Answer:
3645
Step-by-step explanation:
f(1)=5
f(2)=3*5=15.
f(3)=45, basically it's a geometric sequence with formula an=5*(3)^(n-1). The 7th term is 5*(3)^6=3645
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answer:
width = 7, length = 11
Step-by-step explanation:
area = 77
length = 3w - 10
width = w
w(3w - 10) = 77
3w^2 - 10w - 77 = 0
(3w + 11)(w - 7) = 0
we rule out 3w + 11 = 0 because w would be negative
so we use w - 7 = 0
so the width = 7
length = 3w - 10
length = 21 - 10
length = 11
Decompose -6x/(x+2)(x+8) into partial fractions.
The partial fraction expansion takes the form
-6x/((x + 2) (x + 8)) = a/(x + 2) + b/(x + 8)
Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.
Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:
-6x = a (x + 8) + b (x + 2)
Expand the right side and collect terms by powers of x :
-6x = (a + b) x + (8a + 2b)
It follows that
a + b = -6 and 8a + 2b = 0
==> a = -2 and b = 8
So we end up with
-6x/((x + 2) (x + 8)) = -2/(x + 2) + 8/(x + 8)
A certain university has 25,000 registered students. To estimate the percentage who are living at home, a simple random sample of 400 students is drawn. It turns out that 317 of them are living at home. Now, 317 out of 400 is (about) 79%. Indicate whether each quantity is actual or estimated from the data. You'll get partial credit for
Answer:
Indication of Actual Quantity and Estimated Quantity
Actual Quantity:
Registered students in the university = 25,000
Sample of students = 400
Students living at home = 317
Estimated Quantity:
317 out of 400 students
79%
Step-by-step explanation:
An actual quantity does not require to be estimated. It is usually given in the question or scenario. For example, the number of registered students in the university is an actual quantity. The percentage of students who live at home from the simple random sample of 400 is an estimated quantity.
A tank contains 9,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
(a) How much salt is in the tank after t minutes?
(b) How much salt is in the tank after 20 minutes?
Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.
The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation
dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min
or, more succintly,
x' = -1/100 x
This equation is separable as
dx/x = -1/100 dt
Integrating both sides gives
∫ dx/x = -1/100 ∫ dt
ln|x| = -1/100 t + C
x = exp(-1/100 t + C )
x = C exp(-t/100)
(a) Using the initial condition x (0) = 18, we find
18 = C exp(0) ==> C = 18
so that
x(t) = 18 exp(-t/100)
(b) After 20 minutes, we have
x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74
so the tank contains approximately 14.74 kg of salt after this time.
Your true height is 70.2 inches. A laser device at a health clinic that gives measurements to thenearest hundredth reads your height as 71.05 inches. A tape measure gives reading to the nearest haftinches gives your height as 69.5 inches. State which measurement is more precise and which measurementis more accurate and explain why.
Answer:
Accuracy = Tape measurement.
Precision = Laser measurement
Step-by-step explanation:
Given that :
True height, = 70.2 inches
Laser measured height = 71.05 (nearest hundredth)
Tape measured height = 69.5 - nearest half inch.
Accuracy simply means how close a measured value is to the true value of the measurement. ;
True height - tape measurement
70.2 - 69.5 = 0.7
True measurement - laser measurement :
|70.2 - 71.05| = 0.85
Fron the difference in the values, the measurement which is closer to the true height is the tape measurement.
However, in terms of detail in the measured value, the laser measure value is expressed to the nearest hundredth, hence giving it more precision over the tape measured value.
For the same random sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.
Round your answer to the nearest whole number (percent).
Answer:
95%
Step-by-step explanation:
Mean , xbar = 64.3; standard deviation, s= 2.4
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
percent of heights that lie between 59.5 inches and 69.1 inches.
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4
-2 < Z < 2
Thia is within 2 standard deviations of the means :
2 standard deviation form the mean = 95% according to the empirical rule.
Find the measure of the incanted angle to the nearest degree
Answer:
15.4 degrees
Step-by-step explanation:
b= 53
h = 55
cos -¹( 53/53)= 15.4
write fifty and two hundreds eight thousandths as a mixed decimal
Answer:
Pretty sure it's 0.528
Anyone knows the answer?
Please!
Answer:
C
Step-by-step explanation:
sin(theta)=7/8, theta=arcsin(7/8)=61
13. 30 of the 100 iPads in an inventory are known to be cracked. What
is the probability you randomly select one that is not cracked?
Answer:
7/10 or 0.7
Step-by-step explanation:
a probability is always the ratio of possible cases over all cases.
"all cases" here is 100.
possible cases are all iPads not cracked in the inventory = 70 (because 30 are cracked, that leaves 100-30=70 not cracked).
so, the probability to select a non-cracked unit is
70/100 or simplified 7/10 (or 0.7)
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
Put the following equation of a line into slope-intercept form, simplifying all fractions 2x-2y=14
Answer: y = x - 7
Slope intercept form: y = mx + b
[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]
Which of the following pairs of functions are inverses of each other?
A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x -9 and g(x)=x+9/2
C. f(x) = 3-6 and g(x)=x+6/2
D. f(x)= x/3+4 and g(x) = 3x - 4
The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's analyze the given options:
A. f(x) = 5 + x and g(x) = 5 - x
To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.
B. f(x) = 2x - 9 and g(x) = x + 9/2
By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.
C. f(x) = 3 - 6 and g(x) = x + 6/2
Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.
D. f(x) = x/3 + 4 and g(x) = 3x - 4
After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.
In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
Learn more about function here:
https://brainly.com/question/782311
#SPJ8
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test
6 less than six times a number is 42 what is the number
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
6x - 6 = 42
Step 2: Solve for x
[Addition Property of Equality] Add 6 on both sides: 6x = 48[Division Property of Equality] Divide 6 on both sides: x = 8Answer: -6
Step-by-step explanation:
We can create an equation based on the info given.
6-6x=42 Now you solve for x, the unknown number.
-6 -6 Subtract 6 on both sides
-6x=36
/-6 /-6 Divide by -6 on both sides
x=-6
The number is -6.
Julie is tracking the growth of a plant for a science project. The height of the plant on the 2nd day she measured was 8 inches and on the 7th day it was 20.5 inches. Assume the relationship is linear
Answer:
Step-by-step explanation:
The relationship is linear, so the plant grows the same amount each day.
The height on the 2nd day was 8 inches:
h₂ = 8
The height on the 7th day was 20.5 inches:
h₇ = h₂ + (7-2)d = 8 + 5d = 20.5
d = 2.5
The plant grows 2.5 inches each day.
The product of 10 and the difference between 8 and -9?
Hi there!
»»————- ★ ————-««
I believe your answer is:
170
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\text{The phrase can be rewritten as:}\\\\10 * (8-(-9))\\---------------\\\rightarrow 8-(-9) = 8 + 9 = 17\\\\\rightarrow 10 * 17\\\\\rightarrow \boxed{170}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Given parallelogram RUST and m< RUT=43, what other angle has the same measurement
9514 1404 393
Answer:
(b) ∠STU
Step-by-step explanation:
Transversal UT between parallel sides RU and ST creates alternate interior angles RUT and STU. These are congruent.
∠STU has the same measure as ∠RUT
_____
The figure shown is a trapezoid, not a parallelogram.
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 40 feet per second. The ball's height h (in feet) after t seconds is given by the following. h=4+40t-16t2 Find all values of for which the ball's height is 26 feet.
Answer:
Step-by-step explanation:
To find the times that the height is 26 feet, we set the position equation equal to 26 and solve for t:
[tex]26=-16t^2+40t+4[/tex] and
[tex]0=-16t^2+40t-22[/tex] and factor that however you are factoring in class to solve a problem like this. When you do that you get
t = .86 seconds and t = 1.68 seconds. That means that .86 seconds after the ball is thrown into the air, it reaches a height of 26 feet; it goes up to its max height and then gravity takes over and pulls it back down. When this happens, it will pass 26 feet again on its way back down. This second time is after 1.68 seconds.
The maximum and minimum values of a quadratic function are called as________of the function.
Vertex is the point where the function is at its maximum/ minimum.
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
9514 1404 393
Answer:
m = n = 5
Step-by-step explanation:
The side ratios in a 45°-45°-90° triangle are 1 : 1 : √2. That is, the hypotenuse is √2 times the side length. Here, the hypotenuse is 5√2, so the side length must be 5.
m = n = 5
Please help!
Answers
A,B,C and D
The information is already in the chart
( ignore the charts below question 2.)
I believe the answer is B!
Hope this helped you! Please follow my account, thanks!
poonam wants to invest in an account today
to have $4000 at the end of 8 years.
If she can invest at 4.25% Compounded
Semi-annually, how much does she need
to invest?
Answer:
2055.15
Step-by-step explanation:
A(1+r)^n=4000
A is the money that she need to invest
r is rate
n is the time( depend on monthly or yearly rate)
A(1+4.25%)^16=4000
A=2055.15
A =
1
9
4 1 −8
7 4 4
4 −8 1
I don't know sorry I am weak in math
5+(-7)=
A-12
B
-2
с
2
D
12
E
none of these
Answer:
-2
Step-by-step explanation:
5 + (-7)
Since the 7 is larger than 5, the 7 will overpower the 5 in a way. So, all you do is subtract 7 and 5.
7 - 5 = 2
But the 7 has a negative with it (since it's larger), so you add the negative to the 2.
7 - 5 = -2
The answer will be -2.
Solve |6k + 12| + 9 = 9 for k.
Step-by-step explanation:
6k + 12 + 9=9
6k + 12 = 9 - 9
6k + 12 = 0
12 = -6k
12/-6 = -6k/-6
2/-1 = k
k = -2
Answer:
k=-2
Step-by-step explanation:
6k+12+9=9
subtract 9 from both sides
6k+12=0
subtract 12 from not sides
6k= -12
divide both sides by 6 (isolating the variable)
k= -12/6
simplify
k= -2
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Determine what type of transformation is represented.
A. none of these
B. reflection
C. dilation
D. rotation
Answer:
The answer is "Option D"
Step-by-step explanation:
In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.
An expression is shown below:
10n3 − 15n2 + 20xn2 − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
Part B: Rewrite the expression completely factored. Show the steps of your work.
Answer:
An expression is shown below:
10n³− 15n² + 20xn² − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
10n³− 15n² + 20xn² − 30xn
2*5*n*n*n-5*3*n*n+2*5*2*x*n*n-2*5*3*x*n
Greatest common factor=5*n=5n
Part B: Rewrite the expression completely factored. Show the steps of your work.
Solution given;
10n³− 15n² + 20xn² − 30xn
5n(2n²-3n+4xn-6x)
5n(2n²+4xn-3n-6x)
5n(2n(n+2x)-3(n+2x))
5n(n+2x)(2n-3)
Answer:
[tex]5n(2n-3)(n+2x)[/tex]
Step-by-step explanation:
Step 1: Rewrite the expression so the GCF is factored completely
[tex]10n^{3} - 15n^{2} + 20xn^{2} - 30xn[/tex]
The GCF is 5n so factor it out
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
Step 2: Rewrite the expression completely factored
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
[tex]5n(2n(n+2x)-3(n+2x))[/tex]
[tex]5n(2n-3)(n+2x)[/tex]
Answer: [tex]5n(2n-3)(n+2x)[/tex]
PLEASE HELP
Write the equation of the line that is perpendicular to the given segment and that passes through the point (-6, -3). A. 1 V=--x-3 2 B. 1 V=--X-6 2 C. y = 2x + 9 D. = 2x-6.
Answer:
C
Step-by-step explanation:
The slope of the line will be (2) and the equation will be C
