HELPPPPP!!!!
An investment in a savings account grows to three times the initial value after t years.
If the rate of interest is 5%, compounded continuously, t = years.
Answers
Answer:
t = 21.97 years
Step-by-step explanation:
The formula for the continuous compounding if given by:
A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
It is given that p = $x, r = 5%, and A = $3x. In this part, t is unknown. Therefore: 3x = x*e^(0.05t). This implies 3 = e^(0.05t). Taking natural logarithm on both sides yields ln(3) = ln(e^(0.05t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(3) = 0.05t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(3)/0.05. This means that t = 21.97 years (rounded to the nearest 2 decimal places)!!!
Answer:
t = 22 years
Step-by-step explanation:
* Lets explain the compound continuous interest
- Compound continuous interest can be calculated using the formula:
A = P e^rt
# A = the future value of the investment, including interest
# P = the principal investment amount (the initial amount)
# r = the interest rate
# t = the time the money is invested for
- The formula gives you the future value of an investment,
which is compound continuous interest plus the
principal.
* Now lets solve the problem
∵ The initial investment amount is P
∵ The future amount after t years is three times the initial value
∴ A = 3P
∵ The rate of interest is 5%
∴ r = 5/100 = 0.05
- Lets use the rule above to find t
∵ A = P e^rt
∴ 3P = P e^(0.05t)
- Divide both sides by P
∴ 3 = e^(0.05t)
- Insert ㏑ for both sides
∴ ㏑(3) = ㏑(e^0.05t)
- Remember ㏑(e^n) = n ㏑(e) and ㏑(e) = 1, then ㏑(e^n) = n
∴ ㏑(3) = 0.05t
- Divide both sides by 0.05
∴ t = ㏑(3)/0.05 = 21.97 ≅ 22
* t = 22 years
Related Questions
Geometry:
The vertices of triangle ABC are A(0, 0), B(8, 1), and C(5, 5). Find the coordinates of the image of triangle ABC after a rotation of 90 degrees counterclockwise about the origin, a reflection over the x-axis, and a translation using the rule (x, y) → (x + 6, y - 1).
Answers
Answer:
Step-by-step explanation:
The transformations you want are ...
90° CCW: (x, y) ⇒ (-y, x)reflection over x-axis: (x, y) ⇒ (x, -y)translation by your rule: (x, y) ⇒ (x+6, y-1)Taken together, these make the transformation ...
(x, y) ⇒ (-y+6, -x-1)
So, your points become ...
A(0, 0) ⇒ A'(6, -1)
B(8, 1) ⇒ B'(5, -9)
C(5, 5) ⇒ C'(1, -6)
___
The attachment shows the original triangle in red and the progression to the final triangle in blue.
Find the volume and surface area of the composite figure. Give four answer in terms of π.
Answers
Answer:
V = 99π in³; S = 81π in²
Step-by-step explanation:
Volume is that of a hemisphere of radius 3 in together with that of a cylinder of radius 3 in and height 9 in.
V = (2/3)πr³ +πr²h = (πr²)(2/3r +h)
= 9π(2 +9) = 99π . . . . in³
__
The area is that of a hemisphere, the side of the cylinder, and the circular bottom of the cylinder.
S = 2πr² +2πrh +πr² = πr(2r +2h +r)
S = 3π(6+18 +3) = 81π . . . . in²
Finley's mother bought soda for her slumber party that has 10 people. Her mother bought 6 liters of soda. How many milliliters of soda can each child have?
Answers
Answer:
Step-by-step explanation:
5/3lit
Answer:young boy
Step-by-step explanation:two two
Which graph shows an even function?
Answers
Answer:
A.Step-by-step explanation:
The graph of even function is symmetrical about the y-axis.
The graph of odd function is symmetrical about the origin.
A. even
B. odd
C. odd
D. neither
(look at the picture)
Answer:
I would be A
Step-by-step explanation:
It has symmetry across the y axis
You bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow you to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on?
Answers
Answer:
1/4
23in * 19 in.
Step-by-step explanation:
The scale factor is 1/4 and the channel size is 92*1/4 * 76 * 1/4
= 23 in * 19 in screen.
