Chuong2: ƯỚC LƯỢNG THAM SỐ, môn thống kê ứng dụng
what are the solutions to the system
[tex]10+y=5x+x^2~~~~.....(i)\\\\5x+y =1~~~....(ii)\\\\\text{From (i):}\\\\10+y = 5x +x ^2\\\\\\\implies y = 5x +x ^2 -10\\\\\text{Substitute y in equation (ii):}\\\\5x+5x+x^2-10=1\\\\\implies x^2 + 10x -11 =0\\\\\implies x^2 +11x -x -11=0\\\\\implies x(x+11) -(x+11) =0\\\\\implies (x-1)(x+11) =0\\\\\implies x =1 ~~ \text{or}~~ x = -11\\\\\text{Substitute x =~1 in equation (ii):}\\ \\5+y =1 \implies y =-4[/tex]
[tex]\\\text{Substitute}~ x =-11~ \text{in equation (ii):}\\\\\ 5(-11) + y = 1 \implies y = 1 +55 = 56 \\\\\text{Hence} (x,y) = (-11,56) ~~\text{and}~~ (x,y)=(1,-4)[/tex]
Express 0.03 as a percentage of 1
Answer:
3%
Step-by-step explanation:
[tex] \frac{0.03}{1} \times 100[/tex]
0.03=3/100 So
[tex] \frac{3}{100} \div 1 \times 100[/tex]
=3%
An arrow is shot at an angle 32 degree from the horizontal. If it's height is increasing at 200 km/hr, how fast is the arrow itself going?
Check the picture below.
Bearing in mind that the angle is not changing all the wihle, namely is constant
[tex]tan(32^o)=\cfrac{y}{x}\implies x = \cfrac{y}{tan(32^o)}\implies x = \cfrac{1}{tan(32^o)}y \\\\\\ \stackrel{\textit{taking the derivative on bot sides}}{\cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}\cfrac{dy}{dt}}\implies \cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}200\implies \cfrac{dx}{dt}\approx 320.07~\frac{km}{hr}[/tex]
simplify 5 − 2(2.5 − 6.7)^2
Answer:
-30.28
Step-by-step explanation:
Write the quadratic function in f(x)=a(x−h)2+k form whose graph is shown below.
The graph shows a downward facing parabola with vertex (negative 3, 4) and y-intercept (0, negative 5).
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{h}{-3}~~,~~\stackrel{k}{4})\qquad \implies f(x) = a[x-(-3)]^2+4\implies f(x) = a(x+3)^2+4 \\\\\\ \textit{we know that} \begin{cases} x=0\\ f(x) = -5 \end{cases}\implies -5=a(0+3)^2+4\implies -5=9a+4 \\\\\\ -9=9a\implies \cfrac{-9}{9}=a\implies \boxed{-1=a}~\hfill \blacktriangleright f(x)=-(x+3)^2+4 \blacktriangleleft[/tex]
100.00 decreased by 20%
Please help
Answer: If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 => Percentage decreased number = 0.8 × Initial value
Step-by-step explanation: Number 100 decreased by 20% (20 percent) of its value (percentage decrease) and calculated absolute change (actual difference)
A basket containing 150mangoes cost 450 find the selling price of an orange if it is to be sold at a profit of 5%
Answer:
The selling price cost 472.5
Step-by-step explanation:
Let's find the profit first.
To find that, let's turn 5% to decimal form.
5 % = 0.05
Then, lets multiply it to the initial price which is 450
450 * 0.05 = 22.5
So the profit costs 22.5
Now, let's add the profit to the initial cost to find the selling price
450 + 22.5 = 472.5
That's it.
What is the algebraic expression for the following word phrase: the product of 7 and the difference of x and y?
Answer:
7(x-y)
Step-by-step explanation:
difference of x and y=x-y
product of 7=7 times the expression
so,
Answer is 7(x-y)
Guided Practice
Write the equation of the parabola in vertex form. The vertex is (3, 2) and the parabola passes through the point (0, 38). Create a rough sketch of the graph to use as a visual aid.
A.
y = 4(x + 3)2 + 2
B.
y = (x + 3)2 + 2
C.
y = 19(x − 2)2 + 3
D.
y = 4(x − 3)2 + 2
Answer:
D.
y = 4(x − 3)^2 + 2
Step-by-step explanation:
A. y = 4(x + 3)^2 + 2 = ( − 3 , 2 )
B. y = (x + 3)^2 + 2 = ( − 3 , 2 )
C. y = 19(x − 2)^2 + 3 = ( 2 , 3 )
D. y = 4(x − 3)^2 + 2 = ( 3 , 2 )
A line has a slope of 5 and passes through the point (1,5). What is its equation in
slope-intercept form?
Answer:
[tex]y=5x[/tex]
Step-by-step explanation:
Insert the information into the point-slope formula to find slope-intercept form.
