if percent of 1 year was 5%:
meaning time between accidents must be atleast 1 week
The mean waiting time that exists between the accidents would be:
- 1 week
'Mean waiting time' is determined through the contemplated value of an odd(random/casual) variable.
Given that,
Probability(P) of no accident taking place in 1 year = 5%
Assuming T be the accidents' number that takes place during a year,
Since 5% is the probability or chance of no accident to take place,
The mean waiting time between accidents = 1 week at least via Poisson process.
Thus, 1 week would be the correct answer.
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Which expression is equivalent to 4+2(1+3x)
Answer:
I'm glad you asked!
Step-by-step explanation:
OK,let's simplify the number for a equivalent expression.
[tex]4+2(1+3x)[/tex]
Distribute:
[tex]=4+(2)(1)+(2)(3x)[/tex]
[tex]= 4+2+6x[/tex]
Combine Like Terms:
[tex]=4+2+6x[/tex]
[tex]=(6x)+(4+2)[/tex]
[tex]=6x+6[/tex]
The Final Answer is : [tex]6x+6[/tex]
The expression that is equivalent to 4+2(1+3x) is 6x+6.
What is an Algebraic expression?Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.
How do simplify the algebraic expression?Given, 4+2(1+3x)
Firstly distribute 2(1+3x) to get 2+6x then,
4+2(1+3x)
=4+2+6x
=6x+6
Thus, 4+2(1+3x)=6x+6
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which is composite number?
Answer:
A whole number that can be made by multiplying other whole numbers.
Example: 18 can be made by 3 × 6 so is a composite number.
16 can be made by 4 x 4 so it is a square root and a composite number
14 can be made by 2 x 7 so is is a composite number.
It is not a prime number as all Composite Number have factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16,
Answer:
We need to examine the natural numbers.
The natural numbers are the counting numbers,
1, 2, 3, 4, 5, 6, ...
The number 1 is neither prime nor composite.
All natural numbers greater than 1 are either prime or composite.
A prime number is a number that has exactly two factors, itself and 1.
A composite number has more than 2 factors.
A composite number is a natural number greater than 2 that is not a prime number.
Examples:
Prime: 2, 3, 5, 7, 11, ...
Composite: 4, 6, 8, 9, 10, 12, ...
What is the measure of angle L in parallelogrami LMNO?
20°
30°
40°
50°
Answer:
40°
Step-by-step explanation:
2x = 3x - 20 add like terms
x = 20 and angle l is equal to 3x minus 20 so 3 × 20 - 20 = 40°
Simplify the expression. Write the answer using scientific notation. (7 × 105)2 a. 4.9 × 1010 b. 4.9 × 1011 c. 4.9 × 109 d. 49 × 1010
Answer:
b. 4.9 × 1011
Step-by-step explanation:
Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2
We open the parenthesis. This may first be expressed as
7² × 10⁽⁵⁾²
Then expand,
= 49 × 10¹⁰
To put in scientific notation, 49 = 4.9 × 10
Hence the expression becomes
= 4.9 × 10 × 10¹⁰
Using the laws of indices
= 4.9 × 10¹¹ in scientific notation
Answer:
4.9 × 1011
Step-by-step explanation:
I did it in grandpoint
In order to solve for the variable in the equation 2 (x + 3) + 5 x = 3 (2 x minus 1), Jaleesa begins by applying the distributive property, then combines like terms. Which equation is the result of these steps?
Answer:
7x+6 = 6x-3
Step-by-step explanation:
2 (x + 3) + 5 x = 3 (2 x - 1)
Distribute
2x+6+5x = 6x-3
Combine like terms
7x+6 = 6x-3
Answer:
7x + 6 = 6x - 3 Option A
Step-by-step explanation:
Now Jalesa wants to simplify this equation.
Firstly applying the distributive property
Distribute the 2 over the parenthesis and distribute the over the parenthesis
that is,
2*x + 2*3 + 5x = 3*2x - 3*1
2x + 6 + 5x = 6x - 3
After that combine like terms
2x + 5x + 6 = 6x - 3
7x + 6 = 6x - 3
Result is:
7x + 6 = 6x - 3
That's the final answer.
1. Mrs. Verner's class has
a total of 15 students. If 8
of them are girls, what
percentage are boys?
Answer:
46.7%
Step-by-step explanation:
Given:
Total number of students in Mrs. Verner's class = 15
Number of girls = 8
To find: percentage are boys
Solution:
Percentage of boys = ( Number of boys / Total number of students ) × 100
Number of boys = Total number of students - Number of girls = 15 - 8 = 7
So,
Percentage of boys = [tex]\frac{7}{15}[/tex] × 100 = 46.7%
What’s the correct answer for this?
Answer:
E:
Step-by-step explanation:
The equation of circles is
(x-a)²+(y-b)²=r²
Where
Center = (a,b) = (-6,-3) and r = 12
Now
The equation becomes
(x+6)²+(x+3)²=144
A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones . 150 customers prefer the Cranberry Walnut Scones . 81 customers who responded were males and prefer the Chocolate Chip Scones . 172 female customers responded . Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones .
1. 25.6%
2. 24.1%
3. 72.9%
4. 98.4%
Answer:
3. 72.9%
Step-by-step explanation:
Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.
So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:
P(M∪C) = P(M) + P(C) - P(M∩C)
Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:
P(M) = 145/317 = 0.4574
There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:
P(C) = 167/317 = 0.5268
Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate chip scones is:
P(M∩C) = 81/317 = 0.2555
Therefore, P(M∪C) is equal to:
P(M∪C) = 0.4574 + 0.5268 - 0.2555
P(M∪C) = 0.7287
P(M∪C) = 72.9%
Answer:
3. 72.9%
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.
There are 172 female customers and 317-172 = 145 male customers.
150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.
81 of those are male, so 167 - 81 = 86 are female.
So the total of desired outcomes is 86 + 145 = 231
Total outcomes:
317 total customers.
Probability:
231/317 = 0.729
So the correct answer is:
3. 72.9%
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
64
Step-by-step explanation:
If the mean is 15, the sum of 5 numbers is:
5*15 = 75Minimum value for the first four numbers would be:
1, 2, 3, 4Then the fifth number is:
75 - (1+2+3+4) = 75 - 10 = 65So the maximum difference is:
65 - 1 = 64In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit
Answer:
The expected value of profit is -$0.65.
Step-by-step explanation:
The rules of the lottery are as follows:
You pay $1 and pick a number from 000 to 999.If your number comes up, you win $350, which is a profit of $349.If you lose, you lose $1.The probability of winning is, P (W) = 0.001.
Then the probability of losing will be,
P (L) = 1 - P (W)
= 1 - 0.001
= 0.999
Let the random variable X represent the amount of profit.
The probability distribution table of the lottery result is as follows:
Result X P (X)
Win +349 0.001
Lose -1 0.999
The formula to compute the expected value of X is:
[tex]E(X)=\sum X\cdot P(X)[/tex]
Compute the expected value of profit as follows:
[tex]E(X)=\sum X\cdot P(X)[/tex]
[tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]
Thus, the expected value of profit is -$0.65.
jack is investing 5000 in an account that earns 4% interest compounded annually. Determine to the nearest month when the investment will be worth 8000
Answer:
The nearest time is 15 years or 180 months
The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. Is the process in control or out of control and why?
Answer:
Step-by-step explanation:
The mean of the reading points is
Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48
The process is out of control if the mean salt level of the readings is greater than 5.4
For the null hypothesis,
µ = 5.4
For the alternative hypothesis,
µ > 5.4
This is a right tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5.4
x = 5.48
σ = 0.3
n = 10
z = (5.48 - 5.4)/(0.3/√10) = 0.84
Looking at the normal distribution table, the probability corresponding to the z score is 0.7996
The probability value to the right of the z score is 1 - 0.7996 = 0.2
Assuming a significance level of 0.05
Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.
If \\(z_1=3+2i\\) and \\(z_2=4+3i\\) and are complex numbers, find \\(z_1z_2\\)
[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]
[tex]z_1z_2=12+8i+9i+6i^2[/tex]
[tex]i^2=-1[/tex], so
[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]
What is the size of angle YXZ?
We have a right triangle and we're given the leg lengths.
tan X = |YZ| / |XZ| = 20/8 = 5/2
X = arctan(5/2) = 68.2°
Answer: 68.2°
tan X = YZ / XZ = 20/8 = 5/2
X = arctan(5/2) = 68.2°
Answer: 68.2°
Give your answers in pi
Answer:
36π
Step-by-step explanation:
area=πr²
=πx6x6
6x6=36
area = 36π
Fraction - Subtrction : 15 5/11 - 7 3/12
Answer:
[tex]= 8 \frac{27}{132} = 8\frac{9}{44}\\ [/tex]
Step-by-step explanation:
[tex]15 \frac{5}{11} - 7 \frac{3}{12} \\ \frac{170}{11} - \frac{87}{12} \\ \frac{2040 - 957}{132} \\ = \frac{1083}{132} \\ = 8 \frac{27}{132} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
8 9/44.
