Answer:
4 , 4 , 5 , 6 , 11
Step-by-step explanation:
Mode = 4
So at least two times 4 should be there in the data.
And median is 5. So the middle term ( 3rd term} should 5.
Let x and y be the 4th term and 5th term
Data set:
4 , 4 , 5 , x , y
Mean =6
[tex]\frac{4+4+5+x+y}{5}=6\\[/tex]
4+4+5 +x + y = 6*5
13 + x + y = 30
x + y = 30 - 13
x + y = 17
x ,y can be any numbers that sum up to 17.
x , y can be 10 , 7 or 6, 11
Data set: 4 , 4 , 5 , 6, 11
I have another question I need help with. How do I solve for the missing angle?
Answer:
The angle measures approximately 18.19°.
Step-by-step explanation:
Since we want to find the angle and we are given the side adjacent to the angle and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 19 and the hypotenuse is 20. Substitute:
[tex]\displaystyle \cos \theta = \frac{19}{20}[/tex]
We can take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{19}{20}[/tex]
Use a calculator (make sure you're in Degrees Mode!). Hence:
[tex]\theta \approx 18.19^\circ[/tex]
The angle measures approximately 18.19°.
Find all possible values of α+
β+γ when tanα+tanβ+tanγ = tanαtanβtanγ (-π/2<α<π/2 , -π/2<β<π/2 , -π/2<γ<π/2)
Show your work too. Thank you!
Answer:
[tex]\rm\displaystyle 0,\pm\pi [/tex]
Step-by-step explanation:
please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation
===========================
we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first
cancel tanγ from both sides which yields:
[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]
factor out tanγ:
[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]
divide both sides by tanαtanβ-1 and that yields:
[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]
multiply both numerator and denominator by-1 which yields:
[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]
recall angle sum indentity of tan:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]
let α+β be t and transform:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]
remember that tan(t)=tan(t±kπ) so
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]
therefore when k is 1 we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]
remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal which yields:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]
when is 0:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]
likewise by Opposite Angle Identity we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal therefore:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]
and we're done!
Answer:
-π, 0, and π
Step-by-step explanation:
You can solve for tan y :
tan y (tan a + tan B - 1) = tan a + tan y
Assuming tan a + tan B ≠ 1, we obtain
[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]
which implies that
y = -a - B + kπ
for some integer k. Thus
a + B + y = kπ
With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.
It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so
[tex]B=\frac{\pi }{2} - a + k\pi[/tex]
but with the given limitation we must have k = 0, because 0 < π/2 - a < π.
On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again
k = 0, so we obtain
[tex]\frac{\pi }{2} - a=-a[/tex]
a contradiction.
Find the number of degrees in the measure of angle x
Answer: x = 82°
Step-by-step explanation:
The angle on the other side of 108° can be calculated as 180° - 108° = 72°
All angles within a triangle add up to 180°, so the x-value can be found as:
x = 180° - 72° - 26° = 82°
Que cantidad se obtiene al resolver la siguiente operacion: [4+{(2-5)2-4(7-5)3+2(15/3)}]- Raiz cuadrada de 16
Respuesta:
-13
Explicación paso a paso:
Dada la ecuación:
[4 + {(2-5) ²-4 (7-5) ³ + 2 (15/3)}] - Raíz cuadrada de 16
La raíz cuadrada de 16 se escribe como √16
[4 + {3² - 4 (2³) + 2 (5)} - √16
4 + {9 - 4 (2 * 2 * 2) + 10} - 4
4 + {9 - 4 (8) + 10} - 4
4 + {9 - 32 + 10} - 4
4 - 13 - 4
= -13
The function graphed to the left is
function.
and continues
The curve has
infinitely in one direction.
each
Each y-value is
corresponding x-value.
Answer: There is a circular
Step-by-step explanation:
Answer:
he function graphed to the left is
✔ a square root
function.
The curve has
✔ one distinct endpoint
and continues infinitely in one direction.
Each y-value is
✔ the square root of
each corresponding x-value.
Step-by-step explanation:
A company is selling specialty ice cream. Their profit is modeled by the equation p(x) = x2 + 3, where x represents the number of cartons sold. Their cost to make the carton is represented by c(x) = -3x + 24, where x represents the number of cartons produced.
