Answer:
0.75
Step-by-step explanation:
The outcomes are equally likely, so the easiest way to work this problem is to write out the 8 outcomes in this sample space. In two outcomes the gender of all three children is the same (GGG, BBB). The other 6 outcomes contain at least one boy and one girl.
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Write 0.2777 as a fraction in lowest terms:
Answer:
27.77
Step-by-step explanation:
To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right).
0.2777 × 100 = 27.77
What is the solution of log 6-log 3 x=-2 ?
Solution of log 6-log 3 x = -2 is , x =200
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x is the expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to given statement,
log 6-log 3 x= -2
using formula of log a - log b, we can write the eq. as
[tex]log \frac{6}{3x} = -2[/tex]
=> [tex]6 / 3x = 10^{ -2}[/tex]
=> [tex]3x = 600[/tex]
=> [tex]x =200[/tex]
Thus solution of log 6-log 3 x=-2 is , x =200
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a. How much potential energy would a 41kg diver have standing on a 10-m diving platform?
Potential energy required is 4,018 kg m² /s²
What is Potential Energy ?
Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy. Potential energy always measures if we know the height of the object and the mass of the object on which energy is applied as well.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
g= -9.8m/s² , h = 10 m , m = 41kg
as, U = mgh
= (41 )(9.8)(10)
= 4,018 kg m² /s²
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Put the reasons in the correct order that will justify the statements given
The reasons arranged in the order that correctly completes the two column table to prove that ‹2 and ‹3 are supplementary is as follows;
Given(‹1 and ‹2 form a linear pair)Supplementary theorem Definition of supplementary angles Given (‹1 and ‹3 are congruent)Definition of congruency Substitution Definition of supplementary angles What are supplementary angles?Supplementary angles are angles that have a sum of 180°.
The completed table is presented as follows;
Statements Reasons
1. ‹1 and ‹2 form a linear pair; Given(‹1 and ‹2 form a linear pair)
2. ‹1 and ‹2 are supplementary; Supplementary theorem
3. m‹1 and m‹2 = 180°; Definition of supplementary angles
4. ‹1 congruent ‹3;Given (‹1 and ‹3 are congruent)
5. m‹1 = m‹3; Definition of congruency
6. m‹3 + m‹2 = 180°; Substitution
7. ‹2 and ‹3 are supplementary; Definition of supplementary angles
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Carlos was having a house.The blueprints are shown below
Kindly check if any file is attached.
The actual width of the entire building is 28 feet and the length of the entire building is 84 feet.
Step-by-step explanation:The scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object. The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.Now, width = 8 inches in feet is 4 × 7 =28 feetLength = 14+10 =24 inches in feet is 12 × 7 = 84 feetTherefore, the actual width of the entire building is 28 feet and the length of the entire building is 84 feet.In 2009,the population of brazil was 191.5 million. this represented a decrease in population of $3.7%from 2000 .what was the population of brazil in 2000 round to the nearest tenth of a million
Population in the year 2000= 198.85million
From the question, we get to know that the population in 2009 was 191.5 million.
And we have to find the population of the year 2000 which is 3.7%more than the 2009 population.
So let us take the population of the year 2000 to be x.
From the above, we can form an equation:
(population of year 2000 * ( 100-3.7 /100) = (population of year 2009)
i.e., x * 100-3.7/ 100 = 191.5
x * 96.3 = 191.5
x = 198.85
So 198.85 is the population of 2000.
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Using the Completing the Square method, what are the zeros of the quadratic function f(x) = 2x2² +8x-3? O x=-2- O x=-2- O x=2- Ox=2- 11 72 11 F and x = -2 + and x = -2 + and x = 2 + and x = 2 + 7 - 2 Jul 12 LL 72 11 11 2
the zeroes of the function f (x) = 2 x² + 8 x - 3 are x = - 2 ± √ 11 / 2.
We are given a function:
f (x) = 2 x² + 8 x - 3
We need to use the completing the square method to find the zeroes.
f (x) = 2 x² + 8 x - 3
f (x) = x² + 4 x - 3 / 2
f (x) = ( x )² + 2 (2) (x) + (2)² - (2)² - 3 / 2
f (x) = ( x + 2 )² - 4 - 3 / 2
f (x) = ( x + 2 )² - 11 / 2
(x + 2)² = 11 / 2
x + 2 = ± √ 11 / 2
x = - 2 ± √ 11 / 2
Therefore, the zeroes of the function f (x) = 2 x² + 8 x - 3 are x = - 2 ± √ 11 / 2.
