Answer:
See explanation
Step-by-step explanation:
Rules to follow when rounding
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Eg: 56 rounded to the nearest ten is 60
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 23 rounded to the nearest ten is 20
3. All the numbers to the right of the place you are rounding to become zero
1.Round 3 601 111 to the nearest million
= 4,000,000
2. Round 17.81 to the nearest whole number
= 18
An whole number is a number without a decimal point
3. Round 59.52 to the nearest 1 d.p.
= 59.5
1 d.p means one digits after the decimal point
4. Round 7.176 to the nearest 2d.p.
= 7.18
2 d.p means two digits after the decimal point
The population of rabbits on an island is growing exponentially. In the year 1998, the population of rabbits was 9400, and by 2006 the population had grown to 32000. Predict the population of rabbits in the year 2011, to the nearest whole number.
Answer: 68,819 rabbits
Step-by-step explanation:
First find the annual rate of growth that took the number of rabbits from 9,400 in 1998 to 32,000 in 2006.
Use the future value formula:
Number of years = 2006 - 1998 = 8 years
Future value formula:
Future value = Current value * ( 1 + rate) ^ number of years
Assume 2006 is the future and 1998 is present.
32,000 = 9,400 * (1 + r) ⁸
32,000 / 9,400 = (1 + r)⁸
(1 + r)⁸ = 3.404255319
1 + r = ⁸√3.404255319
r = ⁸√3.404255319 - 1
r = 16.55%
Use that rate to find the number of rabbits in 2011:
= Current value * (1 + rate) ^ number of years
Number of years = 2011 - 2006 = 5 years
= 32,000 * ( 1 + 16.55%)⁵
= 68,819 rabbits
Simplify the expression (5)2.
25
-10
-25
10
Answer:
10
Step-by-step explanation:
5 (2) is the same as 5 × 2 which equals 10
Answer:
10Step-by-step explanation:
Given here,
(5)2
= 5 × 2.
= 10 (Ans)
Elisa decided to take a vacation. The distance she plans to travel each day will form a geometric sequence
find the value of Y
.....
Answer:
[tex] y = 6 \sqrt{3} \: units[/tex]
Step-by-step explanation:
In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.
By geometric mean theorem:
Length of the perpendicular
[tex] =\sqrt{9\times 3}[/tex]
[tex] =\sqrt{27}\: units [/tex]
Next, by Pythagoras theorem:
[tex] {y}^{2} = {9}^{2} + {( \sqrt{27} )}^{2} \\ \\ {y}^{2} = 81 + 27 \\ \\ {y}^{2} = 108 \\ \\ y = \sqrt{108} \\ \\ y = \sqrt{36 \times 3} \\ \\ y = \sqrt{ {6}^{2} \times 3} \\ \\ y = 6 \sqrt{3} \: units[/tex]
WILL MARK AS BRAINLIEST
Answer:
B
Step-by-step explanation:
mulitiply by 2
Natasha is 50 m due east of Michelle. Natasha walks 20 m due north, and Michelle walks 10 m due
south. Find the distance and bearing of Michelle from Natasha now.
Please use diagrams to explain.
Answer:
Let's define East as the positive x-axis and North as the positive y-axis.
If Michelle's initial position is (0, 0)m
We know that Nathasha is 50m due East of Michelle.
Then the position of Natasha is (50, 0)m
Now we know that Natasha walks 20m due North, then the new position of her's is:
(50, 0 + 20)m = (50, 20)m
While Michelle walks 10m due South (South would be the negative y-axis, then we subtract 10 meters)
Michelle's new position will be:
(0, 0 - 10)m = (0, -10)m
Now we want to know the distance and bearing of Michelle from Natasha.
First, remember that the distance between two points (a, b) and (c, d) is given by:
Distance = √( (a - c)^2 + (b - d)^2)
Then the distance between Michelle and Natasha is:
Distance = √( (50m - 0m)^2 + (20m - (-10m))^2)
Distance = √( (50m)^2 + (30m)^2) = 58.31m
Now to find the bearing you can see the image below:
Point B is Michelle's position and point A is Natasha's position.
To find the bearing, we can make a triangle rectangle as the one shown in the image:
Also remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus).
Where the opposite cathetus is the difference between the x-values of each position, this is:
opposite cathetus = 50m - 0m = 50m
And the adjacent cathetus is the difference between the y-values, this is:
adjacent cathetus = 20m - (-10m) = 30m
Then:
Tan(a) = 50m/30m
Tan(a) = 5/3
Now if we apply the inverse Tan function to both sides, Atan(x) we get:
Atan(Tan(a)) = Atan(5/3)
a = Atan(5/3) = 59°
So the bearing is of 59°.
Calcula el ancho de un terreno rectangular si el largo mide 20 metros y la superficie es de 280 metros cuadrados
Answer:14 m
Step-by-step explanation:
Dada
larga [tex]l=20\ m[/tex]
superficie [tex]A=280\ m^2[/tex]
Suponga que el ancho es w
La superficie está dada por el producto de la longitud y la anchura.
[tex]\therefore A=lw\\\Rightarrow 280=20\times w\\\Rightarrow w=14\ m[/tex]
Por lo tanto, el ancho es de 14 m.
Point P is outside a circle with center O and is 10 cm from the center. The circle has a radius of 5 cm. Lines PA and PB are two different lines tangent to the circle at points A and B.
Find the measure of angle PAO. Round to the nearest whole degree
Find the measure of angle APO. Round to the nearest whole degree
Find the measure of angle AOB. Round to the nearest whole degree
Find PB rounded to the nearest tenth.
9514 1404 393
Answer:
∠PAO = 90°∠APO = 30°∠AOB = 120°PB ≈ 8.7Step-by-step explanation:
A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.
OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.
__
As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.
a bag with 3 red marbles,4 blue marbles and 5 yellow marbles.what is the probability you draw a blue marble?
Answer:
4/12
Step-by-step explanation:
add up all the marbles, and take how many blue marbels there are and put both numbers in fraction form
i need help u guysss
Answer:
Step-by-step explanation:
3 = 1(1 + x)^4
let q = 1 + x
3 = q^4
ln(3) = 4 ln(q)
ln(3)/4 = ln(q)
.274 = ln(q)
q = e^.274 = 1.316
x = .316
Future amount = 48(1+.316)^4
Future amount = 143.96
Which are correct representations of the inequality –3(2x-5) <5(2 - x)? Select two options.
u x<5
. -6x-5 < 10 - X
0 -6x + 15 <10 - 5x
-3
--2
-1
0
2
3
5
to
6
7
-7
1-6
-5
-3 -2 -1 0
2
3
Answer:
Step-by-step explanation:
-6 and up going left
The graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k: a parabola with a vertex of 4, negative 2 What is the value of k?
Answer:
k = -2
Step-by-step explanation:
f(x) = (x − h)² + k
(h, k) is the (x, y) coordinate of the vertex
For a vertex of (4, -2)
h = 4
k = -2
a) Complete the table of values for y = x2 - 4x
ONLY A THANKS
ming mile from his house to the library and 2/3 mile from the library to the grocery store. of 11/12 mile it he goes from his house to the library to the grocery store. It is 1/4 Brandon claims that he walks a total of Which of the following shows whether Brandon is correct and why or why not?
Answer:
Brandon is correct
Step-by-step explanation:
Brandon is running errands for his mother.
It is 1/4 mile from his house to the library and 2/3 mile from the library to the grocery store .
Brandon claims that he walked a total of 11/12 mile if he goes from his house to the library to the grocery store.
Distance from his house to the library = 1/4 mile
Distance from the library to the grocery store = 2/3 mile
Total distance Brandon walks from his house to the library to the grocery store = Distance from his house to the library + Distance from the library to the grocery store
= 1/4 + 2/3
Make both 1/4 and 2/3 have the same denominator to be able to add
The lowest common multiple (LCM) of 4 and 3 is 12
Therefore,
1/4 + 2/3
= (3+8)/12
= 11/12
Total distance Brandon walks from his house to the library to the grocery store = 11/12 mile
Simplify (2x^2 + 4x) - (7x - 3x^2 + 5)
Answer:
5x^2 - 3x -5
Step-by-step explanation:
You simplify the like terms
Remember to use distributive property to do the (7x-3x^2+5) part
Two toy rockets are launched straight up into the air. The height, in feet, of each rocket at t seconds after launch is given by the polynomial equations shown. Write an equation to find the "difference" in height of Rocket A and Rocket B. Rocket A: -15t^2 + 100t and Rocket B: -14t^2 + 85t+3.
Given:
The height, in feet, of each rocket at t seconds after launch is given by the polynomial equations:
Rocket A: [tex]-15t^2+100t[/tex]
Rocket B: [tex]-14t^2+85t+3[/tex]
To find:
The equation to find the "difference" in height of Rocket A and Rocket B.
Solution:
The difference in height of Rocket A and Rocket B is:
Difference = Height of Rocket A - Height of Rocket B
[tex]\text{Difference}=(-15t^2+100t)-(-14t^2+85t+3)[/tex]
[tex]\text{Difference}=-15t^2+100t+14t^2-85t-3[/tex]
[tex]\text{Difference}=(-15t^2+14t^2)+(100t-85t)-3[/tex]
[tex]\text{Difference}=-t^2+15t-3[/tex]
Therefore, the difference in height of Rocket A and Rocket B is [tex]-t^2+15t-3[/tex].
A sequence has a second term of 1 and a common difference of -3.
The fifth term of the sequence is _____.
A)-11
B)-8
C)-5
D)10
Answer:
B
Step-by-step explanation:
firstly as we know that,
nth term of an A.P. is n= a1 + (n-1)d
here d is -3 so, A1 = 1-(-3) = 4
so, 5th term = 4 + ( 5-1)( -3) = 4 + 4(-3) = 4 - 12 = -8
so the answer is -8 which is option B.
Hope this answer helps. I got a little help from my tutors on Gauthmath app which is really good. you can check it out too. :)
4 - (x + 1) = 6
Someone please help :^:
Hope this helps please mark me brainliest
Answer:
x = -3
please help! 10 points, thank you
Answer:
261.5 ft^2
Step-by-step explanation:
Surface Area of a rectangular prism = Length x Width x Height
= 8.5ft x 6ft x 5.5ft
= 261.5 ft
Need help quick and fast!
Solve: x/2 = -10
the / means divided
Answer:
x=-20
Step-by-step explanation:
x=-10•2
• means multipled
I need to show my work but I don’t know how to do these can someone help me??
State if the two triangles are congruent.
Answer:
The triangles are congruent by HL
Step-by-step explanation:
The triangles are right triangles so we can use either HL ( hypotenuse leg) or LL (leg leg) if we know that two sides are congruent
We know one leg is equal to the other by the red line. The hypotenuse is the same since it is the same line.
The triangles are congruent by HL
I need help ASAP I wasn’t paying attention and lowkey forgot all of this
Answer:
35
Step-by-step explanation:
Only if u put x as 35 will the whole triangle sum equal 180 as necessary for the theorem to be true.
Which side lengths do not form a right triangle?
a. 5, 12, 13
b. 10, 24, 28
c. 15, 36, 39
d. 50, 120, 130
Answer:
B.
Step-by-step explanation:
28 is not a multiple of 13.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ASAP PLSSS
Answer:
63
Step-by-step explanation:
mark me brainliest plzzz
[tex]\sf\purple{The\:value\:of\:x\:is\:63.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{3}{8} = \frac{x}{168} \\ \\ ✒ \: \frac{3 \times 168}{8} = x \\ \\ ✒ \: \frac{504}{8} = x \\ \\✒ \: 63 = x[/tex]
Therefore, the value of [tex]x[/tex] is 63.
[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]
[tex] \frac{3}{8} = \frac{63}{168}\\ \\✒ \: 0.375 = 0.375 \\ \\✒ \: L.H.S.=R. H. S [/tex]
Hence verified. ✔
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
which choices are equivalent to the expression below? check all that apply. rad -9 A.3i B.-3 C.irad-9 D.-rad9
Given:
Consider the expression is:
[tex]\sqrt{-9}[/tex]
To find:
The equivalent expression.
Solution:
We have,
[tex]\sqrt{-9}[/tex]
It can be written as:
[tex]\sqrt{-9}=\sqrt{-1\times 9}[/tex]
[tex]\sqrt{-9}=\sqrt{-1}\times \sqrt{9}[/tex]
[tex]\sqrt{-9}=i\times 3[/tex] [tex][\because \sqrt{-1}=i][/tex]
[tex]\sqrt{-9}=3i[/tex]
The expression [tex]3i[/tex] is equivalent to the given expression.
Therefore, the correct option is A.
In the data set below, what is the mean absolute deviation? 3,1,9,9,7
When the outlier(s) are removed, how does the mean change?
The mean decreases by 1.9.
The mean increases by 2.4.
The mean increases by 1.9.
There are no outliers.
Answer:
The mean increases by 2.
Step-by-step explanation:
Find the surface area of the prisms below to create a riddle then scan the qr code to answer the riddle round the nearest tenth if necessary
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the prisms and the riddle are not given.
The riddle aspect of the question cannot be attempted, else there are clues.
So, I will give a general rule on how to calculate the surface areas of prisms.
For rectangular prisms, the surface area is:
[tex]Area = 2*(Length * Width + Length * Height + Width * Height)[/tex]
For the attached rectangular prism, the area is:
[tex]Area = 2 *(10*11 + 11 * 15 + 10 * 15)[/tex]
[tex]Area = 2 *(425)[/tex]
[tex]Area = 850m^2[/tex]
For triangular prisms, the surface area is:
[tex]Area = L + 2 * B[/tex]
Where
[tex]L \to[/tex] Lateral Area
[tex]B \to[/tex] Base Area
The area of the attached triangular prism is:
[tex]L = (a + b + c) * h[/tex]
[tex]L = (6 + 8 + 10) * 12[/tex]
[tex]L = 24 * 12[/tex]
[tex]L = 288[/tex]
[tex]B = \frac{1}{2} * bh[/tex]
[tex]B = \frac{1}{2} * 6 * 8[/tex]
[tex]B = 24[/tex]
So, we have:
[tex]Area = L + 2 * B[/tex]
[tex]Area = 288 + 2 * 24[/tex]
[tex]Area = 288 + 48[/tex]
[tex]Area = 336ft^2[/tex]