The exponential function that gives the profit after x weeks is given by:
[tex]P(x) = 200(1.2)^x[/tex].
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
Buffy finds that each week his profits increase by 20% over what they were the previous week, hence r = 0.2.In his first week of business his profits were $200, hence A(0) = 200.Thus, the equation is given by:
[tex]A(x) = 200(1 + 0.2)^x[/tex]
[tex]A(x) = 200(1.2)^x[/tex]
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What is the perimeter of the parallelogram?
Answer:
2(a+b)
Step-by-step explanation:
The length of AB is four times the length of BC.
AC = 75 cm.
=
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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Building a Storage Container
You are being asked to design an enclosed water storage container. You are given a budget of
$100 to build the container. It has been determined that the best material to make the container
costs $10 per m². (In other words your surface can not cost more than $100.) What is the
largest amount of water your container can hold? You will need to explain to your boss the
reasoning because they have a business degree and do not really remember any of their
geometry work from school.
Answer:
2973.5 liters
Step-by-step explanation:
You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.
__
areaThe available area is ...
($100) / ($10/m²) = 10 m²
diameterThe area of a sphere with diameter d is ...
A = πd²
Then the diameter for the given area is ...
10 m² = πd²
(10/π) m² = d² . . . . . divide by π
√(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere
volumeThe volume of a sphere is given by ...
V = 4/3πr³ = (π/6)d³
For the diameter found above, the volume of the sphere will be ...
V = (π/6)(1.78412 m)³ ≈ 2.97354 m³
There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...
2.97354 m³ × (1000 L/m³) = 2973.54 L
The largest amount of water the container can hold is about 2973.5 liters.
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:
2. Noah is solving the equation x² + 8x + 15 = 3. He begins by rewriting the
expression on the left in factored form and writes (x + 3)(x + 5) = 3. He
does not know what to do next.
Noah knows that the solutions are x = -2 and x = -6, but is not sure how
get to these values from his equation.
Solve the original equation by completing the square.
Answer:
The solution set is {-6, -2}.
Step-by-step explanation:
x^2 + 8x + 15 = 3
x^2 + 8x = -12
Completing the square:
(x + 4)^2 - 16 = -12
(x + 4)^2 = 4
Taking square roots of both sides:
x + 4 = +/- 2
x = 2 - 4 = -2 or x = -2-4 = -6.
What is the area of a triangle whose vertices are R(3, 4), S(6, 2), and T(7, 10)?
Enter your answer in the box.
According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.
How to calculate the area of a triangle by knowing its sides
In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.
First, we determine the length of each side:
[tex]RS = \sqrt{(6-3)^{2}+(2-4)^{2}}[/tex]
[tex]RS = \sqrt{3^{2}+(-2)^{2}}[/tex]
[tex]RS = \sqrt{13}[/tex]
[tex]ST = \sqrt{(7-6)^{2}+(10-2)^{2}}[/tex]
[tex]ST = \sqrt{1^{2}+8^{2}}[/tex]
[tex]ST = \sqrt{65}[/tex]
[tex]RT = \sqrt{(7-3)^{2}+(10-4)^{2}}[/tex]
[tex]RT = \sqrt{4^{2}+6^{2}}[/tex]
[tex]RT = \sqrt{80}[/tex]
Now we calculate the area of the triangle by Heron's formula:
[tex]s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}[/tex]
s ≈ 10.306
[tex]A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}[/tex]
A ≈ 14.525
According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.
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What's the square root of Pi times the c length of a right triangle with the a measurement of 12 and the b measurement of 10?
Answer:
[tex]2\sqrt{61\pi }[/tex]
Step-by-step explanation:
Let's find c by using the Pythagorean Theorem: [tex]10^2 + 12^2 = c^2[/tex] so [tex]c = \sqrt{10^2 + 12^2}[/tex]. I'm going to leave c like this so it is easier to multiply by [tex]\sqrt{\pi }[/tex]. [tex]c\sqrt{\pi } = \sqrt{10^2 + 12^2}\sqrt{\pi } = 2\sqrt{61\pi }.[/tex]
Hope this helped! :)
-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.
[tex]\log _ { 5 } ( 2 m + 5 ) = 3log5(2m+5)=3[/tex]
solution needed
with briefly explained
Answer:
m = 60
Step-by-step explanation:
log is another way to write an exponent.
Example:
exponent form:
7^2 = 49
log form:
log_7 (49) = 2
In your question, we need to change to exponent form, from log form.
log_5 (2m+5)=3
5 is the base. 3 is the exponent.
Now it can be solved.
5^3 = 2m+5
125 = 2m + 5
120 = 2m
60 = m
(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]
Please Help! I need This quickly!!!
The area of the smallest box that a circular pizza will fit into = 1661 squared cm.
What is Area of Circle?
The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.
The circular pizza requires the same amount of dough as the square pizza.
Area of the square pizza =40 cm * 40 cm
= 1600 [tex]cm^{2}[/tex].
Area of circle= [tex]\pi\; r^{2}[/tex]
1600 = 3.14 *[tex]r^{2}[/tex]
[tex]r^{2}[/tex] = 510
r= 22.58
r = 23 cm approx.
Area of circle= [tex]\pi\; r^{2}[/tex]
= [tex]3.14 * (23)^{2}[/tex]
= 1661.06 squared cm
The area of the smallest box that a circular pizza will fit into = 1661 squared cm.
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someone please help me and solve for the unknowns and give reasons please
or can you just solve for the unknowns please
Answer:
Step-by-step explanation:
The angles labeled with 2x, 4x, and 3x are on a straight line so their sum is equal to 180
2x + 4x + 3x = 180 add like terms
9x = 180 divide both sides by 9
x = 20
The angle represented with 3x - 30 and the angle represented with 2x + 10 are alternate and their measurement is same
3x - 30 = 2x + 10 export like terms to same side of the equation
3x - 2x = 10 + 30
x = 40
to find the angles replace x with the value found for each.
help me whats 93458 divided by 19435
scan qr code for assignment question!
Answer:
[tex]\frac{93458}{19435}[/tex] ≈ 4.81
Step-by-step explanation:
[tex]\frac{93458}{19435}[/tex] can not be simplified
5-2i-2(3+i) can you help me with this answer
Answer:
-1 - 4 i
Step-by-step explanation:
5 - (2 * i) - (2 * (3 + i)) =
-1 - 4 i
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
Sydney is considering two jobs. One job pays $45,000 per year. The other job pays a
weekly salary of $950. Which job pays better?
Answer:
The first job pays more
Step-by-step explanation:
950 x 3 = One month pay = 2,850
2,859 x 12 = One year = 34,308 Per Year
Comparing them both
$45,000 One Year, First Job
$34,308 One Year, Second Job
What is 8.92 cm² Converted To Meters?
[tex]8.92 ~ \text{cm}^2\\\\=8.92 \times \left( 1 ~ \text{cm} \right)^2\\\\=8.92 \times \left(10^{-2}~ \text{m} \right)^2~~~~~~;\left[1~ \text{cm} = \dfrac{1}{100}~ \text m} = 10^{-2}~ \text{ m} \right]\\\\=8.92 \times 10^{-4}~ \text{m}^2\\\\=0.000892~ \text{m}^2[/tex]
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
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
Write an expression for "the quotient of 999 and c."
Answer:
"quotient" indicates division
999 ÷ c = ?
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.
(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
Solve the system of equations by the substitution method.
10x + 2y = 2
- 5x = y + 10
Select the correct choice below and, if necessary, fill in the answ
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
The expression 3200(1.06)^t represents the
enrollment of a high school t years after 2000.
describe how the enrollment changes
each year.
a. increases 1.06%
b. increases 6%
c. decreases 1.06%
d. decreases 6%
Expression 3200(1.06)^t represents the enrollment of a high school t years after 2000 will increase by 6%.
What is the percentage?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
The given expression is as follows:-
= 3200 ( 1.06 ) [tex],^t[/tex]
Here when the time has increased the percentage is also increased by 6%.
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please help!! i’ll give brainliest
Solve for x.
x = [?]
Answer:
3x +18+4x+15=180
7x+33=180
7x=180-33
7x=147
7x÷7=147÷7
x=21
Answer:
[tex]\boxed{\bf x = {21}^{o} }[/tex]
Step-by-step explanation:
We know that the sum of angles of a linear pair is always equal to 180°, they are also known as supplementary angles.
[tex]\sf 3x + 18 + 4x + 15 = {180}^{o} [/tex][tex]\sf 7x = 180 - 18 - 15[/tex][tex]\sf 7x = 147[/tex][tex]\sf \cfrac{ 7x}{7} = \cfrac{147}{7} [/tex][tex]\sf x = {21}^{o} [/tex]«•••••••••••••••«»•••••••••••••••»
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
in the figure below lines p and q are parallel. what do you notice? IREADY
100 points
Answer:
alternate interior anglesthe sameStep-by-step explanation:
The problem is concerned with angles 4 and 5, which lie between the lines given as parallel. They are on opposite sides of the line cutting across those parallel lines (the transversal), so they are ...
alternate interior anglescongruent__
Being congruent angles, their measures are ...
equalthe same_____
Additional comment
For questions like this, there are many descriptions that are true. It would be helpful to know the possible answer choices.
Please help me if really appreciate it!!