Answer:
x=8
Step-by-step explanation:
[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]
using the horizontal line test, which of the following can be confused about the inverse of the graph?
Answer:
I think D
Step-by-step explanation:
Verticle or horizontal line test, it would be a function either way
Please help, much needed. A lot of points
Answer:
A. -9
Step-by-step explanation:
If one of the variables were negative than, it would not be able to equal 2/7.
9. A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?
Answer: 97
Step-by-step explanation:
Formula to compute the required sample size :
[tex]n= (\dfrac{\sigma\times z_{\alpha/2}}{E})^2[/tex]
, where [tex]\sigma[/tex] = standard deviation
E= Margin of error
[tex]z_{\alpha/2}[/tex] = Two tailed z-value.
Here, E= 20
[tex]\sigma[/tex] = 100
For 95% confidence level: [tex]z_{\alpha/2}[/tex] =1.96
Required sample size:
[tex]n=(\dfrac{100\times1.96}{20})^2\\\\=(5\times1.96)^2\\\\=96.04\approx97[/tex]
Hence, the required sample size : 97
A salesperson earns 6% commission on $25,000. How much
commission was earned?
Answer:
1,500
Step-by-step explanation:
[tex]6*(\frac{25,000}{100} )=1,500[/tex]
Find the solution(s) of the quadratic equation 2x2 – 3x – 35 = 0
Answer: x = 5, x = -7/2
Step-by-step explanation:
2x² - 3x - 35 = 0
Step 1: Find two values whose product = 2(-35) and sum = -3: -10 & 7
Step 2: Replace the b-value of -3x with -10x + 7x:
2x² - 10x + 7x - 35 = 0
Step 3: Factor the first two terms and the second two terms:
2x(x - 5) +7(x - 5) = 0
Step 4: Write the factored form:
Notice that the parenthesis are identical. This is one of the factors. The outside values are the other factor:
Parenthesis: (x - 5)
Outside: (2x + 7)
Factored form: (x - 5)(2x + 7) = 0
Step 5: Set each factor each to zero and solve for x:
x - 5 = 0 2x + 7 = 0
x - 5 [tex]x=-\dfrac{7}{2}[/tex]
The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.
Given that:
2x² - 3x - 35 = 0
This is a quadratic equation.
It is required to find the solutions of this equation.
The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
From the given equation:
a = 2
b = -3
c = -35
Substitute to the quadratic formula.
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]
[tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]
[tex]=\frac{3\pm \sqrt{289}}{4}[/tex]
[tex]=\frac{3\pm 17}{4}[/tex]
So, the solutions are:
[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]
Hence, the solutions are x =5, -3.5.
Learn more about Quadratic Formula here :
https://brainly.com/question/22364785
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The Escobar family and the Johnson family each used their sprinklers last month. The water output rate forthe Escobar family's sprinkler was 20 gallons per hour. The water output rate for the Johnson family's sprinkler was40 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total wateroutput of 960 gallons. How many hours was each family’s sprinkler used?
Answer:
J = 32
E = 0
Step-by-step explanation:
E is the number of hours for the Escobar family
J is the number of hours for the Johnson family
E + J = 32
E * 20 + J * 30 = 960
Multiply the first equation by -20 so we can use elimination
-20 E -20 J = -640
Add this to the second equation
E * 20 + J * 30 = 960
-20 E -20 J = -640
---------------------------------
10 J = 320
Divide by 10
J = 32
Now find E
E + J = 32
E + 32 = 32
E = 0
a test consists of 10 true false questions to pass a test a student must answer at least six questions correctly if a student guesses on each question what is the probability that the student will pass the test A. 0.172 B. 0.205 C. 0.828 D. 0.377
Answer:
[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]
[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]
[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]
[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]
[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]
And adding the values we got:
[tex] P(X\geq 6) = 0.377[/tex]
The best answer would be:
D. 0.377
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=10, p=0.5)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
For this case in order to pass he needs to answer at leat 6 questions and we can rewrite this:
[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]
[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]
[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]
[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]
[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]
And adding the values we got:
[tex] P(X\geq 6) = 0.377[/tex]
The best answer would be:
D. 0.377
A sample of 900 computer chips revealed that 75% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that above 72% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim
Answer:
No the evidence is not sufficient
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 900[/tex]
The sample proportion is [tex]\r p = 0.75[/tex]
The population proportion is [tex]p = 0.72[/tex]
The Null hypothesis is
[tex]H_o : p = 0.72[/tex]
The Alternative hypothesis is
[tex]H_a : p > 0.72[/tex]
The level of significance is given as [tex]\alpha = 0.05[/tex]
The critical value for the level of significance is [tex]t_{\alpha } = 1.645[/tex]
Now the test statistic is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{\frac{p(1-p)}{\sqrt{n} } } }[/tex]
substituting values
[tex]t = \frac{ 0.75 - 0.72 }{ \sqrt{\frac{0.72 (1-0.72)}{\sqrt{900} } } }[/tex]
[tex]t = 0.366[/tex]
Since the critical value is greater than the test statistics then the Null hypothesis is rejected which there is no sufficient evidence to support the claim
2.4.6.8. 10.... geometrical,arithmetic or neither?
