Answers
first off, let's take a peek at the picture above
hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.
now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.
[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}[/tex]
Related Questions
The data in a data set are normally distributed with a mean of 170 and a standard deviation of 20. Estimate the percent of the data that are less than 150 or greater than 190.
Answers
Using the normal distribution, we find that 32% of the data that is less than 150 or greater than 190.
----------------------------
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.
----------------------------
The data in a data set are normally distributed with a mean of 170 and a standard deviation of 20.
This means that [tex]\mu = 170, \sigma = 20[/tex]
----------------------------
Less than 150:
As a proportion, it is the p-value of Z when X = 150, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 170}{20}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16.
0.16x100% = 16%
----------------------------
More than 190:
As a proportion, it is 1 subtracted by the p-value of Z when X = 190, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{190 - 170}{20}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16
0.16x100% = 16%
----------------------------
Estimate the percent of the data that are less than 150 or greater than 190.
We add both percentages, thus:
16% + 16% = 32%
32% of the data that is less than 150 or greater than 190.
A similar question is given at https://brainly.com/question/14694610
A chili cook-off has adult tickets (a) and child tickets (c) . A group of Visitors buy three adult tickets and two child tickets and pays a total of $26. Another group buys five adult tickets and 3 child tickets and pays $42. Write and solve a system of equations to find the price of each type of ticket. (I just need the equations)
Answers
Answer:
Equation 1 would be: 3a+2C
Equation 2 would be: 5a+3C
Step-by-step explanation:
Lola is putting a border on the quilt she is making. The quilt is shaped like a rectangle. The width of the quilt is 48 inches and its length is twice its width. How much border does Lola need?
Group of answer choices
Answers
Answer:
288in
Step-by-step explanation:
48 times 2 is 96
96 plus 96 plus 48 plus 48 for all sides of the rectangle = the perimeter or border
In football, a field goal is kicked from a position on the field
through a goal post that is 360 inches beyond the goal line. If a
field goal is kicked from the 38-yard line, what is the distance in feet to the goal post
Answers
Answer:
144 ft. i just had this question on my test .
Step-by-step explanation:
PLs help quick,Jonna has 5 yards of fabric.She needs 100 inches of fabric to make curtains.Does she have enough fabric to make curtains?
Answers
Answer:
Yes, she has 80 more inches
Why?
Because one yard is 36 inches and she has 5 yards and 5x36=180 and she has 100 inches and 180>100.
She has 80 more.
Hope it helps :)
a hardware factory produces 3.6 •10^5 bolts in 2400 minutes. what is the factory rate of production in bolts per minute
Answers
100,000*3.6
360,000
360,000/2400
I believe it’s 150 bolts per minute
Write and solve an equation for the following.
Four more than one-half a number is three. What is the number?
Answers
Answer:
4+ [tex]\frac{1}{2}[/tex]x = 3
Step-by-step explanation:
4 + [tex]\frac{1}{2}[/tex]x = 3 (subtract 4 from both sides)
[tex]\frac{1}{2}[/tex]x = -1 (multiply both sides by 2)
x = -2
Answer:
4+ 1/2 x = 3
Step-by-step explanation:
X =-2
Find the area of the shaded sector.
158°
Answers
Answer:
120 degree in a while and I am fan of the African American women who have served and are fight with you and I am fan of these days and then I will be there in a few days ago y I love u too
Step-by-step explanation:
fftt fight for you to be a good day at work and you are so cute and I am fan of these people are so cute and I am fan of these game and my name was on the phone with my mom is going to be a good day at add me on the phone with my mom is going to be a good day at work and you are so t I don't know what I said it will be there in a few days ago I got the job at the end of my favorite thing in life that is the best thing that I have to be a good day at work and you are so sweet to say that I have to go back to the for us to be a good day at work and I'm so excited about this one is it a Main St apt c u at work and you are not a bad mood today so I can do it for me to come back in my head and I am fan and I am fan on my is on the phone and it is not a type of settlement of the African American women who have participated and are you doing today I am so proud of u and I am fan on my is on the phone number and you can do it for me to come
find the length of DE
Answers
Then using A^2+B^2=C^2
We can say 4.7^2+B^2=13^2
22.09 +B^2 = 169
169-22.09= 146.91
B^2=146.91
Square rooting both sides gives you
B=12.12
Verify the identity.
cos x/1+sin x = sec x - tanx
Answers
Answer:
See below for proof
Step-by-step explanation:
[tex]\displaystyle \frac{\cos x}{1+\sin x}=\frac{\cos x(1-\sin x)}{(1+\sin x)(1-\sin x)}\\\\\frac{\cos x}{1+\sin x}=\frac{\cos x(1-\sin x)}{1-\sin^2x}\\\\\frac{\cos x}{1+\sin x}=\frac{\cos x(1-\sin x)}{\cos^2x}\\\\\frac{\cos x}{1+\sin x}=\frac{1-\sin x}{\cos x}\\\\\frac{\cos x}{1+\sin x}=\frac{1}{\cos x}-\frac{\sin x}{\cos x}\\\\\frac{\cos x}{1+\sin x}=\sec x-\tan x[/tex]
What is the value of the missing angle?
Answers
180-115= 65
the missing angle is 65°
Answer:
65°
Step-by-step explanation:
All angles in a triangle added up make 180° so you have to add 68° and 47° whih equals 115° and then simply subtract it from 180° so 180°-115°=65°
|al-|b| + IcI. if a=-8;6=-5;c=1
Pls no links and only give answer if you know it
Answers
Answer:
4Step-by-step explanation:
Given
a = -8;b = -5;c = 1Absolute value is always positive:
|al - |b| + IcI = |-8l - |-5| + I1I =8 - 5 + 1 =4Which ordered pair is the solution to the system of linear equations y =-7x+2 and y = 9x-14?
• (-5,1)
• (1,-5)
(5,-1)
(-1,5)
Answers
Answer:
(1, -5)
Step-by-step explanation:
Solve the system by setting the equations equal to each other, and solving for x:
-7x + 2 = 9x - 14
2 = 16x - 14
16 = 16x
1 = x
So, the x coordinate of the solution will be 1.
Plug in 1 as x into one of the equations, and solve for y
y = -7x + 2
y = -7(1) + 2
y = -7 + 2
y = -5
So, the y coordinate is -5.
The ordered pair solution is (1, -5)
Answer:
Solution in photo
Mrs. Crosland asked students to factor the expression 28x - 8. The students offered the answers shown in the box. Which student(s) offered answer(s) equivalent to the original expression? A. only Danny B. only Irene C. both Carlos and Danny D. both Carlos and Irene
Answers
Answer:
Step-by-step explanation:
I can't see the factorisation that the students did. That is, Danny, Carlos and Irene. You either forgot to upload, or you couldn't.
However, I will factorise the expression for you, while you check you book to know who did the exact same factorisation.
28x - 8
This equation can be factorised when divided by 2, into
2(14x - 4)
At the same time, it can be factorised when divided by 4, into
4(7x - 2)
Basically, either of the students who choose between 2(14x - 4) and 4(7x - 2) is/are whom you'd pick for your answer.
Help me ASPA PLEASE help
Answers
Answer:
85
Step-by-step explanation:
1 Which expression can be used to find the volume, in cubic centimeters, of the solid shown? Choose all that apply. 3 cm 4 cm 7 cm 5 cm 9 cm A (3 X 4 X 5) + (3 X 5 X 9) B (3 X 5 X 6) + (5 X 4 X 3) C (9 X 5 X 3) + (3 X 5 X 7) D (7 X 5 X 3) + (6 X 5 X 3) E (3 X4 X 7) + (6 X 5 X 4)
Answers
Answer:
I think its D
Step-by-step explanation:
Question 14
Find the volume of this sphere. Round to the nearest hundredth.
6.5 cm
cm cubed
Answers
Answer:
1150.35
Step-by-step explanation:
Anna charges $8.50 an hour to babysit how long will it take to make $51.00
Answers
Answer:
6 hours
Step-by-step explanation:
$51.00 ÷ $8.50 = 6 hours
hope this helps ! :))
In a random sample of 8 people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.4 minutes. A 90% confidence interval using the t-distribution was calculated to be (30.5,40.5). After researching commute times to work, it was found that the population standard deviation is 9.3 minutes. Find the margin of error and construct a 90% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.
Answers
Answer:
Margin of Error = 5.4088 ;
Confidence interval = (30.1 ; 40.9)
Interval estimate are almost the same
Step-by-step explanation:
Given that :
Population standard deviation, σ = 9.3
Sample size, n = 8
Xbar = 35.5
Confidence level = 90%
The confidence interval:
Xbar ± Margin of error
Margin of Error = Zcritical * σ/sqrt(n)
Zcritical at 90% = 1.645
Margin of Error = 1.645 * 9.3/sqrt(8) = 5.4088
Confidence interval :
Xbar ± Margin of error
35.5 ± 5.4088
Lower boundary = (35.5 - 5.4088) = 30.0912 = 30.1
Upper boundary = (35.5 + 5.4088) = 40.9088 = 40.9
(30.1 ; 40.9)
T distribution =. (30.5 ; 40.5)
Normal distribution = (30.1, 40.9)
Assume that the weight of cereal in a "12.6 ounce box" is N(µ,0.42). The Food and Drug Association (FDA) allows only a small percentage of boxes to contain less than 12.6 ounces. You collect a random sample of n = 35 boxes and find that the sample mean is 12.8. Test the null hypothesis H0: µ = 13 against the alternative hypothesis HA: µ < 13 at level of significance α = 0.01
Answers
Answer:
We reject the null hypothesis and accept the alternate hypothesis, that is, that the mean is less than 13 ounces.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0}: \mu = 13[/tex]
The alternate hypotesis is:
[tex]H_{a}: \mu < 13[/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.
13 is tested at the null hypothesis:
This means that [tex]\mu = 13[/tex]
N(µ,0.42)
This means that the standard deviation is 0.42, that is, [tex]\sigma = 0.42[/tex]
You collect a random sample of n = 35 boxes and find that the sample mean is 12.8.
This means that [tex]n = 35, X = 12.8[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{12.8 - 13}{\frac{0.42}{\sqrt{35}}}[/tex]
[tex]z = -2.82[/tex]
Pvalue of the test:
The pvalue of the test is the pvalue of z = -2.82.
Looking at the z table, z = -2.82 has a pvalue of 0.0024
0.0024 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis, that is, that the mean is less than 13 ounces.
Demand for a specific design of dinning sets has been fairly large in the past several years and Statewide Furnishings, Inc. usually orders new dinning sets 10 times a year. It is estimated that the ordering cost is $400 per order. The carrying cost is $50 per unit per year. Furthermore, State Wide Furnishings, Inc. has estimated that the stock out cost is $120 per unit per year. Based on forecast, the annual demand is 600 units. State Wide Furnishings, Inc. has 350 working days in a year and its lead time is 14 working days. Assume the inventory policy of Statewide Furnishings, Inc. does not allow stock out. Determine the economic order quantity.
1. Assume shortage is allowed and the store manager is sure that shortages will not become lost sales, determine the maximum allowable shortage.
a. 117.
b. 98.
c. 34.
d. 24.
2. Assume shortage is allowed and the store manager is sure that shortages will not become lost sales, determine the annual ordering cost.
a. 592.82.
b. 1472.01.
c. 2051.28.
d. 4116.11.
e. none of the above.
3. Assume shortage is allowed and the store manager is sure that shortages will not become lost sales, determine the annual holding cost.
a. 592.82.
b. 1472.01.
c. 2051.28.
d. 4116.11.
e. none of the above.
4. Assume shortage is allowed and the store manager is sure that shortages will not become lost sales, determine the annual shortage cost.
a. 592.82.
b. 1472.01.
c. 2051.28.
d. 4116.11.
e. none of the above.
5. Assume shortage is allowed and the store manager is sure that shortages will not become lost sales, determine the annual total relevant, including ordering, holding and shortage, cost.
a. 592.82.
b. 1472.01.
c. 2051.28.
d. 4116.11.
e. none of the above.
6. Assume shortage is allowed and the store manager is sure that shortages will not become lost sales, determine the reorder point.
a. 10.
b. –10.
c. 34.
d. 24.
e. none of the above.
