Answer:
240.
Step-by-step explanation:
200 * 6/5
= 1200/5
= 240
according to a survey, the population of a city doubled in 12 years.
The annual rate of increase of the population of this city is approximately _____. The population will grow to three times its current size in approximately ______.
First box of answers: 2.50, 5.78, 12.0, 50.0
Second box of answers: 18, 19, 23, 24.
Answer:
5.78
19
Step-by-step explanation:
Let original population be, P = x
Growth in 12 years, A = 2x
Rate be = r
Time = 12years
Find the rate :
[tex]A = P(1 + \frac{r}{100})^t[/tex]
[tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]
The annual rate of increase of the population of this city is approximately 5.78.
Find time in which the population becomes 3 times.
That is A = 3x
P = x
R= 5.78%
[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]
The population will grow to three times its current size in approximately 19years .
5.78% ,19 years are the answers.
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0578*100=5.78%
3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years
What is an exponential growth model?
Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky
exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.
The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.
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Helppppppppp meeeeeeeeeeee
Which of the following steps were applied to ABCD to obtain A'B'C'D'?
PLZZZZ HELP
Answer:
D
Step-by-step explanation:
Since all the points were shifted the same way, I'll just use point A and point A'.
Point A starts at (3,5) and A' is at (5,2)
If the subract the x coordinates: 5-3=2
Then subtract the y coordinates: 2-5=-3
The 2 is positive, so it is 2 units to the right (the positive x direction) and -3 is negative so 3 units down (negative y direction)
Help plz..And No links!! I repeat No links!!
Answer:54 is the54 d
Step-by-step explanation:
no sorry
Which Statement About The Data Is True? 52 56 60 64 68 72 76 80 A. The difference between the medians is about 4 times the range. B. The difference between the medians is about 4 times the IQR. C. The difference between the medians is about 2 times the range. D. The difference between the medians is about 2 times the IQR.
Answer:
The answer is "Option B".
Step-by-step explanation:
IQR for the first boxplot [tex]= Q_3 - Q_1 = 77-73 = 4[/tex]
IQR for the first boxplot [tex]= Q_3 - Q_1 = 63-59 = 4[/tex]
Calculating the median for the first boxplot [tex]= 76[/tex]
Calculating the median for the second boxplot [tex]= 60[/tex]
Calculating the difference:
[tex]\to 76-60 = 16[/tex]
therefore, the difference between medians is about 4 times the IQR.
Answer:
B
Step-by-step explanation:
did the test
Jackson's cupcake recipe calls for 1 3/4 cups of sugar. He plans to make 3 1/2 times the recipe. How much sugar, in
cups, will Jackson need?
Answer:
6 1/8 cups
Step-by-step explanation:
multiply both numbers together
If y = 100 when x = 15, which equation could you use to find the value
of k?
Answer:
y+x=k
Step-by-step explanation:
|48+(-6)|+|-35+7|
Please help me with this! Thank you!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{|48 - 6| + |- 35 + 7|}[/tex]
[tex]\mathsf{|48 - 6| = \boxed{\bf 42}}[/tex]
[tex]\mathsf{= 42 +| -35 + 7|}[/tex]
[tex]\mathsf{|-35 + 7| = \boxed{\bf -28}}[/tex]
[tex]\mathsf{= 42 + |- 28|}[/tex]
[tex]\mathsf{= 42 + 28}[/tex]
[tex]\boxed{\mathsf{= \bf 70}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 70}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
find the midpoint of Line ac
Answer:
-28
Step-by-step explanation:
-2-13=-15
-13-15=-28
Answer:
-28
Step-by-step explanation:
Solve for x.
Please helpppp!
Answer:
Pythagoreas Theorem
Step-by-step explanation:
a^2+b^2=c^2
4^2+b^2=15^2
16+b^2=225
b^2= 209
14.45=b
Which is NOT a proposition
A. Marlon is eating his lunch
B. Will you be at school tomorrow.
C. The earth is rectangular
D. 10 + 5 = 15
Answer:the answer is b
Step-by-step explanation:reason being that the question will you be at school tmrw?cat be given a choice to say wether it’s true or false so Yh...I don’t know if that helped
Find the circumference of a circle whose area is /. A. B. C. D. Please select the best answer from the choices provided A B C D
Answer:
Circumference of circle = (15.5)π cm
Step-by-step explanation:
Missing information:
Area of circle = 60π cm²
Find:
Circumference of circle
Computation:
Area of circle = πr²
Area of given circle = π(Radius of circle)²
60π = πr²
60 = r²
Radius of circle = 7.75 cm (Approx)
Circumference of circle = 2πr
Circumference of circle = 2(π)(7.75)
Circumference of circle = (15.5)π cm
2) find the volume of the trapezoid prism 7in 6in 4in 12in
Answer: 228 in3 (sorry I don’t know how to do the mini number at the top)
Which value for the constant d makes x=-1 an extraneous solution in the following equation? square 8-x = 2x + d. PLEASE
The value for the constant, d which makes x= -1 an extraneous solution is; d=5.
Which value for the constant d makes x=-1 an extraneous solution in the equation?The constant d as given in the task content can be evaluated as follows where, x =-1;
√(8+1) + = 2(-1) +d
√9 = -2 +d
3 = -2 +d.
d = 5.
Read more on equations;
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Answer:
Step-by-step explanation:
Given the function g(x) = 2x2 - 3
Is this statement true or false? g(2) = g(-2)
Twice the complement of an angle is 25 less than 3 times the angle. Find the measure of both angles.
Answer:
Step-by-step explanation:
Let the angles size = x
The complement of the angle is 90 - x
Two times the compliment is 2*(90 - x)
Three times the angle is 3x
25 less than 3 times the angle = 3x - 25
Now you have to equate the two bolded pieces of information.
3x - 25 = 2(90 - x) Remove the brackets
3x - 25 = 180 - 2x Add 25 to both sides
25 25
3x = 205 - 2x Add 2x to both sides.
2x 2x
5x = 205 Divide by 5
5x/5 = 205/5
x = 41
The compliment of x = 90 - 41 = 49
The angle itself = 41
pls help me ill give brainliest and no links pls ty!:)
Given : GH bisects ∠FGI
It means : ∠FGH and ∠HGI are equal
Given :
∠FGH = (5x - 8)°
∠HGI = (6x - 15)°
⇒ 5x - 8 = 6x - 15
⇒ 6x - 5x = 15 - 8
⇒ x = 7°
Substituting the value of x, We get :
∠FGH = 5(7) - 8 = (35 - 8) = 27°
∠HGI = 6(7) - 15 = (42 - 15) = 27°
∠FGI = ∠FGH + ∠HGI = (27 + 27) = 54°
Need help on this please ASAP ????? DUE SOON
Answer:
[tex]33.5\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a cone is given by [tex]V=\frac{1}{3}\cdot r^2\pi\cdot h[/tex], where [tex]r[/tex] is the radius of the cone and [tex]h[/tex] is its height.
What we're given:
[tex]r[/tex] of 2 [tex]h[/tex] of 8Solving, we get:
[tex]V=\frac{1}{3}\cdot 2^2\pi\cdot 8\approx\boxed{33.5}[/tex]
Answer:
The volume of cone is 33.5ft ³.
Step-by-step explanation:
Using Formula,
Volume of cone = 1/3 × π × r ² × h
Where, r is the radius and h is the height of the cone.
We have givenRadius of cone, r = 2 ft
Height of cone , h = 8 ft
substitute the values into the formula
Volume of cone = 1/3 × 3.14 × ( 2ft ) ² × 8ft
Volume of cone = 1/3 = 3.14 × 4 ft ²× 8ft
multiply
Volume of cone = 1/3 × 100.8 ft ³
divide, we get
Volume of cone = 33.50 ft ³.
Therefore,the volume of cone is 33.50 ft³.
Aline having a slope of 3/4 passes through the point (-8,4) What would the
equation look like before you solve it, if you were plugging these numbers into the
slope-intercept equation (y=mx+b)?
HELP ME
Answer:
y=3/4x + 10
Step-by-step explanation:
First, lets put this into Point-Slope form: y-4 = 3/4(x+8)
Now, lets modify the equation in our favor, getting the "y" alone on the left hand side: y-4 = 3/4(x+8)
+4 +4
-----------------------------------------------
y=3/4(x+8)+4
Now, lets simplify....
y=3/4x + 6 + 4 = y = 3/4x+10
And we are done!
A supermarket sells various brands of peanut butter.
• Brand A costs $1.92 per jar, and each jar contains 12 ounces.
• Brand B costs $2.40 per jar, and each jar contains 16 ounces.
Which brand costs less per ounce
Describe the relationship between ∠2 and ∠8
Answer:
Alternate Interior Angles
Step-by-step explanation:
Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.
Answer:
They are alternate interior angles
Step-by-step explanation:
<2 and <8 are inside the parallel lines and on opposite sides of the transversal
They are alternate interior angles
Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below:
Answer:
The answer is "158.489"
Step-by-step explanation:
for san francisco earthquake:
[tex]\log(\frac{a_1}{T}) + B = 7.8\\\\\log(\frac{a_1}{T})+\log(10^{B}) = 7.8\\\\\log(\frac{a_1}{T} \times 10^{B})=7.8\\\\(\frac{a_1}{T} \times 10^B=10^{7.8}...............(i)[/tex]
similarly , for coloumbia earthquake:
[tex]\frac{a_2}{T}\times 10^B = 10^{5.6}.................(ii)[/tex]
divide equation (i) and (ii):
[tex]\frac{a_1}{a_2}=\frac{10^{7.8}}{10^{5.6}}\\\\\frac{a_1}{a_2}=10^{2.2}\approx 158.489[/tex]
[tex]\huge\mathfrak\green{please \: help...} \\ \\ \huge\mathfrak\red{5 {}^{2} + 6 {}^{2} = {?} ...}[/tex]
61 is a required answer.
