Relative dimensions which will make the surface area a maximum is
x=y = \sqrt{area/3 }
z = 1/2( \sqrt{area/3 })
Volume = 2xh
Let the box have dimensions x,y,z>0.
The surface area is A=xy+2xz+2yz
The volume is V=xyz
The Lagrangian is L=V−λ(A−constant)=xyz−λ(xy+2xz+2yz−constant).
∂L∂x=yz−λ(y+2z)=0
∂L∂y=xz−λ(x+2z)=0
∂L∂z=xy−λ(2x+2y)=0
Hence, λ=yzy+2z=xzx+2z=xy2x+2y
On cross multiplication,
xyz+2yz2=xyz+2xz2which implies x=y.
Cross-multiplying the middle and the right expressions ,2x2z+2xyz=x2y+2xyzwhich implies z=12y.
So, optimal volume with fixed surface area is to have the width and the depth equal and the height to be half the width and depth.
To find x,y,z given a fixed surface area Area one would use x=y=2z in the equation
Area=xy+2xz+2yz=x2+x2+x2 so
x=y = \sqrt{area/3 }
z = 1/2( \sqrt{area/3 })
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial units or SI-derived units, such as the cubic metre and litre, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
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the following data were collected for a two-factor anova with two treatments and three blocks. treatment block 1 2 a 46 31 b 37 26 c 44 35 using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ. required: a. state the null and alternate hypotheses for treatments. b. state the decision rule for treatments. (round your answer to 1 decimal place.) c. state the null and alternate hypotheses for blocks. also, state the decision rule for blocks. (round your answer to 1 decimal place.)
The test hypothesis using 0.05 significance level has the following results:The treatment means differ, The block means do not differ.
What is hypothesis testing?A poll or study's findings can be tested using the statistical procedure known as hypothesis testing to see if the findings are significant. By calculating the likelihood that the findings happened by chance, you are basically evaluating if the findings are genuine. If it's possible that your results were a coincidence, the experiment won't be reproducible and won't be of much help.
Hypothesis testing may be one of the most perplexing components for students, mostly because you must first determine what your null is so that you can conduct a test. These challenging word problems that you encounter might sometimes be challenging to understand.
Make a plan for your null hypothesis.
Write down your null hypothesis
Determine the type of test you must do,
How to solve?
Describe the null and alternate treatment hypotheses:
Null hypothesis: No difference in treatment means
Alternative interpretation: The means differ
Indicate the treatment decision-making process:
F(1,2)=18.51 as seen in the table
Reject the null hypothesis if the estimated F exceeds 18.51.
Treatments Calculated F=43.75 > 18.51; hence, the null hypothesis is rejected.
As a result, we find that the treatment means differ.
Write out the null and alternative hypotheses for blocks.
Block means are not different under the null hypothesis.
A different theory There exists at least one pair of distinct meanings.
State the block decision rule as well:
Table F(2,2)=19.0 value
If the estimated F is greater than 19, reject the null hypothesis.
Blocks determined that F=8.14 19.0, thus we did not reject the null hypothesis.
Our conclusion is that the block means are equivalent.
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Suppose X1,..., XM iid Binomial(n,p) is a set of M observations drawn independently from a Binomial distribution. (a) Write out the likelihood function. (b) Write out the log-likelihood function. (c) Find the score function by taking the partial derivative of the log-likelihood function. (d) Set the score function equal to zero and solve for the parameter p. (e) Take the second partial derivative of the score function. (f) Check to make sure this value is negative to ensure that the log-likelihood function is concave down.
Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).
What is binomial distribution ?The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.
The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.
The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.
Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).
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1) Brian is playing a game of dice. He gets 10 points for each 6 he rolls. He loses 4 points
every time he does not roll a 6. After 20 tries, Brian's score was 144 points. How many
times did he not roll a 6?
Answer:
He rolled a 6, 16 times
He rolled not a 6, 4 times
Brian did not roll 6 in the dice 14 times.
