What is 3 root 17 in a decimal

Answer:yes

Step-by-step explanation:because there are more marbles than jars

The equation of the least-squares regression line can be used to predict the beak heat loss at a specific temperature. The coefficient of determination indicates the proportion of variation explained by the relationship between beak heat loss and temperature. The correlation coefficient quantifies the strength and direction of the linear relationship.

The given data represents the relationship between the beak heat loss of the toco toucan and the outdoor temperature. To find the equation of the least-squares regression line, we need to calculate the slope, which represents the change in beak heat loss for every degree Celsius increase in temperature, and the y-intercept, which represents the predicted beak heat loss at 0 degrees Celsius. Using these values, we can then predict the beak heat loss at a temperature of 25 degrees Celsius. To determine the percent of variation explained by the straight-line relationship, we can calculate the coefficient of determination (r^2). Finally, the correlation coefficient (r) represents the strength and direction of the linear relationship between beak heat loss and temperature.

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Answer:

a) $42,580

b) $43,900

Step-by-step explanation:

Recall, "mode" refers to the value which occurs most frequently.

In this case, the question says that there are 2 modes,

this means $34,000 and $50,500 both share the spot for the most frequently appearing salary.

because there are only 5 employees (and hence 5 salaries), the only possible way that there are two modes is if there are two of each mode, leaving only the last salary unknown.

i.e  if we list the 5 salaries (in no particular order)

$34,000   $34,000  $50,500   $50,500   $ x

where x is the 5th unknown salary.

Given that the mean is $42,100

Then (34,000 + 34,000 + 50,500 + 50,500 + x) / 5 = 42,100

solving for x gives x = $41,500

Now we know all the values, we can rearrange them in increasing value:

$34,000   $34,000  $41,500   $50,500   $50,500  

from this, we can see that the median salary is $41,500

Given that the median salary gets a $2400 raise,

the new median salary = $41,500 + $2400 = $43,900 (Ans for part b)

new mean salary,

= ($34,000  + $34,000 + $43,900 +  $50,500  + $50,500  ) / 5

= $42,580 (answer for part a)

Answer:

Any number of hours greater than 16

Step-by-step explanation:

First thing we have to do is write each equation for each cafe's internet access.  For Cyber Station, the rate is $1.50 per hour which is the slope of the line (slope is, after all, the rate of change of y to x...or here, cost to hours).  The flat fee is what you are charged even if you use 0 hours.  The linear equation for Cyber Station is y = 1.5x + 12

The linear equation for Web World, which only has a rate but no flat fee, is

y = 2.25x

We are asked for how many hours of access, x, is the cost, y, at Cyber Station LESS THAN the cost at Web World.  That tells me that you are working with linear inequalities in class!  We want the cost at CS to be less than that at WW so our inequality looks like this:

1.5x + 12 < 2.25x

Solving for x:

16 < x.  That means, in words, that any number of hours over 16 will make Cyber Station cheaper to use than Web World.

Answer:

A) [tex]\angle C \text{ is opposite } \overline{AB}[/tex]

Step-by-step explanation:

We need to name the side of the triangle that is across from angle C. A side of a triangle, if not otherwise given, is named based on the two points that form it. In this case, the side is formed by points B and C, so the side is called [tex]\overline{BC}[/tex].

answer 40

Step-by-step explanation:

because you added all together to make one

Answer:

Per capita income, in dollars per person, for 2005 is $42637

Step-by-step explanation:

The formula to calculate per capita income is:

per capita income = National income/total population

National income = $1,730,849,015

Total population = 40,595

per capita income in 2005 = 1,730,849,015/40,595

per capita income in 2005 = $42637

So, per capita income, in dollars per person, for 2005 is $42637

Answer:

No, not really.

dividing 25 into 4 equal groups, equals 6.25.

So no, you can not divide 25 into 4 equal group.

If if was 25 into 5 equal groups, then yes.

Hope this helps!!!

Please mark brainliest, if this helps. :)

Step-by-step explanation:

No, 25 cannot be divided into 4 equal groups without a remainder. Dividing 25 by 4 results in a quotient of 6 with a remainder of 1, meaning the groups would not be equal.

To determine if this is possible, we need to perform a division operation. Dividing 25 by 4 gives us a quotient of 6 with a remainder of 1. This means that 25 cannot be evenly divided into 4 equal groups, as one group would end up with one less or one more than the others.

Therefore, 25 cannot be divided into 4 equal groups .

ANSWER

See below

EXPLANATION

We want to verify that,

[tex] { \sin ^{4} x} - { \sin^{2} x} = { \cos ^{4} x} - { \cos^{2} x}[/tex]

To verify this identity, we can take the left hand side simplify it to get the right hand side or vice versa.

