Answer:
-99
Step-by-step explanation:
Log(x-1)²=2
Log(x-1)²=Log(100)
(x-1)²=100
x-1=10 and x-1=-10
x₁=11 and x₂=-9
x₁ × x₂ = 11 × (-9) = -99
You work no more than 12 hours a week at your two jobs. The first job pays you $8 an hour, and the second job pays you $10 an hour. You must earn at least $100 each week. Which graph represents this situation (let x represent hours at job 1 and y represent hours at job 2)?
Answer:
10 hours at job (1)
2 hours at job (2)
Step-by-step explanation:
As per the given information, one earns ($8) dollars at one of their jobs, and ($10) hours at the other. One must earn a total of ($100) dollars, and can work no more than (12) hours. Let (x) be the hours worked at job 1 and (y) be the hours worked at job two.
Since one can work no more than (12) hours, the sum of (x) and (y) must be (12), therefore the following equation can be formed;
[tex]x+y=12[/tex]
One earns ($8) dollars at one of their jobs and ($10) at the other, but one earns a total of (100) one can form an equation to represent this situation. Multiply the hours worked by the money earn per hour for each job, add up the result and set it equal to (100).
[tex]8x+10y=100[/tex]
Now set up these equations in a system;
[tex]\left \{ {{x+y=12} \atop {8x+10y=100}} \right.[/tex]
Use the process of elimination to solve this system. The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations in the system such that one of the variable coefficients is the additive inverse of the other. That way, when one adds the equation, the variable cancels, one can solve for the other variable then back solve to find the value of the first variable,
[tex]\left \{ {{x+y=12} \atop {8x+10y=100}} \right.[/tex]
Manipulate,
[tex]= \left \{ {{(*-8)(x+y=12)} \atop {8x+10y=100}} \right.\\\\[/tex]
Simplify,
[tex]= \left \{ {{-8x-8y=-96} \atop {8x+10y=100}} \right.\\[/tex]
Add,
[tex]=2y=4[/tex]
Inverse operations,
[tex]y=2[/tex]
Backsolve for (x), use equation one to achieve this,
[tex]x+y=12\\[/tex]
Substitute,
[tex]x+2=12[/tex]
Inverse operations,
[tex]x=10[/tex]
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
Check explanation
Step-by-step explanation:
I'll give you my way of solving it and you can figure it out from there.
<CEA = <DEB due to vertical angles
AE = ED due to midpoint theorem
<CAD = <ADB due to alternating angles theorem
thus two triangles congruent due to ASA
Given the functions below,find (f -g) (-1).
f(x) = x2 + 3
g(x) = 4x - 3
Answer:
f(x)=-1,(-1)2+3=-2+3=1g(x)=-1 4(-1)-3=4-3=1(Step-by-step explanation:
(f-g)=1
function travelSpeed = CalculateTravelSpeed(startX, startY, endX, endY, travelTime) % startX, startY: Starting coordinates % endX, endY: Ending coordinates % travelTime: Travel time in hours % Write an anonymous function to compute distance given two coordinates % Function name: EuclideanDist % Function inputs: x1, y1, x2, y2 % EuclideanDist = ... % Do not modify the statement below travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime; end
Answer:
The functions in Python is as follows:
from math import *
def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):
travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime
return travelSpeed
def EuclideanDist(startX, startY, endX, endY):
dist = sqrt((startX - endX)**2 + (startY - endY)**2)
return dist
Step-by-step explanation:
from math import *
This defines the CalculateTravelSpeed function
def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):
This calls the EuclideanDist function to calculate the distance; Next, the speed is calculated
travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime
This returns the calculated speed
return travelSpeed
This defines the EuclideanDist function
def EuclideanDist(startX, startY, endX, endY):
This calculates the distance from the given coordinates
dist = sqrt((startX - endX)**2 + (startY - endY)**2)
This returns the calculated distance
return dist
GIVING OUT BRAINLIEST HELP PLEASE ❤️
Answer:
C
Step-by-step explanation:
$1400 is invested at 4% per annum simple interest. How long will it take for the amount to reach $1624? Show you working.
Answer:
4 years
Step-by-step explanation:
I = prt
F = p + prt
F = 1400 + 1400 * 0.04 * t
1624 = 1400 + 1400 * 0.04 * t
224 = 56t
t = 4
Answer: 4 years
PLEASE help! I really appreciate it thanks!
Answer:
h=A-πr²÷2πr
Step-by-step explanation:
Making h subject
A=2πrh+πr²
A-πr²=2πrh
A-πr²÷2πr=h
h=A-πr²÷2πr
Answer:
The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
Step-by-step explanation:
To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].
Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
can someone help me with this question
Answer:
D
Step-by-step explanation:
this answer is correct , i think if you think of it in logically
I need help with this math problem please
Solve the system of equations.
y = 3x
y = x2 - 10
A. (2,6) and (5, 15)
B. (2,6) and (-5, -15)
C. (-2,-6) and (-5, -15)
D. (-2,-6) and (5, 15)
Answer:
D. (-2, -6) and (5,15)
Step-by-step explanation:
When you set the equations together, you get x^2-3x-10. You then set this equation equal to zero and get (x-5)(x+2) or x=-2 and x=5. Then, plug these x-values into each equation to get your y-values.
A state sales tax of 6% and a local sales tax of 1% are levied in Tampa, Florida. Suppose the price of a
particular car in Tampa is $15,000, and an oil change at a certain auto center is $29.
Which statement is true about the total cost of the car and the oil change after sales tax has been
calculated?
Answer:
16050, 31.03
Step-by-step explanation:
15000x1.07 (adds 7% tax)=16050
29x1.07(adds 7% tax to price)=31.03
Solve this im stuck please solve!
What is the measure of angle O in parallelogram LMNO?
Answer:
O=74
Step-by-step explanation:
L=N
180-106=74
M=O
Select the correct answer.
Roger works part-time as a waiter at a pizza joint. He earns $9 per hour. How much does he earn for 20 hours of work?
A.
$100
B.
$120
C.
$150
D.
$180
Answer:
180
Step-by-step explanation:
9x20= 180
Answer:
Step-by-step explanation:
Well You Know you have to multiply
multiply 9 times 20
9 times 2 18
then add the zeros
The answer is 180
g The downtime per day for a computing facility has mean 4 hours and standard deviation 0.9 hour. What assumptions must be true to use the result of the central limit theorem to obtain a valid approximation for probabilities about the average daily downtime
Answer:
To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.
How many ways can a person toss a coin 16 times so that the number of heads is between 7 and 14 inclusive
50626 ways with a probability of 0.77
Step-by-step explanation:If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2
If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4
If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.
Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.
From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;
Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]
Where;
n = number of tosses
x = number of selection
number of ways of getting 7 heads;
n = 16
x = 7
=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]
=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]
=> C₁₆, ₇ = 11440
number of ways of getting 8 heads;
n = 16
x = 8
=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]
=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]
=> C₁₆, ₈ = 12870
number of ways of getting 9 heads;
n = 16
x = 9
=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]
=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]
=> C₁₆, ₉ = 11440
number of ways of getting 10 heads;
n = 16
x = 10
=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]
=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]
=> C₁₆, ₁₀ = 8008
number of ways of getting 11 heads;
n = 16
x = 11
=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]
=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]
=> C₁₆, ₁₁ = 4368
number of ways of getting 12 heads;
n = 16
x = 12
=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]
=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]
=> C₁₆, ₁₂ = 1820
number of ways of getting 13 heads;
n = 16
x = 13
=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]
=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]
=> C₁₆, ₁₃ = 560
number of ways of getting 14 heads;
n = 16
x = 14
=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]
=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]
=> C₁₆, ₁₄ = 120
Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e
11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways
P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]
= [tex]\frac{50626}{65536}[/tex]
= 0.77
Please answer question 4
Answer:
53
Step-by-step explanation:
Here are the first three terms of a different sequence.
1
3
9
Write down two numbers that could be the 4th term and the 5th term of this sequence.
Give the rule you have used to get your numbers.
please helpp
Step-by-step explanation:
everything can be found in the picture
which of the following statements is true
Answer: B ACE is similar to DCB
Step-by-step explanation:
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 14 cups of coffee, using 204 ounces of coffee, while collecting a total of $16.70. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answer:
Step-by-step explanation:
Lets assume that Kyle fill "a" 10-oz cups of coffee, "b" 14-oz cups of coffee and "c" 20 oz cups of coffee.
a + b + c = 16 (1)
10*a + 14*b + 20*c = 224 (2)
0.95*a + 1.15*b + 1.50*c = 18.60 (3)
Now, multiplying equation (1) by 10 and subtracting it from equation (2), we get
4b + 10c = 64 (4)
Again, multiplying equation (1) by 0.95 and substracting it from equation (3), we get,
0.2b + 0.55c = 3.4 (5)
Now,
Multiplying equation (5) by 20 and subtracting it from equation (4), we get
-c = -4,
Hence, c= 4
Putting this value in equation (4),
4b + 40 = 64
Hence, 4b = 24
So, b = 6
Again, putting the values of b and c in equation (1),
a + 6 + 4 = 16
Thus,
a = 6
Hence, the solution is
a = 6, 10oz cups of coffee
b = 6, 14 oz cups of coffee
c = 4, 20 oz cups of coffee
33. A labourer is engaged for 20 days on the condition that he will receive 120 for each day he
works and will be fined 10 for each day he is absent. If he receives 1880 in all, for how
many days did he remain absent?
thind of his nronerty to his son one-fourth to his daughter and
Answer:
false
Step-by-step explanation:
Dùng kiến thức về suy luận
3.1. Phát biểu các quy tắc suy diễn modus ponens, lựa chọn và bắc cầu.
3.2. Em hãy viết một đoạn văn ngắn (không quá 30 từ, không giống giáo trình) thỏa:
1) Quy tắc modus tollens.
2) Quy tắc
, ( )
( )
x p x
p a
∀
.
3.3. Em hãy xem đoạn suy luận sau đây theo quy tắc logic nào, có hợp logic hay không?
1) Một đất nước muốn phát triển về nhiều mặt thì cần phải hội nhập quốc tế. Việt Nam muốn
phát triển về nhiều mặt. Vậy Việt Nam cần phải hội nhập quốc tế.
2) Nếu trường học không có thầy giáo tốt và không có cơ sở vật chất tốt thì không có chất
lượng giáo dục tốt. Trường X không có cơ sở vật chất tốt mà có chất lượng giáo dục tốt.
Vậy trường X có thầy giáo tốt.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hagg
Pls help as fast as u can pls...
Answer:
226=2×113
321=3×107
305=5×61
133=7×19
Name the types of angles shown.
Check all that apply
A supplementary angles
B straight angle
C complementary angle
D right angle
Answer: C) complementary angle and D) right angle
Step-by-step explanation:
A is wrong because supplementary angles add up to 180 and this shows a right angle not a straight line
B is wrong because this a right angle not a straight angle
C is correct because complementary angles are two angles that add up to 90 degrees. angle EFH is split into EFG and GFH which adds up to 90 degrees.
D is correct because you can see the right angle symbol for angle EFH
The given angles shown in the figure are right angles and complementary angles.
Supplementary angles are two angles that add up to 180 degrees.
A straight angle is an angle that measures exactly 180 degrees.
It is a straight line, so it forms a straight angle.
A complementary angle is a pair of angles that add up to 90 degrees.
∠EFG and ∠GFH together are complementary angles as their sum is 90 degrees.
A right angle is an angle that measures exactly 90 degrees.
∠EFH is a right angle.
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ7
4. Steven drove from place A to place B at an average speed of 50 km/h. At the same
time, Joseph drove from place B to place A at an average speed of 60 km/h using
the same route. If the distance between A and B were 300 km, what is the distance
between Steven and Joseph after one and one half hours?
5.An owner jeep traveling at an average speed of 70 km/h left the town at 2:00 pm
If it arrived in another town at 6:00 p.m., how far are the two towns?
Answer:
1. 10 km
2.280 km
please mark my answer as brainliest answer.
the answer is surely correct
If one dog eats 5 pounds of food each week, how many dogs will 65 pounds of food feed for a week
Answer:
It will feed 13 dogs.
Step-by-step explanation:
1 dog = 5 lbs
Set up an equation:
Variable x = number of dogs
1/5 = x/65
Cross multiply:
1 × 65 = 5 × x
65 = 5x
Divide both sides by 5:
13
Check your work:
13 dogs × 5 lbs = 65 lbs
65 = 65
Correct!
Bob's Gift Shop sold 650 cards for Mother's Day. One salesman, Scarlett, sold 10% of
the cards sold for Mother's Day. How many cards did Scarlett sell?
Answer:
65
Step-by-step explanation:
To find the amount of something given a percentage, we first must translate the percentage into a fraction or decimal. One way to do this is to divide the percentage by 100. In this case, we can divide 10% by 100 to get 0.1
We can then multiply the percent by the total, or 100%. In this case, we have 0.1 of 650, so we multiply the two to get 0.1 * 650 = 65 as 10% of 650, or how many cards Scarlett sold
Answer:
65
Step-by-step explanation:
650 x .10 (or 10%)=65
Please help me in this! you get 30 points!
Answer:
y=3x-2
Step-by-step explanation:
You can verify it's not D because the y-intercept is at -2.
You can verify it's not A because that would mean the x-intercept is 2 despite it appearing to be closer to one.
You can verify it's not B because that would mean the x-intercept is 1.5
1. My number has two digits.
2. Double my number is less than 150.
Follo
ther
3. I am not divisible by 12.
4. My digits are different from each other.
5. The second digit in my number is divisible
by an odd number.
6. My first digit is less than my second digit.
7. My digits add up to 14.
way.
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {Your\:answer\:is\:59.}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
1. My number has two digits.
59 is a two-digit number. ✔2. Double my number is less than 150.
Double of 59 is 118, which is less than 150. ✔3. I am not divisible by 12.
Since 59 is an odd number, hence it is not divisible by 12. ✔4. My digits are different from each other.
The digits 5 and 9 are different. ✔5. The second digit in my number is divisible by an odd number.
9 is divisible by an odd number, i.e. 3. ✔6. My first digit is less than my second digit.
5 is less than 9. ✔7. My digits add up to 14.
5 + 9 gives us 14. ✔Therefore, the required number is [tex]\sf\pink{59}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Answer:
59
Step-by-step explanation:
two digits, 59=118, unable to divide by twelve since its an odd number, 9÷3=3, 5<9, 5+9=14
You deposit $ 755 each month into an IRA earning 1.3 % interest compounded monthly
How much will you have in the account in 23 years?
Answer:
FV= $242,731.14
Step-by-step explanation:
Giving the following information:
Annual investment (A)= $755
Number of periods (n)= 23*12= 276 months
Interest rate (i)= 0.013/12= 0.0010833
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {755*[(1.0010833^276) - 1]} / 0.0010833
FV= $242,731.14