Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county.
Cases of Lyme Disease Drowning Deaths Month
2 0 J
1 1 F
3 2 M
4 1 A
5 3 M
1 5 J
2 2 J
1 3 A
6 3 S
5 3 O
4 1 N
1 0 D
Requried:
a. Draw a scatter diagram of the data.
b. Determine the linear correlation coefficient between Lyme disease and drowning deaths.
c. Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths?
Answers
Answer:
Step-by-step explanation:
Let cases of Lyme disease = x
x = 2, 1, 3, 4, 5, 1, 2, 1, 6, 5, 4, 1
[tex]\sum x = 35[/tex]
[tex]\sum x^2 = 139[/tex]
y = 0, 1, 2, 1, 3, 5, 2, 3, 3, 3, 1, 0
[tex]\sum y = 24[/tex]
[tex]\sum y^2 = 72[/tex]
[tex]\sum xy = 55[/tex]
[tex]S_{xx} = \sum x^2 - (\sum x)^2/n\\S_{xx} = 139 - 35^2/12\\S_{xx} = 36.92\\S_{yy} = \sum y^2 - (\sum y)^2/n\\S_{yy} = 72 - 24^2/12\\S_{yy} = 24[/tex]
[tex]S_{xy} = \sum xy - ( \sum x \sum y)/n\\S_{xy} = 55 - (35*24)/12\\S_{xy} = -15[/tex]
b) Linear correlation between Lyme disease and drowning deaths.
[tex]r = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}} }[/tex]
r = -15/ √(24*36.92)
r = -0.504
Related Questions
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)
Answers
Answer:
(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
Step-by-step explanation:
In the triangle, the exterior angle = pThe adjacent interior angle =oThe two opposite angles are marked m and nThe steps followed by the student are:
Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).
p is outside the triangle, therefore it cannot form one of the angles in the triangle.
A person has a bag containing dimes and nickels. There are a total of 120 coins in the bag, and the total value of the coins is $9.25. Determine how many dimes and nickels are in the bag. There are _____dimes. There are _____ nickels.
Answers
Answer:
There are 65 dimes. There are 55 nickels.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of dimes
y is the number of nickels.
There are a total of 120 coins in the bag
This means that x + y = 120.
The total value of the coins is $9.25.
The dime is worth $0.10 and the nickel is worth $0.05. So
0.1x + 0.05y = 9.25
System:
[tex]x + y = 120[/tex]
[tex]0.1x + 0.05y = 9.25[/tex]
From the first equation:
[tex]y = 120 - x[/tex]
Replacing in the second:
[tex]0.1x + 0.05y = 9.25[/tex]
[tex]0.1x + 0.05(120 - x) = 9.25[/tex]
[tex]0.1x + 6 - 0.05x = 9.25[/tex]
[tex]0.05x = 3.25[/tex]
[tex]x = \frac{3.25}{0.05}[/tex]
[tex]x = 65[/tex]
[tex]y = 120 - x = 120 - 65 = 55[/tex]
There are 65 dimes. There are 55 nickels.
Determine whether the point (–3,–6) is in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2
Answers
Answer:
The point (–3,–6) is not in the solution set of the system of inequalities below.
x ≤ –3 y < 5∕3x + 2
Step-by-step explanation:
Given point (-3, -6)
inequality
x ≤ –3
It means that value of x should be less than or equal to -3
since in point (-3,-6) , -3 is point for representing x which is equal to -3 and hence satisfy the criteria for valid value of x,
thus, -3 lie in the solution set of inequality x ≤ –3
lets now see for y = -6
to do that we will put x = -3 in the given below inequality
y < 5∕3x + 2
y < 5∕3*-6 + 2
y < -10 + 2
y < - 8
Thus, inequality suggests that value of y should be less than -8.
but here y is -6, if we see number line -6 is greater than -8 and hence does not belong to the solution set y < 5∕3x + 2 when x = -3
Thus, the point (–3,–6) is not in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2
What is the length of Line segment A C? Round to the nearest tenth.
