[tex]\\\\\\[/tex]
Therefore
[tex]\sf{Option~ D ~is ~correct }[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Answer:
-8x² -6x + 35
Step-by-step explanation:
A expression is given to us and we need to find out the quadratic equation . For that Multiply the two terms of the quadratic equation. The given expression is ,
Given expression :-
[tex]\rm\implies ( 2x +5)( 7 - 4x ) [/tex]
Multiply the terms :-
[tex]\rm\implies 2x ( 7 - 4x )+5(7-4x) [/tex]
Simplifying the brackets :-
[tex]\rm\implies 14x - 8x^2 + 35 - 20x [/tex]
Rearrange and simplify :-
[tex]\rm\implies -8x^2 -6x + 35 [/tex]
Therefore :-
[tex]\rm\implies\boxed{ \rm Quadratic\ Equation \ = -8x^2 -6x + 35} [/tex]
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
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
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]
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 }
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
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
Can someone please help me with my hw 20 points?
Answer:
The first equation; x-2y=8
Step-by-step explanation:
Hi there!
We're told that Ty wants to isolate x in one of the equations. To do so in either, he will need to use inverse operations to cancel out values and leave just x remaining on one side of the equation.
In the second equation, he would need to subtract both sides by 6y and then divide both sides by 4 to isolate x. It's a two-step process.
However, in the first equation, he only needs to add 2y to both sides to isolate x.
I hope this helps!
Answer:
using the first equation
cause Being that the first equation has the simplest coefficients (1, -2, for x, and y respectively), it seems logical to use it to develop a definition of one variable in terms of the other
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.
p{x:x is a natural number x (9
Answer:
you need a photo my dude
Step-by-step explanation:
Help me write this as an absolute value function!
Answer:13
Step-by-step explanation:11
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
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).
what is the product of ten and the sum of two and a number is five times the number
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.
PLEASE EMERGENCY!!!!
Which of the following statements is FALSE?
Answer:
Third one.
BO is not 7.8 cm
Step-by-step explanation:
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
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and
hair color among students. The table below contains the results of the survey.
Hair Color
Blue
Eye Color
Gray Green Brown Marginal Totals
5 21 10
78
Blond
42
Red
12
22
19
12
65
Brown
22
5
12
34
73
Black
9
3
11
64
87
Marginal Totals
85
35
63
120
303
From the sample population of students with blond hair, what is the approximate value of the relative frequency of students with green eyes?
Answer:
27%
Step-by-step explanation:
The approximate value of the relative frequency of students with green eyes from the given sample population is; 27%
What is the Relative Frequency?From the given table, the number of students with Blonde hair = 78
Number of students with blonde hair and green eyes = 21
Now, relative frequency is defined as the ratio of the number of outcomes in which a specified event occurs to the total number of trials, in an actual experiment.
Thus, in this question;
Relative frequency of students with green eyes = 21/78 = 2.7 = 27%
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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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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
(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]
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
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
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
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
How long will it take the same crew to clear the entire plot of 2 1/2 acres?
Answer:
It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Step-by-step explanation:
Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:
1/3 = 0.333
1/2 = 0.5
0.333 = 2
2.5 = X
2.5 x 2 / 0.333 = X
15 = X
Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
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:
1/3=?/24
Which number is missing to make the equation true?
Answer:
8
Step-by-step explanation:
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.
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f(x) = 1
g(x) = x - 4
Can you evaluate (g•f)(0)? Explain why or why not?
Answer:
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Step-by-step explanation:
We are given the following functions:
[tex]f(x) = 1[/tex]
[tex]g(x) = x - 4[/tex]
Can you evaluate (g•f)(0)?
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Answer:
To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.
You must evaluate the function f first.
Division by 0 is undefined.
The composition cannot be evaluated.
