Answer:
120 + 4w
Step-by-step explanation:
I am indeed doing it aswell
A sample of bacteria is growing at an hourly rate of 10% compounded continuously. The sample began with 4 bacteria. How many bacteria will be in the sample after 18 hours?
Answer:
24
Step-by-step explanation:
The computation of the number of bacteria in the sample after 18 hours is shown below:
We assume the following things
P = 4 = beginning number of bacteria
rate = r = 0.1
Now
We applied the following formula
[tex]A = Pe^{rt}[/tex]
[tex]= 4\times e^{18\times0.1}[/tex]
[tex]=4e^{1.8}[/tex]
[tex]= 4\times6.049647464[/tex]
= 24
We simply applied the above formula to determine the number of bacteria after the 18 hours
Pls help!! Thank you sooooo much if you help me on this, pls show proof
Answer:
√468 = 6√13
Step-by-step explanation:
ABCDEF is a regular hexagon of side length 6.
A'B'C'D'E'F' is the reflection of ABCDEF across BC.
The line FE' is the line from F to E'. It is also the hypotenuse of the right triangle FEE'. FE = 6, and EE' = 4a, where a is the apothem of the hexagon.
To find the apothem, draw the 30-60-90 triangle formed by the apothem and the radius (essentially 1/12th of the hexagon).
Using properties of a 30-60-90 triangle:
a = (6/2)√3
a = 3√3
4a = 12√3
Using Pythagorean theorem:
x² = (6)² + (12√3)²
x² = 36 + 432
x = √468
x = 6√13
in the life of a car engine, calculatedin miles, is normally distributed, with a mean of 17,000 miels and a standard deviation of 16,500 miles, what should be the guarantee period if the company wants less than 2% of the engines to fail while under warranty g
Answer:
the guarantee period should be less than 136010 miles
Step-by-step explanation:
From the given information;
Let consider Y to be the life of a car engine
with a mean μ = 170000
and a standard deviation σ = 16500
The objective is to determine what should be the guarantee period T if the company wants less than 2% of the engines to fail.
i.e
P(Y < T ) < 0.02
For the variable of z ; we have:
[tex]z = \dfrac{x - \mu }{\sigma}[/tex]
[tex]z = \dfrac{x - 170000 }{16500}[/tex]
Now;
[tex]P(Y < T ) = P( Z < \dfrac{T- 170000}{16500})[/tex]
[tex]P( Z < \dfrac{T- 170000}{16500})< 0.02[/tex]
From Z table ;
At P(Z < -2.06) ≅ 0.0197 which is close to 0.02
[tex]\dfrac{T- 170000}{16500}<- 2.06[/tex]
[tex]{T- 170000}<- 2.06({16500})[/tex]
[tex]{T- 170000}< - 33990[/tex]
[tex]{T}< - 33990+ 170000[/tex]
[tex]{T}<136010[/tex]
Thus; the guarantee period should be less than 136010 miles
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Answer: y > 2x + 1
Step-by-step explanation:
In the graph first, we can see two things:
The line is not solid (so the values in the line are not included), and the shaded part is above, so we will be using the symbol:
y > f(x)
Now, in the line we can see that when x = 0, y = 1.
So the linear equation must be something like:
f(x) = a*x + 1
The only one that has an y-intercept equal to 1 is y > 2x + 1
Answer:
C or y>2x +1
Step-by-step explanation:
edge
What is the missing term that makes these ratios equivalent? 1.5:3, 31.5:____
=========================================
Work Shown:
1.5/3 = 31.5/x
1.5x = 3*31.5 cross multiply
1.5x = 94.5
x = 94.5/1.5 dividing both sides by 1.5
x = 63
-----------
An alternative equation to solve is
1.5/31.5 = 3/x
1.5x = 31.5*3
1.5x = 94.5
The remainder of the steps are the same as in the previous section above.
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)
Answer:
b. [tex]g(x)=f(x)-5[/tex]
Step-by-step explanation:
You have that the function f(x) has its y-intercept for y=3.
Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.
In this case you have that f(x) has been translated vertically downward.
The general way to translate a function vertically in the coordinate system is:
[tex]g(x)=f(x)+a[/tex] (1)
being a positive or negative.
if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:
a = -2 -3 = -5
Then, the answer is:
b. [tex]g(x)=f(x)-5[/tex]
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
Hong buys a bag of 11 tangerines for $2.86.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
Solve the equation below for x. -1 2(3x - 4) = 11
Answer:
x= 37/36
Step-by-step explanation:
−12(3x−4)=11
Step 1: Simplify both sides of the equation.
−12(3x−4)=11
(−12)(3x)+(−12)(−4)=11(Distribute)
−36x+48=11
Step 2: Subtract 48 from both sides.
−36x+48−48=11−48
−36x=−37
Step 3: Divide both sides by -36.
−36x
−36
=
−37
−36
x=
37
36
Answer:
x=
37
36
-1/2(3x-4) = 11
Multiply both sides by -2:
3x-4 = -22
Add 4 to both sides:
3x = -18
Divide both sides by 3:
X = -6
find the domain and range of
f(x) = 2sinπx
please help me!
how do I graph this function
Step-by-step explanation:
The general form of a sine wave is:
y = A sin(2π/T x − B) + C
where A is the amplitude,
T is the period,
B is the phase (horizontal shift),
and C is the midline (vertical shift).
f(x) = 2 sin(πx)
This is a sine wave with an amplitude of 2, a period of 2, a phase of 0, and a midline of y=0.
To graph, the wave is centered at y=0 and has zeros every half period (x = 0, 1, 2, 3, etc.). Between the zeros, the wave is either a min or max (±2).
The domain of the function is (-∞, ∞).
The range of the function is [-2, 2].
Answer:
For
[tex]f(x) = 2\sin(\pi x)[/tex]
the domain is the real numbers, Range = [-2,2]
Step-by-step explanation:
About the domain, you can take any number, remember that the domain are the "x" that you can plug in on your function, for this case, you can plug in any value and you will have no problem.
Think about it like this, if you have f(x)= 1/x , you can't plug in x=0, but you can plug in all the other numbers, so the domain of that function would be all numbers except 0.
Therefore for
[tex]f(x) = 2\sin(\pi x)[/tex]
the domain is the real numbers.
About the range, it is the "y" axis, which numbers can you reach on the "y" axis, if you graph the function you will see that it is between [-2,2]
Range = [-2,2]
check the image I attach.
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
What is the square root of nine?
Answer:
3 or -3
Step-by-step explanation:
sqrt(9)
What number multiplied by itself will give you 9
3*3 =9
-3 * -3 =9
The square root of 9 is 3 or -3
Which is the graph of g(x) = (0.5)x + 3 – 4? On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, negative 4). On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 3. It crosses the y-axis at (0, 3). On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, 4). On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 4. It crosses the y-axis at (0, 12).
Answer:
The graph will be an exponential function that crosses the y-axis at about (0, -4).
Step-by-step explanation:
[tex]g(x) = (0.5)^{x + 3} - 4[/tex]
That means that when x = 0...
[tex]g(0) = (0.5)^{0 + 3} - 4[/tex]
[tex]g(0) = (0.5)^{3} - 4[/tex]
[tex]g(0) = 0.125 - 4[/tex]
[tex]g(0) = -3.875[/tex]
So, the graph will be an exponential function that crosses the y-axis at about (0, -4).
Hope this helps!
Answer:
its a
Step-by-step explanation:
i put the equation in desmos and the graph looked exactly like a lol
please help Find: ∠x ∠a ∠b
Answer:
x = 22
<a = 88°
<b = 92°
Step-by-step explanation:
To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.
To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:
[tex] (5x - 18) + (3x + 22) = 180 [/tex]
Solve for x
[tex] 5x - 18 + 3x + 22 = 180 [/tex]
[tex] 5x + 3x - 18 + 22 = 180 [/tex]
[tex] 8x + 4 = 180 [/tex]
Subtract 4 from both sides:
[tex] 8x + 4 - 4 = 180 - 4 [/tex]
[tex] 8x = 176 [/tex]
Divide both sides by 8
[tex] \frac{8x}{8} = \frac{176}{8} [/tex]
[tex] x = 22 [/tex]
=>Find <a:
According to the properties of parallel lines, alternate interior angles are equal. Therefore:
<a = 3x + 22
Plug in the value of x
<a = 3(22) + 22 = 66 + 22
<a = 88°
=>Find <b:
According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,
<b = 5x - 18
Plug in the value of x to find <b
<b = 5(22) - 18
<b = 110 - 18 = 92°
6th grade math , help me please :)
Answer:
A. Eric rode 2 more miles per week than Kim rode
Step-by-step explanation:
Number of miles Kim rode bicycle in 9 weeks = 135 miles
Let x be the number of miles per week.
135miles => 9 weeks
x miles => 1 week
[tex] x = \frac{135}{9} [/tex]
[tex] x = 15 [/tex]
Kim rode the bicycle 15 miles per week
Number of miles Eric rode bicycle in 6 weeks = 102 miles
Let x be the number of miles per week Eric rides the bicycle.
102 miles => 6 weeks
x miles => 1 week
[tex] x = \frac{102}{6} [/tex]
[tex] x = 17 [/tex]
Kim rode the bicycle 17 miles per week
Comparing the number of miles per week they rode, we would conclude that: "Eric rode 2 more miles per week than Kim rode".
0.3% of a country has a certain disease. The test for the disease has a sensitivity of 92% (i.e., of those we know have the disease, the test comes back positive 92% of the time.) It has a specificity of 96% (i.e., of those who do NOT have the disease, the test comes back negative 96% of the time.) Determine the ACCURACY of this test (round to 5 decimals) Remember, ACCURACY is correct values (i.e. true positives true negatives)
Answer:
0.95988 (Accuracy of the test )
Step-by-step explanation:
To determine the accuracy of this test we have to list out the given values
Prevalence rate of the disease = 0.3% = 0.003
sensitivity rate of the disease = 92% = 0.92
specificity rate for the test = 96% = 0.96
The accuracy of the test can be found using this equation
Accuracy = sensitivity * prevalence + specificity ( 1 - prevalence )
= 0.92 * 0.003 + 0.96 ( 1 - 0.003 )
= 0.00276 + 0.95712
= 0.95988
Ifx + iy = 1
1+i/
1-i
prove that, x² + y² = 1
HI MATE
Which inequality has a dashed boundary line when graphed? A y>=3/5x+1 B y>= -1/3x+1 C y>3x+1
Answer: C y>3x+1
Step-by-step explanation:
When we graph an inequality with strictly greater of less than sign ('<' or '>'), then the graph has a dashed boundary line .Further it indicates that it does not include the points on the line.From all the given options , only C contains inequality with '>' sign .
Hence, y>3x+1 is the inequality has a dashed boundary line when graphed.
hence, the correct option is C.
The Escobar family and the Johnson family each used their sprinklers last month. The water output rate forthe Escobar family's sprinkler was 20 gallons per hour. The water output rate for the Johnson family's sprinkler was40 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total wateroutput of 960 gallons. How many hours was each family’s sprinkler used?
Answer:
J = 32
E = 0
Step-by-step explanation:
E is the number of hours for the Escobar family
J is the number of hours for the Johnson family
E + J = 32
E * 20 + J * 30 = 960
Multiply the first equation by -20 so we can use elimination
-20 E -20 J = -640
Add this to the second equation
E * 20 + J * 30 = 960
-20 E -20 J = -640
---------------------------------
10 J = 320
Divide by 10
J = 32
Now find E
E + J = 32
E + 32 = 32
E = 0
Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.
Answer:
23
Step-by-step explanation:
since the number is relatively prime to the product of the first 20 positive numbers
It number must not have factor of (1-20)
Therefore the smallest possible number is the next prime after 20
Answer is 23
The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).
Hence, The smallest possible number is the next prime after 20 is, 23
Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
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A card is drawn from a well shuffled deck of 52 cards. What is the probability of drawing an ace or a 9? Round to nearest thousandth
Answer:
.154
Step-by-step explanation:
There are 52 cards
There are 4 aces and 4 9's for a total of 8 cars
P (ace or 9) = number of aces or 9's / total
= 8/52 = 2 /13 =.153846154
To the nearest thousandth
= .154
Answer:
0.154
Step-by-step explanation:
We want to find the probability of drawing an ace or a 9.
P(ace or 9)= aces and 9s / total cards
There are 4 aces and 4 9s in a standard deck of cards. This means there is a total of 8 aces and 9s.
In a standard deck of cards, there is a total of 52 cards.
P(ace or 9)= aces and 9s / total
aces and 9s= 8
total= 52
P(ace or 9)= 8/52
This fraction can be simplified. Both the numerator and denominator can be evenly divided by 4.
P(ace or 9)= (8/4) / (52/4)
P(ace or 9)= 2/13
P(ace or 9)= 0.153846153846154
Round to the nearest thousandth. The 8 in the ten thousandth place tell sus to round the 3 up to a 4.
P(ace or 9) = 0.154
The probability of drawing an ace or 9 is 0.154
f(x)= x^2– 3x + 9
g(x) = 3x^3+ 2x^2– 4x – 9
Find (f - g)(x).
Answer:
[tex]\large \boxed{\sf \ \ -3x^3-x^2+x+18 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex](f-g)(x)=f(x)-g(x)=x^2-3x+9-(3x^3+2x^2-4x-9)\\\\=x^2-3x+9-3x^3-2x^2+4x+9\\\\=\boxed{-3x^3-x^2+x+18}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
verify sin(360 - etheta = -sin etheta
Answer:
see explanation
Step-by-step explanation:
Using the subtraction identity for sine
sin(a + b) = sinacosb - cosasinb
Given
sin(360 - Θ)°
= sin360°cosΘ° - cos360°sinΘ°
= (0 × cosΘ ) - (1 × sinΘ)
= 0 - sinΘ
= - sinΘ ← as required
a hardware store ordered cartons of hammers at 100$ per carton and cartons wrenches at 150$ per carton if there were a total of 25 cartons in this order And the total cost of the order was 3,000$ how many cartons of hammers were ordered
Answer:
15 cartons of Hammers were ordered
Step-by-step explanation:
Cost per carton of Hammer = $100
Cost per carton of Wrenches = $150
Total Carton = 25
Total Cost = $3,000
Required
Determine the numbers of Hammer and Wrenches
Represent the hammers with H and the wrenches with W
So;
[tex]H + W = 25[/tex]
and
[tex]100H + 150W = 3000[/tex]
Make W the subject of formula in the first equation:
[tex]H + W = 25[/tex]
[tex]W = 25 - H[/tex]
Substitute 25 - H for W in the second equation
[tex]100H + 150(25 - H) = 3000[/tex]
[tex]100H + 3750 - 150H = 3000[/tex]
Collect Like Terms
[tex]100H - 150H = 3000 - 3750[/tex]
[tex]-50H = -750[/tex]
Divide both sides by -50
[tex]\frac{-50H}{=50} = \frac{-750}{-50}[/tex]
[tex]H = \frac{-750}{-50}[/tex]
[tex]H = 15[/tex]
Hence, 15 cartons of Hammers were ordered
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
In 2010 polls indicated that 75% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2010?
We test the hypothesis that the percentage supporting mandatory testing is less than 75% this year The p-value is 0.013
Which of the following interpretation of this p-value is valid?
A. The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
B. There is a 1.3% chance that the null hypothesis is true.
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Answer:
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.
Need help finding the length
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
What is the best way to remember the 6 trigonometric ratios?
Answer:
SOHCAHTOA
Step-by-step explanation:
Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.
Answer: SOHCAHTOA
Step-by-step explanation:
The pneumonic I learned is SOH-CAH-TOA. it says that Sin = opposite/hypotenuse. Cos = adjacent/hypotenuse. Tan = opposite/adjacent.
Hope it helps <3
Help ASAP!!!
A recursive sequence is a sequence where each term is found by adding a common difference
True or false
Answer:
True
Step-by-step explanation: