Addison worked 6 more hours this week than last week. In total, she worked 72 hours this week and last week. Using the equation 2h + 6 = 72, how many hours (h) did Addison work last week?
Answer:
h = 33 hours
Step-by-step explanation:
Given that,
Addison worked 6 more hours this week than last week. In total, she worked 72 hours this week and last week.
The equation is :
2h + 6 = 72
We need to find the number of hours
2h = 72 - 6
2h = 66
h = 33
Hence, Adison worked for 33 hours last week.
Geometry
What is the value of x?
Enter your answer in the box.
x = °
Answer:
x = 80
Step-by-step explanation:
The sum of the angles of a triangle is 180
30+70+x = 180
100 +x = 180
x = 180-100
x = 80
Two competing companies are having sales on laptops. Laptop #AX330M has a retail price of $2,100. The Buy Less is advertising #AX330M for 15% off, while Sell More has stated they will match any competitor’s advertised special and take an additional 10% off of the competitor’s advertised price. How much money is saved by purchasing the laptop from Sell More instead of Buy Less?
Answer: I only need the points :) <3
Step-by-step explanation: Two competing companies are having sales on laptops. Laptop #AX330M has a retail price of $2,100. The Buy Less is advertising #AX330M for 15% off, while Sell More has stated they will match any competitor’s advertised special and take an additional 10% off of the competitor’s advertised price. How much money is saved by purchasing the laptop from Sell More instead of Buy Less?
A bookshelf holds 5 sports magazines and 5 architecture magazines.
When 3 magazines are taken from the shelf at random, without replacement, what is the probability that all 3 are architecture magazines?
3/25
1/125
1/12
1/8
Answer:
1/12
Step-by-step explanation:
The first time the person picks a magazine, they have a 5/10 chance of drawing an architecture magazine.
The second time, they have a 4/9 chance because they have already removed one magazine from the bookshelf
The third time, they have a 3/8 chance because they have already removed 2 magazines.
Multiply all of the probabilities together
5/10 * 4/9 * 3/8 = 60/720
Simplify:
60/60 / 720/60 = 1 / 12
Hope this helps!
A line through the point (2,5) forms a right triangle with the x-axis
and y-axis in the 1st quadrant. Determine the equation of the line that
will minimize the area of this triangle.
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Answer:
5x +2y = 20
Step-by-step explanation:
Suppose 'a' is the x-intercept of the line.
Then the slope is given by the slope formula ...
m = (y2 -y1)/(x2 -x1)
m = (0 -5)/(a -2)
And the y-intercept is ...
b = y -mx = 5 -(-5/(a-2))(2) = 5 +10/(a -2)
The area of the triangle is half the product of 'a' and 'b', so is ...
A = 1/2ab
A = 1/2(a)(5 +10/(a -2)) = 2.5a +5a/(a-2)
The area is minimized when the derivative of this is zero.
A' = 2.5 -10/(a -2)^2 = 0
Solving for 'a' gives ...
(a -2)^2 = 10/2.5 = 4
a = 2 + 2 = 4 . . . . . . . . . . . x-intercept
b = 5 +10/(4 -2) = 10 . . . . . y-intercept
m = -5/(4 -2) = -5/2 . . . . . . slope
An equation of the line is ...
y = -5/2x +10 . . . . . slope-intercept form
5x +2y = 20 . . . . . standard form
__
You may have noticed that the x-and y-intercepts are double the x- and y-values of the given point. That is, the given point is the midpoint of the hypotenuse of the triangle with minimum area. That is the general solution of this sort of problem.
The cost of 120 PSP is Dh 15000. Find the cost of one PSP
Answer:
125
Step-by-step explanation:
120 units cost 15000.
so, 1 unit is then the 120th part of the total costs.
price of 1 unit = 15000/120 = 1500/12 = 125
the perimeter of a regular octagon is 18 cm find the length of each side
Answer:
Each side will measure 2.25 cm
Step-by-step explanation:
Perimeter is the sum of all the sides of a shape.
Since an octagon has 8 sides and the perimeter is 18,we simply divide 18 by 8.
