Answer:
(x, y) = (-34,-19)
Step-by-step explanation:
...................................................
The mean age of 5 people in a room is 27 years.
A person enters the room.
The mean age is now 35.
What is the age of the person who entered the room?
Answer:
main age = total age/total people
if Main age is = 27
[tex]27 = \frac{ \times }{5} [/tex]
and x = 135
Total age is = 135
then main age is 35
[tex][35 = \frac{y}{6} [/tex]
and y = 210
first main age - second main age = age of the person participating
210 - 135 = 75
the age is = 75HAVE A NİCE DAY
Step-by-step explanation:
GREETINGS FROM TURKEY
if A={1,2,3,4,5},B={4,5,6,7} and C={2,3,4}find (A-B)-C
Answer:
(A - B) - C = { 1 , 4 , 6 , 7 }
Step-by-step explanation:
A = { 1 , 2 , 3 , 4 , 5 }
B = { 4 , 5 , 6 , 7 }
A - B = { 1 , 2, 3 ,6 , 7 }
C = { 2 , 3 , 4 }
(A - B) - C = { 1 , 4 , 6 , 7 }
Số táo của An, Bình, Chi là như nhau. An cho đi 17 quả , Chi cho đi 19 quả thì lúc này số táo của Chi gấp 5 lần tổng số táo còn lại của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo? ( Giải bài toán trên bằng phương trình hoặc hệ phương trình )
Answer:
So, the initial number of apples is 7.
Step-by-step explanation:
The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)
Let the initial numbers of apples is a.
An gave 17 apples
Chi gave 19 apples
So,
x - 19 = 5 (x - 17 + x)
x - 19 = 5 (2x - 17)
x - 19 = 10 x - 85
9 x = 66
x = 7
AC if TC = 20q + 10q^2?
Answer:
AC = (20+ 10q)
Step-by-step explanation:
Given that,
Total cost, TC = 20q + 10q²
We need to find AC i.e. average cost.
It can be solved as follows :
[tex]AC=\dfrac{TC}{q}\\\\AC=\dfrac{20q + 10q^2}{q}\\\\AC=\dfrac{q(20+ 10q)}{q}\\\\AC={(20+ 10q)}[/tex]
So, the value of AC is (20+ 10q).
circle A has a center of (2,3) and a radius of 5 and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B
Answer:
12
Step-by-step explanation:
Is the distance a baseball travels in the air after being hit a discrete random variable, a continuous random variable, or not a random variable?
Answer: a continuous random variable
Step-by-step explanation:
Can you count the distance it traveled? You can't, so it couldn't be discrete because you can count discrete variables.
Can you measure the distance it traveled? You sure can, that makes it a continuous random variable.
Do you know the exact distance it's going to travel? You won't, therefore it's a random variable since you don't know the value beforehand.
A.For a group of individuals, the random variable x denotes the number of credit cards per individual with the following distribution. x: 0 1 2 3 4 5 P(x): .27 .28 .20 .15 .08 .02 a. find the mean, variance and standard deviation of x b. find the probability that a randomly selected individual holds at least 1 card.
Answer:
1.55
2.66
1.631
Step-by-step explanation:
Given :
x: 0 1 2 3 4 5
P(x): .27 .28 .20 .15 .08 .02
The expected mean, E(X) = Σ(x*p(x))
E(X) = (0*0.27)+(1*0.28)+(2*0.20)+(3*0.15)+(4*0.08)+(5*0.02)
E(X) = 1.55
The expected variance :
Σx²*p(x) - E(X)
(0^2*0.27)+(1^2*0.28)+(2^2*0.20)+(3^2*0.15)+(4^2*0.08)+(5^2*0.02) - 1.55
4.21 - 1.55 = 2.66
The standard deviation :
√variance = √2.66 = 1.631
A cyclist rides at an average speed of 25 miles per hour. If she wants to bike 195 km, how long (in hours) must she ride
1km = 0.621371miles
195 km= ?
cross multiplication
= 121.167 miles
25 miles= 1hour
121.167miles = ?hours
121.167=25x
divide by 25x both sides
=4.84 hours
approx 5hours
She must ride for 5 hours if she wants to bike 195 km.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Given that cyclist rides at an average speed of 25 miles per hour.
Since 1 km = 0.621371 miles
So 195 km = 121.167 miles
The speed of the cyclist (s) = 24 miles per hour.
Distance covered by the rider = 195 km
Distance covered by the rider (d) = 121.167 miles
By using the formula, time taken by a body, we calculate the time,
⇒ t = d/s
Substitute the value of d and s in above the equation
⇒ t = 121.167/ 24
Apply the division operation,
⇒ t = 5
Hence, she must ride for 5 hours if she wants to bike 195 km.
Learn more about the average speed here :
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Which of the following statements must be true about this diagram? Check all
that apply.
4 3
1
1
N
A. The degree measure of 23 equals the sum of the degree
measures of 21 and 22.
B. m23 is greater than m 2
C. The degree measure of 24 equals the sum of the degree
measures of 22 and 23.
