Answer:7.5=−k(2.5)−7.52.5=kma=−7.5x2.5my′′+9y′+−3y=0,y(0)=2.5,y(5)=0−9±81+4(m)(3)−−−−−−−−−−−√2m−92m±81+12m−−−−−−−−√2my=Ae−(9/2)xcos(81+12m−−−−−−−−√2mx)+Be−(9/2)xsin(81+12m−−−−−−−−√2mx)2.5=A+B⋅00=(2.5)e−45/2cos(81+12m−−−−−−−−√52m)+Be−45/2sin(81+12m−−−−−−−−√52m)
Step-by-step explanation:
What are the coordinates of the terminal point for 8 = 4pie/3?
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Answer:
B
Step-by-step explanation:
(4π)/3 is a 3rd-quadrant angle with a reference angle of π/3 = 60°. This means both coordinates of the terminal point are negative, and the x-coordinate has the smaller magnitude. The only applicable choice is ...
B. (-1/2, -√3/2)
which of the following values are in the range of the function graphed below?
Answer:
f)0
Step-by-step explanation:
HELP PLEASE
Question: 1. Line segment AB has endpoints A(8, 3) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2. 2. Line segment AB has endpoints A(6, 4) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.
Answer:
a) (6,4)
b) (5, 4.5)
Step-by-step explanation:
much like when you find them midpoint where you average the x-coordinates and the y-coordinates to find the midpoint coordinates, you'll do the same thing here.
to set context, a midpoint would break the segment into a ratio of 1:1.
so in the first part, a ratio of 1:2 means you are breaking the segment into 3-parts. So you'll do this for the coordinates:
[tex]x = \frac{8 + 2}{3} \: and \: y = \frac{3 + 6}{3} [/tex]
for the second part as the ratio is 1:3, you are breaking the segment into 4 parts.
[tex]x = \frac{6 + 2}{4} \: and \: y = \frac{4 + 6}{4} [/tex]
Evaluate each expression given that a =-5, b=2 and c=1
b) b-a+c
c) 2b+6c
d)abc
e) -2ab/c
Answer:
Given
a=-5
b=2
c=1
i) b - a + c
= 2 -(-5) + 1
=2 + 5 + 1
=8.
ii)2b + 6c
= 2(2) + 6(1)
=4 + 6
=10.
iii) abc = (-5)(2)(1)
= -10.
iv) -2ab/c
= -2(-5)(2)/1
= 20.
10. Use the formula for the
volume of a pyramid (V = {Bh) to
find the volume of a pyramid with
the following measurements:
B = 36 m2; h = 4m.
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Answer:
48 m³
Step-by-step explanation:
The correct formula for the volume of a pyramid is ...
V = 1/3Bh
For the given values, the volume is ...
V = 1/3(36 m²)(4 m) = 48 m³
please help me do this i need it
Answer:
(x+1)(3x+2) is the answer
Answer:
Step-by-step explanation:
3x^2+5x+2
3x^2+(3+2)x+2
3x^2+3x+2x+2
3x(x+1)+2(x+1)
(3x+2)(x+1)
Point P is the center of the circle below. What is the exact area
of the shaded sector in terms of pi?
A. 16 pie units?
B. 48 pi units?
C. 120 pi units?
D. 192pi units
NEED HELP ASAP PLEASE
Answer:
[tex]Area =192\pi[/tex]
Step-by-step explanation:
Given
[tex]\theta = 120^o[/tex]
[tex]r =24[/tex]
Required
The area of the shaded sector
This is calculated as:
[tex]Area =\frac{\theta}{360} * \pi r^2[/tex]
This gives
[tex]Area =\frac{!20}{360} * \pi *24^2[/tex]
[tex]Area =\frac{1}{3} * \pi *576[/tex]
[tex]Area =\pi *192[/tex]
[tex]Area =192\pi[/tex]
For the sample standard deviation(s) for situations involving means, explain whether it affects the width of a confidence interval, the center of a confidence interval, neither, or both.
Answer:
Affects the width of a confidence interval, as the margin of error is a function of the sample standard deviation.
Step-by-step explanation:
When we have the standard deviation for the sample, the t-distribution is used to solve the question.
It does not affect the center of the interval, which is a function only of the sample mean.
Width of a confidence interval:
The width of a confidence interval is a function of the margin of error, which is:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In which s is related to the sample standard deviation. Thus, since s and M are directly proportional, a higher standard deviation makes the interval wider, lower standard deviation makes the interval narrower, and thus, the sample standard deviation affects the the width of a confidence interval.
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 2916 with a mean life of 518 minutes. If the claim is true, in a sample of 81 batteries, what is the probability that the mean battery life would be greater than 526.4 minutes
Answer:
0.0808 = 8.08% probability that the mean battery life would be greater than 526.4 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The design engineer claims they have a variance of 2916 with a mean life of 518 minutes.
This means that [tex]\sigma = \sqrt{2916} = 54, \mu = 518[/tex]
Sample of 81 batteries
This means that [tex]n = 81, s = \frac{54}{\sqrt{81}} = 6[/tex]
What is the probability that the mean battery life would be greater than 526.4 minutes?
1 subtracted by the p-value of Z when X = 526.4. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{526.4 - 518}{6}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value of 0.9192
1 - 0.9192 = 0.0808
0.0808 = 8.08% probability that the mean battery life would be greater than 526.4 minutes
PLEASE HELP I WILL MARK BRAINLIEST
Answer:
8 x 13 = 104 yd^2
Step-by-step explanation:
To find the area of a rectangle we use the basic formula:
L x W
In this case 13 is your width and 8 is your length, multiply the two given lengths to get your area which is 104.
The scores on an exam are normally distributed, with a mean of 82 and a standard deviation of 10. What percent of the scores are less than 62?
Answer:a
a
Step-by-step explanation:
i took the test
(–2) + 6 + 1 = 1 + 6 + (–2) =
Answer:
5=5
Step-by-step explanation:
An auto parts chain asked customers to complete a survey rating the chain's customer service as average, above average, or below average. The following shows the results from the survey: Average Below Average Average Above Average Above Average Above Average Below Average Average Average Below Average Average Below Average Below Average Below Average Below Average The proportion of customers who felt the customer service was Average is the closest to _______.
Answer:
The right answer is "0.33".
Step-by-step explanation:
As per the question,
n = 15
Average will be "x = 5"
Now,
The required proportion will be:
⇒ [tex]p=\frac{x}{n}[/tex]
By putting the values, we get
⇒ [tex]=\frac{5}{15}[/tex]
⇒ [tex]=0.33[/tex]
Thus, the above is the appropriate solution.
The ratio of Luke's age to Jack's age is 3:2. If Luke is 36, how old is Jack?
Answer:
Jack is 24
Step-by-step explanation:
Luke : jack
3 2
We know like is 36
3*12 = 36, so we need to multiply by 12
Luke : jack
3*12 2*12
36 24
Answer:
24
Step-by-step explanation
Notice that Luke's real age is 12 times the number in the ratio, which is a simplified version of the original ratio, where they used division by 12 on both sides to get 3:2. Just do the opposite of division, which is multiplication, and multiply both sides of the ratio to get 36:24, which means that Jack is 24 years old!
Hope this helped you!
Karen and Dale and Tom sent a total of 84 messages during the weekend. Dale sent six fewer messages and Karen and Tom sent four times as many as Karen. How many did they send each.
Answer:
Karen: 15; Dale: 9; Tom: 60
Step-by-step explanation:
"Karen and Dale and Tom sent a total of 84 messages during the weekend."
k + d + t = 84
"Dale sent six fewer messages than Karen"
d = k - 6
"Tom sent four times as many as Karen."
t = 4k
Substitute k - 6 for d and 4k for t in the first equation.
k + d + t = 84
k + k - 6 + 4k = 84
6k - 6 = 84
6k = 90
k = 15
d = k - 6 = 16 - 6 = 9
t = 4k = 4(15) = 60
Answer: Karen: 15; Dale: 9; Tom: 60
measure the bearing from b to a then bearing from a to b
Answer:
[tex]ax \: \: \: \: \: \: \: \:xb[/tex]
find the midpoint of A and B where A has tge coordinates (8, 5) and B has the coordinates (3, 7)
Answer:
[tex]midpoint = ( \frac{8 + 3}{2} , \: \frac{5 + 7}{2} ) \\ = ( \frac{11}{2} , \: \frac{12}{2} ) \\ = (5.5, \: 6)[/tex]
A study found that 62% of drivers believe that they are equally capable of driving a car when texting and when not texting. Of those 62%, 34% had been in an accident; 75% of those had been texting. Which of the following inferences can be made from this data?
A large number of drivers overestimate their abilities.
Most drivers are capable of texting and driving simultaneously.
25% of those texting do not get into accidents.
38% of drivers are more cautious than the rest.
Answer:
your answer is c
Step-by-step explanation:
Jessica has 3 cards in a bag, each marked with a letter. The letters are X, Y , and
Z. Without looking, she reaches into the bag, pulls out a card, and then puts the card
back in the bag. If Jessica does this 3 times, what is the probability she pulls out the
X card first, then the Y card, and then the Z card?
1/27
Step-by-step explanation:
get one card is 1/3 so you do 1/3x1/3x1/3
With sales tax, it costs $707 to buy a $700 dining room table. What is the sales tax
percentage?
Write your answer using a percent sign (%).
Answer:
1%
Step-by-step explanation:
707-700=7 tax
700 x tax percentage=7
tax percentage =7/700
Tax percentage= .01 0r 1%
What is the nth term rule of the linear sequence below?
22
,
18
,
14
,
10
,
6
,
.
.
.
Answer:
tn=a+(n-1)d
tn=22+(n-1)4
tn=22+4n-4
tn=4n+18
Find the circumference of a circle with diameter,
d
= 6cm.
Give your answer in terms of
π
.
Answer:
6π cm
Step-by-step explanation:
simplify 22+[55-{72÷(7+5×2-11)+3}+2]
Answer:
64Step-by-step explanation:
In the picture
How many times does the graph of the function below intersect or touch the x-axis y=-x^2+x+6
5/4 to the 3rd power
Answer:
1.953125 is the answer I believe
or 125/64
or 1 61/64
help me pleaseeeeeewew fqe
Answer:
Step-by-step explanation:
2x+3x-5=180 degree(being co interior angles)
5x=180+5
x=185/5
x=37
substitute the value of x
VWT=3x-5
=3*37-5
=111-5
=106
therefore VWT=106 degree
Special Right Triangles
Guided Practice
Find the values of x and y.
A. x=30, y=10V3
B. x= 10, y=30V3
C. x= 30 V3, y=10
D. x=10V3, y=30
y
30°
2013
Need help ASAP
Answer:
A.
x = 30
y = 10√3
Step-by-step explanation:
Reference angle = 30°
Opposite = y
Adjacent = x
Hypotenuse = 20√3
✔️To find x, apply CAH:
Cos 30 = Adj/Hyp
Cos 30 = x/20√3
20√3 × Cos 30 = x
20√3 × √3/2 = x (cos 30 = √3/2)
(20√3 × √3)/2 = x
(20 × 3)/2 = x
60/2 = x
30 = x
x = 30
✔️To find y, apply SOH:
Sin 30 = Opp/Hyp
Sin 30 = y/20√3
20√3 × Sin 30 = y
20√3 × ½ = y (sin 30 = ½)
(20√3 × 1)/2 = y
(20√3)/2 = y
10√3 = y
y = 10√3
4. Gravetter/Wallnau/Forzano, Essentials - Chapter 6 - End-of-chapter question 4 A psychology class consists of 32 freshmen and 48 sophomores. If the professor selects names from the class list using random sampling. What is the probability that the first student selected will be a freshman
Answer:
ANS.1
Freshmen F = 32
Sophomore S = 48
Total students = 80 students
P(F) = Favorables cases/Total cases
= 32/80
Hope this helps!
Answer:
32/80 or 2/5 simplified
Step-by-step explanation:
P(Freshman) = 32/80 or 2/5 simplified
. Chad's pay rate for babysitting is y = 9x, where x is the number of hours he babysits, and y is the number of dollars he earns. Horatio's pay rate is shown in the graph below. Horatio's Babysitting Pay Rate. Which of the following statements is true? * HORATIO'S BABYSITTING PAY RATE 100 90 80 70 60 Dollars Earned (8.60) 50 40 30 20 10 (4, 30) 0 1 2 3 4 5 6 7 8 9 10 Hours A. Chad makes $1.00 more per hour than Horatio. O B. Chad makes $1.50 more per hour than Horatio. C. Chad makes $1.00 less per hour than Horatio. D. Chad makes $1.50 less per hour than Horatio.
Answer: Chad Makes $1.50 more
Step-by-step explanation:
You have to divide 30 from 4 to see Horatio’s hourly rate which is 7.5 and then you will see that 9 - 7.5 is 1.5. I hope this helped
Solve for x if ab ≠ 2c
[tex]x = \frac{ac + b}{2c - ab} [/tex]
Refer to the attachment for step by step explaination.
Answer:
[tex]x=\frac{b+ax}{2c-ba}[/tex]
Step-by-step explanation:
When given the following expression, one is asked to solve for (x):
[tex]\frac{2x-a}{b}=\frac{ax+1}{c}[/tex]
Use cross products to rid the variable in the denominator,
[tex]c(2x-a)=b(ax+1)[/tex]
Simplify, distribute, multiply every term in the parenthesis by the term outside of it,
[tex]2xc-ac=bax+b[/tex]
Inverse operations, collect all terms with variable (x) on one side of the equation:
[tex]2xc-ac = bax + b\\\\2xc - bax = b + ac[/tex]
Factor, remove a like term that exists in both of these expressions,
[tex]x(2c-ba)=b+ax[/tex]
Inverse operations,
[tex]x=\frac{b+ax}{2c-ba}[/tex]