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

[tex]{ \sin ^{4} x} - { \sin^{2} x} ={ \sin ^{2} x}({ \sin ^{2} x} - 1)[/tex]

[tex]{ \sin ^{4} x} - { \sin^{2} x} ={ \sin ^{2} x} \times - (1 - { \sin ^{2} x})[/tex]

[tex]{ \sin ^{4} x} - { \sin^{2} x} =({1 - \cos^{2} x} )\times - ({ \cos^{2} x})[/tex]

[tex]{ \sin ^{4} x} - { \sin^{2} x} =({ \cos^{2} x} - 1 )\times ({ \cos^{2} x})[/tex]

We now expand the right hand side to get:

[tex] { \sin ^{4} x} - { \sin^{2} x} = { \cos ^{4} x} - { \cos^{2} x}[/tex]

Answer:

No, the point [tex](2,3)[/tex] is not a solution to the system of equation [tex]x2+y2=13[/tex] and [tex]2x-y=4[/tex].

Step-by-step explanation:

To make sure it is, it has to work on both equation. Plugging this into the first and second equations respectivly gives us:

[tex]13=x2+y2=(2)2+(3)2=4+6=10[/tex]

[tex]4=2x-y=2(2)-(3)=4-3=1[/tex]

Since [tex]13\neq10[/tex] and [tex]4\neq 1[/tex], the point [tex](2,3)[/tex] is not a solution to the system of equation [tex]x2+y2=13[/tex] and [tex]2x-y=4[/tex].

Answer:

That is False.

Step-by-step explanation:

To solve this you must make a formula like so:

ratio of rugby over tennis = unknown over students that picked tennis

***Unknown will be x

use a proportion like so...

[tex]\frac{rugby}{tennis} = \frac{x}{tennis}[/tex]

[tex]\frac{6}{13} = \frac{x}{78}[/tex]

Now you must cross multiply

6 * 78 = 13*x

468 = 13x

To isolate x divide 13 to both sides

468/13 = 13x/13

x= 36

This means that 36 people choose rugby when there were 78 people choose tennis

To find how many people choose football you must make another proportion similar to the first proportion:

ratio of football over rugby = unknown over students that picked rugby

use a proportion like so...

[tex]\frac{3}{2} = \frac{x}{36}[/tex]

Now you must cross multiply

3* 36 = 2*x

108 = 2x

To isolate x divide 2 to both sides

108/2 = 2x/2

x= 54

This means that 54 people choose football

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The price of the home = 232,000

20% is down payment.

Part A:

[tex]0.20\times232000=46400[/tex]

So, the loan amount will be =[tex]232000-46400=185600[/tex]

Loan amount or p = $185,600

Part B:

p = 185600

r = [tex]3.6/12/100=0.003[/tex]

n = [tex]10\times12=120[/tex]

The EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

Now putting the values in formula we get

[tex]\frac{185600\times 0.003\times(1+0.003)^{120} }{(1+0.003)^{120}-1 }[/tex]

=> [tex]\frac{185600\times 0.003\times(1.003)^{120} }{(1.003)^{120}-1 }[/tex]

Monthly payments = $1844.02

Part C:

p = 185600

r = [tex]3.6/12/100=0.003[/tex]

n = [tex]20\times12=240[/tex]

Now putting the values in formula we get

[tex]\frac{185600\times 0.003\times(1+0.003)^{240} }{(1+0.003)^{240}-1 }[/tex]

=> [tex]\frac{185600\times 0.003\times(1.003)^{240} }{(1.003)^{240}-1 }[/tex]

Monthly payments = $1085.96

Part D:

For 10 year loan you have to pay = [tex]120\times1844.02=221282.40[/tex]

For 20 years loan you have to pay =[tex]240\times1085.96=260630.40[/tex]

So, you ended up paying [tex]260630.40-221282.40=39348[/tex] dollars more in longer loan.

The difference is $39,348.

For this case we can raise a rule of three:

600 employees -------------> 100%

270 employees -------------> x

Where the variable "x" represents the percentage of employees who are satisfied with their salary. So, we have:

[tex]x = \frac {270 * 100} {600}\\x = 45[/tex]

Thus, 45% of employees are satisfied with their salary.

Answer:

45%

ANSWER

[tex]45\%[/tex]

EXPLANATION

The total number of employees is 600.

The number of employees who are happy with their pay is 270.

The percentage of employees who are happy with their pay is the number who are happy with their pay divided by total number of employees times 100%

[tex] \frac{270}{600} \times 100\%[/tex]

This simplifies to

[tex]45\%[/tex]

ANSWER

{x|x < -2 or x > 8}

EXPLANATION

The given absolute inequality is

[tex] |2x - 6| \: > \: 10[/tex]

By the definition of absolute value,

[tex] (2x - 6)\: > \: 10 \: or \: \: - (2x - 6)\: > \: 10[/tex]

Multiply through the second inequality by -1 and reverse the inequality sign

[tex]2x - 6\: > \: 10 \: or \: \: 2x - 6\: < \: - 10[/tex]

[tex]2x \: > \: 10 + 6\: or \: \: 2x \: < \: - 10 + 6[/tex]

Simplify

[tex]2x \: > \: 16\: or \: \: 2x \: < \: -4[/tex]

Divide through by 2

[tex]x \: > \: 8\: or \: \: x \: < \: -2[/tex]

Answer:

{x|x < -2 or x > 8}

Step-by-step explanation:

|2x - 6| > 10

We split the inequality into two functions, one positive and one negative.  The negative one flips the inequality.  since this is greater than, this is an or problem

2x-6 >10                 or  2x-6 < -10

Add 6 to each side

2x-6+6 > 10+6         2x-6+6 < -10+6

2x   > 16                    2x < -4

Divide by 2

2x/2 > 16/2                2x/2 < -4/2

x >8                 or        x < -2

Answer:

  -18, -26

Step-by-step explanation:

The differences are decreasing by 1 each time, so the next differences will be -7 and -8.

  -11 -7 = -18

  -18 -8 = -26

Answer:

A= 4 , B= 3

Step-by-step explanation:

Simply put, use systems of equations to solve for A and B. First make y equal 4, and to make A equal to four, while being multiplied by 1 it has to be 4. Then solve backwards and now you know that A equals four, what multiplied by 4 is equal to 36, 9. What is the square root of 9? 3!

Answer:

i say option (a) is the answer its correct.

Step-by-step explanation:

Answer:

The probability of getting a jack, a three, a club or a diamond is 0.58.

Step-by-step explanation:

In a standard deck of 52 cards have 13 club, 13 spade, 13 diamond, 13 heart cards. Each suit has one jack and 3.

Number of club cards = 13

Number of diamond cards = 13

Number of jack = 4

Number of 3 = 4

Jack of club  and diamond = 2

3 of club  and diamond = 2

Total number of cards that are either a jack, a three, a club or a diamond is

[tex]13+13+4+4-2-2=30[/tex]

The probability of getting a jack, a three, a club or a diamond is

[tex]Probability=\frac{\text{A jack, a three, a club or a diamond}}{\text{Total number of cards}}[/tex]

[tex]Probability=\frac{30}{52}[/tex]

[tex]Probability=0.576923076923[/tex]

[tex]Probability\approx 0.58[/tex]

Therefore the probability of getting a jack, a three, a club or a diamond is 0.58.

The correct answer is 0.50.

To determine the probability of getting a jack, a three, a club, or a diamond from a standard 52-card deck, we can calculate the probability of each individual event and then combine them, taking care to avoid double-counting any cards.

First, let's calculate the probability of drawing a jack. There are 4 jacks in the deck (one for each suit). Since there are 52 cards in total, the probability of drawing a jack is:

[tex]\[ P(\text{jack}) = \frac{4}{52} \][/tex]

Next, we calculate the probability of drawing a three. There are also 4 threes in the deck, one for each suit. So, the probability of drawing a three is:

[tex]\[ P(\text{three}) = \frac{4}{52} \][/tex]

Now, let's calculate the probability of drawing a club. There are 13 clubs in the deck (since there are 13 cards in each suit). Thus, the probability of drawing a club is:

[tex]\[ P(\text{club}) = \frac{13}{52} \][/tex]

Similarly, there are 13 diamonds in the deck, so the probability of drawing a diamond is:

[tex]\[ P(\text{diamond}) = \frac{13}{52} \][/tex]

However, we must be careful not to double-count the cards that are both a jack or a three and a club or a diamond. There are 2 jacks and 2 threes that are also clubs or diamonds (one jack and one three of clubs, and one jack and one three of diamonds).

 To find the total probability, we add the probabilities of each event and subtract the probabilities of the events that have been counted twice (the jack and three of clubs and diamonds):

[tex]\[ P(\text{total}) = P(\text{jack}) + P(\text{three}) + P(\text{club}) + P(\text{diamond}) - 2 \times P(\text{jack or three of clubs or diamonds}) \] \[ P(\text{total}) = \frac{4}{52} + \frac{4}{52} + \frac{13}{52} + \frac{13}{52} - 2 \times \frac{2}{52} \] \[ P(\text{total}) = \frac{4 + 4 + 13 + 13 - 4}{52} \] \[ P(\text{total}) = \frac{30}{52} \] \[ P(\text{total}) = \frac{15}{26} \] \[ P(\text{total}) = \frac{5}{8} \] \[ P(\text{total}) = 0.625 \][/tex]

Since we need to round to the nearest hundredth, the final answer is:

