Answer:
Step-by-step explanation:
330
Apply what you know about rates from mathematics to a problem involving water consumption. An aquifer holds 146,000 cubic feet of water. Water exits through a well at a steady rate of 500 cubic feet per day, and the aquifer is replenished at a constant rate of x cubic feet per day. If the water in the aquifer is used up in a year (365 days), what is the value of x? ignore evaporation and other losses.
The value of x found by expressing the information as an equation is 100
What is an equation?An equation is a statement usually made using mathematical symbols, numbers and variables, that consists of joining two expressions with an 'equals' sign.
The volume of water in the aquifer = 146,000 ft³
The rate at which water exits the aquifer daily = 500 ft³ per day
Rate at which the aquifer is replenished = x ft³ per day
The time it takes the water to be used up = 1 year
The number of days in a year = 365 days
The value of x can be found by expressing the information as an equation as follows;
The sum of the volume of water in the aquifer and the volume of water that replenishes the aquifer in a year, less the water that exits the aquifer in a year is zero, therefore;
Water in the aquifer; 146,000 - 500 × 365 + x × 365 = 0
-36500 + 365·x = 0
365·x = 36500
x = 36500 ÷ 365 = 100
x = 100
The value of x is 100
The water is replenished at 100 cubic feet per day
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A bicycle wheel has a diameter of 62 cm. The wheel makes 80 full turns. How far does the bicycle travel? Provide your answer in meters
5. The table below shows the number of people (in millions) who voted in U.S. Presidential elections.
Year
Voters
1984 1988 1992 1996 2004
91.6 104.4 96.3
92.7
122.3
a. Find the line of best fit.
1980
86.5
b. Predict the number of voters in 2012.
Find line of best fit
Predict the number of voters in 2012
a) y=-2780.85+1.447x
b) There are 142.09 voters estimated in the year 2012
What is line of regression ?Regression analysis is a group of statistical techniques used in statistical modelling to identify relationships between a dependent variable and one or more independent variables. The dependent variable is frequently referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon (often referred to as "predictors," "covariates," "explanatory variables," or "features"). The line (or more complex linear combination) that most closely matches the data in terms of a specified mathematical criterion is found in linear regression, the most common type of regression analysis. For instance, the line (or hyperplane) that minimises the sum of squared differences between the real data and that line is determined when using the ordinary least squares approach (or hyperplane).
Calculationx = 11940 / 6 = 1990y = 593.8/6 = 98.9667
let the regression equation be y = a + bx
b = [tex]\frac{ ∑xy - nxy }{∑x^{2} -nx^{2} }[/tex] = [tex]\frac{1182067 - 6 * 1990 * 98.9667}{23760880 - 6 * 1990^{2} }[/tex] = 1.447
a = y - bx = 98.667 - 1.447 x 1990 = -2780.85
The regression equation is
x = 2020 in regression equation
substituting x=2020 in the regression equation
y = 142.09
There are 142.09 voters estimated in the year 2012
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A cyclist rode at an average speed of 15 mph for 30 miles. how long was the ride? responses 0.5 hours 0.5 hours 1 hour 1 hour 2 hours 2 hours 3 hours
A cyclist rode at an average speed of 15 mph for 30 miles.
It will take 2 hours to cover 30 miles so option (C) is correct.
What are the ratio and proportion?
The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
A cyclist rode at an average speed of 15 mph for 30 miles.
So,
15 miles ⇒ hour
Multiply by 2
2 hours ⇒ 30 miles.
Hence "It will take 2 hours to cover 30 miles".
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the product of negative five and a number is greater than twice the sum of the same and three?
Answer:
-5 X x > 2(-5 X x) +3
-5x >2(-5x + 3)
-5x > -10x + 6
-5x + 10x > 6
5x > 6
x > 6/5
A ride-sharing company charges a pick-up fee of $3.50 plus a charge of $4.00 per mile. Write an equation that represents the situation.
In a case whereby ride-sharing company charges a pick-up fee of $3.50 plus a charge of $4.00 per mile the equation that represents the situation is y = $4.00 x + $3.50 .
What is an equation?An equation can be described as the mathematical statement which is made up of two expressions connected by an equal sign. The concept that will be used is the concept of equation
From the question, pick-up fee of $3.50 was given
charge of $4.00 per mile was made
Then the equation that models this can be written as y = $4.00 x + $3.50 .
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Find the mean, range, and median of the values: 12, 4, −2, 0, 9, −2, 1, 7, 8, 2
Answer: Mean:3.9 Range:14 Median:3
Step-by-step explanation:
3) Abigail makes a sale of 900.00 naira in a day and Lola makes a sale 720.00 naira what is the ratio of Abigail's sales to Lola's sales??
the ucl and lcl for an chart are 25 and 15 respectively. the central line is 20, and the process variability is considered to be in statistical control. the results of the next six sample means are 18, 23, 17, 21, 24, and 16. what should you do? group of answer choices explore the assignable causes because the second, fourth, and fifth samples are above the mean. explore the assignable causes because there is a run. explore the assignable causes because there is a trend. nothing; the process is in control.
19.8 The process is in control as no point is outside the upper or lower control limit.
What does a math centerline mean?
Simply put, the centerline is the midpoint of the vertical y-distance between the maximum and minimum y-values. In other words, the centerline would be at y = 0 if y = A sinx, amplitude = 1, maximum y = 1, minimum y = 1, and maximum amplitude = 1.The data for the next six means is 18, 23, 17, 21, 24, and 16.
The central line is k = 20
Generally the mean of the next six mean is mathematically represented as
C = 18 + 23 + 17 + 21 + 24 + 16/6
C = 19.8
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In his last last game, the Ram's quarterback completed 10 out of 18 passes he threw. At this rate how many passes will he attempt if he completes 15 passes?
(a² +__+1)-(__a² +5a +__ = 4a²-2a +7
Answer:
(a^2+3a+1) -(3a^2+5a+(-6)) =4a^2-2a+7
Step-by-step explanation:
So, first of all, we can look at the equation and separate them based on the power of each number, and sense we are subtracting, we need to distribute the negative sign all across the second set of numbers.
So, for a^2 we have
a^2-(x) =4a^2
If we subtract a^2 on each side, we get
-(x) =3a^2 but since we don't want a negative, we divide each side by -1 which gives us that the mystery value must equal -3.
x=3a^2
Next, we got to take the second set of like terms
(x)-5a=-2a
We got to add 5a on each side which gives us
x=3a
Finally, we take the last set of like terms
1+-(x) =7
we subtract one from each side to get
-(x) =6
We don't want x to be negative therefore we divide each side by -1 so it will end out
x=-6
Please answer the 5 questions and number them when you have answered them
Will mark branliest
The amount paid each month is, $503.75
What is monthly payment?
The monthly payment is the sum paid each month to cover the loan's outstanding balance over its term. When a loan is obtained, not only the principal, or the sum that was initially lent, but also the interest accrued, must be repaid.
1) As the discount is 7%.
So he pays, 100 - 7 = 93% of the car value
Now, 93% x 6500 = 6045.
This is the value for one year.
From this we have to find the amount paid for each month.
6045/12 = $503.75
Hence, the amount paid for each month is $503.75.
2) Let, the value of Zlatan's house is $749000 after a increase in the value of house.
So, the total percentage increase price is 107% (100 + 7).
We have to fine the initial value of the house.
So,
Initial value of the house = New value of the house / total percentage increase
= 749000/107%
Initial value of the house = $700000
Hence, the initial value of the house is $700000.
3) Assume that Carol's initial weekly wage be $x.
There is 10% decrease in weekly wage.
So,
10% weekly wage = 10% of x = 0.1x
Here,
New wage after 10% decrease = initial weekly wage - 10% of x.
= x - 0.1x
= 0.9x
As given the new weekly wage is $306.
We equate $306 and 0.9x.
So
0.9x = 306
x = 340
Therefore, the initial weekly wages are $340.
Now to find weekly wage when there is 10% increase.
10% of initial weekly wage = (10/100) x 340 = 34
Hence, Wage after 10 % increase = 340 + 34 = $374
4) Let $2000 is placed into a bank account that pays 3% compound interest per year.
We have to find the amount after two years.
Here, P = $2000, r = 3% = 0.03, n = 2
Amount = P(1 + r)^n = 2000(1 + 0.03)^2 = 2000(1.03)^2 = 2121.80
Hence, $2121.80 will be in the account after 2 years.
5) Let Mary invests $12000 in a savings account. The account pays 1.5% compound interest per year.
We have to find the value after two years.
Here, P = $12000, r = 1.5%, n = 2
So,
Amount = P(1 + r)^n = 12000(1 + 0.015)^2 = 12000(1.015)^2 = 12362.70
Hence, $12362.70 is the value of her investment after 2 years.
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A new hybrid car costs £26000.
Each year the value of the car depreciates by 15%.
How many years will it take before the car is worth half of its original value?
help pls
The years it will take for the hybrid car to depreciates to half of it original value is 4.26 years.
What is depreciation?Depreciation is what happens when assets lose value over time until the value of the asset becomes zero, or negligible.
To calculate the amount of years it will take the car to worth half its original value, we use the formula below.
Formula:
A' = A(1-R/100)ⁿ............ Equation 1Where:
A' = Half the original value of the carA = Original value of the carn = Amount of yearsR = Depreciation Rate.From the question,
Given:
A = £26000R = 15%A' = £26000/2 = £13000Substitute these values into equation 1 and solve for n
13000 = 26000(1-0.15)ⁿ(1-0.15)ⁿ = 13000/260000.85ⁿ = 0.5Taking the logarithm of both side,
Log(0.85ⁿ) = Log(0.5)nLog(0.85) = Log(0.5)n = Log(0.5)/Log(0.85)n = 4.26 years.Hence, the years it will take is 4.26 years.
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At a store, the Jenson family puts 12.4 gallons of gas in their van at a cost of $3.80 per gallon.
besoin d aide pour math
What is 125% of 64
Explanation please
Answer: 80
Step-by-step explanation:
Answer: 125% of 64 would be 80
Step-by-step explanation: First we convert the percent to a decimal. 125%/100 = 1.25. Then we multiply 1.25 by 64 and we would get 80.
Hoped This Helped! Also The Answer Would Obviously Be Above 64 Because Its 125%.
A school wants to sell 900 sweatshirts for a fundraiser. All sweatshirts have the same price, and they want to make a total of $34,254.00 in sales.
Answer:
38.06 but if rounded up 38
Step-by-step explanation:
34,254 divided by 900 equals 38.06
A farm lets you pick 3 pints of raspberries for $12.00. What is the cost per pint?
Answer:
$4
Step-by-step explanation:
Answer:
$4 per pint
Step-by-step explanation:
12 divided by 3 is 4
4$ per pint
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What is the solution to this system of linear equations 2x 3y 37x 3y 24?.
The solution to the system of linear equations is (3, -1).
What is a linear equation ?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. . The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
2x + 3y = 3
7x - 3y = 24
By adding both the linear equations,
9x = 27
x = 27/9 = 3
x = 3
Substitute the value of x in either of the equations
2 (3) + 3y = 3
6 + 3y = 3
3y = -3
y=-1
Therefore, the solution to the system of linear equations is (3, -1).
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Twice the sum of a number and 9 is equal to three times the difference of the number and 9 Find the number.
Answer:
45
Step-by-step explanation:
You want the number described by, "twice the sum of a number and 9 is equal to three times the difference of the number and 9."
SetupLet x represent the number. Then "twice the sum of the number and 9" is ...
2(x +9)
and "three times the difference of the number and 9" is ...
3(x -9)
These are equal, so we have ...
2(x +9) = 3(x -9)
SolutionEliminating parentheses gives ...
2x +18 = 3x -27
45 = x . . . . . . . . . . . add 27-2x
The number is 45.
Samuel has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $303.02.
He buys 2 bicycle reflectors for $3.53 each and a pair of bike gloves for $28.12.
He plans to spend some or all of the money he has left to buy new biking outfits for $55.45 each.
Use the drop-down menu below to write an inequality representing o, the number of outfits he can buy while staying within his budget.
Answer:
4 outfits
Step-by-step explanation:
560-303.02-3.53-28.12=225.33
225.33 -55.45x4=$3.53 remaining
he can buy 4 outfits for $55.45 each
Identify the quadratic function that contains the points (-1,1), (0,-2) and (2,4). F(x) = 2x2 - x - 1 f(x) = 2x2 + x + 1 f(x) = 2x2 - x - 2 f(x) = 2x2 - x + 2.
The quadratic function that contains the points (-1,1), (0,-2) and (2,4) is f(x) =
2x²-x-2.
To find the quadratic equation we need to put the points in the equation to satisfy it,
The only equation doing it is f(x) = 2x²-x-2 as,
f(x) = 2x²-x-2
For (-1, 1)
1 = 2×(-1)² + 1 -2
1 = 1
Hence (-1,1) satisfies f(x) = 2x²-x-2
For (0, -2)
-2 = 2×(0)² - 0 -2
-2 = -2
Hence (0, -2) satisfies f(x) = 2x²-x-2
For (2, 4)
4 = 2×(2)² -2 -2
4 = 4
Hence (2,4) satisfies f(x) = 2x²-x-2
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In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out? round your answer to the nearest tenth.
Answer:
AC = 127,26 f distance from home plate to second base
Step-by-step explanation:
Let call A , B , C Home plate, first base and second base respectively
These three point form a right triangle with legs ( AB = BC = 90 feet)
we have an isosceles triangle with a right angle and two angles of 45⁰
So we need to compute distance AC (hypotenuse)
AC² = AB² + BC² ⇒ AC² = 2AB² ⇒ AC = AB √2
AC = 90 * 1,414
AC = 127,26 f
Here's a problem! (will give Brainliest)
A recipe calls for 1 1/2 teaspoons of cinnamon to make 2 dozen
oatmeal cookies. How many teaspoons of cinnamon are needed to
make 60 oatmeal cookies?
Answer:3 3/4th teaspoons are needed for 5 dozen(60 cookies)
Step-by-step explanation:
Answer:
[tex]3\frac{3}{4} teaspoons[/tex]
Step-by-step explanation:
2 dozens is 24 oatmeal cookies
We divide 1 1/2 by 24 to find how much for each cookie
1 1/2/24
3/2*1/24=3/48=1/16
Now we multiply 1/16 by60
1/16*60/1
60/16
3 12/16
3 3/4 teaspoons
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Your friend claims that the SAS Congruence Theorem (Theorem 5.5) will apply to a triangle and its image after the triangle has been translated, reflected, rotated, and dilated. Is your friend correct? Explain you reasoning.
No this is incorrect. when a triangle undergoes translation, reflection and rotation congruence of the triangle is still maintained however dilation makes the triangle not to be congruent.
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation types mentioned are all rigid transformation hence all the angles will remain same
Hence we can say that a triangle's congruence is maintained when it is subjected to translation, reflection, and rotation; nevertheless, dilatation renders the triangle incongruent.
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A STOCK YOU ARE
WATCHING IS TRADING AT
$73.84 PER SHARE TODAY.
YESTERDAY, IT WAS
TRADING AT $72.14.
(percent change)
Take the difference between the starting value and the final value to determine the percent change.Subtract the beginning value from its absolute value.Add 100 to the result.
How do you find a percent change?First, figure out how much the two numbers you are comparing differ (rise).After that, multiply the result by 100 and divide the increase by the original number.% growth is calculated as Growth divided by 100.Your response is a percentage decrease if it is a negative amount.
Initial cost = $73.84
Final cost = $72.14
Then
Amount of change = (73.84- 72.14) dollars
= 1.7dollars
Then
Percentage change = (1.7/72.14) * 100
= 170/72.14 percent
= 2.35 percent
So from the above deduction we can easily conclude that the percentage change is 2.35%. I hope the procedure is simple enough for you to easily understand. You can generally use this method for solving similar kind of problems in future without requiring any kind of help from outside.
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what is the piecewise function for this:For dogs that weight 0 to 15 lbs. you charge $5.00.
For dogs between 15 lbs to 45 lbs. you charge $7.00
Dogs over 45 lbs. you charge $9.00.
I need this done ASAP please help
whats the perfect square less than the number 47
whats the perfect square greater than the number 47
whats the perfect square number closer to 47
Answer:
Perfect square less than number 47 : 36
Perfect square greater than number 47 : 49
Perect square number closer to 47 : 49
Step-by-step explanation:
The perfect square which is less than 47 is 36 ; 6 x 6 = 36.
The perfect square which is greater than 47 is 49 ; 7 x 7 = 49.
The perfect square number closer to 47 is 49 ; 47 - 36 = 11, 49 - 47 = 2
2 is less than 11 so we know that 49 is the perfect square number closer to 47.
Solve the system of equations using elimination
The solution using elimination, for the given system of equation is x = 6 and y = -3.
What is system of equation?
A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is the one which has two equations and two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.
Given system of equations,
x - y = 9, equation 1
-4x -y = -21, equation 2
Subtracting equation 1 from equation 2 to eliminate y,
-5x = -30,
x = 6
Putting the value of 6 in equation 1,
6 - y = 9
y = -3
Hence, the solution for the given system of equation is x = 6 and y = -3.
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What is the slope of a line parallel to the line whose equation is 8x+10y=608x+10y=60. Fully simplify your answer.
The slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5
What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
Given the equation,
8x + 10y = 60
We know, the equation of line is in form of
y = mx + b
m = slope and b = y-intercept
Now, evaluate the given equation
8x + 10y = 60
10y = 60 - 8x
y = (60 - 8x) / 10
y = 60/10 - 8x/10
y = 6 - 4/5x
y = -4/5x + 6
Which is in the form of equation of line
y = -4/5x + 6
Now, from this slope is - 4/5 and y-intercept is 6
Hence, the slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5
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