Answer:
[tex]\large \boxed{\sf 15 \ \ and \ \ 24 \ \ }[/tex]
Step-by-step explanation:
Hello,
We can write the following, x being the second number.
[tex](2x-6)^2+x^2=801\\\\6^2-2\cdot 6 \cdot 2x + (2x)^2+x^2=801\\\\36-24x+4x^2+x^2=801\\\\5x^2-24x+36-801=0\\\\5x^2-24x-765=0\\\\[/tex]
Let's use the discriminant.
[tex]\Delta=b^4-4ac=24^2+4*5*765=15876=126^2[/tex]
There are two solutions and the positive one is
[tex]\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{24+126}{10}=\dfrac{150}{10}=15[/tex]
So the solutions are 15 and 15*2-6 = 30-6 = 24
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
work is shown and pictured
Answer:
2/3
Step-by-step explanation:
got right n edg 2021
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
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]
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]
When solving the equation, which is the best first step to begin to simplify the equation? Equation: -2 (x + 3) = -10 A: (-2)(-2)(x+3)= -10(-2) B: -1/2(-2)(x+3)= -10(-1/2) C: -2/2(x+3)= -10/2 D: -2/-10(x+3)= -10/-10
Answer:
Step-by-step explanation:
Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B
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 .
linear regression model describing the relationship between the carat weight and price of very high quality diamonds is summarized below.
A diamond seller lists a very high quality diamond weighing 0.8 carats at a price of $10,999. Does this model over- or under-predict the price of this diamond? Select the option below that best summarizes the answer.
A. The model under-predicts the price of this diamond because the residual is positive.
B. The model over-predicts the price of this diamond because the residual is positive.
C. The model over-predicts the price of this diamond because the residual is negative.
D. We do not have enough information to answer this question.
E. The model under-predicts the price of this diamond because the residual is negative.
Answer:
A. The model under-predicts the price of this diamond because the residual is positive.
Step-by-step explanation:
The diamond seller has listed its 0.8 weighting diamonds at a price of $10,999. The price of the diamond is set as the market maker. The model is used to predict the price of the diamonds. This model has under predicted the value of diamonds and actual price of diamonds must be higher.
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
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
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
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
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
Factories A, B and C produce computers. Factory A produces 4 times as manycomputers as factory C, and factory B produces 7 times as many computers asfactory C. The probability that a computer produced by factory A is defective is0.04, the probability that a computer produced by factory B is defective is 0.02,and the probability that a computer produced by factory C is defective is 0.03. Acomputer is selected at random and found to be defective. What is the probabilityit came from factory A?
Answer:
The probability is [tex]P(A') = 0.485[/tex]
Step-by-step explanation:
Let assume that the number of computer produced by factory C is k = 1
So From the question we are told that
The number produced by factory A is 4k = 4
The number produced by factory B is 7k = 7
The probability of defective computers from A is [tex]P(A) = 0.04[/tex]
The probability of defective computers from B is [tex]P(B) = 0.02[/tex]
The probability of defective computers from C is [tex]P(C) = 0.03[/tex]
Now the probability of factory A producing a defective computer out of the 4 computers produced is
[tex]P(a) = 4 * P(A)[/tex]
substituting values
[tex]P(a) = 4 * 0.04[/tex]
[tex]P(a) = 0.16[/tex]
The probability of factory B producing a defective computer out of the 7 computers produced is
[tex]P(b) = 7 * P(B)[/tex]
substituting values
[tex]P(b) = 7 * 0.02[/tex]
[tex]P(b) = 0.14[/tex]
The probability of factory C producing a defective computer out of the 1 computer produced is
[tex]P(c) = 1 * P(C)[/tex]
substituting values
[tex]P(c) = 1 * 0.03[/tex]
[tex]P(b) = 0.03[/tex]
So the probability that the a computer produced from the three factory will be defective is
[tex]P(t) = P(a) + P(b) + P(c)[/tex]
substituting values
[tex]P(t) = 0.16 + 0.14 + 0.03[/tex]
[tex]P(t) = 0.33[/tex]
Now the probability that the defective computer is produced from factory A is
[tex]P(A') = \frac{P(a)}{P(t)}[/tex]
[tex]P(A') = \frac{ 0.16}{0.33}[/tex]
[tex]P(A') = 0.485[/tex]
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
PLEASE, NEED HELP WITH ALGEBRA ASAP!
Answer: The answer is (D) t = √2d/₅
Step-by-step explanation:
Since a = 2d/t²
Now making t the subject of the formula
at² = 2d
t² = 2d/a, to find t , take the square root of both sides
t = √2d/₅ since a = 5m⁻².
The answer is d
A line is definitely by the equation y = -x + 3 which shows the graph of this line ?
Answer:
A graph with a slope of -1, and a y-intercept (crosses the y-axis) at 3
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
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
Solve the equation 2x^2-3x-6=0 give your answer correct to two decimal places
Answer:
x = - 1.14 or x = 2.64Step-by-step explanation:
2x² - 3x - 6 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = 2 , b = - 3 , c = 6
Substituting the values into the above formula
We have
[tex]x = \frac{ - - 3± \sqrt{ { - 3}^{2} - 4(2)( - 6)} }{2(2)} [/tex]
[tex]x = \frac{3± \sqrt{9 +48 } }{4} [/tex]
[tex]x = \frac{3± \sqrt{57} }{4} [/tex]
[tex]x = \frac{3 - \sqrt{57} }{4} \: \: \: \: or \: \: \: \: \: x = \frac{3 + \sqrt{57} }{4} [/tex]
We have the final answer as
x = - 1.14 or x = 2.64Hope this helps you
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
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
(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]
Which equation is the inverse of y = 16x2 + 1? y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 4 EndFraction
Answer:
The inverse is ±sqrt((x-1))/ 4
Step-by-step explanation:
y = 16x^2 + 1
To find the inverse, exchange x and y
x = 16 y^2 +1
Then solve for y
Subtract 1
x-1 = 16 y^2
Divide by 16
(x-1)/16 = y^2
Take the square root of each side
±sqrt((x-1)/16) = sqrt(y^2)
±sqrt((x-1))/ sqrt(16) = y
±sqrt((x-1))/ 4 = y
The inverse is ±sqrt((x-1))/ 4
Answer:
D
Step-by-step explanation:
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.
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:
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
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
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.
HELP ASAP PLEASE :(!!!
given the following linear function sketch the graph of the function and find the domain and range. Upload your
document in the box below.
f(x) = -3x+7
Answer:
Step-by-step explanation:
You have the following function:
[tex]f(x)=-3x+7[/tex]
The y-intercept of the function is given by the independent coefficient, which is 7.
y-intercept = 7
To obtain the x-intercept you equal the function to zero and solve for x, as follow:
[tex]0=-3x+7\\\\3x=7\\\\x=\frac{7}{3}\approx2.33[/tex]
x-intercept = 2.33
Due to the coefficient of x is negative, the slope of the function is negative.
The function is a straight line, then, its domain all all real numbers and its range are all real numbers.
The graph of the function is attached in the image below.