see screenshot below
Answer:
4x^2 +2x +1
Step-by-step explanation:
(4x^3 -14x^2 -7x-4) / (x-4)
Using synthetic division
Bringing down the 4 and multiplying and adding
4 4 -14 -7 -4
↓ 16 8 4
-------------------------------
4 2 1 0
The quotient is 4x^2 +2x +1 and the remainder is 0
Answer:
[tex] {4x}^{2} + 2x + 1[/tex]
Step-by-step explanation:
the most handy way to solve the question is Polynomial long division which is done below:
[tex] \begin{array}{ccc} \qquad {4x}^{2} + 2x + 1 \\ \hline x - 4 \Bigg)4 {x}^{3} - {14x}^{2} - 7x - 4 \\ - {4x}^{3} + 16 {x}^{2} \\ \hline \qquad \qquad \qquad {2x}^{2} - 7x - 4 \\ \qquad \qquad- {2x}^{2} + 8x \\ \hline \qquad \qquad \qquad \qquad \qquad x - 4 \\ \qquad \qquad \qquad \qquad \qquad - x + 4 \\ \hline\qquad \qquad \qquad \qquad \qquad0 \end{array}[/tex]
since our remainder is 0 we'll put the answer in P(x) form only
note: please see the answer in the brainly app for a better view
Suppose x(t) is the continuous-time function given by x(t) = 1 on the interval [0; 1] and x(t) = 0 elsewhere. a) Calculate the continuous time Fourier transform of x(t). Call this X(j????). b) Suppose x1 (t) = x(2t). Provide the explicit definition for x1 (t) (i.e. over what interval
Answer:
a) X( w ) = 1 /jw - e^-jw / jw
b) X1(t) = 1 for 0.5
X1(t) = 0 for elsewhere
Step-by-step explanation:
x(t) continuous time function = 1
interval ( 0,1 ) also x(t) = 0 outside the given interval
a) Determine the continuous time Fourier transformation of x(t)
x( t ) = u(t) - u(t - 1 )
x ( w ) = 1 /jw - e^-jw / jw
b) supposing x1(t) = x(2t)
x1(t) = u(t) - u ( t - 0.5 )
x1(t) = 1 for 0.5
x1(t) = 0 for elsewhere
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defective unit. The ABCD Electronics Company has just manufactured 4500 write-rewrite CDs, and 150 are defective. If 4 of these CDs are randomly selected and tested, what is the probability that the entire batch will be rejected
Answer:
0.1269 = 12.69% probability that the entire batch will be rejected.
Step-by-step explanation:
CD's are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
4500 CDs, which means that [tex]N = 5000[/tex]
150 defective, which means that [tex]k = 150[/tex]
4 are selected, which means that [tex]n = 4[/tex]
What is the probability that the entire batch will be rejected?
At least 1 defective, which is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,4500,4,150) = \frac{C_{150,0}*C_{4350,4}}{C_{4500,4}} = 0.8731[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8731 = 0.1269[/tex]
0.1269 = 12.69% probability that the entire batch will be rejected.
Write as an equation: a triangle has two equal sides and a third side that is 15cm long. How long is each of the equal sides if the perimeter is 50?
Answer:
Step-by-step explanation:
X+x+15=50
S is the centroid of the triangle. Find IT if ST =9
Answer:
27
Step-by-step explanation:
The centroid divide a median in two parts, with ratio 1/3 and 2/3.
In particular the part between the centroid and the point where the median touches the side is 1/3 of the median.
We can build this proportion:
ST : 1/3 = IT : 3/3
9 : 1/3 = IT : 1
IT = 9 * 3 = 27
simplify.
[tex] {y }^{ - 3} [/tex]
Options:
3/y
-1/y^3
-3y
1/y^3
Answer:
Rewrite the expression using the negative exponent rule [text]{b}^{-n } = 1/bn
Step-by-step explanation:
1/y^3
2 1/3 divided by 1/4
¿Cuál es interés simple generado en un plazo fijo, por una capital de $10.000.000, al 4% bimestral durante 4 años?
Answer:
S.I = $1,608,000
Step-by-step explanation:
Given the following data;
Principal = $10.000.000Interest rate = 4%Time = 4 yearsTo find the simple interest, we would use the formula;
S.I = PRT
Where;
S.I is the simple interest.P is the principal.R is the interest rate.T is the time.Since the interest is being paid every two months (six times a year), the 4% interest will be divided by 6.