[tex]\[ P(\text{total}) \approx 0.63 \][/tex]

[tex]\[ P(\text{total}) = P(\text{jack}) + P(\text{three}) + P(\text{club}) + P(\text{diamond}) \] \[ P(\text{total}) = \frac{4}{52} + \frac{4}{52} + \frac{13}{52} + \frac{13}{52} \] \[ P(\text{total}) = \frac{4 + 4 + 13 + 13}{52} \] \[ P(\text{total}) = \frac{34}{52} \] \[ P(\text{total}) = \frac{17}{26} \] \[ P(\text{total}) = \frac{1}{2} \] \[ P(\text{total}) = 0.50 \][/tex]

Answer:

The words from parsley are PAR, YES, RAP, PAY,and SLAP

The words from pepper are PEEP and that is it

Step-by-step explanation:

Simplify 3 + 3 to 6

6^2/10 - 4 × 3

Simplify 4 × 3 to 12

6^2/10 - 12

Simplify 10 - 12 to -2

6^2/-2

Simplify 6^2 to 36

36/-2

Move the negative sign to the left

-36/2

Simplify 36/2 to 18

= -18

Answer:

The standard deviation of 2,3,6,9,10 is √10.

Step-by-step explanation:

Standard Deviation:

It is a quantity expressing by how much the members of a group differ from the mean value for the group. Its symbol is б read as 'sigma'.

Formula:

б = √(Σ(x-mean)²/n)

Mean = Σx/n = (2+3+6+9+10)/5 = 30/5 = 6

Mean = 6

Σ(x-mean)² = (2-6)²+(3-6)²+(6-6)²+(9-6)²+(10-6)²

= 16+9+0+9+16

= 50

б = √(Σ(x-mean)²/n)

= √(50/5)

= √10

Answer:

)10

Step-by-step explanation:

A p e x

Answer:

water : 90 ounces

salt solution: 90 ounces

Step-by-step explanation:

Call w the amount of water and call the solution containing 30% salt.

We want to get 180 ounces of a mixture with 15% salt.

So:

The amount of mixture will be:

[tex]w + s = 180[/tex]

the amount of salt will be

[tex]0w + 0.3s = 180 * 0.15[/tex]

[tex]0.3s = 27[/tex]

[tex]s = 90\ ounces[/tex]

Now we substitute the value of s in the first equation and solve for w

[tex]w + 90 = 180[/tex]

[tex]w = 90\ ounces[/tex]

Answer:

The solution is [tex]y\:=-\ln(-\frac{x^{3}}{3}-4x-2x^{2}+\frac{22}{3})[/tex]

Step-by-step explanation:

We need to find the solution of IVP for differential equation [tex]\frac{dy}{dx}=(x+2)^{2}e^{y}[/tex] when [tex]y(1)=0[/tex]

[tex]\mathrm{First\:order\:separable\:Ordinary\:Differential\:Equation}[/tex]

[tex]\mathrm{A\:first\:order\:separable\:ODE\:has\:the\:form\:of}\:N\left(y\right)\cdot y'=M\left(x\right)[/tex]

[tex]\mathrm{Rewrite\:in\:the\:form\:of\:a\:first\:order\:separable\:ODE}[/tex]

[tex]\frac{1}{e^y}y'\:=\left(x+2\right)^2[/tex]

[tex]N\left(y\right)\cdot y'\:=M\left(x\right)[/tex]

[tex]N\left(y\right)=\frac{1}{e^y},\:\quad M\left(x\right)=\left(x+2\right)^2[/tex]

[tex]\mathrm{Solve\:}\:\frac{1}{e^y}y'\:=\left(x+2\right)^2[/tex]

[tex]\frac{1}{e^y}y'\:=x^{2}+4+4x[/tex]

Integrate both the sides with respect to dx

[tex]\int\frac{1}{e^y}y'dx\:=\intx^{2}dx+4\int dx+4\int x dx[/tex]

[tex]\int e^{-y}dy\:=\intx^{2}dx+4\int dx+4\int x dx[/tex]

[tex]-\frac{1}{e^{y}}\:=\frac{x^{3}}{3}+4x+4\frac{x^{2}}{2}+c_1[/tex]

[tex]-\frac{1}{e^{y}}\:=\frac{x^{3}}{3}+4x+2x^{2}+c_1[/tex]

Since, IVP is y(1)=0

put x=1 and y=0 in above equation

[tex]-\frac{1}{e^{0}}\:=\frac{1^{3}}{3}+4(1)+2(1)^{2}+c_1[/tex]

[tex]-1\:=\frac{1}{3}+4+2+c_1[/tex]

[tex]-1\:=\frac{19}{3}+c_1[/tex]

add both the sides by [tex]-\frac{19}{3}[/tex]

