The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k
The equation is given as:
x^2 + (1 - k).x+k-3 = 0
For an equation to have real root, then the following must be true:
[tex]b^2 \ge 4ac[/tex]
In x^2 + (1 - k).x+k-3 = 0, we have:
a = 1
b = 1 - k
c = k - 3
So, we have:
[tex](1 - k)^2 \ge 4 * 1 * (k - 3)[/tex]
Evaluate
[tex]1 - 2k + k^2 \ge 4k - 12[/tex]
Collect like terms
[tex]k^2 - 2k - 4k + 1 + 12 \ge 0[/tex]
[tex]k^2 - 6k + 13 \ge 0[/tex]
Using a graphing calculator, the value of k is all real numbers
Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k
Read more about real values at:
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5th grade math. Correct answer will be marked brainliest
Answer:
3,5
Step-by-step explanation:
Please answer I’ll give Brainly
Answer:
62.5%
Step-by-step explanation:
There are a total of 8 people on the data plot.
5 of them got 15 questions or more correct, meaning 5/8 people got 15 or more questions correct.
5/8 = 5 ÷ 8
5 ÷ 8 = 0.625
0.625 = 62.5%
Helppppppppppp AND NO LINKS
Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 32 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9370 with a standard deviation of 0.0090, within what interval will 99 percent of the sample means fall
Answer:
99% of the sample means will fall between 0.93288 and 0.94112.
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 estabilishes 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.
The true mean is .9370 with a standard deviation of 0.0090
This means that [tex]\mu = 0.9370, \sigma = 0.0090[/tex]
Sample of 32:
This means that [tex]n = 32, s = \frac{0.009}{32} = 0.0016[/tex]
Within what interval will 99 percent of the sample means fall?
Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.575 = \frac{X - 0.9370}{0.0016}[/tex]
[tex]X - 0.9370 = -2.575*0.0016[/tex]
[tex]X = 0.93288[/tex]
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.575 = \frac{X - 0.9370}{0.0016}[/tex]
[tex]X - 0.9370 = 2.575*0.0016[/tex]
[tex]X = 0.94112[/tex]
99% of the sample means will fall between 0.93288 and 0.94112.
Select all the expressions that equal 4-12.
Select ALL the correct answers.
A pitcher for a professional baseball team allows runs in the first nine games he starts this season. Let A be the set of the number of
runs allowed by the pitcher in his first nine starts.
A = {1, 4, 2, 2, 3, 1, 1, 2, 1}
In the tenth game he starts, he allows 9 runs. Let B represent the set of the number of runs allowed in all ten games he has started.
Select the true statements.
The median of Bis 1 run more than the median of A.
The interquartile range of B is greater than the interquartile range of A.
The interquartile range of A is 1 less than the interquartile range of B.
The median of A is the same as the median of B.
Including the runs allowed in the tenth game does not cause the spread of the data to
change
Answer:
The median of A is the same as the median of B.
The interquartile range of B is greater than the interquartile range of A.
Step-by-step explanation:
Given that:
A = number of runs allowed in first 9 games
A = {1, 4, 2, 2, 3, 1, 1, 2, 1}
Rearranging A : 1, 1, 1, 1, 2, 2, 2, 3, 4
Median A = 1/2(n + 1) th term
Median A = 1/2(10) = 5th term = 2
Q1 of A = 1/4(10) = 2.5th term = (1 + 1)/ 2 = 1
Q3 of A = 3/4(10) = 7.5th term = (2+3)/2 = 2.5
Interquartile range = Q3 - Q1 = 2.5 - 1 = 1.5
Number of runs allowed in 10th game = 9
B = {1, 4, 2, 2, 3, 1, 1, 2, 1, 9}
Rearranging B = 1, 1, 1, 1, 2, 2, 2, 3, 4, 9
Median A = 1/2(n + 1) th term
Median A = 1/2(11) = 5.5th term = (2+2)/2 = 2
Q1 of A = 1/4(11) = 2.75th tetm = (1 + 1)/ 2 = 1
Q3 of A = 3/4(11) = 8.25th term = (3+4)/2 = 3.5
Interquartile range = Q3 - Q1 = 3.5 - 1 = 2.5
Median A = 2 ; median B = 2
IQR B = 2.5 ; IQR A = 1.5 ; IQR B > IQR A
Trapezoid ABCD has an area of 525 cm squared. If height AB = 21 cm and BC = 37 cm, what is the measure of AD?
Answer:
AD = 13
Step-by-step explanation:
Area of trapezoid ABCD
[tex] = \frac{1}{2} (AB + AD) \times AB \\ \\ 525= \frac{1}{2} (37+ AD) \times21\\ \\ 525 \times 2= (37+ AD) \times21 \\ \\ 1050 = 21 \times 37 + 21AD \\ \\ 1050 = 777+ 21AD \\ \\ 21AD = 1050 - 777 \\ \\ 21AD = 273 \\ \\ AD = \frac{273}{21} \\ \\ AD = 13[/tex]
Answer it. -10 x -2 =
Answer: 20
Step-by-step explanation: it is 20 because 2 negative numbers multiplied by each other will always be positive
Lin went hiking on five different weekends. The table shows the
elevation changes in feet for each of her five hikes. Fill in the
missing numbers
Initial Elevation
Elevation Change Final Elevation
hike
768
1
-96
672
hike
2
82
20
hike
62
3
- 100
hike
354
4
129
hike
-20
-40
-60
5
Explain what each of the numbers-20, -40, and -60 tells you about
hike 5. What does it mean for the numbers to be negative in this
situation?
Answer:
Hike 1 : 768, -96, 672
Hike 2: -62, 82, 20
Hike 3: 62, -100, -38
Hike 4: 354, -225, 129
Hike 5: -20, -40, -60
The -20 is at what surface level Lin began Hike 5 at. From there, they continued to go in this situation lower by - 40, and arrive at the surface region of -60.
Negative numbers in the present circumstance mean under 0. (Underneath surface region)
??????????????????????
Answer:
A = 254.34
Step-by-step explanation:
Area of a circle formula:
A = πr²
r = d/2 = 9
A = 3.14(9²)
A = 3.14(81)
A = 254.34
Answer:
254.34
Step-by-step explanation:
Good luck!
The following figure is made of a square and a rectangle.
4 cm
4 cm
7
10 cm
What is the perimeter of the figure?
cm
分
타
Sin Of = f (m + You
3
Answer:
what do you mean by your question I didn't understand it
The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)
Answer:
A sample of 2017 people should be taken.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Suppose a 95% confidence level:
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Preliminary estimate of the proportion who smoke of .30.
This means that [tex]\pi = 0.3[/tex]
a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)
This is n for which M = 0.02. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.02})^2[/tex]
[tex]n = 2016.84[/tex]
To the nearest whole number, 2017.
A sample of 2017 people should be taken.
4x10^3 times what number is equal to 16x10^5
Answer:
4 × 10²
Step-by-step explanation:
16 x 10^5 ÷ 4 x 10³ = 4 × 10²
4 * 10² is the number when multiplied to 4 * 10³ gives 16 * 10⁵
What is division exponent theorem ?To divide exponents (or powers) with the same base, subtract the exponents.
Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.
The given expression is
4 * 10³ multplies with ____ = 16 * 10⁵
We have to solve this ,
Let the number be x
4 * 10³ multplies with __x__ = 16 * 10⁵
x = (16 * 10⁵ )/(4 * 10³)
x= ( 4² * 10⁵ )/(4 * 10³)
Therefore the numerator and denominator has the same base so
[tex]\rm 4^{2-1} \times 10^{5-3}\\\\\\4^{1} \times 10^{2}\\\\\\4\times 10^{2}[/tex]is the number that when multiplied to 4 * 10³ gives 16 * 10⁵
To know more about Exponent Theorem
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Complete the following to describe how to draw to diagram to represent the answer 3÷3/5
Answer:
you can do a diagram representing this product by drawing a box with six squares and then putting three lines for each box and divide 3÷3 and you will get 5
true or false: a well-designed sample survey, the sample percentage is very likely to equal the population percentage. explain.
Answer:
false
Step-by-step explanation:
There's going to be some variabilty between the sample and population percentages, cus the sample only contains part of of the population. Even if it is a well designed survey, it doesn't affect this, because no matter how good the sample is, there will always be variability between the two (unless the sample includes the whole population). I hope this helps :)
can someone help me understand this problem?
Hello!
a. 10
b. 1
c. -11
To evaluate f(x) at a certain x, you simply substitute that value of x into the equation for x.
For example:
a. f(x) = 2x, find f(5)
Plug in 5 for x into f(x):
f(5) = 2(5) = 10.
b. f(x) = 4x + 5, find f(-1)
f(-1) = 4(-1) + 5 = 1
c. f(x) = -3x - 5, find f(2)
f(2) = -3(2) - 5 = -11
please answer quickly
noah has $14 more then his brother jared. jared has $51. how much money does noah have?
Answer:
$65
Step-by-step explanation:
$51 + $14
$65
Answer:
$65
Step-by-step explanation:
14+51=61
A town has a population of 5000 and grows at 3.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 7300?
Answer:
Step-by-step explanation:
This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is
where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then
a = 5000
If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So
b = 1.035
Our function is
where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.
and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.
Begin by dividing both sides by 5000 to get
and take the natural log of both sides:
The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:
To solve for x, we now divide both sides by ln(1.035):
Do that division on your calculator and get that
x = 11.0 years.
That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)
A rectangle has vertices at P (16,16), Q(16,-16), R(-16,-16) and S(-16,16). The origin is the center of dilation and the rule of a dilation is (x,y)→(1/4x, 1/4y) What is P' of the dilated image, PQ’R’S’?
Answer:
(4, 4)
Step-by-step explanation:
So you're trying to find what P' is, and P' would be the dilation of P. This means that you apply the rule (x, y) --> (1/4x, 1/4y) with the coordinate point (16, 16). This would be:
(16, 16) --> (1/4 * 16, 1/4 * 16) = (4, 4)
Select the correct answer. What is the fractional form of 0.02 ? A. 2/99 B. 1/11 C. 2/100 D. 1/12
Answer:
C) 2/100
Step-by-step explanation:
0.02 = 2/100
Answer:
It Is C
Step-by-step explanation:
A surgeon has found that she can model the number of surgeries done per week with a Poisson distribution
in which y = 24.5.
How many surgeries would be expected in a year? assume no vacation or time off.
Round to one decimal if needed.
Answer:
94.5
Step-by-step explanation:
please help me on this question. I forgot how to do it
Answer:
141
Step-by-step explanation:
Area of triangle = 24
Area of Trapezoid= 117
117+24
141
A company offers a flood insurance policy that costs a homeowner $200 per year, and the company will make a payout of $100,000 to the homeowner if they have a flood in that year. The company set this price based on the probability of a flood in the area being 0.001. The table below displays the probability distribution of X=X= the company's profit from one of these policies.
No flood Flood
X=profit $200 -$99,800
P(X) 0.999 0.001
Given that μX=$100, calculate σX.
You may round your answer to the nearest dollar.
Answer:
σX = 3161
Step-by-step explanation:
The standard deviation is the square root of the multiplication of each probability multiplied by the squared difference between the values and the mean.
In this question:
[tex]\sigma X = \sqrt{0.999*(200-100)^2 + 0.001*(-99800-100)^2} = 3160.7[/tex]
Rounding to the nearest dollar, σX = 3161
What is the area of a rectangle with a length of 7 feet and a width of 3 ¾ feet?
Answer:
105/4 ft^2
Step-by-step explanation:
Multiply length and width: 7*15/4 = 105/4 ft^2
Xander had $24, he spent 3/4 of it how much money does he have left?
Answer:
6.25
Step-by-step explanation:
question is above in the picture
Answer:
Known
Step-by-step explanation:
I hope this helps :)
Answer:
Known. The other answers are absurd.
Step-by-step explanation:
In geometry, often times you must have at least one angle to problem solve and find the rest. So having a known angle to build off of is important. Vertical Angles and Supplementary Angles are examples of things that require a known angle to find the rest. Why?
Say you only know one angle and the other is congruent to that angle, but across from it...Due to the theory of vertical angles, you now know the other side has to be the same/congruent. For supplementary angles, say you're dealing with a shape like the one I've attached. Once you have a or b, you can determine c. You have to know at least one of those angles to determine it's other unknown angles.
Will give brainlest, find the area
A student bought a truck with a down payment of $4,000 and monthly payments of
$250 for four years. What was the total cost of the truck?
what is the greatest decimal in hundredths that can be rounded to 14.5? What is the least
Answer:
14.45 and 14.54Step-by-step explanation:
Rule for rounding:
Round up if number is between 5 and 9Round down if number is between 0 and 4What numbers in hundredths can be rounded to 14.5?
14.45 to 14.49and
14.50 to 14.54From above we see that:
The greatest decimal is 14.54The least decimal is 14.45