If two water tanks are 50 inches tall and tank a is empty and for each minute the water increases by 3.7 inches and tank b is draining and the water decreases by 1.9 inches each minute, then the minutes after which the height of the water in each tank is the same is equal to 9.
The time in minutes after which the height of the water in each tank is the same can be determined by using a linear equation.
The equation for this problem can be given as,
0 + 3.7(x) = 50 - 1.9(x)
Here x is equal to minutes. To find the minutes after which the water level will be the same can be determined by calculating the value of x in this linear equation.
3.7(x) + 1.9(x) - 50 = 0
5.6(x) = 50
x = 50 / 5.6
x = 8.92 ≈ 9
Hence, the height of the water in tank a and tank b is equal after 9 minutes.
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Simplify the expression. negative 17 plus the quantity negative 2 and three tenths plus 8 and 12 hundredths end quantity divided by 6 all times 4 squared minus 8 and 6 tenths
Simplifying the expression given in words gives - 256.08
Given data
the expression. negative 17 plus the quantity negative 2 and three tenths plus 8 and 12 hundredths end quantity divided by 6 all times 4 squared minus 8 and 6 tenths
How to find the expressionrewriting the expression gives:
= ( -17 + ( -2 3/10 + 8 12/100 ) / 6) * 4^2 - 8 6/10
= ( -17 + ( -2.3 + 8.12 ) / 6) * 4^2 - 8.6
= ( -17 + ( 5.82 ) / 6 ) * 16 - 8.6
= ( -17 + ( 0.97 ) * 16 - 8.6
= ( -16.03 ) * 16 - 8.6
= -256.48 - 8.6
= -256.08
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Work out the radius of this circle.
circumference = 46 mm
mm
Not drawn accurately
The radius of the circle whose circumference is 46mm comes out to be 7.32 mm
As we are been provided with that circumference of the circle is 46mm and we are told to find out the radius of the circle
The formula for circumference of circle = dπ where d is the diameter of the circle
Let us put the given values in the formula
46 = d (3.14)
46/3.14 = d
d= 14.64
The radius of the circle is half of the diameter of the circle which means r = d/2
The radius of the circle = 14.64/2 = 7.32mm
Hence, the radius of the circle whose circumference is 46mm comes out to be 7.32 mm
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Subtract.
(2x4+5x3-8)-(9x² - 8x+8)
(2x4+5x3-8)-(9x² - 8x + 8) =
(Simplify your answer.)
after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.
We are given an expression:
( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 )
We need to subtract the expression and simplify the result.
We get that:
Subtracting the expression, we get that:
2 x⁴ + 5 x³ - 8 - 9 x ² + 8 x - 8
Simplifying the expression, we get that:
= 2 x⁴ + 5 x³ - 9 x² + 8 x - 16
Therefore, after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.
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X -2= -22 need to know the answer I am late for my home work
Answer:
x=-20
Step-by-step explanation:
x-2=-22
x=-22+2=-20
Answer:
-20.
Step-by-step explanation:
X - 2 = -22
Add +2 to both sides I the equation, and we have :
X - 2 + 2 = -22 + 2
X + 0 = -20
.: X = -20
Find the least integer greater than each number. Do not use a calculator.
log₁.₅2.5
The answer to this question is log₁.₅ 2.5 = 3
A logarithm is the degree to which a number must be raised in order to produce another number. For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 10² = 100.
Let y = log₁.₅ 2.5
We know, logₐ x = y, only if a^y= x
Therefore, 1.5^y= 2.5
So, we must find an integer y such that 1.5 > 2.5
1.5^y > 2.5
1.5^3 > 2.5
(As, 1.5² = 2.25; 1.5³ = 3.375)
(Since, 1.5² < 2.5, the answer will be 1.5³, as 1.5³ > 2.5)In this case, y = 3 will be the least integer to satisfy this inequality.
Therefore, the the value of the equation log₁.₅ 2.5 is 3
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Suppose the diameter of a similarly shaped crater is 1 km . What is the volume of the crater? Use the formula given in Problem 3 .
The volume of crater is 0.0375 km³.
We are given the diameter of crater which is 1 kilometer. Now, the formula to be used for calculation of volume is -
d = 2∛(V÷0.3)
Keep the value of diameter in the formula to find the volume of crater -
1 = 2∛(V÷0.3)
Dividing both sides of the equation by the number 2
1/2 = (2∛(V÷0.3))/2
Solving the equation we get -
0.5 = ∛(V÷0.3)
Taking cube on both sides of the equation
0.5³ = (∛(V÷0.3))³
On solving we get
0.125 = V÷0.3
Shifting 0.3 to numerator on Left Hand Side of the equation
V = 0.125×3
Performing multiplication on Right Hand Side on the equation
V = 0.0375 km³
Hence, the volume of crater is 0.0375 km³.
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E.
DATE
Topic
PERI
mountain road is 5 miles long and gains elevation at a constant rate.
fter 2 miles, the elevation is 5,500 feet above sea level.
Fter 4 miles, the elevation is 6,200 feet above sea level. (Lesson 3-6)
Find the elevation of the road at the point where the road begins.
Step-by-step explanation:
this is about the overall slope of the mountain road.
remember, the slope is (y change / x change). in this case it is elevation change / distance change.
getting from 2 to 4 miles the changes are
distance changes by +2
elevation changes by + 700 (from 5500 to 6200).
the slope is +700/+2 = 350/1 = 350.
the road begins at distance = 0.
the elevation of the begin of the road = x.
so going from 2 miles down again to 0 the changes are
distance changes by -2 (from 2 to 0)
elevation changes by x - 5500 (from 5500 to x).
the slope there must be the same as the slope further up (as it is said it has a constant rate) :
(x - 5500)/-2 = 700/2
(5500 - x)/2 = 700/2
5500 - x = 700
x = 5500 - 700 = 4,800 ft
the road started at an elevation of 4,800 ft above sea level.
illustrative
Mathematics
esson 3 Practice Problems
1. The box plot represents the distribution of speeds, in miles per hour, of 100 cars as
they passed through a busy intersection.
4 8 12 16 20 24 28 32 36 40 44 48
speed of cars (miles per hour)
a. What is the smallest value in the data set? Interpret this value in the situation.
The smallest value is 8.
the largest value is 44.
the median is 20.
the first quartile(Q1) is 12.
the third quartile (Q3) is 24
it represents among 100 cars the smallest speed is equal to 8 mph when passing through a busy intersection.
it represents among 100 cars the biggest speed is equal to 44 mph when passing through a busy intersection.
it represents among 100 cars half of them, their speed is equal to or less than 20 mph when passing through a busy intersection.
it represents among 100 cars 25% of them, their speed is equal to or less than 12 mph when passing through a busy intersection.
it represents among 100 cars half of them, their speed is equal to or less than 20 mph when passing through a busy intersection.
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The variables x and y are related proportionally. When x=8 and y=12. Find y when x=80
Y= 120
Given :
Function :
trigonometric function, in mathematics, one of six functions (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) that represent ratios of sides of right triangles. These six trigonometric functions in relation to a right triangle are displayed in the figure.
They are also known as circular functions since their values can be defined as ratios of the x and y coordinates (see coordinate system) of points on a circle of radius 1 that correspond to angles in standard positions. Trigonometry can be easily applied to surveying, engineering, and navigation problems in which one of a right triangle’s acute angles and the length of a side are known and the lengths of the other sides are to be found.
The fundamental trigonometric identity is sin2θ + cos2θ = 1, in which θ is an angle.
X = 8
Y = 12
f (x) = x*3/2
f(8) = 8*3/2 = 12
y = 12
hence proof f(x)=x*3/2
x = 80
f(x) =x*3/2
f(80) = 80*3/ 2
y = 40 *3
y = 120
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What is another name for AÉ?
Answer:almost everywhere.
Step-by-step explanation:
Find the approximate length (in Earth years) of each planet's year.
a. A Venusian year if Venus is 0.72 AU from the sun.
The approximate length is 0.62 years or 225 days.
A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon, and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.
The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.
Jupiter completes a Single orbit once every 4333 days, due to which one Jupiter year is equivalent to 11.86 earth years.
A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon, and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.
The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.
The second, closest planet to our Sun, Venus, completes a Single orbit once every 224.7 days, due to which one Venus year is equivalent to 0.6152 earth years.
Now, if Venus is 0.72 AU away from Sun, then we can calculate the length of the planet's year.
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PLEASEEE HELPP
If a₁ = 10 and an
10 and an = -4an-1 then find the value of a4.
Given the recursive relation:
[tex]a_{n}=-4a_{n-1}[/tex]
[tex]a_{2}=-4a_{2-1} = -4a_{1} = - 4(10) = -40 \\ a_{3}=-4a_{3-1} = -4a_{2} = - 4( -4 0) = 160 \\ a_{4}=-4a_{4-1} = -4a_{3} = - 4(160) = -640[/tex]
The velocity of the water that flows from an opening at the base of a tank depends on the height of water above the opening. The function v(x)=√2gx models the velocity v in feet per second where g , the acceleration due to gravity, is about 32ft/s² and x is the height in feet of the water. What is the depth of water when the flow is 40ft/s, and when the flow is 20ft/s ?How can you use the inverse function to help you find the answer?What restrictions are on the domain of v(x) ? of v⁻¹(x) ?
The depth is 0.884 feet when the water flows at 40 ft. / s and the depth is 0.442 feet when the water flows at 20 ft. / s.
We are given the function:
v(x) = √2 g x
where v = velocity
g = gravity's acceleration
x = height / depth of water
Also, we are given that g = 32 ft. / s²
Now, we have v = 40 ft. / s
So, we get that:
40 = √ 2 (32) x
40 / 32 = √ 2 x
5 / 4 = √2 x
x = 5 / 4√2
x = 0.884 feet.
Now, we have v = 20 ft. / s
So, we get that:
20 = √ 2 (32) x
20 / 32 = √ 2 x
5 / 8 = √2 x
x = 5 / 8√2
x = 0.442 feet.
Therefore, we get that, the depth is 0.884 feet when the water flows at 40 ft. / s and the depth is 0.442 feet when the water flows at 20 ft. / s.
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All students in peters class have $1.05, consisting of nickels and or dimes and or quarters. each student has a different combination of coins. what is the probability peter is unable to give his friend jenny change for $1.00
Answer:
2 is to 4
Step-by-step explanation:
when u comnbkdkd the osapkbdbd
Answer:
Step-by-step explanation:
Answer: 2/31
Explanation: When doing this question, it is best to make a chart with all the possibilities. From there, look and see which possibilities cannot get a change of a dollar to get the answer.
Solve the math problem
Answer: 4.9 years old
Step-by-step explanation: it’s the ages added up divided by the total (to find the average)
Answer:
hiya not sure of this is right but I would add all the dots up so with 3 add 3+3+3+3+3. because there is 5 dots do this with all of them and then divided by the amount of dots hope this helps
answer 4.9
Evaluate each logarithm.
log₆₄ 4
Evaluation of logarithm is [tex]log_{64}4 = \frac{1}{3}[/tex]
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 define 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 statement,
[tex]log_{64}4\\[/tex]
this equation can be written as
[tex]log_{2^6} 4 \\= > \frac{1}{6}log_24 \\\\ = > \frac{1}{6}log_2{2^2}\\\\= > \frac{1}{6}2log_2{2}\\\\= > \frac{1}{6}. 2 = \frac{1}{3}[/tex]
Thus solution for this equation is [tex]log_{64}4 = \frac{1}{3}[/tex]
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A local clothing store has several standing orders with a supplier. The store receives new clothes on this schedule:
a shipment of sweaters every 5 days,
a shipment of jeans every 6 days,
a shipment of dresses every 8 days, and
a shipment of shoes every 12 days.
The store received shipments of all four items today. Which of these are true? Select ALL that apply.
A.
The next time the clothing store will receive shipments of both jeans and sweaters is in 11 days.
B.
The next time the clothing store will receive shipments of both jeans and dresses is in 24 days.
C.
The next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.
D.
The next time the clothing store will receive shipments of jeans, sweaters, and dresses is in 60 days.
E.
The next time the clothing store will receive shipments of both shoes and jeans is in 18 days.
The true statements include:
B. The next time the clothing store will receive shipments of both jeans and dresses is in 24 days.
C. The next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.
How to illustrate the information?It should be noted the information is simply about factor. In this case, you've to look at the least common factors between the terms.
Therefore, the next time the clothing store will receive shipments of both jeans and dresses is in 24 days. This is because 6 and 8 has a LCM of 24.
Also, the next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.
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pls solve this question with steps
Answer:
hope this will help you...
Can someone please help me on this
5z+3y-15x+9
The factorized expression of 5z + 3y - 15x + 9 is 5(z - 3x) + 3(y + 3)
How to evaluate the expression?The expression is given as
5z+3y-15x+9
Rewrite the above expression properly
So, we have
5z + 3y - 15x + 9
Regroup the expression, as follows
So, we have:
5z + 3y - 15x + 9 = 5z - 15x + 3y + 9
Factorize the expression, as follows
So, we have:
5z + 3y - 15x + 9 = 5(z - 3x) + 3(y + 3)
Hence, the factorized expression of 5z + 3y - 15x + 9 is 5(z - 3x) + 3(y + 3)
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Find the minimum of the objective
function, f, subject to the constraints
f = 7x + 4y
5x + y ≥
60
x+6y ≥ 60
4x+6y ≥ 204
x ≥ 0, y ≥0
Minimum =[?]
The minimum of the objective function, f, subject to the constraints is (10.3, 8.3)
Plugging in 5 points, the intersections of the bounds of the 5 constraints, yields the least solution, f = 7x + 4y.
(0,60) provides 240
(6,30) f= 42+120 = 162
(10.3,8.3) = 72.1+ 33.2 = 105.3
(48,2) = 336+ 8 = 344
(60,0) = 420
At the moment when the minimum f is approximately (10.3,8,3)
5x+y = 60 and x+6y = 60 intersect at that point. Multiply the first equation by 6 and take the second equation out to get 30x + 6y = 360.
x + 6y = 60
29x = 300
Rounding to 10.3, x = 300/29 = about 10.345
adjusted to 8.3, y = 60-5x = 60 - 5(10.345) = 60-51.724
10.3, 8.3 reduces the value of the function f = 7x+4y.
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In a lab, a substance was heated by 6 Celsius each hour for 42 hours. What was the total change in temperature?
Answer: 7
Step-by-step explanation: 42 divided by 6 is 7.
Repost cause someone decided to troll
Answer:
Maths: 70
English: 0
Music: 140
The rest remain the same
Science: 87.5
History: 52.5
Step-by-step explanation:
350/10 = 35
35 x 4 = 140
140/2 = 70
35 + 35 + 70 = 140
Lisa gathered and shelled 12 lbs of pecans from her backyard.
She is going to make
3/4 lb bags of pecans for gifts.
How many
3/4 lb bags of pecans can Lisa make?
A .15
B. 16
C.11 1/4
D.9
Lisa can make 16 '3/4 lb' bags of pecans.
Given,
Amount of lbs of pecans Lisa gathered from her backyard = 12 lbs
Amount of lb bags of pecans Lisa going to make for gifts = 3/4 lb
We have to find the number of 3/4 lb bags of pecans Lisa can make:
That is,
Total number of 3/4 lb bags = (Amount gathered from backyard) ÷ (Amount of lb bags going to make for gifts)
= 12 ÷ 3/4
= 12 × 4/3
= 4 × 4
= 16
Therefore, Lisa can make 16 3/4 lb bags of pecans.
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FAST!!!!!!!!!!!plss HELPPPP(Did you know that chickens sometimes eat vegetables and fruits? A farmer likes to give the chickens apples to share. The farmer observes that 5 chickens eat 8 apples. What is the ratio of the number of chickens to apples?)
a
3:8
b
5:8
c
8:3
d
8:5
Answer:
B or 5:8
Step-by-step explanation:
If you see in the question it says "The farmer observes that 5 chickens eat 8 apples." and thats your answer every 5 chickens eat 8 apples.
Prior to an election, 6,504 people vote in the advance polls for a riding. On election day, thepolling stations for that riding record an average of 407 voters per hour. How long were thepolls open on election day, if a total of 10,167 people voted in that riding?
**USE LET STATEMENTS, AND THEREFORE STATEMENTS**
Answer:
The polls were open for 9 hours on election day.
Step-by-step explanation:
10167 - 6504 = 3663
3663 / 407 = 9
Suppose you pick a marble from a box containing five red and seven blue marbles. You record the color and put the marble back in the box. What is the probability of getting a red marble both times if you do this twice?.
Simplify each expression.
-5(1+2 i)+3 i(3-4 i)
Answer: The answer would be 4+1i
Step-by-step explanation: First I multiplied -5 to within the parentheses and go -5-10i and then the 3 to get 9-12i. Then I simplified even further to get 4+1i.
. Leah spends $63 on books. Each book
costs $9. How many books does Leah
buy? Write the multiplication or division
fact you used to solve the problem.
Answer:
7 books
Step-by-step explanation:
Since Leah spent $63 on books which cost 9$ each you would need to divide the 2.
63 / 9 would equal 7
After spending $63 and each book costs $9 Leah will be able to buy 7 books .
Given, that each book cost $9 .
Now when the total amount spend on books is $63 with each book costing $9 the total books bought can be given by the division equation.
Division fact:
The rules for multiplication and division are:
(1) positive × or ÷ positive = positive
(2) positive × or ÷ negative = negative
(3) negative × or ÷ negative = positive
Since Leah spent $63 on books which cost 9$,
= [tex]\frac{63}{9}[/tex]
= 7 books
Hence Leah can buy 7 books in total.
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Hurry and help , there is only five minutes left
100+ points and brainly
Answer:
The explanation is the same as the previous question.
Factor each expression completely. 9 x²+48 x+64
The factoring of the expression 9 x²+48 x+64 is (3x+8)²
To solve this exercise, we have to follow the rules of factoring:
9 x²+48 x+64
1. Factor 48 from 48x:
9 x²+48 x+64
9 x²+(24+24) x+64
2. Apply the distributive property:
9 x² + 24x + 24x + 64
3. Groups the first two terms and the last two terms:
(9 x² + 24x) + 24x + 64
4. Factorize the greatest common denominator (GCM) of each group:
3x(3x + 8x) + 8(3x + 8)
5. Simplify the common term (3x + 8) with the distributive property:
(3x+8) (3x+8)
6. Rewriting as the square of a binomial, we get:
(3x+8)²
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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