To calculate mean and standard deviation for a binomial distribution, use the formulas μ = np and σ = √npq. Ensure both np and nq are greater than five to use the normal approximation.
Explanation:To find the mean (μ) and standard deviation (σ) for a binomial distribution, you use the formulas μ = np and σ = √npq respectively. Here, 'n' represents the number of trials, 'p' is the probability of success on a single trial, and 'q' is the probability of failure on a single trial, which is calculated as q=1-p.
If you want to determine whether you can use the normal approximation to the binomial, it is essential to ensure that both np and nq are greater than five. This is because the normal approximation is most accurate when the binomial distribution is symmetrical, which typically occurs when both np and nq exceed five.
So turns out I’m not good at this math stuff. I someone help me with this monstrosity.?!
The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).
What is the perimeter of the polygon to the nearest tenth of a unit?
15.3 units
16.9 units
17.5 units
17.9 units
The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.
Further explanation:
The distance between the two points can be calculated as follows,
[tex]\boxed{{\text{Distance}}=\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}}[/tex]
Given:
The coordinates of the vertices of the polygon are [tex]\left({ - 2, - 2}\right),\left( {3, - 3}\right),\left( {4, - 6}\right),\left( {1, - 6}\right)[/tex] and [tex]\left( { - 2, - 4}\right).[/tex]
Explanation:
Consider the points as A [tex]\left( { - 2, - 2} \right), B\left( {3, - 3} \right), C\left( {4, - 6} \right), D\left( {1, - 6} \right)[/tex] and [tex]E\left({ - 2, - 4} \right).[/tex]
The distance between point A and point B can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( { - 3 + 2}\right)}^2}}\\ &= \sqrt {25 + 1}\\&= \sqrt {26}\\&= 5.2\\\end{aligned}[/tex]
The distance between point B and point C can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( { - 6 + 3} \right)}^2}}\\&= \sqrt {{1^2} + 9}\\&= \sqrt {10}\\&= 3.17\\\end{aligned}[/tex]
The distance between point C and point D can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left({1 - 4} \right)}^2} + {{\left( { - 6 + 6}\right)}^2}} \\&=\sqrt {{3^2} + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]
The distance between point D and point E can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 2 - 1}\right)}^2} + {{\left( { - 4 + 6}\right)}^2}}\\&= \sqrt{ - {3^2} + {2^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.61\\\end{aligned}[/tex]
The distance between point E and point A can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 + 2} \right)}^2} + {{\left( { - 4 + 2} \right)}^2}}\\ &= \sqrt {{0^2} + {2^2}}\\&=\sqrt4\\&= 2\\\end{aligned}[/tex]
The perimeter of the polygon can be calculated as follows,
[tex]\begin{aligned}{\text{Perimeter}}&= 5.12 + 3.17 + 3 + 3.61 + 2\\&= 16.9\\\end{aligned}[/tex]
Option (a) is not correct.
Option (b) is correct.
Option (c) is not correct.
Option (d) is not correct.
The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.
Answer:
here is the answer
Step-by-step explanation:
Two bicycles depart from miami beach going in opposite directions. the first bicycle is traveling at 10 miles per hour. the second bicycle travels at 5 miles per hour. how long does it take until the bikes are 45 miles apart?
Ohhhhhh!!! I have a math problem I also have a Brainliest
A cord is cut into two pieces of different lengths. the sum of the two lengths is 10 centimeters, and the difference between the two lengths is 4 centimeters. find the lengths of the two pieces of cord.
Answer:
Start with x+y=10 and x-y=4
Add the equations to eliminate y:
x+y=10
+ x-y=4
2x =14
So now solve for x:
2x=14 (Divide each side by 2 to get x by itself)
x=7
Now you have solved for x, but you still need to solve for y:
x+y=10
7+y=10 (Subtract 7 from both sides to get y by itself)
y=3
Now you have both x and y but to check it, just plug it into the original equations:
x+y=10 ----> 7+3=10 (That's correct)
x-y=4 ----> 7-3=4 (That's correct)
Step-by-step explanation:
compare 6.51326 and the square root of 39. (show work)
After estimating and calculating, we find that 6.51326 is greater than the square root of 39, which is approximately 6.245.
To compare 6.51326 and the square root of 39, we first need to calculate the square root of 39 to see how it measures up against 6.51326. Since the exact square root of 39 is not easily found without a calculator, we can estimate it by finding the nearest perfect squares that surround 39.
36 and 49 are the nearest perfect squares to 39, and their square roots are 6 and 7, respectively. Since 39 is closer to 36 than to 49, we can estimate the square root of 39 to be slightly more than 6. Therefore, without performing the exact calculation, we can intuit that the square root of 39 will be between 6 and 7, but closer to 6.
Doing the exact calculation or using a calculator, we find that the square root of 39 is approximately 6.245, which means that 6.51326 is greater than the square root of 39.
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Question 8 the price of a cup of coffee was $2.55 yesterday. today, the price fell to $2.40 . find the percentage decrease. round your answer to the nearest tenth of a percent. %
the perimeter of a scalene triangle is 14.5 cm. the longest side is twice that of the shortest side. which equation can be used to find the side lengths if the longest side measures 6.2cm?
Answer:
9.3+b=14.5
Step-by-step explanation:
John has 6 green marbles and 4 purple marbles. He chooses a marble at random, writes down its color, and then puts the marble back. He performs this process 5 times. What is the probability that he chooses exactly two green marbles?
The probability that John chooses exactly two green marbles is calculated using the binomial probability formula and is found to be 720/3125.
To solve this problem, we can use the binomial probability formula because John is performing independent trials of the same experiment and he is interested in the probability of exactly two successes (picking a green marble) in a specific number of trials (5).
The binomial probability formula is: [tex]P(X = k) = (n choose k) \times p^k \times (1-p)^{n-k[/tex]
For John's case:
n = 5 (since he is picking 5 marbles).
k = 2 (he wants exactly two green marbles).
p = 6/10 or 3/5 (because there are 6 green marbles out of a total of 10 marbles).
Using the formula, the probability that John picks exactly two green marbles is:
[tex]P(X = 2) = (5 choose 2) \times (3/5)^2 \times (2/5)^{5-2[/tex]
Calculating further:
[tex]P(X = 2) = 10 \times (3/5)^2 \times (2/5)^3 = 10 \times 9/25 \times 8/125 \\P(X = 2) = 720/3125[/tex]
which function represents g(x) , a reflection of f(x)= 2/5 (10) x across the x-axis ?
Answer: The correct option is A.
Explanation:
The given function is,
[tex]f(x)=\frac{2}{5}(10)^x[/tex]
If a function is reflect across the x-axis, then the x-coordinate remains the same but the sign of y coordinate change.
[tex](x,y)\rightarrow(x,-y)[/tex]
[tex]g(x)=-f(x)[/tex]
[tex]g(x)=-\frac{2}{5}(10)^x[/tex]
The graph of f(x) and g(x) in shown in below figure.
Therefore option A is correct.
2(x+14)+(2x-14)= do you know this
The simplified form of the expression 2(x+14)+(2x-14) is 4x + 14.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
An expression,
2(x+14)+(2x-14).
Simplifying,
2(x+14)+(2x-14),
= 2x + 28 + 2x - 14
= 4x + 28 - 14
= 4x + 14
Therefore, the solution is 4x + 14.
To learn more about the expression;
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A public interest group hires students to solicit donations by telephone. After a brief training period students make calls to potential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 80% of them give up their jobs in their first two weeks of employment. The group hires 7 students, which can be viewed as a random sample.
1=logx solve this equation for x. Round your answer to the nearest hundred.
The probability of tossing three coins simultaneously and obtaining two heads and one tail is
There are 4 dogs, 6 cats, a rooster and 8 pigs on a farm. What is the ratio of pigs to all the other animals?
Answer:
Its 8:11 because theres eleven animals and 8 pigs
Step-by-step explanation:
Which number is equivalent to 0.45 repeating?
Answer:
5/11
Step-by-step explanation:
5/11 is the equivalent number because its the fraction of the repeating decimal ^^
A nut mixture of almonds and macadamia nuts at a small fair is $1.00 per pound of almonds and $5.93 per pound of macadamia nuts. Over the entire day, 102 pounds of the nut mixture were sold for $452.03. If p is the number almonds and n is the number of macadamia nuts, then the system of equations that models this scenario is: p+n=102p+5.93n=452.03p+n=102p+5.93n=452.03 Determine the correct description and amount of pounds for almonds and macadamia nuts that were sold
Final answer:
Approximately 71 pounds of macadamia nuts and 31 pounds of almonds were sold, after solving the system of equations p + n = 102 and 1.00p + 5.93n = 452.03.
Explanation:
To determine the amount of almonds and macadamia nuts sold, we need to solve the given system of equations:
p + n = 102 (where p is the number of pounds of almonds and n is the number of pounds of macadamia nuts)1.00p + 5.93n = 452.03Let's start by solving the first equation for p:
p = 102 - n
Now, substitute p in the second equation:
1.00(102 - n) + 5.93n = 452.03
Next, distribute and combine like terms:
102 - n + 5.93n = 452.03
4.93n = 350.03
n ≈ 71.041 (macadamia nuts)
Using n to find p:
p = 102 - 71.041 ≈ 30.959 (almonds)
Therefore, approximately 71 pounds of macadamia nuts and 31 pounds of almonds were sold.
A barrel of oil contains 42.0 gallons. how many liters is this? (1 gal = 3.785 l)
Final answer:
A 42.0-gallon barrel of oil is equivalent to 158.97 liters, calculated by multiplying the number of gallons by the conversion factor of 3.785 liters per gallon.
Explanation:
To discover out how numerous liters are in 42.0 gallons of oil, given that 1 gallon is proportionate to 3.785 liters, you'd perform the taking after calculation:
Multiply the number of gallons by the conversion factor from gallons to liters.
42.0 gallons × 3.785 liters/gallon = 158.97 liters.
Therefore, a barrel of oil, which contains 42.0 gallons, is equivalent to 158.97 liters.
A cell phone company charges a monthly fee plus $0.25$0.25 for each text message. The monthly fee is $30.00$30.00 and you owe $59.50$59.50. Write and solve an equation to find how many text messages xx you had.An equation is
which property is illustrated the following statement? 3z+4=4+3z
Answer:
Commutative additive property.
Step-by-step explanation:
Given : 3z+4=4+3z
To find : which property is illustrated the following statement.
Solution : We have given
3z + 4 = 4 + 3z.
Commutative additive property : a + b = b + a .
Example : 2 + 3 = 3 +2 = 5.
Hence this the commutative additive property 3z + 4 = 4 + 3z.
Therefore, Commutative additive property.
For a cylinder open at one end with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 44 cm3.
To find the dimensions of a cylinder with one open end that minimizes its surface area given a volume of 44 cm³, use calculus and the formulas for the cylinder's volume and surface area. The solution results in radius r ≈ 1.34 cm and height h ≈ 9.87 cm.
Explanation:For a cylinder open at one end, the surface area is given by the formula A = πr² + πrh, where r is the radius and h is the height.
The volume of a cylinder is given by the formula V = πr²h. Given that V=44 cm³, we can write the volume equation as h = V / (πr²).
Substituting this into the surface area equation, we get A = πr² + πr(V / (πr²)) = πr² + V/r.
We want to minimize the surface area, so we take the derivative of A with respect to r, set it equal to zero and solve for r.
Doing this gives us: dA/dr = 2πr - V/r² = 0 => r = cuberoot(V/2π).
Substituting V=44 cm³ into this, we get r = cuberoot(22/π) ≈ 1.34 cm.
