Answer:
5(x+4) ≥ 19
x ≤ -1/5
Step-by-step explanation:
5(x+4) ≥ 19
5x + 20 ≥ 19
5x ≤ -1
x ≤ -1/5
The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 120 cm^2?
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!
-32-38r=84+-112r+-42
Answer:
Move r to left or right then divide the numbers
Can y’all determine the measure of angle a
Answer:si
Step-by-step explanation:
16.43 in word form math
Answer:
Sixteen and forty-three hundredths
Step-by-step explanation:
A random sample of 1028 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1028 adults surveyed, 521 indicated that televisions are a luxury they could do without.
Answer:
lol
Step-by-step explanation:
what is the question
I need help with this please
Let the factors, a1, a2, … a9 of a9 be written in a square 3 by 3 array as indicated. Let a1 Help me plz
Answer:
61.2
Step-by-step explanation:
To solve this, we would have to use the arithmetic progression formula
S(n) = a + (n - 1) d, where
S(n) = is the value of the nth term
a = value of the first term
n = the nth term we're interested in
d = difference between successive terms
We're given that the first term, a1 = 1.we also know that the 6th term, a6 = 44
If so, we can use this to get our "d", saying
44 = 1 + (6 - 1) d
where
44 is the value of the 6th term, and n is 6. Also, the first term a = 1. Simplifying further we have
44 = 1 + 5d
5d = 44 - 1
5d = 43
d = 43/5
d = 8.6
This means that the difference between successive term is 8.6, we then use this "d" to find our 8th term
S(n) = 1 + (8 - 1) 8.6
S(n) = 1 + 7 * 8.6
S(n) = 1 + 60.2
S(n) = 61.2
Therefore, the 8th term is 61.2
The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. The distribution of this particular variable is very right skewed.(a) Suppose we let (X-bar) be the mean number of accidents per week at the intersection during 9 randomly chosen weeks. What is the probability that (X-bar) is less than 2?(b) Now let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the probability that X is less than 2?
Answer:
The probability that sample mean is less than 2 is 0.1423.
Step-by-step explanation:
Let X denote the number of accidents per week at a hazardous intersection.
It is provided that the mean and standard deviation of X are, μ = 2.2 and σ = 1.4.
(a)
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
As the sample size is not large enough, i.e. n = 9 < 30, the Central Limit Theorem cannot be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.
And since the distribution of X is not specified, the probability cannot be computed.
(b)
In this case, the sample size is large enough, i.e. n = 52 > 30, the Central Limit Theorem can be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.
Compute the probability that sample mean is less than 2 as follows:
[tex]P(\bar X<2)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{2-2.2}{1.4/\sqrt{56}})\\\\=P(Z<-1.07)\\\\=0.14231\\\\\approx 0.1423[/tex]
Thus, the probability that sample mean is less than 2 is 0.1423.
What is the measure of 1 Explain
Answer:
what measure one
Step-by-step explanation:
What are u talking bout
There is no picture or anything
Answer:
I wish I could help.
Step-by-step explanation:
There is no picture or a complex explanation.
how many terms are there in the expression 2x - 3y + 8?
Answer:
Three. 2x, -3y, and 8.
Step-by-step explanation:
For every constant or variable, there is a term.
In this expression, there are two variables (x and y) and there is a constant (8).
Hence, there are three terms.
Hope this helped!
hey everyone! I need help with 2 things! the first one is what 9+(-8) and -5+-4
Answer:
1. 9+(-8) = 1
2. -5+-4 = -9
Step-by-step explanation:
I need help on this one
Suppose that E and f are two events and that P(E and F)=0.3 and P(E)=0.5. What is P(F/E)?
Answer:
[tex]P(F/E) = 0.6[/tex]
Step-by-step explanation:
If we are given two dependent events [tex]A[/tex] and [tex]B[/tex] such that their chances of occurrence or the probabilities of the events are: [tex]P(A)[/tex] and [tex]P(B)[/tex].
Then the conditional probability that the event [tex]B[/tex] will occur given that [tex]A[/tex] has already occurred is given by the following formula:
[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}[/tex]
Here the two events given are [tex]E[/tex] and [tex]F[/tex].
[tex]P(E\ and\ F)\ or\ P(E\cup F) = 0.3[/tex]
and [tex]P(E) = 0.5[/tex]
As per the above formula that we have already discussed, the formula can be written as:
[tex]P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}[/tex]
To finish a certain job in 8 days, 6 workers are needed. If it is required to finish the same job in 2 days advance, how many workers have to work? *
8 points
Answer: 96 workers
Step-by-step explanation:
First you multiply 8 and 6 then by 2.
8 x 6= 48
48 x 2= 96
96 workers to help the business
What is the median 5,7,9,10,16,17,20
Answer:
10
Step-by-step explanation:
For an odd number of values, the median is the middle value when you write the values in ascending order.
5, 7, 9, 10, 16, 17, 20
The median is 10.
What is the u equal to -4=u/2-8
Answer:12. V is not needed, and just substitute the letters with the numbers the correspond to.
Step-by-step explanation:
*Find 6 5/8% of $1,480.90. Round to the nearest cent.
9514 1404 393
Answer:
$98.11
Step-by-step explanation:
If your calculator doesn't work with mixed numbers, you must first convert 6 5/8% to a decimal fraction.
6 5/8 = (6·8+5)/8 = 53/8 = 6.625
6 5/8% = 0.01×6.625 = 0.06625
Then the desired amount is ...
0.06625 × $1480.90 = $98.109625 ≈ $98.11
6 5/8% of $1,480.90 is $98.11.
what is the slope of (-4,-4) and (16,1)
Answer:
1/4
Step-by-step explanation:
-4 - 1 = -5
-4 - 16 = -20
-5/-20 = 1/4
identify the variables in 3a+7b(c-8)
If a line has a rise of 2 and a run of 2, what is its slope
Answer:
It's a positive slope it's not going down it's going up every time you go up to you go over to making it a positive slope
Step-by-step explanation:
Ava's cat is 3 pounds heavier than her puppy. if their combined weight is 27 pounds, how much does her cat weight
Answer:
12
Step-by-step explanation:
(3+x)+x=27
2x+3=27
2x=24
x=12
Find the coordinates of the reflection: B (7,-1) is reflected over the x-axis B’=?
Answer:
(7;1)
Step-by-step explanation:
The abscissa of B' is going to be the same as abscissa of B , becuse the points are simmetrical over axis x.
However the ordinate of the point B' will have the opposite sign as ardinate B. However the module of ordinate B' is going to be the same as module of orrdinate B.
Which number is divisible by 3?
A) 1,794
B) 1,912
C) 1,270
D) 473
Answer:
Step-by-step explanation:
should be A.
In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 151 lb, that the standard deviation is 25 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken:
a. What is the expected value of the sample mean of their weights?
b. What is the standard deviation of the sampling distribution of the sample mean weight?
c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb?
d. What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit?
Answer:
Explained below.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
a
The expected value of the sample mean of their weights is same as the population mean, μ = 1515 lbs.
b
The standard deviation of the sampling distribution of the sample mean weight is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{25}{\sqrt{16}}=6.25[/tex]
c.
The average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lbs. is:
[tex]\text{Average Weight}=\frac{2500}{16}=156.25[/tex]
d
Compute the probability that a random sample of 16 persons on the elevator will exceed the weight limit as follows:
[tex]P(\bar X > 156.25)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{156.25-151}{6.25})\\\\=P(Z>0.84)\\\\=1-P(Z<0.84)\\\\=1-0.79955\\\\=0.20045\\\\\approx 0.20[/tex]
solve equation for Y. 23=5x-2y
Answer:
y=5/2x-23/2 or y=2.5x-11.5
Step-by-step explanation:
First, add 2y to move it to the other side of the equation. This should give you 2y+23=5x. Now, subtract 23, giving you 2y=5x-23. Divide the whole equation by 2 so that y will be by itself. Written in fraction form, it would be: y=5/2x-23/2. Written in decimal form: y=2.5x-11.5.
Cuánto le falta a 3/5para llegar a 9/10
Answer:
3/10
Step-by-step explanation:
3/5 se puede convertir en 6/10
(3x2)/(5x2).
9/10 - 6/10 = 3/10
le falta 3/10 para llegar a 9/10.
Please help! BRAINLIEST to correct answer!
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[tex]2 {x}^{3} + 2 {x}^{2} - 40x = [/tex]
[tex]2x( {x}^{2} + x - 20) = [/tex]
[tex]2x(x - 4)(x + 5)[/tex]
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The correct answer is (( a )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The first option is the correct one.
[tex]2 {x}^{3} + 2 {x}^{2} - 40x[/tex]
[tex]2x( {x}^{2} + x - 20)[/tex]
[tex]2x(x - 4)(x + 5)[/tex]
1+8 pls help me nowwwwww
Answer:
9
Step-by-step explanation:
The answer is 9. You can figure it out by counting up from 8!
ASAP HELP PLEASE ITS IS VERY NEEDED
Answer:
D. no solution because the other answers if you plug them in dont work
Subtract using the number line. - 1/3-(-1/2)
Answer:
answer is 1/1
Step-by-step explanation: