Answer:
Step-by-step explanation:
-3×2x)+(-3×5)
-6x+-15
310
Which law would you use to simplify the expression
quotient of powers
power of a quotient
product of powers
power of a product
power of a quotient
edge 2021
The law used to simplify the expression is quotient of powers.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,
3¹⁰ / 3⁴
For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.
By the definition we have the property of the power quotient of the same base set:
xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾
So, using the same,
3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶
Thus, to simplify the expression we must use the property of the power quotient of the same base.
Hence, the law used to simplify the expression is quotient of powers.
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Determine the surface area of a sphere with a diameter of 16 cm. Question 4 options: A) 804.2 cm2 B) 1,024 cm2 C) 201.0 cm2 D) 3,216.9 cm2
Answer:
The answer is option A.
804.2cm²Step-by-step explanation:
Surface area of a sphere is 4πr²
where r is the radius
radius = diameter / 2
radius = 16/2 = 8cm
Surface area of the sphere is
4π (8)²
= 4(64)π
= 256π
= 804.2cm²
Hope this helps you.
A motor is 85.4 % efficient: that is, the output is 85.4 % of the input.
What is the input if the motor delivers 10.75 hp. ( Round your answer to 1
decimal place.)
Answer:
12.6 hp
Step-by-step explanation:
output of motor = 85.4% of input of motor.
Given that motor delivers 10.75 hp, it means output of motor is 10.75hp
Using both the given conditions
10.75 = 85.4% of input of motor
=> 10.75 = 85.4/100 * input of motor
=> input of motor = 10.75*100/85.4 = 1075/85.5 hp = 12.57 hp.
Input of motor rounded to 1 decimal place = 12.6 hp
A team of 15 soccer players needs to choose a captain and a co-captain. Is this an example of permutations or combination. Then find the number of possiblities.
Answer:
Permuation; 210 possibilites
Step-by-step explanation:
With permutations we care about the order of the elements, whereas with combinations we don’t. For this question order matters, because you have two different positions you want to fill (captain, and co-captain).
This would be written as 15p2
To find the number of possibilities we want to use the permuation equation.
(,)=!(−)!
P=permutation
n= the set or population (15 soccer players)
r= subset (1 captain and 1 co-captain, total of 2)
(,)=(15,2)
=15!(15−2)!
= 210
If u are confused about !(factorial) in the equation here is a quick explanation
Many calculators have a factorial key (look for the ! symbol). This function of the calculator will automate the multiplications, but if you do not have a calculator that can compute factorials you just have to go like this
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362880
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800
etc
Hope this helps!!
The number of possibilities in choosing captain and co-captain are 210 ways.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, a team of 15 soccer players needs to choose a captain and a co-captain.
Number of captains can be choose from 15 players.
Number of co-captains can be choose from 15-1=14 players.
So, the number of possibilities= 15×14
= 210 ways
Therefore, the number of possibilities in choosing captain and co-captain are 210 ways.
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explain the words and the connections of population ,area, urban,and density
Step-by-step explanation:
1. Population Area: this can be defined as a group of similar species
inhabiting/ co-existing in a defined location or space
2. Urban population: urban areas are often more developed areas with greater population than rural environments
it's the people living in cities.
3. Population density: this is a measurement of population per unit area..
Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2? StartFraction x Superscript one-half baseline Over y z squared EndFraction StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction StartFraction y Superscript one-half Baseline Over x z squared EndFraction
Answer:
[tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]
Step-by-step explanation:
Given
[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]
Required
Find the equivalent
To find the equivalent of the given expression; we have to apply laws of indices;
As a law;
[tex]a^{-m} = \frac{1}{a^m}[/tex]
So; the expression [tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex] becomes
[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}}*\frac{1}{z^2}[/tex]
This is further simplified to
[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}} * z^2}[/tex]
[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}z^2}[/tex]
Combine to form a single fraction
[tex]\frac{x^{\frac{1}{2}}*1}{y^{\frac{1}{4}}z^2}[/tex]
Multiply numerator
[tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]
The expression can not be further simplified
Hence [tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex] is equivalent to [tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]
Answer:
c
Step-by-step explanation:
x has a exponent of -1 after multiplying 1/2 and -2, so x has to be in the denominator of the answer no matter what.
Hope this helped other than the guy above lol
2. Points A, B and C are all on the
circumference of the circle.o
represents the centre.
DA and DB are tangents to the
circle. Angle BDO = 31
Work out the size of angle.
Question
Points A, B and C are all on the
circumference of the circle. O represents the centre. DA and DB are tangents to the circle. Angle BDO = 31°
Work out the size of angle x
Answer:
62°
Step-by-step explanation:
To solve for the above question, we would be using circle theorems.
Step 1
Angle OBD = 90° This is because a radius and a tangent meet at 90°
Step 2
The sum of Angles in a triangle = 180°
180° = Angle OBD + Angle BDO + Angle BOD
180° = 90° + 31° + Angle BOD
Angle BOD = 180° - (90° + 31°)
= 180° - 121°
Angle BOD = 59°
Step 3
Angle BOD = Angle AOD because they are congruent ,therefore, Angle AOD = 59°
Step 4
The sum of angles of a straight line = 180°
Angle BOD, Angle AOD and Angle x are angles on a straight line
Hence,
180° = Angle BOD + Angle AOD + Angle x
180° = 59° + 59° + x
x = 180° - ( 59 + 59)°
x = 180° - 118°
x = 62°
Therefore Angle x = 62°
steve can run 3.5 miles in 30 minutes. if he increases his rate by 1/2 mile per hour, how far will he run in 2 hours?
Answer:
15 miles
Step-by-step explanation:
Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.
Answer:
15
Step-by-step explanation:
because its correct just did the thing.
Find the missing length indicated.
Answer:
Step-by-step explanation:
x=✓25*9
x=✓5^2*3^2
x=5*3
x=15
can anyone help me with these questions
Answer:
1. 31.14
2. 46
Step-by-step explanation:
1. Using order of operations, we first simplify what's in the parentheses, so we do 4.1-(-6.2), or 4.1+6.2. This gives us -5+3.8(10.3). Next is multiplication, so we do 3.8(10.3), which gets us to -5+39.14. Lastly, we add, to get 31.14.
2. First, we solve in the parentheses. Within the parentheses, we do multiplication first, so we first do 3*-2, to get us 8-4(-6+(-13))÷2. Then, we solve inside the parentheses, so we do -6+(-13), to get 8-4(-19) ÷2.
Next, since multiplication and division are on the same level, we go from left to right, so we do -4*-19 first, to get 8+76÷2. Now we do division, to get 8+38. Lastly, we add, to get 46.
Answer:
9) 34.14
10) 46
Step-by-step explanation:
HELP!!! How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked?
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles:
Choose the best answer that represents the property used to rewrite the expression.
log5 6 − log5 3 = log5 2
Answer:
The Quotient Property.
Step-by-step explanation:
Since all three logarithms have the same base (base-5), and you are subtracting 6 and 3, to solve this all you need to do is 6 / 3 because of the Quotient Property.
You aren't multiplying anything, so you wouldn't use the Product Property.
You are not messing around with powers, so you wouldn't use the Power Property.
And you aren't using addition or multiplication, so you wouldn't use the Commutative Property.
Hope this helps!
If a sample consists of the following data values, what is the sample mean?
