Answer:
[tex]\sum\limits^3_{k=1}(k^3 - 6) = 18[/tex]
Step-by-step explanation:
Given
[tex]\sum\limits^3_{k=1}(k^3 - 6)[/tex]
Required
Evaluate
This means that we substitute 1 to 3 for k.
So, we have:
[tex]\sum\limits^3_{k=1}(k^3 - 6) = (1^3 - 6)+(2^3 - 6)+(3^3 - 6)[/tex]
[tex]\sum\limits^3_{k=1}(k^3 - 6) = (1 - 6)+(8 - 6)+(27 - 6)[/tex]
[tex]\sum\limits^3_{k=1}(k^3 - 6) = -5+2+21[/tex]
[tex]\sum\limits^3_{k=1}(k^3 - 6) = 18[/tex]
Ava works at a florist shop and earns $7.50 an hour plus a fixed bonus for each bouquet she arranges. Write a formula that will help her determine how much she will make in a week. Let's Let a= total amount earned, h= hours worked in one week, n= number of bouquets she arranged, and b= bonus amount for bouquets
Answer: a = 7.5h + bn
Step-by-step explanation:
Since Ava works at a florist shop and earns $7.50 an hour plus a fixed bonus for each bouquet she arranges.
where,
a = total amount earned,
h= hours worked in one week,
n = number of bouquets she arranged
b= bonus amount for bouquets
Then, the formula that will help her determine how much she will make in a week will be:
a = (7.5 × h) + (b × n)
a = 7.5h + bn
The formula is a = 7.5h + bn.
Evaluate the function requested. Write your answer as a fraction in lowest terms. Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 39, adjacent A C is 36, Opposite B C is 15. Find tan A.
Answer:
tanA = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{15}{36}[/tex] = [tex]\frac{5}{12}[/tex]
Let a and b be real numbers where a 0. Which of the following functions could represent the graph below?
f(x) = x(x – a)3(x – b)3
f(x) = (x – a)2(x – b)4
f(x) = x(x – a)6(x – b)2
f(x) = (x – a)5(x – b)
Answer:
D
Step-by-step explanation:
D on edg
Helppp and explain please and ty ;)
Answer:
Does this seem right to you?
Which fraction converts to a repeating decimal number?
CA.
1
12
B.
718
C.
127
27
D.
E.
6
10
Reset
Answer: A.
Step-by-step explanation:
Data: Fraction that turning into a repeating decimal number=x
Only step: Divide all the fractions, 1/12, 7/8, 14/25, 17/20, 6/10
Explanation: The only way to find which fraction turns into a repeating decimal is by dividing all the fractions, this can be done in any order but for this problem, lets start with 1/12 which, when divided, turns into 0.083... which is a repeating decimal
With that being said, the answer would be A.(1/12)
I hope this helps(Mark brainliest if you'd like to)
Find f ′(x) for f(x) = cos (5x2).
Answer:
I think its No Solution
Step-by-step explanation:
Hope it helps
if 2x + 3y = 12 and xy = 6, find the value of 8x^3 + 27y^3
Answer:
The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.
Step-by-step explanation:
Let be the following system of equations:
[tex]2\cdot x + 3\cdot y = 12[/tex] (1)
[tex]x\cdot y = 6[/tex] (2)
Then, we solve both for [tex]x[/tex] and [tex]y[/tex]:
From (1):
[tex]2\cdot x + 3\cdot y = 12[/tex]
[tex]2\cdot x = 12- 3\cdot y[/tex]
[tex]x = 6 - \frac{3}{2}\cdot y[/tex]
(1) in (2):
[tex]\left(6-\frac{3}{2}\cdot y \right)\cdot y = 6[/tex]
[tex]6\cdot y-\frac{3}{2}\cdot y^{2} = 6[/tex]
[tex]\frac{3}{2}\cdot y^{2}-6\cdot y + 6 = 0[/tex]
The roots of the polynomial are determined by the Quadratic Formula:
[tex]y_{1} = y_{2} = 2[/tex]
By (1):
[tex]x = 6 - \frac{3}{2}\cdot (2)[/tex]
[tex]x = 3[/tex]
If we know that [tex]x = 3[/tex] and [tex]y = 2[/tex], then the final value is:
[tex]z = 8\cdot x^{3}+27\cdot y^{3}[/tex]
[tex]z = 8\cdot 3^{3}+27\cdot 2^{3}[/tex]
[tex]z = 432[/tex]
The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.
Please help I’ll give brainliest
Answer:
2 is the base
Step-by-step explanation:
2^3
2 is the base and 3 is the exponent
f(x) = 4x2 – 10x + 2
Find f(-7)
Answer:
f(-7) = 268
Step-by-step explanation:
f(x) = 4x^2 – 10x + 2
Let x = -7
f(-7) = 4(-7)^2 – 10(-7) + 2
Exponents first
f(-7) = 4(49) – 10(-7) + 2
Multiply
f(-7) = 196 + 70 + 2
f(-7) = 268
Six teammates are competing for first, second, and third place in a race.
How many possibilities are there for the top three positions?
20
30
120
240
Step-by-step explanation:
there Are 120 possibilities for the top three positions
We will see that there are 120 different possibilities for the top 3 positions.
How many possibilities are there for the top three positions?Here we need to count the number of options for each of the positions.
For the first position, there are 6 options (6 team members).For the second position, there are 5 options (because one is already in the first position).For the third position, there are 4 options.The total number of different combinations is given by the product between the numbers of options, we will get:
C = 6*5*4 = 120
There are 120 different possibilities for the 3 positions.
If you want to learn more about combinations, you can read:
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A carnival game gives players a 25% chance of winning every time it has played a player plays the game four times let XP the number of times a player wins in for place what is the most probable value of X what is the probable that the player will win at least once
Answer:
0.6836 = 68.36% probability that the player will win at least once.
Step-by-step explanation:
For each game, there are only two possible outcomes. Either the player wins, or the player loses. The probability of winning a game is independent of any other game, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
25% chance of winning
This means that [tex]p = 0.25[/tex]
Plays the game four times
This means that [tex]n = 4[/tex]
What is the probability that the player will win at least once?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.25)^{0}.(0.75)^{4} = 0.3164[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.3164 = 0.6836[/tex]
0.6836 = 68.36% probability that the player will win at least once.
A) m + n
B) 0
C) m - 1
D) -(m+n)
the required answer is 2m- (m-n)(m-1)
Expand 3(c + 3).
3(c + 3) =
Answer:
3c + 9
Step-by-step explanation:
Remember to multiply everything in the brackets by the number outside the brackets.
HELP I HAVE 10 MINS
If AB and CD have endpoints at A(- 1,3), B(6,8), C(4, 10) and D(9,3), are AB and CD parallel,
perpendicular, or neither? Explain.
Answer:
perpendicular
joey is going shopping for a new pair of sneakers. He finds a pair that have an original price of $155. They are on sale today for 30% off. How much does Joey pay for the sneakers including 8% sales tax?
Answer:, Joey will pay $117.18 for sneakers.
Step-by-step explanation:
Given: original price = $155
Discount rate = 30%
Tax rate = 8%
Price after discount = Original price - (Discount) x (original price)
[tex]= 155-0.30\times 155\\\\=155-46.5\\\\=\$\ 108.5[/tex]
Tax = Tax rate x (Price after discount)
[tex]= 0.08 \times 108.5[/tex]
= $ 8.68
Final price for sneakers = Price after discount + Tax
= $ (108.5+8.68)
= $ 117.18
Hence
Please solve with explanation.
Answer:
Area = 160 cm²
Perimeter = 55.31 cm
Step-by-step explanation:
Applying,
Area of the figure = area of the rectangle- area of the triangle
A = lw+bh/2............... Equation 1
From the question,
Given: l = 16 cm, w = 12 cm, h = 8cm, b = 8 cm
Substitute these values into equation 1
A = (16×12)-(8×8/2)
A = 192-32
A = 160 cm²
Perimeter P = /BC/+/CD/+/DE/+/EF/+/FG/+/GA/
Applying pythagoras theorem to get /FG/
FG² = GE²+EF²
FG² = 8²+8²
FG² = 64+64
FG² = 128
FG = √128
FG = 11.31 cm
Therefore,
P = 16+12+4+8+11.31+4
P = 55.31 cm
Line p is parallel to line q
Which set of statements about the angles is true ?
Grade 10 Math. Solve for y. Will mark right answer brainliest :)
Answer:
y=5, y=[tex]\frac{38}{11}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation
[tex]\frac{y+2}{y-3}[/tex]+[tex]\frac{y-1}{y-4}[/tex]=[tex]\frac{15}{2}[/tex] and we need to solve for y
first, we need to find the domain, which is which is the set of values that y CANNOT be, as the denominator of the fractions cannot be 0
which means that y-3≠0, or y≠3, and y-4≠0, or y≠4
[tex]\frac{y+2}{y-3}[/tex] and [tex]\frac{y-1}{y-4}[/tex] are algebraic fractions, meaning that they are fractions (notice the fraction bar), but BOTH the numerator and denominator have algebraic expressions
Nonetheless, they are still fractions, and we need to add them.
To add fractions, we need to find a common denominator
One of the easiest ways to find a common denominator is to multiply the denominators of the fractions together
Let's do that here;
on [tex]\frac{y+2}{y-3}[/tex], multiply the numerator and denominator by y-4
[tex]\frac{(y+2)(y-4)}{(y-3)(y-4)}[/tex]; simplify by multiplying the binomials together using FOIL to get:
[tex]\frac{y^{2}-2y-8}{y^{2}-7y+12}[/tex]
Now on [tex]\frac{y-1}{y-4}[/tex], multiply the numerator and denominator by y-3
[tex]\frac{(y-1)(y-3)}{(y-4)(y-3)}[/tex]; simplify by multiplying the binomials together using FOIL to get:
[tex]\frac{y^{2}-4y+3}{y^{2}-7y+12}[/tex]
now add [tex]\frac{y^{2}-2y-8}{y^{2}-7y+12}[/tex] and [tex]\frac{y^{2}-4y+3}{y^{2}-7y+12}[/tex] together
Remember: since they have the same denominator, we add the numerators together
[tex]\frac{y^{2}-2y-8+y^{2}-4y+3}{y^{2}-7y+12}[/tex]
simplify by combining like terms
the result is:
[tex]\frac{2y^{2}-6y-5}{y^{2}-7y+12}[/tex]
remember, that's set equal to [tex]\frac{15}{2}[/tex]
here is our equation now:
[tex]\frac{2y^{2}-6y-5}{y^{2}-7y+12}[/tex]=[tex]\frac{15}{2}[/tex]
it is a proportion, so you may cross multiply
2(2y²-6y-5)=15(y²-7y+12)
do the distributive property
4y²-12y-10=15y²-105y+180
subtract 4y² from both sides
-12y-10=11y²-105y+180
add 12 y to both sides
-10=11y²-93y+180
add 10 to both sides
11y²-93y+190=0
now we have a quadratic equation
Let's solve this using the quadratic formula
Recall that the quadratic formula is y=(-b±√(b²-4ac))/2a, where a, b, and c are the coefficients of the numbers in a quadratic equation
in this case,
a=11
b=-93
c=190
substitute into the formula
y=(93±√(8649-4(11*190))/2*11
simplify the part under the radical
y=(93±√289)/22
take the square root of 289
y=(93±17)/22
split into 2 separate equations:
y=[tex]\frac{93+17}{22}[/tex]
y=[tex]\frac{110}{22}[/tex]
y=5
and:
y=[tex]\frac{93-17}{22}[/tex]
y=[tex]\frac{76}{22}[/tex]
y=[tex]\frac{38}{11}[/tex]
Both numbers work in this case (remember: the domain is y≠3, y≠4)
So the answer is:
y=5, y=[tex]\frac{38}{11}[/tex]
Hope this helps! :)
Can someone please answer this I’ll give brainliest
Answer:
Step-by-step explanation:
If you look at the diagram, you notice there are two triangular bases and three rectangular faces.