Answers
Step-by-step explanation:
To find AC we use tan
tan ∅ = opposite / adjacent
From the question
15 is the opposite
AC is the adjacent
tan 55 = 15 / AC
AC = 15 / tan 55
AC = 10.503
AC is 11 to the nearest tenthHope this helps you
Answer:
A: 10.5 m
Step-by-step explanation:
it's what i think it is, i may be wrong! hope this helps!!~
7
Which statement best describes the relationship
between storage space and number of music files?
As the number of files remains constant, the storage
space used decreases.
As the number of files remains constant, the storage
space used increases.
As the number of files increases, the storage space
used decreases.
Wh
As the number of files increases, the storage space
used increases.
Answers
Answer:
The answer is "As the number of files increases, the storage space used decreases."
Step-by-step explanation:
When the music files are put into storage they take up space, this causes the storage space to decrease.
Answer:
As the number of files increases, the storage space used increases.
Find the variance of the given data rounded to the nearest hundredth 5.6 5.2 4.6 4.9 5.7 6.4
Answers
Answer:
0.41
Step-by-step explanation:
Given;
5.6, 5.2, 4.6, 4.9, 5.7, 6.4
To calculate the variance of a given set of ungrouped data, follow the following steps;
(i). First calculate the mean (average) of the data as follows;
[tex]\frac{5.6 +5.2 +4.6+ 4.9 +5.7 +6.4}{6}[/tex] = [tex]\frac{32.4}{6}[/tex] = 5.4
(ii) Secondly, find the deviation of each point data from the mean as follows;
5.6 - 5.4 = 0.2
5.2 - 5.4 = -0.2
4.6 - 5.4 = -0.8
4.9 - 5.4 = -0.5
5.7 - 5.4 = 0.3
6.4 - 5.4 = 1.0
(iii) Thirdly, find the square of each of the results in step ii.
(0.2)² = 0.04
(-0.2)² = 0.04
(-0.8)² = 0.64
(-0.5)² = 0.25
(0.3)² = 0.09
(1.0)² = 1.0
(iv) Fourthly, find the sum of the results in step iii.
0.04 + 0.04 + 0.64 + 0.25 + 0.09 + 1.0 = 2.06
(v) The variance, v, is now the quotient of the result in step (iv) and n-1. i.e
v = [tex]\frac{2.06}{n-1}[/tex]
Where;
n = number of data in the set
n = 6 in this case
Therefore,
v = [tex]\frac{2.06}{6-1}[/tex]
v = [tex]\frac{2.06}{5}[/tex]
v = 0.412
Therefore, the variance is 0.41 to the nearest hundredth
Answer:
.34
Step-by-step explanation:
god this is so boring
Two cities whose longitudes are 10E and 20W on the equator are apart
Answers
Step-by-step explanation:
to be honest I'm not sure how to do
the quotient of F and the product of r,s, and T
Answers
Behold the quotient of F and the product of r,s, and T: F / (r·s·T)
The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).
What are quotient, remainder, divisor, and dividend?The number which is being divided is the dividend.
The number with which we are dividing is the divisor.
The result when a dividend is divided by the divisor is the quotient.
A remainder is the extra portion of a number when it isn't completely divisible.
Given, Are some variables F, r, s, and t.
Now, The product of r,s, and T is,
= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,
F/(r×s×T).
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someone help please, already tried 168 says its wrong??
Answers
Answer:
245 might be the answer
Step-by-step explanation:
(7*7*10)/2
One condition for performing a hypothesis test is that the observations are independent. Marta is going to take a sample from a population of 600 students. How many students will Marta have to sample without replacement to treat the observations as independent?
Answers
Answer:
The correct answer to the following question will be "60 students".
Step-by-step explanation:
Marta will be taking a sampling frame from some kind of 600 student group.
