Answer: 0.0497870 ; 0.87754
Step-by-step explanation:
Given that :
λ = 0.0003
Defining a continuous distribution function :
F(x) = 1 - e^-λx = 1 - e^-0.0003x ; x ≥ 0
a. What proportion of the fans will last at least 10,000 hours?
P(x ≥ 10000) = e^-0.0003(10000) = 0.0497870
b. What proportion of the fans will last at most 7000 hours?
P(x ≥ 7000) = 1 - p(x ≤ 7000) = 1 - e^-0.0003(7000)
1 - 0.12245642825 = 0.87754
Find the product
1. (-3) (8)
2. (-12)(-8)
3. -72 ÷ (-9)
Answer: 1.) -24
2.) 96
3.) 8
Step-by-step explanation:
1.) A negative number multiplied times a positive number will automatically equal a negative answer. Ex: (-9) (5) = -45
2.) A negative number multiplied times a negative number will autimatically equal a positive answer. Ex: (-4) (-5) = 20
3.) This is the same as the statement above, but all you're doing this time is dividing. A negative number divided by a negative number will equal a positive number. Ex: -36 ÷ (-9) = 4
Solve the system of equations algebraically.
5x - 3y = 6
6x - 4y = 2
a. many solutions
C.
no solution
b. (8, 14
d. (9. 13)
Please select the best answer from the choices provided
Ο Α
ОВ
О С
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=9,\:y=13[/tex]
the option 'd' is correct.
Step-by-step explanation:
Given the system of the equations
[tex]\begin{bmatrix}5x-3y=6\\ 6x-4y=2\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}5x-3y=6\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:30x-18y=36[/tex]
[tex]\mathrm{Multiply\:}6x-4y=2\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:30x-20y=10[/tex]
[tex]\begin{bmatrix}30x-18y=36\\ 30x-20y=10\end{bmatrix}[/tex]
[tex]30x-20y=10[/tex]
[tex]-[/tex]
[tex]\underline{30x-18y=36}[/tex]
[tex]-2y=-26[/tex]
[tex]\begin{bmatrix}30x-18y=36\\ -2y=-26\end{bmatrix}[/tex]
solve for y
[tex]-2y=-26[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-2[/tex]
[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]
[tex]y=13[/tex]
[tex]\mathrm{For\:}30x-18y=36\mathrm{\:plug\:in\:}y=13[/tex]
[tex]30x-18\cdot \:13=36[/tex]
[tex]30x-234=36[/tex]
[tex]30x=270[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}30[/tex]
[tex]\frac{30x}{30}=\frac{270}{30}[/tex]
[tex]x=9[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=9,\:y=13[/tex]
Therefore, the option 'd' is correct.
4x - 2y = -20
7x + 2y = -2
Answer:
(-2, 6)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
4x - 2y = -20
7x + 2y = -2
Step 2: Rewrite systems
4x - 2y = -20
Add 2y to both sides: 4x = 2y - 20Divide 4 on both sides: x = 1/2y - 5Step 3: Redefine systems
x = 1/2y - 5
7x + 2y = -2
Step 4: Solve for y
Substitution
Substitute in x: 7(1/2y - 5) + 2y = =-2Distribute 7: 7/2y - 35 + 2y = -2Combine like terms: 11/2y - 35 = -2Add 35 to both sides: 11/2y = 33Isolate y: y = 6Step 5: Solve for x
Define original equation: 7x + 2y = -2Substitute in y: 7x + 2(6) = -2Multiply: 7x + 12 = -2Subtract 12 on both sides: 7x = -14Divide 7 on both sides: x = -2Step 6: Graph systems
Check the system.
At his birthday party, Mr Green would not directly tell how old he was. He said, "If you add the year of my birth to this year, subtract the year of my tenth birthday and the year of my fiftieth birthday, then add my age, the result is 122". How old is Mr Green
Answer:
61 years old in the year 2020Step-by-step explanation:
Let us assume the question was asked in the year 2020, that is this year
Say that Mr. Green was born in year x
The mathematical expression for his statement is given as
[tex]x + 2020 - (x + 10 + x + 50) + (2020 - x) = 122[/tex]
Solve for x
x + 2020 + 2020 - x - x - 60 - x = 122
4040- 122- 2x = 0
3918= 2x
divide both sides by 2
3918/2= x
x=1959
He was born in 1959, so now
he is (2020-1959)
=61 years old.
Which is the mode for the data set? −1, 0, 3, 4, −3, −1
Answer:
-1
Step-by-step explanation:
The mode is just the data point that is present the most, which is -1.
Answer:
-1
explanation:
Yes, AA
Yes, SAS
Not similar
Yes, SSS
Answer:
Yes, AA
Step-by-step explanation:
These triangles are similar because 2 angles in each triangle are congruent.
An image of a celebrity is going to be used on a promotional billboard. The person is 6 feet tall in real life, and 24 feet tall on the billboard. What is the scale factor of this dilation?
Answer:
3.5
Step-by-step explanation:
which is equivalent to 2(5m)+m? options are 11m, 12m, 5m+2 or 7m+2m
Answer:
11m
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define expression
2(5m) + m
Step 2: Simplify
Multiply: 10m + mAdd: 11mAnswer:
11m
Step-by-step explanation:
2 times 5m equals 10m and 10m plus m equals 11m
Sam's new room is square, and each side measures 15 feet. What is the
area of the room?
Answer:
225 feet
Step-by-step explanation:
Square sides are always the same size so just multiply 15x15.
im scared to tell my parents im gay plz give me motivation
Same here love!! Remember that if the living environment can get dangerous that it's better to stay in the closet, but besides that Good luck!
A fairly good estimate for a long-term loan with a moderate or high interest rate is that the monthly payment is _____ as large as the principal times the monthly interest rate.
Answer:
at least
Step-by-step explanation:
A fairly good estimate for a long-term loan with a moderate or high interest rate is that the monthly payment is AT LEAST as large as the principal times the monthly interest rate.
The correct word that missing in the statement is at least.
Given that, a statment is given we have to determine which word is missing the statment.
What is the investment?Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.
The monthly payment being at least equal to the principal multiplied by the monthly interest rate is a reasonable estimate for a long-term loan with a moderate or high-interest rate. So the correct statement is given as,
"A fairly good estimate for a long-term loan with a moderate or high-interest rate is that the monthly payment is at least as large as the principal times the monthly interest rate."
Thus, the correct word that missing in the statement is at least.
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What is the equation in slope-intercept from of the line that passes through the point (3, 1) and is parallel to the line represented by y = 2.4x + 6.5?
Do you guys know this
Answer:
18
Step-by-step explanation:
You solve the inner first, then move to the outer.
Let's take a look at g(x) first. It's stated that g(x) = [tex]x^2[/tex]. We plug in 3 for x and get 9 as the answer.
We then use this answer in f(x). The formula stated is f(x) = 2x. We plug in 9 for x and get 18.
If u cant see it well zoom in
Butt please help me i need this now!
Simplify the numerator [n] and give the factors of the denominator [d] after simpifying.
Hi... U should do like this...
I need help guys, what's the line segment of PN.
Answer:
It's a shared side???? It's a leg of a right triangle??? What are you specifically asking for? I need numbers
Step-by-step explanation:
A heater raises the temperature in a room by 3 degrees Celsius per hour. What is the rate in degrees Fahrenheit per minute? Hint: search for convert celsius to fahrenheit
Answer:
...you can just look up a Fahenheit to Celsius/vice versa/ calculator. it would have been so much faster and easier, but *sigh*
approx. 0.623 F per minute
Step-by-step explanation:
2
Viviana is ordering carpet
for 16 square rooms in a
hotel. Each room will need
100 square feet of
carpet. What is the
length of 1 room?
Answer:
Length of a room is 10ft
Step-by-step explanation:
Given
[tex]Rooms = 16[/tex]
[tex]Carpet\ Area = 100ft^2[/tex]
Required
Determine the length of each room
Here, we'll assume that the carpet will cover each room completely.
If so:
[tex]Carpet\ Area = Length * Length[/tex]
[tex]100ft^2 = Length * Length[/tex]
[tex]100ft^2 = Length^2[/tex]
Take square root of both sides
[tex]\sqrt{100ft^2} = \sqrt{Length^2}[/tex]
[tex]\sqrt{100ft^2} = Length[/tex]
Take positive square root
[tex]10ft = Length[/tex]
[tex]Length = 10ft[/tex]
Hence, the length of a room is 10ft
5*Hi please answer this very fast!! which answer is correct the left or right one?
Answer:
right i think
Step-by-step explanation:
Please help 30 points!!'
Write an equation based on the following conditions in slope/y intercept form
Perpendicular to 3x-4y=9 through (-15,-4)
also can yall provide some shown work as my geometry teacher asked for shown work
Answer:
The equation of line perpendicular to given line passing through (-15,-4) is:
[tex]y = -\frac{4}{3}x-24[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x-4y = 9[/tex]
The given equation is in standard form. We have to convert it into slope intercept form first.
The slope intercept form is:
[tex]y = mx+b[/tex]
So,
[tex]3x-4y=9\\3x-9 = 4y\\4y = 3x-9\\\frac{4y}{4} = \frac{3x-9}{4}\\y = \frac{3}{4}x - \frac{9}{4}[/tex]
The co-efficient of x is the slope of the line.
m = 3/4
The product of slopes of two perpendicular lines is: -1
Let m1 be the slope of line perpendicular to given line then
[tex]m.m_1 =-1\\\frac{3}{4} . m_1 = -1\\m_1 = -1 * \frac{4}{3} \\m_1 = -\frac{4}{3}[/tex]
Putting in slope-intercept form
[tex]y = m_1x+b\\y = -\frac{4}{3}x+b[/tex]
To find the value of b, putting (-15,-4) in equation
[tex]-4 = -\frac{4}{3}(-15) +b\\-4 = 20+b\\-4-20 = b\\b = -24[/tex]
The equation will be:
[tex]y = -\frac{4}{3}x-24[/tex]
Hence,
The equation of line perpendicular to given line passing through (-15,-4) is:
[tex]y = -\frac{4}{3}x-24[/tex]
A circle has a diameter of 4 inches. A square has a side length of 4 inches. What is true about the areas of these two figures?
What is 7.504-2.3792 rounded to the hundred
Answer:
0
Step-by-step explanation:
First what we have to do is subtract 7.504 and 2.3792 7.504 - 2.3792 = 5.1248then what we do isfind the number in the number in the hundreds place 0 and look one place to the to the right for the rounding digit 0. Round up if this number is greater than or equal to 5 and round down if less than five.Since zero is less than five we would round down
so our answer is zero
Hope this helps
Hope u get it right
(I'LL BE GIVING BRAINLIEST TO WHO EVER HELPS ME!!
Which expression results in a sum or difference of three and four forty eighths?
A) two and two twenty fourths plus one and one half
B) one and three twelves plus two and one quarter
C) seven and nine sixteenths minus four and one third
D) six and two sixths minus three and two eighths
(Here is an image if needed) :
Answer:
Step-by-step explanation:
D) six and two sixths minus three and two eighths
Answer:
D) six and two sixths minus three and two eighths
Step-by-step explanation:
What is 0.62x10 yo the power of 3
Answer:
62
Step-by-step explanation:
Answer:
238.328
Step-by-step explanation:
The product of 0.62 x 10 is 6.2. So, I did 6.2 to the power of 3, which is 238.328.
A submarine started at the
surface of the water and was moving underwater at
22 feet per minute toward the ocean floor. The submarine traveled at this rate
for 75 minutes before coming to rest on the ocean floor. Which of the following
integers represent the depth of the ocean floor in feet?
Answer:
1650
Step-by-step explanation:
75x22+1650
In △ABC, G is the centroid. If CG=12 find CD.
Answer:
CD = 24
Step-by-step explanation:
If G is the centroid, then CG = GD. (12 = 12)
Since CD is CG and GD combined, we would just add these two numbers to find the total length of CD.
CG + GD = CD
12 + 12 = 24
3(2^2x+3)-5(2^x+2)-156=0 in logarithm form
Answer:12x-157-5.2x
Step-by-step explanation:Like this or you want us to solve it lol
The given equation can be written in logarithmic form as xlog(2) + log(3 × 2ˣ - 5) = log(157).
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
Logarithm of any number is always positive.
For negative numbers, the logarithm are complex numbers.
The given equation is [tex]3(2^{2x}+3)-5(2^{x} + 2)-156 = 0[/tex]
Suppose 2ˣ be t, then the equation can be rewritten as,
3(t² + 3) - 5(t + 2) - 156 = 0
⇒ 3t² - 5t = 157
⇒ t(3t - 5) = 157
Take logarithm both sides to get,
log(t(3t - 5)) = log(157)
Use the property log(ab) = log(a) + log(b) to get,
log(t) + log(3t - 5) = log(157)
Substitute t = 2ˣ as and apply log(aⁿ) = nlog(a) as,
xlog(2) + log(3 × 2ˣ - 5) = log(157)
Hence, the logarithm form of the given equation is obtained as xlog(2) + log(3 × 2ˣ - 5) = log(157).
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A normal body temperature for a human is approximately 98°F. What is this temperature in degrees Celsius? Round your answer to the nearest 10th.
Answer:
36.67
Step-by-step explanation:
when you solbe you get 36.667 then round to become 36.67
Answer:
37°C
Step-by-step explanation:
The normal body temperature of a human is 98°F. To convert it into Celsius we know the realtion between Celsius and Farenheight as ,
➳ C/5 = F -32/9
➳ C/5 = 98 - 32/9
➳ C/5 = 66/9
➳ C = 66/9 × 5
➳ C = 36.66 °C ≈ 37°C
Hence the body temperature in Celsius measure is 37°C .Find the value of y
Im so lost can someone help and explain
please help with this question will give brainlyest if you get it right
the answer choices are
9 and 22/40
9 and 3/28
10 and 22/40
10 and 11/13
please help!!!!!!!
We need to first make these improper fractions. 5 = 40/8, so 40/8+6/8 = 46/8. Similarly, 4 = 20/5, so 20/5+4/5=24/5.
So we need to find the value of 46/8+24/5. Multiply the first fraction by 5/5 and second fraction by 8/8 to get the same denominator. We get (46*5+24*8)/8*5 = 422/40. This is equal to 400/40 + 22/40 = 10+22/40.
So the third answer choice is correct.
Hope that helped!