Answer:
The base is decreasing at 2 cm/min.
Step-by-step explanation:
The area (A) of a triangle is given by:
[tex] A = \frac{1}{2}bh [/tex] (1)
Where:
b: is the base
h: is the altitude = 10 cm
If we take the derivative of equation (1) as a function of time we have:
[tex] \frac{dA}{dt} = \frac{1}{2}(\frac{db}{dt}h + \frac{dh}{dt}b) [/tex]
We can find the base by solving equation (1) for b:
[tex] b = \frac{2A}{h} = \frac{2*120 cm^{2}}{10 cm} = 24 cm [/tex]
Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:
[tex] 2 cm^{2}/min = \frac{1}{2}(\frac{db}{dt}*10 cm + 1 cm/min*24 cm) [/tex]
[tex]\frac{db}{dt} = \frac{2*2 cm^{2}/min - 1 cm/min*24 cm}{10 cm} = -2 cm/min[/tex]
Therefore, the base is decreasing at 2 cm/min.
I hope it helps you!
The amount of mustard dispensed from a standard dispenser is normally distributed with a mean of 0.9oz and a variance of 0.01oz. If a family of six buys ten hotdogs total and dispenses mustard onto each one using the standard dispenser, what is the probability that more than 3 of them will have more than one ounce of mustard?
Answer:
the probability that more than 3 of them will have more than one ounce of mustard is 0.05975
Step-by-step explanation:
Given te data in the question;
let x rep the quantity of mustard on a hotdog ( in oz)
so
X → N ( u = 0.9, α² = 0.01 )
now P( more than one ounces of mustard on a hotdog) will be
P( X>1 ) = P( Z > ((1-0.9)/(√0.01)) ) = P( Z > 1 ) = 1 - P( Z < 1 )
= 1 - 0.84134 = 0.15866
Also let Y rep the number of hotdogs that have more than one ounces of mustard, so
Y → Bin( n = 10, p = 0.15866 )
P( y = y ) = (¹⁰ _y) ( 0.15855)⁰ ( 1 - 0.15866 )^10-y, y = 0,1,2,3......, 10
so required probability = P(Y > 3) = 1 - P(Y ≤ 3)
= 1 - P(Y=0) - P(Y=1) - P(Y=2) - P(Y=3)
=1 - (¹⁰ ₀) ( 0.15855)⁰ (1 - 0.15855)¹⁰⁻⁰ - (¹⁰ ₁) ( 0.15855)¹ (1 - 0.15855)¹⁰⁻¹ - (¹⁰ ₂) ( 0.15855)² (1 - 0.15855)¹⁰⁻² - (¹⁰ ₃) ( 0.15855)³ (1 - 0.15855)¹⁰⁻³
= 0.05975
Therefore the probability that more than 3 of them will have more than one ounce of mustard is 0.05975
1
The middle school girl's basketball team has
9 seventh-grade students and 5 sixth-grade
students. What is the ratio of sixth-grade
students to seventh-grade students on the
team?
Answer:
ratioed by ur name
Step-by-step explanation:
Helpppppppppppppp I’ll mark u
Suppose that the log-ons to a computer network follow a Poisson process with an average of three counts per minute.
Required:
a. What is the mean time between counts?
b. What is the standard deviation between counts (in minutes)?
c. If it is an average of 3 counts per minute, find the value of x such that P(X < x) = 0.95
Answer:
a. E(X) = 0.333 minutes
b. [tex]\mathbf{\sigma_x =0.333 \ minutes}[/tex]
c. 0.9986
Step-by-step explanation:
a.
To find the mean time between counts
Let X be the random variable that illustrates the time between the successive log-ons, then X is exponential with the rate [tex]\lambda = 3[/tex] log-ons per minute.
i.e.
[tex]E(X) = \dfrac{1}{\lambda}[/tex]
[tex]E(X) = \dfrac{1}{3}[/tex]
E(X) = 0.333 minutes
b. Since X is attributed to an exponential distribution, The standard deviation between counts is:
[tex]\sigma_x = \dfrac{1}{3}[/tex]
[tex]\mathbf{\sigma_x =0.333 \ minutes}[/tex]
c.
Given that;
The average number of count per minute = 3
The value of X such that P(X < x) = 0.95 can be calculated as;
[tex]\int \limits ^x_0 \lambda e^{-\lambda t}= 0.95[/tex]
[tex]3\int \limits ^x_0 \lambda e^{3 t}= 0.95[/tex]
[tex]\bigg [ -e^{3t}\bigg ]^x_0 = 0.95[/tex]
[tex]e^{3t} = 1-0.95[/tex]
-3x = ㏑ (0.05)
-3x = - 2.9957
x = -2.9957/ -3
x = 0.9986
The value of x = 0.9986
Answer:
a) 3
b)3
c) 8.9872
Step-by-step explanation:
a) According to the question, mean is 3.
b) Since it is an exponential distribution, standard deviation equals to mean. Therefore, the answer is 3.
c) P[x<X]=0.95
f(x)= λ*e^(-λ*x)
∫f(x)dx, 0 to x
mean = 1/λ =3. So, λ= 1/3.
∫(1/3)*e^(-x/3)dx= 1/3*e^(-x/3)/(-1/3)=-e^(-x/3) 0 to x
-e^(-x/3)+1 = 0.95
-e^(-x/3)=-0.05
x/3=ln(0.05)
x=ln(0.05)*3= 8.9872
The height distribution of NBA players follows a normal distribution with a mean of 79 inches and standard deviation of 3.5 inches. What would be the sampling distribution of the mean height of a random sample of 16 NBA players?
Answer:
The probability will be "0.0111".
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu[/tex] = 79
Standard deviation,
[tex]\sigma[/tex] = 3.5
Now,
⇒ [tex]\sigma\bar x = \frac{\sigma}{\sqrt n}[/tex]
[tex]= \frac{3.5}{\sqrt 16}[/tex]
[tex]=0.875[/tex]
⇒ [tex]P(\bar x > 81) = 1 - P(\bar x < 81)[/tex]
So,
= [tex]1 - P{\frac{(\bar x - \mu \bar x )}{ \sigma \bar x} < \frac{(81 - 79) }{0.875} ][/tex]
= [tex]1 - P(z < 2.2857)[/tex]
= [tex]0.0111[/tex]
Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?
Answer:
A) 120
Step-by-step explanation:
A factorial is represented with an !
Ex: 7! = 7*6*5*4*3*2*1
In this case, we would use 5! which equals 120.
120 should be your answer.
The value of a school bus reduces from $512000 to $343000in 3 years. Find the
uniform rate of depreciation per annum (R).
Answer:
The uniform rate of depreciation is $56,333 per year, or 11% per year.
Step-by-step explanation:
Rate of Depreciation
If some object has a certain value P and after some time t its value decreases to Q, the rate of depreciation is a measure of how much its value changed per unit time.
It can be calculated as:
[tex]\displaystyle R=\frac{P-Q}{t}[/tex]
It can also be expressed as a percentage, dividing the previous value by P.
The school bus reduces its value from $512,000 to $343,000 in 3 years, thus:
[tex]\displaystyle R=\frac{512,000-343,000}{3}[/tex]
[tex]\displaystyle R=\frac{169,000}{3}[/tex]
R = 56,333 $/year
Expressed as a percentage:
R = 56,333 / 512,000 = 0.11
R = 11%/year
The uniform rate of depreciation is $56,333 per year, or 11% per year.
a) Kenyans went elections and they had to choose between three coalitions; Jubilee
Cord and Amani. They must choose one, if they have no preference, can choose
all the three or, if against one option, they choose for the two they prefer. A
sample of 200 voters revealed the following information
30 chose Jubilee and Amani but not Cord
130 chose Cord only
102 chose Amani only
30 chose Jubilee and Cord
234 chose for either Jubilee or Cord, or both Jubilee and Cord, but not Amani
256 chose for either Cord or Amani, or both Cord and Amani, but not Jubilee
How
many
students chose
i) All the three options
(2 marks
ii) Only one option
(2 marks
iii) Jubilee irrespective of Cord or Amani
(2 marks
Answer:
iii is right..................
help, i will do brainliest!!!
a)
Four gallons of water weigh 33.4 lb
How much do 7.5 gallons of water weigh?
b)
Four gallons of water weigh 33.4 lb
Find the constant of variation.
Answer:
a) 62.625 lb
b) 8.35
Step-by-step explanation:
a)
Use a proportion.
4 gal is to 33.4 lb as 7.5 gal is to x lb.
4/33.4 = 7.5/x
4x = 33.4 * 7.5
4x = 250.5
x = 62.625
Answer: 62.625 lb
b)
33.4/4 = 8.35
1) Cost of 7.5 gallons of water = 62.63 lb
2) The constant of variation = 8.35 lb
We have to given that,
1) Cost of 4 gallons = 33.4 lb
2) And, Cost of 4 gallon of water = 33.4 lb
Hence, We can simplify it as,
1) Since, Cost of 4 gallons = 33.4 lb
Hence, Cost of 7.5 gallons = 7.5 × 33.4 / 4 lb
= 62.63 lb
2) Since, Cost of 4 gallon of water = 33.4 lb
Hence, the constant of variation = 33.4 / 4
= 8.35
Learn more about the divide visit:
https://brainly.com/question/28119824
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48% = StartFraction 48 Over 100 EndFraction = StartFraction a Over 25 EndFraction
a =
Answer:
12 over 25
Step-by-step explanation:
48 over 100 = 12 over 25
Which of the following can you determine when you use deduction and start from a given set of rules and conditions
Answer:
What must be true
Step-by-step explanation:
I don’t understand this question can you also help me figure it out step by step I would greatly appreciated it
Answer:
If a shape is a square, then it is a quadrilateral
Step-by-step explanation:
Quadrilateral means four sided shape, so automatically, because a square has 4 sides, you know it is a quadrilateral. But not all quadrilaterals are a square, you could have a rectangle which is four sides so you know that this statement is wrong "If a shape is a quadrilateral, then it is a square." Therefore, the answer is "If a shape is a square, then it is a quadrilateral
to convert measurements in the metric system you can move the decimal point left or right why does this work?
Answer:
C
Step-by-step explanation:
i took the assignment
what is le 2+2?
im -2 years old
Answer: The answer is 4
Step-by-step explanation: and FYI nobody is -2 years old
Find the value of x that will make a and b parallel 5x+9 and 3x+11
Answer:
Step-by-step explanation:
5x + 9 = 3x + 11 ( Alternate angles )
5x - 3x = 11 - 9
2x = 2
x = 2/2
x = 1
Hope this helps
plz mark as brainliest!!!!!
Three times the sum of three consecutive integers is 72. What are the integers? a. 4, 5, 6 c. 9, 10, 11 b. 7, 8, 9 d. 6, 7, 8
Answer:
B
Step-by-step explanation:
7+ 8+ 9= 24
24 x 3= 72
Answer:
The three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9
Step-by-step explanation:
Let x, y, and z be the three consecutive integers
The sum of x, y, and z will be: x+y+z
The three times the sum of three consecutive integers is 72.
so the equation becomes:
3(x+y+z)=72
Now, putting x = 7, y=8 and z=9 in the L.H.S equation to check
3(x+y+z)
⇒ 3(7+8+9)
⇒ 3(24)
⇒ 72
Therefore, it is clear that the three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9
5 men build a wall in 10 days how long will it take one man
Answer:
50 days?
Step-by-step explanation:
Answer:
i think it is 2 because
10 divide by 5 = 2
1 x 2 = 2
2 days
Just the image below.
Answer:
Step-by-step explanation:
P(x) + Q(x) = 4x^2 + 6x - 9 -7x^2 - 12x +8
x^2 terms: 4x^2 - 7x^2 = - 3x^2
x terms : +6x - 12x = - 6x
linear term: - 9 + 8 = - 1
Answer: -3x^2 - 6x - 1
YALL BETTER HELP ME WITH THIS :/
Answer:
Step-by-step explanation:
2. 4
3. 180°; multiplication
4. 4
6?. 32; 148
i think thats right. i hope this helps
Answer: I thinks it 32 degrees and 148 degrees
Step-by-step explanation:
Compare. Select <, >, or=.