What is subtraction?Subtraction is mathematic operation. Which is used to remove terms or objects in expression.
Given, Brian is playing a game of dice. He gets 10 points for each 6 he rolls. He loses 4 points every time he does not roll a 6.
After 20 tries his score is 144 points.
If he rolled 6 each time,
his score would be 200.
Subtracting the number 144 to 200.
200 - 144
= 56
And 56/4
= 14
That means he did not roll 6, 14 times.
Therefore, 14 times he did not roll 6.
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The cost of `20` cans of dog food at Store B is `\$18.40`.
Calculate the price for `11` cans of dog food.
Answer:
33.45 is the price of 11 dog food cans
in a random sample of 200 items, 42 are defective. if the null hypothesis is that 23% of the items in the population are defective, what is the value of zstat?
The value of z-stat is -0.6721.
What is z stat?
The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.
One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.
Solution Explained:
We use the formula,
[tex]z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}[/tex], where P is the observed proportion, π is the hypothesized proportion
Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23
Putting the values in
[tex]z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}[/tex]
After calculating, z-stat is therefore equal to -0.6721
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This equation has one solution. 5(x – 1) 3x = 7(x + 1) what is the solution?
The quadratic equation 15[tex]x^{2}[/tex]-22x -7 = 0 has solution x = 1.7355 or -0.26886
In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as
a[tex]x^{2}[/tex] + bx + c =0
where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation
given that
5(x-1)3x = 7(x+1)
15[tex]x^{2}[/tex]-15x = 7x +7
15[tex]x^{2}[/tex]-22x -7 = 0
x = -b ± [tex]\sqrt{b^{2}-4ac }[/tex]/2a
x = -(-22) ± [tex]\sqrt{(-22)-4(15)(-7)}[/tex] /2(15)
x = 1.7355 or -0.26886
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Answer: x = 12
Step-by-step explanation:
Distribute the parenthesis on both sides of the equation
5x - 5 + 3x = 7x + 7
8x - 5 = 7x + 7 ( subtract 7x from both sides )
x - 5 = 7 ( add 5 to both sides )
x = 12
Therefore, your answer is: x = 12
Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?
(–6, 0.8)
(–6, 3.2)
(6, 3.2)
(6, 0.8)
The points (-10, 0) and (0, 5), on the path of the first boat that can be modeled by a quadratic function and the point (10, 4) on the path of the linear function modelling the second boat, indicates that besides the common starting location, the solution for the point at which the paths of the boats cross again at (6, 3.2)
What is a solution for a system of equations?The solution to a system of equation is the value of the input variable at which the output of the equations in the system of equations are the same.
Location of the port = (-10, 0)
The vertex of the path of the first boat that can be modeled by a quadratic function = (0, 5)
Point through which the boat that follows a path that can be modeled as a linear function passes = (10, 4)
The vertex form of the equation of a parabola is; y = a·(x - h)² + k
Where;'
(h, k) = The coordinates of the vertex
(h, k) = (0, 5)
Therefore;
y = a·(x - 0)² + 5 = a·x² + 5
When x = -10, y = 0, therefore;
y = 0 = a·(-10)² + 5 = 100·a + 5
0 = 100·a + 5
a = -5/100 = -1/20
a = -0.05
The equation is therefore; y = -0.05·x² + 5
The slope of the straight line path of the other boat is; m = (4 - 0)/(10 - (-10)) = 1/5 = 0.2
The equation is therefore; y - 0 = 0.2·(x - (-10)) = 0.2·x + 2
y = 0.2·x + 2
The point where the two paths cross is therefore;
-0.05·x² + 5 = 0.2·x + 2
-0.05·x² - 0.2·x + 5 - 2
-0.05·x² - 0.2·x + 3 = 0
x = (0.2 ± √((-0.2)² - 4 × (-0.05) × 3))/(2×(-0.05))
Therefore;
x = -10 and x = 6
The x-coordinate of the point the two paths cross, besides the starting location is x = 6
Therefore;
y = 0.2 × 6 + 2 = 3.2
The point besides the common starting location, the paths of the boats cross is; (6, 3.2)
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Answer:
(–6, 3.2)
Step-by-step explanation:
The answer above is correct.
