Using Laws of exponents, the solution to the expression √(3p⁹q⁷r⁶)/(16x⁶y¹²) is; (p⁴q³r³/(x³y⁶))√(3pq/16)
How to use laws of exponents?The different laws of exponents are;
1) Product With the Same Bases; a^m × a^n = a^(m+n)
where;
m and n are real numbers.
2) Quotient with Same Bases;
a^m/a^n = a^(m-n)
where;
a is a non-zero term and m and n are integers.
3) Power Raised to a Power; (a^m)^n = a^(mn)
where;
a is a non-zero term and m and n are integers.
4) Product to a Power; a^n * b^n = (ab)^(n)
where;
a is a non-zero term and n is the integer.
5) Quotient to a Power; It states that the fraction of two different bases with the same power is represented as; a^n/b^n = (a/b)^n
where;
a and b are non-zero terms and n is an integer.
6) Zero Power; When the power of any integer is zero, then it means that its' value is equal to 1, such that;
a⁰ = 1
where;
a is any non-zero term.
7) Negative Exponent Rule; a^(-m) = 1/(a^m)
We are given the expression as;
√(3p⁹q⁷r⁶)/(16x⁶y¹²)
Applying the laws of exponents, we will have;
√(3p⁹q⁷r⁶)/(16x⁶y¹²) = (p⁴q³r³/(x³y⁶))√(3pq/16)
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I need assistance with this math assignment
The value at which acceleration is zero is t = 5/3
How to determine the value of t at which acceleration is zero?Acceleration is defined as the rate at which velocity changes with time, in terms of both speed and direction
Given: the equation of motion, velocity, s = t⁶ - 2t⁵
Since acceleration is the rate at which velocity changes with time. You need to differentiate the velocity with respect to time. Thus:
ds/dt = 6t⁵ - 10t⁴ (Note: ds/dt is the acceleration)
Also, acceleration is equal to zero. That is:
6t⁵ - 10t⁴ = 0
6t⁵ = 10t⁴
6t = 10
t = 10/6 = 5/3
Therefore, the value of t at which acceleration is zero is t = 5/3
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Solve the system of equations by graphing.
x+y=3
5x+5y=15
The system of equations are graphed in the image below, showing that they have infinitely many solutions, which include (3, 0) and (0, 3).
What is the Solution to the System of Equations?The values of a pair of x and y that will make two different equations in a system true is the solution to the system of equations.
By graphing, we can determine the solution by finding the x and y coordinates of the point that both lines of the equations intersect at.
The lines of x + y = 3 and 5x + 5y = 15 are graphed in the image below, which is the same blue line. This shows that the equations have infinitely many solutions such as (3, 0) and (0, 3).
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You flip three coins eight times. Are you guaranteed to get three heads at least once
When one flip three coins eight times, there no guarantee to get three heads at least once as the probability is low.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
The probability of getting a head in a coin is 1/2.
Therefore, the probability of getting three heads on there flips will be:
= P(head)³
= 1/2 × 1/2 × 1/2
= 1/8
Therefore, the probability is low and the heads aren't guaranteed.
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A paper company need to ship paper to a large printing house. The paper will be shipped in small boxes and large boxes. The volume of each large box is 14 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. Write a system of equation that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you can use to white the system.
Answer:
See belowStep-by-step explanation:
Let the number of small boxes is s and number of large boxes is l.
s and l are our variables.
Total number of boxes is 21:
s + l = 21This is your first equation.
The volume of a small box is a (since it is not given, if you have it please replace it with that number), and the volume of all small boxes is as.
The volume of a larger box is 14 cubic feet, and the volume of all large boxes is 14l cubic feet.
Total volume is 252 cubic feet, add the two volumes together:
as + 14l = 252And this is your second equation (don't forget to replace a with the volume of a small box).
Suppose that white wool (W) is dominant over brown wool (w) in sheep. If two heterozygous sheep are crossed, what is the probability that their babies would have brown wool?
A:50%
B:75%
C:100%
D:25%
The probability that their babies would have brown wool will be 25%.
What is heterozygous?When two or more alleles for the same characters are present at the same loci on homologous chromosomes, a cell, a nucleus, or a single organism is said to be heterozygous. In contrast to homozygous, where the alleles are identical, it signifies that the alleles that code for the same gene or characteristic are different.
Given, the two-parent sheep would need to have heterozygosity for their genotype if we were to assume straightforward Mendelian genetics. Black would not be dominant in this situation; instead, the parents would be, shall we say, Rr for color. Imagine that each parent can only contribute one allele (either the R or the r). If both should chance to deliver the r, the child would be black.
Therefore, 25% of the following generation's children are likely to be black. There would be a 25% probability of a homozygous dominant offspring, a 50% chance of a heterozygous offspring, and a 25% chance of a homozygous recessive offspring if you filled out a Punnett square for this issue. Since white is the dominant allele in this situation, both the homozygous dominant allele, which accounts for 75% of the possibilities and the heterozygous child will be white. Since two recessive alleles are required to manifest the recessive phenotype, the remaining 25% of people are black.
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2. Write the correct equation that you would use to solve for side x.
Z
X
520
y = 13cm
Z
Y
Answer: Using SOH CAH TOA you get 10.24
Step-by-step explanation:
you can determine what the value of X is and it is 10.24
This is gotten by sin52=x/13
Because we are trying to get x which is opposite the angle, and we have the value of the hypotenuse already (13) we can using SOH that is sin 52= x divided by 13
Cross multiply and you'll get 10.2441398
Find the square root of
441
Answer:
21
Step-by-step explanation:
√441
Take factors of 441
-> 1,3,7,9,21,49,63,147,441
If you know all of them like this and it’s an odd number, find the middle value that doesn’t have a pair and it’s 21.
If you don’t just take a different value that has a square root. Let’s do 9.
Separate the root into √9*49
Woah, both of those are squares!!
Take the square root of both of those numbers
√9*√49
3*7=21, voila.
It is very easy, we just have to take the square root as it tells us in the problem:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{ \sqrt{441 }} = \orange{21}[/tex]
You may ask ¿why 21?
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{21 \times 21} = \orange{441} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf So , \: the \: result \: is \\ \sf \: \: \: \: \longmapsto \orange{21} [/tex]
A certain element decays at a constant rate of 4% per year. If you start with 18 grams of the element, how long will it take before there are only two grams left? Round your answer to the nearest whole number.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & 2\\ P=\textit{initial amount}\dotfill &18\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases}[/tex]
[tex]2=18(1 - 0.04)^{t}\implies \cfrac{2}{18}=(1 - 0.04)^{t}\implies \cfrac{1}{9}=0.96^t \\\\\\ \log\left(\cfrac{1}{9} \right)=\log(0.96^t)\implies \log\left(\cfrac{1}{9} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left(\frac{1}{9} \right)}{ ~~ \log(0.96) ~~ }=t\implies 53.82\approx t\qquad \textit{about 53 years and 301 days}[/tex]
It will take approximately 54 years for the element to decay from 18 grams to 2 grams at a rate of 4% per year.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
To determine how long it takes for an element to decay from 18 grams to 2 grams, you can use the formula:
t = (ln(A/B)) / (-r)
where:
t is the time it takes for the decay to occur
A is the initial amount of the element, in this case 18 grams
B is the final amount of the element, in this case 2 grams
r is the decay rate, in this case 4% per year
Plugging these values into the formula gives you:
t = (ln(18/2)) / (-0.04)
t = (ln(9)) / (-0.04)
t = (2.1972) / (-0.04)
t = -54.30
Hence, It will take approximately 54 years.
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How to find each polynomial expression of 3x^2+2x+8
Using the factorization of polynomial, the factor of the given expression is (3x-4)(x+2).
In the given question we have to find the each polynomial expression of 3x^2+2x-8.
The given expression is 3x^2+2x-8.
Now finding the factor of the given expression.
The multiply of the first and third variable is 24. The middle term is 2.
So the possible factor is 6 and 4.
3x^2+2x-8 = 3x^2+(6-4)x-8
3x^2+2x-8 = 3x^2+6x-4x-8
3x^2+2x-8 = 3x(x+2)-4(x+2)
3x^2+2x-8 = (3x-4)(x+2)
Hence, the factor of the given expression is (3x-4)(x+2).
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The right expression is 3x^2+2x-8.
Find -12x for each value of x.
