Answer:
480 cubic feet
Step-by-step explanation:
The volume of any rectangular prism can be found by multiplying together the length, width and height. In this case, 8*6*10=48*10=480 cubic feet. Hope this helps!
Answer:
[tex]480 {ft}^{3} [/tex]
Step-by-step explanation:
[tex]area \\ = l \times b \times h \\ = 8 \times 6 \times 10 \\ = 48 \times 10 \\ = 480 {ft}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
I NEEEED HELP RN the following table shows a proportional relationship. x y 2 9 5 22.5 8 36 write an equation to describe the relationship
Answer:
y = 4.5x
Step-by-step explanation:
y=ax is form of proportional relationship
checking the first pair of numbers:
9=2a ⇒ a= 4.5checking other lines
5*4.5= 22.5- correct8*4.5= 36 - correctSo the equation is:
y = 4.5xScott made a casserole for dinner. He gave equal portions of Ask Your Teacher of the casserole to 3 friends. What diagram could Scott use to find the fraction of the whole casserole that each friend got? what is the answer
Answer:
1/6
Question: Scott made a casserole for dinner he gave equal portions of 1/2 the casserole to 3 friends what diagram could scott use to find the fraction of the whole casserole that each friend got?
Step-by-step explanation:
Find attached the diagram Scott used to find the portion each friend got.
The shaded part indicate the portion of the casserole.
When Scott prepared the dinner = 1 portion of casserole
He shared 1/2 the portion to 3 of his friends:
Divide the diagram of the full portion into 2 to get ½ of the casserole
1/2 of the casserole = ½ × 1 portion = ½ portion
Each of his 3 friends would have equal portions = ⅓ of the ½ portion
The diagram of the ½ portion would be divided into 3 equal part
In terms of calculation = ½ × ⅓
= 1/6
Each of his friends would have 1/6 portion of the casserole.
Hello! I provided the answer to your problem in a picture.
Ex. (3/6)
Identify whether the following equation has a unique solution, no solution, or infinitely many solutions.
4( − 11) = 15 − 4
Answer:
no solution
Step-by-step explanation:
4( − 11) = 15 − 4
-44 = 11
Since this iS FALSE, it means that the equation given has no solution
What’s the correct answer for this?
Answer:
P = 4/13
Step-by-step explanation:
In a deck of 52 cards, there are 3 aces(spade, heart, diamond), 1 club ace, and 12 remaining club cards
=> The probability of randomly drawing 1 card that is an ace card or a club card:
P = number of elements/total number of elements
P = (3 + 1 + 12)/52
P = 16/52
P = 4/13
=> Option A is correct
Lee put $10,000 into a stock market index mutual fund that grew at an average of 7% per year for 10 years. About how much is in Lee's mutual fund account after 10 years? Ignore compounding.
Answer:
17000
Step-by-step explanation:
we can use the equation I=PRT
I=10,000(10)(0.07)
I=100,000(0.07)
i=7000
7000+ the initial 10,000=17000
A patient is using Humulin insulin U100, the patient is to use 35units three times a day, how many milliliters will be used each day
Answer:
Step-by-step explanation:
(35 units three times a day) comes out to (35 units / day)(3 times per day), or
105 units per day
Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park.† Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. (Round your answers to four decimal places.)
(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?
(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?
(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?(d) What is the probability that more than 55 visitors have no recorded point of entry?
Answer:
a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance
b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance
c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.
d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 175[/tex]
(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?
46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that [tex]p = 0.467[/tex]. So
[tex]\mu = E(X) = np = 175*0.467 = 81.725[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6[/tex]
This probability, using continuity correction, is [tex]P(X \geq 85 - 0.5) = P(X \geq 84.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 84.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{84.5 - 81.725}{6.6}[/tex]
[tex]Z = 0.42[/tex]
[tex]Z = 0.42[/tex] has a pvalue of 0.6628.
66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.
(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?
Using continuity correction, this is [tex]P(80 - 0.5 \leq X < 90 - 0.5) = P(79.5 \leq X \leq 89.5)[/tex], which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So
X = 89.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{89.5 - 81.725}{6.6}[/tex]
[tex]Z = 1.18[/tex]
[tex]Z = 1.18[/tex] has a pvalue of 0.8810.
X = 79.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{79.5 - 81.725}{6.6}[/tex]
[tex]Z = -0.34[/tex]
[tex]Z = -0.34[/tex] has a pvalue of 0.3669.