18 ÷ 8 = 2.25
Have a wonderful day.
The equation D = StartFraction 13 Over V EndFraction shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?
Answer:
As the volume approaches 0,
The density approaches infinity
Step-by-step explanation:
The graph of the equation is a hyperbola with the asymptote at v = 0. This means that when the value of v is very close to 0, the value of the density is very large.
As the volume approaches 0,
The density approaches infinity
Answer:
The density approaches infinity.
Step-by-step explanation:
PLEASE HELP WILL MARK YOU!!!
Answers:
a = 69b = 47c = 116d = 93e = 86==========================================================
Explanation:
For now, focus on the triangle with angles 'a', 71 and 40 degrees.
Recall that for any triangle, the inside angles always add to 180
a+71+40 = 180
a+111 = 180
a = 180-111
a = 69
---------------
Notice how angles b and 133 are adjacent and form a straight angle. This makes them supplementary. Meaning they add to 180
b+133 = 180
b = 180-133
b = 47
---------------
Let angle f be adjacent to angle c, and part of the triangle with angles 'a' and b.
Use the rule mentioned in the first section
a+b+f = 180
69+47+f = 180
116+f = 180
f = 180-116
f = 64
Now we can find angle c, because angles f and c are supplementary
c+f = 180
c+64 = 180
c = 180-64
c = 116
We could also use the remote interior angle theorem to say that a+b = c, so c = a+b = 69+47 = 116
---------------
Next, focus your attention on the 140 degree angle. The missing adjacent angle to this is 180-140 = 40 degrees
Now focus on the triangle that has angles d, 40, and 47. The "40" being what we just calculated in the previous paragraph.
We'll do the same thing as before
d+40+47 = 180
d+87 = 180
d = 180-87
d = 93
---------------
The angle just above angle d is also the same (vertical angles). This upper triangle has angles 40, d and g, where g is unknown. Let's find it.
40+d+g = 180
40+93+g = 180
133+g = 180
g = 180-133
g = 47
The vertical angle across from this is also 47 degrees.
Similarly, we can move that angle b over to its vertical pairing counterpart.
The smallest triangle at the very top has angles e, b, and g
e+b+g = 180
e+47+47 = 180
e+94 = 180
e = 180-94
e = 86
Express the given set in roster form.
Answer:
E= { 13 , 14 , 15 , .........94 }Step-by-step explanation:
hope it may help u
please mark as brainlist
(๑˙❥˙๑)
Will mark Brainlest (if you were to roll the dice one time ,what is the probabilty that it will land on an even number) step by step pls
we learned this in our lower i dont remember exactly but i think~
the probability that it will land on an even number will be 3 as there are 3 odd number and 3 even number
Answer:
1/2
Step-by-step explanation:
n(E) = 9
n(S) = 18
p(E1) = [tex]\frac{n(E1)}{n(S)}[/tex]
=9/18
=1/2
let f(x)=x-1 and g(x)=x^2+1
f(g)=___
Answer:f(g)=2
Step-by-step explanation:
What is the common ratio for the geometric sequence below, written as a fraction?
768, 480, 300, 187.5, …
/
Answer:
5/8
Step-by-step explanation:
Find the common ratio by dividing one of the numbers in the sequence by the previous one:
480/768
= 0.625
Convert this to a fraction:
0.625
= 5/8
So, the common ratio is 5/8
Select the statement that represents all the solutions of the inequality. d < 7 all rational numbers equal to 7 all integers less than 7 all rational numbers greater than 7 all rational numbers less than 7
the answer is :
all rational numbers less than 7
have a good day <3
Aspongebob at the bottom of the sea
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
Answer:
Step-by-step explanation:
anything 1-6
factorise m2+10m-24 please step by step
m^2+10m-24
=m^2+12m-2m-24
=m (m+12)-2 (m+12)
=(m-2)(m+12)
Answer:(m-2)(m+12)
if wrong correct me pls
I hope it helps mate
HAVE A GREAT DAY
#Liliflim
Solve the following equation using the quadratic formula. x^2 - 8x + 97 = 0
Answer:
undefined in the set of real numbers
Step-by-step explanation:
See image below:)
The midpoint of a segment is (4,3) and one endpoint is (10,8). Find the coordinates of the other endpoint.
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Answer:
(-2, -2)
Step-by-step explanation:
The midpoint M is calculated from end points A and B as ...
M = (A +B)/2
Solving for end point B, we get ...
2M = A +B . . . . . . multiply by 2
B = 2M -A . . . . . . subtract A
Then the other end point is ...
B = 2(4, 3) -(10, 8) = (2·4 -10, 2·3 -8) = (8-10, 6-8)
B = (-2, -2)
The other end point has coordinates (-2, -2).
choose the appropriate postulate of the following pair lf triangles are congruent.
Answer:
ASA
Step-by-step explanation:
they share the side in the middle (reflexive property) and have two congruent angles
Find the equation of the line with slope m=3/5 that contains the point (−5,−6).
Answer:
y = 3/5x - 1
Step-by-step explanation:
y = mx + b
m = slope
m = 3/5
to find the y - intercept we have to make x = 0 by adding or subtracting
in this case it is +5
add five to both x and y
[tex](-5, -6) + (5, 5) = (0, -1)[/tex]
the y intercept focuses on what y is when x is 0
the y intercept in this case is -1
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six
12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two
For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)
2 + 4 + 6 + . . . + 2n = n(n+1)
1. The given series is
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =
For n=1
L.H.S=4.6=24
R.H.S=[4×5×15]÷6
=300÷6
=50
So, for n=1,
L.H.S≠ R.H.S
Since the given expression is true for n=1 ,
So , the given series is untrue.
we should replace R.H.S by=4(n+1)(n+2)(4n-3)²
2.
12+42+72+.......+(3 n -2)2=
For n=1,
L.H.S=12
R.H.S=1×(6-3-1)/2
=2/2
=1
As L.H.S≠ R.H.S
We should Replace R.H.S by [(3 n-1)(3 n-2)]2
3.The given sequence is
2+4+6+....+2n=n(n+1)
L.H.S
P(1)=2
R.H.S
1×(1+1)
=1×2
=2
( b) L.H.S
P(n)=2+4+6+.....2 k
This is an A.P having n terms.
tex]S_{n}=
= n(n+ 1)
R.H.S=n(n+1)
So, P(k)=k(k+1)
(c) P(k+1)=2+4+6+.......+2(k+1)
This is an A.P having (k+1) terms.
=(k+1)(k+2)
So, P(k+1)= (k+1)(k+2)
(Btw this is not my answer)
Select the objects that hold the same amount of liquid as 160 fluid ounce jug spect all that apply A four 8 ounce fluid glasses and four 1-pint bottles B four 1 quart bottles C Five 1 quart bottles D four 1 quart bottles and two 1 pint bottles E three 1 quart bottle and 8 ounce fluid glasses
PLEASE HELP !!! URGENT
Answer:
The answer is B--> 111 degrees
Answer:
Here
X=75+36(Exterior angle of a triangle is equal to sum of interior opposite angle)
X=111
Express the number CMLXXVI in our numeration sytem.
Answer:
976
Step-by-step explanation:
CMLXXVI = − C (100) + M (1000) + L (50) + X (10) + X (10) + V (5) + I (1) = 976
In the accompanying diagram of parallelogram ABCD, m
Answer:
m<D = 120°
Step-by-step explanation:
Adjacent angles are supplementary in a parallelogram.
