Answer:C
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
Source: Dude trust me
if a polynomial is divided by (x-a) and the remainder equals zero, then (x-a) is a factor of the polynomial
Answer:
True.
Step-by-step explanation:
This is the basis for polynomial division/remainder theorem.
Given a polynomial p(x) and a divisor (x - a), if p(a) = 0, then the expression factors in perfectly.
Likewise, if the remainder in p(x)/(x-a) = 0, then the expression factors in perfectly.
I hope this helps!
Answer:
True
Step-by-step explanation:
a p e x
Laura placed a bucket of water in her garden. Over the course of a week, she watched the water evaporate and recorded the volume of water left in the bucket each day.
Laura found the linear model that best fit the data was V=5.00−0.25n, where n is the number of days since she first placed the bucket and V is the volume of water, in liters, remaining in the bucket.
How many liters of water evaporated from the bucket every day?
How may liters where inside the bucket when Laura first placed it in the garden?
Answer:
1. 0.5 L; 2. 5.00 L
Step-by-step explanation:
V = 5.00 - 0.5n
If you include units, the equation becomes
V(in litres) = 5.00 L - (0.5 L/day) × (n days)
1. Rate of evaporation
When you include the units, it becomes easier to see that the water is evaporating at a rate of 0.5 L/day.
That is, 0.5 L of water evaporates each day.
The negative sign shows that the volume of water is decreasing.
2. Volume at the beginning
At the beginning of the experiment, n = 0. Then
V = 5.00 -0.5×0 = 5.00 - 0 = 5.00 L
The bucket originally contained 5.00 L of water.
What value of x makes 3(x + 4) = 3x + 4 true?
Well lets see.
[tex]3(x+4)=3x+4\implies 12 = 4\implies x\notin\mathbb{C}[/tex].
There are no such x-es that satisfy the equation.
A card is drawn from a standard deck of 5252 playing cards. What is the probability that the card will be a heart and not a club? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
The probability of choosing a heart and not a club is
P = 0.1875
Step-by-step explanation:
There are 13 hearts in a deck of 52 cards. The probability that the chosen card will be a heart is given by
Probability = favorable outcome/ Total number of outcomes
P= 13/52= 1/4
There are 13 clubs in a deck of 52 cards.
The probability of not choosing a club would be
P = 52-13/52= 39/52= 3/4
So the combined probability of choosing a heart and not a club is
P = 1/4 * 3/4= 0.25 * 0.75= 0.1875
A machine part consist of a half sphere and a cylinder, as shown in the figure.the total volume of the part is blank pi c
Answer:
Volume of the machine part = 114π inches³
Step-by-step explanation:
Volume of the machine part = Volume of cylinder + Volume of hemisphere
Volume of cylinder = [tex]\pi r^{2}h[/tex]
Where r = radius of the cylinder
h = height of the cylinder
Volume of the cylinder = [tex]\pi(\frac{6}{2})^{2}(12)[/tex]
= 108π inches³
Volume of the hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]
= [tex]\frac{2}{3}\pi (3)^{3}[/tex]
= 6π inches³
Total area of the machine part = 108π + 6π
= 114π inches³
Tamar rides her bike 960 feet in 2 minutes. What is her rate of speed?
Answer:
Rate of speed = 480 feet per minutes
Step-by-step explanation:
Given:
Distance covered by bike = 960 feet
Time taken to covered distance = 2 minutes
Find:
Rate of speed = ?
Computation:
⇒ Speed = Distance / Time
⇒ Rate of speed = Distance covered by bike / Time taken to covered distance
⇒ Rate of speed = 960 / 2
⇒ Rate of speed = 480 feet per minutes
Hey can anyone help me with this 3 3/5 x (-8 1/3)?
Answer:
[tex]-30[/tex]
Step-by-step explanation:
[tex]3\frac{3}{5} \times (-8 \frac{1}{3} )[/tex]
[tex]\frac{18}{5}\times \left(-\frac{25}{3}\right)[/tex]
[tex]\frac{18}{5}\times -\frac{25}{3}[/tex]
[tex]-\frac{18\times \:25}{5\times \:3}[/tex]
[tex]-\frac{450}{15}[/tex]
[tex]=-30[/tex]
Answer:-30
Step-by-step explanation:
3 3/5 x -8 1/3
18/5 x -25/3
-30
3ab-9ab+7ab and hurry up
Answer:ab
Step-by-step explanation:3-9=-6 +7=1 1ab also equals just ab
Answer:
Since its adding and subtracting just add the coefficients of similar terms (coefficient is the number in front, term is the coefficient. and variables, similar terms are terms that have the same variables)
3ab-9ab+7ab
3-9=-6: -6ab+7ab
-6+7=1: 1ab or ab :)
Solve for x. 6−x3=3 x=9 x=−9 x=27 x=−27
are supplementary angles, then
A) Both should be acute B) Both should be obtuse C) one acute other right D) None of these
Answer:
D
Step-by-step explanation:
Answer:
D) None of these
Step-by-step explanation:
Supplementary pairs must equal to 180 degrees. They can either be made up of two right angles, or one acute and one obtuse angle.
Employees at a company produced refrigerators on three shifts. Each shift recorded their quality stats below. A unit was considered defective if it at least one part was assembled wrong or was missing. Management believes that quality depends on the the shift it was produced. Test the claim that shifts are independent of quality using chi-square at alpha = 0.05. SHOW YOUR WORK
Answer:
Step-by-step explanation:
Hello!
So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.
Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.
The hypotheses are:
H₀: The variables are independent.
H₁: The variables are not independent.
α: 0.05
[tex]X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}[/tex]
r= total number of rows
c= total number of columns
i= 1, 2 (categories in rows)
j=1, 2, 3 (categories in columns)
To calculate the statistic you have to calculate the expected frequencies for each category:
[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]
[tex]O_{i.}[/tex] Represents the marginal value of the i-row
[tex]O_{.j}[/tex] Represents the marginal value of the j-column
[tex]E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34[/tex]
Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:
[tex]X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991[/tex]
Decision rule:
If [tex]X^2_{H_0}[/tex] ≥ 5.991, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 5.991, do not reject the null hypothesis.
The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.
At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.
I hope this helps!
Write the equation of the line in slope intercept form
Answer:
y=2x-2
Step-by-step explanation:
When writing the equation of a line in slope intercept form, you need to know two things; the slope, and the y intercept. The slope of the line can be found by seeing how steep the line is. For instance, here the line rises 2 units for every 1 unit it moves to the right, meaning that it has a slope of 2/1=2. The y intercept can be found by just seeing where the graph crosses the y axis, or where x is 0. Here it can be seen to be at -2. Therefore, the equation of this line is y=2x-2. Hope this helps!
Answer:
answer is : y = 2x + 2
Step-by-step explanation:
slope-intercept form is y= mx + b
the y-intercept is: (0, -2) and the x-intercept is (1,0)
the first thing you do is find the slope:
m = (y2-y1) / (x2-x1)
so : ( 0 - -2) / ( 1 - 0) or 2/1 therefore the slope is 2
y = 2x + ? is the next step
then you can substitute the x and y into the formula to find the (b) value
0 = 2 (1)
0 = 2 ?
since 0 equals two plus two the b value is 2.
so the answer is y = 2x + 2
A U.S.-based Internet company offers an online proficiency course in basic accounting. Completing this online course satisfies the "Fundamentals of Accounting" course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. Region Enrollment 1 45 2 60 3 30 4 40 5 50 6 55 7 35 The CEO looked at the data presented and said no they are not equal. It is obvious, since the enrollment in one region is 60 and another 30. However, the CFO said that using a Chi-Square Goodness of Fit Test with a 1% significance level, the frequencies in the regions are not significantly different. Which one is correct? Use statistics to support your answer.
Answer:
[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]
[tex]Expected \ mean = \dfrac{315 }{7}[/tex]
Expected mean = 45
The Chi - Square Value = 15.556
Conclusion:
We conclude that there is equal number of average interest in the course across all regions.
Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.
Step-by-step explanation:
From the question; Let state our null hypothesis and alternative hypothesis
Null Hypothesis
[tex]\mathbf{H_0:}[/tex]There is equal number of average interest in the course across all regions.
Alternative Hypothesis
[tex]\mathbf{H_a:}[/tex] At least one of the region differs in average number of interest in the course.
The table can be better structured as :
Region Enrollment
1 45
2 60
3 30
4 40
5 50
6 55
7 35
From above; we know the number of sample = 7
Then our expected mean can be calculated as :
[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]
[tex]Expected \ mean = \dfrac{315 }{7}[/tex]
Expected mean = 45
SO, let's construct our Chi-Square Statistics Test Table as follows:
Observed Expected Expected (O-E)² [tex]\dfrac{(O-E)^2}{E}[/tex]
(O) (E) proportion
45 45 0.142857 0 0
60 45 0.142857 225 5
30 45 0.142857 225 5
40 45 0.142857 25 0.556
50 45 0.142857 25 0.556
55 45 0.142857 100 2.222
35 45 0.142857 100 2.222
15.556
The Chi - Square Value = 15.556
Degree of freedom = n- 1
Degree of freedom = 7 - 1
Degree of freedom = 6
Level of significance ∝ = 1% = 0.01
The Critical value of Chi Square test statistic at df = 6 and 0.01 significance level is 16.812
The Decision rule is to reject the Null hypothesis if The Chi Square test statistic X² > 16.812
Thus , since the Chi Square test statistic is lesser than the critical value,
i.e 15.556 < 16.812 ,we accept null hypothesis [tex]\mathbf{H_0}[/tex]
Conclusion:
We conclude that there is equal number of average interest in the course across all regions.
Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.
A random sample of 100 observations from a population with standard deviation 6868 yielded a sample mean of 113113. Complete parts a through c below. a. Test the null hypothesis that muμequals=100 against the alternative hypothesis that muμgreater than>100, using alphaαequals=0.05. Interpret the results of the test. What is the value of the test statistic?
Answer:
Null hypothesis is rejected,
test statistic= 15.76
Step-by-step explanation:
sample mean= 113,
sample standard deviation= 68
H0: mean of sample =100
Ha: mean of sample > 100
test statistic= (population mean- sample mean)/√(standard deviation/sample size)
test statistic= (113-100)/√(68/100)= 15.76
Degrees of freeedom= 100-1=99
p-value= 1.658 (from t distribution table for DF=99 and alpha=0.05)
Since p-value is smaller than test statistic, null hypothesis is rejected
Which of the following is the perimeter of a triangle with side lengths of 18 cm, 26 cm, and 32 cm?
Answer:
76 cm
Step-by-step explanation:
To find the perimeter, add up all of the side lengths.
18 cm + 26 cm + 32 cm = 76 cm
I hope this helps :))
A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. What is the probability that the player gets 3 hits in the three bats ?
Answer:
Since there are 2 possibilities for each bat (hit or out), the amount of total possibilities is 2 * 2 * 2 = 8. There is only one possibility out of those eight that gives us three hits, therefore the probability is 1 / 8 or 0.125.
To prove a polygon is a rectangle which of the properties listed must be included in the proof
Answer:
if the diagonals of a parallelogram are congruent, then it's a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it's a rectangle (neither the reverse of the definition nor the converse of a property).
Step-by-step explanation:
Question 2 (1 point)
How much does the prefix milli multiply the value of a base unit?
Answer:1000
Step-by-step explanation:
Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phone company has reason to believe that the proportion is 30%. Before they start a big advertising campaign, they conduct a 99% CL hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Required:
a. Is the actual percentage of households different from 30%?
b. Set up the hypothesis test.
c. What is the success for this problem?
d. Calculate the p-value.
e. Draw conclusion.
Answer:
We conclude that the actual percentage of households is equal to 30%.
Step-by-step explanation:
We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.
Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Let p = proportion of households that have three cell phones NOT known.
So, Null Hypothesis, [tex]H_0[/tex] : p = 30% {means that the actual percentage of households is equal to 30%}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 30% {means that the actual percentage of households different from 30%}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of households having three cell phones = [tex]\frac{43}{150}[/tex] = 0.29
n = sample of households = 150
So, the test statistics = [tex]\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }[/tex]
= -0.27
The value of z test statistic is -0.27.
Also, P-value of the test statistics is given by;
P-value = P(Z < -0.27) = 1 - P(Z [tex]\leq[/tex] 0.27)
= 1 - 0.6064 = 0.3936
Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the actual percentage of households is equal to 30%.
Please everyone help me!
Answer:g=0 is not the solution
Step-byd-step explanation:
-1 1/2 is a negative number and 0 is not negative
Answer:
g=0
Step-by-step explanation:
happy to help ya :)
Environmental Protection Agency standards require that the amount of lead in drinking water be less than 15 ppb. Twelve samples of water from a particular source have the following concentrations, in ppb. 11.4 13.9 11.2 14.5 15.2 8.1 12.4 8.6 10.5 17.1 9.8 15.9 A hypothesis test will be performed to determine whether the water from this source meets the EPA standard.
Required:
a. State the appropriate null and alternate hypotheses.
b. Compute the P-value.
c. Can you conclude that the water from this source meets the EPA standard? Explain.
