The equation in slope intercept form to model the relationship is:
y = 660,000x+2000
Given,
An Olympic sized swimming pool consists of 660,000 gallons of water.
It is currently be drained at a rate of 2,000 gallons a second.
we are asked to determine the equation in slope intercept form = ?
we know the slope intercept form is:
y = mx+c
based on the given conditions, we formulate:
y = 660,000x + 2000
Hence we get the required answer.
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Tariq is going to invest in an account paying an interest rate of 5.8% compounded quarterly. How much would Tariq need to invest, to the nearest hundred dollars, for the value of the account to reach $600 in 20 years?
The amount to be invested today in order to have $600 in 20 years is $189.66.
How much should be invested today?When an account pays interest that is compounded quarterly, it means that both the amount invested and the interest that has already been earned increases in value four times in a year.
In order to determine the amount to be invested today, determine the present value of $600.
The formula for calculating present value:
P = FV / [(1 + r)^nm]
Where:
FV = Future value P = Present value R = interest rate = 5.8 / 4 = 1.45% m = number of compoundingN = number of yearsP = 600 / [(1.0145)^80] = $189.66
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Answer: it is 200
Step-by-step explanation:
HELP MEEE 10x= 13 WHAT IS THE VALUE OF x
Answer:
Step-by-step explanation:
1.3
10/13=1.3
Answer:
[tex]\boxed{\sf \boxed{\sf x=\cfrac{13}{10}}\:or\: \boxed{\sf x=1.3}}[/tex]
Step-by-step explanation:
[tex]\sf 10x= 13[/tex]
Divide both sides by 10:-
[tex]\sf \cfrac{10x}{10}=\cfrac{13}{10}[/tex]
Simplify:-
[tex]\sf x=\cfrac{13}{10}[/tex]
____________________
Hope this helps!
Have a great day!
using a similar argument to solve teh hw problem 1, show that if a is an integer, then 7 divides a^7 -a
The expression a⁷- a is divisible by 7 if a is an integer.
Given that,
7 divides a^7−a
To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7
We can write, where k is an integer
a^7−a=7k
a(a^6−1)=7k
Now if a=k then
a^6−1=7
a^6=8
and a=±1.414 so a^7−a=9.898
If a is not equal to k then
a(a^6−1)=a(a^3+1)(a^3−1)=7k
since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.
Hence, The expression a⁷- a is divisible by 7 if a is an integer.
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Write a linear function f with f(5) =-1 and f(0) =-5
Answer: y = -4/5x - 5
Step-by-step explanation:
So you can view that fancy F with the parenthesis number inside of it as an input, just like X, and when -1 is the output, that means that y=-1, so your first set of numbers is (5,-1) now do the same with the second pair and you get (0,-5), we know that this is the Y intercept because X=0 in this pair.
-5 - (-1) = -4
0-5 = -5
slope = - 4/5
y intercept = -5
Write the following as an inequality.
8 is greater than x, and x is greater than 2.
use x only once in your inequality
Using x only once in the inequality, the inequality expression is 8 > x > 2
How to determine the inequality expression?The mathematical statement is given as
8 is greater than x, and x is greater than 2.
In mathematical expressions, greater than can be represented as >
So, we have the following representations
8 > x, and x > 2
Next, we combine the inequality expressions
This becomes
8 > x > 2
Hence, the inequality expression is 8 > x > 2
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What does an rectangle add up to
Answer:
360
Step-by-step explanation:
it has four right angles 90×4 =360
Can someone please help me I need the ones that are ticked
Answer:
*Note: Perimeter is equal to the sum of all side lengths
1. 3cm + 3cm + 5cm + 4cm = 6cm + 9cm = 15cm
2. 3.5cm + 3cm + 3.5cm + 3.5cm + 3cm + 3.5cm
= 6cm + 7cm + 7cm = 6cm + 14cm = 20cm
3. 2cm + 3cm + 3cm + 3cm + 5cm + 6cm = 5cm + 6cm + 11cm
= 11cm + 11cm = 22cm
7. 9cm + 9cm + 9cm = 27cm
8. Perimeter of a rectangle = 2 times the length plus 2 times the width
P = 2(60m) + 2(48m) = 120m + 96m = 216m
9. 1 roll of 16m of wire = $3,214
216m/16m = 13.5 rolls of wire
13.5 rolls($3,214) = $43,389
Increase 100kg by 25%
Answer: 125
Step-by-step explanation:
100% = 100
25% of 100 = 100/4 = 25
100 + 25% (25) = 125
the angle measures of a quadrilateral are in a ratio of 4 : 5 : 6 : 9. find the measure of the smallest angle.
The measure of the smallest angle of the quadrilateral is 60° .
In the question ,
it is given that ,
the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .
So , the measure of the largest angle is = 9x
and the measure of the smallest angle is = 4x .
we know that the sum of the measure of all the angles of the quadrilateral is 360° .
that means ,
4x + 5x + 6x + 9x = 360°
24x = 360
dividing both sides by 24 ,
x = 360/24
x = 15 .
the smallest angle is = 4(15) = 60°
Therefore , The measure of the smallest angle of the quadrilateral is 60° .
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A regulation baseball field measures 90 feet between each base what is the distance around the bases in yards
The distance around the bases in meters will be 27.432 meters.
How many meters are in 1 feet?
In one feet there are 0.3048 meters.
Given is a baseball field measures 90 feet between each base.
Distance between each base in feet = [d] = 90 feet
The distance between each base in meters will be -
D [meters] = 90 x 1 ft
D [meters] = 90 x 0.3048 meters
D [meters] = 27.432 meters
Therefore, the distance around the bases in meters will be 27.432 meters.
Write the equation in standard form using integers
(no fractions or decimals): y= -2/3 x-1
The standard form of the equation y = -2/3 x - 1 is 2x + 3y = -3.
How to write linear equation in standard form?The standard form for linear equations in two variables is Ax + By = C. Where,
A, B and C are constant.x and y are the variables.The equation is represented in slope intercept form. So, let' represent it in standard form.
Therefore,
y = - 2 / 3 x - 1
add 2 / 3 x to both sides of the equation
y = - 2 / 3 x - 1
y + 2 / 3 x = - 2 / 3 x + 2 / 3 x - 1
y + 2 / 3 x = - 1
Let's multiply all through by 3 to eliminate the fraction
y + 2 / 3 x = - 1
3y + 3(2 / 3 x) = -3
Therefore, the standard form equation is 2x + 3y = -3
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Statements 1 and 2 are true conditional statements.
Statement 1: If a figure is a parallelogram, then it is a quadrilateral.
Statement 2: If a figure is a quadrilateral, then its angles sum to 360°.
Which conclusion is valid?
Multiple choice question.
A)
If Figure A is a quadrilateral, then Figure A is a parallelogram.
B)
If Figure A is not a parallelogram, then Figure A’s angles do not sum to 360°.
C)
If Figure A’s angles do sum to 360°, then Figure A is a parallelogram.
D)
If Figure A is a parallelogram, then Figure A’s angles sum to 360°.
The valid conclusion about statement A and statement B is "If Figure A is a parallelogram, then Figure A’s angles sum to 360°".
The correct answer option is option D.
What is conditional statement?A conditional statement can be defined a statement that is written in the form “If A then B,” where A and B are sentences.
For this conditional statement:
Sentence A is called the hypothesis
Sentence B is called the conclusion.
Hypothesis: This is an assumption taken to be true for the purpose of argument or investigation.
Conclusion: This is the proposition that follows as a necessary consequence of the premises in an argument or syllogism.
Hence, “If A then B” means that B must be true whenever A is true.
Therefore, if a figure is a parallelogram, then it is a quadrilateral; If a figure is a quadrilateral, then its angles sum to 360°.
It can be concluded that if a figure is a parallelogram, then it's angles must sum to 360°.
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what does the solution of equality look like?
Answer:no image I can’t see on mobile
Step-by-step explanation:
h
Find the area of the triangle.
A=?in^2
Answer:
7.5 in²
Step-by-step explanation:
You want the area of a triangle shown as having a base of 6 inches and a height of 2.5 inches.
AreaThe formula for the area of a triangle is ...
A = 1/2bh
where b is the base length, and h is the height.
ApplicationThe figure shows the base of the triangle as 6 in, and the height as 2.5 in. This means the area is ...
A = 1/2(6 in)(2.5 in) = 7.5 in²
__
Additional comment
The attachments show the triangle to be overs-specified. If the side dimensions are correct, the area is actually about 7.48 square inches. If the base and height are correct, at least one side length is slightly off.
please help!! ASAP!!!!!
The amount Heidi earned in commission is $30 and the amount store made from her sale is $720.
We will solve the given problem using percentages.
We are given the following;
A salesperson at a jewelry store eams 4% commission each week.
Last week, Heidi sold $750 worth of jewelry.
We need to find the amount Heidi earned in commission and the amount store made from her sale.
Let us find the amount Heidi earned in commission;
$750 * 4% = 750 * 4 / 100 = 7.5 * 4 = 30
So, Heidi earned $30 from the commission.
Let us find the amount store made from her sale;
The amount store earns
= The total amount of sales - commission of Heidi
= $750 - $30
= $720
So, the store earns $720.
Thus, the amount Heidi earned in commission is $30 and the amount store made from her sale is $720.
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2. If m angle EFD = 75°, then m angle JAB = ??
C
B
A
1.
2.
Answer:
If m angle EFD = 75°, then m angle JAB = ??
C
B
A
1.
2.
An arithmetic sequence has this recursive formula: What is the
explicit formula?
Answer:
the correct answer is -32+43
Step-by-step explanation:
I just know
which of the following is a fair gamble? question 2 options: one coin toss: win $10 if heads, lose $10 if tails. two coin tosses: win $10 if two heads, lose $10 if two tails, no change of wealth otherwise. a game in which you win $100 with probability 50%, lose $200 with probability 25%, and gain nothing with probability 25%. all of the above are fair gambles.
Out of all the given situations, all are fair gambles,
Any gamble is considered to be a fair gamble if the expectation of it is 0. Here, gamble means any situation which has a probabilistic uncertainty attached to it.
The expectation of any game is
E(X) = ∑xp(x)
In the first case
The probability to get a had or tails on flipping a coin is 1/2
Hence the expectation will be
E(X) = 0.5 X 10 + 0.5 X (-10)
= 5 - 5
= 0
Hence this is a fair gamble
In the next gamble, two coins are tosses
The probability to get 2 head is 1/4
The probability to get 2 tails is 1/4
The probability to get one head and one tail is 1/2
Hence,
E(X) = 0.25 X 10 + 0.25 X (-10) + 0.5 X 0
= 2.5 - 2.5
= 0
Hence this too is a fair gamble
Here,it is given that
Probability Gain
0.5 $100
0.25 - $200
0.25 $0
Therefore,
E(X) = 0.5 X 100 + 0.25 X (-200) + 0.25 X 0
= 50 - 50
= 0
Hence, all are fair gambles.
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Correct Question
which of the following is a fair gamble?
one coin toss: win $10 if heads, lose $10 if tails.
two coin tosses: win $10 if two heads, lose $10 if two tails, and no change of wealth otherwise.
a game in which you win $100 with a probability of 50%, lose $200 with a probability of 25%, and gain nothing with a probability of 25%.
all of the above are fair gambles.
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Your mother made some pumpkin cookies and put half of them on a
plate for your brother and you. Your dog Gobbles ate six! Your
brother ate half of what was left, and you ate the last four.
How many cookies did your mother bake altogether?
The total cookies she baked altogether is 28 cookies
What are word problems?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.
Therefore the total cookies put on the plate is 6+4+4= 14cookies
half of all the cookies were put in the plate,
therefore the total cookies made is 14×2= 28cookies.
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Which angle is vertical to ∠BCH?
Please help!!!
SOLVE CORRECTLY FOR 83 POINTS AND BRAINLIEST
The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)
How to Interpret Mathematical Transformations?We are told that the triangle P'Q'R' has been transformed from triangle PQR.
Now, the coordinates of triangle PQR are;
P(-1, 1)
Q(2, 0)
R(-1, -2)
The coordinates of the transformed triangle P'Q'R' are;
P(-5/2, 5/2)
Q(5, 0)
R(-5/2, -5)
Thus, this is clear that the transformation rule used is;
(x, y) → (⁵/₂x, ⁵/₂y)
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4.43 overweight baggage. suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. most airlines charge a fee for baggage that weigh in excess of 50 pounds. determine what percent of airline passengers incur this fee.
The percentage of airline passengers covered by this fee is 85.99%.
If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is
less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.
This is the p-value of Z for X = 50 minus 1 as a
ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%
So, 85.99% of the airline passengers pay this fee.
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Help me please this is my final question involving this method (maybe)
100 Points
Answer:
(-1,3)
Step-by-step explanation:
x+4y=11
-4y. -4y
x=11-4y
3(11-4y)+5y=12
33-12y+5y=12
33-7y=12
-33. -33
-7y=-21
/-7. /-7
y=3
x+4(3)=11
x+12=11
-12. -12
x=-1
Hopes this helps please mark brainliest
Answer:
x= −1 and y= 3
Step-by-step explanation:
Step One: Rewrite Equations
x+ 4y = 11
3x +5y = 12
Step Two: Solve x +4y = 11 for x:
x +4y = 11
x +4y + −4y = 11 + −4y (Add -4y to both sides)
x = −4y +11
Step Three: Substitute −4y +11 for x in 3x +5y = 12:
3x +5y = 12
3(−4y +11) +5y = 12
−7y +33 = 12 (Simplify both sides of the equation)
−7y +33 +−33 = 12 +−33(Add -33 to both sides)
−7y = −21
(-7y/-7) = (-21/-7) (Divide both sides by -7)
y = 3
I sincerely hope this helped you, good luck on your assignment!
The average annual stock return is 11. 3%. If you begin your investment portfolio with $2,000, what will your portfolio be worth in 30 years if the average holds?.
If the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that, the average annual stock return is 11. 3% and you begin your investment portfolio with $2,000,
Suppose the amount he earns in one year is x,
x= 11. 3%. of $2,000
x=220
The portfolio be worth 30 years if the average holds are,
=220 × 30
=$ 6600
The net cost is the sum of the return and the initial investment,
=$ 6600 + $ 2000
=$8600
Thus, if the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.
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Write the slope-intercept form of a line with a slope of 12 and a y-intercept of (0, -7)
Answer:
y=12x-7
Step-by-step explanation:
Slope intercept is y=mx+b
y = slope+y-int
always start with variable y =
slope = 12
y=12
slope needs x
y=12x
y-int = -7 so just plug it in as is
y=12x-7
what is the image point of (0, 2) after a translation left 5 units up to 1 units
The image of the given point after the translation will be (-5,1).
The given point is (0,2).
We have to find out the image of the given point after a translation left 5 units and up to 1 units.
Since it is given that there is a translation left 5 units, starting from point (0,2), the image will be on the negative side of x-axis at point 3.
Similarly, it is given that there is also a translation up to 1 units. This implies starting from point (0,2), the image will be on the positive side of y-axis at point 1.
So, the image of the given point after the translation will be (-3,1).
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At the beginning of spring, Sophia planted a small sunflower in her backyard. When
it was first planted, the sunflower was 25 inches tall. The sunflower then began to
grow at a rate of 3 inches per week. How tall would the sunflower be after 9 weeks?
How tall would the sunflower be after w weeks?
Height after 9 weeks:
Height after w weeks:
The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.
Sophia planted a tiny sunflower in her backyard at the start of spring.
When she planted the sunflower,
The height of the sunflower = Initial height of the sunflower = 25 inches.
Now, The sunflower then began to grow at a rate of 3 inches per week.
Thus, the growth rate of the sunflower = 3 inches/week
The growth in 9 weeks = 3*9 = 27 inches,
The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.
The growth in w week = 3w inches,
The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.
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Subtract. Put you answer in lower terms.
47/50 - 3/10
A. 44/40
B. 32/50
C. 13/60
D. 16/25
The required simplified solution of the given subtraction is 16/25. Option D is correct.
Given that,
To Subtract. and determine the lower terms,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= 47/50 - 3/10
= [47 - 3×5] / 50
= [47 - 15] /50
= 32 / 50
= 16 / 25
The required simplified solution of the given subtraction is 16/25. Option D is correct.
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Answer:
d) 16/25
Step-by-step explanation:
The problem is,
→ (47/50) - (3/10)
Let's solve the problem,
→ (47/50) - (3/10)
→ (47/50) - (15/50)
→ (47 - 15)/50
→ 32/50
→ (32 ÷ 2)/(50 ÷ 2)
→ 16/25
Hence, answer is 16/25.
alfred tried to solve the system of equations shown below. he concluded that the system has an infinite number of solutions. which is the best evaluation of alfred's conclusion? a. he is incorrect. for any positive value of , the corresponding value of is negative, which means the system has no solution. b. he is correct. both equations describe lines that have infinitely many solutions. c. he is incorrect. if the first equation is multiplied by 4 and added to the second equation, the result is , which leads to exactly one solution. d. he is correct. if the first equation is multiplied by 4 and subtracted from the second equation, the result is , which means the system has an infinite number of solutions.
The Correct option is D .
System of linear equations,gives us the result that given system has unique solution such that 13x= 6 or x = 6/13 and y = -40/13 .
If a, b, and c are real numbers, the graph of the equation ax + by = c
is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.
Unique Solution: A system of linear equations has a solution if the graphs intersect at a point.No Solution: If the graph is parallel, the system of linear equations has no solution.Infinitely Many Solutions: There are infinitely many solutions to a system of linear equations if the graph is exactly the same straight line.given system of equations is
2x - y = 4 --(1)
and 5x + 4y = -10 ---(2)
comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2
we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,
c2= -10
Now, the ratio are
a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5
=> a1/a2 not equal to b1/ b2
therefore the given system of equations has unique solution.
Now , we find the soltion of given system using Elimination method,
multipling equation (1) by 4 to making same cofficient of y in both equations of system we get
8x - 4y = 16 --(3) and 5x +4y = -10
adding equation (2) from (3) we get,
8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13
putting this value of x in (1)
2×6/13 - y = 4 => y = 12/13-4 = -40/13
Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.
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Complete Question:
Alfred tried to solve the system of equations shown below..
2x - y = 4 and 5x + 4y = -10
He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?
He is correct. Both equations describe lines that have infinitely many solutions.
He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.
He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.
He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.
HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEE
13. Write an equation of the graph in slope-intercept form.
14. If misty has been traveling for 9 hours, how many miles of the trip does she have remaining?
15. If there are 50 miles in the trip remaining, how many hours has misty been traveling?
The equation of the graph is a straight line written in slope-intercept form as y = -33.3x + 450. When Misty travelled for 9 hours, he drove 150.3 miles.
Equation of Straight LineThe general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.
The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line. The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are point-slope form, slope-intercept form, general form, standard form, etc. Let us go through the formula for the equation of a straight line
13: The equation of graph in slope-intercept form
But for this case, we will represent our equation using point-slope formula which is y = mx + c
Let's find the slope of the line.
To do this, we will pick any two points and solve for the slope.
A = (0, 450), B = (6, 250)
The equation of slope of a line is given as
m = y₂ - y₁ / x₂ - x₁
m = 250 - 450 / 6 - 0
m = -200/6
m = -33.3
The y-intercept is the point which the line touches the y-axis or y-plane and in this case, the y-intercept is 450.
The equation of the line is y = -33.3x + 450
y = miles remainingx = hours travelled.14: If he has been travelling for 9 hours, how many miles left ?
Using the equation y = -33.3x + 450; put x = 9
y = -33.3(9) + 450
y = 150.3 miles
Misty has 150.3 miles left.
15: If there are 50 miles in the trip left, how many hours has Misty travelled.
Using the equation y = -33.3x + 450
50 = -33.3x + 450
-400 = -33.3x
x = 12 hours
Misty has approximately travelled 12 hours.
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