If Sam has 5 blue shirts and 7 red shirt, what is Sam's ratio of blue shirts to red shirts?
Answer: 0.71428 or 5:7 or 5/7
Step-by-step explanation: just divide on a calculator
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of 420 accidents provided the following data.
Sunday 66
Monday 50
Tuesday 53
Wednesday 47
Thursday 55
Friday 69
Saturday 80
A) Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. What is the P-Value? Use a 0.05 level of significance, what is your conclusion?
B) Compute the percentage of traffic accidents occuring on each day of the week. What day has the highest percentage of traffic accidents? Does this seem reasonable? Explain.
Answer:
(A) There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.
(B) Saturday has the highest percentage of traffic accidents.
Step-by-step explanation:
(A)
The Chi-square goodness of fit test would be used to determine if the proportion of traffic accidents is the same for each day of the week.
The hypothesis for the test can be defined as follows:
H₀: The proportion of traffic accidents is the same for each day of the week.
Hₐ: The proportion of traffic accidents is not same for each day of the week.
Assume that the significance level of the test is, α = 0.05.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Compute the values in Excel.
The expected frequency for all the days is 60.
The Chi-square test statistic value is, 14.333.
Compute the p-value using the Excel function "=CHISQ.DIST.RT(14.33,6)".
p-value = 0.0262
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
The p-value is less than 0.05.
The null hypothesis will be rejected.
Conclusion:
There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.
(B)
Compute the percentage of traffic accidents occurring on each day of the week as follows:
[tex]\text{Sunday}=\frac{66}{420}\times 100\approx 16\%\\\\\text{Monday}=\frac{50}{420}\times 100\approx 12\%\\\\\text{Tuesday}=\frac{53}{420}\times 100\approx 13\%\\\\\text{Wednesday}=\frac{47}{420}\times 100\approx 11\%\\\\\text{Thursday}=\frac{55}{420}\times 100\approx 13\%\\\\\text{Friday}=\frac{69}{420}\times 100\approx 16\%\\\\\text{Saturday}=\frac{80}{420}\times 100\approx 19\%[/tex]
Saturday has the highest percentage of traffic accidents.
Find the sum of the first 25 terms of the arithmetic sequnce 17,22,27,32.37
Answer:
Step-by-step explanation:
This sequence is adding 5 so
17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97 102 107 112 117 122 127 132 137 = 1925
Answer: The sum of the first 25 terms of this arithmetic sequence is 1925.
Explanation: This sequence, beginning at 17, increases by 5 per term. By simply adding 5 to the preceding term in the sequence, you can find the next term. The first term is 17, and the last term is 137. This means the list of terms is 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, and 137. The sum of these terms is 1925.
what is the quotient of4/6and2/9
Answer:
3
Step-by-step explanation:
Trust meh
Lia has a red ribbon that is 2 1/12 long she has a blue ribbon that is 4 times inches long
Answer:
The answer would be 8 1/3!
Step-by-step explanation:
This is because when you multiply you would convert 2 1/12 to an improper fraction of 25/12 and multiply it by 4/1 to get 100/12 which equals 8 with a remainder of 4/12 simplified to 1/3 so your answer is 8 1/3!
HOPE THIS HELPS!!
2 3/4 subtracted from 11 is equal to 8 1/4
Answer: 2/3
i think 3 divided by 2/3
Step-by-step explanation:
F(x)=-(2x-1)^2-2. What is the value of f(-3)
Work Shown:
f(x) = -(2x-1)^2 - 2
f(-3) = -(2*(-3)-1)^2 - 2 ... replace every x with -3
f(-3) = -(-6-1)^2 - 2
f(-3) = -(-7)^2 - 2
f(-3) = -49 - 2
f(-3) = -51
Is this correct and why?
Answer:
For a given confidence level, t* is never smaller than z*.
Step-by-step explanation:
t* and z* are the critical value of a confidence interval. For example, at 95% confidence, z* = 1.96. This is because 95% of a normal curve is within ±1.96 standard deviations.
A student's t distribution has the same bell-curve shape as a normal distribution, but is shorter and wider, which is why t* is always larger than z*. As the sample size increases to infinity, the distribution approaches normal.
Compare the values of the 5 in 552,299.
Answer:
552,299
500,000
50,000
500,000 is 10 times greater than 50,000
50,000 is 10 times less than 500,000
Step-by-step explanation:
(3х + 4)°
(8х +11)°
Answer:
11x+15
Step-by-step explanation:
In 1 year, how many more hours of sleep
does a giant armadillo get than a platypus?
Answer:
Step-by-step explanation:
If the given variables are 127 hours of sleep per week for a Giant Armadillo, and 98 hours of sleep per week for a Platypus, to determine which animal gets the most sleep, first multiply the total hours of sleep of each animal per week to the total number of weeks In a year, which is 52. Once you get the answers, which are 6,604 hours of sleep in a year for the Giant Armadillo and 5,096 hours of sleep in a year for a Platypus. You subtract 6,604 and 5,096 together to get the answer, which is 1,508. Therefore we conclude that that the Giant Armadillo has 1,508 hours more hours of sleep than a Platypus in a Year.
Answer:
1508 hour I think !!!!!!!!!!
Evaluate the expression.
(-4)2
Answer:
-8
Step-by-step explanation:
4x2=8
change to negative since a negative times a positive is a negative
-8
Answer: -8
Step-by-step explanation: -4* 2= -8
The use of mathematical methods to study the spread of contagious diseases goes back at least to some work by Daniel Bernoulli in 1760 on smallpox. In more recent years many mathematical models have been proposed and studied for many different diseases. The following problem deals with a few of the simpler models and the conclusions that can be drawn from them. Similar models have also been used to describe the spread of rumors and of consumer products. Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit no overt symptoms. Let x and y denote the proportions of susceptibles and carriers, respectively, in the population. Suppose that carriers are identified and removed from the population at a rate β, so dy/dt = −βy.
(i) Suppose also that the disease spreads at a rate proportional to the product of x and y; thus dx/dt = −αxy.
(ii)
(a) Determine y at any time t by solving Eq. (i) subject to the initial condition y(0) = y0.
y(t) =
(b) Use the result of part (a) to find x at any time t by solving Eq. (ii) subject to the initial condition x(0) = x0.
x(t) =
(c) Find the proportion of the population that escapes the epidemic by finding the limiting value of x as t → [infinity].
Answer:
a
[tex]y(t) = y_o e^{\beta t}[/tex]
b
[tex]x(t) = x_o e^{\frac{-\alpha y_o }{\beta }[e^{-\beta t} - 1] }[/tex]
c
[tex]\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }[/tex]
Step-by-step explanation:
From the question we are told that
[tex]\frac{dy}{y} = -\beta dt[/tex]
Now integrating both sides
[tex]ln y = \beta t + c[/tex]
Now taking the exponent of both sides
[tex]y(t) = e^{\beta t + c}[/tex]
=> [tex]y(t) = e^{\beta t} e^c[/tex]
Let [tex]e^c = C[/tex]
So
[tex]y(t) = C e^{\beta t}[/tex]
Now from the question we are told that
[tex]y(0) = y_o[/tex]
Hence
[tex]y(0) = y_o = Ce^{\beta * 0}[/tex]
=> [tex]y_o = C[/tex]
So
[tex]y(t) = y_o e^{\beta t}[/tex]
From the question we are told that
[tex]\frac{dx}{dt} = -\alpha xy[/tex]
substituting for y
[tex]\frac{dx}{dt} = - \alpha x(y_o e^{-\beta t })[/tex]
=> [tex]\frac{dx}{x} = -\alpha y_oe^{-\beta t} dt[/tex]
Now integrating both sides
[tex]lnx = \alpha \frac{y_o}{\beta } e^{-\beta t} + c[/tex]
Now taking the exponent of both sides
[tex]x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} + c}[/tex]
=> [tex]x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} } e^c[/tex]
Let [tex]e^c = A[/tex]
=> [tex]x(t) =K e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }[/tex]
Now from the question we are told that
[tex]x(0) = x_o[/tex]
So
[tex]x(0)=x_o =K e^{\alpha \frac{y_o}{\beta } e^{-\beta * 0} }[/tex]
=> [tex]x_o = K e^{\frac {\alpha y_o }{\beta } }[/tex]
divide both side by [tex] (K * x_o)[/tex]
=> [tex]K = x_o e^{\frac {\alpha y_o }{\beta } }[/tex]
So
[tex]x(t) =x_o e^{\frac {-\alpha y_o }{\beta } } * e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }[/tex]
=> [tex]x(t)= x_o e^{\frac{-\alpha * y_o }{\beta} + \frac{\alpha y_o}{\beta } e^{-\beta t} }[/tex]
=> [tex]x(t) = x_o e^{\frac{\alpha y_o }{\beta }[e^{-\beta t} - 1] }[/tex]
Generally as t tends to infinity , [tex]e^{- \beta t}[/tex] tends to zero
so
[tex]\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }[/tex]
The Red Ravens Swim Team practices several hours a week to get ready for swim meets. They spend 3 times as many practice hours in the pool as in the weight room.If the swim team practiced 8 hours total last week, how many hours did they spend in the pool?
Answer:
the answer is 24 hope this helped
Step-by-step explanation:
If the swim team worked out for 8 hours last week, 6 of those hours were spent in the pool.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, In order to prepare for swim meets, the Red Ravens Swim Team practices for several hours each week. They practice in the water for three times as long as they practice in the gym.
Since the waiting time is three times as in pool times
Let "t" be the time in the pool during practice
thus, Waiting time = 3t
Also given, the swim team practiced 8 hours total last week
So,
t + 3t = 8
t = 2
Thus, time spent in the pool = 3t = 3*2 = 6
therefore, If the swim team practiced 8 hours total last week, 6 hours they spend in the pool.
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solving equations with one variable
Answer:
1) b= -20
Step-by-step explanation:
You bring the variable you want to find to one side by either bringing over the second term to the other side of the equation and change its sign or if it's a fraction you multiply both sides to remove the denominator and then solve
What is the approximate distance between the points (-6, 8) and (4, 13)?
A.3.87
B.125
C.21.10
D. 11.18
do u have a diagram for this?
Write the following comparison as a ratio reduced to lowest terms 70 days to 3 weeks
Answer:
I think that it is already in lowest terms
Step-by-step explanation:
Right triangle A has a base of 2 inches and a height of 7 inches. Right triangle B has a base of 10 inches and a height of 35 inches. Enter the scale factor applied to Right triangle A to produce Right triangle B.
Given:
Right triangle A: Base = 2 inches and Height = 7 inches.
Right triangle B: Base = 10 inches and Height = 35 inches.
To find:
The scale factor applied to Right triangle A to produce Right triangle B.
Solution:
We have,
Base of right triangle A = 2 inches
Base of right triangle B = 10 inches
Now,
[tex]\text{Scale factor}=\dfrac{\text{Side of right triangle B}}{\text{Corresponding side of right triangle A }}[/tex]
[tex]Scale\text{Scale factor}=\dfrac{\text{Base of right triangle B}}{\text{Base of right triangle A }}[/tex]
[tex]\text{Scale factor}=\dfrac{10}{2}[/tex]
[tex]\text{Scale factor}=5[/tex]
Therefore, the scale factor of 5 applied to Right triangle A to produce Right triangle B.
Simplify the expression 4.5(− 6) + 19.
Answer:
-8
thats the answerr im sure
Answer:
The answer is -8.
Try maybe working it out or using a calculator.
-26 times a number minus 22 is equal to 90 less than the number.
Answer:
[tex]x = \frac{68}{27}[/tex]
Step-by-step explanation:
Let x be the number
Write it out: -26x - 22 = x - 90Combine like terms: -27x + 68 = 0Subtract 68 from each side, so it now looks like this: -27x = -68Divide each side by -27 to cancel out the -27 next to x. It should now look like this: [tex]x = \frac{68}{27}[/tex]I hope this helps!
Are E.F and G Collinear if so name the line on which the lie
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.
[ 1 -2 -5 0 4 3 -3 3 0]
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.
A. The matrix is not invertible. In the given matrix the columns do not form a linearly independent set.
B. The matrix is not invertible. the given matrix is A, the equation Ax b has no solution for at least one b in R.
C. The matrix is invertible. The given matrix is not row equivalent to the nx n identity matrix.
D. The matrix is invertible. The given matrix has 3 pivot positions.
Answer:
This shows 3 pivot position matrixes.
Step-by-step explanation:
The given matrix is:
[tex]\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-3&3&0\end{array}\right][/tex]
The option D is correct for this matrix.
The matrix is invertible and the given matrix has 3 pivot positions.
The matrix is invertible if its determinant is nonzero.
Multiply the 3rd row by 1/3.we get:
[tex]\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-1&1&0\end{array}\right][/tex]
Now, add the first row with third row:
[tex]\left[\begin{array}{ccc}0&-1&-5\\0&4&3\\-1&1&0\end{array}\right][/tex]
Replace third row by first row:
[tex]\left[\begin{array}{ccc}-1&1&0\\0&4&3\\0&-1&-5\end{array}\right][/tex]
This shows 3 pivot position matrixes.
Hence, a matrix is invertible and has 3 pivot positions.
Which of the following best describes how the y values are changing over each interval?
х
y
2
4
1
2.
3
4
5
8
16
32
They are increasing by 2 each time,
They are increasing by 4 each time,
They are being multiplied by 2 each time.
They are being multiplied by 4 each time.
Answer:
C
Step-by-step explanation:
They are being multiplied by 2 each time.
The value of the function is given by y = 2x
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
Let the x values be represented as x = { 1 , 2 , 4 , 8 , 16 }
Let the y values be represented as y = { 2 , 4 , 8 , 16 , 32 }
Now , the values of y are changing over the interval as
when multiplied by 2 , we get
2 = 2 x 1
4 = 2 x 2
8 = 2 x 4
16 = 2 x 8
32 = 2 x 16
Therefore , the values are multiplied by 2
Hence , the function is y = 2x
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2w − w = 15
explain if possible, please
Answer:
2w - w = 15You subtract w from 2w and u remain with w.w = 15In a scale drawing, the length of a rectangular room is 6 inches, and the width is 3 inches. The actual length of the room Is 18 feet. What is the scale of the drawing?
Answer:
1/36
Step-by-step explanation:
6*36+216 inches
216/12(converting into feet)=18
therefore, it is 1/36 scale
Find the equation of a line that contains the points (3,1) and (5,-4). Write the equation in slope-intercept form
Answer:
y= -5x/2+17/2.... (x is between -5/2)
slope intercept= mx+b
y= -5x/2+17/2
Step-by-step explanation:
The equation of line in slope intercept form which passes through the points (3,1) and (5,-4) is [tex]-\frac{5}{2} x+\frac{17}{2}[/tex] .
What is the equation of line in slope intercept form?
The equation of line in the form of [tex]y = mx + b[/tex], is called slope intercept form of a line.
How to find equation of line from two points?The equation of line from two points is given by
[tex]y -y_{1} = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } (x-x_{1} )[/tex]
According to the given question
We have two points (3,1) and (5, -4)
Therefore, the equation of line which passes through the points (3,1) and (5, -4) is given by
[tex](y -1)=\frac{-4-1}{5-3} (x-3)[/tex]
⇒[tex](y-1)=\frac{-5}{2}(x-3)[/tex]
⇒[tex]y -1=\frac{-5}{2}x+\frac{15}{2}[/tex]
⇒[tex]y =-\frac{5}{2} x+\frac{15}{2} +1[/tex]
⇒[tex]y = -\frac{5}{2}x+\frac{17}{2}[/tex]
Hence, the equation of line in slope intercept form which passes through the points (3,1) and (5,-4) is [tex]-\frac{5}{2} x+\frac{17}{2}[/tex] .
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Select 3 ratios that are equivalent to 4 : 3
Answer:
3 ratios that are equivelent to 4 : 3
8 : 6
20 : 15
and 12 : 9
Step-by-step explanation:
Isaac's hair was 12 centimeters long after his last haircut, and it grows 8 centimeters every year. Isaac last got his hair cut 8 years ago. How long is it now? Write and solve an equation to find the answer.
Answer:
76
Step-by-step explanation:
1.) 8 x 8 =64
2.) 12 + 64 =76
Answer: it is 76 cm long and the equation is 8x8+12= length of hair after 8 years.
Step-by-step explanation:
The hair grows 8 cm a year and it has been 8 years so we get 8x8. Then the last time he cut his hair it was 12 inches so we have to add that and yeah...
The cost price of a refrigerator is $1850.00. A buyer who is given a discount of 5% for a cash purchase will pay
Answer:
[tex]\huge\boxed{\$1757.50}[/tex]
Step-by-step explanation:
In order to find a 5% discount off $1850, we have to realize 100% of something is the whole thing.
This means that a 5% discount makes the new cost [tex]100-5=95[/tex]% of the original.
To find 95% of a number, we can convert 95% into a decimal and multiply it by 1850.
When converting a percent to a decimal, we always divide the percent by 100.
[tex]95 \div 100 = 0.95[/tex]
We can now multiply 1850 by 0.95.
[tex]1850 \cdot 0.95 = 1757.50[/tex]
So the buyer only pats $1757.50.
Hope this helped!
What is the probability of a sample mean being greater than a z-value of -0.79?
Select one:
a. 0.7852
b. 0.4500
c. 0.2148
d. 0.2852
Step-by-step explanation:
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