Answer:
This is an arithmetic sequence.
Step-by-step explanation:
The difference between the consecutive terms is constant => sequence is arithmetic.
4-2 = 2
6-4= 2
8-6 = 2
10-8 = 2
Step-by-step explanation:
It's an arithmetic sequences.
Formed by the n th term 2n.
As the difference is 2 between them.
let's find it, by formulae.
n th term = 2n
t1= 2×1=2t2 = 2×2=4t3=2×3=6t4=2×4=8and so on.....
Therefore, it's an arithmetic sequence.
Hope it helps..
Plzzzzzzzzzzzzzzzzzzzzzz find the hcf of 15a²b² and -24ab
Let's take a look at each term separately.
15a^2b^2:
15 has factors 1, 3, 5, 15
a x a
b x b
-24ab
-24 has factors 1, 2, 3, 4, 6, 8, 12, 24
a
b
Now, we can see what each of these terms has in common. Both have a 3 in their factor lists, as well as one a and one b.
Therefore, the greatest common factor is 3ab.
Hope this helps!! :)
Answer:
3ab
Step-by-step explanation:
[tex]15a^{2} b^{2} - 24ab[/tex] is divided by 3
[tex]5a^{2} b^{2} - 8ab[/tex] take away a and b once
hope this helped!!!
[tex]5ab - 8[/tex]
= 3ab
In triangle abc what is the value of cos b A 5/13 B 12/13 C 5/12 D 13/12
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
In the triangle,
Hypotenuse = 13
Opposite = Perpendicular = 5
Adjacent = Base = 12
Now,
Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos B = 12/13
If the triangle is just like in the attached file!
Answer:
B) 12/13
Step-by-step explanation:
what equals 1+1= Why can't I see any answers help i logged off etc is it just me?
Answer:
1 + 1 = 2
Step-by-step explanation:
^
Answer:
no , it's happening to everyone , even I can't see it .
Find the amount necessary to fund the given withdrawals. Semiannual withdrawals of 850 for 6 years,interest rate is 4.7% compounded semiannually.
Answer:
The amount necessary to fund the withdrawal is $8798.820
Step-by-step explanation:
Here, we are interested in calculating the necessary amount to fund the withdrawal given in the question.
From the question, we can identify the following;
Principal amount, P= $850
Here, Period rate, i = 0.047/ 2 =0.0235
n = 6*2 = 12
Mathematically;
Present Value of an annuity, Ao=P* [1-(1+i)^{-n}]/i
Ao=850* [1-(1+0.0235)^{-12}] /0.0235
Ao = $8798.820
conditinal probability question. please help! :)
Answer:
P(A|B) = 1 / 6
Step-by-step explanation:
Assuming two fair sided dice with faces numbered 1 to 6.
By intuition, there can only be 6 possible outcomes, so probability is 1/6.
Illustration how to use conditional probability.
Given two events A, B, following is the equation of conditional probability
that A happens given B has already happened and observed.
P(A|B) = P( A intersect B ) / P(B)
In the given problem,
A = casting a double-six
B = casting a double
P(A) = (1 / 6) * (1 / 6) = 1/36
P(B) = (6/6) * (1/6) = 1/6
P(A|B) = 1/36 / (1/6) = 1/6
At a firm, ten entry-level employees earn $40,000 a year, 6 junior-level employees earn $60,000 a year, and 3 managers earn $80,000 a year per person respectively. Find the weighted average of the firm.
Answer: answer is: 1000000/19
Step-by-step explanation:
10/19 - 40k -> 10/19*40k= 400000/19
6/19- 60k -> 6/19*60k= 360000/19
3/19 - 80k -> 3/19*80k=240000/19
400000/19+360000/19+240000/19=1000000/19
answer is: 1000000/19
Do you play brawl stars the game? Real question: (x-8)^2
Answer:
your answer is x^2 - 16x + 64.
Answer:
x^2 - 16x + 64
Step-by-step explanation:
Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers who floss twice a day is less than 40%. To test this claim, a group of 400 teenagers are randomly selected and its determined that 149 floss twice a day. The following is the setup for this hypothesis test: H0:p=0.40 H0:p<0.40 The p-value for this hypothesis test is 0.131. At the 5% significance level, should the dentist reject or fail to reject the null hypothesis?
Answer:
The dentist should fail to reject the Null hypothesis
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The sample mean is [tex]\= x = 149[/tex]
The level of significance is 5% = 0.05
The Null hypothesis is [tex]H_o : p = 0.40[/tex]
The Alternative hypothesis is [tex]H_a : p < 0.40[/tex]
The p-value is [tex]p-value = 0.131[/tex]
Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
Which one doesn’t belong? Why? Explain.
Answer:
IT IS (M-4)(M+1)
Step-by-step explanation:
BECAUSE ALL THE OTHER QUESTION HAVE THE VARIABLE AS X
AND THIS ONE IS M
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
The biology faculty at a college consists of 8 professors, 11 asscociate professors , 12 assistant professors and 4 instructors. If one faculty members is randomly selected , find probability of choosing a professor or instructor. Round to nearest thousandth
Answer:
0.343
Step-by-step explanation:
First, find the different ways one can chose a professor or instructor. In this case, there are 8 professors and 4 instructors. So there are a total of 12 ways you can choose a professor or instructor.
Second, you want to find the different ways you can choose any member of the faculty. In this example, since you are only choosing one person, then you just find the total number of people in the faculty, which is 8 + 11 + 12 + 4 = 35.
Third, all you do is divide the different ways you can get a professor or instructor by the total different ways you can choose. So it's 12/35, or 0.343.
The following data was collected from the manufacturing of an auto component. It represents the diameter (in mm) of that component. What is the LCL for a control chart using this data (z=3)? Sample Obs 1 Obs 2 Obs 3 Obs 4 1 10 12 12 14 2 12 11 13 16 3 11 13 14 14 4 11 10 7 8 5 13 12 14 13
Answer:
14.6
Step-by-step explanation:
(A). STEP ONE: Calculate the mean
(1). Row one = (10 + 12 + 12 + 14 ) = 48/4 = 12.
(2). Row Two: (12 + 11 + 13 + 16 ) = 52/4 = 13.
(3). Row three : (11 + 13 + 14 + 14)/4 = 13.
(4). Row four: (11 + 10 + 7 + 8)/4 = 36/4 = 9.
(5). Row five: (13 +12 + 14 + 13)/4 = 52/4 = 13.
(B). STEP TWO:
- determine the maximum and minimum value for each row.
- for each row, maximum - minimum.
Maximum values for each row:
Row one = 14, row two= 16, row three = 14, row four = 11 and row five = 14.
Minimum value for each row:
Row one = 10, row two = 11, row three = 11, row four =7 and row five = 12.
DIFFERENCES in each row :
row one = 14 - 10 = 4, row two = 16 - 11 = 5, row three = 14 - 11 = 3, row four = 11 - 7 = 4 and row five = 14 -12 = 2.
(C). STEP THREE: Calculate the mean of all the rows = 60/5 = 12.
(D). STEP FOUR : Calculate the Average Range = 18/5 = 3.6.
(E). STEP FIVE : Calculate the UCL.
A = Average rage × 0.729 = 3.6 × 0.729.
B = overall mean = 12.
UCL = A + B = 14.6.
In this exercise, we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 924,900, and the population was increasing at roughly 9400 people per year. The average annual income was $30,388 per capita, and this average was increasing at about $1400 per year (a little above the national average of about $1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999.
Answer:
the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion
Step-by-step explanation:
From the given information:
Let consider y to represent the number of years after 1999
Then the population in time (y) can be expressed as:
P(y) = 9400y + 924900
The average annual income can be written as:
A(y) = 1400y + 30388
The total personal income = P(y) × A(y)
The rate at which the total personal income is rising is T'(y) :
T'(y) = P'(y) × A(y) + P(y) × A'(y)
T'(y) = (9400y + 924900)' (1400y + 30388) + (9400y + 924900) (1400y + 30388)'
T'(y) = 9400(1400y + 30388) + (9400y + 924900) 1400
Since in 1999 y =0
Then:
T'(0) = 9400(1400(0) + 30388) + (9400(0) + 924900) 1400
T'(0) = 9400(30388) + (924900)1400
T'(0) = $1,580,507,200 billion
Therefore; the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion
Find one solution for the equation. Assume that all angles involved are acute angles. tangent (3 Upper B minus 32 degrees )equals cotangent (5 Upper B plus 10 degrees )
Answer:
Step-by-step explanation:
Equation given
tan(3B-32 ) = cot ( 5B +10 ) = tan [ 90 - ( 5B + 10 ) ]
tan(3B-32 ) = tan (90 - 5B - 10 )
(3B-32 ) = (90 - 5B - 10 )
8B = 32 + 80
B = 14° .
Find a formula for an for the arithmetic sequence.
Answer:
a(n)= a(n+1)+4
Step-by-step explanation:
The first terms of this sequence are: 4,0, -4, -8, -12
Let 4 be a0 and 0 a1.
● a1-a0 = 0-4
●a1-a0 = -4
●a1 = -4+a0
So this relation links the first term with the second one.
replace 1 in a1 with n.
0 in a0 will be n-1
● an = -4+a(n-1)
Add one in n
● a(n+1) = a(n)-4
● a(n) = a(n+1)+4
A bicycle tire has a radius of 5 inches. To the nearest inch, how far does the tire travel when it makes 8 revolutions?
Answer:
251 inches
Step-by-step explanation:
c = 2πr
c = 2(3.14)(5) = 31.4
31.4 x 8 rev. = 251 inches
15) In a recent study of 35 ninth-grade students, the mean number of hours per week that they played video games was 16.6. The standard deviation of the population was 2.8. Find the 95 % confidence interval of the mean of the time playing video games.
Answer:
The 95 % confidence interval of the mean of the time playing video games. is
[tex]15.67< \mu <17.52[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 35[/tex]
The sample mean is [tex]\= x = 16.6[/tex]
The standard deviation is [tex]\sigma = 2.8[/tex]
The confidence level is 95% hence the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Now the critical value of half of this level of significance obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason for the half is that we are considering the two tails of the normal distribution curve which we use to obtain the interval
Now the standard error of the mean is mathematically evaluated as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{2.8 }{\sqrt{35} }[/tex]
[tex]\sigma _{\= x} = 0.473[/tex]
the 95 % confidence interval of the mean of the time playing video games.
is mathematically evaluated as
[tex]\= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x }) < \mu < \= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x })[/tex]
substituting values
[tex]16.6 - (1.96 * 0.473) < \mu < 16.6 + (1.96 * 0.473)[/tex]
[tex]15.67< \mu <17.52[/tex]
(1/6 + 3/7) + 2/7=
Answer:
37/42 or 0.88
Step-by-step explanation:
[tex]( \frac{1}{6} + \frac{3}{7} ) + \frac{2}{7} \\ ( \frac{1}{6} + \frac{3}{7} ) = \frac{25}{42} \\ [/tex]
[tex]\frac{25}{42} + \frac{2}{7} = \frac{37}{42} \\ \\ answer = \frac{37}{42} [/tex]
Given: △ABC, AB=5√2 m∠A=45°, m∠C=30° Find: BC and AC
Answer:
BC = 10, AC= approximately 13.66 OR 5+5 √3
Step-by-step explanation:
Law of Sines
ANSWER NEEDED ASAP!According to the table below, what is the probability that the age of a student chosen at random will be 15 or younger?
A) 0.74
B) 0.59
C) 0.56
D) 0.54
The correct answer is C) 0.56
Explanation:
In general terms, the probability of two or more events can be calculated by adding the probability of each event. This rule applies when an event is considered as mutually exclusive. Age is considered as a mutually exclusive event because if a random individual is selected he/she will be only one age. In this context, if you need to know the probability that a student is 15 or younger it is necessary to add the probability that a student is 15, the probability that the student is 14, and the probability that the student is 13. The process is shown below:
P (A or B or C) = P(A) + P(B) + P(C)
P = P(13) + P(14) + P(15)
P= 0.001 + 0.25 + 0.30
P= 0.56
Answer:
0.59
Step-by-step explanation:
add the probabilities of 13, 14, and 15
0.01 + 0.28 + 0.3 = 0.59
What is the inverse of the function
Answer:
A
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{19}{x^3}[/tex] ( multiply both sides by x³ )
x³y = 19 ( divide both sides by y )
x³ = [tex]\frac{19}{y}[/tex] ( take the cube root of both sides )
x = [tex]\sqrt[3]{\frac{19}{y} }[/tex]
Change y back into terms of x, then
[tex]f^{-1}[/tex] (x) = [tex]\sqrt[3]{\frac{19}{x} }[/tex] = [tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex] → A