Mean,
N = 60
Although the sampling method could perhaps consist of the following components 10% of the population,
⇒ [tex]600\times 10 \ percent[/tex]
⇒ [tex]60[/tex]
In order to view these findings as autonomous, 60 students would then have to analyze Marta lacking replacements.
Marta have to sample 60 students without replacement to treat the observations as independent.
Given,
Marta is going to take a sample from a population of 600 students.
We have to find the no. of students Marta have to sample without replacement.
The 10% condition states that sample sizes should be no more than 10% of the population. Normally, Bernoulli trials are independent, but it's okay to violate that rule as long as the sample size is less than 10% of the population.
So,
[tex]N=10\% \ of \ 600[/tex]
[tex]N=\frac{10}{100} \times600[/tex]
[tex]N=60[/tex]
Hence, Marta have to sample 60 students without replacement to treat the observations as independent.
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The initial population of a town in the year 2010 was 20 000. By 2014, the population had grown exponentially to 32 500 people. Write an equation to represent the population of the town (P) over time in years (n).
Answers
Answer:
P = 20000×1.625^(n/4)
Step-by-step explanation:
An exponential equation can be written using the given data:
value = (initial value)×(growth factor in period)^(n/(period))
Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...
P = 20000×1.625^(n/4)
Find the equation of a line passing through the point (-4,1) and perpendicular to the
line 3y = 12x - 9.
Answers
Answer:
A. y=-1/4x
Step-by-step explanation:
We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.
Terry has a collection of 50 coins. There are only quarters and dimes in the collection. The total value of the coins is $8.00. How many dimes does he have?
Answers
Answer:
30 dimes and 20 quarters
30×.10=$3.00
20×.25=$5.00
30+20=50
$3+$5=$8
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answers
Answer:
When describing a property line drawn down the center of a creek bed
answer if u love cats & dogs
Answers
Answer:
(7, 5.25) lies on the graph.
Step-by-step explanation:
We are given the following values
x = 4, 6, 8, 12 and corresponding y values are:
y = 3, 4.5, 6, 9
Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.
Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]y=mx+c[/tex]
where m is the slope.
(x,y) are the coordinates from where the line passes.
c is the y intercept.
Here,
[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]
Formula for slope is:
[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]
Now, the equation of line becomes:
[tex]y=\dfrac{3}{4}x+c[/tex]
Putting the point (4,3) in the above equation to find c:
[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]
So, final equation of given function is:
[tex]y=\dfrac{3}{4}x[/tex]
OR
[tex]4y=3x[/tex]
As per the given options, the point (7, 5.25) satisfies the equation.
So correct answer is [tex](7, 5.25)[/tex].
Ms. Walker's science class is doing an egg drop experiment from the balcony of their school. Each egg is protected by a contraption that the students collectively designed. The height of the egg, in feet, after x seconds is given by the expression below. What do the zeros of the expression represent? A. the maximum height of the egg B. the time at which the egg reaches its maximum height C. the horizontal distance traveled by the egg D. the time at which the egg reaches the ground
Answers
Answer:
An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.
See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?
July 10 book Science up55 down8
AA BB
CC DD
Step-by-step explanation:
m∠1=28°, m∠6=65°, m∠5=65°. Find m∠MAX
Answers
Answer:
<MAX = 93
Step-by-step explanation:
Since <MAX is technically <1 + <5, we know that <1 is 28 and <5 is 65. We can add both of these angles up to solve for <MAX, which is 28 + 65 = 93.
The angle of MAX is 93 degrees.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Since m∠MAX = m∠1 + m∠5,
we know that m∠1 = 28 and m∠5 = 65.
To solve for m∠MAX, which is 28 + 65 = 93.
Thus, the angle of MAX is 93 degrees.
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Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
Answers
Answer:
z = 10
Step-by-step explanation:
The value of the z-statistic is given by:
[tex]z = \frac{X - \mu}{s}[/tex]
In which:
X is the measured value.
[tex]\mu[/tex] is the expected value.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.
