Graph the line y=-2x+5
Answers
Hope this helps!! :)
Related Questions
Me.perez drove a total of 40 miles in 5 days she drove the same number of miles each day.how many miles did me.perez drive each day?
Answers
Answer:
She drove 8 miles each day.
Step-by-step explanation:
Given that she drove equal number of miles in 5 days. So in order to find the number of miles in each days, you have to divide it by 5,
[tex]5days = 40miles[/tex]
[tex]1day = 40 \div 5[/tex]
[tex]1day = 8miles[/tex]
Given the function f(x) = 2|x + 6|- 4, for what values of x is f(x) = 6?
x=-1, x = 11
x=-1, x=-11
x = 14, x=-26
x = 26. x=-14
Answers
Answer:
solution is [tex]\boxed{x=-1,x=-11}[/tex]
Step-by-step explanation:
f(x)=2|x+6|-4
either x+6 is positive and then |x+6|=x+6
or it is negative and |x+6| = -(x+6)=-x-6
case 1: x>=-6
f(x)= 2x+12-4=2x+8
f(x)=6 <=> 2x+8=6 <=> 2x = 6-8=-2 <=> x = -1
case 2: x<=-6
f(x)=-2x-12-4=-2x-16
f(x)=6 <=> -2x-16=6 <=> 2x=-16-6 = -22 <=> x = -11
so to recap, the solutions are x=-1 and x=-11
The value of x from the modulus value function is x = -1 and x = -11
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 2 | x + 6 | - 4 be equation (1)
On simplifying , we get
when the value of f ( x ) = 6
Substituting the value of f ( x ) = 6 , we get
6 = 2 | x + 6 | - 4
Adding 4 on both sides , we get
2 | x + 6 | = 10
Divide by 2 on both sides , we get
| x + 6 | = 5
And , If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
So , the two values of x are given by
when x + 6 = -5 and x + 6 = 5
x = -1 and x = -11
Hence , the values of x of modulus function is x = -1 and x = -11
To learn more about modulus function click :
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What’s the correct answer for this question?
Answers
Answer:
C.
Step-by-step explanation:
Central angle = 360-52=308°
In radians
308° = 308π/180
Now
S = r∅
S = 3×308π/180
S = 924π /180
S = 77π/15 in.
Answer:
answer is 13π/15
Step-by-step explanation:
correct answer is 13π/15.
If theta=3pi/4
Sin theta=?
Cos theta=?
Answers
Answer:
For ease of writing, θ [tex]=x[/tex]
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Our angle is [tex]x=\frac{3\pi }{4}[/tex]
To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).
Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.
And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.
For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]
This means that
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
A completely randomized design Group of answer choices has one factor and one block. has one factor and one block and multiple values. can have more than one factor, each with several treatment groups. has only one factor with several treatment groups.
Answers
Answer:
C. can have more than one factor, each with several treatment groups.
Step-by-step explanation:
A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.
Completely randomized design has found application in agricultural and environmental researches.
There are 10 balls in a bag, 4 red balls and 6 black balls. If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag. Now you pick two times and each time you can only take one ball. What is the probability that you will pick two red balls
Answers
Answer:
The probability of selecting two red balls is 0.132.
Step-by-step explanation:
In a bag there are 10 balls in a bag, 4 red balls and 6 black balls.
The conditions of selecting a ball are:
If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag.It is also provided that only one ball can be picked at a time.
Now, it is given that two balls are picked.
The number of ways to select a red ball in the first draw is: [tex]{4\choose 1}=4\ \text{ways}[/tex]
Compute the probability of selecting a red ball in the first draw as follows:
[tex]P(\text{First ball is Red})=\frac{{4\choose 1}}{{10\choose 1}}=\frac{4}{10}=0.40[/tex]
Now as a red ball is selected it will not be replaced.
So, there are 9 balls in the bag now.