Value of x value of -12x
2
4
-3
6
Amy weighs 150 pounds on earth and 350 on another planet. Find West lose weight on that planet if he weighs 130 pounds on earth.
Answer:
do you speak English
Step-by-step explanation:
Amy weighs 150 pounds on earth and 350 on another planet. Find West lose weight on that planet if he weighs 130 pounds on earth.
Complete the number sentence.
2 + (-10) = ?
-9 + (-13) =?
-25 + ? = -9
? + (-13) = -29
2.3² + √5.6
Help me please
Answer:
7.65643191
Step-by-step explanation:
2.3^2 = 5.29 √5.6 = 2.36643191324
5.29 + 2.36643191324 = 7.65643191
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
f(x) = 3(x +1)² +2
Step-by-step explanation:
You want the equation in vertex form of the parabola 3x² after its vertex is translated to (-1, 2).
Vertex form equationThe given form is the "vertex form" of the equation for a parabola. That is, in the form ...
f(x) = a(x -h)² +k
the value of 'a' is the leading coefficient, the scale factor, and the values of h and k are the x- and y-coordinates of the vertex.
ApplicationGiven that the scale factor of the desired parabola is a=3, and the desired vertex is (h, k) = (-1, 2). we can fill in these values in the equation to get ...
f(x) = 3(x -(-1))² +2
f(x) = 3(x +1)² +2
Will give brainliest!
Answer:
9: 71 , 10: 110, 11: 52
Step-by-step explanation:
the sum of angles in a triangel is 180°
so for 9:
180 = 78 + 31 + x
180 - 78 - 31 = x = 71
it's a sharp triangel because all angles are smaller than 90°
you can calculate the angles of 10 and 11 the same way
which gives 10: 110°
this is a stump triangel because there s an angle greater than 90°
The last one is a right triangel because it has a 90° angle (marked with the square)
Use prime factorization to rewrite 156 +36 as a product of the GCF and a sum of numbers. Enter the correct numbers in the boxes.
PLEASE HELP THIS IS DUE TOMORROW
Using prime factorization to rewrite 156 +36 as a product of the GCF and a sum of numbers will be 12(13 + 3).
What is prime factorization?Prime factorization simply means the process of writing all numbers based on the product of their prime.
In this case, it's important to note that:
156 = 13 × 12
36 = 3 × 12
Therefore, 156 + 36 will be:
= 12(13 + 3)
This illustrates the numbers.
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Find the number that is oppisit of 1/15 and 1/16
Answer:
The number opposite the product of 1/15 and 1/16 will be 240.
Step-by-step explanation:
Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The number opposite the product of 1/15 and 1/16 will be given as,
1
_____________
(1/15)*(1/16)
1
____
1/240
240
You can afford to spend at most 155 dollars per month on a cell phone plan. If your cell phone plan costs
20 dollars per month, plus 3 dollars per hour of call time how many hours can you afford to call?
Seven more than the product of a number and 4 equals 2.
Answer:
-5/4
Step-by-step explanation:
Step 1: Convert to algebraic equation.
4x +7 = 2
Step 1: Subtract 7 from both sides.
4x +7 −7 = 2 −7
Step 2: Divide both sides by 4.
(4x /4) = (-5 /4)
Step 3: Get your answer!
x = -5/4
Answer:
x = -1.25
Step-by-step explanation:
A number = x
7 + 4x = 2
Subtract 7 on both sides
4x = -5
Divide both sides by 4
x = -1.25 OR -5/4
A cellphone provider has the business objective of wanting to determine the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results indicate that 110 of the subscribers would upgrade to a new cellphone at a reduced cost. Reducing the price will be profitable if at least 20% of the subscribers would upgrade. Complete parts (a) and (b) below
b. What is the test statistic?
The test statistic, using the z-distribution, is given as follows:
z = 1.12.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the proportion is greater than 20%, that is:
[tex]H_0: p \leq 0.2[/tex]
At the alternative hypothesis, it is tested if there is evidence that the proportion is greater than 20%, that is:
[tex]H_0: p > 0.2[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables of the equation are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]p = 0.2, n = 500, \overline{p} = \frac{110}{500} = 0.22[/tex]
Hence the test statistic is given as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.22 - 0.2}{\sqrt{\frac{0.2(0.8)}{500}}}[/tex]
z = 1.12.
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A snack machine sells Crisps (C), Cereal Bars (B) and Soft Drinks (S). Jesse buys 2 different snacks at random.
List all the possible combinations of snacks she could buy. A possible combination would be Crisps and Cereal Bars, written as CB.
Note: Please separate your answers with a comma.
The possible combinations are
Crisps and Cereal BarsCereal Bars and Soft DrinksCrisps and Soft DrinksWhat is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
A snack machine sells Crisps (C), Cereal Bars (B) and Soft Drinks (S).
Jesse buys 2 different drinks at random.
So, the possible combinations for the drinks she buys are:-
CB, CS, BC, BS, SC, SB
Since the order in which Jesse bought the drink does not matter, the possible combinations are
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Solve for m. 2 - 6m = -4m+10 (m=__) also 2.5+1.75= -3.25+1.5x (x=__)
Value of m is -4
Value of x is 5
To solve linear equations, follow the following steps:
Clear fractions and decimals.Simplify each side of the equation by removing parentheses and combining terms.Isolate the variable term on one side of the equation keeping the other terms separateSolve the equation by dividing each side of the equation mathematicallyMatch your steps and the final solution with the correct solutionEquation 1.
2-6m = -4m+10
6m-4m = 2-10
2m = -8
m = -8/2
m = -4
Value of x is -4
Equation 2.
2.5+1.75 = -3.25+1.5x
1.5x = 4.25+3.25
1.5x = 7.5
x = 7.5/1.5
x = 5
Value of x is 5
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what is the best description of the first term in the expression below?
[tex](4x + 9) + \frac{x - 10}{6} [/tex]
A. sum
B. factor
C. product
D. quotient
Answer:
C
Step-by-step explanation:
The first term is 4x. The first term is the product of 4 and x.
Let g(x)=x-5.
Find x when g(x) = -5.
Answer:
x = 0
Step-by-step explanation:
Substitute g(x) for x-5 in the equation,
x-5 = -5
collect like terms or add 5 to both sides
x = -5+5
x = 0
Find the number that is opsite of 1/15 and 1/16
Answer:
The number opposite the product of 1/15 and 1/16 will be 240
Step-by-step explanation:
1
____________
(1/15) x (1/16)
1
____________
1/240
240
What is Algebra?
Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The number opposite the product of 1/15 and 1/16 will be given as,
Help please tough question
What's the slope of a line that passes through the points (1,−2) and (2,2)?
The slope of a line that passes through the points (1,−2) and (2,2) is 4.
The two given points are (1,-2) and (2,2).
We have to find out the slope of the line that passes through the two given points.
We know that the slope of a line passing through two points ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) is -
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Using this formula for the given points (1,-2) and (2,2), we can find out the slope of the line passing through them as -
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\= > m = \frac{2-(-2)}{2-1}\\ = > m = \frac{4}{1}\\ = > m = 4[/tex]
Thus, the slope of a line that passes through the points (1,−2) and (2,2) is 4.
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What is 5×5 Please give me the answer show your work
Answer:
It is the method by multiplication
Step-by-step explanation:
5×5=25
Learn at brainlySuppose that the function fis defined, for all real numbers, as follows.
-2 if x #2
4 if x = 2
Find f(-1), f(2), and f(5).
f(-1) =
f(2) =
ƒ (5) =
For the given defined function f(x) for all real numbers , value of required function are as follow:
f(-1) = -2 , f(2) = 4 and f(5) = -1.
As given in the question,
Function is defined as follow for all the real numbers,
f( x ) = -2 , if x ≠ 2
f(x) = 4 , if x =2
Values of the required function is given by :
f ( -1 ) for the required function x = -1 which is not equal to 2.
Hence , f( -1 ) = -2
f ( 2 ) for the required function x = 2 which is equal to 2.
Hence , f( 2 ) = 4
f ( 5 ) for the required function x = 5 which is not equal to 2.
Hence , f(5 ) = 4.
Therefore, for the given defined function f(x) for all real numbers , value of required function are as follow:
f(-1) = -2 , f(2) = 4 and f(5) = -1.
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36.8 divided by [11.5- (6.25)]
Answer:
7.00
Step-by-step explanation:
36.8/ (11.5-6.25) = 7.00952380952 Now just pick two first numbers two there you go. Dam being a 6 grader Wow