3.568 ? 3.577
Answer:
3.568 < 3.577
Step-by-step explanation:
3.568 < 3.577
So 3.577 is greater than 3.568
Need help please please it due today at 4:50pm really need help please
Answer:
70
Step-by-step explanation:
Find the area A of the polygon with the given vertices. A(−6, 1), B(4, 1), C(4,−8), D(−6,−8)
A= __ square units
u must use the formula
so, the answer is 10 units²
Find the sample size required to estimate the percentage of college students who take a statistics course. Assume that we want 95% confidence that the proportion from the sample is within four percentage points of the true population percentage. Round the answer to the next larger whole number.
Answer:
The sample size is [tex]n = 600 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is E = 4% = 0.04
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Since the sample proportion (point estimate of the population proportion was not give we will assume it to be )
[tex]\^ p = 0.5[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.96}{0.04} ]^2 * 0.5 (1 - 0.5 ) [/tex]
=> [tex]n = 600 [/tex]
[(15 x 3) + 3] = (12-6) = N
Answer:
45+3 = 6=N
48_6= N
42= N
:. N= 42
Step-by-step explanation:
:. N= 42
Answer:
did you mean to put 2 equal signs in this?
Step-by-step explanation:
that would make this false because the first part equals 48 and the second equals 6 and since 48 doesn't equal 6 this is a false statement
Mrs canales class is selling pizza to earn money for a field trip. For every pizza sold the class makes $5.35. They have already earned $182.90 toward their $750 goal. How many more pizzas must they sell to earn $750 (algebraic approach) Thanks
Answer:
They still have to earn:
$750 - $182.9 = $567.1
and if they make $5.35 for every pizza sold:
$567.1 : $5.35 = 106
They must sell 106 pizzas more.
Step-by-step explanation:
A 30 foot cable is being cut into pieces that are 7 1/2 feet long
Answer:
Cool
Step-by-step explanation:
Do you mean a 30 foot cable is being cut into pieces that are 7 1/2 feet long, how many pieces is it cut into?
Answer:
goodluck
Step-by-step explanation:
8.7 x 10 to the 2nd power
Answer:
870
Step-by-step explanation:
10^2=100. 8.7*100 is 870.
Answer:
7,569
Step-by-step explanation:
8.7 × 10= 87
87 squared (to the 2nd power) is 87×87=7,569
Select the correct answer.
You're given three angle measurements of 30°, 70%, and 80°. How many triangles can you construct using these measurements?
A.0
B 1
C. 2
D infinitely many
Answer:
The answer Is D Infinitely many.
Although these triangles will have the same shape and will have proportional sides due to the angle measures, at least one side length must be given to determine the other lengths, and so the size is not specified. Therefore the combination of lengths are infinite. This is because all numbers go on forever, just as you can keep counting without stopping.
which pair of lines are perpendicular lines?
Answer:
D.) y = -1/4x - 6 and y = 4x + 11
Step-by-step explanation:
If two lines are perpendicular, that means that their slopes are opposite reciprocals, or that the product is equal to -1. -1/4 times 4 is -1, so they are perpendicular.
(3x-15)(2x+7) what is x
Answer:
The chosen topic is not meant for use with this type of problem. Try the examples below.
2 = |3x|
−4/5x + 1/25 = 0
3x = 4 − x
Answer
Step-by-step explanation:
This has to be equal to something in order to solve it. I'm going to guess that it is equal to 0
(3x-15)(2x+7) = 0
That means that
3x - 15 = 0
3x = 15
x = 15/3
x = 5
or
2x + 7 = 0
2x = - 7
x = -7/2
x = - 3.5
The only other thing I can think of that this could equal is multiplying the two binomials together.
3x * 2x = 6x^2
3x*7 = 21x
-15*2x = - 30x
-15 * 7 = - 105
6x^2 - 7x - 105
But that does not solve for x.