Thus:
2x + 12 + 5x = 180°
Collect like terms
7x + 12 = 180
7x = 180 - 12
7x = 168
x = 168/7
x = 24
✔️m<D = 5x° (opposite angles in a parallelogram are equal)
Plug in the value of x
m<D = 5(24)
m<D = 120°
A parabolic satellite television antenna has a diameter of 16 feet and is 1 foot deep. How far is the focus from the vertex
Answer:
[tex]P=16ft[/tex]
Step-by-step explanation:
From the question we are told that:
Diameter [tex]d=16ft[/tex]
Depth [tex]dp=1ft[/tex]
Generally the equation for a Parabola is mathematically given by
[tex]y=ax^2[/tex]
Since of the parabola has
Diameter [tex]d=16ft[/tex]
Depth [tex]dp=1ft[/tex]
Therefore it passes through
[tex]x=(8,1)[/tex]
Therefore
[tex]1=a(8)^2[/tex]
[tex]a=\frac{1}{64}[/tex]
Since P(distance from focus to the vertex)
[tex]a=\frac{1}{4p}[/tex]
Substituting
[tex]\frac{1}{64}=\frac{1}{4p}[/tex]
[tex]P=16ft[/tex]
Calculate the volume and area of a , b and c
(Do not convert it to meters)
Answer:
See answers below
Step-by-step explanation:
Volume of the box = length * width * height
Volume of the box = 15 * 12 * 20
Volume of the box = 300 * 12
Volume of the box = 3600 cubic cm
Area of rectangle = Length * Width
Area of rectangle A = 20cm * 12cm
Area of rectangle A = 240sq.cm
Area of rectangle B = 15cm * 20cm
Area of rectangle B = 300 sq.cm
Area of rectangle C = 15cm * 12cm
Area of rectangle C = 180 sq.cm
Use this table to find how much tax you need to pay on a taxable income of 40,000
Answer:
$14,386.25
Step-by-step explanation:
If the function f(2x + 3) = 3x- 8, find f -¹(x)
Answer:
(2x + 35)/3
Step-by-step explanation:
f(2x + 3) = 3x - 8
= 3(2x)/2 - 8
= 3(2x + 3 - 3)/2 - 8
= 3(2x + 3)/2 - 3(3)/2 - 8
= ( 3(2x + 3) - 25)/2
Therefore, f(x) = (3x - 25)/2
Let f(x) = (3x - 25)/2 = y
Therefore,
x = (2y + 35)/3 = f(y)
Hence,
f-¹(x) = f(y) = (2y + 35)/3
Just by merely replacing y,
f-¹(x) = (2x + 35)/3
Answer:
Step-by-step explanation:
[tex]let~g(x)=2x+3,~ then~f\circ g(x)=f(g(x)=3x-8\\\\[/tex]
lets assume that f(x) is a line, so f(x)=mx+b
[tex]f(g(x))=m(2x+3)+b=2mx+3m+b=3x-8[/tex]
the follow equation system results:
[tex]2m=3 \\ 3m+b=-8[/tex]
[tex]m=\frac{3}{2}\\\\b=-\frac{25}{2}[/tex]
finally:
[tex]y=f(x)=\frac{3}{2}x-\frac{25}{2}[/tex]
now is time to calculate the inverse function:
[tex]y=\frac{3}{2}x-\frac{25}{2}=>2y+25=3x=>x=\frac{2}{3}y+\frac{25}{3}[/tex]
so
[tex]f^{-1}(x)=\frac{2}{3}x+\frac{25}{3}[/tex]
Based on a poll, among adults who regret getting tattoos, 25% say that they were too young when they got their tattoos. Assume that four adults who regret getting tattoos are randomly selected, and find the indicated probability. Complete parts (a) through (d) below.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
Answer:
0.3164 = 31.64% probability that none of the selected adults say that they were too young to get tattoos.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either the say their were too young to get tattoos, or they do not say it. The answers for each adult is independent, 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% say that they were too young when they got their tattoos.
This means that [tex]p = 0.25[/tex]
Four adults who regret getting tattoos are randomly selected
This means that [tex]n = 4[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0). So
[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]
0.3164 = 31.64% probability that none of the selected adults say that they were too young to get tattoos.
4x+9=41 x is equal to
Answer and Step-by-step explanation:
Simply solve for x (very easy to do).
4x + 9 = 41
Subtract 9 from both sides of the equation.
4x = 32
Divide both sides of the equation by 4.
x = 8
x is equal to 8.
#teamtrees #PAW (Plant And Water)