0.8810 - 0.3669 = 0.5141
51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance
(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?
6.3% of visitors entered through the Grand Lake park entrance, which means that [tex]p = 0.063[/tex]
[tex]\mu = E(X) = np = 175*0.063 = 11.025[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141[/tex]
This probability, using continuity correction, is [tex]P(X < 12 - 0.5) = P(X < 11.5)[/tex], which is the pvalue of Z when X = 11.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{11.5 - 11.025}{3.2141}[/tex]
[tex]Z = 0.15[/tex]
[tex]Z = 0.15[/tex] has a pvalue of 0.5596.
55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.
(d) What is the probability that more than 55 visitors have no recorded point of entry?
22.7% of visitors had no recorded point of entry to the park. This means that [tex]p = 0.227[/tex]
[tex]\mu = E(X) = np = 175*0.227 = 39.725[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54[/tex]
Using continuity correction, this probability is [tex]P(X \leq 55 + 0.5) = P(X \leq 55.5)[/tex], which is the pvalue of Z when X = 55.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.5 - 39.725}{5.54}[/tex]
[tex]Z = 2.85[/tex]
[tex]Z = 2.85[/tex] has a pvalue of 0.9978
0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry
"Find the coefficient of determination given that the correlation coefficient = -.39"
(Give your answer as a decimal rounded to the ten thousandth decimal place.)
Answer:
[tex] r = -0.39[/tex]
And the determination coeffcient is just the correlation coeffcient square and we got:
[tex] R = r^2 = (-0.39)^2 =0.1521[/tex]
And rounded to the nearest tenth thousand would be 0.1521
Step-by-step explanation:
The correlation coefficient is a measure of variability and is given by this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For this case we have
[tex] r = -0.39[/tex]
And the determination coeffcient is just the correlation coeffcient square and we got:
[tex] R = r^2 = (-0.39)^2 =0.1521[/tex]
And rounded to the nearest tenth thousand would be 0.1521
Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one study of a sample of 185 whistles emitted from bottlenose dolphins in captivity, 100100 were categorized as type a whistles. a. Estimate the true proportion of bottlenose dolphin signature whistles that are type a whistles. Use a 9595% confidence interval.
Answer:
The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 185, \pi = \frac{100}{185} = 0.5405[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 - 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.4687[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123[/tex]
The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).
If the Alpha company is 79% staffed and the Beta company is only 62% staffed, what is the relative change of staffing from the Alpha company to the Beta company?
Answer:
27.41%
Step-by-step explanation:
Data provided in the question
The staffed of Alpha company = 79%
The staffed of Beta company = 62%
Based on the above information, the relative change of staffing from Alpha to beta company is
As we know that
[tex]\bold {\ Relative \ change = \frac{\alpha- \beta }{\beta }}[/tex]
[tex]= \frac{(79 -62)}{62} \% \\\\= \frac{17}{62} \times 100\\\\=0.2741 \times 100\\\\=27.41\ \%[/tex]
By applying the above formula we can get the relative change and the same is to be applied so that the correct percentage could come
Clay weighs 9 times as much as his baby sister clay weighs 63 pounds how much doea hiw baby sister weigh in ounces
Answer:
112 ounces
Step-by-step explanation:
Clay weighs 9 times as much as his baby sister .
Clay weighs 63 pounds.
His baby sister weigh 63/9.
His baby sister weighs 7 pounds.
But to be converted to ounce.
1 pound = 16 ounces
7 pounds = 7*16 ounces
7 pounds = 112 ounces
What’s the correct answer for this?
Answer:
AP = 10
Step-by-step explanation:
According to secant-secant theorem
(PB)(AP)=(PD)(PC)
6(AP) = (5)(12)
AP = 60/6
AP = 10
Answer:
10
Step-by-step explanation:
Applying the secant theorem, we get:
(PB) * (AP) = (PD) * (PC)
6 * (AP) = (5) * (12)
AP = 60/6
= 10
Hope this helps!
my third time posting this question plssss :(
Answer:
Answers are below in bold.
Step-by-step explanation:
The first answer is correct. 1 m² = 10,000cm²
A=2(wl+hl+hw) To find the surface area of the package, use this equation
A=2(18*50+20*50+20*18) Multiply in the parentheses
A=2(900+1000+360) Add in the parentheses
A=2(2260) Multiply
A=4520
The package has a surface area of 4520 cm²
The area of the package is less than the area of the wrapping paper.