Are the expressions 5(m + 1 ) - 1 and 2(2m + 2) + m equivalent
Both the given expression are equivalent expression as 5m + 4.
Given that,
to determine whether the two given expressions are equivalent ot each other,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4
Thus, Both the given expression are equivalent expression as 5m + 4.
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which of these coefficients are statistically significant at a significance level of 0.05? which of these coefficients are statistically significant at a significance level of 0.01?
On solving the provided question, we got - 0.001 is a stronger significance level,
What is Coefficient?any of a product's characteristics taken into account in respect to a certain characteristic. especially: a term's constant component as opposed to its variable. a value that represents a quality or attribute by a number (as of a substance, device, or process)
Describe a coefficient example.Whenever a variable is multiplied, a coefficient is used. In this case, "z" is a variable, making 6 a coefficient. 6z stands for 6 times z. Coefficient 1 applies to variables without a value.
0.001 is a stronger significance level, It means that the probability of error for the statistic is greater than 5 in 100, therefore the researchers concluded that the research is not statistically significant.
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Which shows the solution for the
following system of equations?
y = 2x
2x+y=-4
Marlene wants to determine which podcast adults prefer.
She surveys 30 adults entering a park one morning. Which
type of sample does this represent?
The type of sample that the sample taken by Marlene represents is a Convenience sample.
What is a Convenience sample ?Researchers who use convenience sampling obtain market research data from a pool of respondents who are conveniently accessible. Because it is so rapid, easy, and economical, it is the sampling procedure that is used the most frequently. If members choose to be part of the sample, they are frequently simple to get in touch with.
Therefore, Marlene employed a convenience sampling technique by going to the park, which was close by, and taking a sample of the people present.
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(-4a^5b^3)^2•(-3a^2b)^2
Answer: 144a^14 b^8
Step-by-step explanation:
(-4a^(5)b^(3))^(2)* (-3a^(2)b)^(2) = 144a^14 b^8
Select the simplification that accurately explains the following statement. √9=9 1/2
The simplification that explains the statement is [tex](9^{\frac{1}{2} })^{2} = (9^{\frac{1}{2} } )(9^{\frac{1}{2} } ) = 9^{\frac{1}{2} + \frac{1}{2} } = 9^{\frac{2}{2} } = 9^{1} = 9[/tex]
How to simplify an expression?The law of indices(exponent) can be used to explain the following statement:
[tex]\sqrt{9} = 9^{\frac{1}{2} }[/tex]
Therefore, using the law of indices.
[tex](a^{x}) (a^{y} ) = a^{x+y}[/tex]
Hence, applying this law of exponents.
Exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent:
[tex](9^{\frac{1}{2} })^{2}[/tex]
[tex](9^{\frac{1}{2} } )(9^{\frac{1}{2} } )[/tex]
[tex]9^{\frac{1}{2} + \frac{1}{2} }[/tex]
[tex]9^{1}[/tex]
9
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Point d is on line segment \overline{ce} ce. Given de=x+2,de=x+2, cd=3x+2,cd=3x+2, and ce=5x+2,ce=5x+2, determine the numerical length of \overline{ce}. Ce.
Answer:
Segment CE is 12 units.
Step-by-step explanation:
CD and DE add together to make CE. See image.
Use this idea to write an equation. Combine like terms and solve for x. Use the x value you find to calculate the length of CE. See image.
What is the X and Y intercept?
X: 0, 5, 10, 15, 20, 25, 30, 35, 40
Y: 7, 10, 20, 20, 24, 32, 35, 45, 57
Answer:
y-intercept: (0, 7)x-intercept: cannot be determinedStep-by-step explanation:
You want to know the x- and y-intercepts of a function described by a data table.
InterceptsThe x-intercept is the x-value where y = 0. There is no y=0 entry in the table, and the entries there are not regular enough to support any speculation as to how the function might be extrapolated.
There is no x-intercept.
The y-intercept is shown in the table where x=0.
The y-intercept is (0, 7).
1. 8.92 - 2.618
2. 53.846 + 73.05
3. 873.51 - 26.6
Answer:
6.302126.896846.91Step-by-step explanation:
(attached)
The graph of a linear function is shown on the grid.
#6. Find the slope
#7. Find the y-intercept:
#8. Equation: y=
The slope and y-intercept of the given linear equation are [tex]-\frac{5}{4}[/tex] and [tex]5[/tex] respectively. The equation of the given graph is [tex]y=-\frac{5}{4} x+5[/tex]
What is the Slope of a graph?
The ratio of rise to run is known as a line's slope.When given a line's graph and asked to determine its equation, the first step is to determine the slope.The slope formula is used in the procedure for determining the slope from a graph.If there are two points [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] on the line, then the equation for the slope (m) is given as, [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]What is a y-intercept?
The location where a graph crosses the y-axis is known as the y-intercept (c). Or to put it another way, it is the value of y when x=0.Here, from the graph, we can find a line passing through the two points, [tex](4,0)[/tex] and [tex](0,5)[/tex].
The equation for the slope formula is given as, [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Using the slope formula, we get the slope of the given graph as,
[tex]m=\frac{ 5-0 }{0-4 }\\\implies m=-\frac{5}{4}[/tex]
The y-intercept (c) is the value of y when x equals zero.
The line is passing through the point [tex](0,5)[/tex]
Here, the value of x is equal to 0 and the value of y is equal to 5.
So, the y-intercept of the given graph, [tex]c=5[/tex]
We know that the equation of a straight line is expressed as, [tex]y=mx+c[/tex]
Substituting the values of m and c in the straight line equation form, we get the equation of the given line as,
[tex]y=-\frac{5}{4} x+5[/tex]
Therefore, the slope of the given graph, [tex]m=-\frac{5}{4}[/tex] and the y-intercept, [tex]c=5[/tex].
Also, the equation of the given line is [tex]y=-\frac{5}{4} x+5[/tex]
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Select the correct answer.
An image of four line numbers marked: A, B, C, D. Each line number has the markings from top to bottom: two, one, zero, minus one, minus two. Dots on each line number: at 1.7 on A, at minus 0.7 on B, at 0.7 on C, and at minus 1.7 on D.
Which number line represents the number 0.7?
A.
A
B.
B
C.
C
D.
D
The number line that represents the number 0.7 is number line (B)
How to determine the number line?From the question, we have the following parameters:
Markings = 2, 1, 0, -1, -2. Dots on each line number: at 1.7 on A, at minus 0.7 on B, at 0.7 on C, and at minus 1.7 on D.From the dots on each line, we have the following statement
At minus 0.7 on B
This statement means that
B = -0.7
Hence, the number line represented by the statement is the number line B
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Which set of ordered pairs represents a function?
O {(-6,-4), (2, -1), (-6, 0), (-9, 8)}
O {(7,-7), (8,9), (7, 7), (-4,9)}
O {(-4,-1), (-6, -7), (7,6), (-8,6)}
O {(8,-8), (2, -7), (9,-4), (8,-5)}
Submit Answer
Answer:Answer:
D.
{(-9,8), (-5,-8), (-7,8), (-6,-8)}
Step-by-step explanation:
if a researcher analyzed data using linear regression correlating a performance test and gpa and calculated a slope of 0.028 and y intercept of 0.63. what would be the predicted student's gpa if she scored 63 on the performance test?
The GPA of the student who scored 63 in the performance test is 2.394.
Given, a researcher analyzed data using linear regression correlating a performance test and GPA and calculated a slope of 0.028 and y-intercept of 0.63.
we have find the GPA of a student who scored 63 in the performance test.
Let the score of the student in performance test be, x
and the GPA of the student be, y
So, y = mx + c
as, m = 0.028 and c = 0.63
y = 0.028x + 0.63
at x = 63
y = 0.028×63 + 0.63
y = 2.394
So, the GPA of the student who scored 63 in the performance test is 2.394.
Hence, the GPA of the student who scored 63 in the performance test is 2.394.
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on average, an american professional football game lasts about five hours, even though the ball is actually in play only 11 minutes. assume that game times are normally distributed with a standard deviation of 0.9 hour.
The probability the game lasts less than 4.5 hours is 0.2877.
How to calculate the probability?
μ = mean population = 5
σ = standard deviation = 0.9
The probability for the game lasts less than 4.5 hours can be calculated using z test formula.
P(x < 4.5) = P(z < [tex]\frac{x-\mu}{\sigma}[/tex] )
= P(z < [tex]\frac{4.5-5}{0.9}[/tex])
= P(z < -0.56)
Using z table for P(z < -0.56). So,
= 0.2877
Thus, the probability is 0.2877 for the game lasts less than 4.5 hours.
Your question is incomplete, but most probably your full question was
on average, an american professional football game lasts about five hours, even though the ball is actually in play only 11 minutes. assume that game times are normally distributed with a standard deviation of 0.9 hour. 1. Find the probability that a game lasts less than 4.5 hours.
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Suppose 40-gallon tank is completely filled with water: The water then begins draining from the tank constant rate of 1.5 gallons per minute, Let represcnt tbc number 0f Minutes : sunce the watcr began draining; and let represent Ihe number of gallons of water the tank; Defing- fonula represent the volume of water in the tank, % tcrms of the number of minutes, since the water began draining from the tank: Sketch = graph of v in ters of t, 7Z 30+}s14445 Delermint the following slalemnents aTC false. Sclcci Onseci The graph of v the relalionshp. Letis of t represents all Nirs Wc anu VOMuC vilues (7.5,33.76) convey that when thc tank has been draining noint has35. 75 pallons walcr rcmiltang Sultclan answe For 7.5 minutes lhe solve thc cquation L.5t. t Use the Eraph thc equation above delenmnines
The formula that represents the volume of water in the tank in terms of the number of minutes since the water began draining is v = 40 - 1.5t.
This can be seen by realizing that the volume of water in the tank decreases by 1.5 gallons per minute, so after t minutes the volume will be 40 - 1.5t. The graph of this formula is a straight line with a slope of -1.5 and an intercept of 40. This means that the graph starts at the point (0,40), which represents a tank that is full of water, and decreases linearly as the number of minutes increases.
The statement "The graph of v in terms of t represents all possible values of v and t" is true. This is because the formula v = 40 - 1.5t is defined for all possible values of t, and the graph of this formula includes all possible pairs of (v, t) values that satisfy the formula.
The statement "The point (7.5,35.75) conveys that when the tank has been draining for 7.5 minutes, it has 35.75 gallons of water remaining" is false. This is because the point (7.5,35.75) does not lie on the graph of the equation v = 40 - 1.5t. The correct point on the graph that represents the volume of water in the tank after 7.5 minutes would be (7.5,26.25), which can be found by substituting t = 7.5 into the equation v = 40 - 1.5t.
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an individual is teaching a class on excel macros. the individual plans to break the class up into groups of 4 and wants each group to have a different exercise to practice on. write an equation that expresses the situation, let x be the independent variable and y be the dependent variable.
The required relation between independent and dependent variables is y = x/4.
Explain dependent and independent variables?A simple method for considering independent and dependent variables is, the point at which you're leading an examination, the free factor is what you change, and the reliant variable changes hence. You can likewise consider the autonomous variable the reason and the reliant variable as the impact
According to question:The independent variable x is the total number of students in the class.
And the dependent variable y is number of students in each group.
Therefore,
y = x / 4
Here, when we change the value of x then value of y automatically changed.
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Given the function f(x) =2x-1 what is the value of f(-7)
Answer:
Step-by-step explanation:
hi
an architect designs a diagonal path across a rectangular patio. the path is 29 meters long. the width of the patio is x meters, and the length of the path is 5 meters more than the width. which equation can be used to find the dimensions of the patio? 0.5(x)(x 5)
The equation of the path to find the dimensions of the patio is x² + (x + 5)² = 841.
Here we have to find the equation of the dimensions of the patio.
Data provided:
the path = 29 meters
length of the path is 5 meters more than the width of the path.
So let us assume that the length of the path is x
with this, the width of the path is x + 5
The formula for the diagonal:
Diagonal² = length² + width²
Putting the data we have:
29² = x² + (x +5)²
841 = x² + (x+5)²
Therefore we get the equation as x² +(x + 5)² = 841.
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the perimeter of the rectangle is 50 feet. The length is 18 ft. what is the width?
Answer:
Length=18 feet
Width=7 feet
Hope this helps! :)
Step-by-step explanation:
perimeter=50
length=18
width=w
Rectangle:2l+2w=50 2(18)+2(7)=50
36+2w=50
50-36=14
14/2=7
(36+14+50)
Tell whether x and y are proportional.
Answer:
yes y/x = 5/2
Step-by-step explanation:
y/x = 5/2, 10/4=5/2, 15/6=5/2, 20/8=5/2
Gina reads 120 pages in 4 days. Which reading rate is equivalent?
1: 74 pages in 3 days
2: 60 pages in 2 days
3: 105 pages in 5 days
4:80 pages in 3 days
Answer:
60
Step-by-step explanation:
she read 60 pages in just 2 days
if the length, width and height of the rectangular shaped glasses (in terms of inches) can be represented by 4x 3y, 2x - y, and 5 respectively, find the polynomial expression that represents the volume of each glass.write your answer in descending order. please use the palette below to enter your answer.
Answer:
Step-by-step explanation:
ANSWER: 40x^2+10xy-15y^2
Lenth * Width * Height:
(4x+3y)*(2x-y)*5
Distribute 5 through the parentheses :
(20x+15y)*(2x-y)
Simplify:
40x^2-20xy+30xy-15y^2
Collect like terms:
40x^2+10xy-15y^2
As per the dimensions, the volume of rectangular-shaped glass is equal to 40x² + 10xy - 15y².
What is Volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.
As per the given information in the question,
Use the formula of volume:
Length × Width × Height:
(4x+3y) × (2x-y) × 5
5 should be distributed through parenthesis:
(20x+15y) × (2x-y)
Now, simplify the above equation,
40x² - 20xy + 30xy - 15y²
Now, keep all like terms together,
40x² + 10xy - 15y²
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78. the probability that a marksman will hit a target each time he shoots is 0.89. if he fires 15 times, what is the probability that he hits the target at most 13 times?
The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.
Given that,
A marksman has a 0.89 percent chance of hitting the target each time he fires.
We have to find what is the probability that he will only hit the target 13 times out of 15 shots.
We know that,
The probability of getting exactly k successes in n trials is given by the probability mass function that is,
P(X=k)=[tex](\frac{n}{k} )p^{k}(1-p)^{n-k}[/tex]
Where [tex](\frac{n}{k})= n!/k!(n-k)![/tex]
The probability that he hits the target at most 13 times is,
1-[P(he hits 14 times)+P(he hits 15 times)]
So, calculate the probability that he hits a target 14 times as follows:
P(X=14)=[tex](\frac{15}{14} )0.89^{14}(1-0.89)^{1}[/tex]
P(X=14)=15×(0.89)¹⁴×(0.11)
P(X=14)=0.3228
And the probability that he hits a target 15 times is
P(X=15)=[tex](\frac{15}{15} )0.89^{15}(1-0.89)^{0}[/tex]
P(X=15)=1×(0.89)¹⁵×(1)
P(X=15)=0.1741
And the required probability is
=1-[P(he hits 14 times)+P(he hits 15 times)]
=1-[0.3228+0.1741]
=0.5031
Therefore, The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.
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