Answer:
Scale factor = 1/2, New screen 46 in by 38 in.
Step-by-step explanation:
The dimensions of screen is 92 in. by 76 in.
It has a feature that splits the screen to allow you to watch 4 channels at once as shown in the below figure.
All four parts are equal.
Let the dimensions of new screen be x in. by y in.
[tex]2x=92[/tex] and [tex]2y=76[/tex]
Divide both sides by 2.
[tex]x=46[/tex] and [tex]y=38[/tex]
Scale factor is
[tex]\text{Scale factor}=\frac{\text{New dimension}}{\text{Corresponding original dimension}}[/tex]
[tex]\text{Scale factor}=\frac{46}{92}[/tex]
[tex]\text{Scale factor}=\frac{1}{2}[/tex]
Therefore, the scale factor is 1/2.
PLEASE HELP MEOWT!!!
Rewrite sin^(4)xtan^(2)x in terms of the first power of cosine.
Answers
Step-by-step explanation:
[tex] { \sin(x) }^{4} { \tan(x) }^{2} [/tex]
[tex] { \sin(x) }^{4} \frac{ { \sin(x) }^{2} }{ { \cos(x) }^{2} } [/tex]
[tex] \frac{ ({ {1 - \cos(x) }^{2} })^{3} }{ { \cos(x) }^{2} } [/tex]
hopefully this helps, I'm rusty with my trig identities
Answer:
sin⁴(x)tan²(x) = (10 -15cos(2x) +6cos(4x) -cos(6x))/(16(1 +cos(2x))
Step-by-step explanation:
The relevant identities are ...
[tex]\sin^4{x}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\\\\\tan^2{x}=\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\\cos{(a)}\cos{(b)}=\dfrac{\cos{(a+b)}+\cos{(a-b)}}{2}[/tex]
Then your product is ...
[tex]\sin^4{(x)}\tan^2{(x)}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\cdot\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\=\dfrac{3-4\cos{(2x)}+\cos{(4x)}-3\cos{(2x)}+4\cos^2{(2x)}-\cos{(4x)}\cos{(2x)}}{8(1+\cos{(2x)})}[/tex]
Collecting terms and using the identity for the product of cosines, we get ...
[tex]=\dfrac{3-7\cos{(2x)}+\cos{(4x)}+4\dfrac{1+\cos{(4x)}}{2}-\dfrac{\cos{(6x)}+\cos{(2x)}}{2}}{8(1+\cos{(2x)})}\\\\=\dfrac{10-15\cos{(2x)}+6\cos{(4x)}-\cos{(6x)}}{16(1+\cos{(2x)})}[/tex]
MAJOORRRR HELPPPP!!!
A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
It takes hours for the number of bacteria to increase to 300.
Answers
It takes 24 hours for the number of bacteria to increase to 300.
We have given that,
A scientist running an experiment starts with 100 bacteria cells.
These bacteria double their population every 15 hours.
Find how long it takes for the bacteria cells to increase to 300.
Use the formula, where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
[tex]P_0=100[/tex]
[tex]d=15[/tex]
What is the formula?[tex]P_t=P_02^{\frac{t}{d} }[/tex]
[tex]Pt=300=100\times2^{\frac{t}{15} }[/tex]
[tex]3=2^{\frac{t}{15}}[/tex]
[tex]\frac{t}{15} =1.6[/tex]
t=24
It takes 24 hours for the number of bacteria to increase to 300.
To learn more about the population increase visit:
https://brainly.com/question/11608113
#SPJ2
What is the square footage for this property described by the metes-and-bounds method? Beginning at the point of the southerly side of Smith Street, 200 feet easterly from the corner formed by the intersection of the southerly side of Smith Street and the easterly side of Johnson Street; then east 200 feet; then south 100 feet; then west 200 feet; then north 100 feet to the POB.
A. 20,000 square feetB. 10,000 square feetC. 5,000 square feetD. 15,000 square feet
Answers
Answer:
A. 20,000 square feet
Step-by-step explanation:
The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:
area = (200 ft)(100 ft) = 20,000 ft²
The correct option is option A.
Area of a rectangle:The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.
The formula to finding the area of the rectangle is,
[tex]A=l\times b[/tex]
It is given that,
Length=100 ft
Breadth=200 ft
[tex]A=l\times b[/tex]
Now, substituting the given values into the above formula we get,
[tex]A=200 \times 100\\A=20000[/tex]
The required area is 20,000 square feet.
Learn more about the topic area of the rectangle:
https://brainly.com/question/11202023
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. Her coach used her statistics from last season to design a simulation using a random number generator to predict how many points she would receive in her first race this season.
What is Sandra’s expected value of points awarded for a race?
Integer Value Points Awarded Frequency
1-8 3 20
9-15 2 12
16-9 1 6
20 0 2
Answers
Answer:
2.25
Step-by-step explanation:
The total frequency is:
20 + 12 + 6 + 2 = 40
Calculate the probability of each score:
P(X=3) = 20/40 = 0.50
P(X=2) = 12/40 = 0.30
P(X=1) = 6/40 = 0.15
P(X=0) = 2/40 = 0.05
So the expected value is:
E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)
E = 2.25
Natasha places an online order for plate holders to display her antique plates. She chooses a specific site because it has a promotional offer of 15% off on all purchases. She orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each. There is no sales tax on her purchase, but she must pay a flat rate of $5.35 for shipping and handling. What is the total of Natasha?s online purchase?
Answers
Answer:
Total online purchase is $26.473 .
Step-by-step explanation:
As given
Natasha places an online order for plate holders to display her antique plates.
Natasha orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each.
Thus
Total purchase of Natasha = Number of large holders × Cost of each large holder + Number of medium holders × Cost of each medium holder + Number of small holders × Cost of each small holder .
Put all the values in the above
Total purchase of Natasha = 3 × $4.95+ 2 × $3.25 + 2 × $1.75
= $14.85 + $6.5 + $3.5
= $ 24.85
As given
Site has a promotional offer of 15% off on all purchases.
15% is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Discount amount = 0.15 × Total purchase of Natasha .
= 0.15 × $24.85
= $ 3.7275
Thus
Total purchase of Natasha after discount = Total purchase of Natasha - Discount amount .
= $24.85 - $3.7275
= $ 21.1225
As given
Natasha must pay a flat rate of $5.35 for shipping and handling.
Thus
Total online purchase of Natasha = Total purchase of Natasha after discount + Flat rate for shipping and handling .
Total online purchase of Natasha = $21.1225 + $5.35
= $ 26.4725
= $26.473 (Approx)
Therefore the total online purchase is $26.473 .
Answer:
the order Natasha places is as follows;
3 large holders - $4.95 each - 4.95*3 = 14.85
2 medium holders - $3.25 each - 3.25*2 = 6.5
2 small holders - $1.75 each - 1.75*2 = 3.5
Total value for purchases is - 14.85 + 6.5 + 3.5 = 24.85
she gets 15% for all purchases therefore she has to pay only 85% of the purchase value
$24.85 * 85% = $21.1225
She has to pay an additional $5.35 for shipping and handling
therefore the total amount she has to pay is = 21.1225 + 5.35
total amount = 26.4725 this rounded off to second decimal place,
correct answer
C - $26.47
What is the solution set of y = x2 + 2x + 7 and y = x + 7? A. {(0, 7), (-1, 6)} B. {(0, 7), (-7, 0)} C. {(0, 7), (1, 8)} D. {(-2, 0), (4, 0)}
Answers
Answer:
A.
Step-by-step explanation:
If
[tex]y=x^2+2x+7[/tex] AND
y = x + 7, then by the transitive property of equality:
[tex]x^2+2x+7=x+7[/tex]
We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:
[tex]x^2+x=0[/tex]
We can factor out the common x to get:
x(x + 1) = 0
which tells us by the Zero Product Property that either
x = 0 and/or x + 1 = 0 and x = -1
We are expecting 2 solutions for x since this is a second degree polynomial. We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y
y = 0 + 7 so
y = 7 and the coordinate is (0, 7)
y = -1 + 7 so
y = 6 and the coordinate is (-1, 6)
A person came to work at 8:30 AM, went out at 11:45 AM, had lunch, came in at 12:30 PM, and left work at 5:15 PM. The total number of hours worked by this person was
Answers
Final answer:
The total number of hours worked by the person is calculated by adding the working times from two segments of the day. The morning session contributes 3 hours and 15 minutes, and the afternoon session adds 4 hours and 45 minutes. The combined total working hours are 8 hours.
Explanation:
To calculate the total number of hours worked by the person, we need to break down their workday into segments and sum up the time they spent working.
Morning session: From 8:30 AM to 11:45 AM
Afternoon session: From 12:30 PM to 5:15 PM
Calculating each session separately, we get:
Morning session: 11:45 AM - 8:30 AM = 3 hours and 15 minutes
Afternoon session: 5:15 PM - 12:30 PM = 4 hours and 45 minutes
Adding both sessions together:
3 hours and 15 minutes + 4 hours and 45 minutes = 8 hours total
Final Calculation:
3 hours 15 minutes + 4 hours 45 minutes = 7 hours 60 minutes = 8 hours
Therefore, the total number of hours worked by this person was 8 hours.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
-4x 3 y 2(7xy 4)
Answers
Answer:-28x^4y^2(-4x^3y^6)
Step-by-step explanation: Distribute and add exponents, put in parentheses to make it easier to understand but it's not necessary for the final answer.
Answer:
[tex]-28x^4y^6[/tex]
Step-by-step explanation:
The given expression is
[tex]-4x^3y^2(7xy^4)[/tex]
We need to place the indicated product in the proper location on the grid.
The given expression can be rewritten as
[tex](-4\times 7)(x^3x)(y^2y^4)[/tex]
[tex]-28(x^3x)(y^2y^4)[/tex]
Using the product property of exponent, we get
[tex]-28\times x^{3+1}\times y^{2+4}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]-28\times x^{4}\times y^{6}[/tex]
[tex]-28x^{4}y^{6}[/tex]
Therefore the answer of given product is [tex]-28x^{4}y^{6}[/tex].
What is the value of x in the following equation: x - 2 = 9?
(please and thank you!!!)
Answers
AnswEr:
Add the two, to both sides. -2+2=0
So, the equation would like like this
x -2= 9
+2 +2
Then solve, the 2’s cancel out leaving you with x by itself. Finishing the equation to look like this-> x=11
In this case, you would add the 2 on both sides
making the equation >> x - 0 = 11
you’d drop the zero because it has no value and you get your answer:
x = 11
Select all the exponential functions that have a percentage rate of change of 19%
A) f(x)=3182(0.9)^2x
B) f(x)=1.74(0.81)^3x
C) f(x)=0.2(0.38)^x/2
D) f(x)= 156(1-0.19)^x
Please Help
Answers
Answer:
B) f(x)=1.74(0.81)^3x
and
D) f(x)=156(1-0.19)^x
Step-by-step explanation:
The percentage will always be where the b is, or inside the parentheses. You just have to make sure that, when not greater than 1, you must find out WHAT SUBTRACTS FROM 1 TO GET THAT RESULT. So ask yourself, what decimal number subtracts from 1 to get 0.81?
0.81 is the equivalent to (1-0.19) because (1-0.19) = 0.81.
0.19 is 19%, which is what we're looking for!
The exponential function with a percentage rate of change of 19% is option D) f(x)= 156(1-0.19)ˣ, because it reflects a 19% decrease with the base 0.81 (which is equal to 1 - 0.19).
Exponential functions have a percentage rate of change of 19%, we need to identify the function where the base of the exponent reflects this rate of change. The percentage rate of change can be represented as a decimal where a 19% increase is 1.19 and a 19% decrease is 0.81 (since 1 - 0.19 = 0.81).
Now, let's analyze the given functions:
A) f(x) = 3182(0.9)²ˣ does not represent a 19% rate of change.
B) f(x) = 1.74(0.81)³ˣ does not represent a 19% rate of change as it involves 0.81 to the power of 3x, not x.
C) f(x) = 0.2(0.38)ˣ/² does not represent a 19% rate of change.
D) f(x) = 156(1-0.19)ˣ does represent a 19% rate of change because the base is 0.81 which is equivalent to 1 - 0.19.
Therefore, the correct answer is option D).
What is the correct value of b?
Answers
Answer:
b = 6Step-by-step explanation:
[tex]cosecant=\dfrac{hypotenuse}{opposite}\\\\\text{We have}\ opposite=3b,\ \text{and}\ hypotenuse=22.5,\ \text{and}\ \csc x=\dfrac{5}{4}.\\\\\text{Substitute:}\\\\\dfrac{5}{4}=\dfrac{22.5}{3b}\qquad\text{cross multiply}\\\\(5)(3b)=(4)(22.5)\\\\15b=90\qquad\text{divide both sides by 15}\\\\b=6[/tex]
Factor a number, variable, or expression out of the trinomial shown below:
6x2 – 12x + 9
A. 2(3x2 – 9x + 6)
B. 2(3x2 – 4x)
C. 3(2x2 – 4x + 3)
D. 3(2x2 – 4x + 9)
Answers
Answer:
C. 3(2x2 – 4x + 3)
Step-by-step explanation:
6x^2 – 12x + 9
We can factor out a 3
3(2x^2 -4x+3)
Answer:
c. 3(2x^2-4x+3)
Step-by-step explanation:
The numbers 6, 12, and 9 are all multiples of 3. Divide everything by three, move it to the outside. There are no more common factors between all 3 terms so the trinomial is completely factored. Hope this helped, if not then I apologize.
CAN SOMEONE HELP ME WITH THIS MATH QUESTION ITS ABOUT TRANSLATION
Answers
Answer:
(- 4, 1 )
Step-by-step explanation:
A translation (x + 1), y - 3 ) means add 1 to the original x- coordinate and subtract 3 from the original y- coordinate.
B = (- 5, 4 ), thus
B' = (- 5 + 1, 4 - 3 ) = (- 4, 1 )
[tex]B=(-5,4)\\\\B'=(-5+1,4-3)\\B'=(-4,1)[/tex]
What are the discontinuity and zero of the function f(x) = x^2+5x+4/x+4
Answers
Answer:
The zeros of our function f is at x=-1.
The discontinuity is at x=-4.
These are correct if the function is [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] .
Please let know if I did not interpret your function correctly.
Step-by-step explanation:
I imagine you mean [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] but please correct me if I'm wrong.
The zero's of a rational expression occur from it's numerator.
That is, in a fraction, the only thing that makes that fraction 0 is it's numerator.
So we need to solve [tex]x^2+5x+4=0[/tex] for x.
The cool thing is this one is not bad to factor since the coefficient of x^2 is 1. When the coefficient of x^2 is 1 and you have a quadratic, all you have to do is ask yourself what multiplies to be c and adds to be b.
[tex]x^2+5x+4[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=5,c=4[/tex].
So we are looking for two numbers that multiply to be c and add to be b.
We are looking for two numbers that multiply to be 4 and add to be 5.
Those numbers are 1 and 4 since 1(4)=4 and 1+4=5.
The factored form of [tex]x^2+5x+4[/tex] is [tex](x+1)(x+4)[/tex].
So [tex]x^2+5x+4=0[/tex] becomes [tex](x+1)(x+4)=0[/tex].
If you have a product equals 0 then at least one of the factors is 0.
So we need to solve x+1=0 and x+4=0.
x+1=0 when x=-1 (subtracted 1 on both sides to get this).
x+4=0 when x=-4 (subtracted 4 on both sides to get this).
The zeros of our function f is at x=-1 and x=-4.
Now to find where it is discontinuous. We have to think 'oh this is a fraction and I can't divide by 0 but when is my denominator 0'. If the value for the variable is not obvious to you when the denominator is 0, just solve x+4=0.
x+4=0 when x=-4 (subtracted 4 on both sides).
So we have a contradiction at one of the zeros so x=-4 can't be a zero.
The discontinuity is at x=-4.
Answer:
This function is discontinuous at x = 4, and has a zero at x = -1.
Step-by-step explanation:
If x = -4, the denominator will be zero and thus the function will be undefined. Thus, the discontinuity is at x = -4.
To find the zero(s): Set the numerator = to 0, obtaining
x^2+5x+4 = 0. Factoring this, we get (x + 4)(x + 1) = 0. Thus, we have a zero at x = -1.
Notice that f(x) can be rewritten as
x^2 + 5x + 4 (x+4)(x+1)
f(x) = -------------------- = ---------------- = x + 1 for all x other than x = -4.
x + 4 (x+4)
This function is discontinuous at x = 4, and has a zero at x = -1.
Please help me with this problem
Answers
Answer:
g(x) = -5x
Step-by-step explanation:
If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right. That point will be reflected through the x-axis to land at (1, -5). That means that the equation of the new line would be
g(x) = -5x
A reflection across the x -axis would have the opposite value of the output.
If the value is a positive value, the mirrored value would be a negative value.
The function of g(x) would be g(x) = -5x
BRAINLIEST HURRY!
the griffins bought a netbook for$250.if the small computer depreciates at a rate of 25%a year,what will it be worth afer 3 years
Answers
Answer:
[tex]\$105.47[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$250\\r=25\%=25/100=0.25\\x=3\ years[/tex]
substitute
[tex]V=250(1-0.25)^{3}[/tex]
[tex]V=250(0.75)^{3}[/tex]
[tex]V=\$105.47[/tex]
Answer and Step-by-step explanation:
After three years the worth of it will be [tex]$105.47[/tex]
We know that each year, it's worth 75% of what it was, giving us :
[tex]=0.75*W[/tex] (Note that "W" means "Worth")
Now we calculate it in three years time so,
The first year is :[tex]250*0.75 = $187.50[/tex]
The second year is :[tex]187.5*0.75 = $140.625[/tex]
The third year is :[tex]140.625*0.75 = $105.47[/tex]
Now, we have our answer :
After three years time the worth of it is [tex]$105.47[/tex]
An elevator starts at the main floor and goes up 8 floors. It then goes back fown 5 floors. What integer represents elevator final position with respect to the main floor?
Answers
Answer:
integer 3 represents elevator final position with respect to the main floor.
Step-by-step explanation:
Given : An elevator starts at the main floor and goes up 8 floors. It then goes back down 5 floors.
To find : What integer represents elevator final position with respect to the main floor.
Solution : We have given
Elevator starts at the main floor and goes up floors = + 8 ( for up).
Then goes back down floor = - 5 ( - sign for down).
Final position : 8 - 5 = 3 .
It will reach at 3 floor from the main floor .
Therefore, integer 3 represents elevator final position with respect to the main floor.
A camera is placed in front of a hyperbolic mirror. The equation of the hyperbola that models the mirror is , where x and y are in inches. The camera is pointed toward the vertex of the hyperbolic mirror and is positioned such that the lens is at the nearest focus to that vertex.
Answers
Answer:
The lens is 1 inch from the mirror
Step-by-step explanation:
* Lets revise the equation of the hyperbola with center (0 , 0) and
transverse axis parallel to the y-axis is y²/a² - x²/b² = 1
- The coordinates of the vertices are (0 , ± a)
- The coordinates of the co-vertices are (± b , 0)
- The coordinates of the foci are (0 , ± c) where c² = a² + b²
* Lets solve the problem
∵ The equation of the hyperbola is y²/16 - x²/9 = 1
∵ The form of the equation is y²/a² - x²/b² = 1
∴ a² = 16
∴ a = √16 = 4
∵ The coordinates of the vertices are (0 , ± a)
∴ The coordinates of the vertices are (0 , 4) , (0 , -4)
∴ b² = 9
∴ b = √9 = 3
∵ c² = a² + b²
∴ c² = 16 + 9 = 25
∴ c = √25 = 5
∵ The coordinates of the foci are (0 , ± c)
∴ The coordinates of the foci are (0 , 5) , (0 , -5)
∵ The camera is pointed towards the vertex of the hyperbolic mirror
which is (0 , 4) and is positioned such that the lens is at the nearest
focus to that vertex which is (0 , 5)
∴ The distance between the lens and the mirror equal the distance
between the vertex and the focus
∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)
∴ The distance = 5 - 4 = 1 inch
* The lens is 1 inch from the mirror
In the figure below, if angle ZYX measures 23 degrees, then arc XY measures 45 degrees.
Answers
Answer:
FALSE
Step-by-step explanation:
Assuming ZY is a tangent, the measure of the arc will be twice the measure of the angle. If the angle ZYX is 23°, the measure of arc YX will be 46°.
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer :
22.5 is the answer
MARK ME AS BRANILIST
Answer: 90
Step-by-step explanation:
Basically you reflect twice and then rotate it
n a bag there are two $20 bills, one $10 bill, four $5 bills, and three $1 bills. If Frank picks one bill from the bag, the expected value of the bill he chooses is ____$. If one more $20 bill and one more $10 bill are added to the bag, the expected value will change to _____$.
Answers
Answer:
Initial expected value = 7.3 $
If one more $20 bill and one more $10 bill are added to the bag expected value = 8.57 $
Step-by-step explanation:
a) Total number of bills = 2 + 1 + 4 + 3 = 10
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{2}{10}=0.2\\\\\texttt{Probability of picking 10 dollar bill}=\frac{1}{10}=0.1\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{10}=0.4\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{10}=0.3[/tex]
Expected value = 20 x 0.2 + 10 x 0.1 + 5 x 0.4 + 1 x 0.3 = 7.3$
b)If one more $20 bill and one more $10 bill are added to the bag
Total number of bills = 3 + 2+ 4 + 3 = 12
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{3}{12}=0.25\\\\\texttt{Probability of picking 10 dollar bill}=\frac{2}{12}=0.167\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{12}=0.333\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{12}=0.25[/tex]
Expected value = 20 x 0.25 + 10 x 0.167 + 5 x 0.333 + 1 x 0.25 = 8.57$
Answer:
$7.30 for the first one and $8.58 for the second one
Step-by-step explanation:
ANSWER FOR PLATO
4\sqrt(2)+10
Is this rational or not?
Answers
Answer:
not rational
Step-by-step explanation:
√2 is irrational. Any arithmetic operation (addition, subtraction, multiplication, division) performed on that number and any rational number will result in an irrational number (except for multiplication by 0).
Answer:
Step-by-step explanation:
Because of that sqrt, this expression is irrational. A rational expression is one that can be expressed as the ratio of two integers.
PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer:
Rx-axis (P) is (-4 , 1)
Step-by-step explanation:
* Lets revise the reflection
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Lets solve the problem
∵ The point P is (-4 , -1)
∵ Rx-axis (P) means reflect point P across the x-axis
∵ The reflection of a point (x , y) across the x-axis is (x , -y)
- That means we will change the sign of the y-coordinate of point P
∵ P = (-4 , -1)
∴ The y-coordinate of point P is -1 will change to 1
∴ The image of point P after reflection is (-4 , 1)
* Rx-axis (P) is (-4 , 1)
Answer:
P is -4 , 1
Step-by-step explanation:
The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side
Answers
Answer:
(7.5-2.1) /2
If the shortest side measures 2.1 m.
7.5-2.1 =5.4. Then divide by 2 each side is 2.7m
Answer:
The equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
Step-by-step explanation:
Perimeter of the isosceles triangle = 7.5 m
Length of the shortest side = 2.1 m
Let the length of each of the other sides of the triangle = x meter
Then the equation for the perimeter of the triangle becomes:
Sum of 3 sides f the triangle = 7.5 m
=> 2*x + 2.1 = 7.5
=> 2*x = 7.5 - 2.1 = 5.4
=> x = 5.4/2 = 2.7 m
So the relevant equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
Solve the system of equations.
6d + 3f = 12
2d = 8 - f
a. d= 3, f = 2
b. d = 3, f = 14
c. no solution
d. infinite solutions
Answers
Answer:
c. no solution
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Multiply the second equation by 3
3*2d = 3(8-f)
6d = 24-3f
Substitute into the first equation for 6d
(24-3f) +3f = 12
Combine like terms
24 =12
This is never true, so there are no solutions
Answer:
c. No Solution.
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Rearranging the second equation:
2d + f = 8 Multiply this equation by 3:
6d + 3f = 24
Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.