Answer:
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Step-by-step explanation:
Given
[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]
Required
The general term
The given sequence is geometric.
So first, we calculate the common ratio (r)
[tex]r = T_2/T_1[/tex]
So, we have:
[tex]r = 1/4 \div 1[/tex]
[tex]r = 1/4[/tex]
The function is then calculated using:
[tex]T_n =T_1 * r^{n-1}[/tex]
This gives
[tex]T_n =1 * 1/4^{n-1}[/tex]
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Mark draws one card from a standard deck of 52. He receives $ 0.30 for a heart, $ 0.55 for a queen and $ 0.90 for the queen of hearts. How much should he pay for one draw
Answer
$0.1346
Explanation:
Find probability of each card and the value of each card and then add them together.
Probability of getting a heart = 13/52
Price of one heart =$0.30
Pay for one heart = 13/52×0.30=$0.075
Probability of getting a queen =4/52
Price of one queen =$0.55
Pay for one queen =4/52×$0.55=$0.0423
Probability of getting a queen of hearts =1/52
Price of one queen =$0.90
Pay for one queen =1/52×$0.90=$0.0173
Therefore the pay for one draw= $0.075+$0.0423+$0.0173=$0.1346
Floataway Tours has $420,000 that can be use to purchase new rental boats for hire during the summer. The boats can be purchased from two different manufacturers. Floataway Tours would like to purchase at least 50 boats and would like to purchase the same number from Sleekboat as from Racer to maintain goodwill. At the same time,Floataway Tours wishes to have a total seating capacity of at least 200.
Required:
Formulate this problem as a linear program.
Answer and explanation:
A linear problem is an equation based on known and unknown variables that follow a linear path, usually without exponents and look like this:
y=mx+b. To formulate the linear constraints of the problem above, we look at the unknown variables and known variables and define and equation using this.
From the problem, assume x and y are the prices of the different boat brands:
50x+50y=420000
Assume a and b are number of x brand boats and y brand boats supplied thus:
a+b>=200
in a class of 50 student,35 are boys.what is the ratio of girls to boys in the class?
Answer:
15:35
Step-by-step explanation:
50-35=Girls
50-35=15
Write two pairs of integers (a, b) such that a / b = -4.
One such pair is (8, -2) because 8/ -2 = (-4).
Answer: a= 16 a=8
b=4 b=2
because, 2 when multiplied by 4 gives 8
4 when multiplied gives 16
verify that whether -2 and 3 are zeroes of the polynomial x^2-x=6
PLEASE HELP
Answer:
Both give remainder 0 for the polynomial
Step-by-step explanation:
p(-2) = (-2)² - (-2) - 6
= 6 - 6 = 0
p(3) = (3)² - 3 - 6
= 9 - 9 = 0
Sarah invests £2000 for 2 years in a saving account. She earns 3% per annum in compound interest.
How much did Sarah have in her saving account after 2 years?
£
Use the formula:
A=P(1+r100)n
Where;
A = the amount of money accumulated after n years, including interest
P = the principal sum (the initial amount borrowed or invested)
r = the rate of interest (percentage)
n = the number of years the amount is borrowed or invested
Answer:
£2120.27
Step-by-step explanation:
A = P (1 + r100)
A = 2000 (1+ 0.03/365)^365(2)
A = 2000 ( 1.00008)^730
A = 2000 (1.060)
A = £2120.27
Acellus
First, find the surface area of the yellow prism.
3 cm 3 cm
: ?
4 cm
3 cm
front: [?]
back: [ ]
right: [ ]
left: [ ]
3cm
3cm
4cm
top:[]
5 cm
TOTAL: [ ]
Note: The bottom will not be
included because this is whern
5 cm
Answer:
57 cm²
Step-by-step explanation:
Surface area of the yellow prism = front + back + right + left + top
✔️Area of the front = L * W
L = 4 cm
W = 3 cm
Area of the front = 4*3 = 12 cm²
✔️Area of the back = L * W
L = 4 cm
W = 3 cm
Area of the back = 4*3 = 12 cm²
✔️Area of the right face = L * W
L = 4 cm
W = 3 cm
Area of the right face = 4*3 = 12 cm²
✔️Area of the left face = L * W
L = 4 cm
W = 3 cm
Area of the left face = 4*3 = 12 cm²
✔️Area of the top = L * W
L = 3 cm
W = 3 cm
Area of the top = 3*3 = 9 cm²
✅Total = 12 + 12 + 12 + 12 + 9 = 57 cm²
Using the Fenske equation, calculate the number of theoretical plates for a fractional distillation set up used to separate Ethyl acetate (the more volatile component) from hexane (less volatile component) in a mixture with the following experimental data:
n=log(X/Xb) -log(Y a/Yb)/ log α Fenske Equation
Experimental data: l
The following are the data optained from injection of a 1-microliter sample of the equimolar stock solution used in the distillation experiment into a GČ. The percent of the area under the appropriate peak is idicated.
a = 1.6
GC results of the stock mixture used in the experiment
Component Rt (retention time) Percent Area
Ethyl acetate 1.09 53 82
Hexane 1.58 47 18
GC results of a 1-microliter sample after 3 mL had been collected:
Component Rt (retention time) Percent Area
Ethyl acetate 1.09 82
Hexane 1.58 18
a. 3.9
b. 7.2
c. 7.0
d. 3.0
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 7 minutes and the standard deviation of the waiting time is 1 minute. Find the probability that a person will wait for more than 6 minutes. Round your answer to four decimal places.
Answer:
0.15866
Step-by-step explanation:
6-7/1
=-1
p(x>-1)=1-p(x<1)
=0.15866
Domain and range
O Function
O Not a function
Answer:
Radiation 1- Function
Radiation 2- Not a function
Radiation 3- function
Radiation 4- function
Answer:
1 - Function
2 - Not a function
3 - function
4 - function
Step-by-step explanation:
Make a substitution to express the integrand as a rational function and then evaluate the integral. int_(25)^(81) sqrt(x)/(x-1) dx
Let y = √x, so that y ² = x and 2y dy = dx. Then the integral becomes
[tex]\displaystyle \int_{25}^{81} \frac{\sqrt x}{x-1}\,\mathrm dx = \int_{\sqrt{25}}^{\sqrt{81}} \frac y{y^2-1}(2y\,\mathrm dy) = 2 \int_5^9 \frac{y^2}{y^2-1}\,\mathrm dy[/tex]
Now,
y ² / (y ² - 1) = 1 + 1 / (y ² - 1) = 1 + 1/2 (1/(y - 1) - 1/(y + 1))
so integrating gives us
[tex]\displaystyle 2\int_5^9\frac{y^2}{y^2-1}\,\mathrm dy= \int_5^9\left(2+\frac1{y-1}-\frac1{y+1}\right)\,\mathrm dy \\\\= (2y+\ln|y-1|-\ln|y+1|)\bigg|_5^9 \\\\= \boxed{8+\ln\left(\dfrac65\right)}[/tex]
Which expression is equivalent to -28xy + 35y?
o 7y(-4xy + 5y)
O 7x{-4x+ 5y)
o 7xl-4y+54)
O 7y(-4x+5)
Answer:
[tex]-28xy+35y[/tex]
[tex]GCF ~is~ 7y[/tex]
[tex]=7y(-4+5)[/tex]
The equivalent expression: [tex]7y(-4x+5)[/tex]
-------------------------
hope it helps...
have a great day!!
Given the function, calculate the following values...
f(0) = 56
f(2) = 42
f(-2) = 70
f(x+1) = 7|x-7|
f(x²+2) = 7|x²-6|
Answered by GAUTHMATH
helppppppppppppppppppppppppppppppppppppppp
Answer:
the total square footage = 194
1.88 x 194 = 364.72
Step-by-step explanation:
Area for triangle ends.
A = [tex]\frac{2.5 (8)}{2}[/tex] (Times two, because there are two ends.)
Base of prism = 8 x 10 = 80
Sides of prism = 2(10 x 4.7 ) = 94 (What's the 2? There's two of them)
Add all together : 10 + 10 + 80 + 94 = 194
1.88 x 194 = 364.72
An adult soccer league requires a ratio of at least 2 women per 7 men on the roster. If 14 men are on the roster, how many women are needed to maintain that ratio?
Answer:
Atleast 4 women
Step-by-step explanation:
Ratio of
Women to men = 2 : 7
Number of women needed to maintain the ratio if there are 14 men on the roster :
The minimum number of women required :
(2 : 7) * number of men in roster
(2 / 7) * 14
2 * 2 = 4 women
Atleast 4 women are required to main the ratio
3 coins are flipped.
