Step-by-step explanation:
x²+12x=40
(x+6)²-6²-40=0
(x+6)²-76 = 0
What are the zeros of the polynomial function f(x)=x3-7x2+8x+16
Answer: x=4, -1
Step-by-step explanation:
Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.
Step 1. Replace f(x) with y.
[tex]y = x^3-7x^2+8x+16[/tex]
Step 2. To find the roots of the equation, replace y with 0 and solve.
[tex]0 = x^3-7x^2+8x+16[/tex]
Step 3. Factor the left side of the equation.
[tex](x-4)^2 (x+1)=0[/tex]
Step 4. Set x-4 equal to 0 and solve for x.
[tex]x-4=0[/tex]
Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.
[tex]x=-1[/tex]
The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].
[tex]x=4,-1[/tex]
Square root 1.000441
Answer: 1.00022048
Step-by-step explanation:
Which of the following pairs of functions are inverses of each other?
A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x -9 and g(x)=x+9/2
C. f(x) = 3-6 and g(x)=x+6/2
D. f(x)= x/3+4 and g(x) = 3x - 4
The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's analyze the given options:
A. f(x) = 5 + x and g(x) = 5 - x
To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.
B. f(x) = 2x - 9 and g(x) = x + 9/2
By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.
C. f(x) = 3 - 6 and g(x) = x + 6/2
Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.
D. f(x) = x/3 + 4 and g(x) = 3x - 4
After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.
In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
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The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sample of 36 cans.
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Answer:
a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 6.05 ounces and a standard deviation of .18 ounces.
This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
This is the p-value of z when X = 5.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]
[tex]Z = -2.67[/tex]
[tex]Z = -2.67[/tex] has a p-value of 0.0038.
0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
Is the relationship shown by the data linear? If so, model the data with an equation.
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
The sum of four
consecutive odd number is 8o. Find the number
Answer:
The sum of 4 consecutive odd number is 80
Let X be the first of these numbers
Then the next odd number is X+2
The third is X+4The fourth is X+6
All of these add up to 80
(X) + (X+2) + (X+4) + (X+6) = 80
Using the commutative and associative laws, let's transform this equation into
(X + X + X + X) + (2 + 4 + 6) = 804X + 12 = 80
Subtract 12 from both sides of the equation gives4X = 68
Divide both sides by 4 gives
X = 17
Going back to the original question:What are the 4 consecutive odd numbers: 17, 19, 21, 23Checking our answer:17 + 19 + 21 + 23 = 80 Correct!
find the mid-point of the line segment joining the points (10, 13) and (-7, 7)?
Answer:
(3/2,10)
Step-by-step explanation:
Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)
7. Write the new function, h(x), given the mapping statement: f(X)->-4f(X)
f(X) =(x+3)^2+3
Answer:
hshdhdhdshejiwiwiwiwiwi
I need help ASAP thank you guys
Answer:
The fraction is undefined when x=-2
Step-by-step explanation:
The fraction will be undefined when the denominator is zero
x+2 = 0
x+2-2 = 0-2
x = -2
The fraction is undefined when x=-2
Answer:
as to me 5
Step-by-step explanation:
ask someone else to say that I am not sure if you have any questions or need any further information please contact me at the end of the world
Please help! Thank you.
Answer:
B at -1 minus we go to - ∞
at -1 plus we to + ∞
Step-by-step explanation:
x^2 -x
g(x) = ---------
x+1
Factor out x
x(x-1)
g(x) = ---------
x+1
As x is to the left of -1
x is negative (x-1) is negative
x+1 will be slightly negative
g(-1 minus) = -*-/ - = - and we know that the denominator is very close to zero we are close to infinity so we go to - ∞
As x is to the right of -1
x is negative (x-1) is negative
x+1 will be slightly positive
g(-1 plus) = -*-/ + = + and we know that the denominator is very close to zero we are close to infinity so we go to ∞
find the solution to the system of equations.
y= -7x + 3
y= -x - 3
Answer:
x = 1 y = -4
Step-by-step explanation:
-7x + 3 = -x - 3
-7x = -x - 6
-6x = -6
x = 1
y = - (1) - 3
y = -1 - 3
y = -4
If $ 10000 is deposited at an "interest rate" of 4% per year, annually compounded, what amount will depositors get after 5 years?
Answer:
PTR upon hundreds .by putting these formulas you can solve ti and is 2000
A local school board member randomly sampled private and public high school teachers in his district to compare the proportions of National Board Certified (NBC) teachers in the faculty. The results were:
Answer:
0.025 ;
(-0.7198 ; 0.7698)
Step-by-step explanation:
From the table :
_____________ private schls ___ public schls
Sample size, n _____ 80 __________ 520
P, NBC teachers ___ 0.175 ________ 0.150
P1 = P of private school teachers
P2 = P of public school teachers
Difference in proportion :
P1 - P12 = 0.175 - 0.150.= 0.025
The 90% confidence interval for 2 - sample proportion :
C.I = (p1-p2) ± [Zcritical * √(p1(1-p1)/n1 + (p2(1-p2)/n2)]
Zcritical at 90% = 1.645
C.I = 0.025 ± [1.645 * √((0.175*0.825)/80 + (0.150*0.850)/520)]
C.I = 0.025 ± [1.645 * √(0.0018046875 + 0.0002451)]
C.I = 0.025 ± 1.645 * 0.0452755
C.I = 0.025 ± 0.07448
C.I = (-0.7198 ; 0.7698)
I need help guys thanks so much
Answer:
2
Step-by-step explanation:
8 ^ (5/3) ^ 1/5
We know a^b^c = a^(b*c)
8^ (5/3*1/5)
8^ 1/3
Rewriting 8 as 2^3
2^3 ^1/3
2 ^(3*1/3)
2^1
2
Answer:
2
Step-by-step explanation:
((2^3)^5/3)^1/5
= (2^5)^1/5
= 2
Answered by Gauthmath
f=((-1,1),(1,-2),(3,-4)) g=((5,0),(-3,4),(1,1),(-4,1)) find (f/g)(1)
9514 1404 393
Answer:
-2
Step-by-step explanation:
(f/g)(1) = f(1)/g(1) = -2/1 = -2
__
The value of f(1) is the second number in the ordered pair (1, -2) that is part of the definition of function f. Similarly, for g, we look for the ordered pair that has 1 as its first value. The second value is g(1).
josue bought 7 pounds of pretzels at a local wholesaler for $16.80. his friend ricardo bought 5 pounds of pretzels at the supermarket for $12.75. Ricardo thinks he got the better deal because $12.75 is less than $16.80. Is Ricardo's reasoning correct? Explain why or why not.
Answer:
Ricardo's reasoning is not correct
Step-by-step explanation:
Find who got the better deal by dividing the price by the number of pounds of pretzels:
16.80/7 = $2.40 a pound
12.75/5 = $2.55 a pound
So, Josue got the better deal because he only spent $2.40 a pound on the pretzels, while Ricardo spent $2.55 a pound.
Ricardo did not get the better deal, because he spent more per pound on the pretzels.
Ricardo's reasoning is not correct.
Tay–Sachs Disease Tay–Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that their offspring will develop the disease is approximately .25. Suppose a husband and wife are both carriers of the disease and the wife is pregnant on three different occasions. If the occurrence of Tay–Sachs in any one offspring is independent of the occurrence in any other, what are the probabilities ofthese events?
a. All three children will develop Tay–Sachs disease.
b. Only one child will develop Tay–Sachs disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Answer:
a) 0.0156 = 1.56% probability that all children will develop the disease.
b) 0.4219 = 42.19% probability that only one child will develop the disease.
c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
The probability that their offspring will develop the disease is approximately .25.
This means that [tex]p = 0.25[/tex]
Three children:
This means that [tex]n = 3[/tex]
Question a:
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]
0.0156 = 1.56% probability that all children will develop the disease.
Question b:
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219[/tex]
0.4219 = 42.19% probability that only one child will develop the disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Third independent of the first two, so just multiply the probabilities.
First two do not develop, each with 0.75 probability.
Third develops, which 0.25 probability. So
[tex]p = 0.75*0.75*0.25 = 0.1406[/tex]
0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
If P is (-5, 4) and Q is (7, -5), what is 2/3 of that?
Answer: 10
Step-by-step explanation:
Sqrt (7- -5)^2+(-5-4)^2 =
Sqrt (12)^2+(-9)^2 =
Sqrt 225 = 15
2/3 * 15 = 30/3 = 10
30 points!!!!!!!
There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.
Several trials are performed with the results shown in the table. What is the experimental probability of randomly drawing a red marble?
Red Blue Green
16 30 34
32%
25%
20%
16%
Answer:
C. 20%Step-by-step explanation:
Outcomes with red = 16Total trials = 16 + 30 + 34 = 80P(red) = 16/80 = 1/5 = 20%Correct choice is C
Answer:
20%
Step-by-step explanation:
80 x 20% = 16 red marbles
Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
Solve the equation. - 2(2x-4)= 4x
Answer:
-2(2x-4) = -4x+8 or 2(2x-4) ≠ 4x ; -4x+8 ≠ 4x
Step-by-step explanation:
Did you accidentally write =4x after your expression? If so, then let me explain why my answer is correct. I used distributive property of multiplication, so I multiplied -2 with 2x to get -4x, and -2 multiplied with -4 to get 8. So my final answer was -4x+8. If you did not accidentally put -4x, then my answer would be, 2(2x-4) ≠ 4x or -4x+8 ≠ 4x. Hope this helped.
If a person invested half of her money at 9% and half at 7% and received $160 interest, find the total amount of money invested.
Answer:
$2000
Step-by-step explanation:
let x be the money she invested
lets assume this was for 1 year
0.09(x/2) + 0.07(x/2) = 160
multiply each side by 2 to cancel the denominators:
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Answer: $2000
Let the amount of money she invested be x
Lets assume the time of investment as 1 year
ATQ
0.09(x/2) + 0.07(x/2) = 160
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Must click thanks and mark brainliest
I NEED HELP THANK YOU!!
Answer:
rt3/2
Step-by-step explanation:
first off cosine is the x coordinate
now if you do't want to use a calculator, you can use use the unit circle.
360 - 330 = 30 (360 degrees is a whole circle)
a 30 60 90 triangle is made, then use the law for 30 60 90 triangles:
if the shortest leg is x, the other leg is x*rt3 and the hypotenuse is 2x.
Answer:
D
Step-by-step explanation:
cos 330 = cos (360-330)
= cos 30
= √3 /2
write your answer in simplest radical form
Answer:
[tex]9\sqrt{3}[/tex]
Step-by-step explanation:
This is a 30-60-90 triangle.
It's good to remember this. The side length opposite to the 60 degree angle is always the base multiplied by [tex]\sqrt{3}[/tex]
Answer:
9√3.
Step-by-step explanation:
tan 60 = √3
So w/9 =√3
w = 9√3
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Answer:
Step-by-step explanation:
You need the Law of Cosines for this, namely:
[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.
[tex]x^2=441+196-311.5925[/tex] and
[tex]x^2=325.4075[/tex] so
x = 18.0 or just 18
Ivan invests $5,000 into an account with a 3.5% interest that is compounded semi-annually.
How much money will he have in this account if he keeps it for 15 years?
9514 1404 393
Answer:
$8414
Step-by-step explanation:
The compound interest formula is useful for this.
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years. A is the ending balance.
A = $5000(1 +0.035/2)^(2·15) = $5000·1.0175^30 ≈ $8414.00
Ivan will have $8414 in his account after 15 years.
A survey of 1,500 Canadians reveals that 945 believe that there is too much violence on television. In a survey of 1,500 Americans, 810 believe that there is too much television violence.
a. What would be the most appropriate test here to test the claim that Americans are less sensitive to violence on TV as Canadians?
b. My parameter of interest here would be: __________
c. The direction of test would be {Let Canadians be group 1 and Americans be group 2): __________
The test statistic is given by t and t is calculated with the help of the test statistic formula. The value of t is 4.45.
What is test statistics?The test statistic summarizes the observation data into a unique number using central tendency, the variation, sample, and size in your statistical model.
here, we have,
The given information will be shown below.
The first sample size n₁ = 36
The second sample size n₂ = 34
The mean of the first sample x₁ = 68.5
The mean of second sample x₂ = 70
Then the test statistic will be given as:
t = -4.45
The test statistic | t | = |–4.45| = 4.45
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complete question:
g A test was conducted to determine if there is a difference between Canadian and American average heart rates. A group of 36 Canadians and 34 Americans were randomly selected and their heart rates measured in beats per minute (bpm). The mean heart rate for Canadians was 68.5 and 70 for Americans. The pooled standard deviation of 2.0 beats/minute was calculated. Estimate a plausible range of differences between the mean heart rate of Canadians and Americans. What statistical procedure should be used to answer this research question
A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winner or the women's wheelchair marathon winner, on average. A paired t-test was performed on data from a random selection of 15 of the marathons to determine if there was evidence to indicate that the women's winning wheelchair time is faster than the men's winning running time, on average. What must be true about the population of differences in the women's wheelchair winning times and men's winning times at this marathon for conclusions from the paired t-test to be valid? Choose the correct answer below. A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal. B. Because there were at least 5 years of observations, the distribution of sample means of the differences will be approximately normal by the Central Limit Theorem. C. Because the sample size is large enough, the distribution of differences for all years will be normal. D. Because of the small sample size of differences in winning times between the women's wheelchair winner and the men's running winner, the distribution of sample means of the differences cannot be normal.
Answer:
A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal.
Step-by-step explanation:
In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.
What is the difference between squaring and cubing a value?
Answer:
squaring a number is multiplying it by itself twice and cubing a number is multiplying the number three times itself
Step-by-step explanation:
for example 2²=2×2
=4
and 2³=2×2×2
=8
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