Therefore, the surface area, or the total area of all the bases and faces, would be the area of one triangular base multiplied by 2 and the area of each rectangular face
area of triangle = (1/2)*height*base
area of triangular base = (1/2)*15*28 = 210 cm^2
area of rectangle = base*height
area of rectangular face #1 = 25*30 = 750 cm^2
area of rectangular face #2 = 17*30 = 510 cm^2
area of rectangular face #3 = 28*30 = 840 cm^2
total surface area = 2*210 + 750 + 510 + 840 = 2520 cm^2
Can someone
Please
Help
Me
Find the surface area of this sphere.
Round to the nearest tenth.
16 ft
Formulas for Spheres
S.A. = 4nr?
V = rer
[?] ft?
[tex]804.2\:ft^{2}[/tex]
Step-by-step explanation:
[tex]A=4 \pi r^{2}[/tex]
We are given D = 16 ft, which means that r = (1/2)D = 8 ft. Therefore, the surface area of the sphere is
[tex]A=4 \pi (8 ft)^{2} = 804.2\:ft^{2}[/tex]
The surface area of the sphere is approximately 804.2 square feet.
What is a sphere?It is a three-dimensional figure where the volume is given as:
The volume of a sphere = 4/3 πr³
We have,
The surface area of a sphere with diameter d is given by the formula:
SA = 4πr²
where r is the radius of the sphere, which is half the diameter. In this case, the diameter is 16 feet, so the radius is 8 feet.
Plugging in the value of r, we get:
SA = 4π(8²)
SA = 4π(64)
SA = 256π
Rounding to the nearest tenth gives:
SA ≈ 804.2 square feet
Therefore,
The surface area of the sphere is approximately 804.2 square feet.
Learn more about sphere here:
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What type of angel is 107 degrees
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
⏩ 107° angle will be an obtuse angle because its measurement is more than 90° but less than 180°.
⁺˚*･༓☾✧.* ☽༓･*˚⁺‧
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Answer:
An obtuse angle
Step-by-step explanation:
Angles are classified by how large their degree measure is. Here is a list of the basic classifications of an angle,
acute: degree measure between (0) and (90) degrees
right: exactly (90) degrees,
obtuse: degree measure between (90) and (180) degrees
reflex: degree measure between (180) and (360) degrees
Help Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4/8 = 1/2
Step-by-step explanation:
hope it thepled u
a little bit of help here??
Answer:
balanced
Step-by-step explanation:
The upward force is 75+ 160 =235
The downward force is 235
The force is balanced since the upward force equals the downward force
An object is experiencing an acceleration of 30 m/s2 while traveling in a
circle at a velocity of 3.7 m/s. What is the RADIUS of its motion?
Answer:
[tex]{ \tt{formular :}} \\ { \boxed{ \bf{centripental \: acceleration = \frac{ {v}^{2} }{r} }}} \\ \\ { \tt{30= \frac{ {3.7}^{2} }{r} }} \\ \\ { \tt{r = \frac{ {3.7}^{2} }{30} }} \\ \\ { \tt{radius = 0.456 \: meters}}[/tex]
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
Answer:
x = -5; y = 4, z = 1
Step-by-step explanation:
Given the row echelon form as:
[tex]\left[\begin{array}{cccc}1&0&\ \ 4|&-1\\0&1&-1|&3\\0&0&\ \ 1|&1\end{array}\right][/tex]
This matrix can be represented as:
[tex]\left[\begin{array}{ccc}1&0&4\\0&1&-1\\0&0&1\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right] \\\\Performing\ matrix\ multiplication\ gives:\\\\\left[\begin{array}{c}x+4z\\y-z\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right][/tex]
Therefore:
z = 1
y - z = 3;
y = 3 + z = 3 + 1 = 4.
Hence, y = 4
x + 4z = - 1;
x = -1 - 4z = -1 - 4(1) = -5
x = -5
(4p _ 2k)(3)
in distributive property
Answer:
12 p - 6k
Step-by-step explanation:
Let us assume that _ is meant to be minus sign.
( 4 p - 2k ) ( 3)
use the distributive property
3 × 4p - 3 × 2k
12 p - 6 k
What is the x value of the solution to the system of equations
4y=2x+8
Y=-x+2
Answer:
x=0;y=2
Step-by-step explanation:
4(-x+2)=2x+8 -4x+8=2x+8 -4x-2x=8-8 -6x=0 x=0 y=-x+2 y=0+2 y=2
Which are the solutions of the quadratic equation?
x² = 7x + 4
Answer:
[tex]x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
Which has a larger area, a 4:3 aspect ratio 32 inch TV or a 16:9 aspect ratio 32 inch
TV? Find the side lengths of each of the TV's and the area of each TV to compare.
Explain your reasoning and show all mathematical calculations.
Answers:
The 4:3 tv has the larger areaThe 4:3 tv has width = 25.6 inches and height = 19.2 inches. The area is exactly 491.52 square inchesThe 16:9 tv has width = 27.8904 inches (approximate) and height = 15.68835 inches (approximate). The area is approximately 437.55 square inches.================================================
Explanation:
Let x be some positive real number
The 4:3 aspect ratio means the width (horizontal) portion of the tv is 4x inches while the height (vertical) portion is 3x inches
The ratio 4x:3x reduces to 4:3 after dividing both parts by x.
The 4x by 3x rectangle has the diagonal 32 inches as the instructions state. The tv size is always measured along the diagonal.
So effectively, we have two identical right triangles with legs 4x and 3x, and hypotenuse 32.
Apply the pythagorean theorem to find x
a^2+b^2 = c^2
(4x)^2+(3x)^2 = 32^2
16x^2+9x^2 = 1024
25x^2 = 1024
x^2 = 1024/25
x = sqrt(1024/25)
x = 32/5
x = 6.4
Recall that x is positive, so we ignore the negative square root here.
This 4x by 3x tv then has dimensions of
horizontal width = 4x = 4*6.4 = 25.6 inchesvertical height = 3x = 3*6.4 = 19.2 inchesThese values are exact.
The area is therefore base*height = 25.6*19.2 = 491.52 square inches
This of course only applies to the 4:3 tv that's 32 inches in diagonal.
-------------------------------
Now onto the 16:9 tv.
We'll follow the same steps as the last section. We'll use y this time
The 16:9 ratio becomes 16y:9y
a^2+b^2 = c^2
(16y)^2 + (9y)^2 = 32^2
256y^2 + 81y^2 = 1024
337y^2 = 1024
y^2 = 1024/337
y = sqrt(1024/337)
y = 1.7431510742491 which is approximate
y = 1.74315
So,
horizontal width = 16y = 16*1.74315 = 27.8904vertical height = 9y = 9*1.74315 = 15.68835area = base*height = 27.8904*15.68835 = 437.55435684the area is approximate since the width and height are approximate. It rounds to about 437.55 square inches
-------------------------------
To recap, we found the following:
The 4:3 tv has width and height of 25.6 inches and 19.2 inches respectively. Those values are exact. The area is exactly 491.52 square inches.The 16:9 tv has width and height of approximately 27.8904 inches and 15.68835 inches respectively. The area is approximately 437.55 square inches.The 4:3 tv has larger area.The distance between the parallel lines x – 2y = 3 and 2x – 4y = 12 is
Answer:
???????????????????????
Step-by-step explanation:
sorry di ko po alam yung sagot pasensiya na po
Given :
Parallel lines are
x – 2y = 3 and 2x – 4y = 12
Step-by-step explanation:
Lets write the given lines in slope intercept form y=mx+b
[tex]x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}[/tex]
From the above equation , y intercept of first line is [tex]\frac{-3}{2}[/tex]
Solve the second equation for y and find out y intercept
[tex]2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3[/tex]
y intercept of second line is -3
To find the distance between parallel lines, we subtract the y intercepts
[tex]\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5[/tex]
Answer:
The distance between the parallel lines = 1.5
Reference:
https://brainly.com/question/24145911
