Answer:
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
Step-by-step explanation:
Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.
To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?
Proof -
By the given information, we get the stohastic matrix
[tex]H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right][/tex]
As we know that,
The matrix is a Markov chain [tex]x_{k+1} = Hx_{k}[/tex]
Let
The initial state vector be
[tex]x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right][/tex]
we choose this initial vector because given that If the animal chooses food #1 on an initial trial.
Now,
[tex]x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right][/tex]
∴ we get
[tex]x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right][/tex]
Now,
[tex]x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right][/tex]
∴ we get
[tex]x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right][/tex]
∴ we get
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
In a cylindrical wooden block with a radius of 7 cm and a height of 14 cm, hemispherical blocks with
a radius of 7 cm are carved out from both ends. Find the volume of the resulting solid.
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Answer:
1372π/3 cm^3 ≈ 1436.8 cm^3
Step-by-step explanation:
The diameter and height of the cylinder are both 14 cm. The resulting solid will be a 14 cm sphere. Its volume is ...
V = 4/3πr^3 = 4/3π(7 cm)^3 = 1372π/3 cm^3 ≈ 1436.8 cm^3
Need help I can’t solve it
Answer:
Coupon A is better by $2.80.
Step-by-step explanation:
You want to know how much better the best price is between coupon A's $55 rebate on $87 worth of pants, or coupon B's 60% off.
ReductionThe price reduction offered by coupon B is ...
0.60 × $87 = $52.20
ComparisonClearly, the $55 reduction offered by coupon A is a greater reduction than the $52.20 reduction offered by coupon B. The difference in value is ...
$55.00 -52.20 = $2.80
Coupon A gives the lower price by $2.80.
Juanita runs every fifth day and swims every third day. If Juanita runs and swims today, in how many days will she run and swim again on the same day?
Answer:15
Step-by-step explanation:multiples of 3 and 5 and the LCM of 5 and 3 is 15
Answer:
nadara y correra hasta dentro de 15 días
Step-by-step explanation:
3 y 5 se multiplican y dan 15, entonces durante ese tiempo, Juanita correra 2 veces y nadara 4 veces, cuando sea el día en el que correra por tercera vez, tambien será el día en el que nadará por quinta vez
Solve for x.
\12x + 3
13x + 2
x = [?]
Answer:
x=7
Step-by-step explanation:
25x+5=180
-5 -5
25x=175
/25 /25
Im strugling on these question
Answer and Step-by-step explanation:
How're you struggling with this? Simply look for a point that is inside of the triangle.
The answer is A. (-1, -2)
because this point is INSIDE the triangle.
#teamtrees #PAW (Plant And Water)
Consider the following two questions designed to assess quantitative literacy.
What is 15% of 1000?
A store is offering a 15% off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale?
Suppose the first question is asked of 200 randomly selected college students, with 168 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 147 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.)
State the relevant hypotheses.
H0: p1 − p2 = 0
Ha: p1 − p2 < 0H0: p1 − p2 = 0
Ha: p1 − p2 ≠ 0 H0: p1 − p2 = 0
Ha: p1 − p2 > 0H0: p1 − p2 < 0
Ha: p1 − p2 = 0H0: p1 − p2 > 0
Ha: p1 − p2 = 0
Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z=P-value=
State the conclusion in the problem context.
Fail to reject H0. The data does not suggest that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.Reject H0. The data does not suggest the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one. Fail to reject H0. The data suggests the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.Reject H0. The data suggests that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Answer:
A customer would save $ 150 on the television during this sale and pay
$ 850.
Reject H0. The data suggests that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one
Step-by-step explanation:
15% of 1000
=0.15 *1000= $ 150
A customer would save $ 150 on the television during this sale.
p1 = the true proportion students who answered the question without context = 168/200
p2 = the true proportion of students who answered the question with context correctly = 147/200
The null and alternate hypotheses are
H0: p1 − p2 = 0 i.e the true proportion of correct responses to the question without context is the same as that for the one with context
against the claim
Ha: p1 − p2 > 0 that is the true proportion of correct responses to the question without context exceeds that for the one with context
2) The significance level is set at 0.05
3) The critical region is z > ± 1.645
4) The test statistic
Z= p1-p2/ sqrt [pcqc ( 1/n1+ 1/n2)]
Here p1= 168/200= 0.84
and p2= 147/200=0.735
pc = 168+147/200+200
pc= 315/400= 0.7875
qc= 1-pc= 1-0.7875=0.2125
5) Calculations
Z= p1-p2/ sqrt [pcqc ( 1/n1+ 1/n2)]
z= 0.84-0.735/√ 0.7875*0.2125( 1/200+ 1/200)
z= 0.105/0.0409076
z= 2.5667
6) Conclusion
Since the calculated value of z= 2.5667 lies in the critical region the null hypothesis is rejected and it is concluded that the true proportion of correct responses to the question without context exceeds that for the one with context.
The value of z is 2.5668.
The value of p is 0.01016
The value of 1/2÷1/3=
Ming used the calculations shown to find out how much he would spend on 6 pound of ground beef if 10 pounds cost $25.00 what was mings error
Answer:
6 pounds of ground beef cost $15.
Step-by-step explanation:
[tex]\frac{6}{10} :\frac{y}{25}[/tex]
10 × y = 6 × 25
10y = 150
10y ÷ 10 = 150 ÷ 10
y = 15
Green Valley Middle School wants to raise $7,500 for new equipment. If grades 6 and 7 each raise $2,450.25, how much money does grade 8 need to raise?
Answer:
2599.50
Step-by-step explanation:
7500 - 2(2450.25) = 2599.50
What are four consecutive even integers if the first integer is −4? Responses
A) -4,-3,-2,-1
b) -4,-2,0,2
c) -4,-6,-8,-10
D)-4,-5,-6,-7
The asked consecutive even integers are -4,-2,0,2
What are consecutive integers?Consecutive integers are whole numbers that follow each other without gaps. For example, 15, 16, 17 are consecutive integers.
Given that, what are four consecutive even integers if the first integer is −4
We know that, Consecutive even integers are even integers that follow each other, and they differ by 2. If x is an even integer, then x + 2, x + 4 and x + 6 are consecutive even integers.
Therefore, here x = -4,
-4+2 = -2
-4+4 = 0
-4+6 = 2
Hence, the asked consecutive even integers are -4,-2,0,2
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When calculating the area of a figure that is measured in feet, the answer should be reported as...
Which conditional statement has a false converse? If a figure is a square, then it has four sides. If a point has x-coordinate 0, then it lies on the y-axis. If two angles are congruent, then they have the same measure. If two planes are parallel, then they have no points in common.
The conditional statement has a false converse will be the four-sided polygon may be square. Then the correct option is A.
What is the conditional statement?There have been two main categories of arguments in the studies of logic: conditional statements and polyamorous statements. These assertions, which are referred to as compound statements, are created by combining two other statements.
The converse statement should also be true when its condition is reversed.
Let's check all the options. Then we have
A. If a figure is a square, then it has four sides. The converse of the statement is false.
B. If a point has an x-coordinate 0, then it lies on the y-axis. The converse of the statement is true.
C. If two angles are congruent, then they have the same measure. The converse of the statement is true.
D. If two planes are parallel, then they have no points in common. The converse of the statement is true.
The conditional statement has a false converse will be the four-sided polygon may be square. Then the correct option is A.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
D.
Step-by-step explanation:
4/5 ÷ 3 = 4/5 * 1/3
This is 1/3 of 4/5.
9x9 = ? whattttttttttttttttt
Answer:
81
Step-by-step explanation:
9x9 = 81
Find the area of the following figure
Answer:
880?
Step-by-step explanation:
I just woke up
Answer 880 is your answer
Step-by-step explanation:
What is the probability of the spinner landing on the section labeled G?
Hi there!
[tex]\large\boxed{P = \frac{1}{4}}[/tex]
We can assume from the image that the region G is approximately 1/4 of the total spinner.
Thus, the probability of the spinner landing on section G is 1/4.
4) There are 14 pieces of candy in a bag. Four are broken. What is the probability of reaching into
the bag and pulling out a non-broken piece?
Answer:
I would say it's a 10:4 ratio.
Determine the value of x.
A) 2√3 B) 6√3 C) 12 D) 12√3
The required measure of the value of x is given as 2√3. Option A is correct.
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
here,
Consider the given triangle,
perpendicular = 6
base = x
Applying trigonometric operation,
tan30 = perpendicular/base
tan30 = 6/ x
x = 6/√3
x = 2√3
Thus, the required measure of the value of x is given as 2√3. Option A is correct.
Learn more about trigonometry equations here:
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Helpppppp
Unit rate with fractions. A crew of landscapers mowed 1/5 of a lawn in 20
Answer:
1/5 lawn = 20 min.
? = 1 min
0.05 lawn in 1 minute
rate of 0.05 mowed per minute.
Pls include step by step explaination
Answer:
X = 2/3
Step-by-step explanation:
there is some misinformation here but I’m just gonna assume these rectangles are proportional.
If the longer side for the first one is 3 and the longest side for the second is 2 meaning that the second side is multiplied by 2/3
So if we multiply 1 by 2/3, it will be 2/3 meaning x = 2/3
hope this helps :)
Can somone help with this please and thank you
Answer:
they are equivalent just trust me
Step-by-step explanation:
m/4n m*2 and 4n82 = 2m/9n is same as m/4n *2
Answer:
Equivalent
Step-by-step explanation:
Yes, they are equivalent, we know that because if we multiply both the numerator and the denominator of the first fraction by 2, we will get the second one.
[tex]\frac{m}{4n} = \frac{m * 2}{4n*2} = \frac{2m}{8n}[/tex]
PLEASE HELPP
Classify the solid.
Your answer
Answer:
Pentagonal pyramid
Step-by-step explanation:
Hope this helps
Tamara received a credit of $25 at the yarn store. What amount can she spend using the credit?
$50
$40
$30
$20
Find the area of a regular 12-sided polygon inscribed in a circle of radius
8 cm.
area of n sided polygon inscribed in a circle is
A = (1/2)nr²sin(360/n) (r = radius of circle)
A = (1/2)12*8²*sin30
= 1/2*12*64*1/2
A = 192 square unit
750 dag = kg can u help me
Solve for x.
A: 14
B: 8
C: 11
D: 9
An acute triangle is made up of three acute angles. An obtuse triangle is formed by one acute angle and two obtuse angles and x = 9.7692307692
what is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. In Euclidean geometry, any three points identify a distinct triangle and, concurrently, a distinct plane if they are not collinear.
13x + 3 + 40 + 10 = 180
13x = 127
x = 9.7692307692
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You can perform 6 push-ups in 16 seconds. Write and
graph an equation that represents the relationship between
time and the number of push-ups. At this rate, how many
pushups can you perform in 2 minutes?
Answer:
320 pushups
Step-by-step explanation:
16/6= 8/3
8/3*120=32
Which problem situation matches the
equation $95.25 = 15p?
A Cassie is paid $95.25 for 15 hours
of work. Find p, the amount she
was paid per hour.
B Kris is paid $6.35 per hour for
mowing the lawn. Find p, the
amount he is paid for 15 hours of
mowing.
CA iPad was on sale for $95.25. Find
p, the amount Noah needs to buy
the iPad if he already has $15.
D Fifteen friends spend $95.25 each
for tickets to a Cowboy's game.
Find p, the amount they paid total.
Answer:
Step-by-step explanation:
Which problem situation matches the
equation $95.25 = 15p?
So We Can Just Cross B Cause $6.35 Wasnt Even In The equation
Lets look at A.
So Im pretty sure its A, But Lets look at the rest.
.
D Wouldnt Work Cause It Says The Spend $95.25 EACH
C dont work so its A.
A map has a scale of 1 inch=35 miles. What is the actual distance if the distance on the map is 3.5 inches
Answer:
112.5 miles
Step-by-step explanation:
scale: 1 inch= 35 miles
this means that for every inch on a map, that is 35 miles in real life.
if the distance on a map is 3.5 inches, and you want to find out how much the distant would be in real life, all you have to do is:
3.5 x 35 = 112.5
someone help me please ?
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Answer:
3/2
Step-by-step explanation:
The scale factor is the ratio of corresponding side lengths.
larger/smaller = (21/2)/7 = 21/14 = 3/2
The scale factor is 3/2.