The multiplication law states that
a^m×a^n=a^m+nSo
5³×5-³=15^(3-3)=15⁰=11=1Answer:
1 = 1
Step-by-step explanation:
5^3*5^-3 = 1We all know the law of exponents,the one we'll use to solve this is the multiplication law:
x^y * x^z = x^y+zIf the bases are equal or two numbers then the powers are equal too.Solved:
[tex]5^3 \: * \: 5^{-3} = 1[/tex][tex]5 {}^{3 + ( - 3)} = 1[/tex][tex]5 ^{0} = 1[/tex]x^0 = 1
[tex]1 = 1 \: ( \rm \: Proved)[/tex]Alternate method:
5^3*5^-3 = 15^3*1/5^3 = 15^3 and 5^3 cancels, which results to
1 = 1(d) Two alarm clocks are set to ring at intervals of 42 minutes and 56 minutes respectively. If the alarm clocks ring together at 0830, at what time will they next ring together again?
Answer:
11:18
Step-by-step explanation:
the lowest common multiple [meaning the nearest possible time these clocks will be ringing at the same time] of 42 and 56 is 168
(56 x 3 = 168 ; 42 x 4 = 168)
So, in 168 minutes, the clock will ring together again.
Now, we need to add 168 minutes to 08:30
(168 can be made up of 2 hours and 48 minutes [120 + 48 = 168])
08:30 + 2 hours = 10:30
10:30 + 48 minutes = 11:18
So, at 11:18, these clocks will ring together again
The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the height above water and x is the horizontal distance in feet. If a beam of light is shone upward at an angle modeled by the equation x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?
Answer:
5 feet
The graphs intersect at x = 5.
Round to 2 decimal places 8.041
Answer:
8.04
Step-by-step explanation:
If the last digit in 8.041 is less than 5, then remove the last digit.
I hope this helps!
Max's Market sells 6 eggs for £2.04.
Groceries Galore sells 8 eggs for £2.64.
Fancy Foodstuffs sells 12 eggs for £4.08.
Which shop's price per egg is cheaper?
Answer:
Groceries Galore
Step-by-step explanation:
1) Find the value of 1 egg for each shop.
Max's Market:
2.04 ÷ 6
= £0.34
Groceries Galore:
2.64 ÷ 8
= £0.33
Fancy Foodstuffs:
4.08 ÷ 12
= £0.34
Therefore, Groceries Galore's price per egg is cheaper.
Answer:
Groceries Galore
Step-by-step explanation:
we have to calculate the price of 2 eggs
in each shop apart ,and then we can infer
which shop offers the cheaper price.
…………………………………………………………
• At Max's market :
2 egg costs 2,04÷3 = £0,68
• At Groceries Galore :
2 egg costs 2,64÷4 = £0,66
• At Fancy Foodstuffs :
4,08÷6 = £0,68
………………………………
Conclusion :
Groceries Galore Offers the Lower price.
Note : we can just determine
the price of one egg in each store ,and then compare.
The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score? A) 20 B) 24 C) 32 D) 36
The highest score is 32.
What is mean?The mean refers to the average of a set of values.
Total players = 8
Mean= 14.5
Now, total score of 8 players,
= 14.5*8
=116
and, Total score for the remaining 7 players
= 12 * 7
= 84
Hence, the highest score is 116-84 =32
Learn more about this concept here:
https://brainly.com/question/20375891
#SPJ1
a tree surgeon reduces the height of a beech tree by 32%.
the tree is now 4.42m tall.
how tall was it before it was reduced?
Let original Hieght be X
reduction = 32% = 32/100 X
new hieght = 4.42 m
now, 4.42 = X + 32/100 X
4.42 = 132/100 X
X = 4.42 * 100 / 132
X = 3.34 m
Original Hieght = 3.34 m
(a − b)(2x − 3) + (6x + 7)(a − b)
factorise and ignore the first question it was wrong
Answer:
8ax - 8bx + 4a - 4b
Step-by-step explanation:
(a - b)(2x - 3) + (6x + 7)(a - b)
2ax -3a -2bx +3b + 6ax - 6bx + 7a -7b
8ax + 4a - 8bx - 4b
The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12Ï€ cubic inches 36Ï€ cubic inches 64Ï€ cubic inches 81Ï€ cubic inches.
Answer: 113 inches cubed
Step-by-step explanation:
Volume of a sphere = 4/3 Pi r^3
Radius = 3 inches
Volume = 113 inches cubed
Hope I helped!
Please help me with this ASAP.
Kiran’s mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20% as a tip.
What is the total after the discount and tip? Explain or show your reasoning.
Answer:
See below for both parts
Step-by-step explanation:
A)
Coupon Price:
$25 - 15% ($3.75) = $21.25
10% = 2.50
5% = 1.25
After taking the discount coupon off the final price is $21.25
B)
20% is given as a tip.
