Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:
1.053x = 30.8.
x = 30.8/1.053
x = 29.2.
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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 80% salt. She wants to obtain 120 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base?
x2 + y2 = 32
x squared over 2 squared plus y squared over 3 squared equals 1
x2 = 8y
x squared over 2 squared minus y squared over 3 squared equals 1
The equation of the circle, ellipse, and hyperbola will be x² + y² = 3², x² + y² / 3² = 1, and x² / 2² - y² / 3² = 1, respectively.
What is the conic section?The curve that is derived from the section of the cone is known as conic section.
The following equations are given below.
x² + y² = 3², this is the equation of the circle.
x² + y² / 3² = 1, this is the equation of the ellipse.
x² / 2² - y² / 3² = 1, this is the equation of the hyperbola.
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if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
60200 cm^2
Step-by-step explanation:
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PLEASE HELP!!!!
Which operation should you perform last in the expression 3^2 + 2?
Answer: the +2
Step-by-step explanation: PEMDAS. Exponents are before addition in the sequence. I hope this helps!
(The E standing for exponents and the A standing for addition)
16 Let f(x) and g ) are function such that f () = x+5 and g(x) x+4, what is domain of f(x)+g(x)?
Answer: all real numbers
Step-by-step explanation:
I assume you meant to write:
Let f(x) and g(x) be functions such that f(x) = x+5 and g(x) = x+4. What is domain of f(x)+g(x)?[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]
Since this is a linear function, the domain is all real numbers.
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures the distance from the tree at 14 m and the angle of elevation to the tree at 88°. What is the height of the tree to the nearest tenth of a meter
Answer:
400.9 m
Step-by-step explanation:
the answer to this asap please!
The required work done is 62400 J.
work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m
work done, is define as the product of force and displacement.
since,
work done to lift 1500N to height of 40 m is:
W= FS
= 1500 x 40 = 60000J
now work done for rope
is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J
Thus the required work done to lift 1500N weight to 40m is 62400J.
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what is the value of the rational expression below when is equal to 5?
15-(5)/5-10=10/-5=-2 hope it helps!
The function below has at least one rational zero.
Use this fact to find all zeros of the function.
f(x)=7x³ +9x²-12x-4
Answer:
Using the rational root theorem, we know to divide the function by (x - 1).
(7x³ + 9x² - 12x - 4) / (x - 1) = 7x^2 + 16x + 4
Now we can further factorize 7x^2 + 16x + 4 into (7x + 2) and (x + 2).
Therefore, the original function can be rewritten as (x - 1) (7x + 2) (x + 2).
Using the factorized form above, the zeros of the function are 1, -2/7, and -2.
Account earns 8.5% interest. If you invest $6,609 now how much interest will you earn in 5years
Answer:
simple interest is $281(nearest whole number)
Step-by-step explanation:
S. I=PXTXR
100
P=$6609
T=5
R=8.5 or 85/10
S. I=6609X5X85
100X10
=280.8825
=281
a and b are positive integers and 7a+ 5b= 49. Find the values of a and b.
3.1 What is a?
2 What is b?
Answer:
B = 49/5 - 7a/5
A = = -5b/7 + 7
Step-by-step explanation:
Given that,
7a+ 5b= 49
Solution:
Solving for a:
Add -5b to both sides:
[tex]7a+5b - 5b=49 - 5b[/tex][tex]7a = - 5b + 49[/tex]Divide both sides by 7:
[tex] \cfrac{7a}{7} = \cfrac{ - 5b + 49}{7} [/tex][tex]a = \cfrac{ - 5b}{7} + 7[/tex]Hence,a = -5b/7 + 7.
Solving for b:
Add -7a to both sides:
[tex]7a+5b+( - 7a)=49+(−7a)[/tex][tex]7a + 5b - 7a = 49 - 7a[/tex][tex]5b = 49 - 7a[/tex]Divide both sides by 5:
[tex] \cfrac{5b}{5} = \cfrac{49 - 7a}{5} [/tex][tex]b = \cfrac{49}{5} - \cfrac{7a}{5} [/tex]Hence,b = 49/5 - 7a/5.