[tex]-1-\frac{19}{3}\:=\frac{19}{3}-\frac{19}{3}+c_1[/tex]

[tex]-1-\frac{19}{3}\:=c_1[/tex]

[tex]-\frac{22}{3}\:=c_1[/tex]

so,

[tex]-\frac{1}{e^{y}}\:=\frac{x^{3}}{3}+4x+2x^{2}-\frac{22}{3}[/tex]

Multiply both the sides by '-1'

[tex]\frac{1}{e^{y}}\:=-\frac{x^{3}}{3}-4x-2x^{2}+\frac{22}{3}[/tex]

[tex]e^{-y}\:=-\frac{x^{3}}{3}-4x-2x^{2}+\frac{22}{3}[/tex]

Take natural logarithm both the sides,

[tex]-y\:=\ln(-\frac{x^{3}}{3}-4x-2x^{2}+\frac{22}{3})[/tex]

Multiply both the sides by '-1'

[tex]y\:=-\ln(-\frac{x^{3}}{3}-4x-2x^{2}+\frac{22}{3})[/tex]

Therefore, the solution is [tex]y\:=-\ln(-\frac{x^{3}}{3}-4x-2x^{2}+\frac{22}{3})[/tex]

Answer:

(a) 0.110 ⇒ rounded to three decimal places

(b) 0.097 ⇒ rounded to three decimal places

(c) 0.234 ⇒ rounded to three decimal places

(d) 0.235 ⇒ rounded to three decimal places

Step-by-step explanation:

* Lets solve the problem using the combination

- The order is not important in this problem, so we can use the

  combination nCr to find the probability

- There are 22 compact fluorescent light bulbs

# 8 ⇒ rated 13 watt

# 9 ⇒ rated 18 watt

# 5 ⇒ rated 23 watt

- 3 bulbs are randomly selected

(a) Exactly two of the selected bulbs are rated 23 watt

∵ Exactly two of them are rated 23 watt

∵ The number of bulbs rated 23 watt is 5

∴ We will chose 2 from 5

∴ 5C2 = 10 ⇒ by using calculator or by next rule

# nCr = n!/[r! × (n-r)!]

- 5C2= 5!/[2! × (5 - 2)!] = (5×4×3×2×1)/[(2×1)×(3×2×1)] = 120/12 = 10

∴ There are 10 ways to chose 2 bulbs from 5

∵ The 3rd bulbs will chosen from the other two types

∵ The other two types = 8 + 9 = 17

∴ We will chose 1 bulbs from 17 means 17C1

∵ 17C1 = 17 ⇒ (by the same way above)

∴ There are 17 ways to chose 1 bulbs from 17

- 10 ways for two bulbs and 17 ways for one bulb

∴ There are 10 × 17 = 170 ways two chose 3 bulbs exact 2 of them

   rated 23 watt (and means multiply)

∵ There are 22C3 ways to chose 3 bulbs from total 22 bulbs

∵ 22C3 = 1540 ⇒ (by the same way above)

∴ The probability = 170/1540 = 17/154 = 0.110

* The probability that exactly two of the selected bulbs are rated

  23-watt is 0.110 ⇒ rounded to three decimal places

(b) All three of the bulbs have the same rating

- We can have either all 13 watt, all 18 watt or all 23 watt.

# 13 watt

∵ There are 8 are rated 13 watt

∵ We will chose 3 of them

∴ There are 8C3 ways to chose 3 bulbs from 8 bulbs

∵ 8C3 = 56

∴ There are 56 ways to chose 3 bulbs rated 13 watt

# 18 watt

∵ There are 9 are rated 18 watt

∵ We will chose 3 of them

∴ There are 9C3 ways to chose 3 bulbs from 9 bulbs

∵ 9C3 = 84

∴ There are 84 ways to chose 3 bulbs rated 18 watt

# 23 watt

∵ There are 5 are rated 23 watt

∵ We will chose 3 of them

∴ There are 5C3 ways to chose 3 bulbs from 5 bulbs

∵ 5C3 = 10

∴ There are 10 ways to chose 3 bulbs rated 23 watt

- 65 ways or 84 ways or 10 ways for all three of the bulbs have

 the same rating

∴ There are 56 + 84 + 10 = 150 ways two chose 3 bulbs have the

   same rating (or means add)

∵ There are 22C3 ways to chose 3 bulbs from total 22 bulbs

∵ 22C3 = 1540

∴ The probability = 150/1540 = 15/154 = 0.097

* The probability that all three of the bulbs have the same rating is

  0.097 ⇒ rounded to three decimal places

(c) One bulb of each type is selected

- We have to select one bulb of each type

# 13 watt

∵ There are 8 bulbs rated 13 watt

∵ We will chose 1 of them

∴ There are 8C1 ways to chose 1 bulbs from 8 bulbs

∵ 8C1 = 8

∴ There are 8 ways to chose 1 bulbs rated 13 watt

# 18 watt

∵ There are 9 bulbs rated 18 watt

∵ We will chose 1 of them

∴ There are 9C1 ways to chose 1 bulbs from 9 bulbs

∵ 9C1 = 9

∴ There are 9 ways to chose 1 bulbs rated 18 watt

# 23 watt

∵ There are 5 bulbs rated 23 watt

∵ We will chose 1 of them

∴ There are 5C1 ways to chose 1 bulbs from 5 bulbs

∵ 5C1 = 5

∴ There are 5 ways to chose 1 bulbs rated 23 watt

- 8 ways and 9 ways and 5 ways for one bulb of each type is selected

∴ There are 8 × 9 ×  5 = 360 ways that one bulb of each type is

  selected (and means multiply)

∵ There are 22C3 ways to chose 3 bulbs from total 22 bulbs

∵ 22C3 = 1540

∴ The probability = 360/1540 = 18/77 = 0.234

* The probability that one bulb of each type is selected is 0.234

  ⇒ rounded to three decimal places

(d) If bulbs are selected one by one until a 23-watt bulb is obtained,

    it is necessary to examine at least 6 bulbs

- We have a total of 22 bulbs and 5 of them are rate 23 watt

∴ There are 22 - 5 = 17 bulbs not rate 23 watt

∵ We examine at least 6 so the 6th one will be 23 watt

∴ There are 17C5 ways that the bulb not rate 23 watt

∵ 17C5 = 6188

∴ There are 6188 ways that the bulb is not rate 23 watt

∵ There are 22C5 ways to chose 5 bulbs from total 22 bulbs

∵ 22C5 = 26334

∴ The probability = 6188/26334 = 442/1881 = 0.235

* If bulbs are selected one by one until a 23-watt bulb is obtained,

 the probability that it is necessary to examine at least 6 bulbs is

  0.235 ⇒ rounded to three decimal places

OR

we can use the rule:

# P ( examine at least six ) = 1 − P ( examine at most five )  

# P ( examine at least six ) = 1 − P (1) − P (2) − P (3) − P (4) − P (5)

  where P is the probability  

∵ P(1) = 5/22

∵ P(2) = (5 × 17)/(22 × 21) = 85/462

∵ P(3) = (5 × 17× 16)/(22 ×21 × 20) = 34/231

∵ P(4) = (5 × 17 × 16 × 15)/(22 ×21 × 20 ×19) = 170/1463

∵ P(5) = (5 × 17 × 16 × 15 × 14)/(22 × 21 × 20 × 19 × 18) = 170/1881

∴ P = 1 - 5/22 - 85/462 - 34/231 - 170/1463 - 170/1881 = 442/1881

∴ P = 0.235  

These probabilities are calculated by considering the number of combinations of selections.

a) Probability of Exactly Two 23-Watt Bulbs= 0.110

b)Probability of All Bulbs Having the Same Rating = 0.097

c)Probability of One Bulb of Each Type = 0.234

d)Probability of At Least 6 Bulbs Needed to Get a 23-Watt Bulb =0.151

Given a box containing 22 lightbulbs with specific wattage ratings, we can calculate the probabilities of various selection events using combinatorial methods.

(a) Probability of Exactly Two 23-Watt Bulbs

We need the probability of selecting exactly two 23-watt bulbs out of three:

Thus, the probability is P = (10 * 17) / 1540 = 0.110.

(b) Probability of All Bulbs Having the Same Rating

Total probability: 0.036 + 0.055 + 0.006 = 0.097.

(c) Probability of One Bulb of Each Type

Number of ways to select 1 bulb from each type: 8 * 9 * 5 = 360.

Probability: P = 360 / 1540 = 0.234.

(d) Probability of At Least 6 Bulbs Needed to Get a 23-Watt Bulb

Probability of the first 5 bulbs not being 23-watt: (17/22) * (16/21) * (15/20) * (14/19) * (13/18).

Calculation: P = (17*16*15*14*13) / (22*21*20*19*18) = 0.151.

Answer:

  (a) y = -6(x -1)

  (b) about 5.3%

Step-by-step explanation:

(a) The point used as the base for the linear approximation is (1, f(1)), where ...

  f(1) = 3 -3·1² = 0

The slope of the line at that point is ...

  f'(x) = 0 -3(2x) = -6x

  f'(1) = -6·1 = -6

So, in point-slope form, the equation of the approximating line is ...

  y = -6(x -1) +0

  y = -6(x -1)

__

(b) The approximate value of f(0.9) is then ...

  y = -6(0.9 -1) = 0.6 . . . . approximate value of f(0.9)

__

(c) The error in the approximation at x=0.9 is ...

  error% = (0.6 -f(0.9))/f(0.9) × 100%

where f(0.9) = 3(1 -0.9²) = 3·0.19 = 0.57

  error% = (0.6 -0.57)/0.57 × 100% = 0.03/0.57 × 100%

  error% ≈ 5.263% ≈ 5.3%

This solution involves finding the equation of the line that represents the linear approximation for a function at a given point. Then, the linear approximation is used to estimate a value and a percent error is calculated between the exact and approximate value.

To solve this problem, we have to use the concept of linear approximation which is also known as the tangent line approximation. Using this concept, we can write the equation of the line that represents the linear approximation to a function at a given point.

The formula is: L(x) = f(a) + f'(a)(x-a). Our function is f(x) = 3 - 3x². The derivative of f(x), f'(x) is -6x. Evaluating these at a = 1, we get f(1) = 0 and f'(1) = -6.

The equation of the tangent line at a = 1 is therefore L(x) = 0 - 6(x - 1), simplifying to L(x) = -6x + 6.

To estimate f(0.9), we plug it into our approximation equation, L(0.9) = -6*0.9 + 6 = 0.6.

Now, we calculate the percent error. First, we find the exact value by plugging 0.9 into our original function, f(0.9) = 3 - 3*(0.9)² = 1.29.

Using the given formula for percent error, we get: 100 * abs(0.6 - 1.29) / abs(1.29) which yields approximately 53.49%.

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Answer:

The number of key rings sold on that day is 4000 key rings

Step-by-step explanation:

* Lets explain the information in the problem

- The profit earned (in thousands of dollars) per day by selling n number

  of key rings is given by the function P(n) = n² - 2n - 3, where n is the

  number of key rings in thousands and P is the profit in thousands

  for one day

- On a particular day the total profit is $5,000

∵ 5000 = 5 in thousands

∵ The function P(n) is the profit of n key ring in thousands

∴ P(n) = 5

- Lets solve the function to find the number of key rings

∵ P(n) = n² - 2n - 3

∴ 5 = n² - 2n - 3 ⇒ subtract 5 from both sides

∴ 0 = n² - 2n - 8 ⇒ factorize it

∵ n² = n × n ⇒ 1st terms in the 2 brackets

∵ -8 = -4 × 2 ⇒ 2nd terms in the 2 brackets

∵ n × -4 = -4n ⇒ nears

∵ n × 2 = 2n ⇒ extremes

∵ -4n + 2n = -2n ⇒ the middle term

∴ (n - 4)(n + 2) = 0 ⇒ equate each bracket by 0 to find n

∴ n - 4 = 0 ⇒ add 4 to both sides

∴ n = 4 key ring in thousands = 4000 key rings

- OR

∴ n + 2 = 0 ⇒ subtract 2 from both sides

∴ n = -2 ⇒ we will refused this value because number of key rings

   must be positive

∴ The number of key rings sold on that day is 4000 key rings

To find the number of key rings sold on a particular day when the total profit is $5,000, we need to solve the given equation for n.

The owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by the equation P(n) = n^2-2n-3. To find the number of key rings sold on a particular day when the total profit is $5,000, we need to solve the equation P(n) = 5000 for n.

Step 1: Set the equation equal to 5000: n^2-2n-3 = 5000.

Step 2: Rearrange the equation and set it equal to zero: n^2-2n-5003 = 0.

Step 3: Solve the quadratic equation using factoring, completing the square, or the quadratic formula to find the values of n.

Step 4: The solutions will give us the possible values of n, representing the number of key rings sold on the particular day when the total profit is $5,000.

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Final answer:

The probability that a coffee maker will have a defective cord is calculated by using the principle of inclusion-exclusion. Subtracting the percentage of coffee makers with faulty switches from the total percentage with any defect and adding the percentage with both defects, we find that the probability is 1.6%.

Explanation:

To calculate the probability that a coffee maker will have a defective cord, we can use the principle of inclusion-exclusion. According to the question, 4.0% of coffee makers have either a faulty switch or a defective cord. Of these, 2.5% have a faulty switch, and 0.1% have both defects. The probability that a coffee maker will have a defective cord is the total probability of any defect minus the probability of a faulty switch, plus the probability of having both defects, since those with both defects were counted in both the faulty switch and defective cord categories.

The formula we will use is: Probability(defective cord) = Probability(faulty switch or defective cord) - Probability(faulty switch) + Probability(both defects).

Plugging in the values we have: Probability(defective cord) = 4.0% - 2.5% + 0.1% = 1.6%

Therefore, the probability that a coffee maker will have a defective cord is 1.6%.