13, 91, 44, 68, 54, 16, 88, 74
Answer:
mean =sum of all data values
total number of data
13+91+44+68+54+16+88+74
8
448
8
=56
therefore the mean is 56
Answer: 51
Step-by-step explanation:
Find the missing segment in the attached image
Answer:
The length of the missing segment is 24
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{15}{x} = \frac{15+5}{8+x}[/tex]
[tex]\frac{15}{x} = \frac{20}{8+x}[/tex]
Cross Multiply
[tex]15 * (8 + x) = 20 * x[/tex]
Open bracket
[tex]15*8 + 15 * x = 20 * x[/tex]
[tex]120 + 15x = 20x[/tex]
Subtract 15x from both sides
[tex]120 + 15x -15x= 20x-15x[/tex]
[tex]120 = 20x-15x[/tex]
[tex]120 = 5x[/tex]
Divide both sides by 5
[tex]\frac{120}{5} = \frac{5x}{5}[/tex]
[tex]\frac{120}{5} = x[/tex]
[tex]24 = x[/tex]
[tex]x = 24[/tex]
Hence, the length of the missing segment is 24
-
Given the graph of y = f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of
y = f(x - 4) + 3.
Answer:
The blue point will be at (4, 3)
Step-by-step explanation:
Numbers inside the parenthases only affect x, but are revered. If it is -4, move right 4. lf it is 4, move left 4.
Numbers after the patentheses affect the movement of y. When the point is at (4, 0), move up 3.
approximately 13% of the USA population is left handed. Hiw many lefties would expect in a school of 420 students
Answer:
Approximately 55 students
Step-by-step explanation:
13% of 420 is 54.6 which you can then round up to 55
Hope this helped!
Answer:
55 students
Step-by-step explanation:
Take the percent and multiply by the number of students
13% * 420
.13 * 420
54.6
Rounding up
55 students
Find a quadratic polynomial the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.
Step-by-step explanation:
We khow the sum and the product of the zeroes of this quadratic polynomial
Here is a trick :
when we khow the sum S and the product P ofvtwo numbers we can find them by solving :
x²-Sx+p=0
here S= -8 and P=12
so:
x²+8x+12=0
Let Δ be the discrminant of this equation: a= 1 , b= 8 and c=12
Δ= 8²-4*12 =16
the zeros are:
(-8-4)/2= -6
(-8+4)/2 = -2
verify:
-6+(-2)= -8
-2*(-6)= 12
now the polynomial quadratic is:
(x+6)(x+2)
Help Please I'm Out Of Time ;(
Evaluate 2y² + y² / 3 for x = 1.5 and y = 3.
Show all of your work.
Answer: 6.25 IF my assumption is correct about the missing x!
The Other way around: 4.5 with 2x² + y² / 3
Step-by-step explanation: 2y² + y² / 3 assuming the 2nd y should have been x, 1st y is y, and all divided by 3
2(3)² + (1.5)² / 3
2(9) + 2.25 /3
18 + 2.25 /3
20.25/3
6.25
Edited to correct!________ OR 2y² + y² / 3 assuming the 1st y should have been x, 2nd y is y, and all divided by 3
2(1.5)² + (3)² / 3
2(2.25) + 9 / 3
4.5 + 9 /3
13.5 /3
4.5
Answer:
[tex]\frac{13.5}{3}[/tex]
Step-by-step explanation:
=> [tex]2x^2+y^2/3[/tex]
Where x = 1.5, y = 3
=> 2(1.5)²+(3)² / 3
=> 2(2.25)+9 / 3
=> 4.5 + 9 / 3
=> 13.5 / 3
=> [tex]\frac{13.5}{3}[/tex]
PLEASEEEE HELPP !!In each figure, a//b . Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.
Answer:
No it’s not a translation
Step-by-step explanation:
No it’s not a translation because a translation is when you are just moving a shape not resizing or rotating the shape.
You would like to have $4000 in 3 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 4.5% compounded semiannually. a. Use one of the formulas below to determine how much you should deposit at the end of every six months.
Answer:
666.70 at the end of every six months.
Step-by-step explanation:
At the end of every six months deposit amount is 666.70
What is compound interest ?Compound interest is the interest paid on both principal and interest, compounded at regular intervals.
