\\\implies y - 3 =\dfrac{3-0}{0-7}(x - 0 ) \\\\\implies y - 3 =\dfrac{-3}{7}x \\\\\implies 7y - 2 = -3x \\\\\implies \underline{\underline{3x + 7y -2 = 0 }}[/tex]
Which of the following shows the graph of y=-(2)^3 – 1?
Answer:
The first graph
Step-by-step explanation:
Given
[tex]y = -(2)^x - 1[/tex]
Required
The graph
Set the exponent part to get the minimum/maximum of the graph
So, we have:
[tex]y = 0 - 1[/tex]
[tex]y = - 1[/tex]
The above implies that the curve passes through the y-axis at [tex]y = - 1[/tex].
By comparing the two graphs, we can conclude that the first represents [tex]y = -(2)^x - 1[/tex] because it passes through [tex]y = - 1[/tex]
Tim and Al are bricklayers. Tim can construct an outdoor grill in 5 days. If Al helps Tim, they can build it in only 3 days. How long
would it take Al to build the grill alone? Write your answer as an integer, simplified fraction, or mixed number.
It would take Al
days to build the grill alone.
Answer:
It would take Al 7.5 days to build the grill alone.
Step-by-step explanation:
Since Tim and Al are bricklayers, and Tim can construct an outdoor grill in 5 days, and if Al helps Tim, they can build it in only 3 days, to determine how long would it take Al to build the grill alone should be done the following calculation:
1/5 + X = 1/3
0.20 + X = 0.333
X = 0.333 - 0.20
X = 0.1333333
X = 1 / 7.5
Therefore it would take Al 7.5 days to build the grill alone.
