Answer:
26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities
Step-by-step explanation:
There is nothing stating that the letters and numbers can't be repeated, so all 26 letters of the alphabet and all 10
digits can be used again.
If the first is A, we have 26 possibilities:
AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.
If the first is B, we have 26 possibilities:
BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ
And so on for every letter of the alphabet. There are 26 choices for the first letter and 26 choices for the second letter. The number of different combinations of 2 letters is: 26 × 26 = 676
The same applies for the three digits. There are 10 choices for the first, 10
for the second and 10 for the third:
10 × 10 × 10 = 1000
So for a license plate which has 2 letters and 3 digits, there are: 26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities.
Hope this helps.
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
A large cell phone company would like to know if their clients are happy with the service they provide . Which of the following methods would be the best for choosing a random sample that is a fair representation of their clients?
Answer:
2nd option. this provides an unbiased way to choose the clients surveyed.
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
Answer:
a) percentage of the employees that will experience lost-time accidents in both years = 1.2%
b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%
Step-by-step explanation:
given
percentage of lost time accident last year
P(L) = 8% = 0.08 of the employees
percentage of lost time accident current year
P(C) = 4% = 0.04 of the employees
P(C/L) = 15% = 0.15
using the probability
P(L ∩ C) = P(C/L) × P(L)
= 0.08 × 0.15 = 0.012 = 1.2%
percentage of the employees will experience lost-time accidents in both years = 1.2%
b) Using the probability of the event
P(L ∪ C) = P(L) + P(C) - P(L ∩ C)
= 0.08 + 0.04 -0.012 = 0.108 = 10.8%
percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%
If a person with a height of 58 inches takes 2,601 steps per mile, a person with a height of 64 inches takes 2,357 steps per mile, and a person with a height of 76 inches takes 1,985 steps per mile, what is the average number of steps of three 58-inch people, five 64-inch people, and two 76-inch people. Afterwards, find the weighted average number of steps. How does the average compare with the weighted average? Which value is a more accurate representation of the data?
Answer:
1. Average Number of Steps of
= Total of the different steps / divided by 3
= 6,943/3
= 2,314.3 steps
2. Weighted Average Number of Steps of 3, 58-inch, 5, 64-inc, and 2, 76-inch people
= Total steps by the 10 people divided by 10
= 23,558/10
= 2,355.8 steps
3. The difference is not much.
4. The weighted average (2,355.8 steps) is a more accurate representation of the data. The calculation of the ordinary average steps is more confusing than the weighted average steps.
Step-by-step explanation:
1. Calculation of the Weighted Average Number of Steps of:
3, 58-inch people = 3 x 2,601 = 7,803
5, 64-inch people = 5 x 2,357 = 11,785
2, 76-inch people = 2 x 1,985 = 3,970
10 persons' total steps = 23,558
2. Calculation of the ordinary average:
58-inch people = 2,601
64-inch people = 2,357
76-inch people = 1,985
Total steps 6,943
Find the least common multiple of $6!$ and $(4!)^2.$
Answer:
The least common multiple of $6!$ and $(4!)^2.$
is 6×4! or 144
Simplify the expression.
16 • 4^-4
A. 256
B. -256
C. 1/16
D. -4,096
Answer:
C. 1/16
Step-by-step explanation:
[tex]16 * 4^{-4}[/tex]
16 can be written as a power of 4.
[tex]4^2 * 4^{-4}[/tex]
The bases are same, add exponents.
[tex]4^{2+-4}[/tex]
[tex]4^{-2}[/tex]
Simplify negative exponent.
[tex]\frac{1}{4^2 }[/tex]
[tex]\frac{1}{16}[/tex]
When a button is pressed, a computer program outputs a random even number greater than 0 less than 8. You press the button 4 times.
Can some help me with this?
Answer:
Well all even numbers between 0 and 8 are,
2, 4, 6, 8
Meaning if the button is pressed 4 times 2, 4, 6, or 8 will be outputted.
When press button 4 times. Then output of the program will be, [tex](2,4,6,2)[/tex]
Even number:Any number that can be exactly divided by 2 is called as an even number.
Given that, When a button is pressed, a computer program outputs a random even number greater than 0 less than 8.
Even numbers greater than 0 less than 8 are,
[tex]=2,4,6[/tex]
When press button 4 times. Then output of the program will be,
[tex]=(2,4,6,2)[/tex]
Learn more about the even numbers here:
https://brainly.com/question/581879
What is the complete factorization of 36y2 − 1?
Answer:
36y² - 1
Factorize
We have the final answer as
[tex](y - \frac{1}{6} )(36y + 6)[/tex]
Hope this helps you
The function ƒ(x) = 2x is vertically translated 5 units down and then reflected across the y-axis. What's the new function of g(x)?
Answer:
g(x) = -2x - 5
2x becomes -2x as a reflection across the y-axis
add on -5 to shift the function 5 units down
35=7x Equals What? Like this is os hard for me
Answer:
x=5
Step-by-step explanation:
35 = 7x
Divide each side by 7
35/7 = 7x/7
5 = x
Find the value of y.
[tex]y^2 = 9(9+3)\\\\y^2 = 9(12)\\\\y^2 =3^2\cdot3\cdot2^2\\\\y = 6\sqrt{2}[/tex]
f(x)=x^2+12x+7 f(x)=(x+_)^2+_ Rewrite the function by completing the square
Answer:
f(x) = (x + 6)² - 29
Step-by-step explanation:
Given
f(x) = x² + 12x + 7
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
x² + 2(6)x + 36 - 36 + 7
= (x + 6)² - 29, thus
f(x) = (x + 6)² - 29
answers are 6, and -29
6. Look at the figure below.
Are triangles ABC and DEC congruent?
Explain why or why not.
Answer:
Yes
Step-by-step explanation:
They are congruent by the AAS postulate.
∠A corresponds to and is congruent to ∠D
Side BC corresponds to and is congruent to side EC
∠C is congruent to ∠C by the Vertical Angles Theorem.
So, ΔABC ≅ ΔDEC
At the city museum, child admission is $ 5.30 and adult admission is $ 9.40 . On Sunday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1206.00 . How many child tickets were sold that day?
Answer:
36 tickets
Step-by-step explanation:
At a city museum, child tickets are sold for $5.30, and adult tickets are sold for $9.40
The total sales that were made are $1206
Let x represent the number of child tickets that were sold
Let y represent the number of adult tickets that was sold
5.30x +9.40y= 1206
The number of adult tickets sold was three times greater than the child tickets
y= 3x
Substitute 3x for y in the equation
5.30x + 9.40y= 1206
5.30x + 9.40(3x)= 1206
5.30x + 28.2x= 1206
33.5x= 1206
Divide both sides by the coefficient of x which is 33.5
33.5x/33.5= 1206/33.5
x = 36
Hence the number of child tickets that were sold that day is 36 tickets
Line AB and Line CD are parallel lines. Which translation of the plane can we use to prove angles x and y are congruent, and why?
Answer:
Option C.
Step-by-step explanation:
In the given figure we have two parallel lines AB and CD.
A transversal line FB intersect the parallel lines at point B and C.
We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.
[tex]\angle ABC=\anle ECF[/tex]
[tex]x=y[/tex]
To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.
Therefore, the correct option is C.
evaluate the expression 2(5 -(1/2m)) - 7 where m =4
Answer:
-1
Step-by-step explanation:
since m=4
we substitute in eqn which is 2(5-(1/2m))
2(5-(1/2(4)))
2(5-2)-7
=-1
Reflection Over Parallel Lines Please complete the attached reflection. Thanks!
Answer: A(3, -5)
B(6, -2)
C(9, -2)
Step-by-step explanation:
If we have a point (x, y), and we do a reflection over the axis y = a, then the only thing that will change in our point is the value of x.
Now, the distance between x and a must remain constant before and after the reflection.
so if x - a = d
then the new position of the point will be:
(a - d, y) = (2a - x, y).
I will use that relationship for the 3 points
A)
We start with the point (1, -5)
The reflection over y = -1 leaves.
The distance between 1 and -1 is = 1 - (-1) = 2.
Then the new point is (-1 - 2, -5) = (-3, -5)
Now we do a reflection over y = 1, so D = -3 - 1 = -2
Then the new point is:
A = (1 -(-2), -5) = (3, -5)
B) (2, -2)
Reflection over y = -1.
distance, d = 2 - (-1) = 3
the point is (-1 - 3, -2) = (-4, -2)
Now, a reflection over y = 1.
The distance is D = -4 - 1 = -5
The new point is (1 - (-5), 2) = (6, -2)
C) (5, -2)
reflection over y = -1
Distance: D = 5 - ( - 1) = 6
New point: (-1 - 6, -2) = (-7, -2)
Reflection over y = 1.
Distance D = -7 - 1 = -8
New point ( 1 - (-8), -2) = (9, -2)
Suppose that f(x,y) is a smooth function and that its partial derivatives have the values, fx(8,5)=2 and fy(8,5)=2. Given that f(8,5)=−2, use this information to estimate the value of f(9,6).
Answer:
f(9,6) = 2
Step-by-step explanation:
We know df = (df/dx)dx + (df/dy)dy
From the question, df/dx = fx(8,5) = 2 and df/dy = fy(8,5) = 2
Since we need to find f(9,6) and f(8,5) = -2
dx = 9 - 8 = 1 and dy = 6 - 5 = 1
f(9,6) = f(8,5) + df
df = (df/dx)dx + (df/dy)dy
df = fx(8,5)dx + fy(8,5)dy
Substituting the values of fx(8,5) = 2, fy(8,5) = 2, dx = 1 and dy = 1
df = 2 × 1 + 2 × 1
df = 2 + 2
df = 4
f(9,6) = f(8,5) + df
substituting the value of df and f(8,5) into the equation, we have
f(9,6) = -2 + 4
f(9,4) = 2
The value of f(9,6) = 2
What is the product of the polynomials below? (4x^2-2x-4)(2x+4)
Answer: 8x³ + 12x² - 16x - 16
Step-by-step explanation:
(4x² - 2x - 4)(2x + 4)
= (2x + 4)(4x² - 2x - 4)
= 2x(4x² - 2x - 4) + 4(4x² - 2x - 4)
= 8x³ - 4x² - 8x + 16x² - 8x - 16
= 8x³ + (-4x² + 16x²) + (-8x - 8x) - 16
= 8x³ + 12x² - 16x - 16
Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.
Answer:
Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
Step-by-step explanation:
Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:
[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]
Let integrate both sides in terms of x:
[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]
[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation
Answer:
15
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
30 hcchxfifififififfud7dd7d
One grade of tea costing $3.20 per pound is mixed with another grade costing $2.00 per pound to make 20
pounds of a blend that will sell for $2.72 per pound. How much of the $3.20 grade is needed? Formulate an
equation and then solve it to find how much of the $3.20 grade is needed.
Answer:
X+y = 20... equation 1
3.2x + 2y = 54.4...equation 2
X= 12
12 of $3.2 grade is needed
Step-by-step explanation:
Let x = grade containing$ 3.2 per pound
Let y = grade containing $2.00 per pound
X+y = 20... equation 1
X3.2 +2y = 20(2.72)
3.2x + 2y = 54.4...equation 2
Multiplying equation 1 by 2
2x +2y = 40
3.2x + 2y = 54.4
1.2x = 14.4
X= 12
If x= 12
2x +2y = 40
2(12) + 2y = 40
2y = 40-24
2y = 16
Y= 8
Write the equation of the line in slope intercept form that is perpendicular to the line y=-(3/2)x +7. Show your work
Answer:
the answer is y= 2/3x - 5
Find the slope of the line in each figure. If the slope of the line is undefined, it indicates. Then write an equation for the given line. ASAP !! NEED IT
Answer:
-3
Step-by-step explanation:
Easy way:
Between the two marked points, you can count that you need to go down 6 and over 2. That means the rise/run is -6/2, or -3.
Full way:
Starting Point: (-1,3)
Ending Point: (1,-3)
Slope is given by (y₂-y₁)/(x₂-x₁)
To calculate this, (-3-(3))/(1-(-1))
Clean up the double negatives to get (-3-3)/(1+1), AKA -6/2
-6/2 = -3.
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
A poll shows that 41% of voters in a city favor of a $0.0.1 tax increase. If 25 voters are selected at random, what is that exactly 15 of them will vote in favor of the initiative?
Answer:
The probability is 0.026 to 3 d.p
Step-by-step explanation:
To calculate this , we shall be using the Bernoulli approximation.
let P = percentage of voters supporting the increase = 41% = 41/100 = 0.41
q = percentage of voters not supporting = 100-41% = 59% = 59/100 = 0.59
Now we want to calculate that exactly 15 out of 25 will vote in favor
Mathematically that would be ;
25C15 p^15 q^10
= 25C15 0.41^15 0.59^10
= 0.025981307443 or simply 0.026 to 3 decimal places
Rewrite the equation in =+AxByC form. Use integers for A, B, and C. =−y6−6+x4
Answer:
6x + y = -18
Step-by-step explanation:
The given equation is,
y - 6 = -6(x + 4)
We have to rewrite this equation in the form of Ax + By = C
Where A, B and C are the integers.
By solving the given equation,
y - 6 = -6x - 24 [Distributive property]
y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]
y = -6x - 18
y + 6x = -6x + 6x - 18
6x + y = -18
Here A = 6, B = 1 and C = -18.
Therefore, 6x + y = -18 will be the equation.
In a four-digit number, the sum of the thousands and hundred digits is 3.
The tens digit is 4 times the hundreds digit.
The ones digit is seven more than the thousands digit.
No two digits are equal.
What is the four-digit number?
Answer: 2149
Step-by-step explanation: If the sum of the first two digits is 3, the choices must be 1 and 2 (or 2 and 1) In order to satisfy the other specifications, "the tens digit is 4 times the hundreds digit." the hundreds digit can't be 2 because that would make the tens dight 8. and the ones digit would also have to 8 in order to satisfy the "seven more than the thousands digit" which would be a 1. And that violates the condition, "No two digits are equal."
So the only possible combination is 2149
4 is 4 times 1
9 is 7 +2
Is 6/16 greater or less than 4/10
Answer:
Less than 4/10
Step-by-step explanation:
First lets convert both fractions to a common denominator:
16 and 10 can both go into 80 equally.
Now lets convert the fractions so they have a denominator of 80:
(6/16) *5 = 30/80
(4/10) *8 = 32/80
we can multiply the fractions to get just the numerator (*80)
Now compare 30 to 32. As you can see 32 is greater meaning that 6/16 is less that 4/10.
If Sara drives 60 miles per hour, it takes her 2 hours to reach her parents' house. Write an equation describing the relationship between Sara's speed and the time it takes her to get to her parents' house. (Note that speed and time are inversely proportional).
Question 17 options:
A)
s = 120∕t
B)
s = 60∕t
C)
s = 24∕t
D)
s = 30∕t
Answer: (A) .
because if you travel 60 miles per hour and i takes 2 hours yto get there you have to double 60 miles so 120 miles per 2 hours
The relationship between Sara's speed and the time it takes her to get to her parent's house will be s = 120/t so option (A) will be correct.
What are work and time?Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another illustration of labor is when you finish your meal in an hour, which means that you finished your work in an hour. In essence, work is the length of time it took you to complete any task.
Given that Sara drives 60 miles in 2 hours.
Distance covered by sara is = 60(2) = 120 miles.
We know that
speed = distance/time
Let's say speed is S time is t then
⇒ S = 120/t so the correct equation of the given question will be this.
For more information about the work and time relation
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