Answer:
4
Step-by-step explanation:
Equation:-
2(5-3)
=> 2(2)
=> 4
What is the value of -
-X2 - 4x – 11 if x = -3?
Anyone knows the answer?
Please!
Answer:
C
Step-by-step explanation:
sin(theta)=7/8, theta=arcsin(7/8)=61
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)
complete the square to form a true equation;
x^2-2x+__=(x-__)^2
Answer:
see explanation
Step-by-step explanation:
To complete the square
add ( half the coefficient of the x- term )² to x² - 2x
x² + 2(- 1)x + 1
(x² - 2x + 1 = (x - 1)²
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.
what is 6 3/5 - 4 3/10
Answer:
2 3/10
Step-by-step explanation:
3/5x2=6/10
6/10-3/10=3/10
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?
Answer:
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.
Step-by-step explanation:
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.
At the null hypothesis, we test if the proportion is of at most 0.67, that is:
[tex]H_0: p \leq 0.67[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:
[tex]H_1: p > 0.67[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.67 is tested at the null hypothesis:
This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]
The class randomly selected 100 patrons and found that 82 borrowed books.
This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]
[tex]z = 3.19[/tex]
P-value of the test and decision:
The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.
Looking at the z-table, z = 3.19 has a p-value of 0.9993.
1 - 0.9993 = 0.0007
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
What is the possible proportion of patrons that do borrow books from the Owensboro Library?
The sample proportion of 0.82.
Cho hình thang ABCD vuông tại A và D biết AB=AD=3cm, BC=6cm. Tính góc C và D
Answer:
C=6cm
D=3cm
Step-by-step explanation:
C=6×6cm
36cm
D=3×3cm
=9cm
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
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]
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
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)
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.
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)
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.
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]
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
find the first quartile form the following data 73,58,39,46,61,52,32
Answer:
----------------------------
quartile first = 73
----------------------------
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.
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.
Which one is it------------------
Answer:
you're right
Step-by-step explanation:
As the number of copies increases, the dimensions of the images continue to decrease but never reach 0. Option A is correct.
As of the given statement,
Both copy machines reduce the dimensions of images that run through the machines. which statment is true is to be justified.
In mathematics, dimensions are the measurements of the size or distance of an item, region, or space in one direction. In layman's words, it is the measurement of something's length, width, and height. Length is the most commonly used dimension.
here,
Both copy machines diminish the size of images that pass through them. Which statement is correct must be justified. So, As the number of copies increases, the image dimensions drop but never reach zero.
Thus, the image dimensions decrease as the number of copies grows, but never reaches zero.
Learn more about dimensions here:
https://brainly.com/question/28688567
#SPJ2
Solve each equation for the specified variable
Answer: Solve for the specified variables
Step-by-step explanation:
1. w= A/l
2. d=C/pi
3. s=v-gt
4. y= 5/2x-11/2
5. P^2= P^1V^1 / P^2 Put ^ as lowercase as shown, can't find symbol on my keboard T.T
6. W= Ke2g / V^2
7. h= V / 2/3 pi r^2
8. n=2S/a+k
9. S=A/pi r - r (not 100% sure on that one)
10. r= E/I-R
11. h= E-1/2mv^2/mg
12. a=K+5b/b+3
13. c=ab/b+a
Wooh, finally finished all that. Hope I didn't make any mistakes. Have a great day!
The true length of recovery for patients with knee surgery is normally distributed with a mean of 123 days and a standard deviation of 1 day. What proportion of the patients will recover between 121 and 124 days?
Answer:
0.81859
Step-by-step explanation:
Given that the length of recovery days for patients with knee surgery is normally distributed with :
Mean, μ = 123 days
Standard deviation, σ = 1 day
The proportion of patients that will recover with 121 and 124 days :
We obtain the Probability of Z score :
Z = (x - μ) / σ
P(Z < (x - μ) / σ) < Z < P(Z < (x - μ) / σ)
P(Z < (121 - 123) / 1) < Z < P(Z < (124 - 123) / 1)
P(Z < - 2) < Z < P(Z < 1)
Using the normal distribution table :
P(Z < 1) - P(Z < - 2)
0.84134 - 0.02275
= 0.81859
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink what fraction of the bouquet is pink? There are 12 roses in a dozen.
A. 5/12
B. 7/12
C. 5/7
D. 7/5
Answer:
7/12
Step-by-step explanation:
There are 12 roses - 5 white = 7 pink
7 pink / 12 total
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
4. The rectangle shown below has been broken into four smaller rectangles. The area of three of the smaller
rectangles are shown in the diagram. Find the area of the fourth rectangle and justify your answer. [Think about
shared dimensions.]
Answer:
Step-by-step explanation:
Need the diagram for reference in order to answer...........
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.
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.
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.