Answer:
[tex]\boxed{5²+6²=5*5+6*6=25+36=61}[/tex]
What is the volume of the rectangular prism below
Answer:
D. 501,120mm^3
Step-by-step explanation:
Volume of a rectangle:
length x width x height
So, plug in what you know:
80*104.4*60=
501,120mm^3
A study of a population of 102
parrakeets revealed that 4 out
of every 12 parakeets in the
population are blue.
Based on the results of this
study, how many parakeets in
the population are NOT blue?
Answer:
68
Step-by-step explanation:
4 out of 12 are blue.
Then 8 out 12 are not blue.
8 out of 12 is the same as the fraction 8/12 which can be reduced to 2/3.
2/3 of the birds are not blue.
2/3 of 102 = 2/3 * 102 = 68
Answer: 68
Find the missing angle measurements
Answer:
look at picture.
Step-by-step explanation:
every angle in a triangle equals 180° and every straight line equals 180°. So you just take the angles given in each triangle and subtract from 180° to get the total of the 3rd angle.
Help please I need help
find X
Answer:
[tex]x = 145[/tex]
Step-by-step explanation:
1.Approach
To find the value of (x), one will have to take multiple steps. Since a straight line is (180) degrees, one can use this property. Subtract the measure of the exterior angle (the angle formed between the extension of the side of a triangle, and the side of a triangle) from (180) to find an expression to describe the measure of the angle inside the triangle.
Then one is given a regular octagon, using the sum of interior angles formula, find the measure of any interior angle. The vertical angles that when two lines intersect, the opposite angles are congruent. One can use this property to find the final unknown angle in the triangle.
It is known that the sum of angles in a triangle is (180). Use this to find the measure of (x).
2. Find the measure of two angles in the triangle
The degree measure of a straight angle is (180), therefore, when two angles form a straight line, their sum of (180). One can apply this here by stating,
[tex]x+(unknown)=180[/tex]
Solve for unknown,
[tex]unknown = 180 - x[/tex]
One can also state,
[tex]170+(unknown_2)=180[/tex]
Solve for the unknown,
[tex]unknown_2=10[/tex]
3.Find the degree measure of one of the angles in the octagon
The given octagon (eight-sided figure) is a regular octagon. By its definition, all of the sides in any regular polygon are congruent. This is indicated here, thus the octagon is a regular octagon. One property of a regular polygon is that all of the angles in the figure are cognrunet. This means that the sum of interior angles divided by the number of angles wil give one the measurement of each angle.
The formula to find the sum of interior angles in a polygon is as follows,
[tex]S=180(n-2)[/tex]
Where (n) is the number of sides. Since an octagon has (8) sides substitute this number into the formula and solve for the sum of angles,
[tex]S=180(n-2)\\\\S=180(8-2)[/tex]
Simplify,
[tex]S=180(8-2)\\\\S=180(6)\\\\S= 1080[/tex]
Now divide by the number of angles. The number of angles in an octagon is (8). Since this is a regular octagon, all of the angles are congruent, thus dividing the sum of angles by the number of angles will give on the measure of each angle.
[tex]1080[/tex] ÷ [tex]8 = 135[/tex]
4. Find the measure of the final angle in the triangle
The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. Therefore, the final unknown angle in this triangle is equal to (135) degrees, because the angle opposite in the octagon is equal to (135) degrees.
5. Find the meausre of (x)
The sum of angles in any triangle is (180) degrees. Since one has found the measure or expression of the angle measure of each angle in a triangle, one can form an equation and solve for the unknown,
[tex](180-x)+(10)+(135)=180[/tex]
Simplify,
[tex]325-x=180[/tex]
Inverse operations,
[tex]325-x=180\\\\-x = -145\\\\x=145[/tex]
2x+1>
[tex]2x + 1 \geqslant 5 - x[/tex]
5-x
there is a population of 100,000 bacteria in a colony . if the number of bacteria doubles every 3 hours what will be 6 hours from now
Answer:
400,000 bacteria
Step-by-step explanation:
If we start at 100,000 and double every three hours until 6 hours, to colony will be at 400,000 bacteria.
First find out how many times it will double by dividing 6/3=2. It will double twice in 6 hours. Next double 100,000 once, to get 200,000. Then, double it once more to get to the final answer of 400,000 bacteria.
Hope this helps!
True or False? The blue radius is perpendicular to the green cord.
Answer:
true
Step-by-step explanation:
Answer:
False. if it was perpendicular than the segments would be equal
Step-by-step explanation: