Answer:
Her sales after 6 months are = 127units
Step-by-step explanation:
Percentage increase:- The degree to which a value increases expressed in percent form is known as percentage increase.
formula for % increase = (final value - initial value)/initial value(100)
Here in the question,
percentage increase after every month is = 5%
initial value = 95 units
therefore by applying above formula :-
[(x-95)/95]×100 = 5 [where x is the value of her sales goals after 1 month]
x = (5/100)×95+ 95
x = 99.75
Now this x will be the initial value for the next month
x₂ = (5/100)99.75+ 99.75 [ x₂ = sales goal after 2 months]
x₂ = (5/100)×99.75+ 99.75
x₂ = 104.73
similarly,
(x₃-104.73/104.73)100 = 5 [x₃ = sales after 3 months]
x₃ = 109.96
similarly for 4th month,
(x₄ -109.96/109.96)100 = 5 [x₄ = sales after 4 months]
x₄ = 115.45
for 5th month,
(x₅ -115.45/115.45)100 = 5 [x₅ = sales after 5 months]
x₅ = 121.22
finally for the 6th month
(x₆-121.22/121.22)100 = 5 [x₆ = sales after 6 months]
x₆ = 127.28
therefore,
her sales after 6 months are = 127.28 units or 127 units by rounding off
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Solve:
x-1
——— < 0
x²-4
Answer: x≠±2, x<±2, x>1, x<1, and x>±2
explanation:
for this equation to be true
Case 1
either (x-1) should be a negative while (x²-4) should be positive
which gives:-
x-1<0
so, x<1
also, x²-4>0
so, x²>4
⇒x>±2
Case 2:-
x-1>0 and x²-4<0
which gives
x>1 and x²-4<0
so, x>1 or x<±2
Case 3:-
either way, the denominator can't be 0
so, x²-4≠0
which gives,
x≠±2
compiling all, we have,
x≠±2, x<±2, x>1, x<1, and x>±2
These solutions can be pointed to as points on a number line and the behavior shows their discontinuity.
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The work of a student to solve the equation 2(3x-4)= 8 + 2x + 4 is shown below.
Step 1: 2(3x-4)= 8+2x+4
Step 2: 5x6 = 12 + 2x
Step 3: 5x-2x = 12 +6
Step 4: 3x = 18
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
O Step 2; 6x6 = 2(6+ x + 2)
O Step 2; 6x8 = 12 + 2x
O Step 3; 5x-2x = 12-6
O Step 3; 5x + 2x = 12 +6
I think my other question might've been deleted for some reason
We know that if (x,y) lies on the graph of a function, then (y,x) lies on the graph of its inverse.
This means you need to draw the segment with endpoints (9,1) and (2,3).
The number of goldfish in a tank is 22, and the volume of the tank is 56 cubic feet. What is the density of the tank?.
Answer:
0.39??
Step-by-step explanation:
Please help me with this
Exponential functions are typically organized in this format:
[tex]f(x) = a*c^x[/tex]
To find the equation given the graph of an exponential function:
Identify the horizontal asymptoteSolving the Question
Identify the horizontal asymptote
In this question, it appears to be x = 0.
Identify the y-intercept
The y-intercept is the value of y at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our a value. Plug this into [tex]f(x) = a*c^x[/tex]:
[tex]f(x) = 100*c^x[/tex]
Solve for c
We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for c:
[tex]f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}[/tex]
Plug c back into our original equation:
[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]
Answer[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]
A triangle with vertices at A (0, 0) B (0, 4) and C( 5, 9) is dlated to yeld a triangle with vertices at A(0, 0) , B(0, 10) and C (15, 0) The origins the center of dilation. What is the scale factor of the dilation?
A 1.5
B 2
C 2.5
D 3
For my math assessment, I need to apply trigonometry in a real life situation and explain about it. I've been thinking of 1. trigonometry applied in cricket 2. music (sound waves)... but still not quite sure how to. If anyone has knowledge on how I could work on these or any other new ideas that would be relevant, PLEASE help me!!! Thank you!! <3
Answer:
I know you said relevant so i have two answers.
1) (not so relevant).
You could use it to show how NASA and astronomers use it to calculate the distance between planets and connect it to building rockets and all that cool stuff.
2) (relevant).
For the one about music, you could connect it to sound engineers and use sine and cosine graphs to calculate wavelengths
Answer: Answers below.
Step-by-step explanation: Suppose you want to find the best angle to kick a soccer ball so that it enters the goal. A triangle can be formed with angle ζ facing the goal. Increasing ζ or decreasing ζ will allow you to see the best angle that is the maximum amount of time that you should wait until scoring the ball.
Sine, Cosine, and Tangent waves are used everyday in phones, tablets, computers, and in quantam and normal technology by imitating and creating waves that can be sent to a destination.
You can use inverse trigonometric functions to find the height of a roof, the height of a tree, the height of a pole, and more.
Light waves are, in reality, sine and cosine waves intertwined together.
You can even use trigonometry every day in work places, such as in software engineering. In fact, calculus 1 and 2, as well as Multivariate Calculus, which heavily and fundamentally uses trigonometry, is used widely across computer science. These help you to get $100,000 jobs.
In the equation below, variables X and Y represent two matrices. Which property of matrix addition is illustrated below?
X+Y=Y+X
O inverse property
O commutative property
O associative property
O identity property
Answer: the answer is b
Step-by-step explanation:
Mathmatical proofs. please help
the amount a gardener gets paid is directly proportional to the number of hours it takes for him to complete the job.
the gardener got paid £70 for a 12 hour job.
how much would he get paid for a job that took a total of 18 hours?
Answer:
£105
Step-by-step explanation:
The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:
3/2 × £70 = £105
He would get paid £105 for an 18-hour job.
__
Here are a couple of other solution methods.
as a proportionpay/hours = ?/(18 hours) = £70/(12 hours)
Multiplying by 18 hours, we get ...
? = £70×(18 hours)/(12 hours) = £70×(18/12)
? = £105 . . . . pay for 18 hours
He would get paid £105 for 18 hours.
__
as direct proportion equationThe equation for a directly proportional relationship is ...
y = kx
If we let y represent pay and x represent hours, then we have ...
70 = k(12) ⇒ k = 70/12 = 35/6
Then for 18 hours, the pay is ...
y = (35/6)x
y = (35/6)(18) = 35(3) = 105
He would get paid £105 for 18 hours.
Please help answer this question asap 4/11
The radius is
cm.
The circumference in terms of is
✓ cm.
7
Using 3.14 for л, the approximate circumference of the
circle is
cm.
The circumference of this circle with a radius of 7 cm is equal to 44 cm.
Given the following data:
Radius of circular rug = 7 cm.π = 3.14.How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this formula:
Circumference = 2πr
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
Circumference = 2 × 3.14 × 7
Circumference = 43.96 ≈ 44 cm.
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x2 - x - 42
a=?
b=?
C=?
help me
Step-by-step explanation:
thr standard form for a quadratic equation is:
ax²+bx+c
in this example, a=1, b=(-1), c=(-42)
What is the surface area of the cylinder with height 4 yd and radius 5 yd? Round your answer to the nearest thousandth.
Answer:
282.743 yd²
Step-by-step explanation:
Surface Area of the Cylinder: Top Base + Bottom Base + Side
Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²
Area of Bottom Base (Circle): same as top base = 25π yd²
Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =
2π(5 yd)*(4 yd) = 40π yd²
Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²
Consider the graph of the function f(x)=-(2)^x + 4
I have linked a picture with the intervel.
A large apartment complex has 1,500 units, which are filling up at a rate of 10% per month. If the apartment complex starts with 15 occupied units, how many months will pass before the complex has 800 occupied units? (Assume logistic growth). Round to the nearest tenth.
The number of months before the complex would have 800 occupied units is 40 months.
How many months before the complex has 800 occupied units?The formula that can be used to determine the required value is:
(In FV / PV) / r
Where:
FV = 800 PV = present occupancy rate = 15 r = rate of filling up = 10%(In 800 / 15) / 0.1 = 40 months
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Answer: 47.3 months
Step-by-step explanation:
[tex]-2(bx - 5) = 16[/tex]
Answer:
bx=-3
Step-by-step explanation:
-2(bx-5)=16
Use distributive property.
-2bx+10=16
Now, subtract 10 from both sides.
-2bx=6
Divide -2 from both sides.
bx=-3
Hope this helps!
If not, I am sorry.
What is 3m+5m?
>8
>8m
>8m2
Point M is 6 units away from the origin. Circle the letter by each pair of possible
coordinates.
A. (3, 0)
B. (4, 2)
C. (5, 3)
D. (0, 6)
E. (4, 4)
F. (1, 5)
The distance between the points (0, 0) and (0, 6) on the coordinate plane will be 6 units. Then the correct option is D.
What is the distance between two points?The shortest distance (length of the straight line segment's length connecting both given points) between points (p, q) and (x, y) is:
D² = (x – p)² + (y – q)²
Point M is 6 units away from the origin.
Take option D assuming correct, then the point will be (0, 6)
Then the distance between the points will be
D² = (0 - 0)² + (6 - 0)²
D² = 0² + 6²
D² = 0 + 36
D² = 36
D = 6 units
Then the correct option is D.
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One factor of the function f(x) = x ^ 3 - 9x ^ 2 + 20x - 12 is (x - 6) Describe how to find the x- intercepts and the y-intercept of the graph f(x) without using Show your work and include all intercepts in your answer
Answer:
Therefore, the y-intercept is (-12, 0)
Quadrilateral VWXY is a parallelogram. Find the measure of V
The height of a cone is twice the radius of its base. a cone has a height of 2 x and a radius of x. what expression represents the volume of the cone, in cubic units?
Answer:
Step-by-step explanation:
The volume of a cone is V = 1/3 [tex]\pi[/tex] * h * r^2
The height of the cone = the diameter of its circle.
Here is the expression:
Volume = 1/3 π * 2x * x^2
[tex]\frac{\pi *x^{2} *2x}{3}[/tex]
Hope I helped!
The revenue from selling shirts is r(x) = 11x.
The cost of buying x shirts is c(x) = 6x + 20.
The profit from selling x shirts is p(x) = r(x) - c(x).
What is p(x)?
Answer:
r(x)= 11x
c(x) = 6x + 20
p(x) = r(x) - c(x)
= 11x -( 6x + 20)
= 11x - 6x - 20
= 5x - 20
I read 1/3 of a book in an hour.
How much more of the book will I read in 2 1/5 hours
Answer:
Step-by-step explanation:
To find the number of pages of the book in the given hour:
To find the number of pages in 2 1/5 hours, multiply the number of pages read in 1 hour by 2 1/5 hours.
[tex]\sf \text{ Number of pages read in 2 $\dfrac{1}{5}$ hours = $\dfrac{1}{3}*2\dfrac{1}{5}$ }[/tex]
[tex]\sf = \dfrac{1}{3}*\dfrac{11}{5}\\\\=\dfrac{11}{15}[/tex]
[tex]\sf \text{Number of pages read more in 2 $\dfrac{1}{5}$ hours = $\dfrac{11}{15}-\dfrac{1}{3}$}[/tex]
[tex]\sf =\dfrac{11}{15}-\dfrac{1*5}{3*5}\\\\=\dfrac{11}{15}-\dfrac{5}{15}\\\\=\dfrac{6}{15}[/tex]
Answer:
see below
Step-by-step explanation:
Here is another way
1/3 book / hr * 2 1/5 hr =
1/3 * 11/5 = 11/15 read in 2 1/5 hr
1/3is the same as 5 /15
11/15 - 5 /15 = 6/15 = 2/5 more read in 2 1/5 hr that 1/3 hr
Which function is graphed?
Answer:
science type of food group : fibre
Laurie is trying to stay within 10 feet of her current diving depth of –30 feet (with regard to sea level) so that the light is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the minimum and maximum depths Laurie wants to stay between?
-30 - x = 10 and -30 - x = –10
-30 + x = 10 and -30 + x = –10
x + 10 = 30 and x + 10 = –30
x – 10 = 30 and x – 10 = –30
The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Diving is the art of going down to the depth of the ocean. Divers usually go deep down in the ocean to study the dynamics of ocean life.
The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30
Therefore the equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.
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please help
(a) Is it safe to place the plant box on a window ledge that can support a maximum weight of 2400 grams? Explain why or why not.
(b) Would the density of the soil change if the plant box was only half full? Explain.
Answers:
(a) The ledge can support the plant box. It is safe to put it there.
(b) No the density would not change.
=========================================================
Explanation for part (a)
We'll need the volume of the cube.
volume = side*side*side
volume = 13*13*13
volume = 2,197
Or you could do
volume = (side)^3
volume = (13)^3
volume = 2,197
The volume of the cube is 2,197 cubic cm. Multiply this with the density to determine its weight.
1.33*2197 = 2,922.01
The soil weighs 2,922.01 grams which is below the 2400 gram weight limit. Therefore, the ledge can support the planter.
------------------------------------
Explanation for part (b)
The weight would go down if you only put in half the soil, but the density would not change regardless of how much soil is in there. Why doesn't the density change? Because the density is the amount of stuff per unit volume. The density tells us how packed in a material is. We can scale the amount of material up or down, and retain the same density.
This is based off physics concepts which are bit beyond the scope of this math course, but different materials have different densities. It's common to use a reference table to look up densities of various materials. For instance, ice is less dense than water. This is why ice floats rather than sinks. As another example, gold is more dense than iron. So 1 cubic unit of gold will weigh more compared to 1 cubic unit of iron.
In a class of 20 students:
11 have a brother
9 have a sister
6 have neither
Fill in the Venn Diagram.
The Venn diagram is given below. Then the number of students who have brother and sister will be 6.
What are sets?A set is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
In a class of 20 students:
11 have a brother, 9 have a sister, and 6 have neither.
Then the Venn diagram will be
11 – a + a + 9 – a = 20 – 6
20 – a = 14
a = 6
The Venn diagram is given below.
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Please help!!!!
Write the equation of the circle in general form. Show all your work
Let's first gather all the information we have:
[tex]\rm\hookrightarrow Center: (-3, 2)\\\rm \hookrightarrow Radius: 5[/tex]
Let's put that into standard form [tex](x-h)^2+(y-k)^2 =r^2[/tex]
(h, k): center's coordinater: radius[tex]\rm \hookrightarrow Equation: (x+3)^2+(y-2)^2 = 5^2[/tex]
To put that equation into general form:
⇒ expand all the quadratics on one side and move the radius squared
to the same side as the quadratics
[tex](x+3)^2+(y-2)^2 = 25\\x^2+6x+9+y^2-4y+4=25\\x^2+y^2+6x-4y-12=0[/tex]
Answer: x² + y² + 6x - 4y - 12 = 0
Hope that helps!
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Contamination is a problem in the manufacture of optical storage disks. The number of particles of contamination that occur on an optical disk has a Poisson distribution, and the average number of particles per square centimeter of media surface is 0.1. The area of a disk under study is 100 cm2. Find the probability more than 12 particles occur in the area of a disk under study.
The probability that more than 12 particles occur in the area of a disk under the study is 0.20844.
The number of particles follows a Poisson Distribution.
A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .
In the question, x = 12.
λ = 100*0.1 = 10.
To find : P(X > 12)
P(X > 12) = 1 - P(X ≤ 12) = 1 - poissoncdf(10,12)
As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).
Therefore, P(X > 12) = 1 - 0.79156 = 0.20844.
Therefore, the probability that more than 12 particles occur in the area of a disk under the study is 0.20844.
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