in a five character password the first two characters must be digits and the last three characters must be letters if no characters are allowed to repeat how many unique passwords are possible

Answer:

0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours.

This means that [tex]\sigma = 15, \mu = 520[/tex]

Find the probability of a bulb lasting for at most 528 hours.

This is the p-value of Z when X = 528. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{528 - 520}{15}[/tex]

[tex]Z = 0.533[/tex]

[tex]Z = 0.533[/tex] has a p-value of 0.7031

0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.

Answer:

if x=0 then they have same value

1 and 2 options are out

for x=-1

g(-1)=1

h(-1)=-1

3 is true

4th

FALSE

for all values except 0, g(x)>h(x)

correct ones are

g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

Step-by-step explanation:

Answer:

The original graph was shifted 2 units to the left and 5 units down.

Step-by-step explanation:

y = |x|

From this, we go to: y = |x - 2|.

When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.

y = |x - 2|.

From this, we go to: y = |x - 2| - 5.

Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.

Answer:

Cardinality of the power set of the given set = [tex]2^6=64[/tex]

Step-by-step explanation:

Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.

Example set:

{1,2,3}

All the possible subsets of this set:

{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}

The power set of the above set is written as:

P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })

Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.

Cardinality of the power set of a given set is expressed by a formula: [tex]2^n[/tex]

where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.

Hence in the given case, we have  n = 6.

Answer:

0.14

Step-by-step explanation:

P(A|B) asks for the probability of A, given that B has happened. This is equal to the probability of A and B over the probability of B (see picture)

Here, the question is asking if someone is taking the bus given that they are a senior.

The probability of someone being a senior and taking the bus is 5/100, or 0.05 . The probability of someone being a senior is 35/100, or 0.35

Our answer is then 0.05/0.35 = 1/7 = 0.14

Answer:

8 suits

Step-by-step explanation:

Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then

30 ÷ 3.75 = 8

Then 8 suits can be made from 30 m of cloth

Answer:

Buy 2 lollipops for $2.

Step-by-step explanation:

If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.

Answer:

I started by dividing 2940 by the smallest prime that would fit into it, being 2. This left me with another even number, 1470, so I divided by 2 again. The result, 735, is divisible by 5, but 3 divides in also, and it's smaller, so I divided by 3 to get 245. This is not divisible by 3 but is divisible by 5, so I divided by 5 and got 49, which is divisible by 7.

the SAS similarity theorem

Answer:

.33x = 105.60

$371

Step-by-step explanation:

Answer:

63.44

Step-by-step explanation:

its 63.44697 but you round so its 63.44

Answer:

Table B

Step-by-step explanation:

correct on edge :)

Answer:

It should be 8.6 yards, as 238.64÷3.14 = 74.

√74 = 8.60, or 8.6 :)

Answer:

(a) Temperature: Numerical

(b) Traffic congestion: Categorical

Step-by-step explanation:

Required

Determine the variable type

(a) Temperature

Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.

Hence, the variable is numerical

(b) Traffic congestion

From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....

Hence, the variable is categorical

Answer:

No unless x is being used to define only elements of an integer set.

Step-by-step explanation:

No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....

Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.

{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.

9514 1404 393

Answer:

Step-by-step explanation:

The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.

  x ∈ {5, 7}

__

The graph is below the x-axis between these points, so that is the region where f(x) < 0

  5 < x < 7 . . . . . for f(x) < 0

In interval notation: (5, 7).

Answer:

2nd Graph

Step-by-step explanation:

Bases off the graphs, you gave me, I assume your the equation is

[tex]f(x) = - 4(2) {}^{x} [/tex]

The parent equation of this function is

[tex]f(x) = b {}^{x} [/tex]

Let say x=0

Using the rules of exponets, the y value must be 1 so a critical point is

(0,1)

The function is multiplied by -4.

This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be

(0,-4).

The base 2 the function will get compressed by 1/2.

The best graph that represents this is the second graph

Answer:

if the terms are approaching zero then it is convergent.

Therefore the stated series is convergent

Step-by-step explanation:

Answer:

74 base 10.

Step-by-step explanation:

134 base 7 = 7^2 + 3*7 + 4

= 49 + 21 + 4

= 74 base 10

y = -7(-13)

=> y = -7 × (-13)

= y = 91

9514 1404 393

Answer:

  f⁻¹(138) = 3

Step-by-step explanation:

You want to find the value of x that makes the function have a value of 138:

  f(x) = 5x^3 +3x -6

  138 = 5x^3 +3x -6

  0 = 5x^3 +3x -144

Descartes's rule of signs tells us this has one positive real solution. The rational root theorem gives us 30 possibilities. Rewriting the equation as ...

  x^3 = (144 -3x)/5 = 28.8 -0.6x

suggests that the value of x is less than ∛28.8 ≈ 3.065. Trying x=3, we find that to be a solution.

  (5x² +3)(x) -6 = 0 . . . . rewrite of the above equation

  (5·3² +3)·3 -144 = (48)(3) -144 = 0 . . . . true

Then ...

  f⁻¹(138) = 3

_____

The answer is found easily using a graphing calculator. The solution is the x-intercept of 138 -f(x) = 0.

Answer:

Uhh what??

Step-by-step explanation:

I dont understand you ●___●

Answer:

It would be smaller.

Step-by-step explanation:

Given that :

The number of the strawberries that are unfit for sell, x = 24

The total number of the strawberries to inspect, n = 156

Total number of the strawberries to be picked = 1000 strawberries

Therefore,

[tex]$\widehat p =\frac{x}{n}$[/tex]

  [tex]$=\frac{24}{156}$[/tex]

  = 0.1538

[tex]$\widehat p =\frac{x}{n}$[/tex]

  [tex]$=\frac{24}{1000}$[/tex]

  = 0.024

Therefore, the standard deviation of the sample proportion would be smaller.

Answer:

a. -3

Step-by-step explanation:

-2 turns into 6 by multiplying it by -3.

the same from 6 to -18, from -18 to 54, ...

so, an/an+1 = -3

Answer:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Required

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Multiply by 1

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]

Express 1 as

[tex]\frac{y^2}{y^2} = 1[/tex]

So, the expression becomes:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]

Rewrite as:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]

In limits:

[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]

Convert to polar coordinates; such that:

[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]

Expand

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]

Factor out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]

Cancel out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]

So:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]

In trigonometry:

[tex]\cos^2\theta + \sin^2\theta = 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

Evaluate the limits by substituting 0 for r

[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0}{1+\sin^2\theta}[/tex]

Since the denominator is non-zero; Then, the expression becomes 0 i.e.

[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]

So,

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Answer:

Area swept by the blade = 448[tex]in^{2}[/tex]

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches  from area of sector with radius as 24 inches.

So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]

Simplify it,

                                                  =216[tex]\pi[/tex]

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]

Simplify it

                                          =73.5[tex]\pi[/tex]

So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

                               =447.6769

Round to nearest whole number

So, area swept by the blade = 448[tex]in^{2}[/tex]

Answer:

0.52 = 52% probability that an email is detected as spam.

Step-by-step explanation:

Probability that an email is detected as spam:

99% of 50%(are spam).

5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).

What is the probability that an email is detected as spam?

[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]

0.52 = 52% probability that an email is detected as spam.

Answer:

56"

Step-by-step explanation: