Answer:
63 cubic inches
Step-by-step explanation:
You have to first find the volume of each mold:
6 × 4 × 2= 48 cubic inches
3 × 5 × 1= 15 cubic inches
Add these two volumes together to find the overall volume of the whole sand castle.
48+15= 63 cubic inches
Answer:
The whole castle can hold 63 in² of sand.
Step-by-step explanation:
First, find the volume of the first mold.
V = whl Substitute
V = (6)(2)(4) Multiply
V = 48 in²
Now, find the volume of the second mold.
V = whl Substitute
V = (5)(1)(3) Multiply
V = 15 in²
Add together both volumes to find the volume of the whole castle.
48 + 15 = 63 in²
Seja a função real dada por f(x)=4x-9. Calcule f(6) - f(5). ( ) 4 ( ) 1 ( ) 2 ( ) -4 ( ) -1
Answer:
4
Step-by-step explanation:
A função em questão, f(x), é:
[tex]f(x)=4x-9[/tex]
Primeiramente calcule os valores das funções para x=5 e x=6:
[tex]f(5)=4*5-9\\f(5)=11\\f(6)=4*6-9\\f(6)=15[/tex]
Em seguida, subtraia f(5) de f(6):
[tex]f(6)-f(5) = 15-11\\f(6)-f(5) = 4[/tex]
A resposta para o problema é 4
g/5 - 3 > 37. Solve for g. PLEASE HELPPP TYSM
Answer:
g = 200
Step-by-step explanation:
trust me.
I big brain.
The temperature outside when Colin went to bed was -4°F. When he woke up the next
morning, it was -11°F outside. Describe the change in temperature by completing the
statements.
Step-by-step explanation:
The temperature outside when Colin went to bed was -4°F. When he woke up the next morning, it was -11°F outside
To find the change in the temperature , find the difference in temperature
Change in temperature = temperature in morning - temperature at night
change in temperature = [tex]-11 -(-4)= -7[/tex]
temperature changed by -7 °F
So the temperature is dropped by 7°F
Answer:
the temperature is dropped by 7°F
The temperature change when he woke up the next morning given the data was –7 °F.
Data obtained from the questionFrom the question given above , the following data were obtained:
Temperature at night (T₁) = –4 °F Temperature in the morning (T₂) = –11 °F Change in temperature (ΔT) =? How to determine the change in the temperatureThe temperature change when Colin woke up can be obtained by taking the difference in the temperature at night and morning. This is illustrated as follow:
ΔT = T₂ – T₁
ΔT = –11 – (–4)
ΔT = –11 + 4
ΔT = –7 °F
Thus, from the calculation made above, we can conclude that there was a temperature drop of –7 °F when he woke up the next morning
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 400 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 397 grams with a standard deviation of 25. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answer:
Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]
Step-by-step explanation:
The decision rule for rejecting the null hypothesis is shown below:-
The machine is thought to be underfilling so that the test is left tailed.
Now the Degrees of freedom is
= 9 - 1
= 8
Critical left tailed value t for meaning level [tex]8 \ df[/tex] and 0.025 = -2.306
Therefore Decision rule will be in the following way:
Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]
QUALITY CONTROL1)Specifications for a part for a DVD player state that the part should weigh between 24.6 and 25.6 ounces. The process that produces the parts has a mean of 25.1 ounces and a standard deviation of .26 ounce. The distribution of output is normal. a)What control chart will you use and why?b)With a 2-sigma confidence, what are the upper and lower control limitsif sample of n = 11are taken and the process is in control (random)?c)Is the process in control
Answer:
Step-by-step explanation:
Given that,
μ = 25.1
σ = 0.26
a) since standard deviation is ideal measure of dispersion , a combination of control chart for mean x and standard deviation known as
[tex]\bar x \\\text {and}\\\mu[/tex]
Chart is more appropriate than [tex]\bar x[/tex] and R - chart for controlling process average and variability
so we use
[tex]\bar x \\\text {and}\\\mu[/tex]charts
b)
n = 11
we have use 2 σ confidence
so, control unit for [tex]\bar x[/tex] chart are
upper control limit = [tex]\mu +2\times\frac{ \sigma}{\sqrt{n} }[/tex]
lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]
control limit = μ
μ = 25.1
upper control limit =
[tex]25.1+2\times \frac{0.26}{\sqrt{11} } \\\\=25.2567[/tex]
lower control limit =
[tex]25.1-2\times \frac{0.26}{\sqrt{11} } \\\\=24.9432[/tex]
Upper control limit and lower control limit are in between the specification limits , that is in between 24.9 and 25.6
so, process is in control
c) if we use 3 sigma limit with n = 11
then
upper control limit = [tex]\mu +3\times\frac{ \sigma}{\sqrt{n} }[/tex]
[tex]25.1+3\times\frac{0.26}{\sqrt{11} } \\\\=25.3351[/tex]
lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]
[tex]25.1-3\times\frac{0.26}{\sqrt{11} } \\\\=24.8648[/tex]
control limit is 25.1
Then, process is in control since upper control limit and lower control limit lies between specification limit
So, process is in control
A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle
can take no longer than 3 minutes. Which graph represents the overall equation represented by this scenario (all points
may not apply to the scenario)?
