Solve the following quadratic by factoring.
x² – 3x – 4=0
List the answers separated by a comma. For example, if you found solutions x = 1 and x = 2, you would enter 1, 2.

Answer:

The probability of getting two good coils is 77.33%.

Step-by-step explanation:

Since a batch consists of 12 defective coils and 88 good ones, to determine the probability of getting two good coils when two coils are randomly selected (without replacement), the following calculation must be performed:

88/100 x 87/99 = X

0.88 x 0.878787 = X

0.77333 = X

Therefore, the probability of getting two good coils is 77.33%.

Answer:

(a) 3178

(b) 14231

(c) 33152

Step-by-step explanation:

Given

[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]

[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]

[tex]y = \frac{269573}{1+985*0.08509}[/tex]

[tex]y = \frac{269573}{84.81365}[/tex]

[tex]y = 3178[/tex] --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]

[tex]y = \frac{269573}{1+985*0.01824}[/tex]

[tex]y = \frac{269573}{18.9664}[/tex]

[tex]y = 14213[/tex] --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]

[tex]y = \frac{269573}{1+985*0.00724}[/tex]

[tex]y = \frac{269573}{8.1314}[/tex]

[tex]y = 33152[/tex] --- approximated

Answer:

2424.5

904.16

Step-by-step explanation:

the mean = ∑frequency /n

∑f = 5+17+36+115+125+81+47+45+22+7 = 500

∑xf = 1212250

∑x²f = 3347037625

sample mean = 1212250/500

= 2424.5

variance = 1/500-1[3347037625 - 1212250²]

= 815710.02

standard deviation is = √variance

standard deviation = √815710.02

= 904.16

Answer:

[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]

Step-by-step explanation:

We are given the function:

[tex]Q(x)=2x^2+5x-3[/tex]

And we want to find and simplify:

[tex]Q(a+h)-Q(a-h)[/tex]

Substitute:

[tex]=[2(a+h)^2+5(a+h)-3]-[2(a-h)^2+5(a-h)-3][/tex]

Expand:

[tex]\displaystyle =[2(a^2+2ah+h^2)+5a+5h-3]-[2(a^2-2ah+h^2)+5a-5h-3][/tex]

Distribute:

[tex]=[2a^2+4ah+2h^2+5a+5h-3]-[2a^2-4ah+h^2+5a-5h-3][/tex]

Distribute:

[tex]=(2a^2+4ah+2h^2+5a+5h-3)+(-2a^2+4ah-2h^2-5a+5h+3)[/tex]

Rewrite:

[tex]=(2a^2-2a^2)+(4ah+4ah)+(2h^2-2h^2)+(5a-5a)+(5h+5h)+(-3+3)[/tex]

Combine like terms:

[tex]=8ah+10h[/tex]

Hence:

[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]

Answer:

3/4

Step-by-step explanation:

Let a be the length of the shorter line segment and b be the length of the longer line segment.

Since the length of the line segment is l, we have that the length of the line segment equals length of shorter line segment + length of longer line segment.

So, l = a + b

Since we require that the longer line segment be at least three times longer than the shorter line segment, we have that b = 3a

So, l = a + b

l = a + 3a

l = 4a

The probability that the shorter line segment will be a(or 3 times shorter than b) is P(a) = length of shorter line segment/length of line segment = a/l

Since l = 4a.

a/l = 1/4

So, P(a) = 1/4

The probability that a will be less than 3 times shorter that b is P(a ≤ 1) = P(0) + P(a) = 0 + 1/4 = 1/4

The probability that b will be 3 times or more greater than a is thus P(b ≥ 3) = 1 - P(a ≤ 1) = 1 - 1/4 = 3/4

Answer:

B

Step-by-step explanation:

(6)^1/2 × (8)^1/2

6^1/2 × 2 (2)^1/2

4 (3)^1/2

Answer:

Question 1: x = 6

Question 2: Correct!

Question 3: x = 11

Question 4: Correct!

Step-by-step explanation:

Question 1:

Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.

Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:

First, subtract 50 from 180 to find what angle 22x - 2 will equal:

180 - 50 = 130

130 = 22x - 2

Now use basic algebra to solve for x:

130 = 22x - 2

(add 2 to both sides)

132 = 22x

(divide both sides by 22)

x = 6

Question 3:

Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.

With that in mind, to solve for x, add the two equations and set it equal to 180:

5x + 15 + (9x + 11) = 180

Now use basic algebra to solve for x:

5x + 15 + 9x + 11 = 180

(add like terms)

14x + 26 = 180

(subtract 26 from both sides)

14x = 154

(divide 14 from both sides)

x = 11

Hope it helps (●'◡'●)

Answer:

64 Bottles

Step-by-step explanation:

that is the procedure above

Answer:

x = 27

Step-by-step explanation:

I'm assuming the equation looks like this:

[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]

Here's how to solve for x:

[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]

(subtract 5 from both sides)

[tex]\frac{2}{3}x-\frac{1}{9}x=15[/tex]

(Find the GCF of 3 and 9, which is 3. Multiply 2/3 by 3/3. You get 6/9)

[tex]\frac{6}{9}x-\frac{1}{9}x=15[/tex]

(add like terms)

[tex]\frac{5}{9}x=15[/tex]

(multiply 9/5 to both sides, which is the same as dividing both sides by 5/9)

x = 27

Hope it helps (●'◡'●)

9514 1404 393

Answer:

  6,364.8 lb

Step-by-step explanation:

The centroid of the plate is its center, so is 1.5 ft above the bottom of the pool, or 8.5 ft below the surface. The area of the plate is (3 ft)(4 ft) = 12 ft². Then the fluid force is ...

  (62.4 lb/ft³)(8.5 ft)(12 ft²) = 6,364.8 lb

Answer:

a=5

Step-by-step explanation:

Answer:

0.96784

Step-by-step explanation:

17-13.3/2

=1.85

p(x<1.85)

=0.96784

The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.

Mean [tex]\mu[/tex]=13.3 minutes

Standard deviation[tex]\sigma[/tex]=2 minutes

The value of the z-score tells you how many standard deviations you are away from the mean.

So, the z-score of the above data

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{17-13.3}{2}[/tex]

[tex]z=1.85[/tex]

From the standard normal table, the p-value corresponding to z=1.85

Or, p(x<1.85)=0.9678 or 96.78%

Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.

To get more about the z-score visit:

https://brainly.com/question/25638875

Answer:

221

Step-by-step explanation:

Given sequence is ,

> 5 , 6 , 7 , 8 , 9.

The common difference is 6-5 = 1 .

Therefore , the 221st number will be

> 221 st term = 221 × 1 = 221 .

Hence the 221 st term is 221 .

Answer:

225

Step-by-step explanation:

d = 6 - 5 = 1 (common differences)

a = 5 (first term)

221st term

a+(n-1)d

5 +(221 - 1) 1

5 + 220 =225

Therefore the answer is 225

Answer:

Hello?

Step-by-step explanation:

Answer:

2.409

Step-by-step explanation:

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]

[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]

           = [tex]\frac{5.3}{2.2}[/tex]

           = 2.409

The approximate value of log 200 would be; 2.409

When we raise a number with an exponent, there comes a result.

Let's say you get  a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We have given the values in 9 = 2.2 and 200 – 5.3

We need to find the approximate value of log, 200.

Therefore,

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]

Using the logarithm property;

[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]

=  2.409

Hence, the approximate value of log, 200 would be; 2.409

Learn more about logarithm here:

https://brainly.com/question/20835449

#SPJ2

Answer:

7. [tex]x^{11}[/tex]   8. [tex]y^{2}\\[/tex]  9. [tex]p^{12}[/tex]  10.[tex]a^{3} b^{2}[/tex]  11.[tex]g^{16}[/tex]  12.[tex]r^{9} h^{3}[/tex]  13.[tex]m^{15} p^{6}[/tex]  14.[tex]k^{6} y[/tex]  15.[tex]x^6 z^4[/tex]

Step-by-step explanation:

7. [tex]x^3[/tex] × [tex]x^8[/tex] = [tex]x^{11}[/tex] when multiplying with exponents you add

8. [tex]\frac{y^{6} }{y^{4} }[/tex] = [tex]y^{2}[/tex] when dividing with exponents you subtract

9. [tex](p^{3})^4[/tex] = [tex]p^{12}\\[/tex] when it's power to power, you multiply

10. [tex]\frac{a^{9} b^{4}}{a^{6} b^{2}}[/tex] = [tex]a^{3} b^{2}[/tex]  (subtract exponents)

11. [tex](g^{8})^2[/tex] = [tex]g^{16}[/tex]  (multiply exponents)

12. [tex]r^{4} h^{2} r^{5} h[/tex] = [tex]r^{9} h^{3}[/tex]  (add exponents [tex]r^4 + r^5\\[/tex] and [tex]h^2 +h^1\\[/tex] )

13. [tex](m^{5} p^{2})^3[/tex] = [tex]m^{15} p^{6}[/tex] (multiply exponents)

14. [tex]\frac{k^{7} y^{4}}{y^{3}k}[/tex] =  [tex]k^{6} y[/tex] (subtract exponents [tex]k^7-k^1[/tex] and [tex]y^4-y^3\\[/tex] )

15. [tex]x^3 z^2 x^3 z^2[/tex] = [tex]x^6 z^4[/tex] (add exponents same as #12)

Answer:

a)  [tex]h=286.8ft[/tex]

b)  [tex]\frac{dh}{dt}=5.7ft/s[/tex]

Step-by-step explanation:

From the question we are told that:

Angle [tex]\theta=35[/tex]

a)

Slant height [tex]h_s=500ft[/tex]

Generally the trigonometric equation for Height is mathematically given by

[tex]h=h_ssin\theta[/tex]

[tex]h=500sin35[/tex]

[tex]h=286.8ft[/tex]

b)

Rate of release

[tex]\frac{dl}{dt}=10ft/sec[/tex]

Generally the trigonometric equation for Height is mathematically given by

[tex]h=lsin35[/tex]

Differentiate

[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]

[tex]\frac{dh}{dt}=10sin35[/tex]

[tex]\frac{dh}{dt}=5.7ft/s[/tex]

Answer:

45 mph

Step-by-step explanation:

This is a really good question to know the answer to. It is tricky and a bit indirect (which means you have to find something else before you can find the speed of the car.)