Question:-
[tex] \dfrac{1}{2} + \dfrac{1}{4} [/tex]
Help!!
:"(
[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \red{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} }[/tex]
Step by step explanation :-
The only thing you have to do is add the numerator to the denominator, in this case you have to add the first ones from the front, which can be these 2+1/4, which would result in 3/4, and this is called the Commutative Property.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \gray{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{1}{4} + \dfrac{1}{2} }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\dfrac{2 + 1}{4} = \dfrac{1 + 2}{4} }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{3}{4} = \dfrac{3}{4}} }[/tex]
Answer :- The answer is 3/4
¿What is commutative property?
It is to change different ways in order of the addends the result would be the same.
Example :-
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{a}{b} + \dfrac{c}{d}} = {\dfrac{c}{d} + \dfrac{a}{b}} }[/tex]
I hope I've helped : )
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Final \:\: value = \cfrac{3}{4}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} + \cfrac{1}{4} [/tex]
[ take LCM ]
[tex]\qquad \tt \rightarrow \: \cfrac{2}{4} + \cfrac{1}{4} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{2 + 1}{4} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{3}{4} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Let f(x)=(3)^x−3. What is f(0) in fraction form?
Answer:
1/27
Step-by-step explanation:
We can substitute x=0 into the function to get:
f(0) = 3^(0-3)f(0) = 3^(-3)f(0) = 1/270000
O
1. Simplify 3 + 2 - 1
+6
2-5
03 A
О 25
Answer:
10
Step-by-step explanation:
3+2-1+6=5-1+6=4+6=10
the table shows the length of time in hours ,some children spent watching tv last week
The histogram of the distribution plotted on the y - axis and the interval for the length of time on the x - axis is attached below.
How to denote the histogram?The first bar denotes the length of time between 0 and 10 having a frequency of 8. The second bar denoted the interval between 10 and 15 with a frequency of 15
The third bar denoted the interval between 15 and 20 with a frequency of 10. The fourth bar denoted the interval between 20 and 30 with a frequency of 11
Therefore, the histogram of the distribution is attached below.
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Assume that a procedure yeilds a binomial with n trial and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation. Also, use the range rule of thumb to find the minimum usual value mean -2standard deviation and the maximum usual value mean + 2 standard deviation n=1490,p=2/5
The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]
The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]
Given the values of the parameters of Binomial Distribution are,
Total number of trials (n) = 1490
probability of success in one trial is (p) = 2/5
The probability of failure in on trial is given by,
[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]
For Binomial distribution we know that,
Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]
and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]
Now, calculating the required measurement we get,
The minimum usual value is given by,
Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]
The maximum usual value is given by,
Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]
Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.
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Please Expand the following:
3q(r – 2q)
Answer:
3qr - 6q²
Step-by-step explanation:
3q(r - 2q) ← multiply each term inside the parenthesis by 3q
= 3qr - 6q²
Answer:
3qr – 6q²
Step-by-step explanation:
3q(r – 2q)
E X P A N D I N G :-
3qr – 6q²
John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the function V = 20 , 000 ( 0 . 84 ) t , where t is the number of years from the time of purchase. One of the factors John is using to make his decision is the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this context?
A. all real numbers greater than or equal to 0 and less than 2.8
B. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
C. all real numbers greater than or equal to 0
D. all real numbers greater than or equal to 0 and less than 4
Option D is the correct answer.
All real numbers greater than or equal to 0 and less than 4.
What is Domain?The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.
Here, The function of the car value is given as:
V(x) = 20000 X (0.84)ˣ
When the car reaches half its value, we have:
V(x) = 10000
Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ
10000 = 20000 X (0.84)ˣ
Divide both sides by 20000
0.84ˣ = 0.5
Take the logarithm of both sides
x log(0.84) = log(0.5)
Divide both sides by log(0.84)
x = 4
This means that the maximum value of x is 4.
Thus, all real numbers greater than or equal to 0 and less than 4.
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The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
The number of cars that have passed through the intersection is 245.
How many cars passed through the intersection?Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.