Answer:
The inequality representing the time taken by the entire cycle is:
[tex]4x+y\leq 3[/tex]
Step-by-step explanation:
The time taken to complete one cycle of a manufacturing machine is no longer than 3 minutes.
It is provided that the manufacturing machine has two processes.
One of them is repeated 4 times and the second only once.
Assume that the variable x represents the time taken to complete the first process once.
Then the time taken to complete the first process 4 times would be, 4x.
Also assume that the variable y represents the time taken to complete the second process.
Then the inequality representing the time taken by the entire cycle is:
[tex]4x+y\leq 3[/tex]
Consider the graph below representing the above equation.
Answer: D
Step-by-step explanation:
Given that circle Q has a radius of 5 and a center of (1,4), which point lies on the perimeter of circle Q?
Answer:
(x-1)^2 + (y-4)^2 = 5^2
Step-by-step explanation:
In order to find the points that lie on the perimeter of the circle, you find the algebraic equation of the circle.
The general equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (1)
The last is a circle centered at the point (h,k) and with radius r.
In this case you have a circle with a radius of r = 5, and the circle is centered at (1,4). Then, you have:
h = 1
k = 4
r = 5
You replace the values of h, k and r in the equation (1):
[tex](x-1)^2+(y-4)^2=5^2[/tex]
All point that lies on the curve of the last equation, are point that lie on the perimeter of the circle
Please answer this question !! Thank you !! Will give brainliest !! Really important !!
Answer:
0 = 3x -2y -6
Step-by-step explanation:
The general form of the equation of a line is 0 = Ax + By + C
y = 3/2x -3
Subtract y from each side
0 = 3/2x -y -3
Multiply each side by 2
0 = 3x -2y -6
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a gender selection method used to increase the likelihood of a baby being born a girl, 1961 users of the method gave birth to 961 boys and 1000 girls. There is about a 20% chance of getting that many girls if the method had no effect. 1. Does the weight loss program have statistical significance?A. Yes, the program is statistically significant because the results are unlikely to occur by chance.B. Yes, the program is statistically significant because the results are likely to occur by chance.C. No, the program is not statistically significant because the results are likely to occur by chance.D. No, the program is not statistically significant because the results are unlikely to occur by chance.2. Does the weight loss program have practical significance?A. Yes, the program is practically significant because the results are too unlikely to occur by chance.B. No, the program is not practically significant because the results are likely to occur even if the weight loss program has no effect.C. No, the program is not practically significant because the amount of weight lost is trivial.D. Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.
Answer:
C. No, the program is not statistically significant because the results are likely to occur by chance.
Step-by-step explanation:
At a significance level that is smaller than 0.2, the effect is not significant.
We have a P-value of 20%, which means that we have 20% chances of getting this sample given that the method has no effect.
We then can conclude that there is not enough evidence to support the claim that the method is effective.
prove
cos A /(1- sin A) = (1 + sin A)/cos A
Answer:
answer is in exaplation
Step-by-step explanation:
cosA
+
cosA
1+sinA
=2secA
Step-by-step explanation:
\begin{lgathered}LHS = \frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=\frac{cos^{2}A+(1+sinA)^{2}}{(1+sinA)cosA}\\=\frac{cos^{2}A+1^{2}+sin^{2}A+2sinA}{(1+sinA)cosA}\\=\frac{(cos^{2}A+sin^{2}A)+1+2sinA}{(1+sinA)cosA}\\=\frac{1+1+2sinA}{(1+sinA)cosA}\end{lgathered}
LHS=
1+sinA
cosA
+
cosA
1+sinA
=
(1+sinA)cosA
cos
2
A+(1+sinA)
2
=
(1+sinA)cosA
cos
2
A+1
2
+sin
2
A+2sinA
=
(1+sinA)cosA
(cos
2
A+sin
2
A)+1+2sinA
=
(1+sinA)cosA
1+1+2sinA
/* By Trigonometric identity:
cos² A+ sin² A = 1 */
\begin{lgathered}=\frac{2+2sinA}{(1+sinA)cosA}\\=\frac{2(1+sinA)}{(1+sinA)cosA}\\\end{lgathered}
=
(1+sinA)cosA
2+2sinA
=
(1+sinA)cosA
2(1+sinA)
After cancellation,we get
\begin{lgathered}= \frac{2}{cosA}\\=2secA\\=RHS\end{lgathered}
=
cosA
2
=2secA
=RHS
Therefore,
\begin{lgathered}\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=2secA\end{lgathered}
1+sinA
cosA
+
cosA
1+sinA
=2secA
A curved graph could be a example of
Answer:On a graph, these values form a curved, U-shaped line called a parabola. All quadratic functions form a parabola on a graph. ... Quadratic functions are used to describe things with smooth symmetrical curves, like the path of a bouncing ball or the arch of a bridge.
Step-by-step explanation:
Keep gettin those wrong. Please help!!!
Answer: About 14.14 in^3
Step-by-step explanation:
We know that the circumference of a sphere is C=2πr. We are given that the circumference is 9.42 in. We can find the radius to get our volume.
[tex]9.42=2\pi r[/tex]
[tex]4.71=\pi r[/tex]
[tex]r=1.5\\[/tex]
Now that we know radius, we can find our volume.
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]
[tex]V=14.14in^3[/tex]
36 inches, 20 inches, and 24 inches. What type of triangle did Rosa draw?
Answer:
Scalene triangle
Step-by-step explanation:
PPPLLLLLEEAAASSSEEE HELP!!!!!!!!!
Consider the following situation, which involves two options. Determine which option is less expensive. Are there unstated factors that might affect your decision?
You currently drive 275 miles per week in a car that gets 16 miles per gallon of gas. You are considering buying a new fuel-efficient car for $18 comma 000 (after trade-in on your current car) that gets 44 miles per gallon. Insurance premiums for the new and old car are $1000 and $600 per year, respectively. You anticipate spending $1100 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?
Over a five-year period, the cost of the old car is $____ and the cost of the new car is $_____
Thus, over a five-year period, it is less expensive to keep the old car or buy the new car?
Answer:
Step-by-step explanation:
Please answer this correctly
Answer:
20% is the correct answer
Answer:
50%
Step-by-step explanation:
40 is the median.
From median to upper quartile is 25% & form from upper quartile to maximum is 25%
So, 25 + 25 = 50 %
A customer will be charged extra if the weight of their suitcase is above 48 pounds.
Write an inequality to represent w, the weight of the suitcase in pounds, that will have an extra charge.
Enter your answer by clicking and using the expression evaluator.
Answer:
[tex]w>48[/tex] pounds
Step-by-step explanation:
The customer will be charged extra if the weight of their suitcase is above 48 pounds.
Let the weight of the suitcase = w (in pounds)
Therefore, w above (greater than) 48 pounds is written mathematically as:
[tex]w>48[/tex] pounds
This is the inequality that represents w, the weight of the suitcase in pounds, that will have an extra charge.
How to solve? What are the rules in BODMAS
Answer:
18/35
Step-by-step explanation:
1 1/5 ÷ 2 1/3
Change from mixed numbers to improper fractions
1 1/5 = (5*1+1)/5 = 6/5
2 1/3 = (3*2+1)/3 = 7/3
6/5÷ 7/3
Copy dot flip
6/5* 3/7
18/35
Answer:
Step-by-step explanation:
I don't say you must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me my friend...
Gracie went to Home Depot to buy wall-to-wall carpeting for her house. She needs 104.8 square yards for downstairs, 17.4 square yards for halls, and 165.8 square yards for the upstairs bedrooms. Gracie chose a shag carpet that costs $13.95 per square yard. She ordered foam padding at $2.75 per square yard. The installers quoted Gracie a labor cost of $5.75 per square yard in installation.Whatb will the total job cost Gracy?
Add the rooms together to find total square yards:
104.8 + 17.4 + 165.8 = 288 square yards
Add the costs together: 13.95 + 2.75 + 5.75 = $22.45 per square yard
For total cost, multiply total square yards by total cost per square yard
288 x 22.45 = 6,465.60
Total cost: $6,465.60
The total job cost Gracie is $6,465.60.
To find the total job cost Gracie doneStep 1:
Add the rooms together to find total square yards
=104.8 + 17.4 + 165.8
= 288 square yards
Step 2:
Add the costs together
= 13.95 + 2.75 + 5.75
= $22.45 per square yard
Step 3:
For total cost, multiply total square yards by total cost per square yard
=288 x 22.45
= 6,465.60
Therefore, the total cost: $6,465.60
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Using the graph as your guide, complete the following statement.
The discriminant of the function is
O A. negative
OB zero
O C positive
Answer:it’s ZERO
Step-by-step explanation:
The discriminant of the function is zero
What is a function?A relation is a function if it has only One y-value for each x-value.
The discriminant tells you where the graph of the parabola goes through the x-axis, if at all.
If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis;
if the discriminant is positive the parabola will go through the x axis in 2 places;
if the discriminant is 0 the parabola will touch the x-axis in 1 place.
Our discriminant is 0 since the parabola only touches the x-axis but does not go through.
Hence, the discriminant of the function is zero
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1 point
4. A tin can in the shape of the cylinder shown is filled with coconut oil. If
coconut oil costs $0.01 per cubic centimeter, what is the cost of filling the
tin can with coconut oil?
8 cm
O
A. $603.10
B. $12.06
O ooo
c. $6.03
O
D. $1.92
Answer:
$6.03
Step-by-step explanation:
Let's begin by listing out the given variables:
height (h) = 12 cm, diameter (d) = 8 cm, r = d ÷ 2 ⇒ r = 4 cm, cost of coconut oil (c) = $0.01 /cm³
The formula of cylinder is given by:
V = πr²h = π * 4² * 12 = 603.1858 cm³
cost of filling the tin can with coconut oil = cost of coconut oil * Volume of cylinder
Cost = c * V = 0.01 * 603.1858
Cost = $6.03
Nia and Trey both had sore throats, so their mom told them to gargle with warm salt water. Nia mixed 1 teaspoon salt with 3 cups warm water. Trey mixes 1 /2 teaspoon salt with one and 1/2 cups warm water. Nia tasted Trey’s water and said, “I added more salt, so I expected that mine would be more salty, but they taste the same! Explain why both salt water mixtures taste the same.
Answer:
Each mixture has the same amount of salt for every 1 cup of water.
Step-by-step explanation:
It is provided that:
Nia mixed 1 teaspoon salt with 3 cups warm water. Trey mixes 1 /2 teaspoon salt with one and 1/2 cups warm water.The ratio of the number of teaspoons of salt to the number of cups of water is 1 : 3 in Nia's solution.
On dividing the amount of salt and the amount of water by 3, the ratio will be the same.
[tex]\text{Salt}: 1\div3=\frac{1}{3}\\\\\text{Water}:3\div3=1\\[/tex]
Thus 1 : 3 is equivalent to the ratio [tex]\frac{1}{3}:1[/tex], which means that Nia's solution has [tex]\frac{1}{3}[/tex]teaspoon of salt for every cup of water.
The ratio of the number of teaspoons of salt to the number of cups of water is [tex]\frac{1}{2}:1\frac{1}{2}[/tex] in Trey’s solution.
On dividing the amount of salt and the amount of water by [tex]1\frac{1}{2}[/tex], the ratio will be the same.
[tex]\text{salt}:\frac{1}{2}\div 1\frac{1}{2}=\frac{1}{3}\\\\\text{Water}:1\frac{1}{2}\div1\frac{1}{2}=1[/tex]
So Trey’s ratio is also equal to the ratio [tex]\frac{1}{3}:1[/tex].
Since each mixture has the same amount of salt for every 1 cup of water, they are equally salty and taste the same.
There are 4, 6, and 7 points on three lines. How many quadrilaterals is it possible to create with given points as vertices?
Answer:
1707
Step-by-step explanation:
Let's designate the three sets of collinear points, A, B, C, having 4, 6, 7 points, respectively.
Since there are 3 sets of collinear points, exactly two of the vertices must come from the same set.
