Given:
The given expression is
[tex](-4)^{-3}[/tex]
To find:
The value of given expression.
Solution:
We have,
[tex](-4)^{-3}[/tex]
Applying the negative exponents rule, we get
[tex](-4)^{-3}=\dfrac{1}{(-4)^3}[/tex] [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]
Expanding the exponent, we get
[tex](-4)^{-3}=\dfrac{1}{(-4)(-4)(-4)}[/tex]
[tex](-4)^{-3}=\dfrac{1}{-64}[/tex]
[tex](-4)^{-3}=-\dfrac{1}{64}[/tex]
The value of given expression is [tex]-\dfrac{1}{64}[/tex].
Therefore, the correct option is A.
Answer:
a
Step-by-step explanation:
-1/64
A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 8 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?
Answer:
Step-by-step explanation:
This question bothers on combination. combination has to do with selection.
If 4 faculty members are chosen from total of 8 faculty members, this can be done in 8C4 number of ways.
8C4 = 8!/(8-4)!4!
8C4 = 8!/4!4!
8C4 = 8*7*6*5*4!/4!*4*3*2
8c4 = 8*7*6*5/24
8C4 = 7*5*2
8C4 =70 ways
Similarly, 5 students are to be selected from a pool of 13 students, this can be done in 13C5 number of ways.
13C5 = 13!/(13-5)!5!
13C5 = 13!/8!5!
13C5 = 13*12*11*10*9*8!/8!*5*4*3*2
13C5 = 13*12*11*10*9/120
13C5 = 1,287 ways
The total number of ways the committee can be formed is 8C4 * 13C5 = 70*1287
The total number of ways the committee can be formed is 90,090 ways
Question in the photo :) (Please help with my other questions!)
Answer:
a
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]u_{n}[/tex] = u₁ + (n - 1)d
given u₂₀ = 100 and u₂₅ = 115 , then
u₁ + 19d = 100 → (1)
u₁ + 24d = 115 → (2)
subtract (1) from (2) term by term to eliminate u₁
0 + 5d = 15
5d = 15 ( divide both sides by 5 )
d = 3
substitute d = 3 into (1) and solve for u₁
u₁ + 19(3) = 100
u₁ + 57 = 100 ( subtract 57 from both sides )
u₁ = 43
Answer:
a) u₁ = 43, d = 3
Step-by-step explanation:
Given :-
u₂₀ = 100
u₂₅ = 115
To Find :-
u₁ and d
Solving :-
u₂₀ = u₁ + 19d = 100 -(1)
u₂₅ = u₁ + 24d = 115 -(2)
(2) - (1)
5d = 15
d = 3
u₁ + 19(3) = 100
u₁ + 57 = 100
u₁ = 43
Solution :-
a) u₁ = 43, d = 3
when is the temperature constant?
Answer:
From 11 am until 2 pm
Step-by-step explanation:
The line is straight meaning its constant throughout the time 11pm - 2pm, it is neither rising nor falling like the other two.
EASY POINTS
Thomas has some leftover paint that he would like to sell. He mixes
4 3/8
gallons of blue paint with 6 5/8
gallons of white paint. Then, he pours this light-blue mixture into
1/4
gallon containers. To find out how many of these
1/4
gallon containers he can fill, which two equations would you need?
Answer:
4 3/8+6 5/8=x and x÷1/4=number of gallons
Answer:
4 3/8+6 5/8=x and x÷1/4=number of gallons
Step-by-step explanation:
Q2. Find the value of x
Answer:
x= -7
Step-by-step explanation:
subtract 139 from both sides
x-139-139=x
132-139= -7
Please help, for math 100 points!!!
Note:-
Calculated approximate values as we can't use ruler in screen !
#1
Sides are
6in3in7in4inPerimeter=20in=20(8)=160ft#2
Perimeter=2(2+1.5)=2(3.5)=7in=7(8)=56ft#3
Width:-
2in2(8)16ftPls help me with this questions
Answer:
1. First, we need to find the area of the rectangle, then subtract the non-shaded region from the total of the rectangle's area.
Area of rectangle formula;
A = LW
Where 'L' represents the length, and 'W' represents the width.
Plug in your values:
A = LW
A = 8(13)
A = 104, now that we've found the area of this total rectangle, we need to find the area of the triangle and subtract that from the area of the rectangle.
Formula for area of triangle;
A = BH x 1/2
Where 'B' represents the base, and 'H' represents the height and 1/2 is just 1/2.
But, if we look at this triangle we can see that we don't have the base.
So what we have to do is subtract the given side lengths beside it (which you add up) from the total width.
Given length beside unknown base: 4 and 4
So, (4 + 4) = 8, and the total width is 13.
So: 13 - 8 = 5, 5 is our base.
Now we plug these into our formula:
A = BH x 1/2
A = 5(6) x 1/2
A = 30 x 1/2
A = 30/2, which equals to 15.
Now we subtract the non shaded region(triangle) from the shaded region(total area of rectangle).
104 - 15 = 89 meters.
2. In this figure, we find the area of the whole triangle, not considering the small empty vertical-positioned rectangle to the bottom left corner.
Let's find the total base and total height.
As we can see, in the bottom triangle the height is 4, the other triangle has a height of 5. Combine these to get (4 + 5) = 9 is our total height of the whole triangle.
Now we find the base, 5 is the base of the bottom triangle and the other triangle has a base of 2, combine these to get: (5 + 2) = 7 is the total base of the whole triangle.
Now plug these into our formula of area of triangle;
A = BH x 1/2
A= 7(9) x 1/2
A = 63/2
A = 31.5, is the area of the whole triangle.
Now let's find the area of the empty rectangle to our bottom left corner.
Our length is 4, our width is 2.
A = LW
A = 4(2)
A = 8
Now subtract the empty rectangle's area from the total area of the triangle:-
31.5 - 8 = 23.5 inches.
3. We can see that in this figure, there is an empty semi circle(that has no area) apart of a square.
So to find the area of the unfinished square, we find the area of the semi circle and subtract it from the total area of the square.
Formula for area of a circle:
A = π[tex]r^{2}[/tex]
Where 'π' represents pi aka (22/7 or 3.14), and 'r' represents the radius which is being squared.
But if we were to find the area of a semi circle, we would have to divide the whole formula of a regular circle by 2.
So, A = π[tex]r^{2}[/tex]/2
Now, we plug in the values showing in the diagram into our equation.
Though, since we are given a diameter of 6, we need to find the radius which is 1/2(half) of the diameter.
SO,
1/2 x 6 = 3.
Now that we have our radius, we can finally plug this into our equation:-
A = π[tex]r^{2}[/tex]/2
A = 3.14(3^2)/2
A = 3.14(9)/2
A = 28.26/2
A = 14.13, is our area of the semi circle.
Now we have to find the total area of the square, which we easily just multiply the two lengths.
6(length) x 6(width)
= 36, is the area of the total square.
Now we subtract the area of the semi circle from the area of the total square:
36 - 14.13 = 21.87 feet.
4. To find the area of this, we must split the figure into two shapes, a rectangle and a semi circle.
Using the formulas we applied to our past problems;
(Rectangle)
A = LW
A = 20(8)
A = 160, is the area of the rectangle
Now the semi circle (ignore the 12.56, because it's just the circumference):
We have to find the radius, (1/2 x diameter), so: (1/2 x 8) = 4 is our radius.
A = π[tex]r^{2}[/tex]/2
A = 3.14(4^2)/2
A = 3.14(16)/2
A = 50.24/2
A = 25.12, is the area of the semi circle.
Now we add the two areas,
160 + 25.12 = 185.12 feet.
5. We split this figure into two shapes, a rectangle and a triangle.
Using the formulas we applied earlier to our past problems.
(Rectangle)
A = LW
A = 14(12)
A = 168, is the area of the rectangle.
(Triangle)
A = BH x 1/2
A = 8(12) x 1/2
A = 96 x 1/2
A = 96/2
A = 48, is the area of the triangle.
Now we add these areas;
168 + 48 = 216 centimetres.
The Stock Market alexzander is a stockbroker. Earns 12% commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Answer:
Commission in March = $648
Commission in 2011 = $33696
Step-by-step explanation:
Given
[tex]Stocks = \$5400[/tex]
[tex]Commission = 12\%[/tex]
Required
- Determine the amount of commission
- Determine the amount of commission in 2011
This is calculated as
[tex]Amount = Commission * Stocks[/tex]
[tex]Amount = 12\% * 5400[/tex]
[tex]Amount = 0.12 * 5400[/tex]
[tex]Amount = \$648[/tex]
Since the number of weeks in a year is 52.
[tex]Yearly\ Commission = 52 * \$648[/tex]
[tex]Yearly\ Commission = \$33696[/tex]
Please help with homework
PLEASE ANSWER THIS QUESTION I WILL GIVE BRAINLIEST!!!
Find the value of x in this case-
Already answered here: https://brainly.com/question/26946183
Find the approximate radius of a circle with a circumference of 7.92 centimetres. Use 3.14 for Π. Round to the nearest hundredth if needed.
Answer:
1.26
Step-by-step explanation:
Using the equation that the of the circumference:
C = 2Πr, you can plug in the given circumference:
7.92 = 2(3.14)r | Now you can isolate r:
7.92 = 6.28r
7.92/6.28 = r
r =1.26
600 people attended a football game. If 25% of the people who attended were teenagers, how many teenagers attended the game?
Answer:
150 Teenagers would have attended the game
What number makes the equation true enter the answer in the text box
Answer:
2
Step-by-step explanation:
because 2x4=8
so 2/8=4
Answer:
32
Step-by-step explanation:
firstly do the inverse which is 4 times 8 which is 32
then to check if ur answer is correct do 32 ÷8 which is 4
What is the £ to € exchange rate?
What is the ratio 15 : 24 written in lowest terms? 0 3:4 07:8 0 3:5 c 5:8
Answer 5:8
Step-by-step explanation:
in an election, candidate a got 75% of the total valid votes. if 15% of the total votes were declared invalid and the total numbers of votes is 560 000, find the number of valid votes polled in favor of candidate.
Answer:
357000Step-by-step explanation:
in an election, candidate a got 75% of the total valid votes. if 15% of the total votes were declared invalid and the total numbers of votes is 560 000, find the number of valid votes polled in favor of candidate.
find total valid votes
560000 - 15% = 476000
find 75% of valid votes
476000 : 100 * 75 = 357000
Solve the system using Gaussian elimination. 6x−y+3z=−9 5x + 5y−5z = 20 3x−y+4z = −5 A (2,12,−3)open paren 2 comma 12 comma negative 3 close paren B (2,2,0)open paren 2 comma 2 comma 0 close paren C (−1,6,1)open paren negative 1 comma 6 comma 1 close paren D (−2,6,3)
Answer:
C. (-1,6,1)
Step-by-step explanation:
Given the system of equation
6x−y+3z=−9 ...... 1
5x + 5y−5z = 20 ...... 2
3x−y+4z = −5 ...... 3
Reduce the equations to two variables with 2unknown
Multiply equation 3 by 2 and add to 1.
Equation 3×2; 6x−2y+8z = −10 ...... 4
Subtract 4 from 1
-y-(-2y)+3z-8z = -9-(-10)
-y+2y-5z = -9+10
y-5z = 1 ...... 5
Also multiply eqn 2 by 3 and 3 by 5
Equation 2×3; 15x+15y-15z= 60
Equation 3×5; 15x-5y+20z = -25
Subtract
15y+5y-15z-20z = 60+25
20y-35z = 85
Divide through by 5:
4y-7z = 17 ...... 6
...................................
Solve 5 and 6
y-5z = 1 ...... 5 × 4
4y-7z = 17 ...... 6 × 1
....................................
4y-20z = 4
4y-7z = 17
Subtract
-20z+7z = 4-17
-13z = -13
z = -13/-13
z = 1
Substitute z = 1 into equation 5 to get y:
From 5: y-5z = 1
y - 5(1) = 1
y-5 = 1
y = 1+5
y = 6
Substitute y = 6 and z = 1 into equation 3 to get x;
From 3: 3x−y+4z = −5
3x-6+4(1) = -5
3x -6+4 = -5
3x-2 = -5
3x = -5+2
3x = -3
x = -3/3
x = -1
Hence x = -1, y = 6 and z = 1
The correct answer is (-1, 6, 1)
Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (0,4), (8,4), (8,0)
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid
The quadrilateral with vertices (0, 0), (0, 4), (8, 4) and (8,0) makes the rectangle.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
The given points are,
(0, 0), (0, 4), (8, 4) and (8,0).
To determine the section for the quadrilateral,
Find distance between points.
The distance between two points A(x₁, y₁) and B(x₂, y₂)
Distance
= √(x₂ - x₁)² + (y₂ - y₁)²
The distance between (0, 0) and (0, 4)
= √(0-0)² + (4-0)² = √(0)² + (4)² = √(4)² = 4
The distance between (0, 4) and (8, 4)
= √(8-0)² + (4-4)² = √(8)² + (0)² = √(8)² = 8
The distance between (8, 4) and (8, 0)
= √(8 - 8)² + (0 - (4))² = √(0)² + (4)² = √(4)² = 4
The distance between (8, 0) and (0, 0)
= √(0 - 8)² + (0- 0)² = √(-8)² + (0)² = √(8)² = 8
Since, the opposite sides are equal,
Therefore, the quadrilateral is rectangle.
To know more about Rectangle on:
https://brainly.com/question/15019502
#SPJ2
(07.05 MC)
A polynomial function can be written as (2x + 5)(x + 3)(x − 1). What are the zeros of this function? (1 point)
Group of answer choices
A. x= -1, -5/2 ,3
B. x = -3, -5/2, -1
C. x= 1, 5/2, 3
D. x = -3, -5/2, 1
Answer:
D
Step-by-step explanation:
(2x + 5)(x + 3)(x − 1)=0
Use null factor law to solve for x
Which line matches the equation below? *
f(x) = 31
O
Red
Blue
Green
Purple
Step-by-step explanation:
there is a mistake in your question for sure.
because none of the lines match the function.
f(x) = 31
is a constant function represented by a straight horizontal line going through y = 31.
there is no such line in the graph.
The roaming cell phone company charges $15.00 per month plus $0.20 per minute of airtime usage. If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?
Answer:
$63.00
Step-by-step explanation
Since you have sales tax, you would do a 10% sales tax for 15 dollar
10/100 = x/15
Therefore you will calculate x and 100 divided by 15 which would be 6.6 repeated
You would round to the nearest tenth and get 6.6 then you would add 56.4 as in the tip+ month airtime usage and get 63 dollars
brainly please...maybe
Answer with step-by-step explanation:
x = $63.00
Since you have sales tax, you would do a 10% sales tax for 15 dollar
Equation = 10/100 = x/15
Therefore you will calculate x and 100 divided by 15 which would be 6.6 repeated
You would round to the nearest tenth and get 6.6 then you would add 56.4 as in the tip+ month airtime usage and get 63 dollars.
Hope this helped! (brainliest please)
What is the opposite of (x+120)?
Answer:
-(x+120)
Step-by-step explanation:
a car travelled 300km and used 24 litres of petrol.
1) ) how many litres of petrol is needed by the car to travel 400km?
2) how far can the car travel if it's petrol tank has 36 litres of petrol?
Answer:
1. 8liters
2.5
Step -by - step explaination:
8litres= 100
16litres=200
24litres=300
32litres=400
and so on
which of the following lines are perpendicular to the line y= 3/4x - 8? select all that apply
a. y=4/3x+8
b.y=-4/3x-12
c.y+4/3x=2
d.y-3/4x=1
e.6y=-8x+12
Answer:
B and C that's the answers
Aline etlea, deux coiffeuses contactent le même. fournisseur . Aline commande 10 lots de champoing à 15,60 l,unite et paie la meme somme que lea qui a commande 2 tondeuses et 2 lots dechampoing. Combien coûte une tondeuse? c,est undm note aidez moi reponse
Answer:
on my screen it sayes its 50938
Step-by-step explanation:
A gift shop wants to make gift baskets for its regular customers. There are 24 bottles of shampoo, 36 tubes of hand lotion, and 60 bars of soap. The same number of each item should be in each basket. What is the greatest number of baskets that can be made.
Answer:
12 baskets
Step-by-step explanation:
We solve this question using the Greatest Common Factor method.
We are told that:
There are
24 bottles of shampoo
36 tubes of hand lotion
60 bars of soap.
The same number of each item should be in each basket.
The greatest number of baskets is calculated as follows:
Step 1
We find the factors of 24, 36, 60
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Step 2
We Identify the number that is greatest and common amongst 24, 36 and 60
This is 12.
Then the greatest common factor is 12
Therefore, the greatest number of baskets is 12 baskets
A dinner plate is in the shaper of an isosceles right triangle. The leg length is 13 inches. What is the length of the perimeter of the hypotenuse, round to the nearest tenth?
Answer: 18.4 inches
Step-by-step explanation:
4.678
written to one decimal point would be
Answer:
hello
4.678 = 4 678 / 1000
Step-by-step explanation:
The drawing shows how to___?
A. Construct an angle congruent to a given angle
B. construct an equilateral triangle
C. draw an angle bisector
D. draw a perpendicular line through a point on the line
Answer:
C. draw an angle bisector
Step-by-step explanation:
For this sequence describe (in words) a way to produce each new term from the previous term.
Find common ratio:-
1/9/(1/3)=31/3(3)=11(3)=33(3)=9Just Multiply 3 with previous term to get next one