So, Dayson can completely cover the package with the wrapping paper.
Sales of the first Quality Mini Buses were as follows: 250 yellow, 150, green, and 100 blue. Assume the relative frequency method is used to assign probabilities for color choice and the color of each car sold is independent of that of any other car sold.
What is the probability that the next bus sold will be yellow or green?
a. 0.10
b. 0.40
c. 0.80
d. 0.50
e. 0.70
Answer:
c. 0.80
Step-by-step explanation:
Probability from relative frequency:
The probability is the number of desired outcomes divided by the number of total outcomes.
What is the probability that the next bus sold will be yellow or green?
250+150+100 = 500 buses sold
Of those, 250+150 = 400 are yellow or green.
400/500 = 0.8
So the correct answer is:
c. 0.80
Person A can complete a task in 1.5 hours. Person B does the same task in 1 hour 20 minutes. Write the ratio of these times in the simplest whole number form.
Answer:
9/8
Step-by-step explanation:
time A / time B = (3/2)/(4/3) = (3/2)(3/4) = (3·3)/(4·2)
time A / time B = 9/8
Danessa needs to compare the area of one large circle with a diameter of 8 to the total area of 2 smalle
diameter one-half that of the large circle.
Which statements about the areas are true? Select three options.
The area of the large circle is 16
The area of one small circle is 4
The area of one small circle will be one-half of the area of the large circle.
The total area of the two small circles will equal that of the large circle
The total area of the two small circles will be one-half of the area of the large circle
Answer:
The area of the large circle is 16π
The area of one small circle is 4π
The total area of the two small circles will be one-half of the area of the large circle
Step by step explanation:
Area if circle = πr²
area of one large circle with a diameter of 8:
r = diameter/2 = 8/2 = 4
Area = π×4² = 16π
total area of 2 smaller diameter one-half that of the large circle.
Area = πr²
Diameter of small circle = 1/2(bigger circle diameter)
Diameter = 8/2 = 4
radius = 4/2 = 2
Area of one small circle = π×(2)² = 4π
Total Area of Two smaller circles= 2(4π) = 8π
Area of two smaller circle = 1/2(area of bigger circle) = 1/2(16π) 8π
Therefore, based on the answer:
The area of the large circle is 16π
The area of one small circle is 4π
The total area of the two small circles will be one-half of the area of the large circle
Answer:
The area of the large circle is 16 pi.
The area of one small circle is 4 pi.
The total area of the two small circles will be one-half of the area of the large circle.
Step-by-step explanation:
To shorten this down for ya lazy people like me the answers are 1, 2, and 5!!!
I got this right on my UNit test review!!!!!
I hope this helps!!!!!!
(x^2-7)(x^2-4) using the FOIL method, multiply the terms of the binomial
Answer:
[tex]x^{4} -11x^{2} +28[/tex]
Step-by-step explanation:
[tex](x^{2} -7)(x^{2} -4)[/tex]
[tex]x^{4} -4x^{2} -7x^{2} +28[/tex]
[tex]x^{4} -11x^{2} +28[/tex]
through: (-1,4), perpendicular to y = x
Answer:
y = -x + 3
Step-by-step explanation:
I graphed the equation on the graph below to show you that it goes through (-1,4) and is perpendicular to y = x.
Which of the following tables shows a valid probability density function? a. x P(X=x) 0 38 1 14 2 38 b. x P(X=x) 0 0.2 1 0.1 2 0.35 3 0.17 c. x P(X=x) 0 910 1 −310 2 310 3 110 d. x P(X=x) 0 0.06 1 0.01 2 0.07 3 0.86 e. x P(X=x) 0 12 1 18 2 14 3 18 f. x P(X=x) 0 110 1 110 2 310 3
Answer:
Step-by-step explanation:
Since we know that for a distribution be a probability density function sum of all the probability events should be equal to 1 and all individual events should have probability between 0 and 1
a. x P(X=x)
0 -----3/8
1 -----1/4
2 -----3/8
P(X=0)+P(X=1)+P(X=2) = 3/8 + 1/4 + 3/8
P(X=0)+P(X=1)+P(X=2) = 6/8 + 2/8 = 1
This is a probability density function
b. x P(X=x)
0 ----0.2
1 ----0.1
2 ----0.35
3 ----0.17
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.2 + 0.1 + 0.35 + 0.17
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.65 + 0.17 = 0.82 ≠ 1
Therefore this is NOT a probability density function
c. x P(X=x)
0---- 9/10
1 ---- −3/10
2 ---- 3/10
3 ---- 1/10
Since P(X=1) is not between 0 and 1
Therefore this is NOT a probability density function
d. x P(X=x)
0 ----0.06
1 ----0.01
2 ----0.07
3 ----0.86
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.06 + 0.01 + 0.07 + 0.86
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.14 + 0.86 = 1
Therefore this is a probability density function
e. x P(X=x)
0 ----1/2
1 ----1/8
2 ----1/4
3 ----1/8
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/8 + 1/4 + 1/8
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/2 = 1
Therefore this is a probability density function
f. x P(X=x)
0 ----1/10
1 ----1/10
2 ----3/10
3 ----1/5
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/10 + 1/10 + 3/10 + 1/5
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 2/10 + 5/10 = 7/10 ≠ 1
Therefore this is NOT a probability density function
In un trapezio rettangolo la base minore, il lato obliquo e l'altezza misurano rispettivamente 60 cm. 95 cm è 76 cm. Calcola il perimetro e l'area del trapezio. THANKS
Answer:
[tex]2p=348 cm\: S=6726 cm^{2}[/tex]
Step-by-step explanation:
Ciao, come stai?
1) Per prima cosa, dobbiamo trovare la misura della base più grande. Scomponendo la figura possiamo visualizzare un triangolo e un quadrato. Ci sono somiglianze con gli angoli. Quindi è un triangolo rettangolo. Applichiamo il teorema di Pitagora:
[tex]a^2=b^2+c^2\\95^2=b^2+76^2\\57=b[/tex]
2) Perimetro:
[tex]2p=60+57+76+60+95\\2p=348 cm[/tex]
3) L' area
[tex]\frac{(B+b)h}{2} =\frac{(117+60)76}{2} =6726 \:cm^{2}[/tex]
A company plans to manufacture a rectangular bin with a square base, an open top, and a volume of 13,500 in3. Determine the dimensions of the bin that will minimize the surface area. What is the minimum surface area
Answer:
Dimensions 30 in x 30 in x 15 in
Surface Area = 2,700 in²
Step-by-step explanation:
Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:
[tex]V=13,500=h*r^2\\h=\frac{13,500}{r^2}[/tex]
The total surface area is given by:
[tex]A=4*hr+r^2[/tex]
Rewriting the surface area function as a function of 'r':
[tex]A=4*\frac{13,500}{r^2} *r+r^2\\A=\frac{54,000}{r}+r^2[/tex]
The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:
[tex]A=54,000*r^{-1}+r^2\\\frac{dA}{dr}=0= -54,000*r^{-2}+2r\\\frac{54,000}{r^2}=2r\\ r=\sqrt[3]{27,000}\\r=30\ in[/tex]
The value of 'h' is:
[tex]h=\frac{13,500}{30^2}\\ h=15\ in[/tex]
The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.
The surface area is:
[tex]A=4*15*30+30^2\\A=2,700\ in^2[/tex]
Na którym rysunku narysowano symetralną odcinka KL?
Która z tych liter nie ma osii symetrii?
Answer:
- Only Drawing D has KL being a symmetrical segment.
- Drawings A, B and C have no axis of symmetry.
- Tylko rysunek D ma KL będący segmentem symetrycznym.
- Rysunki A, B i C nie mają osi symetrii.
Step-by-step explanation:
English Translation
In which drawing was the symmetrical segment of KL drawn? Which of these letters has no axis of symmetry?
Solution
The attached image to the question is presented in the attached image to this Solution.
Symmetry is a concept where a figure/shape has half of its part being a mirror image of the other part.
About the line or axis of symmetry, the structure or figure can be rotated at right angles or whole number multiples of right angles and the resulting structure is still the same as the one we started with.
Of the 4 drawings, only drawing D satisfies this conditions/criteria. And Hence, it is the only drawing amongst the four with an axis of symmetry.
In Polish/Po polsku
Załączony obraz do pytania jest przedstawiony na załączonym obrazku do tego rozwiązania.
Symetria to koncepcja, w której figura / kształt ma połowę swojej części stanowiącą odbicie lustrzane drugiej części.
W odniesieniu do linii lub osi symetrii, strukturę lub figurę można obracać pod kątem prostym lub wielokrotności liczby całkowitej pod kątem prostym, a wynikowa struktura jest nadal taka sama jak ta, od której zaczęliśmy.