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Let z and y be positive integers and x > y. Which expression in equivalent to 19^z/19^y
Answer:
[tex]19^{z-y}[/tex]
Step-by-step explanation:
assuming you meant z > y
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex] ( m > n ) , then
[tex]\frac{19^{z} }{19^{y} }[/tex] = [tex]19^{z-y}[/tex]
The measure of a side of a square is x units. A new square is formed with each side 6 units longer than the original square's side. Write a simplified expression to represent the area of the new square.
Answer:
[tex]A = x^2 + 12x + 36[/tex]
Step-by-step explanation:
The new square's side can be algebraically expressed as [tex]x + 6[/tex], as we know it's 6 units longer than the previous square with side length [tex]x[/tex].
Therefore, its area would be:
[tex]A = (x + 6)^2 \text{ // Remember: } (a + b)^2 = a^2 + 2ab + b^2\\\to A = x^2 + 12x + 36[/tex]
At a grocery store, you want to buy 3 1/2
lb of turkey . What decimal should the digital scale show?
The decimal value the digital scale will show for 3¹/₂ lb of turkey is 3.5.
What is a decimal value?A decimal value is a fractional value. Sometimes, a decimal contains a whole number and some fractions.
In a decimal number, the first digit after the decimal is in the tenth place. The next digit after the first decimal value represents the hundredth place.
Decimal values are obtained during the mathematical operation of divisions to show that there are remainders or uneven dividends.
Thus, the decimal value that the digital scale will show for 3¹/₂ lb of turkey is 3.5.
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5. a bag of chocolates is labeled to contain 0.384 pounds of chocolates. the actual weight of the chocolates is 0.3798 pounds. a. are the chocolates heavier or lighter than the weight stated on the label? explain how you know. b. how much heavier or lighter are the chocolates than stated on the label? show your
Comparing the values by subtraction, the chocolates are lighter than the weight stated on the label by 0.0042 pounds.
When comparing two values whether which is greater, compare the digits from left to right.
Comparing 0.384 to 0.3798, where the first digits are both 0, and the digit after the decimal are also the same, compare the hundredth's place.
8 > 7
Hence, the actual weight of the chocolates is less than or lighter than the weight stated on the label.
Using subtraction, two values can also be compared by getting how much one exceeds the other.
Subtracting the two values,
0.384 - 0.3798 = 0.0042 pounds
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pls help w this pretty urgent
Answer:
Step-by-step explanation:
Given
Solve each equation.
log 5-log 2 x=1
log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
log(5) - (log (2x)) =1
=> log (5) - [log (2) + log (x)] = 1 (as log(ab) = log(a) + log (b))
=>log (5) - log (2) - log (x) = 1
=> log ([tex]\frac{5}{2}[/tex]) - log (x) = 1
=> 0.3979 - log (x) = 1
=> log (x) = 0.3979 - 1
Since, generally the base of log is 10, raising them to 10
=> [tex]10^{log_{10}x} = 10^{-0.6021}[/tex]
=> x = 0.2499
Hence, log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.
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Solve for X
x-9.8/-2.2=9.7
The value of x in the equation is 5. 25
What are algebraic expressions?
Algebraic expressions are defined as expressions comprising of terms, variables, coefficients, factors, and constants.
They are also made up of mathematical operations such as addition, multiplication, division, bracket, etc
Given the expression;
x - 9.8 / -2.2 = 9.7
Find the quotient
x - (-4. 45) = 9. 7
expand the bracket
x + 4. 45 = 9. 7
collect like terms
x = 9. 7 - 4. 45
Subtract like terms
x = 5. 25
Thus, the value of x in the equation is 5. 25
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Write each expression in simplest form. (-32y¹⁵)¹/₅
The simplest form of the expression is determined by solving the fractional exponent.
If an exponent of the base (number) is expressed in a fraction, it is called a fractional exponent. In an expression say x^1/y, 1/y is the fractional exponent. Fractional exponent represents the power and root together.
In the given expression, the base term is -32y^15, while the exponent is 1/5.
Since, (ab)^m=a^mb^m
Hence, (-32y¹⁵)^¹/₅=(-32)^1/5*(y^15)^1/5
When a base number has a negative sign, and the power is an odd number, the negative sign is extracted.
(-32)^1/5*(y^15)^1/5=-(32)^1/5*(y^15)^1/5
Since, (a^m)^n=a^m*n
-(32)^1/5*(y^15)^1/5=-32^1/5y^15*1/5
As 32=2*2*2*2*2=2^5
The expression becomes.
-(2^5)^1/5*(y^15^)1/5
Multiplying the powers,
-(25)^1/5*(y^15)^1/5=-(2^5*1/5)(y^15*1/5)=-2y^3
The simplest form of expression is (-32y¹⁵)^¹/₅ is -2y^3.
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Mrs Chua has a bag of sweets for some children. If each child gets 8 sweets, there will be 3 sweets extra. If she gives each child 9 sweets, there will be 2 sweets short. Find the extra number if sweets Mrs Chua needs to buy in order for each child to get either 8 or 9 sweets
Answer:
38
Step-by-step explanation:
It is clear that the number of sweets that should be bought so that each child can get either 8 or 9 sweets should be divisible by both 8 and 9
This is called the LCM or least common multiple of 8 and 9
Since 8 and 9 have no divisors in common LCM of 8 and 9 is 72 so 72 is the minimum number of sweets to buy so that there are no leftovers if each child gets 8 or 9 sweets
Let's compute the number of sweets that were bought the first time. Let the number of children be X
Since each child got 8 sweets and 2 were left over, the total of sweets must be 8X + 2
If each child were to get 9 sweets each then there would be 2 sweets short
This can be written as 9X -2 for the total number of sweets
Since these have to be equal,
9X - 2 = 8X + 2
Add 2 to both sides:
9X - 2 + 2 = 8X +2 + 2
9X = 8X + 4
Subtract 8X from both sides
9X - 8X = 8X - 8X + 4
1X = 4
==> X = 4
So number of children is 4
Total number of sweets bought
= 8 x 4 + 2 = 34
or
= 9 x 4 - 2 = 34
Therefore number of extra sweets to be bought = 72 - 34 = 38
Hope that helps and if you don't understand and need more explanation, please post a comment
In january of 2019, the american midwest experienced record-breaking freezing temperatures. A certain metropolitan area in wisconsin, with a residential population of over 1. 15 million, experienced daily average temperatures as low as minus 28 degrees fahrenheit. Hospitals saw a steady stream of patients reporting symptoms of frostbite. In the aftermath, a survey was conducted in order to estimate the true proportions of individuals afflicted by frostbite during the extreme weather. 289 residents were selected via simple random sampling and 273 reported not having any symptoms. What was the sample proportion obtained by the survey? give your answer to 3 decimal places. For help on how to input a numeric answer, please see instructions for inputting a numeric response.
The proportion of the sample obtained from the survey is 0.055
What is a percentage?
The percentage is a mathematical operation that is expressed with the symbol "%" is a relationship that allows us to know the portion of an initial value to represent a set.
It could also be defined as a representation of an original value that lets us know a certain number of elements that we want from that original value or set.
To solve this problem, we use a simple rule of three to find the percentage value of the sample.
289 -------- 100%
273 --------- x
x = (273 * 100%) / 289
x = 94.46%
100% - 94.46% = 5.53%
The ratio in propotion with 3 decimals is
5.53/100 = 0.055
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Suppose you plan to purchase 10 items that each cost $4.95. How much will it cost for the ten items using mental math? Group of answer choices
It will cost $49.5 for the ten items.
What is arithmetic operation?Arithmetic operation is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Now it is given that,
Total items purchased = 10
Each item cost = $4.95
Thus, Cost of 10 items = 10*Each item cost
Putting the value we get,
Cost of 10 items = 10*4.95
Solving we get,
Cost of 10 items = $49.5
this is the required cost for the ten items.
Thus, It will cost $49.5 for the ten items.
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One angle of an isosceles triangle measures 30°. What measures are possible for the other
two angles? Choose all that apply.