The equation that represents direct variation is; c = wk
Where:
c = number of carsw = number of wrecks k = constant of proportionality1085 = k31
k = 1085 / 31
k = 35
c = 7 x 35
c = 245
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find the area for this pls
Answer:
Area = 3.36 in²
Step-by-step explanation:
[tex]Area\space\ of \space\ trapezium = \frac{a \space\ + \space\ b}{2} h[/tex] ,
where a and b are the two parallel sides, and h is the height.
[tex]Area = \frac{1.3 \space\ + \space\ 3.5}{2} (1.4)\\\\Area = 3.36 \space\ in^{2}[/tex]
Which numbers are irrational???
Answer:
√2/4, √3/4, and √5/4.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Giving the brainliest to those who answer!
A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ?
39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:
We can write a mixed fraction in a fraction:
6 1/2 = 13/2
8 1/2 = 33/2
7 3/4 = 31/4
8 1/12 = 97/12
8 5/12 = 101/12
Adding all the fractions:
[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{33}{2}[/tex]
[tex]=23+\dfrac{64}{4}[/tex]
= 39 hours
Thus, 39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
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can someone turn the equation 3−2=13 into a word problem. (i already know answer)
The word problem for given equation is : When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .
The complete equation will be 3x - 2y =13
What is an Equation ?When an algebraic expression is equated by an equal sign to a constant or any other algebraic expression , then an equation is formed .
The equation given in the question is
3x-2y =13
When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .
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please help! due very soon!
Answer:
{x | x = -6, -1, 0, 3}
(first option listed)
Step-by-step explanation:
The domain of a function is all possible x-values for that function
So, we can see (from the x-value portion of our table) that the possible x-values are:
-6 , -1, 0, and 3
We write domain and range in lowest - highest number value order, so we write our domain as such:
{x | x = -6, -1, 0, 3}
{range is all possible y-values, and this would include -7 , 1, 9, and -2}
hope this helps!!
If a participant skips hard to answer questions in a survey, it causes
A.nonadherent bias
B.sampling bias
C.response bias
D.nonresponse bias
E.researcher bias
Answer:
I think non response bias because response bias includes answering incorrectly on a survey to get it over with so that is my answer
Step-by-step explanation:
Solve the following subtraction problem. Remember to borrow as necessary.
9cu yd113cu in
− 4cu ft129cu in
−−−−−−−−−−−−−−−−−−−−−−
The subtraction of the expression will be 238 cubic feet, 551 cubic inches.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The expressions are given below.
9 cubic yd 113 cubic in and 4 cubic ft 129 cubic in
1 cubic yard = 27 cubic feet
1 cubic feet = 1728 cubic inches
Then the subtraction will be
242 cu ft 1841 cu in
− 4 cu ft 1290 cu in
238 cu ft 551 cu in
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meijun had some money. she used 1/3 of it on a watch and 1/9 of it on a gift. the watch and the gift cost $144 altogether. how much money did she have at first?
Answer:
$324
Step-by-step explanation:
let x be the amount of money she had at first , then
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{9}[/tex] x = 144 ( multiply through by 9 to clear the fractions )
3x + x = 1296
4x = 1296 ( divide both sides by 4 )
x = 324
she had $324 at first
The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].
How to deal with a negative exponent?When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:
[tex]a^{-b} = \frac{1}{a^b}[/tex]
Hence, in this problem, the equivalent expression is:
[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]
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Bret is planning a long hike. He figures that he will need at least 0.75 liters of water for each hour on the trail. He also wants to have 1.8 liters of water in reserve at all times. If he can only carry 9 liters of water maximum, how many hours can he hike?
The number of hours that Bret can hike with 9 liters of water is 9.6 hours.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
Water needed = 0.75 liters per hour
For x number of hours = 0.75x liters
Reserved water = 1.8 liters.
Total water needs for x hours = (0.75x + 1.8)
The number of hours that can be hiked with 9 liters will be as,
(0.75x + 1.8) = 9
x = 9.6 hours.
Hence "The number of hours that Bret can hike with 9 liters of water is 9.6 hours".
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