Answer:
4, -1
Step-by-step explanation:
We can reverse the FOIL (First, outside, inside, last) method to break down the equation. The question is asking to solve by factoring so you want to find the right combination of numbers this equation can be broken down into:
x^2 - 3x - 4 = 0
Because we want x squared, x needs to be multiplied by itself, so we can put x in the first slot for each.
(x + or - ?) ( x + or - ?) = 0
Then we need to find numbers that could be added to get -3 and multiplied to get -4. The only set of numbers that works for this is -4 and 1. Note that the sign you put in front of each number has an impact on your answers. With this we get:
(x - 4) (x + 1) = 0
To test that this is equal to the original equation, simply multiply it out using FOIL.
x * x = x^2
x * 1 = x
x * -4 = -4x
-4 * 1 = -4
Putting each component into an equation:
x^2 + x - 4x - 4 = 0
Simplifying:
x^2 - 3x - 4 = 0
Once we are sure it is still the same equation, we find the solutions. We know 0 multiplied by anything equals 0, so to get 0 as the answer, one of the sets in the parentheses must equal 0. (It doesn't matter what the other one is as long is one equals 0)
Therefore, we have 2 solutions, 4, and -1 because if x is 4, 4-4 is 0 which solves the equation, and if x is -1, then -1 + 1 is 0 which also solves the equation.
You can also check your answers by plugging them back into the original equation.
a, b, c are prime numbers and 5≤a
Answer:
a=5
Step-by-step explanation:
Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)
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]
Joe bikes at the speed of 30 km/h from his home toward his work. If Joe's wife leaves home 5 mins later by car, how fast should she drive in order to overtake him in 10 minutes.
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
How would I simplify the expressions on the picture?
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)
9. Mariah has 28 centimeters of reed
and 37/100 meters of reed for weaving
baskets. How many meters of reed
does she have? Write your answer as a
decimal and explain your answer. (The first time time I asked I forgot to put the 37/100)
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
Which of the following situations WOULD NOT represent a binomial application? A. Choosing a card randomly from a standard deck and noting its color (remember color has only two outcomes black or red) B. Choosing a card randomly from a standard deck and noting whether its a face card C. Choosing a card randomly from a standard deck and noting its suit D. Choosing a card randomly from a standard deck and noting whether or not it's an ace
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)
Find the value of x.
Answer:
the value of x is 29°
hope it helps
have a nice day
4
5
start fraction, 5, divided by, 4, end fraction hour ==equals
minutes
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:
A point is selected at random from a line segment of length l, dividing it into two line segments. What is the probability that the longer line segment is at least three times as long as the shorter segment
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
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected (without replacement).
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%.
A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.
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
In one state lottery game, you must select four digits (digits may be repeated). If your number matches exactly the four digits selected by the lottery commission, you win.
1) How many different numbers may be chosen?
2) If you purchase one lottery ticket, what is your chance of winning?
3) There are ___ different numbers that can be chosen. (Type a whole number.)
4) There is a ___ chance of winning.*
*The answer choices for number 4 are:
1 in 10,000
1 in 6,561
1 in 100
1 in 1,000
1 in 9,999
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.
would someone mind looking over my answers to geometry!!
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 (●'◡'●)
Which choice is equivalent to(√6)( √8). How do you solve
A. 4√6
B. 4√3
C. 16√3
D. 3√16
Answer:
B
Step-by-step explanation:
(6)^1/2 × (8)^1/2
6^1/2 × 2 (2)^1/2
4 (3)^1/2
Use the values in 9 = 2.2 and In 200 – 5.3 to find the approximate value of log, 200.
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{ln 200}{ln 9}[/tex]= [tex]\frac{5.3}{2.2}[/tex]
= 2.409
The approximate value of log 200 would be; 2.409
What is a logarithm?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
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-moves "The string of a kite is perfectly taut" and always makes an angle of 35 degrees above horizontal. (a) If the kite flyer has let out 500 feet of string, how high is the kite? (b) If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?
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]
what is 221st number out of 5,6,7,8,9
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
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
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
What is a z-score?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
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. No withdrawals were made from the accounts. Answer the questions below. Do not do any rounding. (a) What was the total interest earned at the end of year? (b) What was the percent interest for the total deposited?
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%.
2498x2364
explaine how to solve
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
A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
In a pool of water filled to a depth of 10 ft, calculate the fluid force on one side of a 3 ft by 4 ft rectangular plate if it rests vertically on its 4 ft edge at the bottom of the pool. Remember that water weighs 62.4 lb/ft3
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:
Hello?
Step-by-step explanation:
Square Footage Frequency
0-499 5
500-999 17
1000-1499 36
1500-1999 115
2000-2499 125
2500-2999 81
3000-3499 47
3500-3999 45
4000-4499 22
4500-4999 7
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
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
A town recently dismissed 5 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50
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
In the accompanying diagram of isosceles triangle ABC, overline AB cong overline BC , BAC =X , and m angle ABC=3x+70
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.
Can you please help me with this question
r=4+7x-sx
I need help so any one can help with this
Solve the equation for x.
2/3x-1/9x+5=20
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 (●'◡'●)
Name some real-life situations where graphing could be useful. Discuss your ideas. Name some real-life situations where finding the coordinates of the midpoint of a line segment could be useful.
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.