[tex]y-y_1=m(x-x_1)\\\\y-5=5(x-1)\\\\y-5=5x-5\\\\y=5x[/tex]
In grade 10, the ratio of boys to girls is 2: 3. There are 75 girls. How many are boys?
HELP PLEASE .. I WILL GIVE A BRAINLIEST !
Answer:
150
Step-by-step explanation:
The ration is 2/3 in this example means they are twice as many boys than girls. If boys = 2/3, than girls = 1/3.
So, to find the answer, you must multiply 75 by 2, which is 150.
You don't need this, but they are 75 + 150 = 225 boys and grils in grade 10.
Which methods of evaluating a capital investment project ignore the time value of money?
Answer: Varies
Step-by-step explanation:
It involves any that is not concerned with making a profit.
URGENT WILL GIVE BRAINILY
Alex drives at a speed of 60 miles per hour. How long will it take to drive 330 miles?
Answer:
5.5 hours
Step-by-step explanation:
time = distance/speed
t = 330/60
t = 5.5 hours
You are in charge of financial services and must calculate overtime pay for employees in your division. Due to a heavy workload, an employee had to do 35 hours of overtime in two weeks. Seven of these hours are at "double time" (i.e. twice usual pay), the rest are at "time-and-a-half". The employee's usual pay is $375 a week at $10 an hour. How much overtime money should the employee be paid for the two week period?
Answer:
$2,100
Step-by-step explanation:
'regular' pay is 375/10 or $37.50 per hour
'time-and-a-half' would be 37.50 + 18.75 = $56.25 per hour
'double time' would be (2)37.50 = $75.00
35 hours in 2 weeks and 7 hours at 'double time' and 28 at 'time-and-a-half'
so:
(7)75 + (28)56.25 = 525 + 1575
Total overtime pay for 2-week period is $2,100
You buy a $266,000 home.with. a.down payment of 21%. Find the amount of the down payment and the mortgage amount.
down payment mortgage amount
28. Marta Sanchez purchased a sweater for $15.67, a pair of socks for $2.13, and a bracelet for $6.78. For all
purchases she must pay the state sales tax of 7.5% and the county tax of 0.5%. What is the tax on her
purchases?
Answer:
$ 1.94
Hope I helped
positive and negative relationships are both examples of linear relationships
A. True
B false
Answer: A. True.
Step-by-step explanation:
A relationship is linear when the points on a scatterplot follow a somewhat straight line pattern. This is the relationship that we will examine. Linear relationships can be either positive or negative. Positive relationships have points that incline upwards to the right. As x values increase, y values increase.
1. Transplant operations have become routine. One common transplant operation is for kidneys. The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. There are several new drugs available for such circumstances and the earlier the drug is administered, the higher the probability of averting rejection. The New England Journal of Medicine recently reported the development of a new urine test to detect early warning signs that the body is rejecting a transplanted kidney. However, like most other tests, the new test is not perfect. In fact, 20% of patients that experience kidney rejection and 9% of patients that do not experience kidney rejection receive a test result that proves to be incorrect. Physicians know that in about 30% of kidney transplants the body tries to reject the organ. If the new test has a positive result (indicating early warning of rejection), what is the probability that the body is attempting to reject the kidney?
Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Positive test.Event B: Body attempting to reject the kidney.The percentages associated with a positive test are:
80% of 30%(experience kidney rejection).9% of 70%(do not experience kidney rejection).Hence:
[tex]P(A) = 0.8(0.3) + 0.09(0.7) = 0.303[/tex]
The probability of both a positive test and the body attempting to reject the kidney is:
[tex]P(A \cap B) = 0.8(0.3) = 0.24[/tex]
Hence, the conditional probability is:
[tex]P(B|A) = \frac{0.24}{0.303} = 0.7921[/tex]
0.7921 = 79.21% probability that the body is attempting to reject the kidney.
A similar problem is given at https://brainly.com/question/25553471
The difference of twice a number and 7 is 20. Find the number.
Answer:
twice the difference gives 2(difference). 7 = 14 20 = 40
Step-by-step explanation:
A right triangle with a hypotenuse of square root of 61 has an area of 15 square inches. Find the lengths of the other two sides.
The lengths of the other two sides are 6 inches and 5 inches
Let b represent the base of the right triangle, h represent the height of the right triangle and x represent the hypotenuse.
Since the area of the triangle is 15 in², hence:
Area(A) = (1/2) * base * height
15 = (1/2)bh
bh = 30
b = 30/h (1)
Applying Pythagoras theorem also:
x² = b² + h²
(√61)² = b² + h²
61 = (30/h)² + h²
61 = 900/h² + h²
61h² = 900 + h⁴
h⁴ - 61h² + 900 = 0
h = -6, -5, 5, 6
Since the length cant be negative, hence h = 5 or h = 6
When h = 5; b = 30/5 = 6
When h = 6; b = 30/6 = 5
Therefore the lengths of the other two sides are 6 inches and 5 inches
Find out more at: https://brainly.com/question/2773823
I need the answer and how you done it please
Answer:
x=11/17
Step-by-step explanation:
determine the defined range
11/x 17
11/x =17 then x is canceled out
11=17x
17x=11 dividing both sides
x=11/17
Below is an excerpt from the home loan contract Kyle signed with his bank.