For two vertices from set A, the remaining two must come from the 13 members of sets B and C. There are a total of (4C2)(13C2) = 468 such quadrilaterals.
For two vertices from set B, we have already counted the quadrilaterals that result when the remaining two are from set A. There are 4·7 = 28 ways to have one each from sets A and C, and 7C2 = 21 ways to have two from set C. Thus, the additional number of quadrilaterals having 2 vertices in set B is ...
(6C2)(28 +21) = 735
For two vertices from set C, we have already counted the cases where two are from A or two are from B. There are 4·6 = 24 ways to have one each of the remaining vertices from sets A and B. Then the number of additional quadrilaterals having two points from set C is ...
(7C2)(4)(6) = 504
So, the total number of unique quadrilaterals is ...
468 +735 +504 = 1707
__
nCk means "the number of ways to choose k from n"
nCk = n!/(k!(n-k)!)
An athlete eats 85 grams of protein per day while training. How much is this in milligrams (mg)? plz hurry I have a test soon
Represent the relationship between the total cost and the number of items, if total cost t is proportional to the number n of items purchased at a constant price p.
Answer:
t = pn
Step-by-step explanation:
We are to find the relationship between total cost and the number of items.
First we would represent the relationship between total cost and number of items with variables
Let the total cost = t
and the number of items = n
Total cost t is proportional to the number n of items:
t ∝ n
t = kn
where k is constant
Since it is purchased at a constant price p, the constant of proportionality would be p. the k would be replaced with p
t = pn
Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and the event that the A2 right leg tag is lost. Suppose these two events are independent and P(A1)=P(A2)=0.4. Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).
Answer:
0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost
Step-by-step explanation:
Independent events:
If two events, A and B, are independent, then:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
Conditional probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: At least one tag is lost
Event B: Exactly one tag is lost.
Each tag has a 40% = 0.4 probability of being lost.
Probability of at least one tag is lost:
Either no tags are lost, or at least one is. The sum of the probabilities of these events is 1. Then
[tex]p + P(A) = 1[/tex]
p is the probability none are lost. Each one has a 60% = 0.6 probability of not being lost, and they are independent. So
p = 0.6*0.6 = 0.36
Then
[tex]P(A) = 1 - p = 1 - 0.36 = 0.64[/tex]
Intersection:
The intersection between at least one lost(A) and exactly one lost(B) is exactly one lost.
Then
Probability at least one lost:
First lost(0.4 probability) and second not lost(0.6 probability)
Or
First not lost(0.6 probability) and second lost(0.4 probability)
So
[tex]P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48[/tex]
Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).
[tex]P(B|A) = \frac{0.48}{0.64} = 0.75[/tex]
0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost
if the perimeter of a square gardern is 84feet . what is the area of the qardern
Answer:
441
Step-by-step explanation:
84 / 4 = 21
21 x 21 = 441
Answer:
441
Step-by-step explanation:
84/2=42
Please help! Correct answer only, please! Consider the matrix shown below: Find the inverse of the matrix A: (i.e Find A^-1).
Answer: A
Step-by-step explanation:
Formula for inverse of a matrix is:
[tex]A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\qquad \rightarrow \qquad A^{-1}=\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
[tex]A=\left[\begin{array}{cc}2&5\\3&8\end{array}\right] \qquad \rightarrow \qquad A^{-1}=\dfrac{1}{2(8)-5(3)}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\dfrac{1}{1}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right][/tex]
We have that Option A is the correct option as its the correct in verse of the Matrix A
From the question we are told that:
[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]
Inverse of a Matrix
The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^{-1}, and A.A^{-1} = I.
Therefore the inverse of the Matrix A is
[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]
Giving
[tex]A^{-1}= \begin{vmatrix}8 & -5 \\-3 & -2\end{vmatrix}[/tex]
In conclusion
The correct Option is Option A as its the correct in verse of the Matrix A
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In conclusion
Which of these relations on the set {0, 1, 2, 3} are equivalence relations? If not, please give reasons why. (In other words, if a relation is not an equivalence relation, please list each property that is missing and the reason why it is missing.) (1) {(0,0), (1,1), (2,2), (3,3)} (2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)} (3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)} (4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}
Answer:
(1)Equivalence Relation
(2)Not Transitive, (0,3) is missing
(3)Equivalence Relation
(4)Not symmetric and Not Transitive, (2,1) is not in the set
Step-by-step explanation:
A set is said to be an equivalence relation if it satisfies the following conditions:
Reflexivity: If [tex]\forall x \in A, x \rightarrow x[/tex]Symmetry: [tex]\forall x,y \in A, $if x \rightarrow y,$ then y \rightarrow x[/tex]Transitivity: [tex]\forall x,y,z \in A, $if x \rightarrow y,$ and y \rightarrow z, $ then x \rightarrow z[/tex](1) {(0,0), (1,1), (2,2), (3,3)}
(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}
The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.
(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}
In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.
Therefore, It is not transitive.
As a result, the set (2) is not an equivalence relation.
(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}
(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric
Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.
1. (a) The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours. What is the probability that a bulb picked at random from this company’s products will have a life time of:
(i) at least 300 hours,
(ii) at most 100 hours,
(iii) between 150 and 250 hours.
(b) In a contest, two friends, Kofi and Mensah were asked to solve a problem. The
probability that Kofi will solve it correctly is ' and the probability that Mensah
(
will solve it correctly is ) . Find the probability that neither of them solved it correctly.
*
Answer:
1a) (i) 0.0537
(ii) 0.0250
(iii) 0.6188
1b) The probability that neither Kofi nor Mensah solves the problem correctly = (9/20) = 0.45
Step-by-step explanation:
The complete Question is presented in the attached image to this answer.
1a) This is a normal distribution problem with
Mean lifetime of bulbs = μ = 210 hours
Standard deviation = σ = 56 hours
(i) at least 300 hours, P(x ≥ 300)
We first standardize 300 hours
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (300 - 210)/56 = 1.61
To determine the required probability
P(x ≥ 300) = P(z ≥ 1.61)
We'll use data from the normal probability table for these probabilities
P(x ≥ 300) = P(z ≥ 1.61) = 1 - P(z < 1.61)
= 1 - 0.94630 = 0.0537
(ii) at most 100 hours, P(x ≤ 100)
We first standardize 100 hours
z = (x - μ)/σ = (100 - 210)/56 = -1.96
To determine the required probability
P(x ≤ 100) = P(z ≤ -1.96)
We'll use data from the normal probability table for these probabilities
P(x ≤ 100) = P(z ≤ -1.96) = 0.0250
(iii) between 150 and 250 hours.
P(150 < x < 250)
We first standardize 150 and 250 hours
For 150 hours
z = (x - μ)/σ = (150 - 210)/56 = -1.07
For 250 hours
z = (x - μ)/σ = (250 - 210)/56 = 0.71
To determined the required probability
P(150 < x < 250) = P(-1.07 < z < 0.71)
We'll use data from the normal probability table for these probabilities
P(150 < x < 250) = P(-1.07 < z < 0.71)
= P(z < 0.71) - P(z < -1.07)
= 0.76115 - 0.14231
= 0.61884 = 0.6188 to 4 d.p.
1b) Probability that Kofi solves the problem correctly = P(K) = (1/4)
Probability that Mensah solves the problem correctly = P(M) = (2/5)
Probability that Kofi does NOT solve the problem correctly = P(K') = 1 - P(K) = 1 - (1/4) = (3/4)
Probability that Mensah does NOT solve the problem correctly = P(M') = 1 - P(M) = 1 - (2/5) = (3/5)
To find the probability that neither of them solves the problem correctly, we first make the logical assumption that the probabilities of either of them solving the problem are independent of each other.
Hence, the probability that neither of them solves the problem correctly = P(K' n M')
P(K' n M') = P(K') × P(M') = (3/4) × (3/5) = (9/20) = 0.45
Hope this Helps!!!
2. 4 masks and 1 pack of gloves costs $18. Three packs of gloves and 4 masks costs $22. What is the cost of one pack of gloves and one mask?
Answer:
One mask=$4
One pack of glove=$2
Step-by-step explanation:
Let mask=m
Let glove=g
4m+g=18 (1)
4m+3g=22 (2)
From (1)
g=18-4m
Substitute g=18-4m into equation (2)
4m+3g=22
4m+3(18-4m)=22
4m+54-12m=22
4m-12m=22-54
-8m=-32
Divide both sides by -8
m=4
Substitute m=4 into equation (1)
4m+g=18
4(4)+g=18
16+g=18
g=18-16
g=2
One mask=$4
One pack of glove=$2
