Answer: -4/3x - 6
Step-by-step explanation:
First, let's find the slope of the line
y=- -4/3x+11
As the equation is already in slope-intercept form y=mx+c ,
Slope = -4/3
Let a point (x,y) be on the new line.
By finding the slope again,
y−2/x+6= -4/3
y−2= -4/3(x+6)
y−2= -4/3x−8
y = -4/3x - 6
find the circumference of a circle with a diameter of 6 cm
Circumference = πd
~substitute → (π)(6 cm)
~simplify → 6π cm.
So the circumference of the circle shown here is 6π cm.
Answer:
18.85 cm
Step-by-step explanation:
The circumference of a circle has a formula.
Circumference = π × diameter
The diameter is 6 centimeters.
Circumference = π × 6
Circumference ≈ 18.85
The circumference of the circle is 18.85 centimeters.
The average life a manufacturer's blender is 5 years, with a standard deviation of 1 year. Assuming that the lives of these blenders follow approximately a normal distribution, find the probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
Answer:
55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 5, \sigma = 1, n = 9, s = \frac{1}{\sqrt{9}} = 0.3333[/tex]
Find the probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
This is the pvalue of Z when X = 5.1 subtracted by the pvalue of Z when X = 4.5. So
X = 5.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.1 - 5}{0.3333}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a pvalue of 0.6179
X = 4.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.5 - 5}{0.3333}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.6179 - 0.0668 = 0.5511
55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.
The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5. Construct a 97.5% confidence interval for the mean amount of juice in all such bottles. Assume an approximate Normal distribution.
Answer:
The required 97.5% confidence interval is
[tex]\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\[/tex]
Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces
.
Step-by-step explanation:
The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5
Let us first compute the mean and standard deviation of the given data.
Using Excel,
=AVERAGE(number1, number2,....)
The mean is found to be
[tex]\bar{x} = 15.5[/tex]
=STDEV(number1, number2,....)
The standard deviation is found to be
[tex]s = 0.31[/tex]
The confidence interval for the mean amount of juice in all such bottles is given by
[tex]$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean, n is the samplesize, s is the sample standard deviation and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 97.5% confidence level.
The t-score corresponding to a 97.5% confidence level is
Significance level = α = 1 - 0.975 = 0.025/2 = 0.0125
Degree of freedom = n - 1 = 8 - 1 = 7
From the t-table at α = 0.0125 and DoF = 7
t-score = 2.8412
So the required 97.5% confidence interval is
[tex]\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\[/tex]
Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces.
What is the equation of the line graphed below?
Answer:
C. y = 4x -6
Step-by-step explanation:
The line intercepts the y-axis at -6, consistent with the first three answer choices.
It appears to have an x-intercept of about 1.5 (certainly, less than 2), so between that point and the y-intercept, there is a "rise" of 6 and a "run" of about 1.5.
Then the slope is rise/run = 6/1.5 = 4. This will be the x-coefficient in the slope-intercept form:
y = mx + b
y = 4x -6
The lines shown below are parallel. If the green line has a slope of -1, what is
the slope of the red line?
A. 1
6
0
B. -1
C.-2
5
D. 2
Answer:
-1
Step-by-step explanation:
Parallel lines have the same slope. If the slope of the green line is -1, the slope of the red line is -1
The slope of the red line is -1
What are parallel lines?"These are the lines in the same plane that are at equal distance from each other and never meet."
What is slope of a line?"It is the change in y coordinate with respect to the change in x coordinate."
For given question,
The red line and the green line shown in the figure are parallel lines.
The slope of the green line is -1.
We know that the slope of the parallel lines is equal.
This means the slope of red line would be -1
Therefore, the slope of the red line is -1
Learn more about slope of a line here:
https://brainly.com/question/14511992
#SPJ2
Martin had 24 5 pounds of grapes left. Which expression shows the pounds of grapes Martin has if he doubles his current amount?
Answer:
x=2*2 4/5
Step-by-step explanation:
: Martin had 2 4/5 pounds of grapes left.
So x=2*2 4/5
x=2* 14/5
x=28/5
x=5 3/5
The expression shows the pounds of grapes Martin has if he doubles his current amount of grapes. x=2*2 4/5
An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct a relative frequency table for the instructor using five classes. Use the minimum value from the data set as the lower class limit for the first row, and use the lowest possible whole-number class width that will allow the table to account for all of the responses. Use integers or decimals for all answers.
48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
Provide your answer below:
Lower Class Limit Upper Class Limit Relative Frequency
Answer:
The frequency table is shown below.
Step-by-step explanation:
The data set arranged ascending order is:
S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58, 60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}
It is asked to use the minimum value from the data set as the lower class limit for the first row.
So, the lower class limit for the first class interval is 33.
To determine the class width compute the range as follows:
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
[tex]=84-33\\=51[/tex]
The number of classes requires is 5.
The class width is:
[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]
So, the class width is 10.
The classes are:
33 - 42
43 - 52
53 - 62
63 - 72
73 - 82
83 - 92
Compute the frequencies of each class as follows:
Class Interval Values Frequency
33 - 42 33 , 34 , 39 3
43 - 52 48 , 49 , 50 3
53 - 62 53 , 54 , 55 , 56 , 58 , 58, 60 7
63 - 72 63 , 64 , 65 , 70 , 71 5
73 - 82 74 1
83 - 92 84 1
TOTAL 20
Compute the relative frequencies as follows:
Class Interval Frequency Relative Frequency
33 - 42 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
43 - 52 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
53 - 62 7 [tex]\frac{7}{20}\times 100\%=35\%[/tex]
63 - 72 5 [tex]\frac{5}{20}\times 100\%=25\%[/tex]
73 - 82 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
83 - 92 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
TOTAL 20 100%
Which of the following best describes the algebraic expression 5(x + 2) - 3 ?
bre
Answer:
D
Step-by-step explanation:
What is the solution to the system of equations? please explain I really need help
Answer:
The solution is the point where the lines intersect.
The answer is (-3 , -8)
a) Al usar un microscopio el microscopio se amplía una célula 400 veces. Escribe el factor de ampliación como cociente o como escala.
b) La imagen de una célula usando dicho microscopio mide 1,5 mm ¿ Cuánto mide la célula en la realidad?
Answer:
x = 0,00375 mm
Step-by-step explanation:
a) El factor de ampliación es 400/1 es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio
b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:
Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)
Es decir 1,5 mm ⇒ 400
x (mm) ⇒ 1 (tamaño real de la célula)
Entonces
x = 1,5 /400
x = 0,00375 mm
Simplify the expression (5j+5) – (5j+5)
Answer:
0
Step-by-step explanation:
multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!
Answer:
0
Explanation:
step 1 - remove the parenthesis from the expression
(5j + 5) - (5j + 5)
5j + 5 - 5j - 5
step 2 - combine like terms
5j + 5 - 5j - 5
5j - 5j + 5 - 5
0 + 0
0
therefore, the simplified form of the given expression is 0.
A small regional carrier accepted 16 reservations for a particular flight with 12 seats. 8 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 48% chance, independently of each other.
A) Find the probability that overbooking occurs.
B) Find the probability that the flight has empty seats.
Answer:
a) 32.04% probability that overbooking occurs.
b) 40.79% probability that the flight has empty seats.
Step-by-step explanation:
For each booked passenger, there are only two possible outcomes. Either they arrive for the flight, or they do not arrive. The probability of a passenger arriving is independent of other passengers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Our variable of interest are the 8 reservations that went for the passengers with a 48% probability of arriving.
This means that [tex]n = 8, p = 0.48[/tex]
A) Find the probability that overbooking occurs.
12 seats, 8 of which are already occupied. So overbooking occurs if more than 4 of the reservated arrive.
[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{8,5}.(0.48)^{5}.(0.52)^{3} = 0.2006[/tex]
[tex]P(X = 6) = C_{8,6}.(0.48)^{6}.(0.52)^{2} = 0.0926[/tex]
[tex]P(X = 7) = C_{8,7}.(0.48)^{7}.(0.52)^{7} = 0.0244[/tex]
[tex]P(X = 8) = C_{8,5}.(0.48)^{8}.(0.52)^{0} = 0.0028[/tex]
[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2006 + 0.0926 + 0.0244 + 0.0028 = 0.3204[/tex]
32.04% probability that overbooking occurs.
B) Find the probability that the flight has empty seats.
Less than 4 of the booked passengers arrive.
To make it easier, i will use
[tex]P(X < 4) = 1 - (P(X = 4) + P(X > 4))[/tex]
From a), P(X > 4) = 0.3204
[tex]P(X = 4) = C_{8,4}.(0.48)^{4}.(0.52)^{4} = 0.2717[/tex]
[tex]P(X < 4) = 1 - (P(X = 4) + P(X > 4)) = 1 - (0.2717 + 0.3204) = 1 - 0.5921 = 0.4079[/tex]
40.79% probability that the flight has empty seats.
M/J Grade 8 Pre-Algebra-PT-FL-1205070-003
Answer:
Following are the description of the given course code:
Step-by-step explanation:
The given course code is Pre-Algebra, which is just an introduction arithmetic course programs to train high school in the Algebra 1. This course aims to strengthen required problem solving skills, datatypes, equations, as well as graphing.
In this course students start to see the "big picture" of maths but also understand that mathematical, algorithmic, and angular principles are intertwined to form a basis for higher mathematics education.The duration of this code is in year and it is divided into two levels. In this, code it includes PreK to 12 Education Courses , with the general mathematics .Answer:
A
Step-by-step explanation:
2830000000 who can write this number in “Scientific Notation.”
Answer:
[tex]2.83*10^{9}[/tex]
Step-by-step explanation:
what is the equation of the line that is parallel to the given line and passes through the point (2, 3) ? a. x + 2y = 4 b. x + 2y = 8 c. 2x + y =4 d. 2x + y = 8
Answer:
see explanations
Step-by-step explanation:
The given blue line has a slope of m = -1/2.
The line parallel to the given line passing through point (x0,y0)=(2,3) is given by the point-slope form:
(y-y0)=m(x-x0)
substitute values
(y-3) = (-1/2)(x-2)
Expand and transpose
y = (-1/2)x + 1 + 3
y = (-1/2)x + 4 ....................(1)
We choose the second equation b. x+2y=8 and convert to slope-intercept form:
2y=-x+8
y = (-1/2)x + 4, which is exactly equation (1)
So
b. x+2y=8 is the correct answer.
Answer:
b. x + 2y = 8
Step-by-step explanation:
Will give brainliest amswer
Answer:
A= 12.55363262
Step-by-step explanation:
C=2πr
12.56=2πr
12.56=6.283185307r
12.56 ÷6.283185307 = 6.283185307r ÷6.283185307
1.998986085 = r
A=πr^2
A=π(1.998986085)^2
A= 12.55363262
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $800, 3 prizes of $200, 5 prizes of $50, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answer:
The expected value of this raffle if you buy 1 ticket is $0.41.
Step-by-step explanation:
The expected value of the raffle if we buy one ticket is the sum of the prizes multiplied by each of its probabilities.
This can be written as:
[tex]E(X)=\sum p_iX_i[/tex]
For example, the first prize is $800 and we have only 1 prize, that divided by the number of tickets gives us a probability of 1/5000.
If we do this with all the prizes, we can calculate the expected value of a ticket.
[tex]E(X)=\sum p_iX_i\\\\\\E(X)=\dfrac{1\cdot800+3\cdot200+5\cdot50+20\cdot20}{5000}\\\\\\E(X)=\dfrac{800+600+250+400}{5000}=\dfrac{2050}{5000}=0.41[/tex]
Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.
Answer: D
Step-by-step explanation:
According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year
The initial population Po = 114000
Rate = 1.5% = 0.015
The declining population formula will be:
P = Po( 1 - R%)x^2
The decay formula
Since the population is decreasing, take away 0.015 from 1
1 - 0.015 = 0.985
Substitutes all the parameters into the formula
P(s) = 114000(0.985)x^2
P(s) = 114000× 0985x^2
The correct answer is written above.
Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.
Jess is cutting bows of ribbon which will be used to wrap gifts. If jess needs 1 7/11 feet of ribbon to make a bow and she has 36 feet of ribbon, then how many bows can jess make?
Answer:
22
Step-by-step explanation:
You need to divide 36 ft by 1 7/11 ft, and then round down if you don't get a whole number.
[tex]\dfrac{36~ft}{1 \frac{7}{11}~ft} =[/tex]
[tex]= \dfrac{36}{\frac{18}{11}}[/tex]
[tex] = \dfrac{36}{1} \times \dfrac{11}{18} [/tex]
[tex] = \dfrac{36 \times 11}{1 \times 18} [/tex]
[tex] = 22 [/tex]
Answer: 22
Pleaase help me..........
Answer: 12/25
Steps:
1. Turn 0.48 into 48/100
2. Divide the numerator and denominator of 48/100 by 4, which ends up as 12/25.
0.48 as a fraction is 48/100
We can simplify this fraction.
48÷2/100÷2 → 24/50
24÷2/50÷2 → 12/25
Therefore, the answer is A.
Best of Luck!
find the solutions to 9x^2-54x=0
Answer:
x₁ = 0
x₂ = 6
Step-by-step explanation:
9x² - 54x = 0
9x(x - 6) = 0
x(x - 6) = 0
x = 0
x - 6 = 0 → x = 6
Hope this helps! :)
Answer:
x₁ = 0
x₂ = 6
Step-by-step explanation:
9x² - 54x = 0
9x(x - 6) = 0
9x = 0 => x₁ = 0
x - 6 = 0 => x₂ = 6
A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Answer:
x = y = 26 cm; z = 13 cm
Step-by-step explanation:
We can calculate the dimensions of the square base as
∛(2·8788) = 26 cm
the height of the box will be half of 26/2 which is 13 cm.
x = y = 26 cm; z = 13 cm
then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier
area = xy +2(xz +yz)
But we were given the volume as 8788
Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then
L = xy +2(xz +yz) +λ(xyz -8788)
For x: we have
y+2z +λyz=0
For y we have
y: x +2z +λxz=0
For z we have 2x+2y +λxy=0............eqn(*)
For we have xyz -8788=0
If we simplify the partial derivative equation of y and x above then we have
λ = (y +2z)/(yz).
= 1/z +2/y............eqn(1)
λ = (x +2z)/(xz)
= 1/z +2/x.............eqn(2)
Set eqn(1 and 2) to equate we have
1/z +2/y = 1/z +2/x
x = y
From eqn(*) we can get z
λ = (2x +2y)/(xy) = 2/y +2/x
If we simplify we have
1/z +2y = 2/x +2/y
Then z = x/2
26/2 =13
Therefore,
x = y = 2z = ∛(2·8788)
X= 26
y = 26 cm
z = 13 cm
50 pts If You Get IT RIGHT!!!
Kellianne lined up the interior angles of the triangle along line p below. Triangle A B C. Angle A, B, and C are on line p. Which statements are true for line p? Check all that apply.
Answer:
angles a and b are lined up
In a study of the accuracy of fast food drive-through orders, one restaurant had 40 orders that were not accurate among 307 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is greater than 10%. State the test result in terms of the claim. Identify the null and alternative hypotheses for this test The test statistic for this hypothesis test is? The P-value for this hypothesis test is? Identify the conclusion for this hypothesis test. State the test result in terms of the claim.
Answer:
We conclude that the rate of inaccurate orders is greater than 10%.
Step-by-step explanation:
We are given that in a study of the accuracy of fast food drive-through orders, one restaurant had 40 orders that were not accurate among 307 orders observed.
Let p = population proportion rate of inaccurate orders
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10% {means that the rate of inaccurate orders is less than or equal to 10%}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that the rate of inaccurate orders is greater than 10%}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of inaccurate orders = [tex]\frac{40}{307}[/tex] = 0.13
n = sample of orders = 307
So, the test statistics = [tex]\frac{0.13-0.10}{\sqrt{\frac{0.10(1-0.10)}{307} } }[/tex]
= 1.75
The value of z-test statistics is 1.75.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)
= 1 - 0.95994 = 0.04006
Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 1.75 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the rate of inaccurate orders is greater than 10%.
Find the missing side. Round your answer to the nearest tenth.
Please answer this correctly without making mistakes
Answer:
Question 2
Step-by-step explanation:
2) The time when she woke up was - 3° C
During nature walk, temperature got 3° C warmer than when she woke up.
So, temperature during nature walk = - 3 + 3 = 0° C
Plz help! correct answer will get another brainliest!
Answer:
2.2360679774998
mean-7
Step-by-step explanation:
Answer:
The mean is going to be 7 and the standard deviation is 2.5819
Step-by-step explanation:
The mean is every number added together then divided by the number of numbers present.
4+6+8+10= 28
There are 4 numbers so divide 28 by 4 and you get 7.
I hope this helps you.
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
The average number of tunnel construction projects that take place at any one time in a certain state is 3. Find the probability of exactly five tunnel construction projects taking place in this state.
Answer: 0.1008188
Step-by-step explanation:
The question will usng the poisson distribution formula:
Given :
Mean(λ) number of occurrence in a given interval = 3
P(X=x) = Probability of exactly x occurrence in a given interval
Number of desired occurence(x) = 5
P(X=x) = [(λ^x) * (e^-λ)] / x!
Where ; e = base of natural logarithm = 2.7182818
P(X=5) = [(3^5) * (e^-3)] / 5!
P(X=5) = [(243) * (0.0497870)] / 120
P(X=5) = [12.098257] / 120
P(X=5) = 0.1008188
Answer:0.10
Step-by-step explanation:
2.
On a spinner numbered 1-9, what is the probability of spinning a multiple of 3?
0
1/2
1/3
2/3
Answer:
1/3
Step-by-step explanation:
the multiples of three is three, six, and nine
which is 3/9 bc the total is 9
hope this helps