Substituting r back into h = V / (πr²), we derive that h = 44 / (π * (1.34)²) ≈ 9.87 cm.
Therefore, the dimensions that will minimize the surface area of the cylinder given that the volume is 44 cm³, are approximately r = 1.34 cm and h = 9.87 cm.
This is a classic problem of optimization in calculus.
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Can someone help me find DB TR and SR thank you :)
Which of the following statements about trapezoids is true?? (Help asap) !!!!!!
george wants to save money for a car, he invests $700 into an account that pays 7.25 percent interest, how many years will it take to reach $14,300
Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Determine the minimum number of whole days it will take for him to be able to spell at least 75 words.
Peter needs 33 whole days to be able to speak 75 words.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Peter begins his kindergarten year able to spell 10 words.
He is going to learn to spell 2 new words every day.
Assuming no. of days it will take him to be able to spell at least 75 words
is d.
∴ The inequality that represents this scenario is 2d + 10 ≥ 75.
2d ≥ 65.
d ≥ 32.5 but it will take him 33 whole days to learn 75 words.'
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The function y = -0.017x^2 + 0.55x models the height y, in feet, of your pet frog's jump, where x is the horizontal distance, in feet, from the start of the jump. How far did the frog jump? How high did it go? Round your answer to the nearest hundredth. Be sure to show work / explain your reasoning.
The frog jumped approximately 16.18 feet horizontally. The maximum height it jumped was approximately 4.65 feet.
Explanation:The function y = -0.017x^2 + 0.55x models the frog's jump, it represents a parabola where the highest point, the vertex, means the highest point the frog reached, and where it hits the x-axis indicates the horizontal distance the frog jumped. We can find the distance of the frog's jump by setting y to 0 and solving the equation for x, whereas, the maximum height of the frog's jump will be determined by the vertex of the parabola.
For a function in the form y = ax^2 + bx + c, the x-value of the vertex, which is the maximum height in this context, can be found by using the formula -b/2a.
Substituting the given values from the equation, -b/2a = -0.55/(-2*-0.017) = 16.18 feet approximately.
Substitute x = 16.18 feet into the given function to find the maximum height the frog jumped: y = -0.017*(16.18)^2 + 0.55*16.18 = 4.65 feet approximately.
So, the frog jumped approximately 16.18 feet horizontally and the maximum height it jumped was approximately 4.65 feet.
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The frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet. We found this by setting the quadratic function to zero and solving for the horizontal distance, and by calculating the vertex of the parabola for the maximum height of the jump.
The function y = -0.017x^2 + 0.55x models the height y, in feet, of your pet frog's jump, where x is the horizontal distance, in feet, from the start of the jump. To determine how far the frog jumped, we look for the value of x when y equals zero, which represents when the frog lands back on the ground. To find this, we set the equation equal to zero and solve for x:
0 = -0.017x^2 + 0.55x
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = -0.017, b = 0.55, and c = 0. We can solve this by factoring or using the quadratic formula. The solutions to this equation represent the starting point (x=0) and the landing point of the jump. Ignoring the x=0 solution, we find that the frog lands at approximately x = 32.35 feet (after rounding to the nearest hundredth).
To determine how high the frog went, we need to find the vertex of the parabola because this represents the highest point of the jump. The x-coordinate of the vertex is given by -b/(2a), so we calculate:
x = -0.55 / (2 * -0.017) = 16.18 (rounded to the nearest hundredth)
We plug this value into the original equation to find the height:
y = -0.017(16.18)^2 + 0.55(16.18) = approximately 4.71 feet (after rounding to the nearest hundredth)
Therefore, the frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet.
Patty has 8 flowerpots, and she wants to plant a different type of flower in each pot. There are 11 types of flower available at the garden shop. How many different ways can choose the flowers?
In a right triangle the legs have lenths of 8 and 15 what is the perimeter of this triangle
The solution to 2 x - 2 + 5 = 13 is___.