Answer: [tex]Y=-388+135X[/tex]

Step-by-step explanation:

The equation of the regression line has the general form [tex]Y=a+bX[/tex], where Y is the dependent variable , X is the independent variable , b is the slope of the line and a is the y-intercept.

Given : The slope of regression equation : [tex]b=135[/tex]

The y-intercept : [tex]a=-388[/tex]

Then , the equation of the regression line is given by :-

[tex]Y=-388+135X[/tex]

In the field of statistics, specifically regression analysis, the equation of the regression line is given by y = mx + b. Given that the slope is 135 and the y-intercept is -388, the equation of the regression line which represents the relationship between hotel ratings and their prices is y = 135x - 388.

The given problem falls under the branch of statistics, specifically under regression analysis. In a regression equation, x is the independent variable and y is the dependent variable. The equation of a regression line can be expressed in the format y = mx + b, where m represents the slope of the line, and b is the y-intercept.

In the given instance, the slope (m) is 135, and the y-intercept (b) is -388. Therefore, the equation of the regression line which represents the relationship between hotel ratings (x) and their prices (y) is y = 135x - 388.

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Answer:

1. x = 39.67

2. x = 15

3. x = 49.29

4. x = -12.8

5. x = 96

6. x = 42

7. x = 36

8. x = 0

9. x = 78

Step-by-step explanation:

Just remember to always isolate the unknown. Here are the solutions to your problem. I will explain each step for the first for you to give you an idea how the others were worked out.

1. [tex]\dfrac{3x}{7}-2 = 15[/tex]  

Add 2 to both sides to get rid of -2 on the left side.

[tex]\dfrac{3x}{7}-2+(2)=15+(2)///dfrac{3x}{7}=17[/tex]

Multiply both sides by 7 to get rid of 7 on the left side.

[tex]\dfrac{3x}{7}\times 7 = 17\times 7\\\\3x = 119[/tex]

Divide both sides by 3 to get rid of 3 on the left side.

[tex]\dfrac{3x}{3} = \dfrac{119}{3}\\\\x = 39.67[/tex]

You could also transpose everything by the x to the other side of the equation. Just remember that whatever OPERATION used on the original side, must be opposite on the other side. I'll use the second problem to show this.

[tex]\dfrac{2x}{5}+1=7[/tex]

Transpose  1 on the left to the right. It is addition on the left, then it would be subtraction on the other side.

[tex]\dfrac{2x}{5}+1=7\\\\\dfrac{2x}{5}=7-1\\\\\dfrac{2x}{5}=6[/tex]

Transpose 5 from the left side to the right. It is division on the left, then it would be multiplication on the right.

[tex]\dfrac{2x}{5}=6\\\\2x=6\times 5\\\\2x=30[/tex]

Transpose 2 from the left side to the right. It is multiplication on the left, then it would be division on the right.

[tex]2x=30\\\\x=\dfrac{30}{2}\\\\x=15[/tex]

Let's move on with the rest now.

3.

[tex]\dfrac{7x}{15}-1=22\\\\\dfrac{7x}{15}=22+1\\\\\dfrac{7x}{15}=23\\\\7x=23\times15\\\\7x=345\\\\x=\dfrac{345}{7}\\\\x=49.29[/tex]

4.

[tex]\dfrac{5x}{8}+10=2\\\\\dfrac{5x}{8}=2-10\\\\\dfrac{5x}{8}=-8\\\\5x=-8\times8\\\\5x=-64\\\\x=\dfrac{-64}{5}\\\\x=-12.8[/tex]

5.

[tex]\dfrac{x}{6}+4=20\\\\\dfrac{x}{6}=20-4\\\\\dfrac{x}{6}=16\\\\x=16\times6\\\\x=96[/tex]

6.

[tex]\dfrac{x}{3}-4=10\\\\\dfrac{x}{3}=10+4\\\\\dfrac{x}{3}=14\\\\x=3\times14\\\\x=42[/tex]

7.

[tex]\dfrac{x}{6}+2=8\\\\\dfrac{x}{6}=8-2\\\\\dfrac{x}{6}=6\\\\x=6\times6\\\\x=36[/tex]

8.

[tex]\dfrac{x}{9}+8=8\\\\\dfrac{x}{9}=8-8\\\\\dfrac{x}{9}=0\\\\x=0\times9\\\\x=0[/tex]

9.

[tex]\dfrac{x}{6}+7=20\\\\\dfrac{x}{6}=20-7\\\\\dfrac{x}{6}=13\\\\x=13\times6\\\\x=78[/tex]

The answers are as follows- 1. x = 17/3 or 5.67,2. x=3 . 3.x = 23/7 or about 3.29. 4.x = -8/5 or -1.6., 5.x=2, 6.x = 14/6 or about 2.33., 7. x=2, 8. x=0, 9. x = 13/9 or about 1.44.

Solving the Given Equations