Answer:
True
Step-by-step explanation:
Hope this helps :)
If a^2 and b are directly proportional, and a=2 when b=9, then what is b when a=6?
Answer:
b = 81
Step-by-step explanation:
given a² and b are directly proportional then the equation relating them is
a² = kb ← k is the constant of proportionality
to find k use the condition a = 2 when b = 9 , then
2² = 9k
4 = 9k ( divide both sides by 9 )
[tex]\frac{4}{9}[/tex] = k
a² = [tex]\frac{4}{9}[/tex] b ← equation of proportion
when a = 6 , then
6² = [tex]\frac{4}{9}[/tex] b
36 = [tex]\frac{4}{9}[/tex] b ( multiply both sides by 9 to clear the fraction )
324 = 4b ( divide both sides by 4 )
81 = b
hello guys, can you give me the answers
The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)
How to differentiate functions?
1) We want to differentiate the function;
[tex]\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }[/tex]
Differentiating this gives;
dy/dx = [tex]\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }[/tex]
That can be simplified to get;
dy/dx = [tex]\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}[/tex]
2) We want to differentiate the function;
y = sin(2 sin⁻¹x)
Differentiating the function gives;
dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)
We know from trigonometric identity that;
cos²x = 1 - sin²x
Thus;
1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)
But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)
Thus; √(1 - y²) = cos(2 sin⁻¹x)
dy/dx = d√(1 - y²)]/(√1 - x²)
Read more about Differentiation of Functions at; https://brainly.com/question/5313449
#SPJ1
Describe how the variability of the distribution changes as the sample size increases.
Answer:
As the sample size increases, the variability decreases.
Step-by-step explanation:
The actual departures from the mean are used to quantify variability. The variance would be lower the fewer the deviations.
By using the central limit theorem, we can determine that the sample mean for random samples of size n follows a normal distribution.
The standard deviation of the X bar will be [tex]\frac{s}{\sqrt{n} }[/tex].
where s is the sample's variance's square root.
As a result, we discover that the standard deviation, or variability, is inversely proportional to the square root of the sample size. Therefore, standard error lowers as sample size grows. The variability falls off as sample size rises.
can anyone give me answer for this question -
[tex] \frac{ {3}^{6} \times {5}^{3} }{ {9}^{2} \times {5}^{2} } \\ \\ \frac{ {3}^{6} \times {5}^{3 - 2} }{ {3}^{4} } \\ \\ {3}^{6 - 4} \times {5}^{1} \\ \\ {3}^{2} \times 5 \\ \\ 9 \times 5 \\ \\ 45.[/tex]
What is the value of m, when 2⁶ x 4 = 418
Answer:
The answer should be 3.3/4
Step-by-step explanation:
A shopkeeper sold a watch for rupees 992 allowing 20% discount find its marked price
Answer:
⇒ Let marked price be Rs.x.
⇒ Discount = 20% of marked price.
⇒ Discount=
100
20
×x=
100
20x
⇒ Selling price = Marked price - Discount.
⇒ 192=x−
100
20x
⇒ 192=
100
80x
⇒ x=
80
19200
=Rs.240
MARK IT AS BRAINLIESTAND FOLLOW ME.Answer:
S.p = 992
discount = 20%
marked price = S. p + discount
= 992 + 20/100*992
= 992 + 198.4
= 1190.4
Add/Subtract the linear expression. -4(3x - 2) - 2(7x + 1)
Answer:
10
Step-by-step explanation:
multiply -4 and 3 to get -12
multiply -12 and -2 to get 24
multiply 2 and 7 to get 14
multiply 14 and 1 to get 14
subtract 14 from 24 to get 10
Prove that for all integers n ≥ 3, n+1P3 −n P3 = 3 · n P2
The permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3
How to prove the equation?We have:
[tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex]
Apply the following permutation formula
[tex]^{n}P_r = \frac{n!}{(n- r)!}[/tex]
So, we have:
[tex]\frac{(n + 1)!}{(n + 1 - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]
Evaluate the difference
[tex]\frac{(n + 1)!}{(n - 2)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]
Expand
[tex]\frac{(n + 1)!}{(n - 2)(n - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)(n - 3)!}[/tex]
Multiply through by (n - 3)!
[tex]\frac{(n + 1)!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]
Expand
[tex]\frac{(n + 1) * n!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]
Divide through by n!
[tex]\frac{(n + 1)}{(n - 2)} - 1 = \frac{3}{(n - 2)}[/tex]
Take the LCM
[tex]\frac{n + 1 - n + 2}{(n - 2)} = \frac{3}{(n - 2)}[/tex]
Evaluate the like terms
[tex]\frac{3}{(n - 2)} = \frac{3}{(n - 2)}[/tex]
Both sides of the equations are the same.
