You are giving the angle and opposite leg.
Using the law of sines:
Sin(angle) = opposite leg / hypotenuse
Sin(30) = 2/ hypotenuse
Hypotenuse = 2/sin(30)
Hypotenuse = 4 meters
The maximum length of the seesaw is : (C). 4 meters
Meaning of Maximum lengthMaximum length can be defined as the total distance between two point in consideration.
Maximum length can also be said to be the total sum of all the length along a distance.
In the case above, the hypotenuse side is the maximum length.
In conclusion, The maximum length of the seesaw is : 4 meters
Learn more about maximum length : https://brainly.com/question/16172081
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I need help answering this ASAP
Answer:
x=13
Step-by-step explanation:
f(x) = sqrt(x-11)
The square root must be greater than or equal to zero
sqrt(x-11)≥0
Square each side
x-11≥0
x ≥11
The only answer that is greater than or equal to 11 is
x=13
Determine if the table below represents a linear function. If so, what's the rate of change?
A) No; it's a non-linear function.
B) Yes; rate of change = 4
C) Yes; rate of change = 2
D) Yes; rate of change = 3
Answer:
A
Step-by-step explanation:
Its not a linear function; there is no consistent rate of change between each of the points.
WHAT IS X³-27 SIMPLIFIED
Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test
thank you for the help every one
Answer:
1. 1.66in
2. 6.66in
3. 3.33in
4. 1inch
Step-by-step explanation:
the area of a rectangle is found by multiplying the length times width or the two sides.
5 x 1/3 is about 1.66 inches
5 x 4/3 is about 6.66 inches
5/2 x 4/3 is about 3.33 inches
and 7/6 x 6/7 is 1 inch
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y = -6x -6
Step-by-step explanation:
The general form of the equation of a line in the slope-intercept form may be given as
y = mx + c where
m is the slope and c is the intercept
Hence given the equation
18x + 3y = -18
subtract 18x from both sides
3y = -18x - 18
Divide both sides of the equation by 3
y = -6x -6
This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept
can anybody help me with this?
Answer:
Option (a)
Step-by-step explanation:
[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Solve this question:Зх <-24
Answer:
x< - 8
Step-by-step explanation:
3x <-24
x < - 24
3
x< - 8
x < - 8
Step-by-step explanation:
3x < - 24
Divide 3 on both sides,
3x / 3 < - 24 / 3
x < - 8
What is the discriminat of 2x+5x^=1
Answer:
don't know...........
How much bigger is the Sum of first 50 even numbers than the sum of first 50 odd numbers?
Answer:
50
Step-by-step explanation:
Sum Even numbers
n = 50
d = 2
a1 = 2
The last number is
an = a1 + (n-1)d
an = 2 + (50 - 1)*2
an = 2 + 49 * 2
an = 2 + 98
an = 100
Sum of the even numbers
Sum = (a1 + a50)*n/ 2
Sum = (2 + 100)*50/2
sum = 102 * 25
sum = 2550
Sum of the first 50 odd numbers
a1 = 1
n = 50
d = 2
l = ?
Find l
l = a1 + (n - 1)*2
l = 1 + 49*2
l = 99
Sum
Sum = (1 + 99)*50/2
Sum = 2500
The difference and answer is 2550 - 2500 = 50
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
find the perimeter of 6 CM 6 CM 6 CM 6 CM
Answer:
P = 24
Step-by-step explanation:
Since all the sides are the same length, the shape is a square.
Multiply all sides by 6.
6 cm x 4 sides = 24
A particle is moving with the given data. Find the position of the particle.
a(t) = [tex]t^{2}[/tex] − 4t + 5, s(0) = 0, s(1) = 20
How do I find s(t)=?
Recall that
[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]
Integrating this expression, we get
[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]
Also, recall that
[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or
[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]
Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us
[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]
[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]
or
[tex]C_1 = \dfrac{217}{12}[/tex]
Therefore, s(t) can be written as
[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]
Solve -9 < 4x + 3 5 19.
Answer:
C -3 < x ≤ 4
Step-by-step explanation:
-9 < 4x + 3 ≤ 19.
Subtract 3 from all sides
-9-3 < 4x + 3-3 ≤ 19-3
-12 < 4x ≤ 16
Divide by 4
-12/4 < 4x/4 ≤ 16/4
-3 < x ≤ 4
Which of the following is an advantage of using systematic random sampling?
Systematic random sampling reduces sampling variability.
Systematic random sampling does not require a finite population size.
Systematic random sampling could inadvertently miss patterns in the population.
Systematic random sampling uses clusters, which are close in proximity, making data collection easier.
This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Systematic:
One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.
Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.
It also does not reduce sampling variability, thus the first option is wrong.
From this, it can be concluded that the correct option is:
Systematic random sampling does not require a finite population size.
For another example of systematic random sampling, you can check https://brainly.com/question/21100042
y = −1 / 4 (x + 4) 2 −1 on a coordinate plane using its vertex, focus, and directrix.
Answer:
Hello,
Step-by-step explanation:
do I remind you of the formula :
where (a,b) is the vertex and y=k the directrix
[tex]y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\\\y=-\dfrac{(x+4)^2}{4} -1 \\\\Using\ identification:\\a=-4\\2(b-k)=-4\\b+k=-2\\\\\left\{\begin{array}{ccc}b-k&=&-2\\b+k&=&-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2b&=&-4\\2k&=&0\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b&=&-2\\k&=&0\\\end{array}\right.\\[/tex]
Focus=(-4,-2)
Directrix: y=0
Vertex=(-4,-1)
a) An orange weighs 155 grams.
What's the weight of the orange in kilograms?
Answer: 0.155
Step-by-step explanation:
g / 1000 = kilograms
155 / 1000 = 0.155
If it takes 247.2 yards of yarn to knit 2.5 baby bibs, how many yards of yarn would it take to knit 4 baby bibs? SHOW ALL WORK! ONLY ANSWER IF YOU KNOW THE ANSWER!
Answer:
395.52
Step-by-step explanation:
247.2/2.5=98.88(1 bib)
98.88x4=395.52(4 bibs)
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
Give the domain and range of G={(6.0),(-9,-3),(1,-3)}
Answer:
Step-by-step explanation:
D={ 6 , -9 , 1 }
R={ 0 ,-3 }
i need help figuring it out
I don’t get it. If u can actually answer it
Answer:
A is the answer! I think you know because the formula is given at the top.
4. A Pelican was flying 3 feet above sea level, when it dove to catch a fish that was 2 feet below sea level. How far did the pelican dive?
Answer: The pelican dove 5ft
Step-by-step explanation:
Pelican = 3ft
Fish = -2ft
Went down 3ft to get to 0, went down 2 more feet to get the fish.
What is the domain of the function represented by the graph
Answer:
C
Step-by-step explanation:
Domain of the function is the whole R
Solve the following system of equations: y + 5 = x
y= x2 – 3x – 5
Answer:
X=0,y=-5
x=4,y=-1
Step-by-step explanation:
Replace all occurrences of y with x^2-3x-5
(x^2-3x-5)+5=x
x^2-3x=x
X^2-4x=0
so :x=0,4
enter the value of x in the equation then find y
y=-5,-1
PLEASE HELP
select all the statistical questions.
A what is the typical amount of rainfall for the month of June in the galapagus islands
B how much did it rain yesterday at the Mexico City International airport
C why do you like to listen to music
D how many songs does the class usually listen to each day
E how many songs did you listen to today
F what is the capital of Canada
G how long does it typically take for 2nd graders to walk a lap around the track
The selected statistical questions are as follows:
A what is the typical amount of rainfall for the month of June in the Galapagos islands
D how many songs does the class usually listen to each day
G how long does it typically take for 2nd graders to walk a lap around the track
Statistical questions are known by these two main characteristics:
they are answered by the collection of datathere is always variability in the data collectedThis means that the data vary. They are not the same data. For example, "How old is Monday?" is not a statistical question because it has one answer.
Thus, statistical questions are not answered by a single number or answer, especially when the correct answer is just one.
Learn more examples of statistical questions here: https://brainly.com/question/15729334
In the figure above, AABC is an equilateral
triangle and each circle is tangent to the other
two circles. If each circle has diameter 10, what
is the distance h?
(A) 103
(B) 1513
(C) 15+513
(D) 10+1013
(E) 10+5/5
Answer:
B
Step-by-step explanation:
John has a rectangular garden with an area of 22.6 square feet. If the length of the garden is 5.2 feet, what is the length of the diagonal of the garden? Round to the nearest tenth.
Group of answer choices
6.1 feet
4.1 feet
8.1 feet
6.8 feet
Answer:
6.8 feet
Answer From Gauth Math
Width = area/length = 22.6/5.2 = 113 ≈/26
Diagonal = √[length² + width²] ≈ √23.0 feet
The range is the set of________
A) First Coordinates
B) Ordered Pairs
C) Second coordinates
Answer:
The range is the set of first coordinates