Step-by-step explanation:
15 5/11 - 7 3/12
= 15 - 7 + 5/11 - 1/4 The LCD of 4 and 11 is 44 so we have:
15 - 7 + 20/44 - 11/44
= 8 + 9/44
= 8 9/44.
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 61% C: Scores below the top 39% and above the bottom 21% D: Scores below the top 79% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 67.7 and a standard deviation of 7.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 77.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 67.7, \sigma = 7.8[/tex]
Find the minimum score required for an A grade.
Top 12% of scores get an A.
100-12 = 88th percentile.
The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.175 = \frac{X - 67.7}{7.8}[/tex]
[tex]X - 67.7 = 7.8*1.175[/tex]
[tex]X = 76.865[/tex]
Rounding to the nearest whole number:
The minimum score required for an A grade is 77.
2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
F(x)=2x-6 and g(x)=3x+9,find (f+g)(x)
Answer: 5x-3
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Knowing this, we add the 2 functions together.
2x-6+3x+9
5x-3
What’s the correct answer for this question?
Answer:
107 meters
Step-by-step explanation:
Central angle = 123°
In radians
123° = 123π/180
123° = 2.147 radians
Putting in formula
S = r∅
S = (50)(2.147)
S = 107 meters
The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is ….
Answer:
63.45
Step-by-step explanation:
First, it should be noted that the question is incorrect because 64 can't be divided by 11 but assuming that the question is correct, the solution is as follows
Given
LCM = 368
HCF = 11
One number = 64
Required
The other number
Let both numbers be represented by m and n, such that
[tex]m = 64[/tex]
From laws of HCF and LCM
The product of both numbers = Product of HCF and LCM
i.e.
[tex]m * n = HCF * LCM[/tex]
By substituting 68 for m; 368 for LCM and 11 for HCF
[tex]m * n = HCF * LCM[/tex] becomes
[tex]64 * n = 368 * 11[/tex]
[tex]64n = 4048[/tex]
Divide both sides by 64
[tex]\frac{64n}{64} = \frac{4048}{64}[/tex]
[tex]n = \frac{4048}{64}[/tex]
[tex]n = 63.25[/tex]
Please answer this correctly
Answer:
40 - 59 ⇒ 6
60 - 79 ⇒ 5
Answer:
40-59: 6
60-79: 5
Step-by-step explanation:
If you just added up, you can find all the values.
The following data show the brand, price , and the overall score for stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from (lowest) to (highest). The estimated regression equation for these data is = 23.194 + 0.318x, where x = price ($) and y = overall score.
Brand Price Score
Bose 180 76
Scullcandy 150 71
Koss 95 62
Phillips/O'Neill 70 57
Denon 70 30
JVC 35 34
Required:
a. Compute SST, SSR, and SSE (to 3 decimals).
b. Compute the coefficient of determination r2.
c. What is the value of the sample correlation coefficient?
