Answers
Answer:
The answer to your question is given below.
Step-by-step explanation:
6x⁴ + 4x³ – 10x
The greatest common factor can be obtained as follow:
6x⁴ = 2 * 3 * x * x * x * x
4x³ = 2 * 2 * x * x * x
10x = 2 × 5 * x
Greatest common factor = 2 * x
= 2x
Thus, the expression 6x⁴ + 4x³ – 10x can be written as:
6x⁴ + 4x³ – 10x = 2x(3x³ + 2x² – 5)
Related Questions
Find f(4),f(0),f(-1) & f(x)=6x-7
Answers
Answer:
f(4) = 31
f(0) = 7
f(-1) = 1
Step-by-step explanation:
f(x) = 6x + 7
f(4) = 6(4) + 7
f(4) = 24 + 7
f(4) = 31
f(0) = 6(0) + 7
f(0) = 0 + 7
f(0) = 7
f(-1) = 6(-1) + 7
f(-1) = -6 + 7
f(-1) = 1
6. What are the coordinates of W? (0,t) W 0 (,0) Rhombus (0, -1) o (-r, o) (0,r). (t,0)
Answers
Answer:
B. (-r, 0)
Step-by-step explanation:
W is on the x axis, so the y coordinate is 0.
It is also r away from the origin, so the x coordinate is -r
Hope this helps!
Question 9 of 44 What is the measure of 0 ?
A. 2.5. radians
B. 4 radians
C. 5 radians
D. 2.5 Π radians
Answers
Answer:
the answer to your question is B. 4 radians
According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0746 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 318 independent returns from this year, what is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Answers
Answer:
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.
This means that [tex]p = 0.0746[/tex]
Random sample of 318 independent returns
This means that [tex]n = 318[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]
What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?
Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]
[tex]Z = -0.26[/tex]
[tex]Z = -0.26[/tex] has a p-value of 0.3974.
1 - 0.3974 = 0.6026
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
What two methods are the best choices to factor this expression?
18x2 − 8
Answers
Answer:
18x2 is 36 but you have to minus it so the answer is 28.
Suppose z varies directly with x and inversely with the square of y. If z = 16 when x = 4 and y = 1 , what is z when x = 8 and y = 9 ?
Answers
Answer:
z = 3.6
Step-by-step explanation:
Given that,
z varies directly with x and inversely with the square of y. We can write it as :
[tex]z\propto \dfrac{x}{y}\\\\z=\dfrac{kx}{y}[/tex]
Where
k is constant
Put z = 16 when x = 4 and y = 1
[tex]16=\dfrac{k\times 4}{1}\\\\k=4[/tex]
Now put k = 4, x = 8 and y = 9
[tex]z=\dfrac{4\times 8}{9}\\\\z=3.6[/tex]
So, the value of z is equal to 3.6.
Find the time required for an investment of 5000 dollars to grow to 8600 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answers
Answer:
about 7.3 years
Step-by-step explanation:
[tex]8600=5000(1+\frac{.075}{4})^{4*t}\\1.72=(1.01875)^{4t}\\log_{1.01875}1.72=4t\\29.19428479=4t\\t=7.298571198[/tex]
Answer:
The answer is t=7.3
Graph g(x)=-8|x |+1.
Answers
Answer:
[tex] g(x)=-8|x |+1. = 9552815 \geqslant 6[/tex]
consider this equation sin(theta) = -4 square root of 29/29 if theta is an angle in quadrant IV what is the value of cos (theta)
Answers
Answer:
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
Step-by-step explanation:
Given
[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression
Required
[tex]\cos(\theta)[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta)= 1[/tex]
Make [tex]\cos^2(\theta)[/tex] the subject
[tex]\cos^2(\theta)= 1 - \sin^2(\theta)[/tex]
Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]
[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]
Evaluate all squares
[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]
Take LCM
[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]
[tex]\cos^2(\theta)= \frac{13}{29}[/tex]
Take square roots of both sides
[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]
cosine is positive in the 4th quadrant;
So:
[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]
Split
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]
Rationalize
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
Please help asap i will give brainliest. Find the exact perimeter and area of the triangle.
Answers
Answer:
perimeter=9cm
Area=2cm^2
step by step explanation:
Firstly solve the sides that don't have figures using trigonometry
#1..sin15°=opposite/hypotenuse
sin15=opposite/4
opposite=sin15×4
=1.035, round off to 1cm
Then find the value of the base
tan15=opposite/adjacent
tan15=1/adjacent
1=tan15adjascent
1/tan15=adjacent
adjacent or base=3.7 round off to 4cm
After finding these values find the perimeter
p=side+side+side
p=4cm+4cm+1cm
p=9cm
Find the area
1/2bh
1/2×4×1
A=2cm2
A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 90% reliable. In other words, if an individual lies, there is a 0.90 probability that the test will detect a lie. Let there also be a 0.045 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions
a. What is the probability of a Type I error? (Round your answer to 3 decimal places.)
b. What is the probability of a Type II error? (Round your answer to 2 decimal places.
Answers
Answer:
A) P(Type I error) = 0.045
B) P(Type II) error = 0.1
Step-by-step explanation:
We are told that the reliability of the test is 90% reliable.
Also, we are told that the probability that the test erroneously detects a lie even when the individual is actually telling the truth is 0.045.
Thus;
A) To calculate the probability of type I error:
From statistics, in this question we can say that the probability of a type I error is the probability that the test will erroneously detect a lie even though the individual is actually telling the truth. Thus;
Probability of (type I error) = P(rejecting true null) = 0.045
B) For probability of type II error, it is defined as the error where we accept a null hypothesis that is false. We can say that it produces a false negative and the formula is;
P(Type II) error = 1 - reliability
Reliability in the question is 0.90
Thus;
P(Type II) error = 1 - 0.9
P(Type II) error = 0.1
Help please asap!!! Thank you!
Answers
Answer:
Here's your answer.
Step-by-step explanation:
Just multiply in
The sum of two numbers is 125. Their difference is 47. The two numbers are:
a)39 and 86.
b)40 and 85.
c)47 and 78.
d)None of these choices are correct.
Answers
Answer:
let x represent the bigger number
x+x-47=125
2x-47=125
2x=125+47
2x=172
2x/2=172/2
x=86
the smaller number=x-47
86-47
39
therefore the answer is a) 39 and 86
Answer:
A
Step-by-step explanation:
To find the sum of 125, you have to add the numbers.
39+86 = 125
To find the difference of 47, you have to subtract the numbers.
86-39 = 47
A rectangular garden is 5 ft longer than it is wide. Its area is 1800ft^2. What are its dimensions?
Answers
Answer:
The dimensions are 45 feet by 40 feet.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A=w\ell[/tex]
Where w is the width and l is the length.
The length is five feet longer than the width. Thus, we can write that:
[tex]\ell = w+5[/tex]
The total area is 1800 square feet. Substitute:
[tex]1800=w(w+5)[/tex]
Solve for w. Distribute:
[tex]w^2+5w=1800[/tex]
Subtract 1800 from both sides:
[tex]w^2+5w-1800=0[/tex]
Factor. We can use 45 and -40. Hence:
[tex]\displaystyle (w+45)(w-40)=0[/tex]
Zero Product Property:
[tex]w+45=0\text{ or } w-40=0[/tex]
Solve for each case:
[tex]\displaystyle w=-45\text{ or } w=40[/tex]
Since the width cannot be negative, we can ignore the first solution.
So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.
The dimensions are 45 feet by 40 feet.
a Given: △CDE, DK ⊥ CE ,CD=DE Area of △CDE = 29cm2 m∠CDE=31° Find: DK
Answers
Answer:
DK = 10.23 units (approx)
Step-by-step explanation:
(DK * (CK + KE))/2 = 29
DK * CK = 29
180 - 31 = 149
149/2 = 74.5 --> degree of other angles
tan 74.5 = DK/CK
CK * tan 74.5 = DK
CK * CK * tan 74.5 = 29
CK = 2.83591462
2.83591462 * tan 74.5 = DK
DK = 10.22597776
So DK is approximately 10.23 units.
Hope this helps!
(x + 3)(x + 7) ≡ x2 + ax + 21
Answers
Find all solutions of the equation in the interval [0, 2pi); sqrt(3) * csc(theta) - 2 = 0
Answers
Answer:
Step-by-step explanation:
Solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the [ 0, 2π) is [tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].
What is trigonometric ratio?" Trigonometric ratios are defined as relation of the ratio of the sides of the triangle to the acute angle of the given triangle enclosed in it."
Formula used
[tex]cosec\theta = \frac{1}{sin\theta}[/tex]
According to the question,
Given trigonometric ratio equation,
[tex]\sqrt{3} (cosec\theta) -2=0[/tex]
Replace trigonometric ratio [tex]cosec\theta[/tex] by [tex]sin\theta[/tex] in the above equation we get,
[tex]\sqrt{3} (\frac{1}{sin\theta} ) -2=0\\\\\implies \sqrt{3} (\frac{1}{sin\theta} ) = 2\\\\\implies sin\theta=\frac{\sqrt{3} }{2}[/tex]
As per given condition of the interval [ 0, 2π) we have,
[tex]\theta = sin^{-1} \frac{\sqrt{3} }{2} \\\\\ implies \theta = \frac{\pi }{3} or \frac{2\pi }{3}[/tex]
Hence, solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the [ 0, 2π) is
[tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].
Learn more about trigonometric ratio here
https://brainly.com/question/1201366
#SPJ3
A rare baseball card just sold for $12,000. Sports experts anticipate this baseball card to increase in value by 9% each decade.
According to the experts, about how much should the baseball card be worth in 30 years?
Hint: A decade is equal to 10 years.
$15,540.35
$159,212.14
$83,614.45
$9042.85
Answers
Answer:
$15,540
Step-by-step explanation:
I DONT KNOW IF ITS RIGHT THO BUT
9% = 1,800
Find out the quotient
-72 ÷ (-2) = ?
-72 ÷ 2 = ?
72 ÷ (-2) = ?
(Thank you to whoever helps me out )
Answers
Answer/Step-by-step explanation:
✔️-72 ÷ (-2)
The division of two negative numbers will give us a positive number. i.e. - ÷ - = +
Therefore:
-72 ÷ (-2) = 36
✔️-72 ÷ 2
The division of a negative number and a positive number will give us a negative number. i.e. - ÷ + = -
Therefore:
-72 ÷ 2 = -36
✔️72 ÷ (-2)
The division of a positive number and a negative number will give us a negative number. i.e. + ÷ - = -
Therefore:
72 ÷ (-2) = -36
Which statements apply to the expression
? Check all that apply.
3
The base is 5
The base is 3.
The exponent is 3.
3 3 3
The expanded form is 555.
3.3.3
The expanded form is
5
Answers
Answer:
A, C, D, F
Step-by-step explanation:
Given the expression : (3/5)³
Recall :
a^b where, a = base ; b = exponent
In ; (3/5)^3
Base = 3/5 ; exponent = 3
Similarly ;
a^b = a in b places
(3/5)^3 = (3/5) * (3/5) * (3/5)
(3/5) * (3/5) * (3/5) = (3*3*3) / (5*5*5) = 27/125
Hence, A, C, D and F are all correct
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
Answers
John's age 4 years ago, if he will be y years old in 5 years
Answers
9514 1404 393
Answer:
y -9
Step-by-step explanation:
From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.
John's age 4 years ago is y-9 years.
Some number times 7 is equal to the number increased by 9
Write out the equation. Do not solve the equation.
Answers
Answer:
7x = x + 9.
Step-by-step explanation:
7 × something = something + 9, right?
So, 7x = x + 9.
PLEASE HELP ME PLEASE
Answers
Answer:
Ok so these triangle are the same with equivalent angles
so we can add up the angles 80+26=106
now we subtract from 180
180-106=74
so the measure of angle b is 74
Hope This Helps!!!
Find the image of the given point
under the given translation.
P(4, -7)
T(x, y) = (x+1, y + 3)
P' = ([?], []).
Answers
Answer:
P' (5, -4)
Step-by-step explanation:
P (4, -7)
x = 4 & Y =-7
T(4,. -7) = (4 + 1, -7 +3)
P' = (5, -4)
HELPPP
3p-4-8p<-19
i need the steps as well
Answers
9514 1404 393
Answer:
p > 3
Step-by-step explanation:
3p -4 -8p < -19 . . . . . . given
-5p -4 < - 19 . . . . . . . . collect terms
-5p < -15 . . . . . . . . . . . add 4
p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)
if cars A and B are traveling at the speed of 55km/hr and 75km/hr respectively. What is their average speed?
Answers
But
I
Really
Don’t
Know
Answer:
130 km/hr
Step-by-step explanation:
Average Speed = Total Distance / Total Time.
Let us just make up 2 distances from a time
A: 55 km/hour for 2 hours = 110 km
B: 75 km/hour for 2 hours = 150 km
Total Distance = 260 km
Total Time = 2 hours.
Average Speed = 260 / 2 = 130 km/hr
Now let's try it again. If we get a different answer, then the problem is unanswerable.
A: 55 km/hr for 3 hours = 165 km
B: 75 km/hr for 3 hours = 225 km
Total distance = 390 km
Total time = 3 hours
Average speed = 390 / 3 = 130 which is the same answer we got before.
Please help with this
Answers
Answer:
i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds
Simultaneous equations 5x-4y=19
X+2y=8
Answers
Answer:
x=5
y=3/2
Step-by-step explanation:
Take it or leave it, that's what the computer said.
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the x-test statistic, and use the x-distribution to find the p-value of the test. Category Observed (Expected) A 25 (20) B 35(40) C 50(60) D 90(80) Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places. chi-square statistic = p-value = i
Answers
Answer:
χ² = 4.80
Pvalue = 0.1874
Step-by-step explanation:
Given :
Category Observed (Expected)
A 25 (20)
B 35(40)
C 50(60)
D 90(80)
The Chisquare statistic (χ²) is given by :
χ² = Σ(observed - Expected)² / Expected
χ² = (25-20)²/20 + (35-40)/40 + (50-60)²/60 + (90-80)²/80
χ² = 1.25 + 0.625 + 1.67 + 1.25
χ² = 4.795
χ² = 4.80 (2 decimal places)
Using the Chisquare Pvalue calculator :
df = n - 1 = 4 - 1 = 3
Pvalue = 0.1874