Z 4 rysunków tylko rysunek D spełnia te warunki / kryteria. I dlatego jest to jedyny rysunek wśród czterech z osią symetrii.
Hope this Helps!!!
Mam nadzieję że to pomoże!!!
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) – 9? (5 points)
O The graph of y = f(x) will shift up 9 units.
O The graph of y = f(x) will shift down 9 units.
The graph of yf(x) will shift left 9 units,
The groph of yf(x) will shift right 9 units.
Answer:
the graph of y=f(x)will shift up 9 units
Write a real-world situation that could be represented by the system
Y=3x+10
Y=5x+20
Answer:
I have two types of packages that i sell. one has 3 apples and 10 pears, another one has 5 apples and 20 pears. what are the minumum quantitys of each do i have to buy so i can make either all package #1 or only make package#2 with oout any left over pears and apples?
Step-by-step explanation:
i don't know how to explain it but i;ll try. you take the lcm i beleive of the two. i think i may have done it wrong
Kindly tell me the answers of these three
Answer:
1) -4/5,3 Decimal form x= -0.8,3
2) ?
3)sq (x+2)(x+3)+sq x^2 +5x-4=0
Step-by-step explanation:
Hope this helps
Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.
Answer:
Step-by-step explanation:
This is a test of the mean difference between 2 independent groups or populations.
Let μ1 be the mean annual bonus of Company A's employees and μ2 be the mean annual bonus of Company B's employees.
The random variable is μ1 - μ2 = difference in the mean annual bonus of Company A's employees and the mean annual bonus of Company B's employees
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≤ μ2 H0 : μ1 - μ2 ≤ 100
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 100
This is a right tailed test because of the inequality sign at the alternative hypothesis. We need to take samples of annual bonuses from both company's employees and find the averages. Then we would determine the test statistic as well as the p value. We would use the p value with the level of significance to make decisions
find the slope of a line perpendicular to the graph of the equation y=-3x
Answer:
1/3
Step-by-step explanation:
The slope of a perpendicular line is always the negative reciprocal of the slope of the original line.
-1/-3 = 1/3
A restaurant manager determined that about 12 of all customers would wait 20 minutes or more for a table. Which simulation could NOT be used to answer questions about whether a customer would wait?
Answer:
spinner green or blue
Step-by-step explanation:
Flipping a coin is 1/2 probability
Rolling a die and getting a number less than 4 is 1/2 probability
spinner green or blue is (4/6) = 2/3
Marbles is 1/2
Lockheed Martin, the defense contractor designs and build communication satellite systems to be used by the U.S. military. Because of the very high cost the company performs numerous test on every component. These test tend to extend the component assembly time. Suppose the time required to construct and test (called build time) a particular component is thought to be normally distributed, with a mean equal to 60 hours and a standard deviation equal to 9.4 hours. To keep the assembly flow moving on schedule, this component needs to have a build time between 52 and 70 hours. Find the probability that the build time will be such that assembly will stay on schedule.
Answer:
[tex]P(52<X<70)=P(\frac{52-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{70-\mu}{\sigma})=P(\frac{52-60}{9.4}<Z<\frac{70-60}{9.4})=P(-0.851<z<1.064)[/tex]
And we can find this probability with this difference:
[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)[/tex]
And if we use the normal standard distribution or excel we got:
[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)=0.856-0.197=0.659[/tex]
Step-by-step explanation:
Let X the random variable that represent the time required to construct and test a particular component of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(60,9.4)[/tex]
Where [tex]\mu=60[/tex] and [tex]\sigma=9.4[/tex]
We want to find this probability:
[tex]P(52<X<70)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(52<X<70)=P(\frac{52-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{70-\mu}{\sigma})=P(\frac{52-60}{9.4}<Z<\frac{70-60}{9.4})=P(-0.851<z<1.064)[/tex]
And we can find this probability with this difference:
[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)[/tex]
And if we use the normal standard distribution or excel we got:
[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)=0.856-0.197=0.659[/tex]
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean
Answer:
The margin of error for a 95% confidence interval for the population mean is of 1.05 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population(square root of the variance) and n is the size of the sample.
What is the margin of error for a 95% confidence interval for the population mean
36 students, so [tex]n = 36[/tex]
Variance of 10.24, so [tex]\sigma = \sqrt{10.24} = 3.2[/tex]
[tex]M = 1.96*\frac{3.2}{\sqrt{36}} = 1.05[/tex]
The margin of error for a 95% confidence interval for the population mean is of 1.05 years.