20% of $21.25 = $4.25
10% = 2.125
$21.25 + $4.25 = $25.50
Final price with tip is $25.50
A seamstress was hired to make band uniforms for Hinsdale High school. The seamstress bought 148 yards of material. There were 16 students in the concert band and 20 students in the symphonic band. How much material did she have for each uniform?
Answer:
4.11 yards/uniform
Step-by-step explanation:
We aren't told that there will be any differences in the uniforms among the 16 concert and 20 symphonic band students. No information on sizes, styles, or anything else.
In the absence of this information, we must assume all uniforms are the same.
(16 + 20) = 36 students/uniforms
148 yards of material
148 yards/36 uniforms = 4.11 yards per uniform.
Solve for DG. Show all work
32/40 = 24/dg
32dg = 40 x 24
32dg = 960
dg = 960/32
dg = 30
Answer: DG = 30
Answer:
DG = 30 unitsStep-by-step explanation:
these are 2 similar triangles, so we can solve with an equation
FC : CE = DG : ED
24 : 32 = x : 40
x = 24 * 40 : 32
x = 960 : 32
x = 30
DG = 30 units
------------------------------
check24 : 32 = 30 : 40
0.75 = 0.75
The answer is good
What is the gradient of the blue line?
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car
can travel on 7 gallons of gas?
Answer:
147 miles
Step-by-step explanation:
The first step is to find the number of miles traveled per gallon of gas
63 miles / 3 gallons = 21 miles per gallon
Take the rate and multiply by the number of gallons used to get the distance traveled
d = r * g
d = 21 * 7
d =147
The distance traveled is 147 miles
Find x.
7x
6x+1
4x+6
Answer:
this is the answer
Step-by-step explanation:
6x+1=0
6x=-1
x=-1/6
x=0,166
7x=7×x
what is the degree of the polynomial below?
2 times x squared plus 3 times x plus 1
Answer:
2
Step-by-step explanation:
The degree of a polynomial is the highest of the degrees of the polynomial's monomials with non-zero coefficients. In 2x^2 + 3x +1, our highest degree is 2.
Can someone explain how I do this?
Answer:
oh soooooooooooooooo sorry
Step-by-step explanation:
sorry
Answer:
12.5N
Step-by-step explanation:
See attached image.
Helena sees this recipe for pastry. she says that the ratio of margarine to flour is 4:1 is Helena correct? explain your answer
pastry:200g flour pinch salt
50g margarine water to mix
50g lard
Answer:
NOsince it talks about a ratio of margarine to flour, we should write it in this form:
MARGARINE : FLOURSince we have a 50g margarine and a 200g flour, therefore, we write it as
➡️ 50 : 200 ➡️ 1 : 4
FINAL ANSWER SHOULD BE:
1 : 4Step-by-step explanation:
Ratio of MARGARINE TO FLOUR
Given that margarine is 50g and flour is 200g. Therefore,
Margarine:Flour ➡️ 50:200 = 1:4
To check:
A:B= C:D ➡️ 50:200= 1:4
▶️AD= BC ➡️ (50) (4) = (200) (1)
➡️ 200 = 200
☑️
Hope it helps
Do this for me x+y=6
Answer:
A = 8 ; B = 6 and C = 4
Step-by-step explanation:
(-2) + A = 6
A = 6 + 2
A = 8
0 + B = 6
B = 6
2 + C = 6
C = 6-2
C = 4
Six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that a girl wins the first place award while boys will receive the second and third place awards? express your answer as a percent.
Answer:
the probability is 10%
Step-by-step explanation:
please solve and tell me all that apply
Answer:
-x+4, 4+-x
Step-by-step explanation:
Obtain these answers by moving the X and 4 around and multiplying the equation by -1
Solve the given proportion.
X/3 = 6/2
x = [?]
Answer:
x = 9
Step-by-step explanation:
x/3 = 6/2
~Simplify
x/3 = 3
~Rewrite
1/3x = 3
~Multiply 3 to both sides
x = 9
Best of Luck!
Answer: x=9 ✅
Step-by-step explanation:
Hii student, I'd love to help you out! (:
In this problem, we need to solve a proportion. This is fun, right?
3,2,1 - start!
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solving proportions is easy as winking, if you are familiar with a skill that is known as "cross multiplying".
We have these two proportions:
(oh and by the way, proportions are just equivalent (equal) fractions. That's all proportions are. Nothing more)
Our proportions are:
[tex]\large\boldsymbol{\cfrac{x}{3}=\cfrac{6}{2}}[/tex]
We multiply x times 2 and 3 times 6; upon doing that we obtain.
[tex]\multimap\quad \tt 2x=18[/tex]
Did you see that? 2 fractions turned into a little equation that we can solve within 5 seconds (or faster)!
