Answer:
0.098415
Step-by-step explanation:
The way the question is worded is odd and you should probably actually include “don’t grow into a healthy plant” or something. You can use the binomial distribution. Suppose ∼Bin(6,0.1) so the probability that k trees don’t grow into a healthy plant is
Pr( = ) = (6 / ) 0.16^ 0.9^6−
Then the probability that two don’t grow into healthy plants is
Pr( = 2) = (6/2) 0.1^2 0.9^4
this is equal to 0.098415
To calculate the probability of exactly 4 out of 7 seeds failing to grow, use the binomial probability formula with n = 7, p = 0.10, and k = 4. The calculation involves combinations and exponentiation.
Explanation:The question is asking for the probability of exactly 4 seeds out of 7 failing to grow. Given that each seed has a 90% chance of growing into a healthy plant, which means each seed has a 10% (1 - 0.90) chance of not growing. To solve this, we can use the binomial probability formula: P(X = k) = C(n, k) * (pk) * ((1 - p)n - k), where n is the number of trials, p is the probability of success, and k is the exact number of successes. In this case, n = 7, p = 0.10 and k = 4. So, we get:
P(X = 4) = C(7, 4) * (0.104) * (0.907 - 4)
The calculation of this probability requires the use of combinations and exponentiation, providing the specific likelihood of having exactly 4 seeds out of 7 not growing into a healthy plant.
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4x-5=4x+10 solve for x
The equation 4x - 5 = 4x + 10 has no solution because subtracting 4x from both sides yields -5 = 10, which is a contradiction.
Explanation:The equation 4x - 5 = 4x + 10 cannot be solved for x in the usual way because attempting to isolate x on one side will result in a contradiction. If we subtract 4x from both sides of the equation, we get -5 = 10, which is not true for any value of x. Therefore, this equation has no solution.
HELP ROUND 604703.472883 TO THE NEAREST HUNDRED
Answer:
The required number is 604703
Step-by-step explanation:
Consider the provided number 604703.472883
The rule for rounding a number is:
If the number on the right side of rounding digit is 0, 1, 2, 3, 4 then no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
If the number on the right side of rounding digit is 5, 6, 7, 8, 9 then rounding digit rounds up by one number and change the rest of the digit right to rounding digit with 0.
The number on the hundred place is 7 and the number on right side is 0.
Thus, no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
Hence, the required number is 604703
A certain bag of potting soil is 1/4 peat moss,and the rest is dirt. What part is dirt?
The part of the bag that consist of dirt is:
3/4
Step-by-step explanation:It is given that the amount of peat moss that is present in a bag of potting soil is:
1/4
Hence, the remaining space that is left in the bag consist of dirt.
Remaining space is calculated as :
[tex]1-\dfrac{1}{4}\\\\\\=\dfrac{3}{4}[/tex]
( Since we subtract 1/4 from a whole of a bag)
Hence, the part that is dirt in the bag of potting soil is:
3/4
A line with a slope of 4 passes through (6, 11). Which choice is an equation of this line?
Answer:PLEASE MARK AS BRAINIEST
y – 11 = 4(x – 6)
Kris wanted to understand whether studentstudents at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:
In favor
Opposed
Undecided
Grade 9
6
4
8
Grade 10
10
11
9
Grade 11
12
15
11
Grade 12
15
6
14
If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day?
Answer:
The probability that the student is opposed to extending the school day is 0.3666 or 36.67% approx.
Step-by-step explanation:
Arranging the table properly and adding a column of total students.
In favor Opposed Undecided Total students
Grade 9 6 4 8 18
Grade 10 10 11 9 30
Grade 11 12 15 11 38
Grade 12 15 6 14 35
If the principal randomly selects a student in grade 10 from this survey, this means we will only consider grade 10 students.
The probability that the student is opposed to extending the school day is = [tex]\frac{number of opposed students}{total number of students}[/tex]
There are 11 students who are opposed and total students in grade 10 are 30.
So, probability is : [tex]\frac{11}{30}= 0.3666[/tex] or 36.67% approx.
Find the 5th term in the expansion of (x – 3y)8
Step by step on how to solve that equation
I I'm not good with math
a) total cost = 499 + 49.99x
b) x = 5 games
total cost = 499 + 49.99(5) = 499 + 249.95 = 748.95
A quadratic equation is shown below:
9x2 − 16x + 60 = 0
Describe the solution(s) to the equation by just determining the radicand. Show your work.
: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.
hello :
help :
the discriminat of each quadratic equation :
ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x =
(-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
Suppose triangle ABC has vertices at A(1, 0), B(10, 0), and C(2, 6). After a 60° counterclockwise rotation about the origin, vertex B' has coordinates (5, ?).
Evaluate f(x)= -x^2+1 for x=-3
A.4
B.-4
C.-8
D.-9
Line k is the perpendicular bisector of (line)PQ. If line k intersects (line)PQ at point R, which of the following statements must be true?
check all that apply
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
D. Point R is the midpoint of line k
E. Line k is parallel to PQ
Answer:
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
Step-by-step explanation:
A perpendicular bisector of a line is a segment that cuts right in the middle a line, and that segment forms a 90º degree angle with the line. This means that the point where the segment cuts the line would be exactly the half, making both resultant segments on the line congruent. So the options that are correct are ABC.
Alyosha and Ivan are standing between two buildings they know to be equal height. The buildings are 500 feet apart. Looking up at the westernmost building, they form a 30 degree angle. Looking to the northeastern building, they form a 45 degree angle.
A) Ivan guesses they are halfway between the buildings. Why is this a bad guess?
B) How far away from each building are they?
Solve this equation using an algebraic method: (x + 4)( x - 4) = 9
Help me out please
A science experiment begins with a metal at −100° Celsius. The following function describes the temperature change per minute: f(x) = 89x − 100°. How will the graph of this function change if the metal is at 25° at the start of the experiment?
Answer:
A
Step-by-step explanation:
Jacobysontop!
Could someone show me the work for 1/2 divided by 2/3 x 3/4
Anthony was tracking the increasing number of animals in the zoo. at 9
a.m., there were 56 animals. at 11
a.m., there were 60 animals. if anthony made the function f(x) = 2x − 38, what would the 2 represent? the number of animals at midnight the rate at which the number of animals was increasing the length of time he recorded for the total change in the number of animals
It’s a little surprising that this question didn’t come up earlier. Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2). A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.
Answer:
2 would represent the rate at which the animals were increasing
Step-by-step explanation: This all comes back to the slope intercept form:
y = mx + b
2x is the slope, and the slope is the rate of which a point will increase or decrease.
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
The formula v = (radical)64h can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 23 feet. Round your answer to the nearest hundredth.
A ) 184 feet per second
B ) 306.93 feet per second
C ) 38.37 feet per second
D ) 736 feet per second
Answer:
The answer is the option C
[tex]V=38.37\ ft/sec[/tex]
Step-by-step explanation:
we have that
[tex]V=\sqrt{64h}[/tex]
In this problem we have
[tex]h=23\ ft[/tex]
Substitute in the formula and solve for V
[tex]V=\sqrt{64(23)}[/tex]
[tex]V=\sqrt{1,472}\ ft/sec[/tex]
[tex]V=38.37\ ft/sec[/tex]
8/3 , 2.28, 10/12 , 0.199 what number in the list above has the greatest value?
Answer:
[tex]\frac{8}{3}[/tex] is the greatest value.
Step-by-step explanation:
The given numbers are [tex]\frac{8}{3}[/tex], 2.28, [tex]\frac{10}{12}[/tex], 0.199
In this question we have to find out greatest value.
So, first we convert all the values in decimals.
To convert [tex]\frac{8}{3}[/tex] in decimal form, we divide 8 by 3. The answer would be 2.67
2.28
[tex]\frac{10}{12}[/tex] = 0.83
0.199
Now we arrange these numbers in the increasing order.
0.199 < 0.83 < 2.28 < 2.67
So the greatest number is 2.67 that is [tex]\frac{8}{3}[/tex].
How do you complete the square using fractions
Completing the square with fractions involves transforming the quadratic equation into a perfect square trinomial by adding the square of half the coefficient of x to both sides. This enables solving the equation more easily by then taking the square root of both sides and isolating x.
Completing the square using fractions involves a few steps tailored to work with fractional coefficients. To make it understandable, let's explain the process step by step:
Start with the quadratic equation and ensure it is in the form ax2 + bx + c = 0.Divide all terms by 'a' (the coefficient of x2) if 'a' is not equal to 1, to make the coefficient of x2 equal to 1.Rearrange the equation so that the constant 'c' is on the other side of the equation.Take half of the coefficient of x, which is now 'b/a', and square it. This value is added both sides of the equation to form a perfect square on one side.Rewrite the left side of the equation as a squared binomial.Finally, solve for x by taking the square root of both sides and then add or subtract the constant term.For example, let's complete the square for the equation x2 + (3/2)x = 4. We take half of the coefficient of x, (3/2)/2 or 3/4, and square it to get 9/16. Adding 9/16 to both sides gives us (x + 3/4)2 = 4 + 9/16. Simplify the right side to get a single fraction, and then proceed to solve for x. Additionally, in some scenarios, we might need to multiply both the numerator and denominator by a skillfully chosen factor, such as 1/2, to facilitate simplifying or cancelling out terms.
What do the parallel lines shown on segment BD and segment DC represent?
it means both sections are equal.
so BD = 18 and DC = 18
How many ways can we put 7 adults and 3 kids in line (where order matters) so that no two kids are next to each other?
A data set has the following characteristics: Mean: 4.9 Median: 6 Mode: 6 Variance: 4 The z-score is the number of
Answer:
Standard deviations and mean
Step-by-step explanation:
Answer:
I.
standard deviations
mean
II.
-1.95
0.05
0.8
Step-by-step explanation:
I.
The z-score is the number of standard deviations a data value is away from the mean.
II.
z1 = -1.95
z5 = 0.05
z6.5 = 0.8
Use Gauss-Jordan elimination to solve the following linear system.
x – 2z = 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
A. (–5,–3,0)
B. (3,2,–3)
C. (5,3,–5)
D. (3,6,–4)
By using Gauss-Jordan elimination the solution to the linear equation is (3, 2, –3). The correct option is B.
What is Gauss-Jordan's elimination method?
In mathematics, the algorithm known as Gaussian elimination, commonly referred to as row reduction, is used to solve systems of linear equations. It comprises a series of operations carried out on the relevant coefficients matrix.
x – 2z = 9 so x = 2z + 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
Substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
Multiply (1st) equation by 5 and (2nd) equation by 2.
-10y + 35z = - 125
10y - 14z = 62
21z = - 63
z = -3
Substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
Substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
Therefore, the solution to the linear equation is (3, 2, –3). The correct option is B.
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For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range. The vertex is (3, –1), the domain is all real numbers, and the range is y ≥ –1. The vertex is (3, –1), the domain is all real numbers, and the range is y ≤ –1. The vertex is (–3, –1), the domain is all real numbers, and the range is y ≤ –1. The vertex is (–3, –1), the domain is all real numbers, and the range is y ≥ –1.
we have
[tex]f(x)=-2(x+3)^{2}-1[/tex]
we know that
the equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
[tex](h,k)[/tex] is the vertex
If [tex]a > 0[/tex] ------> then the parabola open upward (vertex is a minimum)
If [tex]a < 0[/tex] ------> then the parabola open downward (vertex is a maximum)
In this problem
the vertex is the point [tex](-3,-1)[/tex]
[tex]a=-2[/tex]
so
[tex]-2 < 0[/tex] ------> then the parabola open downward (vertex is a maximum)
The domain is the interval-------> (-∞,∞)
that means------> all real numbers
The range is the interval--------> (-∞, -1]
[tex]y\leq-1[/tex]
that means
all real numbers less than or equal to [tex]-1[/tex]
therefore
the answer is
a) the vertex is the point [tex](-3,-1)[/tex]
b) the domain is all real numbers
c) the range is [tex]y\leq-1[/tex]
see the attached figure to better understand the problem
If 5+3+2=151012, 9+2+4=183662, 8+6+3=482466, 5+4+5= 202504 , then 7+2+5= ?
a.141035
b.143510
c.143542
d.143524
Denise is a professional swimmer who trains, in part, by running. she would like to estimate the average number of miles she runs in each week. for a random sample of 20 weeks, the mean is = 17.5 miles with standard deviation s = 3.8 miles. find a 99% confidence interval for the population mean number of miles denise runs. use a graphing calculator for this one and not the t chart from the book.
Using a 99% confidence level and the given data, the confidence interval for Denise's average weekly running mileage can be calculated using the sample mean, standard deviation, and z-score for the confidence level.
Explanation:Denise, a professional swimmer, uses her running mileage as part of her training analysis. To estimate the population mean for the number of miles she runs weekly, we will calculate the 99% confidence interval using the sample mean and standard deviation from her 20 weeks of data. The formula for a confidence interval is:
CI = mean ± (z* × (s/sqrt(n)))
Where mean is the sample mean, z* is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.
The given data for Denise's running mileage is a mean (μ) of 17.5 miles and standard deviation (s) of 3.8 miles with a sample size (n) of 20 weeks. Since the sample size is greater than 30, we can use the z-distribution to approximate the t-distribution.
To find the appropriate z-score for a 99% confidence interval, we can use a graphing calculator or a z-table. The z-score for a 99% confidence level is approximately 2.576. Plugging the values into the confidence interval formula:
CI = 17.5 ± (2.576 × (3.8/sqrt(20)))
Calculating the margins of error and applying them to the sample mean, we will obtain the confidence interval for the average number of miles Denise runs in a week.
Over what interval of time in minutes was the jogger heart rate changing at the constant rate
We have a graph of the heart rate vs time.
We want to find on what interval the heart rate increases with a constant rate.
That interval is 3min ≤ t ≤ 4 min
The general function that increases with a constant rate is the general linear function:
y = a*x + b
Where a is the slope and also defines the constant rate of change.
Then the interval where the jogger heart rate changes at a constant rate is the part where we have a linear function (not the horizontal line, there the heart rate does not change).
Then the interval where the heart rate changes with a constant rate is:
3min ≤ t ≤ 4 min
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We generally report a measurement by recording all of the certain digits plus ______ uncertain digit(s).
We generally report a measurement by recording all of the certain digits plus one uncertain digit.
What are significant figures?In positional nomenclature, a number's real numbers are its dependable and essential digits for indicating how much of something there is.
If a measurement's result is expressed by a number with more digits than the measurement resolution permits, only those digits up to the measuring resolution's maximum are trustworthy, and only those digits could be significant figures.
Typically, we record all the confirmed digits of measurement together with one questionable digit.
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