Answers
Answer:
1. a. 117.
2. $2,051.48
3. 592.82
4. 1472.01
5. d. 4116.11
6. d. 24
Step-by-step explanation:
Economic Order Quantity : [tex]\sqrt{\frac{2 * Annual Demand *ordering cost}{Holding cost per unit } ( \frac{Holding cost + Shortage Cost}{Shortage cost }) }[/tex]
Economic order quantity is [tex]\sqrt{\frac{2 * 600 * 400}{50} (\frac{50 + 120}{120} )}[/tex]
EOQ = 117
2. ordering cost :
( total demand / EOQ ) * Ordering cost
( 600 / 117 ) * 400 = $2051.28
3. Holding cost :
Total demand * holding cost per unit
= 592.82
Reorder Point = Daily Demand * lead time
Reorder point = 600 / 350 * 14 = 24
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
Circumference=25.13 Area=50.27
It is desired to check the calibration of a scale by weighing a standard 10-gram weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10 and out of calibration if μ ≠ 10. A test is made of the hypotheses H0 : μ = 10 versus H1 : μ ≠ 10. Which of the three conclusions is best if H0 is rejected?
Answers
Complete question :
It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let µ be the population mean reading on the scale, so that the scale is in calibration if µ = 10. A test is made of the hypotheses H0:µ = 10 versus H1:µ ≠ 10. Consider three possible conclusions: (i) The scale is in calibration, (ii) The scale is out of calibration, (iii) The scale might be in calibration.
Which of the three conclusions is best ifH0 is rejected?
Answer:
The scale is out of calibration
Step-by-step explanation:
The null hypothesis ; H0
H0 : μ = 10 ; if this hold true, then the scale is in calibration
Alternative hypothesis ; H1
H1 : μ ≠ 10 ; if this holds true, then the scale is out of calibration
If the Null hypothesis, H0 is rejected, it means that, there is significant evidence to support the alternative hypothesis ; that the scale is out of calibration.
Hence, the best conclusion is that, the scale is out of calibration.
Help quick!!!!!!!!!!!!!!!!!
Answers
Answer:
P = 56.562
Step-by-step explanation:
Perimeter of a semicircle:
P = πr + 2r
Given:
r = 11
Work:
P = πr + 2r
P = 3.142(11) + 2(11)
P = 34.562 + 22
P = 56.562
Which expression is NOT equivalent to
(m-5) *3?
a) 3 * m -15
b) 3 * m - 5
c) 3m - 15
d) 3 * m - 3 * 5
Answers
Answer:
b) 3 * m - 5
Step-by-step explanation:
i rember a test i took on these
1. If y varies inversely as x and y = 2 when x = 10, find y when x = 5.
2. If y varies directly as z and inversely as x and y = 10 and z = 5 when x = 12.5, find z when y = 37.5 and x = 2.
Answers
Answer:
1.45
Step-by-step explanation:
I don't really know if this is right
Find the volume of the cone below. Leave your answer in terms of pi.
Answers
Answer:
ahaha it's B my guy
Step-by-step explanation:
peace out
A track star jumped 6 feet. The record is 84 inches. How much further does he need to jump to beat the record?
thank you!!
Answers
Answer:
12 inches or 1 ft.
Step-by-step explanation:
Firstly, convert the 6 feet to inches.
(There are 12 inches in 1 foot)
So, 6 feet is 72 inches (6 * 12)
Now, you can subtract this total from the record, to find how much farther he needs to jump:
84 - 72 = How much further
84 - 72 = 12
Therefore, he needs to jump 12 inches further.
To place in feet form, then convert 12 inches to feet.
(There are 12 inches in a foot)
So, 12 inches is 1 foot
Answer:
1 foot or 12 inches.
Step-by-step explanation:
Since there are 12 incher in every foot, we divide 84 by 12, giving us a total of 7ft. He has to jump 1 foot, or 12 inches more, to beat the record.
Which of the following scatterplots would have a trend line with a positive slope?
Answers
Answer:a
Step-by-step explanation:
ten vegetable selections available, how many 3 vegetable plates can be made