D. m 4 is greater than m_2.
E. m24 is greater than m 1.
F. The degree measure of 24 equals the sum of the degree measures
of 21 and 22.
Answer:
D, E, and F
Step-by-step explanation:
✔️Statement D is true:
Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2
✔️Statement E is true:
Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1
✔️Statement F is true:
Rationale:
m<4 is an external angle of the triangle.
m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,
m<4 = m<1 + m<2
identify the system by type
Answer:
Inconsistent system
Step-by-step explanation:
Given
The attached graph
Required
The type of system
When two lines are parallel, it means they have the same slope and as such, the system has no solution.
Equations with the same slope are:
[tex]y = 2x + 6[/tex]
[tex]y = 2x- 8[/tex]
Both have a slope of 2
Such system are referred to inconsistent system.
Hence, (c) is correct.
Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Answer:
The interval is [98,132]
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 115 and standard deviation 25.
This means that [tex]\mu = 115, \sigma = 25[/tex]
Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = -0.675*25[/tex]
[tex]X = 98[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = 0.675*25[/tex]
[tex]X = 132[/tex]
The interval is [98,132]
Round your answer to one decimal digit. The volume of a cylinder is 1800cm squared. if the height of the cylinder is 40cm then the diameter of cylinder is
[tex]_____________________________________[/tex]
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
Use formula:
[tex]\sf{V = \pi(\frac{d}{2})^2h}[/tex]
Solving for diameter:
[tex]\sf d = 2 \times \sqrt{ \frac{V}{\pi h} } \\ \sf = 2 \times \sqrt{ \frac{40}{\pi \times 1800} } \approx0.16821 \\ = \sf \large\boxed{\sf{\green{d = 0.17}}}[/tex]
[tex]\sf\huge\underline\red{FINAL \: ANSWER}[/tex]
[tex]\large\boxed{\sf{\green{d=0.17}}}[/tex]
[tex]_____________________________________[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢ
by what number should 2/9 be divided to obtain 8/3
Answer:
[tex] \frac{1}{12} [/tex]
Step-by-step explanation:
[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]
So, if you divide 2/9 by 1/12, you'll get 8/3
Answered by GAUTHMATH
Help me write this as an absolute value function!
Answer:13
Step-by-step explanation:11
What is the factored form of x2 − 4x − 5?
(x + 5)(x − 1)
(x + 5)(x + 1)
(x − 5)(x − 1)
(x − 5)(x + 1)
Answer:
x2 - 4x - 5 factored form is (x - 5)(x + 1)
Answer:
(x − 5)(x + 1)
Step-by-step explanation:
The answer above is correct.
Which critical thinking issue is most relevant to the following situation:
A research journal reports that there are on average 2.773829473 TVs in homes of Endor college educators as opposed to 2.682390934 TVs in homes of Endor bank tellers.
perceived lack of anonnymity
loaded or leading question
nonresponse bias or missing data
voluntary response bias
assumed accuracy from overly precise numbers
self-interest study
9514 1404 393
Answer:
assumed accuracy from overly precise numbers
Step-by-step explanation:
Except when counting large sums of money or considering definitions, most real-world numbers are not accurate beyond about 6 significant figures. When considering survey or sample results, the accuracy can be considerably less than that, often not even good to 3 significant figures. (Margin of error is usually some number of percentage points greater than 1.)
Expressing the given ratios to 10 significant figures substantially misstates their accuracy. (10^-9 television is less than 1 day's accumulated dust).
CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars. You take a simple random sample of 56 auto insurance policies. Find the probability that a single randomly selected value is less than 995 dollars. P(X < 995)
Answer:
P(X < 995) = 0.4761
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars.
This means that [tex]\mu = 1013, \sigma = 284[/tex]
Find the probability that a single randomly selected value is less than 995 dollars.
This is the p-value of Z when X = 995. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{995 - 1013}{284}[/tex]
[tex]Z = -0.06[/tex]
[tex]Z = -0.06[/tex] has a p-value of 0.4761. So
P(X < 995) = 0.4761
PLEASE EMERGENCY!!!!
Which of the following statements is FALSE?
Answer:
Third one.
BO is not 7.8 cm
Step-by-step explanation:
find the equation of the line
Answer:
y = x + 6
Step-by-step explanation:
rise = 1
run = 1
slope = rise/run = 1
y-intercept = 6
y = mx + b
y = x + 6
HELP PLS ASAP!
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function &
Substitute a numerical value for k into the function equation.
Step-by-step explanation:
The horizontal stretch or compression for a function f(x) is given by g = f(bx) where b is a constant. If b> 0 then the graph of a function is compressed.
As it is given in the question that the function is transformed by a compression factor of 3.
Given function
The value of k will be 3 if the function is transformed by a compression factor of 3
The farmer is buying fence panels.
He needs a total length of 200 m of fence panels.
Each fence panel is 2.5 m in length.
Work out how many fence panels the farmer will need to buy?
Answer:
80 panels
Step-by-step explanation
p{x:x is a natural number x (9
Answer:
you need a photo my dude
Step-by-step explanation:
On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. What is the probability P(X < 3)?
Answer:
P(X < 3) = 0.14254
Step-by-step explanation:
We have only the mean, which means that the Poisson distribution is used to solve this question.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour.
This means that [tex]\mu = 4.8[/tex]
What is the probability P(X < 3)?
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-4.8}*4.8^{0}}{(0)!} = 0.00823[/tex]
[tex]P(X = 1) = \frac{e^{-4.8}*4.8^{1}}{(1)!} = 0.03950[/tex]
[tex]P(X = 2) = \frac{e^{-4.8}*4.8^{2}}{(2)!} = 0.09481[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00823 + 0.03950 + 0.09481 = 0.14254[/tex]
P(X < 3) = 0.14254
Simplify the following expression.
3^{0}
Answer:
Anything to the power of zero (with the exception of zero itself) is equal to one.
So 3⁰ = 1
Which statement is false?
A. Every irrational number is also real.
B. Every integer is also a rational number.
• C. Every rational number is also an integer.
D. No rational number is irrational.
Answer:
A. false B. true C. false D. true
Whope you all like this answer
Identify the percent, amount, and base in this problem.
What percent of 80 is 40?
Answer:
50Step-by-step explanation:
40: 80x100 =100 =(40x100): 80 =100): 80 =4000: 80 = 50The percentage of the number 80 is 40 will be 50%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The percentage is given as,
P = [(80 - 40) / 80] x 100
P = (40 / 80) x 100
P = 0.50 x 100
P = 50%
The percentage of the number 80 is 40 will be 50%.
More about the percentage link is given below.
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if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
what is the product of ten and the sum of two and a number is five times the number
Find a, b, c, and d such that the cubic function f(x) = ax3 + bx? + cx + d satisfies the given conditions.
Relative maximum: (2,9)
Relative minimum: (4,3)
Inflection point: (3,6)
a =
b =
C=
d =
Answer:
[tex]\displaystyle f(x)=\frac{3}{2}x^3-\frac{27}{2}x^2+36x-21[/tex]
Where:
[tex]\displaystyle a=\frac{3}{2}, \, b=-\frac{27}{2}, \, c=36, \text{and } d=-21[/tex]
Step-by-step explanation:
We are given a cubic function:
[tex]f(x)=ax^3+bx^2+cx+d[/tex]
And we want to find a, b, c and d such that the function has a relative maximum at (2, 9); a relative mininum at (4, 3); and an inflection point at (3, 6).
Since the function has a relative maximum at (2, 9), this means that:
[tex]f(2)=9=a(2)^3+b(2)^2+c(2)+d[/tex]
Simplify:
[tex]8a+4b+2c+d=9[/tex]
Likewise, since it has a relative minimum at (4, 3):
[tex]f(4)=3=a(4)^3+b(4)^2+c(4)+d[/tex]
Simplify:
[tex]64a+16b+4c+d=3[/tex]
We can subtract the first equation from the second. So:
[tex](64a+16b+4c+d)-(8a+4b+2c+d)=(3)-(9)[/tex]
Simplify:
[tex]56a+12b+2c=-6[/tex]
Divide both sides by two. Hence:
[tex]28a+6b+c=-3[/tex]
Relative minima occurs only at the critical points of a function. That is, it occurs whenever the first derivative equals zero.
Find the first derivative. We can treat a, b, c and d as constant. Hence:
[tex]f'(x)=3ax^2+2bx+c[/tex]
Since it has a minima at (2, 9), it means that:
[tex]f'(2)=3a(2)^2+2b(2)+c=0[/tex]
Thus:
[tex]12a+4b+c=0[/tex]
(We will only need one of the two points to complete the problem.)
Inflection points occurs whenever the second derivative of a function equals zero. Find the second derivative:
[tex]f''(x)=6ax+2b[/tex]
Since there is a inflection point at (3, 6):
[tex]18a+2b=0\Rightarrow 9a+b=0[/tex]
Solve for b:
[tex]b=-9a[/tex]
Substitute this into the above equation:
[tex]12a+4(-9a)+c=0[/tex]
Solve for c:
[tex]c=24a[/tex]
Substitute b and c into the previously acquired equation:
[tex]28a+6(-9a)+(24a)=-3[/tex]
Solve for a:
[tex]\displaystyle -2a=-3\Rightarrow a=\frac{3}{2}[/tex]
Solve for b and c:
[tex]\displaystyle b=-9\left(\frac{3}{2}\right)=-\frac{27}{2}\text{ and } c=24\left(\frac{3}{2}\right)=36[/tex]
Using either the very first or second equation, solve for d:
[tex]\displaystyle 8\left(\frac{3}{2}\right)+4\left(-\frac{27}{2}\right)+2(36)+d=9[/tex]
Hence:
[tex]d=-21[/tex]
Hence, our function is:
[tex]\displaystyle f(x)=\frac{3}{2}x^3-\frac{27}{2}x^2+36x-21[/tex]
(6^2)^4 simplify the expression
Answer:
36
Step-by-step explanation:
(6^2)^4
(6)^2+4
6^6
36
simplify the expression : (6²)⁴= (36)⁴= 1679616
Or
[tex]{6}^{2 \times 8} = 1679616[/tex]
