Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Given:
Total number of glasses = 16
Number of glasses containing prune juice = 4
Number of glasses containing apple juice = 2
To find: fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice
Solution:
A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.
Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10
Total number of glasses = 16
So,
Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = [tex]\frac{10}{16}=\frac{5}{8}[/tex]
Consider Statement A and Statement B below:
1. If neither of two real numbers is zero, then their product is also not zero.
2. If a and b are two real numbers, and if ab = 0, then either a = 0 or b= 0.
A. These two statements are equivalent because statement A is the converse of statement B.
B. These two statements are equivalent because statement A is the contrapositive of statement B.
C. These two statements are not equivalent.
Answer:
These two statements are equivalent because statement A is the contrapositive of statement B.
Step-by-step explanation:
In logic, when we have an "if" statement we can have its contrapositive or its converse.
Given a "if p, then q" (p is the hypothesis and q is the conclusion), the converse is "if q, then p", in other words, we interchange the hypothesis and the conclusion.
Now, given a "if p, then q", the contrapositive is "if not q, then not p". In other words, we take the negation of both the hypothesis and the conclusion and then we interchange them.
Now, let's take a look at our statements:
If a and b are two real numbers, and if ab = 0, then either a = 0 or b = 0.
In this case:
p = a and b are two real numbers and ab=0
q = either a = 0 or b = 0
Now, let's take the negative of p and q:
The negative of p would be: a and b are two real numbers and their product is not zero.
The negative of q would be: neither of the two real numbers is zero
Now, given than the contrapositive is "if not q, then not p" we would have:
If neither of two real numbers is zero, then their product is not zero.
We can see that this last sentence is the contrapositive of the first one and thus:
These two statements are equivalent because statement A is the contrapositive of statement B.
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
Solve this inequality.
-35 – 2 >7
A.
B.
C.
D. > -3
Answer:
-2> 7+35
-2>42
0<21
the answer is 0 is less than 21
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
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
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
Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?
Answer:
Reese read 26 pages on Sunday.
Step-by-step explanation:
If she read twice the amount on Saturday than she read on Sunday, then you can replace the days with variables. 2x for Saturday and x for Sunday. That leaves you with 2x + x = 78. This can be simplified to 3x = 78. We can solve this by dividing both sides by 3. This leaves you with x = 26. If x represents the pages read on Sunday then Reese read 26 pages on Sunday.
A miner is trapped in a mine containing 3 doors:1. The first door leads to a tunnel that will take him to safety after 3 hours of travel.2. The second door leads to a tunnel that will return him to the mine after 5 hours of travel.3. The third door leads to a tunnel that will return him to the mine after 7 hours.If we assume that the miner is at all times equally likely to choose any one of the doors (supposing themine shaft is so disorienting that he cannot tell which door he chose before), LetXdenote the lengthof time until the miner reaches safety.Compute the variance, Var(X).
Answer:
The miner should take door number 1
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
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 = 4.5xmy 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.
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
There are 2 new seats in each row in a school auditorium. There are 20 rows in the auditorium. Each new seat costs $84 what is the cost for the new seats
Write the algebraic expression that represents the following:
a. The difference between six times a number and two
b. Five less than the quotient of nine and a number
c. One half of the sum of six times a number and twenty-two
d. Nine less than twice the difference between a number and seven
e. Eleven less than a number squared
Find the population density of domesticated dogs if there are 43,600,000 dogs in the United States and the area of the United States is 3,794,083 square miles. Round to the nearest 10th
Answer:
11.49 dogs/ square mile
Step-by-step explanation:
Population density of any place is number of living being living in that area per unit area.
Population density = number of living being/ area of the place
given
number of dogs= 43,600,000
area = 3,794,083 square miles
population density of domesticated dogs = 43,600,000 /3,794,083
= 11.4915 dogs/ square mile
population density of domesticated dogs, rounded to the nearest 10th
is 11.49 dogs/ square mile.
Question 1
A student said, "To find the value of 109.2 : 6 I can divide 1,092 by 60."
Do you agree with her? Explain your reasoning.
B 1 U
14
X,
E = = =
[D] TTT
12pt
Answer:
Yes, her reasoning is correct
Step-by-step explanation:
Given the ratio: 109.2 : 6
Written in fractional form, we have:
[tex]109.2: 6=\dfrac{109.2}{6}[/tex]
Now:
[tex]\dfrac{109.2}{6}=\dfrac{109.2}{6}X1, $ Let 1=\dfrac{10}{10}, \\\\=\dfrac{109.2}{6}X\dfrac{10}{10}\\\\=\dfrac{1092}{60}[/tex]
Therefore, the student's reasoning is correct. In fact, as a check:
[tex]\dfrac{109.2}{6}=18.2\\\\\dfrac{1092}{60}=18.2[/tex]
We would obtain the same result in both cases.
Answer:
yes
Step-by-step explanation:
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
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]
The number of people attending graduate school at a university may be
modeled by the quadratic regression equation y = 10x2 - 40x+8, where x
represents the year. Based on the regression equation, which year is the best
prediction for when 2528 people will attend graduate school?
O A. Year 15
B. Year 23
O C. Year 18
D. Year 20
Answer:
It’s C
Step-by-step explanation:
But thanks for helping me get it wrong toxo360❤️
In the regression equation, Year 18 is the best prediction for when 2528 people will attend graduate school.
What is the quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of: ax² + bx + c = 0.
The number of people attending graduate school at a university may be modeled by the quadratic regression equation y = 10x2 - 40x+8, where x represents the year.
The regression equation, which year is the best prediction for when 2528 people will attend graduate school is;
[tex]\rm y = 10x^2 - 40x+8\\\\2528 = 10x^2 - 40x+8\\\\ 10x^2 - 40x+8\\\\ 10x^2 - 40x+8-2528=0 \\\\ 10x^2 - 40x-2520=0\\\\\text{Divide by 10 both sides}\\\\x^2-4x-252=0\\\\x^2-18x+14x-252=0\\\\x(x-18)+14(x-18)=0\\\\(x-18)(x+14)=0\\\\x-18=0, \ x=18\\\\x+14=0, \ x=-14[/tex]
Hence, the regression equation, Year 18 is the best prediction for when 2528 people will attend graduate school.
Learn more about quadratic equations here;
https://brainly.com/question/24298861
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how much of other chemicals must be evaporated from 400grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? correct your answer to the nearest whole number
Answer:
80 grams
Step-by-step explanation:
Weight of 24% solution = 400 grams
Alcohol content= 24%
Amount of alcohol= 400*0.24= 96 grams
Weight of 30% solution with same amount of alcohol:
96/0.3= 320 gramsThe difference in weights is the other chemicals evaporated:
400-320=80 gramsWhen is a rectangle a square?
Answer:
A. When its sides are congruent
Step-by-step explanation:
By definition a square is a four sided polygon (shape) which has four right angles and four sides of equal length.
So, when a rectangle has all congruent sides, its a square because its a rectangle so it has four right angles, and congruent sides are sides of the same length.
B is incorrect because a rectangle can have four right angles but have differing side lengths
C is incorrect because again a rectangle can have parallel sides but have differing side lengths
D is incorrect because it can have convex angles but again have differing side lengths
When sides of rectangle are congruent, then it is a square. Therefore, the correct answer is option A.
A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
If all the sides of rectangle are congruent, then it is square.
Therefore, the correct answer is option A.
Learn more about the square here:
brainly.com/question/28776767.
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Henry hoards a hundred hens. Every day, each hen lays an egg with probability 0.8 independently of all others. Henry sells each egg for 3 cents, except that on half the days, his dog Barkie breaks half the eggs laid that day (and 1.5 eggs is as sellable as 1), and on the remaining half of the days, Barkie breaks 30 eggs. What is the probability that Henry makes more than a $1.30 today
Answer:
99.27%
Step-by-step explanation:
We have to:
sample size (n) = 100
p = 0.8
1 egg = 3 * 0.01 = 0.03
eggs = 100 - 30 broken eggs = 70
Let's find the probability of winning more than $ 1.30 today:
p (x> 1.30) = p (z, (x -m) / sd)
average earnings:
per day would be:
m1 = 100 / 1.5 * 0.8 * 0.03
m1 = 1.6
sd1 = (m1 * (1 - p)) ^ (1/2) = (1.6 * (1 - 0.8)) ^ (1/2)
sd1 = 0.566
earnings for broken eggs:
m2 = 70 * 0.8 * 0.03
m2 = 1.68
sd2 = (m2 * (1 - p)) ^ (1/2) = (1.68 * (1 - 0.8)) ^ (1/2)
sd2 = 0.58
Now the total profit would be:
m = m1 + m2 = 1.6 + 1.68
m = 3.28
sd = sd1 ^ 2 + sd2 ^ 2 = 0.566 ^ 2 + 0.58 ^ 2
sd = 0.81
now yes, replacing:
p (x> 1.30) = p (z> (1.3 - 3.28) /0.81)
p (x> 1.30) = p (z> -2.44)
for this z = 0.0073
Therefore the probability would be:
1 - 0.0073 = 0.9927
That is, we would have a 99.27% probability of achieving the goal.
In a random sample of 25 laptop computers the mean repair cost was $150 with a standard deviation of $35. Compute the 99% confidence interval for u
Answer:
[tex]150-2.797\frac{35}{\sqrt{25}}=130.421[/tex]
[tex]150+2.797\frac{35}{\sqrt{25}}=169.579[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=150[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=35 represent the sample standard deviation
n=25 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=25-1=24[/tex]
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex] and the critical value for this case [tex]t_{\alpha/2}=2.797[/tex]
Now we have everything in order to replace into formula (1):
[tex]150-2.797\frac{35}{\sqrt{25}}=130.421[/tex]
[tex]150+2.797\frac{35}{\sqrt{25}}=169.579[/tex]
Please see picture of problem
Answer:
w = 9, l = 12
Step-by-step explanation:
If w is the width and l is the length, then:
l = 2w − 6
The area of the rectangle is width times length.
A = wl
Substituting and solving:
108 = w (2w − 6)
108 = 2w² − 6w
54 = w² − 3w
0 = w² − 3w − 54
0 = (w + 6) (w − 9)
w = -6 or 9
The width is 9, so the length is 12.
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:
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!
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]
Box has 10 M&M candies: 5 red and 5 blue.
Two candies are taken from this box.
Find the probability that the first randomly taken candy will be red and second will be red again.
Taken candy doesn't go back to the box.
Simplify final fraction.
Answer:
As a simplified fraction, the probability that the first randomly taken candy will be red and second will be red again is [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the candies are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
2 candies from a set of 5. So
[tex]D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]
Total outcomes:
2 candies from a set of 10. So
[tex]T = C_{10,2} = \frac{10!}{2!(10-2)!} = 45[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{10}{45} = \frac{2}{9}[/tex]
As a simplified fraction, the probability that the first randomly taken candy will be red and second will be red again is [tex]\frac{2}{9}[/tex]
Mark Brainliest .........
Answer:
work is shown and pictured
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