Formula of compound interest :
[tex]A = P(1+\frac{r}{100} )^{n}[/tex]
where,
A = final amount
P = initial principal
n = time in years
r = rate per annum
According to the question
Final Amount needed for a special vacation (A) = $4000
Time in years needed to collect Amount (n) = 3 years
Rate per compounded semiannually (r) = 4.5%
Substituting values in formula for six months
Now time (n) = 3 * 6 = 18 years
using formula of compound interest
[tex]A = P(1+\frac{r}{100} )^{n}[/tex]
[tex]4000 = P(1+\frac{4.5}{100} )^{18}[/tex]
[tex]4000 = P(1.045 )^{18}[/tex]
now,
P = 666.70
Hence, at the end of every six months deposit amount is 666.70
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1 kilogram
One ratio you could use for converting units is
1,000 grams
A. True
O B. False
Answer:
True
Step-by-step explanation:
For every kilogram, there are 1000 grams
A nautical mile is the unit of length used in sea and air navigation. A
nautical mile is equal to 6,174 feet. What percent of a statute mile, (5,360
feet) is a nautical mile? (Round to the nearest hundredth.)
Answer:
86.82%
Step-by-step explanation:
A nautical mile = 6,174 feet.
Statute mile =5,360 feet
The percentage of a statute mile to a nautical mile is calculated as:
5360/6174 × 100
= 0.8681567865 × 100
= 86.81567865%
Approximately to the nearest hundredth = 86.82%
Therefore, the percent of a statute mile that is a nautical mile rounded to the nearest hundredth is 86.82%
Which function has the same graph as x+y= 11?
A. Ax) = -y + 11
B.
Rx) = -x + 11
C.
A x) = x-11
D.
*x) = y- 11
Answer:
the answer is b= -x+11
Answer:b
Step-by-step explanation:
A company wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 100 customers and asks them about their level of satisfaction with the company.what type of sampling method is use
Answer:
The type of sampling method used is:
Simple random sampling.Step-by-step explanation:
A simple random sampling is a method where the pollster, in this case, the company, from a finite or infinite population (the costumers in the database) takes a representative sampling (in this case 100 costumers) to apply the survey and obtain data that can be used to deduce the way of thinking of all the costumers, though to actually identify this way of thinking, the sampling must be proportional to the size of the population, on the contrary, the data obtained won't be useful to reveal the real level of the satisfaction (In this case securely the database is 10,000 costumers or less, then the sampling is at least the 1% of the population). Another characteristic is all the people in the population should have the same opportunity to be part of the sampling, this is identified in the paragraph where says that the selection was random.
Answer:
B. simple random sampling
Step-by-step explanation:
right on edge
A doctor prescribes 500 milligrams of a therapeutic drug that decays by about 19% each hour.
a) To the nearest minute, what is the half-life of the drug?
b)
Write an exponential model representing the amount of the drug remaining in the patient's
system after t hours. (2 points)
c)
Use your formula to find the amount of drug that would remain in the patient's system after 24
hours. Round your answer to the nearest hundredth of a gram. (2 points)
Answer:
a) half life is 3h 17 minutes
b) function of residue drug after t hours with initial quantity = 500 mg
f(t) = 500 (0.81^t)
c) drug left in patient's system after 24 hours
= 0.00 grams (to the hundredth of a gram.
Step-by-step explanation:
Given:
Drug initial active weight, A = 500 mg
Residue active weight, f(t) = A 0.81^t
t = time in hours.
a) half life
Half life is T, such that f(T) = 0.5A =>
0.5A = A(0.81^t)
0.81^t = 0.5
t*log(0.81) = log(0.5)
t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours
= 3 h 17.36 minutes
b) Equation of function of residue drug as a function of time t in hours
A=500 mg
f(t) = A(0.81^t) substitute A = 500 mg
= 500(0.81^t) mg
c) weight of residue drug after 24 hours to the hundredth of a gram.
t=24 hours
A=500
f(t) = 500(0.81^t) substitute t=24 hours
= 500(0.81^24)
= 3.181 mg
= 0.003181 g
GPAs at CCSU are normally distributed with a mean of 2.38 and a standard deviation of 0.45. Find the z-score for a GPA of 3.06. and discuss the significance of the z-score.