Thus: 4% every two months = [tex] 4 * \frac {2}{12} [/tex] = [tex] \frac {8}{12} [/tex] = 0.67% = 0.0067
4 years = 4 * 6 = 24 two-month years.
Substituting the values into the formula, we have;
S.I = 10.000.000 * 0.0067 * 24
S.I = $1,608,000
Find the slope.
Directions: For problems 1 through 3, graph the line by using the given X values and find its slope.
Answer:
Answer is in the picture.
Instructions: Find the missing side. Round your answer to the nearest
tenth.
49
х
66°
X
[tex]\sin(66) = \frac{49}{x} \\ 0.913 = \frac{49}{x} \\ x = 53.6 \\ x = 54[/tex]
The missing side is 53.6 units for the given right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The right triangle is given in the question, as shown.
The ratio of the length of the side opposite the angle to the length of the hypotenuse of the triangle. The sine function is denoted by the symbol "sin" and is defined as follows:
sin(θ) = opposite / hypotenuse
Here, θ = 66°
Using the sine ratio in the given triangle, we get
sin 66° = perdenicular/hypertanuas
Substitute the known values in the above ratio,
sin 66° = 49/x
x = 49/sin 66°
x = 53.63717
Rounded to the nearest tenth,
x ≈ 53.6
Thus, the missing side is 53.6 units for the given right triangle.
Learn more about the right triangle here:
https://brainly.com/question/11899922
#SPJ7
A rectangular park of length 60 m breadth 50 m encloses w volleyball court of length 18 m and breadth 10 m. Find the area of the park excluding the court at the rate of Rs 110 per square meter.
Given
A rectangular park of length 60 m breadth 50 m encloses with volleyball court of length 18 m and breadth 10 m.
To find:
The area of the park excluding the court at the rate of Rs 110 per square meter.
Solution:
Area of a rectangle is:
[tex]Area=length \times breadth[/tex]
Area of whole park is:
[tex]A_1=60 \times 50[/tex]
[tex]A_1=3000[/tex]
Area of volleyball court is:
[tex]A_2=18 \times 10[/tex]
[tex]A_2=180[/tex]
Now, the area of the park excluding the court is:
[tex]A=A_1-A_2[/tex]
[tex]A=3000-180[/tex]
[tex]A=2820[/tex]
Therefore, the area of the park excluding the court is 2820 square meter.
Need helppppp I’m stuckkkk
Answer:
b) 94
Step-by-step explanation:
The Total Degree of a Triangle is 180 degrees. Knowing this, set up an equation.
68+26+x=180.
x is the complementary angle of the "?" angle.
Solve the equation.
94+x=180
x=86
Then Subtract 86 from 180 to find "?"
180-86=94
I hope this helps!
Answer:
94;b
Step-by-step explanation:
68+26=94. 180-94=86. 180-86=94.
here are the first five terms of a quadratic sequence (1 8, 21, 40, 65). the nth term of this sequence can be written in the form (an2 + bn). where a and b are integers. work out the value of a and the value of b
Answer:
a=3 and b=-2
Step-by-step explanation:
We are given that five terms of a quadratic sequence are
1 8, 21, 40, 65.
The nth term of this sequence
=[tex]an^2+bn[/tex]
We have to find the value of a and b where a and b are integers.
For n=1
[tex]a+b=1[/tex] ......(1)
For n=2
[tex](2)^2a+2b=8[/tex]
[tex]4a+2b=8[/tex]
[tex]2a+b=4[/tex] .....(2)
Subtract equation (1) from (2) we get
[tex]2a-a=4-1=3[/tex]
[tex]a=3[/tex]
Using the value of a=3 in equation (1)
[tex]3+b=1[/tex]
[tex]b=1-3=-2[/tex]
Hence, the value of
a=3 and b=-2
Someone plz help me on this one
Answer:
76
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp side/ adj side
tan ? = 40 / 10
tan ? = 4
Taking the inverse of each side
tan ^ -1 (tan ?) = tan ^-1(4)
? =75.96375653
To the nearest degree
? = 76
One vertex of a polygon is located at (3, –2). After a rotation, the vertex is located at (2, 3). Which transformations could have taken place? Select two options. R0, 90° R0, 180° R0, 270° R0, –90° R0, –270°
Answer:
R0, 90°
R0, –270
Step-by-step explanation:
Answer:
A, E
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Step
Statement
1
2
- 6 = 15
-1-6+6 = 15 + 6
* = 21
-2.-= -2.21
3
4
5
y = -42
Use the table to complete each statement.
