Which expression is equivalent to startfraction (3 m superscript negative 2 baseline n) superscript negative 3 baseline over 6 m n superscript negative 2 baseline endfraction? assume m not-equals 0, n not-equals 0.
The expression that is equivalent to the given statement was reduced.
The given expression is:
[tex]\frac{(3m^{-2}n)^{-3} }{6mn^{-2} }[/tex]
What are some important power rules?Some important power rules are:
[tex](ab)^n=a^nb^n[/tex]
[tex](a^{m} )^n=a^{mn}[/tex]
[tex]a^m.a^n=a^{m+n}[/tex]
[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]a^{-m} =\frac{1}{a^m}[/tex]
So, the given expression can be written as:
[tex]\frac{3^{-3} m^{6} n^{-3} }{6mn^{-2} }[/tex]
=[tex](\frac{3^{-3} }{6} )*(\frac{m^{6} }{m} )*(\frac{n^{-3} }{n^{-2} } )[/tex]
=[tex](\frac{1}{3^{3} *6} )*m^{5} *(\frac{1}{n^{3} *n^{-2} } )[/tex]
=[tex]\frac{m^5}{162n}[/tex]
Hence, the expression that is equivalent to the given statement was reduced.
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6. Which is cheaper?
A) $12 for 800ml or
B) $14 for 1 L
Answer:
A
Step-by-step explanation:
factorise fully 2ab2+ 8a2b
[tex]2 {ab}^{2} + {8a}^{2} b[/tex]
solution:[tex]2ab(b + 4a)[/tex]
to factorise first, find the highest common factor of each of the terms in the expression then, write the highest common factor (HCF) in front of any brackets atlast, fill in each term in the brackets by multiplying out.
The value of the expression after factorization will be;
⇒ 2ab (b + 4a)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2ab² + 8a²b
Now,
Factorize the expression as;
⇒ 2ab² + 8a²b
⇒ 2ab × b + 2×2×2a×a×b
⇒ 2ab (b + 4a)
Thus, The value of the expression after factorization will be;
⇒ 2ab (b + 4a)
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In 1983, a winter hat cost $12.95. today, a winter hat costs $24.50. if the cpi is 219, what is the percent relation of the actual price of a winter hat to the expected price? a. the actual price is 39.3% higher than the expected price. b. the actual price is 15.8% higher than the expected price. c. the actual price is 13.6% lower than the expected price. d. the actual price is 29.8% lower than the expected price.
The actual price is 13.6% lower than the expected price.
What is cpi?CPI or Consumer Price Index is a measure of determining retail inflation in an economy, based on price variations in a fixed basket of goods and services, over overtime periods.
Let's suppose the expected price is x.
The percent relation of the actual price of a winter hat to the expected price is given by;
CPI = ( expected price ) : ( price in 1983 ) × 100
219 = ( x : 12.95 ) × 100
Divide both sides by 100.
x : 12.95 = 2.19
x =2.19 × 12.95
x = $28.36 ( expected price )
p = ( 24.50 × 100 ) / 28.36
p= 2450/28.36
p = 86.4 %
100 % - 86.4 % = 13.6 %
Hence, the actual price is 13.6% lower than the expected price.
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pls help thanks!!!!!!
Answer:
he will have 29 nickles
Step-by-step explanation:
I just solved it on paper, hope it helps and if it's right
PLEASE HELPPP!!! I will give brainly points
Answer:
b
Step-by-step explanation:
Answer:
The correct answer is B, because B. is a compression of 6 and x, with 6 added in just like they said in the question.
If you start with the equation x-6, what equation do you have when you add 3 to both sides
Please do number 3 or number 5
Answer:
No 3.
[tex]165 \: \times \frac{103}{100} [/tex]
No 5.
[tex]15 \: \times \frac{100 + 17}{100} [/tex]
its been a long time
do you mind mark me as the brainliest
Answer:
3. 169.95
How:
165x1.03 = 169.95
Sheree purchased a digital camera for $367.99. She received a manufacturer’s $45 mail-in rebate and a $25 rebate from Jack’s Camera Store. What is the final price?
Answer:
297.99
Step-by-step explanation:
367.99-45-25=297.99
if a rectangle has a perimeter of 18 cm, and a height of 4 cm, what is the area?
Answer:
20 cm²
Step-by-step explanation:
Look at the diagram attached.
If the height is 4cm, we will have two sides that are 4cm for our rectangle.
We can label the other sides as x.
They are both x since opposite sides of a rectangle are equal in length.
We can make an equation with our perimeter:
[tex]2(4) + 2(x) = 18\\8 + 2x = 18\\2x = 10\\x = 5[/tex]
Now that we know the length & height, we can calculate the area:
4 × 5 = 20 cm²
Bobby was bringing his friends scalloping in Crystal River, FL. While searching for the ideal spot, he recorded the following depth of water at each stop throughout the day.
5,7,3,6,8,5,6,4,15
Mean (Round your answer to the nearest hundredth):
Median:
Mode:
Range:
Answer: Below:
Step-by-step explanation:
Mean: (5+7+3+6+8+5+6+4+15)/9 = 6.55555 ≅6.56
Median: 6
Mode: 5, 6
Range: 12
-3 and -1/2 form quadratic polynomial
Answer:
2x² + 7x + 3 = 0
Step-by-step explanation:
[tex]\sf \text{Sum = -3 + $(\dfrac{-1}{2})$}[/tex]
[tex]\sf = \dfrac{-3*2}{1*2}-\dfrac{1}{2}\\\\=\dfrac{-6}{2}-\dfrac{-1}{2}\\\\=\dfrac{-7}{2}[/tex]
[tex]\sf \text{Product =$-3*\dfrac{-1}{2}$}[/tex]
[tex]= \dfrac{3}{2}[/tex]
Quadratic polynomial:
[tex]\boxed{x^{2}-sum *x+product = 0}[/tex]
[tex]x^{2}- \left(\dfrac{-7}{2}\right)x+\dfrac{3}{2}=0\\\\x^{2} + \left(\dfrac{7}{2}\right)x+\dfrac{3}{2}=0\\[/tex]
Multiply the entire equation by 2
[tex]2*x^{2} + 2*\dfrac{7}{2}x +2*\dfrac{3}{2}=0[/tex]
2x² + 7x + 3 = 0
George has 4 sets of socks, and 4 sets of shoes. Each pair has a different color: White, Brown, Black, and Blue. If George selects a pair of socks (same color) and a pair of shoes (same color) at random, what is the theoretical probability that George will choose a white pair of shoes and a pair of socks that are not white
Using it's concept, it is found that there is a [tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
One out of four pairs of shoes are white.Three out of four pairs of socks are not white.Since the events are independent:
[tex]p = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]
[tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.
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Find the area of the shaded sector. round to the nearest tenth. Please help!!
Answer:
Step-by-step explanation:
Remark
If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.
So the way to solve this problem is to multiply the entire area of the circle by (81/360)
Area of the sector = (81/360) * pi * r^2
pi = 3.14
r =8.91 cm
Area of the sector = (81/360) * 3.14 * 8.91^2
Area of the sector = 56.09
Rounded to the nearest tenth, the answer is 56.1
Answer: 56.1 cm^2
Answer this for 20 points and brainliest
Answer:
D
Step-by-step explanation:
If you are solving for something like this, set the given full integer equal to x times the percent given
PLEASE HELP!! 90 POINTS!!!
Dianelys owns a small business selling ice-cream. She knows that in the last week 14 customers paid cash, 121 customers used a debit card, and 3 customers used a credit card. If next week, she is expecting 1100 customers, about how many would you expect to pay with cash? Round your answer to the nearest whole number.
Answer:
112 customers will pay cash next week
Step-by-step explanation:
1,100/138=7.97= approximately 8
Multiply the amount of customers who paid cash, 14 by 8.
What is the rate of change for y=5x+1?
i think the answer is this
Pls help nothings helping !!
Answer:
Step-by-step explanation:
∠BCD=∠DEF=38°(alternate angles)
∠FDE=90-38=52°
Δ BCD≅ΔFED
[tex]\frac{CD}{sin~90} =\frac{10}{sin~38} \\CD=\frac{10}{sin~38} \\\frac{DE}{sin ~90} =\frac{17}{sin ~52} \\DE=\frac{17}{sin~52} \\CE=CD+DE=\frac{10}{sin~38} +\frac{17}{sin~52} \\=?[/tex]
Calvin has a gift card which he is using to buy candy (x), and he has been tracking how much money (y) he spends. He noted that after buying 4 pieces of candy (in all) he has $28.00 left on his card and then after buying 10 pieces of candy (in all) he has $25.00 left on his card. Write the equation of the line that represents his spending on candy.
Answer:
Negative Correlation
Step-by-step explanation:
The plot looks like it's going downwards. If it was an equation, it'd be something with y = -x +b.
Help!
Square pyramids A and B are similar. In pyramid A, each base edge is 20 cm. In pyramid B, each base edge is 5 cm and the volume is 25 cm.
a. Find the volume of pyramid A.
b. Find the ratio of the surface area of A to the surface area of B.
c. Find the surface area of each pyramid.
Answer:
Below in bold.
Step-by-step explanation:
a) The volumes will be in the ratio of the cubes of the edges.
So volume of A / volume B = 20^3 / 5^3
Volume A / 25 = 8000/125
Volume a = (25* 8000) / 125
= 8000/ 5
= 1600 cm^3.
b) ratio of the surface area of A to surface area of B
= 20^2 : 5^2
= 400:25
= 16:1.
c. The volume of pyramid B is 25 cm*3 so it' height is 25 / area of its base = 25/5^2
= 1 cm.