Answer:
just keep writing down outcome on a sheet of paper then count total
Step-by-step explanation:
Find the standard normal area for each of the following (Round your answers to 4 decimal places.): Standard normal area a.P(1.26 < Z < 2.16) b.P(2.05 < Z < 3.05) c.P(-2.05 < Z < 2.05) d.P(Z > .55)
Answer:
The correct answer is:
(a) 0.0884
(b) 0.0190
(c) 0.9596
(d) 0.2921
Step-by-step explanation:
(a)
= [tex]P(1.26<Z<2.16)[/tex]
= [tex]P(Z<2.16)-P(Z<1.26)[/tex]
= [tex]0.9846-0.8962[/tex]
= [tex]0.0884[/tex]
(b)
= [tex]P(2.05<Z<3.05)[/tex]
= [tex]P(Z<3.05)-P(Z<2.05)[/tex]
= [tex]0.9989-0.9798[/tex]
= [tex]0.0190[/tex]
(c)
= [tex]P(-2.05<Z<2.05)[/tex]
= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]
= [tex]0.9798-0.0202[/tex]
= [tex]0.9596[/tex]
(d)
= [tex]P(Z>0.55)[/tex]
= [tex]1-P(Z<0.55)[/tex]
= [tex]1-0.7088[/tex]
= [tex]0.2912[/tex]
Change 84cm into millimetres
Answer:
840 mm
Step-by-step explanation:
multiply by 10
Answer:
840 millimetres
Step-by-step explanation:
To convert cm to mm, multiply the value in cm by 10
84cm x 10 = 840 mm
Hope this helps! <3
A ice cream shop sells 8 different flavors of ice cream with A choice of three different styles of calls how many different ice cream cones are possible if you select one ice cream flavor with one type of ice cream cone
Explanation:
There are 8 different flavors and 3 types of cones. This means there are 8*3 = 24 different combos possible.
Imagine a table with 8 rows and 3 columns. Each row is a different flavor and each column is a different cone type. The table formed has 24 inner cells to represent a different combination of flavor + cone type. So that's why we multiplied those values earlier.
Note: This only works if you're only able to select one type of flavor.
In 1980, the average cost of a pack of cigarettes was $0.88. In 2000, the average cost was $5.31 per pack.
What is the average rate of change of the cost of a pack of cigarettes? What is another name for the average rate of change?
Round your answer to the nearest cent.
Answer:
The average rate of change of the cost of a pack is 22 cents per year.
Another name for the average rate of change is slope.
Step-by-step explanation:
The average rate of change of the cost of a pack ([tex]r[/tex]), in monetary units per year, is equal to the change in the average cost of a pack ([tex]\Delta c[/tex]), in monetary units, divided by the change in time ([tex]\Delta t[/tex]), in years. Then, the average rate of change is:
[tex]r = \frac{\$\,5.31-\$\,0.88}{2000-1980}[/tex]
[tex]r = \$\,0.22\,\frac{1}{yr}[/tex]
The average rate of change of the cost of a pack is 22 cents per year.
Another name for the average rate of change is slope.
20 and 1/2 feet times 13 and 1/8 feet is what total
Answer:
269 and 1/16 feet total (or 269.0625 feet to be precise)
Step-by-step explanation:
20 and 1/2 = 20.5
13 and 1/8 = 13.125
20.5 * 13.125 = 269.0625 feet = 269 and 1/16 feet
find the value of...
Answer:
1
Step-by-step explanation:
tan(1)tan(2)....tan(89)=?
Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.
tan(89)=tan(90-1)=cot(1)
tan(88)=tan(90-2)=cot(2)
tan(87)=tan(90-3)=cot(3)
...
tan(46)=tan(90-44)=cot(44)
tan(45)=tan(90-45)=cot(45)
So we can replace the last half of the factors with cotangent of the angles in the first half.
The only one that doesn't get a partner is the exact middle factor which is tan(45).
So this is whar we have:
tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)
So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....
So the product equals tan(45) and tan(45)=1 using unit circle.
Jeremy bought 3 pairs of pants that cost
The same amount of money. He had a
$10 off coupon for the pants. Using the
coupon, Jeremy spent $35. Write an
equation that can be used to find the cost
of the pants before the coupon was
applied
(use p as your variable)
Help fasttt
Answer:
3p - 10 =35
Step-by-step explanation
You want to cancel out everything, besides the p, on the left side.
then add the ten to 35 to cancel it out
divide 3 by 45 to cancel it out
p equals 15
The answer is 15
Question 1
Points 3
Rese
A carpet is in the shape of a right triangle. The longer leg
measures 8 feet. The hypotenuse is 4 feet more than the
length of the shorter leg. How long is the shorter leg?