Answer:
a. SST = 1816
SSR = 1511.804
SSE = 465.804
b. Coefficient of determination, R² = 0.832491079
c. The correlation coefficient r = 0.8636
Step-by-step explanation:
y = 23.194 + 0.318·x
Where:
x = Price
y = Overall score
The observed data are given as follows;
Brand Price Score
Bose 180 76
Scullcandy 150 71
Koss 95 62
Phillips/O'Neill 70 57
Denon 70 30
JVC 35 34
[tex]SST = \sum \left (y - \bar{y} \right )^{2}[/tex]= 1816
[tex]SSR = \sum \left ({y}'-\bar{y{}'} \right )^{2}[/tex] = 1511.804
[tex]SSE = \sum \left (y - {y}' \right )^{2}[/tex] = 465.804
Coefficient of determination
[tex]Coefficient \, of \, determination = \dfrac{SSR}{SST}[/tex]= 0.832
Coefficient of correlation =
[tex]r = \dfrac{n\left (\sum xy \right )-\left (\sum x \right )\left (\sum y \right )}{\sqrt{\left [n\sum x^{2}-\left (\sum x \right )^{2} \right ]\left [n\sum y^{2}-\left (\sum y \right )^{2} \right ]}}[/tex]
Ʃxy = 37500
Ʃx =600
Ʃy = 330
Ʃx² = 74950
Ʃy² = 19966
[tex]r = \dfrac{6 \left (37500 \right )-\left (600 \right )\left (330 \right )}{\sqrt{\left [6\times 74950-\left (600 \right )^{2} \right ]\left [6 \times 19966-\left (330 \right )^{2} \right ]}} = 0.8636[/tex]
Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. T(X1,X2,X3,X4) = (x1 +4x2, 0, 3x2 +x4, x2 -x4)
The transformation matrix for the mapping T is the matrix T such that
[tex]\mathbf T(\vec x)=T\,\vec x[/tex]
where
[tex]T=\begin{bmatrix}1&4&0&0\\0&0&0&0\\0&3&0&1\\0&1&0&-1\end{bmatrix}[/tex]
The correct matrix A is
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
To find the matrix A that represents the linear transformation T, we need to determine the coefficients that map the input vector (X₁, X₂, X₃, X₄) to the output vector (x₁ +4x₂, 0, 3x₂ +x₄, x₂ -x₄)
By comparing the corresponding entries in the input and output vectors, we can determine the coefficients of the matrix A.
The first row of A will have the coefficients for X₁ and X₂, which are 1 and 4 respectively. The second row will have all zeros since the output vector has a zero in the second position. The third row will have the coefficient 3 for X₂ and 1 for X₄. Finally, the fourth row will have the coefficient 1 for X₂ and -1 for X₄.
Thus, the matrix A that implements the mapping T is:
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
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two lines intersect is more than one point
Answer:
FALSE
Step-by-step explanation:
two lines can be parallel- no intersectstwo lines intersect- one pointWhen Sunita weighed herself on Monday, she found that she had gained 1 1/4 kg. Earlier her weight was 46 3/8 kg. What was her weight on Monday? Please give me Statements! Please Do it fast(Its ok if you dont do it fast ok its not like that much of an urgent) #GoAwayCoronaVirus
Answer:
[tex]47\frac{5}{8}[/tex]
Step-by-step explanation:
Weight from before + Weight gained
[tex]46\frac{3}{8} +1\frac{1}{4}[/tex]
Convert to improper fractions.
[tex]371/8 + 5/4[/tex]
Find the common denominator.
[tex]371/8 + 10/8[/tex]
Add.
[tex]381/8[/tex]
Convert to a mixed fraction.
[tex]47\frac{5}{8}[/tex]
Answer:
47 5/8 kg
Step-by-step explanation:
Ealier weight + gained weight = Monday's weight
46 3/8 + 1 1/4
= 371/8 + 5/4
= 371/8 + 10/8
= 381/8
= 47 5/8 kg
A 10 foot tree create a shadow that is 15 feet long. Find the angle of elevation of the sun
The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long is 33.69 degrees
To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.
Given that:
The tree's height is 10 feet.
The length of the shadow is 15 feet.
Let's assume that the tree's height is "h" feet.
Length of its shadow is represented by "s" feet
The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.
The angle can be determined using the tangent function.
[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]
Now, substitute the given values:
[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]
[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]
The angle of elevation can be obtained by taking the inverse tangent of 2/3
angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]
angle of elevation ≈ 33.66 degrees
So, the angle of elevation of the sun is approximately 33.69 degrees.
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Jaleel and Lisa are simplifying the expression 2(x-2) + 2 as shown
Answer:
Jaleel is correct because 2 (x + 2) = 2x - 4
Step-by-step explanation:
To solve 2 (x - 2) + 2:
2 (x - 2) + 2
Distribute
2x - 4 + 2
Combine like terms
2x - 2
Lisa did not distribute correctly :)
Answer:
D
Step-by-step explanation:
The Sky Train from the terminal to the rental car and longterm parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. What is the average waiting time (in minutes)
Answer:
Average waiting time = 4 minutes
Step-by-step explanation:
From this question, we are told that the sky train is supposed to arrive every 8 minutes.
Thus, the waiting time of the passengers for the train = 8 minutes.
Then, the average waiting time is simply the mean or 50th percentile of the total waiting time.
So, average waiting time = 50% × 8
Average waiting time = 4 minutes
Can someone help me with this I’m sorry I really just don’t know
Answer:
15
Step-by-step explanation:
Because the two triangles are similar:
[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]
Hope this helps!