Now its slant height = √(1^2 + (2.5)^2)
= √7.25
= 2.6926 cm
So surface area = 25 + 4 * 1/2 * 5 * 2.6926
= 51.926
= 51.93 cm^2 to nearest hundredth.
and the surface area of pyramid B = 51.926 * 16
= 830.82 cm^2 to nearest hundredth.
BRAINLIEST TO CORRECT ANSWER!!!!
A circular garden has a diameter of 12 yards. What is the area of the garden?
Use 3.14 for pi.
O A. 452.16 yd
O B. 56.52 yd
O C. 113.04 yd
O D. 37.68 yd
Answer:
As Per Provided Information
Diameter of Garden 12 yards
Radius of Garden will be 12/2
Radius of Garden will be 6 cm
We have been asked to find the area of the circular garden .
Formula Used here
[tex] \underline{\boxed {\bf \: Area_{(Garden)} \: = \pi {r}^{2}}} [/tex]
Just put the value and let's calculate the area of circular garden .
[tex] \qquad \longrightarrow\sf \: Area_{(Garden)} \: = 3.14 \times {6}^{2} \\ \\ \\ \qquad \longrightarrow\sf \: Area_{(Garden)} \: = 3.14 \times 36 \\ \\ \\ \qquad \longrightarrow\sf \: Area_{(Garden)} \: = 113.04 \: {yard}^{2} [/tex]
Therefore,
Area of circular garden is 113.04 yard².Step-by-step explanation:
Given :-
Diameter of garden is 12 yard , so radius will be 6 yardsWe have to find the area of garden
Area of Circle = πr²
Putting the known values ,
Area = 3.14 × 6² yd²
Area = 113.04 yd²
Which of the following sets of 3 side lengths could form a unique triangle?
O side lengths: 18 feet, 9 feet, 6 feet
O side lengths: 12 feet, 9 feet, 4 feet
O side lengths: 6 feet, 3 feet, 2 feet
O side lengths: 24 feet, 14 feet, 4 feet
Answer:
side lengths: 12 feet, 9 feet, 4 feet
Step-by-step explanation:
Conditions for unique triangles with 3 sides:
The sum of the two shorter sides must be greater than the third side.9 + 6 = 15
As 15 < 18 this is NOT a unique triangle
9 + 4 = 13
As 13 > 12 this IS a unique triangle
3 + 2 = 5
As 5 < 6 this is NOT a unique triangle
14 + 4 = 18
As 18 < 24 this is NOT a unique triangle
Deon buys 5 pounds of cherries and pays 12.80. Which is the cost of one pound of cherries
Answer:
$2.56
Step-by-step explanation:
12.80 ÷ 5 = 2.56
A Premier League footballer is value £30 million and after a bad season his transfer value depreciates by 20%. His next season is a good one and his transfer value appreciates by 20%. how Find the value of the footballer after his good season.
How to work out Sir
Answer:
£28.8 Milllion
Step-by-step explanation:
£30,000,000 × 0.8 = £24,000,000 (Depreciates by 20%)
£24,000,000 × 1.2 = £28,800,000 (Appreciates by 20%)
how to I write a one solution function??
The table shows some ordered pairs that belong to quadratic function h.
What is the range of h?
Question 10 options:
All real numbers greater than or equal to -5
All real numbers greater than or equal to 0
All real numbers
All real numbers greater than or equal to -2
Answer: All real numbers greater than or equal to -5
Step-by-step explanation:
The vertex has a y coordinate of -5, and all the other outputs are more than -5.
please help me!!!!!!!
The distance between you and train 1 at time t is
20.6 km + (0.2 km/h) t
and the distance between you and train 2 at time t is
59.7 km - (2.1 km/h) t
The trains are an equal distance away from you when
20.6 km + (0.2 km/h) t = 59.7 km - (2.1 km/h) t
Solve for t :
(2.3 km/h) t = 39.1 km
t = 17 h
at which point they are
20.6 km + (0.2 km/h) (17 h) = 24 km
away from you.
The figures are similar. Find x.
Pls help meee
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Answer:
The answer is C. 2.94
Step-by-step explanation:
All you have to do is take 588 and divide it by 200 which gives you the answer of 2.94.
Lloyd solves the equation 24x + 18(x – 2) = 216 for x. Some of his steps are shown.
Step 1: 24x + 18(x – 2) = 216
Step 2: 24x + 18x – 36 = 216
Step 3: 42x – 36 = 216
Step 4: 42x = 252
Which of the following statements BEST describes what Lloyd did to get from Step 3 to Step 4?
A.
combined liked terms
B.
used the distributive property
C.
used the addition property of equality
D.
used the multiplicative inverse property
Answer:
C. addition property
Step-by-step explanation:
they wouldve had to add 36 to both sides of the equation, so addition