“The sum of the principal of the loan and all applicable interest will be divided into 360 monthly payments according to the amortization schedule.
The Buyer shall make each monthly payment by the first day of the month it is due. A payment not received by the first day of the month it is due will be considered delinquent. A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00. If a payment is not received by the last day of the month it is due, the Buyer and transaction shall be reported to the appropriate credit agencies.
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
Kyle failed to make his payment by the first of this month. Kyle’s monthly payment is currently $1,200. If Kyle decides to split the missing payment into two parts and pay it over the next two months, which of the following statements is false?
a.
Kyle will be reported to a credit agency.
b.
Kyle will be charged a $75 late fee for the missing payment.
c.
Kyle has one business week to inform his bank of the late payment.
d.
Kyle’s monthly payments for the next two months will remain $1,200.
Dеtеrmіnе tһе rаnցе օf tһе fսnсtіօn f(х) = 3х - 5 ԝһеn tһе ԁօmаіn іѕ {-4, 2, 9}.
Answer:
range is { - 17, 1, 22 }
Step-by-step explanation:
Substitute the values from the domain (input) into f(x) for range
f(- 4) = 3(- 4) - 5 = - 12 - 5 = - 17
f(2) = 3(2) - 5 = 6 - 5 = 1
f(9) = 3(9) - 5 = 27 - 5 = 22
range is { - 17, 1, 22 }
What is the equation of this line in standard form?
6x−7y=11
6x−7y=−11
7x−6y=11
6x−5y=−13
9514 1404 393
Answer:
(b) 6x −7y = −11
Step-by-step explanation:
Perhaps the easiest way to approach this is to look at the y-intercept. To find it, set the value of x to zero, and divide by the y-coefficient. The y-intercepts of these equations are ...
a) 11/-7 = -1 4/7
b) -11/-7 = 1 4/7 . . . . possible candidate
c) 11/-6 = -1 5/6
d) -13/-5 = 2 3/5
The only y-intercept that matches the graph is the one for equation ...
6x -7y = -11
_____
You can use any of several other strategies to verify this choice:
1) Putting the given point values into the equation:
for (-3, -1): 6(-3) -7(-1) = -18 +7 = -11 . . . . yes
for (1/2, 2): 6(1/2) -7(2) = 3 -14 = -11 . . . . yes
__
2) Finding the equation from the given points.
m = (y2 -y1)/(x2 -x1) = (2 -(-1))/(1//2 -(-3)) = 3/(3 1/2) = 6/7
Then the point-slope equation is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-1) = 6/7(x -(-3)) . . . . . substitute known values
7y +7 = 6x +18 . . . . multiply by 7, simplify
6x -7y = -11 . . . . . . . add -18 -7y to both sides
number of heads: 0,1,2,3 Frequency: 16,38,34,12 Find the median
Answer:
the median of 0 1 2 3 16 38 34 12 is 9.5
which could be the function graphed below ??
Answer:
D [tex]\sqrt{x+4}[/tex]
Step-by-step explanation:
A number x increased by 4 is less than or equal to 27.
Answer:
x + 4 < 27
-4. -4
x > 24
Step-by-step explanation:
put lines under signs
Alice uses a table to record the number of black cars, b, that passed by her house in h hours.
b is directly proportional to h.
Answer:
1/2
Step-by-step explanation:
b is directly proportional to h.
b = kh
take any (h, b) point
using (28, 14)
14 = k(28)
Divide both sides by 28
1/2 = k
1/2
S.7.G.1.1
Question
In a drawing of a bus, the length is 5 cm. If the scale used
is 1 cm: 9 ft, what is the actual length of the bus?
find the inverse of the function F(x)=x-3
Answer:
f¹(x) = x - 3
To find the inverse of a function, just "trade" and y and solve for the "new" y. The graph of the inverse is the reflection of the original function over the line y = x.
Rewrite the function f(x) = x + 3
as the equation y = x + 3
Trade x and y.
x = y + 3
Solve for the "new" y.
= y + 3
3 - 3
Subtract 3 from both sides
y = x= 3
The symbol for the inverse is f-¹(x)
f¹(x) = x - 3
Step-by-step explanation:
brainlies me plss
[tex]f(x) = x -3 \\\\\text{Write f(x) as}~ y = x -3}\\\\\text{Now replace x and y,}\\\\x = y-3\\\\\text{Solve for y:}\\\\y = x+3 \\\\\implies f^{-1}(x) = x +3 ,~ \text{This is the inverse of given function.}[/tex]