In this question:
The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.
This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]
Random sample of 100 screws.
This means that n = 100.
To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
3 inches, so [tex]X = 3[/tex]
[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{3 - 2.9}{0.01}[/tex]
[tex]z = 10[/tex]
Answer:
-10
Step-by-step explanation:
If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01
Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10
This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.
A confidence interval for the population mean length of hit songs was found to be 4.1 to 5.3 minutes. Find the point estimate (that is, find the midpoint of this confidence interval.)
Answers
Answer:
4.7
Step-by-step explanation:
Given :
initial mean length =4.1 minutes.
Final mean length =5.3 minutes
The mid point of the given interval can be determined by the
[tex]Midpoint \ = \frac{Initial\ Mean\ length\ +Final\ Mean\ length }{2} \\Midpoint \ = \frac{4.1\ +\ 5.3\ }{2} \\Midpoint \ = \frac{9.4 }{2} \\Midpoint \ =4.7\\[/tex]
Therefore 4.7 is the midpoint
6th grade math help me please :)
Answers
Answer:
a. ans=1
b. ans=2/5
c. ans=4
hope u understood...
What is the solution to the system of linear equations below?
x+4y=22
2x+y=9
Answers
Answer:
[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]
Step-by-step explanation:
hello, we have two equation
(1) x + 4y = 22
(2) 2x + y = 9
let's multiply (1) by 2 and subtract (2)
2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35
<=> 2x + 8y -2x -y = 35
<=> 7y = 35
<=> y = 35/7 = 5
we replace this value in (1) and it comes
x + 4*5 = 22
<=> x = 22 - 20 = 2
so the solution is
x = 2 and y = 5
hope this helps
A publisher reports that 31% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 100 found that 21% of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answers
Answer:
[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.162)=0.0306[/tex]
Step-by-step explanation:
Information given
n=100 represent the random sample taken
[tex]\hat p=0.21[/tex] estimated proportion of the readers owned a particular make of car
[tex]p_o=0.31[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:
Null hypothesis:[tex]p=0.31[/tex]
Alternative hypothesis:[tex]p \neq 0.31[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.162)=0.0306[/tex]
Assume that the year has 366 days and all birthdays are equally likely. Find the probability that two people chosen at random were born on the same day of the week.
Answers
Answer:
[tex]\dfrac{1}{7}[/tex]
Step-by-step explanation:
There are 7 days in a week.
For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.
Let Event A be the event that the first person was born on a day of the week.
Therefore:
[tex]P(A)=\dfrac{7}{7}=1[/tex]
The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.
Let Event B be the event that the second person was born.
Therefore, the probability that the second person was born on the same day as the first person:
[tex]P(B|A)=\dfrac{1}{7}[/tex]
By the definition of Conditional Probability
[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]
The probability that both were born on the same day is:
[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]
Let S be a sample space and E and F be events associated with S. Suppose that Pr (Upper E )equals 0.6, Pr (Upper F )equals 0.2 and Pr (Upper E intersect Upper F )equals 0.1. Calculate the following probabilities. (a) Pr (E|F )(b) Pr (F|E )(c) Pr (E| Upper F prime )(d) Pr (Upper E prime | Upper F prime )
Answers
Answer:
(a)0.5
(b)0.17
(c)0.625
(b)0.375
Step-by-step explanation:
Pr(E)=0.6
Pr(F)=0.2
[tex]Pr(E\cap F)=0.1.[/tex]
(a)Pr (E|F )
[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]
(b)Pr (F|E )
[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]
(c)Pr (E|F')
Pr(F')=1-P(F)
=1-0.2=0.8
[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]
Therefore:
[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]
(d)Pr(E'|F')
[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]
Therefore:
[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]
Please need help Please
Answers
Answer: 14/11
Step-by-step explanation:
When 14/11 is multiplied by 1/4, you get a repeating decimal. All repeating decimals are rational.
Hope it helps <3
Solve the equation, x − 5 1 = 8 1 , for the given variable. Write your final answer as a reduced fraction.
Answers
Answer: 132
Step-by-step explanation: To solve this equation we know that x is greater than 81 unless the equation would not make sense. 81 + 51 = 132
Answer: x=132
Step-by-step explanation: Add 51 to 81, as positive 51 is the inverse of -51. You need to get the x alone. Therefore, 51+81=132 and x=132.
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false.
a. There are real numbers u and v with the property that u+v
b. There is a real number x such that x2
c. For all positive integers n,n2≥n.
d. For all real numbers a and b,|a+b|≤|a|+|b|
Answers
Answer:
The answer is given below
Step-by-step explanation:
a) Let u and v be real numbers. The sum of u and v = u + v and the difference between u and v = u - v.
u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.
There exist two real numbers such that their sum is less than the difference between them
This is true when atleast one of the numbers is negative, for example u = 2 and v = -2
u + v = 2 + (-2) = 0 , u - v = 2 - (-2) = 4
u + v < u - v.
b) Let x be a real number and x² be the square of the real number
x² < x means that the square of a real number is less than the real number
We can rewrite the statement as: There exist a real number such that its square is smaller than itself.
The statement is true for x is between 0 and ±1
E.g. for x = 1/2, x² = (1/2)² = 1/4
1/4 < 1/2
c) Let n represent all positive integers. n² is the square of n.
n²≥n means that the square of n is greater or equal to n.
We can rewrite the statement as: For all positive integer numbers, the square of the number is greater than or equal to the number itself
The statement is true.
1² ≥ 1, 2² ≥ 2 e.t.c
d) Let a and b be real numbers. The sum of a and b = a + b. |a| is the absolute value of a and |b| is the absolute value of b
|a+b|≤|a|+|b| means the absolute value of the sum of two real numbers is less than or equal to the sum of their individual absolute value.
We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.
This statement is true for all real numbers.
Evaluating the expressions given using appropriate illustrations, all the statements are True.
Statement 1 :
Real numbers ar both rational and irrational values and hence can be tweaked using arithmetic operators such as addition. Hence, the Statement is True
[tex]1 + \frac{1}{2} [/tex] = [tex]1 \frac{1}{2} [/tex]Statement 2 :
Real numbers can be expressed or raised to the power of another number such as being squared.
2² = 4 ; [tex](\frac{1}{3})^{2} = \frac{1}{9} [/tex]Statement 3 :
The squared Value of all positive integers is always greater than or equal the value.
n = 2 ; n² = 2² = 4 4 > 2Statement 4 :
The absolute value of a sum is always less than or equal to the sum of the absolute values two numbers
a = 3 ; b = - 4
|a + b | = |3-4| ≤ |-3|+|4|
|-1| ≤ 3 + 4
-1 ≤ 7
Therefore, all the statements are true.
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A survey of 61,647 people included several questions about office relationships. Of the respondents, 26% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than ¼ of people say that bosses scream at employees.
Answers
Step-by-step explanation:
n = 61,647, p = 0.26, q = 0.74
μ = p = 0.26
σ = √(pq/n) = 0.00177
At 0.05 significance, z = 1.96.
0.26 ± 1.96 × 0.00177
(0.257, 0.263)
0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answers
Answer:
[tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
Invert the denominator and multiply.
[tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]
Answer:
[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.
Can someone plz help me solved this problem I need the other line which is X! I already have line y but I need X plz someone help i need help!
Answers
Answer: see below
Step-by-step explanation:
Inverse is when you swap the x's and y's.
The Slope-Intercept form is [tex]y=\dfrac{1}{5}x-\dfrac{3}{5}[/tex] which isn't convenient to graph.
So take the points from the original equation (-1, -2) & (0, 3) and switch the x's and y's to get the points (-2, -1) & (3, 0).
Draw a line through points (-2, -1) and (3, 0) to sketch the graph of the inverse.