Hence, the permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3
Read more about permutation at:
https://brainly.com/question/11732255
#SPJ1
Reflection across X=1
It should be noted that a reflection is known as a flip and it's a mirror image of the shape.
How to illustrate the reflection?An image will reflect through a line, known as the line of reflection.
Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.
In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.
The reflection is attached.
Learn more about reflection on:
https://brainly.com/question/1908648
#SPJ1
Find the product of (x − 5)2.
Group of answer choices
x2 + 10x + 25
x2 − 10x + 25
x2 − 25
x2 + 25
Answer:
x² - 10x + 25
Step-by-step explanation:
The formula for squaring any binomial (an expression with two terms) is:
(a ± b)² = a² ± 2ab + b²
Let a = x and b = 5.
∴ Substituting:
(x - 5)² = x² - 2(x)(5) + (-5)²
= x² - 10x + 25
How to graph the linear inequality
Step-by-step explanation:
here I have done you can check it out
This year, a small business had a total revenue of $44,100. If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?
Answer:
look at the picture .
Step-by-step explanation:
look at the picture .
Again, simple questions! asap help please!
15 points!
Answer:
3) r = 1.5
7) y = 18
11) x = -10
Step-by-step explanation:
3) Isolate the variable by dividing each side by factors that don't contain the variable.
7) Solve for y by simplifying both sides of the equation, then isolating the variable.
11) Move all terms that don't contain x to the right side and solve.
what does parallelepiped focus on
Answer:
A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations).
Step-by-step explanation:
A parallelepiped focuses on three-dimensional figures formed by six parallelograms.
How to explain the parallelepiped?A parallelepiped shape has the following features
They are three-dimensional figuresThey are formed by 6 parallelogramsOpposite parallelograms are congruentThink of a cube or a cuboid.
Notice that they contain squares and rectangles
A parallelepiped is to a parallelogram as a square is to a cube and a rectangle to a cuboid
Read more about parallelepiped at:
https://brainly.com/question/3050890
#SPJ11
System of equations
y = x² + 2x + 7
6x=y=3
Which of the numbers below is greater than −7/3? Select all that apply. A) −3 B) −5.5 C) −2 D) −3/2 E) 1.25
Answer:
C, D and E
Step-by-step explanation:
The numbers which are greater than given number are : -2, -1.5, and 1.25.
What is Fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts.
Here, given number: -7/3
or we can write this as -2.33
Now, Converting option fraction value into decimal
A). -3
B) -5.5
C). -2
D). -1.5
E). 1.25
On comparing options from the given value we get
the number which are greater than -2.33; -2, -1.5, and 1.25
Thus, the numbers which are greater than given number are : -2, -1.5, and 1.25.
Learn more about Fraction from:
https://brainly.com/question/10354322
#SPJ1
find the simplified trig ratio (fraction) of tan p
Answer:
8/15
Step-by-step explanation:
For right triangles tan p = opposite leg / adjacent leg
tan p = 24 /45 = 8/15
Need help with number 27 asap
Answer:
Yes
Step-by-step explanation:
Yes; points X and Y are fixed under the reflection, so they must lie on the line of reflection. Since two points determine a line, the line of reflection is XY.
https://www.rcboe.org/cms/lib010/GA01903614/Centricity/Domain/1030/Reflections.pdf
.
what is 2(5+34-67/45*43)^2 equal to?
The value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Evaluating an ExpressionFrom the question, we are to determine the value of
2(5+34-67/45*43)^2
This can be written as
[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]
First, we will simplify the bracket
[tex]2 (\frac{-28}{1935 })^{2}[/tex]
Then, we get
[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]
= [tex]\frac{1568}{3744225}[/tex]
= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Hence, the value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Lear more on Evaluating an expression here: https://brainly.com/question/23133222
#SPJ1
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
1 European euro = 1.3687 US dollars
Un cartero reparte 10.700 cartas al mes. estimar cunats cartas reparte en un semestre
Teniendo en cuenta la regla de tres simple, el cartero reparte 64.200 cartas en un semestre.
Regla de tresLa regla de tres es una forma de resolver problemas de proporcionalidad entre tres valores conocidos y un valor desconocido, estableciendo una relación de proporcionalidad entre todos ellos.
Es decir, lo que se pretende con ella es encontrar el cuarto término de una proporción conociendo los otros tres.
Si la relación entre las magnitudes es directa, es decir, cuando una magnitud aumenta, la otra también (o cuando una magnitud disminuye, la otra también), se debe aplicar la regla de tres directa.
Para resolver una regla de tres directa se debe seguir la siguiente fórmula, siendo a, b y c datos conocidos y x la variable a calcular:
a ⇒ b
c ⇒ x
Entonces: [tex]x=\frac{cxb}{a}[/tex]
Cartas repartidas en un semestreEn este caso, se puede aplicar la regla de tres de la siguiente manera: Entonces, si el cartero en un mes reparte 10.700 cartas, ¿en 6 meses (un semestre) reparte cuántas cartas?
1 mes ⇒ 10.700 cartas
6 meses ⇒ ×
Entonces: [tex]cantidad de cartas=\frac{6 mesesx10.700 cartas}{1 mes}[/tex]
Resolviendo:
cantidad de cartas= 64.200 cartas
En resumen, el cartero reparte 64.200 cartas en un semestre.
Aprende más con estos ejemplos:
https://brainly.com/question/21685920
https://brainly.com/question/24786153
#SPJ1
what function does this graph represent?
Answer:
D
Step-by-step explanation:
The vertex is at (-2,4), so substituting into vertex form, only C and D match.
Also, the graph opens down, so the coefficient of x² is negative.
This eliminates C, leaving us with D
If angle D is an acute angle and its tangent ratio is 1.055, then what is the measure of angle D to the nearest tenth of a degree?
The measure of angle D to the nearest tenth of a degree is 47 degrees
Application of SOH CAH TOAThis theorem is used to determine the measure of sides and angles of a triangle.
According to the theorem
tan theta = opp/adj = 1.055
theta = arctan(1.055)
theta = 46.53 degrees
Hence the measure of angle D to the nearest tenth of a degree is 47 degrees
Learn more on SOH CAH TOA here: https://brainly.com/question/20734777
#SPJ1
A Baker Had 1/3 Cups Of Suger . he Added 1/9 Cups To It Find The Total Number Of Sugar . ( Can Someone Help Me Out)
The total number of sugar will be 9/4.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A Baker Had 1/3 Cups Of Sugar.
he Added 1/9 Cups To It
Let the number of sugar be x
x (1/3) + 1/9x = 1
3x + 1x = 9
4x = 9
x = 9/4
Hence, the total number of sugar will be 9/4.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ1
Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a .
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a .
Using translation concepts, it is found that the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
From triangle X′Y′Z′ to triangle X′′Y′′Z′′, the rule is given by:
(x,y) -> (x, -y)
Hence the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
What is The Value Of X
Answer:
X = 92 degrees
Step-by-step explanation:
the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88
180-88= 92 so X = 92
perimeter =
help me please thank u :)
Answer:
[tex]\fbox {Perimeter = 37.92}[/tex]
Step-by-step explanation:
Finding the missing side :
⇒ Take the tan value of the listed angle
⇒ tan 60° = √3 = 6/x
⇒ x = 6/√3 × √3/√3 = 2√3 = 2(1.73) = 3.46
Solving :
⇒ Perimeter = 10 + 2(6 + 3.46)
⇒ Perimeter = 10 + 2(9.46)
⇒ Perimeter = 19 + 18.92
⇒ Perimeter = 37.92
GEOMETRY! 50 POINTS
Please explain as best as you can for the second part of the question, I dont understand how to do it.
The geometry is that the number of sides for a 15- gon is 15 sides and the angles are 156° each.
How to calculate the angle?The total angles in a 15 gon will be calculated as:
= (n - 2) × 180
= (15 - 2) × 180
= 2340
The value of each angle will be:
= 2340/15
= 156°
The total angles in a 16 gon will be calculated as:
= (n - 2) × 180
= (16 - 2) × 180
= 2520
The value of each angle will be:
= 2520/16
= 157.5°
Learn more about geometry on:
brainly.com/question/24375372
#SPJ1
Find the simplified product. b-5/2b X b^2+3b/b-5
The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]
How to simplify a product?The products can be simplified as follows;
Multiplying fraction,
[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]
Hence,
Let's reduce the fraction by dividing
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]
Hence,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]
learn more on simplification here: https://brainly.com/question/3306438
#SPJ1
Answer:
A, b+3/2
Step-by-step explanation:
Solve equation by using the quadratic formula. 6x^2 +2x =4?
A) x= 3/2, 1 B) x= 2/3, -1 C) x=3/2, -1 D) x=3/2, 0
Answer:
Answer x=2/3, -1
Option B
Step-by-step explanation:
Answer:
B) x =( 2/3, -1)
Step-by-step explanation:
Equation:
[tex]6x {}^{2} + 2x = 4[/tex]
Solution:
We know that,
[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
According to the problem,
a = 6b = 2c = -4Plugging them on the formulae,we obtain,
[tex]x = \cfrac{ - 2 \pm \sqrt{ 2 {}^{2} - 4 \{6 \times ( - 4) \} } }{2 \times 6} [/tex][tex]x = \cfrac{ - 2 \pm \: \sqrt{4 - 4 \{ - 24 \} } }{12} [/tex][tex]x = \cfrac{ - 2 \pm \: 10 }{12} [/tex][tex]x = \cfrac{ - 1 \pm5}{6} [/tex][tex]\boxed{x = \cfrac{2}{3} \: \rm or - 1}[/tex]Choice B is accurate.