In step 2, the
In step 4 the
property of equality was applied.
property of equality was applied.
Answer:
2 addition
4 multiplication
Step-by-step explanation:
In step 2 we are adding 6 to each side so we use the addition property of equality
In step 4 we are multiplying by -2 on each side so we use the multiplication property of equality
Answer:
2- addition
4- mult.
Step-by-step explanation:
Can someone help me with this please
Answer:
.574
Step-by-step explanation:
This can be inputted in a calculator to achieve .57357643
To three decimal places that is .574
The robotics team purchased 3 androids for the purpose of programming. Each of the robots was $398, which included tax. If the tax rate is 8%, what is the TOTAL TAX to be paid?
Answer:
$95.52
Step-by-step explanation:
Number of robots = 3
Cost of each robots = $398
Tax rate = 8%
Amount of tax of each robots = 8% of $398
= 8/100 × $398
= 0.08 × $398
= $31.84
TOTAL TAX to be paid = Amount of tax of each robots × Number of robots
= $31.84 × 3
= $95.52
TOTAL TAX to be paid = $95.52
HELP!
Find x. Round to the nearest tenth.
Cos(angle) = adjacent leg/ hypotenuse
Cos(61) = x/19
X = 19 * cos(61)
X = 9.2114
Rounded to the nearest tenth = 9.2
please help me solve the equations, I re-wrote the question under each of them so you can read it better. Ty
Answer:
45:13/36
46:86/63
47:19/42
48:9/10
49:1/12
Need help with geometry question! Will mark brainliest!
Answer:
Definition of Bisect
Step-by-step explanation:
By definition, when two lines bisect each other, they divide each other into two equal segments.
In statement 2, we see that PO and ON are being labelled as congruent, which is referring back to the given information that MQ bisects PN. Since PO and ON are the two segments bisected by MQ, the two must be congruent simply from the definition of bisect.
If you shift the quadratic parent function, f(x) = x2 right 12 units, what is the
equation of the new function?
A. (x) = x2 - 12
B. AX) = (x + 12)
C. (x) = y2 + 12
D. (X) = (x - 12)
SUBMIT
Answer:
g(x) = (x-12)^2
Step-by-step explanation:
f(x) = x^2
Shifting to theright is of the form
f (x – b) shifts the function b units to the right.
g(x) = (x-12)^2
What is Index Law 2?
please give definition
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers.
Answer:
The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. The a represents the number that is divided by itself and m and n represent the powers. Here is an example for this rule.
If 8 is 8% of S, what does S equal?
Answer: S=100.
Step-by-step explanation:
Since 8 is 8% of 100 we know this is right.
Answer:
S = 100
Step-by-step explanation:
The equation is 8/? = 8/100
Multiply 8 x 100 to get 800, then divide by 8% to get 100.
The number of booker borrowed from a library each week follows a normal distribution. When sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30
Answer:
2.5%
Step-by-step explanation:
Given :
Mean, μ = 190
Standard deviation, σ = 30
Probability that more than 250 books are borrowed ;
x = 250
P(Z > z)
Z = (x - μ) / σ
P[Z > (x - μ) / σ] = P[Z > (250 - 190) / 30]
P(Z > z) = P(Z > 2)
P(Z > 2) = 1 - P(Z < 2) = 1 - 0.97725
P(Z > 2) = 1 - P(Z < 2) = 0.02275
(0.02275 * 100)% = 2.275%
2.5% is closest to 2.275%
please help!! 15 points! I need 5 and 9 answered
Answer:
B: Subtraction property of equality
Bill's five-day schedule continually repeats. It calls for him to work 4 days and then take the 5th day off. What is the greatest number of days of that Bill can take in one month?
Tony runs 100 meters in 10.36 seconds and neal runs the same distance in 10.26 seconds who is the faster runner?
Help on this please
Question 2 of 10
The function Fx) = log 0.5 x is decreasing. true or false
Answer:
True
Step-by-step explanation:
log0.5= -1.6990
so,anwer is negative than the statement is true