15°
75°
120°
30°
Answer:
the correct ones are 30 , 120, 75
what is the formula for arithmetic mean
Answer:
A = arithmetic mean
n = number of values
a_i = data set values
Step-by-step explanation:
Hope it helps! =D
Please help I need to know this
Answer:
Step-by-step explanation:
Step 1: we write 23% in decimal form: 23%=0.23.Step 2: we find the multiplier. Since we're increasing by 23%, we add 0.23 to 1: 1+0.23=1.23.Step 3: we multiply 80 by the multiplier 1.23: 80×1.23=98.4
So that means your answer is 1.23
(10,0) (0,4) in distance formala
The distance is √116.
what is distance formula?The distance formula to calculate the distance between two points (x1,y1) ( x 1 , y 1 ) , and (x2,y2) ( x 2 , y 2 ) is given as,
D=√(x2−x1)²+(y2−y1)²
Given:
(10,0) (0,4)
Using Distance formula
=√(x2 - x1)² + (y2 - y1)²
=√(0-10)² + ( 4-0)²
=√100 + 16
=√116
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What is 5+18÷6 step by step
we may use BODMAS in answering this question you divide 18 by 6 and your answer will be 3 you then add 5 to the 3 to obtain your answer which is 8
How much interest does 2560 earn in 17 months at a rate of 5 1/8%? Round to the nearest cent
The interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.
How to calculate the interest?In the fields of finance and economics, interest is the payment of a sum over and above the principal amount to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. It is not the same as a fee that the borrower might pay to the lender or another entity.
Principal = $2560
Time = 17 months = 1.417 years
Rate = 5.125%
Therefore, the Interest will be:
= (Principal × Rate × Time) / 100
= (2560 × 1.417 × 5.125) / 100
= $185.9
Therefore, the interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.
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Solve the equation r³ = 125.
het ont to able rose à pne
Answer:
[tex]r = 5[/tex]
Step-by-step explanation:
[tex]r^3 = 125 \text{ // Take the 3rd sqrt of both sides}\\\to \sqrt[3]{r^3} = \sqrt[3]{125}\\\to r = 5[/tex]
Answer:
Brainleast Answer
Step-by-step explanation:
r=5
hopebit helps
A cube has six sides that are numbered 1 to 6. The sides numbered 1, 3, and 5 are yellow, and the sides numbered 2, 4, and 6 are orange. What is the probability of rolling the cube and getting a yellow and even number?
Answer:
0.
Step-by-step explanation:
None of the sides colored yellow (1, 3, 5) have an even number that corresponds.
what is the solution to 3 + 8.2 = 26.2
Answer:
Your answer is 26.2 but there is also no solution.
Step-by-step explanation:
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It's Max's birthday and his grandfather just signed over his Social Security check to him for $625.95. Max wants to buy as many new PS 4 Mine craft video games with the money as he can at $32.10 a piece to sell them on Betsy. If he wants to keep one, how many can he have left over?
The number of video games that Max will have left when he keeps one is 18 games.
How to illustrate the information?It should be noted that the total amount that he has is $625.95.
Cost of each video game = $32.10
Therefore, the number of games that he can buy will be:
= Amount / Cost of game
= $625.95 / $32.10
= 19.5
= He can buy 19 games.
Therefore, if he keeps one, the number left will be:
= 19 - 1 = 18
He I'll have 18 left.
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5) Find LM
K
K
9
-4+4x
x-1
L
M
According to the solving the line segment LM of line KM = 3.
What is line segment?A line segment is defined as the area between two different points on a line. A line segment is a section of a line that links two points. A line has no endpoints and stretches in both directions indefinitely, but a line segment includes two fixed or definite endpoints.
What exactly is a line segment?In general, if both end points of a line segment are vertices of such a polygon or polyhedron, the line segment has to be either the edge (of that polygon or polyhedron) if they are both adjacent vertices, or a diagonal. A chord is a line segment whose end points are both on a curve (such as a circle) (of that curve).
According to the given data:KL = 9
LM = x - 1
KM = -4 + 4x
So
KL + LM = KM
Substituting the value we get:
9 + x - 1 = -4 + 4x
8 + x = -4 + 4x
8 + 4 = 4x - x
12 = 3x
x = 4
The value of x = 4 putting the value in the (LM = x - 1):
We get:
LM = x - 1
LM = 4 - 1
= 3
LM = 3
According to the solving the line segment LM of line KM = 3.
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Can someone help me find the radius of the circle