Using linear function concepts, it is found that the representation of the value of 4,000 is given by:
B the gallons of water initially in the pool.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the amount of water in the pool after x hours is modeled by:
y = -720 x + 4000.
4000 is the y-intercept, which is the initial amount of water in the pool, hence option B is correct.
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(4x+3)(6x-3) = 0
What is the positive solution to the problem?
Answer:
The positive solution is 1/2
Step-by-step explanation:
(4x+3)(6x-3) = 0
We can use the zero product property to find the zeros
4x+3 =0 6x-3 =0
4x =-3 6x = 3
x = -3/4 x = 3/6
x = -3/4 x = 1/2
The positive solution is 1/2
somebody please help me with this
Answer:
P(A) = 13/18
P(B) = 7/18
Step-by-step explanation:
A) Sum greater than 5
If the sum needs to be >5, then it can be 6, 7, 8, 9, 10, 11, and 12.
There are 26 out of 36 events where the sum is >5, thus P(A) = 26/36 = 13/18.
B) Sum divisible by 4 or 6
The sum ranges from 2 to 12, there are two methods to calculate this:
B1) Method 1: Calculate the frequency one by one
The sums divisible by 4 or 6 are S = {4, 6, 8, 12}. There are 9 of them, n(S) = 14. Thus P(B) = 14/36 = 7/18.
B2) Method 2: Use the rule of not mutually exclusive events
Not mutually exclusive events (might also be called mutually inclusive) happens when two events can happen together at the same time. In this problem, the sum might be divisible by 4 and 6 at the same time, i.e. the number 12.
The common formula for not mutually exclusive events is P(A∪B) = P(A) + P(B) - P(A∩B). Nb: P(A) isn't talking about the previous problem, nor does P(B) talk about the second section as a whole; the terms P(A) and P(B) will be utilized next, explained with their uses.
P(A) = probability of the sum being divisible by 4, i.e. the number 4, 8 and 12
P(A) = (3+5+1) / 36 = 9/36 = 1/4
P(B) = probability of the sum being divisible by 6, i.e. the number 6 and 12
P(B) = (5+1) / 36 = 6/36 = 1/6
P(A∩B) = probability of the sum being divisible both by 4 and 6, i.e. the number 12
P(A) = 1 / 36 = 1/36
Here comes the use of formula P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 1/4 + 1/6 - 1/36 = 7/18
Nb: As you can see, both method B1 and B2 give the same answer. Method B1 is usually easier to use when facing simpler problems like this. I'd recommend using method B2 for more complex and difficult questions, such as when you can't visualize the problem with a table because there are too much sets of variables.
Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3
A 90% confidence interval is centered at a _____ and is 90% sure to contain the _______.
a) statistic, variable
b) parameter, statistic
c) statistic, parameter
d) parameter, variable
e) variable, parameter
Answer:
See below
Step-by-step explanation:
A 90% confidence interval is centered at a parameter and is 90% sure to contain the statistic.
When you are running a statistical test, you can create a confidence interval centered at the appropriate parameter (such as the mean) to see if the statistic stated in your null hypothesis is true if it's contained in the interval. Whatever the confidence level is determines how wide the interval will be, and as such, will determine how likely the interval will catch the statistic in question.
Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK
Round your answer to the nearest tenth if necessary.
Answer:
Heyyyy!!
The answer is 66.9
please read the explanation... it will help... I promise
Step-by-step explanation:
Okay... Here we go...
The context mentions that the two quadrilaterals are similar... meaning their sides are proportional...
So... you basically have to find the scale factor...
(the math itself is easier than the explanation...
51/16 = 3.1875 (that is the number we multiplied the sides of quadrilateral FGHI to get quadrilateral JKLM...
so to get side JK all you have to do is multiply that scale factor by side FG... which after the use of a calculator results in 66.9 (i rounded, and used a calculator... lol)
but yeah... i hope this helps...
Write an expression for "the quotient of 999 and c."
Answer:
"quotient" indicates division
999 ÷ c = ?
Need help please answer ASAP!
(22-23)
Answer:
Question 22 is
[tex]x - 3[/tex]
Question 23 is
[tex]1.67 \times {10}^{ - 21} g[/tex]
Select the correct answer from each drop-down menu.
Three students used factoring to solve a quadratic equation.
x² + 17x + 72 = 12
Jordan's Solution Keith's Solution Randall's Solution
x² + 17x + 72 = 12 x² + 17x + 72 =12 x² +17x +72 = 12
(x + 8)(x + 9)= 12 x² + 17x +60 =0 x2 +17x = -60
x+8=12 & x+9=12 (x +5)(x +12) +0 x(x +17) = -60
x + 5 =0 & x + 12 = 0 x = -60 & x +17 = -60
The equation was solved correctly by ____. The solutions of the equation are ____
Answer:
Step-by-step explanation:
x = -5 and x = -12 are the solutions.
Looks like Keith's solution is the correct one as he got as far as
x + 5 = 0 and x + 12 = 0.
Which organism will survive best in a damaged ecosystem? (science)
any organism that does not eat the damaged part of the ecosystem
one that eats a wide variety of foods
one that eats primarily one type of food
one that has two main food sources
Answer:
Step-by-step explanation:
Discussion
Think of what it would be like in your own household. If your mom has been away and the food is starting to spoil, you can't be picky. If you are not picky, you will get by until someone goes shopping.
That's the way its going to work in the ecosystem. I would pick B and hope that it the bad times won't last too long.
What is the equation of a line passing through points (1, 2) and (3, 8)?
A.
y = x + 5
B.
y = 1
3 x – 1
C.
y = 3x – 1
D.
y = 1
5 x – 1
E.
y = x + 1
The equation of the line passing through these two points (1, 2) and (3, 8) will be y = 3x – 1. Then the correct option is C.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The points are (1, 2) and (3, 8).
Then the equation of the line passing through these two points (1, 2) and (3, 8) will be
[tex]\rm (y - 2) = \dfrac{ 8- 2}{3-1} (x - 1)[/tex]
On simplifying the equation, we have
y - 2 = 3(x – 1)
y - 2 = 3x – 3
y = 3x – 1
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What is the perimeter of the parallelogram?
Answer:
2(a+b)
Step-by-step explanation:
the value of the power is
Answer:
Is 4
4
Step-by-step explanation:
Answer:
See below ~
Step-by-step explanation:
Power in repeated multiplication form is : 4 x 4 x 4 x 4
Value of the power : 16 x 16 = 256
PLEASE HELP ! <3 !!!!!!!!!!!!!!!!!!!!!!!
Answer:
7 things an investor should consider when picking stocks:
Trends in earnings growth.
Company strength relative to its peers.
Debt-to-equity ratio in line with industry norms.
Price-earnings ratio as an indicator of valuation.
How the company treats dividends.Effectiveness of executive leadership.
Step-by-step explanation:
can someone help me please
Answer:
A
Step-by-step explanation:
If you line up all the numbers/variables you just have to copy down all of them except for 7x and 12x, you just add those and you get 19x so the answer is A.
please help thanks :)
The equation of line A and line B will be y =4 and x = 8, respectively.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
We know the equation of the line parallel to the x-axis.
y = c
The equation of line A will be
y = 4
We know the equation of the line parallel to the y-axis.
x = c
The equation of line B will be
x = 8
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f(x)=3x+2 and g(x)=x-3. Find f(x)-g(x)
a. 4x-1
b. 2x-1
c. 2x+5
d. 2x-5
Answer:
First step is to plug in the given values :[tex] \longrightarrow \tt3x + 2 - ( x - 3)[/tex]
Remove the bracket and change the signs of those terms which are inside bracket since there is a negative sign.[tex] \longrightarrow \tt \: 3x + 2 - x + 3[/tex]
Collect like terms[tex] \longrightarrow \tt 3x - x + 2 + 3[/tex]
[tex] \longrightarrow \boxed{ \tt 2x + 5 }[/tex]
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PLEASE HELP!!!
Solve for x using the Quadratic Formula: x2 + 2x + 1 = 0
-b+Vb2-4ac
X=
2a
Ox=2
Ox= 1
O x = 0
O x = -1
Answer:
last option, x = -1
Step-by-step explanation:
[tex]x^{2} + 2x + 1 = 0\\x_{1} = \frac{-2 + \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{2} = \frac{-2 - \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{1} = \frac{-2 + \sqrt{0} }{2}\\x_{2} = \frac{-2 - \sqrt{0} }{2}\\x = \frac{-2}{2} \\x = -1[/tex]
The value of x by using the Quadratic Formula is,
⇒ x = - 1
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
Equation is,
⇒ x² + 2x + 1
Now, We can use the Quadratic Formula for x as;
⇒ x² + 2x + 1
⇒ x = - 2 ± √2² - 4×1×1 / 2
⇒ x = - 2 ± √4 - 4 / 2
⇒ x = - 2 / 2
⇒ x = - 1
Thus, The value of x by using the Quadratic Formula is,
⇒ x = - 1
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venessa is solving a video game puzzle to open a secret door she must collect between 400 grams (g) and 500 grams (g) of gems she can only collect one type of gem
type of gem mass
Ruby 128.3
Emerald 195.2
Diamond 147.6
Which of the gems should Vanessa try to collect?
A. rubies
B. emeralds
C. diamonds
D. none of the gems will work for opening the secret door
-2(8f+9)-6n use f=5 and n=7
Answer: Correct me if I am wrong, but this is how I think you should solve it.
Step-by-step explanation:
1. Simplify 8×5 to 40.
−2×(40+9)−6×7
2. Simplify 40+9 to 49.
−2×49−6×7
3. Simplify −2×49 to −98.
−98−6×7
4. Simplify 6×7 to 42.
−98−42
5. Simplify
−140
Your all done! Hope this helps.
In the equation x² + 10x + 24 = (x + a)(x+b), bis
an integer. Find algebraically all possible values of
b.
Answer:
The answer is 6...Hope this might help you
5.
—-
help please
—
math geniuses pls help!!!
pls check other questions too!
Answer:
The mean is greater than median
Step-by-step explanation:
Option D
What is the sum of the angles in the diagram?
Please help giving 80 points
Graph the function on the coordinate plain
A)what are the x intercepts
B)what is the y intercepts
C)what is the maximum and minimum value
Answer:
it should be C I did something very very similar to this but different questions
Answer:
a) {-6, 2}
b) -12
c) minimum: -16
Step-by-step explanation:
I find a graphing calculator to be a big help. Its graph is attached.
a) The function can be factored as:
f(x) = (x -2)(x +6)
The factors are zero at the x-intercepts: x = 2, x = -6.
b) The y-intercept is the function value when x=0. That is the constant in the function. The y-intercept is -12.
c) The leading coefficient of the function is positive, so its graph opens upward. The extreme value is a minimum. It is found on the axis of symmetry, at the x-value that is halfway between the x-intercepts: x = (2-6)/2 = -2. The function value there is ...
f(-2) = (-2-2)(-2+6) = -4(4) = -16
The minimum is f(-2) = -16.
23 lbs of onions cost $46. How many lbs of onions can you get with $30 ?
Answer:
15 lbs of onions.
Step-by-step explanation:
23 lbs divided by $46 = 0.5 lbs per $1
0.5 lbs times $30
15 lbs
The length of AB is four times the length of BC.
AC = 75 cm.
=
The length of a rectangle is three times the width. The sum of the length and the width is 24 inches. What is the length of the rectangle?
Answer:
Length: 18 inches
Width: 6 inches
Step-by-step explanation:
l+w=24
l=3w w=1w
3w+w=24
w=6
Length: 3*6=18 inches
Width: 6 inches
(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe?
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.
Find Q
tanQ=Perpendicular/BasetanQ=4/15tanQ=0.26Q=tan^-¹(0.26)Q=14.6°Not safe
Apply Pythagorean theorem
PR²=4²+15²=16+225=241
PR=√241Answer:
a) not safe
b) 15.5 ft (nearest tenth)
Step-by-step explanation:
Part (a)Tan trig ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = xO = PV = 4 ftA = RV = VQ = 15 ftSubstituting the given values into the formula and solving for x:
[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]
[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]
[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]
As 14.9° is not between 18° and 27°, the roof is not safe.
-------------------------------------------------------------------------------------------------
Part (b)Pythagoras’ Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = RV = VQ = 15 ftb = PV = 4 ftc = PRSubstituting the given values into the formula and solving for PR:
[tex]\implies \sf 15^2+4^2=PR^2[/tex]
[tex]\implies \sf 225+16=PR^2[/tex]
[tex]\implies \sf PR^2=241[/tex]
[tex]\implies \sf PR=\sqrt{241}[/tex]
[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]
Consider parallelogram ABCD below.
Use the information given in the figure to find m of angle B, x, and m of angle BCA.
Answer:
Step-by-step explanation:
1) Opposite angles in a parallelogram are congruent, so angle B measures 82 degrees.
2) Opposite sides of a parallelogram are congruent, so 12=6x. Hence, x=2.
3) Opposite sides of a parallelogram are congruent, so by the alternate interior angles theorem, the answer is 62 degrees.
Answer:
see explanation
Step-by-step explanation:
the opposite angles of a parallelogram are congruent , then
∠ B = ∠ D = 82°
the opposite sides of a parallelogram are parallel and congruent , then
AD = BC , that is
6x = 12 ( divide both sides by 6 )
x = 2
∠ BCA and ∠ DAC are alternate angles and are congruent , then
∠ BCA = ∠ DAC = 62°
Find m I need helppp pleasee !!!
Answer:
hope this will help you (✿^‿^)
Step-by-step explanation:
by Pythagorean theorem
h²=p²+b²
12²=9²+b²
b²=12²-9²
b=√63
b=7.9372
Please help me if really appreciate it!!
6 erasers cost $6.60.
Which equation would help determine the cost of 3
erasers?
Answer:
answer is a
Step-by-step explanation:
u just look at 6 and 6.60 thats 1 and 10 every eraser but for 3 its 1.30