The number of ways to select a red ball in the second draw is: [tex]{3\choose 1}=3\ \text{ways}[/tex]
Compute the probability of selecting a red ball in the second draw as follows:
[tex]P(\text{Second ball is Red})=\frac{{3\choose 1}}{{9\choose 1}}=\frac{3}{9}=0.33[/tex]
Compute the probability of selecting two red balls as follows:
[tex]P(\text{Two Red balls})=P(\text{First ball is Red})\times P(\text{Second ball is Red})[/tex]
[tex]=0.40\times 0.33\\\\=0.132[/tex]
Thus, the probability of selecting two red balls is 0.132.
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 38 hours and the median is 34.2 hours. Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours. Step 2 of 5 : Approximately how many families are in the sample? Round your answer to the nearest integer.
Answers
Answer:
There are approximately 171 families in the sample.
Step-by-step explanation:
Percentile meaning:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours.
This means that 24 is 14% of the total number of families.
Approximately how many families are in the sample?
Using a rule of three.
24 - 0.14
x - 1
0.14x = 24
x = 24/0.14
x = 171.4
Rounding to the nearest integer
There are approximately 171 families in the sample.
What is the approximate length of minor arc LM? Round to
the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters
Answers
Answer:its 15.7
Step-by-step explanation:
Answer:
15.7
Step-by-step explanation:
A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
H0: \mu \leq 5 days versus H1: \mu > 5 days. At \alpha = .05, choose the right option.
a) Reject H0 if tcalc < 1.7960
b) Reject H0 if tcalc >1.7960
Answers
Answer:
The degrees of freedom first given by:
[tex]df=n-1=12-1=11[/tex]
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
[tex] t_{\alpha}= 1.796[/tex]
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
Step-by-step explanation:
Information given
5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
System of hypothesis
We want to test if the true mean is higher than 5, the system of hypothesis are :
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The degrees of freedom first given by:
[tex]df=n-1=12-1=11[/tex]
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
[tex] t_{\alpha}= 1.796[/tex]
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
30 points. WILL MARK BRAINLIEST
Which would be a correct first step to solve the following system of equations using the elimination method?
x + 3y = 16
2x + y = -18
A: Add the two equations together
B: Subtract the first equation from the second equation
C: Multiply the first equation by -2
D: Multiply the second equation by 2
Answers
Answer:
C: Multiply the first equation by -2
Step-by-step explanation:
-2 * (x + 3y = 16) = -2x-6y=-32
The resulting equation would be -2x-6y=-32
In the next if you add the two equations, you will successfuly eliminate x and can now solve for y.
-2x-6y=-32
2x + y = -18
Answer:
c
Step-by-step explanation:
x+3y=16________________eqn 1
2x+y=-18_______________eqn 2
multiply first equation by - 2
-2(x+3y=16)
-2x-6y= -32______________eqn 3
using elimination method
-2x-6y= -32
+
2x+y= -18
0-5y= -50
-5y= -50
divide both sides by -5
-5y/5= -50/5
y=10
substitute y in eqn 2 to find the value of x
2x+y= -18
2x+(10)= -18
2x+10= -18
2x= -18-10
2x= -28
divide both sides by 2
2x/2= -28/2
x= -14
Someone claims that the average amount of time that a freshman at TAMU studies is 7 hours. We think it’s higher than that and decide to test, using a random sample of 49 freshmen. The sample mean is 8.5 hours with a sample variance of 4 hours. What are the test statistic and p-value in this case?
Answers
Answer:
Test statistic t = 5.25
P-value = 0.000002 (one-tailed test)
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=7\\\\H_a:\mu> 7[/tex]
The significance level is 0.05.
The sample has a size n=49.
The sample mean is M=8.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√s^2=√4=2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{49}}=0.29[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{8.5-7}{0.29}=\dfrac{1.5}{0.29}=5.25[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=49-1=48[/tex]
This test is a right-tailed test, with 48 degrees of freedom and t=5.25, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>5.25)=0.000002[/tex]
As the P-value (0.000002) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.
A stack of 4 identical books is 6.28 inches high. What is the heigh of 30 of these books?
Answers
4books=6.28inches
30books=?
(30x6.28)/4
47.1 inches
answer47.1 inches
If f(x) = –8 – 5x, what is f(–4)?
Answers
Answer:
12
Step-by-step explanation:
f(-4) = -8-5(-4) = -8+20 = 12
Answer:
f(-4) = 12
Step-by-step explanation:
f(-4) = -8 - 5(-4)
= -8 + 20
= 12
Any help would be appreciated
Answers
Answer:
increase 40
% increase is 40 %
Step-by-step explanation:
Take the new amount and subtract the original amount
140-100 = 40
Divide by the original amount
40/100
.40
Multiply by 100 %
40%
The percent increase is 40%
1. Divide 40/100 and you will get 0.40
2. multiply 0.40 times 100 because of the 100%
Therefore, ur answer is 40%
divide 41000 into two parts such that their amounts at 50% compound interest compounded annually in 2 and 3 years are equal
Answers
Answer:24600 , 16400
Step-by-step explanation:
Let the first part be x
So, second part will be 41000 - x
For amount x
SI = prt / 100
SI = x * 0.50 * 2
SI = 1x
For amount 41000 - x
SI = (41000-x) * 0.50 * 3
SI = 61500 - 1.5x
1x = 61500 - 1.5x
1.5x + x = 61500
2.5x = 61500
x = 61500 / 2.50 = 24600 for 2 years
2nd part = 41000 - 24600 = 16400 for three years
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result
Answers
Answer:
4.76% probability that a randomly selected person from the population has a positive test result
Step-by-step explanation:
We have these following probabilities:
4% probability of having the disease.
If a person has a disease, 95% probability of a positive test.
100-4 = 96% probability a person does not have the disease.
If a person does not have the disease, 1% probability of a positive test.
What is the probability that a randomly selected person from the population has a positive test result
95% of 4% and 1% of 96%. So
p = 0.95*0.04 + 0.01*0.96 = 0.0476
4.76% probability that a randomly selected person from the population has a positive test result
Which point is a solution to y>2X-1
Answers
Answer:
Step-by-step explanation:
Answer:
B) (0,2)
Step-by-step explanation:
2 ≥ 2(0)-1
2 ≥ 0-1
2 ≥ -1
An on-line retailer identified the web browser being used by a sample of 50 shoppers to its online site. The accompanying data table identifies the browser being used by a shopper. Previously in 2010, 64% of shoppers used Browser A, 24% Browser B, 6% Browser C, 3% Browser D, and 3% Browser E.
Required:
a. Using software, tabulate the frequency of the choice of browser used by these shoppers.
b. Present a bar chart and a pie chart of these frequencies. Which is more useful to compare the distribution of these to those observed in 2010?
c. Do you see any changes in the distribution of the choice of browser?
Answers
Answer:
See Explanation
This question is answered using Microsoft Office Excel 2013
Step-by-step explanation:
Given
Browser A - 64%
Browser B - 24%
Browser C - 6%
Browser D - 3%
Browser E - 3%
Total Frequency = 50
a.
To tabulate the frequency of the choice of browser, the total frequency is multiplied by each individual percentage as follows;
Browser A - 64% * 50 = 32
Browser B - 24% * 50 = 12
Browser C - 6% * 50 = 3
Browser D - 3%* 50 = 1.5
Browser E - 3% * 50 = 1.5
See Attachment for frequency table (using software)
b. See Attachment for pie chart and bar chart.
Both charts are useful for data presentation but in this case, the pie chart is a better option to use because it shows how the distribution of each browser and how they make up as a whole.
The main circle of the pie chart shows how individual browser are distributed through segments; This is not so for the bars of the bar chart which.
c. Yes, there are changes in the choice of browser.
Aside from Browser D and E that has the same frequency, other browsers (A-C) have different frequency.
Also, the distribution shows that more users make use of browser A than other browsers and the least frequent used browser are browser D and E.
What is the value of expression below? 7/2-4.5x3+8
Answers
Answer:-2
Step-by-step explanation:
Ok so I’m assuming the x stands for the multiplication sign
7/2-4.5*3+8
Use pemdas
Multiplication first
7/2-4.5*3+8
-4.5*3
7/2-13.5+8
Then addition
-13.5+8
Lastly subtraction
7/2-5
-2
x⁴+1/x⁴=47,find the value of x³+1/x³
Answers
Answer:
The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5
Step-by-step explanation:
x^4 + 1/x^4 = 47
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5
How many degrees was ABCD rotated?
Answers
the answer is 180°
Step-by-step explanation:
because it rotated 2x and 90+90 is 180
Please help me with this math problem
Answers
Answer:
[tex]7x^2-2x-2[/tex]
Step-by-step explanation:
[tex]-3x^2+9+10x^2-11-2x[/tex]
Combine like terms:
[tex]10x^2-3x^2-2x+9-11[/tex]
Simplify:
[tex]7x^2-2x-2[/tex]
Hope this helps!
Answer: 7x^2 - 2x - 2
Step-by-step explanation:
in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.
-3x^2 + 9 + 10x^2 - 11 - 2x rearrange to make easier
-3x^2 + 10x^2 - 2x + 9 - 11 combine like-terms
7x^2 - 2x - 2
5. A company sells small, colored binder clips in packages of 20 and offers a money-back guarantee if two or more of the clips are defective. Suppose a clip is defective with probability 0.01, independently of other clips. Let X denote the number of defective clips in a package of 20. (a) The distribution of the random variable X is (choose one) (i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson. (b) Specify the value of the parameter(s) of the chosen distribution and find the probability that a package sold will be refunded.
Answers
Answer:
a) Binomial.
b) n=20, p=0.01, k≥2
The probability hat a package sold will be refunded is P=0.0169.
Step-by-step explanation:
a) We know that
the defective probability is constant and independent.the sample size is bigger than one subject.The most appropiate distribution to represent this random variable is the binomial.
b) The parameters are:
Sample size (amount of clips in the package): n=20Probability of defective clips: p=0.01.number of defective clips that trigger the money-back guarantee: k≥2The probability of the package being refunded can be calculated as:
[tex]P(x\geq2)=1-(P(x=0)+P(x=1))\\\\\\P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}\\\\\\P(x=0) = \dbinom{20}{0} p^{0}q^{20}=1*1*0.8179=0.8179\\\\\\P(x=1) = \dbinom{20}{1} p^{1}q^{19}=20*0.01*0.8262=0.1652\\\\\\P(x\geq2)=1-(0.8179+0.1652)=1-0.9831=0.0169[/tex]
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?
Answers
Answer:
AB = 2√106 ≈ 20.591
Step-by-step explanation:
The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.
For median AM, we have ...
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have ...
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations is ...
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
The hypotenuse of triangle ABC is then ...
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
Verona is solving the equation –3 + 4x = 9. In order to isolate the variable term using the subtraction property of equality, which number should she subtract from both sides of the equation? –4 –3 3 4
Answers
Answer:
subtract -3
Step-by-step explanation:
–3 + 4x = 9
Add 3 to each side
This is the same as subtracting -3
-3 + 4x - (-3) = 9 - (-3)
4x = 9 +3
4x = 12
She should subtract -3 from both sides
Explanation:
To solve this problem you need to isolate the variable. To do that, you would first subtract both sides by negative three and then divide both sides by 4.
Here is what that would look like:
-3 + 4x = 9
-3 - (-3) + 4x = 9 - (-3)
4x = 12
4x / 4 = 12 / 4
x = 3
Which answer choice contains only equations? 2 + h = 14 and k minus 25 = 2 c minus 14 and d + 134 10 = 3 + s and 22 minus y 15 + x and 55 = r minus 1
Answers
Answer:
2 + h = 14 and k - 25 = 2
Step-by-step explanation:
An equation has an equal sign.
Apparently, your answer choices are of the form ...
(math expression) and (math expression)
In order for this to be "only equations", each "math expression" must contain an equal sign. That is, you must have ...
( ... = ... ) and ( ... = ... )
Something like ...
c -14 and d +134
contains no equal signs, so has no equations.
It looks like your appropriate choice is ...
2 + h = 14 and k - 25 = 2
Answer:
the answer is a
Step-by-step explanation:
i took the test
:)
note: have a wonderful day!
Griffin’s General Store is having a 30% off sale on fans. Robert paid $25 for a fan. What is the original price of the fan?
Answers
Answer:
The original price of the fan is $35.71
Step-by-step explanation:
Since Griffin’s General Store is having a 30% off sale on fans, it simply means that fans are paying for (100%-30%)= 70%.
Let the original price be x;
Therefore, 70% of x equal to $25;
[tex]\frac{70}{100}x=25[/tex]
70/100x = 25
0.7x = 25
[tex]x = \frac{25}{0.7}[/tex]
x = 35. 71
Hence, The original price of the fan is $35.71
Answer:
$35.71
Step-by-step explanation:
The statement indicates that Robert paid $25 for a fan and that it had a 30% discount. To be able to determine the original price, you have to divide the the price with the discount by the result of 1 minus the discount.
Original price= 25/(1-0.3)
Original price= 25/0.7
Original price= 35.71
According to this, the answer is that the original price of the fan is $35.71.
uppose the correlation between two variables, math attitude (x) and math achievement (y) was found to be .78. Based on this statistic, we know that the proportion of the variability seen in math achievement that can be predicted by math attitude is:
Answers
Answer:
The proportion of the variability seen in math achievement that can be predicted by math attitude is 0.78, the same value as the correlation coefficient.
Step-by-step explanation:
The correlation coefficient r between this two variables is found to be 0.78.
This coefficient can be calculated as:
[tex]r=\dfrac{SSY'}{SSY}[/tex]
where SSY' is the sum of the squares deviation from the mean for the predicted value and SSY is the sum of the squares deviation from the mean for the criterion variable.
Then, the value of the coefficient r is giving the proportion of the variability seen in the criterion value Y that can be explained by the predictor variable X.
Answer:
r=SSY'/SSY
Step-by-step explanation:
A teacher figures that final grades in the chemistry department are distributed as: A, 25%; B, 25%;C, 40%;D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic x^2 to determine if the grade distribution for the department is different than expected. Use α = 0.01.
Grade A B C D F
Number 36 42 60 14 8
a. 6.87
b. 0.6375
c. 5.25
d. 4.82
Answers
Answer:
[tex]E_{A} =0.25*160=40[/tex]
[tex]E_{B} =0.25*160=40[/tex]
[tex]E_{C} =0.4*160=64[/tex]
[tex]E_{D} =0.05*160=8[/tex]
[tex]E_{F} =0.05*160=8[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]
The answer would be:
c. 5.25
Step-by-step explanation:
The observed values are given by:
A: 36
B: 42
C: 60
D: 14
E: 8
Total =160
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference in the proportions for the final grades
H1: There is a difference in the proportions for the final grades
The level of significance assumed for this case is [tex]\alpha=0.01[/tex]
The statistic to check the hypothesis is given by:
[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]
And the calculations are given by:
[tex]E_{A} =0.25*160=40[/tex]
[tex]E_{B} =0.25*160=40[/tex]
[tex]E_{C} =0.4*160=64[/tex]
[tex]E_{D} =0.05*160=8[/tex]
[tex]E_{F} =0.05*160=8[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]
The answer would be:
c. 5.25
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=(5-1)=4[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]
The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis
What is the average rate of change of f over the interval [-1, 4] Give an exact number.
Answers
Answer:
1.4
Step-by-step explanation:
The average rate of change is the "rise" divided by the "run".
rise/run = (f(4) -f(-1))/(4 -(-1)) = (0 -(-7))/(4+1)
rise/run = 7/5 = 1.4
The average rate of change on the interval [-1. 4] is 1.4.
We will see that the average rate of change in the given interval is 1.4
How to find the average rate of change?
For a given function f(x), the average rate of change on an interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In this case the interval is [-1, 4], using the graph we can see that:
f(-1) = -7
f(4) = 0
replacing that in the formula we get:
[tex]r = \frac{0 - (-7)}{4 - (-1)} = \frac{7}{5} = 1.4[/tex]
If you want to learn more about rates of change, you can read:
https://brainly.com/question/8728504