Step-by-step explanation:
Z-score = (score-mean)/standard deviation
= (3.06-2.38)/0.45
= +1.51
The significance of z-score will be "1.5111".
Given values are:
Mean,
[tex]\mu = 2.38[/tex]
Standard deviation,
[tex]\sigma = 0.45[/tex]
GPA,
[tex]\bar x = 3.06[/tex]
Now,
→ The z-score will be:
= [tex]\frac{\bar x - \mu}{\sigma}[/tex]
By putting the given values, we get
= [tex]\frac{3.06-2.38}{0.45}[/tex]
= [tex]\frac{0.68}{0.45}[/tex]
= [tex]1.5111[/tex]
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Fill in the blank with a number to make the expression a perfect square.
Answer:
16
Step-by-step explanation:
[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]
Answer:
Step-by-step explanation:
a² + 2ab +b² = (a+ b)²
w² - 8w + _?___
a = w
2ab = -8w
2*w*b = -8w
b = -8w/2w
b = 4
8w = 2 * 4*w
w² - 8w + 4² =w² -8w + 16
Angelo cuts a piece of wood for a project. The first cut is shown and can be represented by the equation y - 5x-1. The second cut needs to be parallel to the first. It will pass through the point (0,6). Identify the equation that
represents Angelo's second cut.
PLEASE HELP!
Answer:
y=5x+6
Step-by-step explanation:
Please see attached
Which of the following applies the law of cosines correctly and could be solved to find m∠E? ANSWERS: A) cos E = 312 + 392 – 2(31)(39) B) C) 562 = 392 – 2(39) ⋅ cos E D) 562 = 312 + 392 – 2(31)(39) ⋅ cos E
This question is incomplete because the options were not properly written.
Complete Question
Which of the following applies the law of cosines correctly and could be solved to find m∠E? ANSWERS:
A) cos E = 31²+ 39² – 2(31)(39)
C) 56² = 39² – 2(39) ⋅ cos E
D) 56² = 31² + 39² – 2(31)(39) ⋅ cos E
Answer:
D) 56² = 31² + 39² – 2(31)(39) ⋅ cos E
Step-by-step explanation:
From the above diagram, we see are told to apply the law of cosines to solve for m∠E i.e Angle E
The formula for the Law of Cosines is given as:
c² = a² + b² − 2ab cos(C)
Because we have sides d , e and f and we are the look for m∠E the law of cosines would be:
e² = d² + f² - 2df cos (E)
e = 56
d = 39
f = 31
56² = 39² + 31² - (2 × 39 × 31) × cos E
Therefore, from the above calculation and step by step calculation, the option that applies the law of cosines correctly and could be solved to find m∠E
Is option D: 56² = 31² + 39² – 2(31)(39) ⋅ cos E
Answer:
[tex]56^2 = 31^2 + 39^2 minus 2(31)(39) cos E[/tex]
Step-by-step explanation:
Hello, I just took the exam got the answer correct
if straykids hyunjin had 50,000 won and wanted to by lots of 45rings for 500 won how much will he have left? b) if changbin and han had 145 lightsicks and sold 75? how much lighsticks will they have now?
Answer:
a) he would have 27500 won
b) changbin and han would have 70 lightsticks
Step-by-step explanation:
a)
multiply 45 rings by 500 won to get the total expense
45 x 500 = 22500
then subtract 22500 won from 50000 to get the amount left after the purchase
50000 - 22500 = 27500
this results in 27500 won total
b)
subtract 75 from 145 to get the amount left
145 - 75 = 70
Answer:
Hyunjin has 27,500 left.
Changbin & Han have 70 lightsticks left.
Step-by-step explanation:
A) 45 × 500 = 22500 50,000 - 22500 = 27500
B) 145 - 75 = 70