To do that we simply divide both sides by 2, since x is multiplied by 2 and we need to get it all by itself on one side of the equal sign)
[tex]\multimap\quad \tt x=9[/tex]
Woohoo! We found the answer! ✨
Cheers! (: ____________________________________Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
what's a frustum and what's the formula of the Almighty Formula
Answer:
the portion of a solid that lies between one or two parallel planes cutting it
Step-by-step explanation:
I need to know which ones are parallel and which ones are perpendicular and the steps thank youu
Answer:
If both equations have the same slope, they are said to be parallel.
If an equation is the reciprocal of another equation (meaning flipped denominator and numerator as well as flipped +/- sign) they are said to be Perpendicular.
Hope it helps!
Y W P 8 cm E R WERP is a square. Find.
1. m2WER=
2. measure of PE =_______
3. measure of WA =
4. Value of y=
1) All interior angles of a square are right angles, so angle WER measures 90°
2) All squares are parallelograms, and diagonals of a parallelogram bisect each other, meaning PA=AE=8 cm. Thus, PE=16 cm
3) All squares are rectangles, and diagonals of a rectangle are congruent, meaning WR=16 cm. Then, using the fact that the diagonals bisect each other, we get that WA=8 cm
4) If we consider right triangle WPR, we know it is isoceles because all sides of a square are congruent. So, the length of WP is:
[tex] \frac{16}{ \sqrt{2} } = 8 \sqrt{2} [/tex]
The largest number of Oscars received by a film in year X was 4. This was different in previous years. Below is a probability distribution for the number of Oscars per Oscar winning film. What is the standard deviation of this distribution
The standard deviation of the given discrete distribution, considering it's formula, is of 1.195.
How to find the mean and the standard deviation of a discrete distribution?The mean is given by the sum of the multiplications of each outcome by it's probability.The standard deviation is given by the square root of the sum of the squares of each outcome subtracted by the mean, multiplied by it's probability.Researching this problem on the internet, the distribution is given by:
P(X = 1) = 0.56.P(X = 2) = 0.23.P(X = 3) = 0.11.P(X = 4) = 0.05.P(X = 5) = 0.03.P(X = 6) = 0.02.Hence the mean is given by:
E(X) = 0.56(1) + 0.23(2) + 0.11(3) + 0.05(4) + 0.03(5) + 0.02(6) = 1.82.
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{0.56(1-1.82)^2+0.23(2-1.82)^2+0.11(3-1.82)^2 + \cdots + 0.02(6-1.82)^2} = 1.195[/tex].
More can be learned about the standard deviation of a discrete distribution at https://brainly.com/question/13008984
#SPJ1
Find (gof)(3)
f(x) = x + 21
g(x) = -x²
a. -25
C.
4
b. 1
d. -15
Please select the best answer from the choices provided
A function assigns the values. The value of (gof)(3) is -576.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Given f(x)=x+21 and g(x)=-x², therefore, the value of (gof)(x) will be,
(gof)(x) = g(f(x))
= -(x+21)²
The value of (gof)(3) will be,
(gof)(3) = -(3+21)²
= -576
Hence, the value of (gof)(3) is -576.
Learn more about Function:
https://brainly.com/question/5245372
#SPJ1
Please hurry i need this asap!!!
Answer:
D
Step-by-step explanation:
d) A number plus eight is five times the number
Step-by-step explanation:Keywords within mathematical phrases can be "translated" into an algebraic equation.
Keywords
First, let's define some of these keywords that can help us answer the question.
"A number" can be replaced with the variable, x"Plus" is obviously used to denote addition"Is" is used in place of an equal sign"Times" is used to show multiplicationWriting Out the Expression
In the figure, we see that the blocks "x" and "8" is equal to the block "5x". So, we can say that x plus 8 is equal to 5x. Then, using the keywords above we can replace the variables and numbers.
This creates the new sentence, "A number plus 8 is equal to five times a number."R is the midpoint of QS. If QR = 7x and QS = 15x − 7, what is QR?
Answer: 49
Step-by-step explanation:
If R is the midpoint of QS, QS=2(QR)=2(RS).
[tex]15x-7=2(7x)\\15x-7=14x\\-7=-x\\\\x=7\\\\QR=7(7)=\boxed{49}[/tex]
What is the polynomial? Quick I need answer
Answer:
An algebraic expression containing two or more terms is called a polynomial
Answer:
Its C
Step-by-step explanation:
it worked finally
Based on the table below, determine the exponential function being used. Use x as your variable. Then, evaluate this expression for x=7.
Input (x) Output
0 1
1 5
2 25
3 125
4 625
The exponential function is used. Use x as your variable common ratio.
This is pretty obviously
If it wasn't obvious we can find the common ratio r by dividing successive values:
5/1=5
25/5=5
125/25=5
625/125=5
What is the common ratio?
The common ratio is the number you multiply or divide by at each stage of the sequence. You can find it by dividing two consecutive pairs of terms.
That's the common ratio. We multiply by the first term, but the first term is one, so that has no effect.
To learn more about the common ratio visit:
https://brainly.com/question/1509142
#SPJ1