A. What does it mean to find the solution to this system?
B. What is the solution to the system? How did you find the solution?
C. What does the solution mean in context of the problem?
D. How do you solve this system when x does not stand for the same thing? What system are you referring to?
Answer:
The given function for the profit of the company is p(x) = x² + 3
The function for the cos of the company, c(x) = -3·x + 24
Where;
x = The number of cartons sold
A. To find the solution of the system means to find the number of cartons sold at which the profit and cost are equal
B. The solution of the system can be found by equating both functions as follows;
p(x) = c(x)
Therefore;
x² + 3 = -3·x + 24
∴ x² + 3 + 3·x - 24 = 0
x² + 3·x - 21 = 0
x = (-3 ± √(3² - 4×1×(-21)))/(2 × 1)
∴ x = (-3 ± √(93))/2
x = (-3 + √(93))/2 ≈ 3.32 or x = (-3 - √(93))/2 ≈ -6.32
Therefore, the possible solution is x = (-3 + √(93))/2 ≈ 3.32
C. The solution means that when the company sells about 3 cartons of specialty ice, the cost to make the carton and the profit from selling the cartons will be approximately equal
D. Part 1
To solve the system, we rewrite the functions using common variables, to obtain a consistent system of equations
Part 2 Inconsistent system of equations
When x does not stand for the same thing in both equations, we have an inconsistent system of equations and there are no solutions
Step-by-step explanation:
asap help answer ---------
Answer:
[tex]C(n)=30-20n[/tex]
Step-by-step explanation:
Arithmetic sequence given in the question is,
10, -10, -30, -50........
Explicit formula of an Arithmetic sequence is given by,
[tex]C(n)=C(1)+(n-1)d[/tex]
Here, [tex]C_1=[/tex] First term
[tex]n=[/tex] number of terms
[tex]d=[/tex] common difference
From the given sequence,
[tex]C(1)=10[/tex]
[tex]d=-10-10[/tex]
[tex]=-20[/tex]
Substitute the values in the formula,
[tex]C(n)=10+(n-1)(-20)[/tex]
[tex]C(n)=10-20n+20[/tex]
[tex]C(n)=30-20n[/tex]
4. Convert 23 miles per hour to kilometers per minute. (1 mile = 1.609 kilometers)
Answer:
Ewan ko lng po when you find someone ma mas better less sa kanya
find the sum of the series
√2 - 2 + 2√2 +__+64√2.
Step-by-step explanation:
The question is not clear to me
someone help me for this algebra task please
Answer:
The answer is
[tex]4+ x[/tex]
Using the definition of linear equation,
[tex]y = 4 + x[/tex]
Is the answer.
Nissa is going to plant 485 485485 trees this year. If Nissa plants 5 55 orchards of trees, how many trees will be in each orchard?
Answer:
There will be 97 trees in each orchard.
Step-by-step explanation:
Given that,
Nissa is going to plant 485 trees this year.
Nissa plants 5 orchards of trees.
We need to find the number of trees in each orchard. Let it is n. So, we can find it as follows :
[tex]n=\dfrac{485}{5}\\\\n=97[/tex]
So, there will be 97 trees in each orchard.
PLEASE HELP URGENT!!!!
The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady.
Answer:
Australia will have about 27 million
China will have about 1.41 billion
Mexico will have 133.35 million
Zaire will have about 100.9 million
Australia 2000 19,169,200 multiply your growth rate by 2 then divide it by your population your growth rate
China 1.2 billion in 2000 multiply your growth rate by 2 then divide it by your population your growth rate
Same for Mexico
and Zaire
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
Answer:
-2,-1,0,1,2
Step-by-step explanation:
Answer:
-2.0
0,0
Step-by-step explanation:
i just did the test
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them earn up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money. Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answer:
25m + 10b = 400
Step-by-step explanation:
Total amount that can be earned = $ 400
Amount earned on mowing a lawn = $ 25
Amount earned per hour on babysitting = $10
Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m
Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b
Using the values from above, we can set up the equation as:
400 = 25m + 10b
or
25m + 10b = 400
This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Hope this helps have a good day
Grafico de deportes: fútbol 30%, atletismo 25%, tenis 5%, voleibol 10%, basquetbol 20%. Si 165 jóvenes prefieren el fútbol ¿cuantos prefieren el basquetbol?
Answer:
33 jóvenes prefieren el basquetbol.
Step-by-step explanation:
Hay 165 jóvenes.
De estos, 20% prefieren el basquetbol.
¿cuantos prefieren el basquetbol?
20% de 165, entonces:
[tex]20\% = \frac{20}{100} = 0.2[/tex]
[tex]0.2*165 = 33[/tex]
33 jóvenes prefieren el basquetbol.
The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.
Solution given:
it is a right angled isosceles triangle
so
perpendicular [p]=base[b]=5
hypotenuse [h]=x
we have
by using Pythagoras law
p²+b²=h²
5²+5²=h²
50=h²
h=[tex]\sqrt{50}[/tex]
x=[tex]\bold{5\sqrt{2}}[/tex]
Which is the graph of the linear inequality x - 2y > -6?
-10-
2
108
0
o
Answer:
the fourth option
Step-by-step explanation:
1/2x - 2y > -6
1/2x + 6 > y
or
y < 1/2x + 6
so, the solution is all the y values smaller (= below) the line function.
and because it is "<" and not "<=" the line itself is not included
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
Sequence 1
Sequence 2
Ordered Pairs
PLZ ANSWER FOR Brainiest
Answer:
1×2+1=3
3×2+1=7
7×2+1=15
15x2+1=31
31×2+1=63
40÷2+4=24
24÷2+4÷16
16÷2+4=12
12÷2+4=10
10÷2+4=9
What is X if line a and b are parallel
Answer:
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
8x = 180 - 148 [ corresponding angles are equal ]
8x = 32
x = 4
The ages of Raju and Ravi are in the ratio 3:4 Four years from now the ratio of their ages will be 4:5 Find their present ages
Answer: Their present age is 12 and 16.
Step-by-step explanation:
Let the required age be 3x and 4x
so
(3x+4)/(4x+4) = 4/5
5(3x+4) = 4(4x+4)
or, 15x + 20 = 16x + 16
or, 15x - 16x = 16-20
or, -x = -4
so, x = 4
now,
3x = 3*4 = 12
4x = 4*4 = 16
A boutique was having a 20% storewide sale.Erica bought 2 dresses which originally cost $80 each.How much savings did Erica enjoy?
Answer: $32
Step-by-step explanation:
Since the boutique was having a 20% storewide sale and Erica bought 2 dresses which originally cost $80 each, therefore the sale for each dress will be:
= $80 - (20% × $80)
= $80 - (0.2 × $80)
= $80 - $16
= $64
Therefore, on each dress Erica saves $16. The amount of savings enjoyed will then be:
= $16 × 2
= $32
HELP ASAP!!!
The circle graph shows the percentage of visitors at a
convention who ordered various flavors of juice. There were 700
visitors at the convention.
About how many visitors ordered grape juice or apple juice?
Enter your answer in the box.
Step-by-step explanation:
40+24+11+8+17= 100
100 - 700
24 - ?
24×700/100
= 168 visitors ordered apple juice
100-700
11-?
11×700/100
=77 people ordered grape juice
PLEASE PLEASE HELP ILL GIVE BRAINLY
Answer:
In this case, we can do substitution.
Step-by-step explanation:
For the first one, (s - t)(x) = ((x - 5) - 4x^2)(x) = x^2 - 21x
For the second one, (s*t)(x) = ((x - 5) *4x^2)(x) = 4x^4 - 20x^3
And for the last one, (s+t)(-2) = ((x - 5) + 4x^2)(-2) = -8x^2 - 2x + 10
Hope your happy with the answer :)
Complete the following proof by dragging and dropping the correct reason in the spaces below
Answer:
2
Step-by-step explanation:
1+1 = 2
So the answer is 2
hope this helps
Please help thank you!
Answer:
2
Step-by-step explanation:
X^2+Y^2=4=2^2
PLEASE HELP! Which of the following ordered pairs is a solution to the given system of equations?
A. (12, 8)
B. (3, 5)
C. (-3, 3)
D. (0, 4)
please don’t use this for points.
Answer:
A.............
Step-by-step explanation:
. ..........
Answer:
C. (3,3)
Step-by-step explanation:
When These equations are both graphed the solution for these equations when they intersect is (-3,3)
Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right
Find the length of the mid segment (median)
Answer:
13
Step-by-step explanation:
Median of a trapezoid = sum of 2 bases divided by 2
Bases = 10 and 16
Median = (10 + 16)/2
10 + 16 = 26
26/2 = 13
Median = 13
Help me solve this problem please
Answer:
A 2,3,6 :)
Step-by-step explanation:
thats answer corect me if im wrong hope it help
Lily owed Megan $129.42. So far, she has paid Megan $32.56.
The remaining amount Lily has yet to pay Megan is $
Answer: $96.86
Step-by-step explanation:
Lily owed megan = $129.42
she has paid megan = $32.56
The remaining amount Lily has yet to pay Megan = $129.42 - $32.56 = $96.86.
Please mark me the brainliest