Let's keep track of what he does in the time allotted.

How far does Joe go in 5 minutes? That's the amount of time he's on the road before she is.

convert 5 minutes into hours. 5 minutes * 1 hour / 60 minutes = 1/12 of an hour

d = r*t

r = 30 km/hour

t = 1/12 hour

d = 30 km/hr * 1/12 hour = 2.5 km

Now she's about to start. She wants to catch him in 10 minutes

d = r*t

r = x mph

t = 10 minutes = 10 minutes * 1 hour * 60 minutes = 1/6 of an hour.

How far does he go in the 10 minute time?

d = 30 * 1/6 = 5 km

What is his total distance

5 km + 2.5 km = 7.5 km

Finally how fast does she need to go to catch him

d = 7.5 km

r = ?   This is what you are trying to find

t = 1/6 of an hour

d = r*t

7.5 km = r * (1/6)hour             divide by 1/6 hour

7.5 km // 1/6 hour = r

r = 7.5 * 6 = 45 mph

Answer:

The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Step-by-step explanation:

Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:

7000 x 0.11 + 1000 x 0.05 = X

770 + 50 = X

820 = X

8000 = 100

820 = X

820 x 100/8000 = X

82,000 / 8,000 = X

10.25 = X

Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Answer:

x = 22

Step-by-step explanation:

In order to solve this, we need to understand that in an isosceles triangle the two angles that are located at its base are equal to each other.

base - (the side that is not one of the two sides that are equivalent to each other)

Knowing this we can see that ∠ACB will equal ∠BAC, therefore ∠ACB will be equal to x°. Since the sum of all inner angles of a triangle is equal to 180°, we can make the following equation...

x° + x° + (3x + 70)° = 180°

2x° + 3x° + 70° = 180°

5x° = 180° - 70°

5x° = 110°

x° = 110° / 5

x° = 22°

x = 22

Therefore, x = 22.

Answer:

Part 1)

10,000 different numbers.

Part 2)

A) 1 in 10,000.

Step-by-step explanation:

Part 1)

Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:

[tex]T=\underbrace{10}_{\text{Choices For First Digit}}\times\underbrace{10}_{\text{Second Digit}}\times\underbrace{10}_{\text{Third Digit}}\times \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000[/tex]

Thus, 10,000 different numbers are possible.

Part 2)

Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.

This is equivalent to 0.0001 or a 0.01% chance of winning.

Answer:

1.25. It would be 1.25 if ur just talking about dividing in general which is pretty tough

Answer:

\dfrac54=-4c+\dfrac14 4 5 ​ =−4c+ 4 1 ​ start fraction, 5, divided by, 4, end fraction, equals, minus, 4, c, plus, start fraction, 1, divided by, 4, end fraction

Step-by-step explanation:

Answer:

0.65m

Step-by-step explanation:

28cm is equal to 0.28m

37/100 is 37% of a metre so 0.37m

0.28 + 0.37 = 0.65m

Answer:

mapping an area

Step-by-step explanation:

One situation and probably the most common is mapping an area. Graphs are great for dividing a geographical location into various sections and creating a model representation of the area. The graph itself allows for specific directions to be shared using the x and y coordinates on the graph. The same applies for finding the midpoint of a line segment. For example, this is useful if you were trying to find a place to meetup with a friend that is an equal distance from where you are and from where your friend is currently located. Therefore, allowing you to meetup at the midpoint.

Answer:

5 905 272

Step-by-step explanation:

you can refer to this lattice multiplication or u can search you tube for the examples of lattice multiplication

Answer:

Choosing a card randomly and noting its suit

Step-by-step explanation:

Choosing a card randomly and noting its suit

This is because binomial distributions only work for bernoulli trials (a trail in which there are only two outcomes)

Answer:

0.7513 = 75.13% probability that no more than 1 employee was over 50

Step-by-step explanation:

The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 + 16 = 20 employees, which means that [tex]N = 20[/tex]

4 over 50, which means that [tex]k = 4[/tex]

5 were dismissed, which means that [tex]n = 5[/tex]

What is the probability that no more than 1 employee was over 50?

Probability of at most one over 50, which is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]

[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]

0.7513 = 75.13% probability that no more than 1 employee was over 50

Answer:

the value of x is 29°

hope it helps

have a nice day