Reset
after
assess
Answer:
6 feetStep-by-step explanation:
Given right triangle with:
Legs s and 8, and hypotenuse s + 4Use Pythagorean and solve for s:
(s + 4)² = s² + 8²s² + 8s + 16 = s² + 648s = 64 - 168s = 48s = 6The quadrilateral KLMN is dilated with the center of dilation located at point M. Which statement is accurate?
1. The scale factor is 3, which means the length of the image of segment KL will be 1/3 times as long.
2. The scale factor is 1/3, which means the length of the image of segment KL will be 1/3 times as long.
3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.
4. The scale factor is 1/3, which means the length of the image of segment KL will be 3 times as long.
Answer:
3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated about the center of dilation located at O(a, b), the new point is at A'[k(x - a) + a, k(y - b) + b].
Quadrilateral KLMN has vertices at K(2, 1), L(-1, -5), M(6, -5) and N(6, 1). If it is dilated by 3, about the center M(6, -5), the new points are:
K' = (3(2 - 6) + 6, 3(1 - (-5)) + (-5)) = (-6, 13)
L' = (3(-1 - 6) + 6, 3(-5 - (-5)) + (-5)) = (-15, -5)
M' = (3(6 - 6) + 6, 3(-5 - (-5)) + (-5)) = (6, -5)
N' = (3(6 - 6) + 6, 3(1 - (-5)) + (-5)) = (6, 13)
Therefore the image of segment KL will be 3 times long.
if sine Theta is less than 0 and tan Theta is greater than 0 then
Answer:
Sine Theta is a negative number, Tan Theta is a greater number then zero.
Step-by-step explanation:
If Sine Theta is less then zero, she is a negative number. So 0 - y = -y.
So if Tan Theta is a greater number than zero, her number is not negative. So 0 + y = y
I hope this helped! I didn’t really understand the question though.
Determine the value of the missing letters in the sum of numbers
below:
ab1
+ ba
abb
49x
Answer:
a=2, b=3,x=6
Step-by-step explanation:
We are given that
We have to find the value of the missing letters in the sum of numbers.
From given sum
1+a+b=x ....(1)
b+b+b=9 .....(2)
a+a=4 ......(3)
From equation (2) we get
[tex]3b=9[/tex]
[tex]\implies b=3[/tex]
From equation (3) we get
[tex]2a=4[/tex]
[tex]a=4/2[/tex]
[tex]a=2[/tex]
Now, substitute the values in equation (1) we get
[tex]1+2+3=x[/tex]
[tex]x=6[/tex]
Therefore,
231+32+233=496
Please help me and answer quick please
Answer:
b
Step-by-step explanation:
the function has exactly one x-intercept
Please tell me the answer I have no idea how to do this
Answer:
60 degrees
Step-by-step explanation:
So we see there's a 90 degree angle and a 150 degree larger angle including it.
So to find out the part that the 150 degree large angle that's not a part of the 90 angle we would do: 150 - 90, and we get 60.
So the bottom right angle is 60 degrees.
Now since we have a straight line from the left to right horizontally, we know that one side has to equal 180 degrees. On the side which the x is on, we already have 2 angles: 90 and 30. 90 + 30 = 120.
Since a straight line equals 180, x + 120 has to equal 180.
So now we do simple algebra.
x + 120 = 180
x = 180 - 120
x = 60
So x is equal to 60 degrees.
Adam borrowed $5,600 from the bank. The bank charges 4.2% simple interest each year.
Which equation represents the amount of money in dollars, x, Adam will owe in one year, if no payments are made?
x=5,600+5,600(42)(12)
x=5,600+5,600(0.042)(1)
x=5,600+5,600(42)(1)
x=5,600+5,600(0.042)(12)
Answer:
[tex]x = 5600 + 5600 * 0.042 * 1[/tex]
Step-by-step explanation:
Given
[tex]P = 5600[/tex] -- Principal
[tex]R = 4.2\%[/tex] -- Rate
[tex]T = 1[/tex] -- Time
Required
The amount (x) to be paid
This is calculated as:
[tex]x = P + I[/tex]
Where:
[tex]I = PRT[/tex]
So, we have:
[tex]x = 5600 + 5600 * 4.2\% * 1[/tex]
Express percentage as decimal
[tex]x = 5600 + 5600 * 0.042 * 1[/tex]
(c) is correct