Answer:
Step-by-step explanation:
Mean = (11.4 + 13.9 + 11.2 + 14.5 + 15.2 + 8.1 + 12.4 + 8.6 + 10.5 + 17.1 + 9.8 + 15.9)/12 = 12.4
Standard deviation = √(summation(x - mean)²/n
n = 12
Summation(x - mean)² = (11.4 - 12.4)^2 + (13.9 - 12.4)^2 + (11.2 - 12.4)^2+ (14.5 - 12.4)^2 + (15.2 - 12.4)^2 + (8.1 - 12.4)^2 + (12.4 - 12.4)^2 + (8.6 - 12.4)^2 + (10.5 - 12.4)^2 + (17.1 - 12.4)^2 + (9.8 - 12.4)^2 + (15.1 - 12.4)^2 = 89.62
Standard deviation = √(89.62/13) = 2.7
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
a) For the null hypothesis,
µ ≤ 15
For the alternative hypothesis,
µ > 15
This is a right tailed test
b) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 12,
Degrees of freedom, df = n - 1 = 12 - 1 = 11
t = (x - µ)/(s/√n)
Where
x = sample mean = 12.4
µ = population mean = 15
s = samples standard deviation = 2.7
t = (12.4 - 15)/(2.7/√12) = - 3.34
We would determine the p value using the t test calculator. It becomes
p = 0.0034
c) Assuming level of significance = 0.05.
Since alpha, 0.05 > than the p value, 0.0034, then we would reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the water from this source does meets the EPA standard. They are higher than 15ppb
Using the t-distribution, we have that:
a)
The null hypothesis is: [tex]H_0: \mu \geq 15[/tex]
The alternative hypothesis is: [tex]H_1: \mu < 15[/tex]
b) The p-value is of 0.0051.
c) Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.
Item a:
At the null hypothesis, it is tested if the mean is of at least 15 ppb, that is:
[tex]H_0: \mu \geq 15[/tex]
At the alternative hypothesis, it is tested if the mean is of less than 15 ppb, that is:
[tex]H_1: \mu < 15[/tex]
Item b:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.In this problem, we have that [tex]\mu = 15, n = 12[/tex]. Additionally, using a calculator, the other parameters are: [tex]\overline{x} = 12.38, s = 2.93[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{12.38 - 15}{\frac{2.93}{\sqrt{12}}}[/tex]
[tex]t = -3.1[/tex]
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.1 and 12 - 1 = 11 df.
Using a calculator, this p-value is of 0.0051.Item c:
Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.
A similar problem is given at https://brainly.com/question/16194574
what the product of the reciprocals of 2/3, 1/8, and 5
Answer:
12/5
Step-by-step explanation:
Reciprocal of 2/3 is 3/2
Reciprocal of 1/8 is 8/1
Reciprocal of 5 is 1/5
[tex]\frac{3}{2} \times \frac{8}{1} \times\frac{1}{5} = \frac{24}{10} \\[/tex]
Can be simplified to
[tex]\frac{12}{5}[/tex]
What is the simplified value of the exponential expression 27 1/3
1/3
1/9
3
9
Answer:
I think its 1/9
Answer:
B
Step-by-step explanation:
A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).
Answer:
x=2
Step-by-step explanation:
Original width = 6
New width 6+x+x
Orignal length 12
New length 12+x+x
A = l*w
160 = ( 6+2x) ( 12+2x)
Factor
160 = 2( 3+x) 2(6+x)
Divide each side by 4
40 = (3+x) (6+x)
FOIL
40 = 18+ 6x+3x+ x^2
40 = 18 +9x+x^2
Subtract 40 from each side
0 = x^2 +9x -22
Factor
0 = (x +11) (x-2)
Using the zero product property
x +11 =0 x-2 =0
x= -11 x=2
Since we cannot have a negative sidewalk
x =2
Answer:
2
Step-by-step explanation:
Original width = 6
New width = 6 + x + x = 6 + 2x
Orignal length = 12
New length = 12 + x + x = 12 + 2x
A = l * w
160 = (6 + 2x)(12 + 2x)
160 = 2(3+x) * 2(6+x)
160 = 4 * (3 + x)(6 + x)
160/4 = (3 + x)(6 + x)
40 = 18 + 6x + 3x + x^2
40 = 18 + 9x + x^2
x^2 + 9x - 22 = 0
= x^2 + 11x - 2x - 22 = 0
= x(x + 11) - 2(x + 11) = 0
= (x + 11) (x - 2) = 0
x = - 11, 2
Since we cannot have a negative width because it's a dimension,
x = 2 is right
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards. A sample of 20 cards are selected from the lot without replacement for functional testing. (a) If 20 cards are defective, what is the probability that at least one defective card appears in the sample
Answer:
The probability that at least one defective card appears in the sample
P(D) = 0.9644 or 96.44%
Step-by-step explanation:
Given;
Total number of cards t = 140
Number of defective cards = 20
Number of non defective cards x = 140-20 = 120
The probability that at least one defective card = 1 - The probability that none none is defective
P(D) = 1 - P(N) ........1
For 20 selections; r = 20
-- 20 cards are selected from the lot without replacement for functional testing
The probability that none none is defective is;
P(N) = (xPr)/(tPr)
P(N) = (120P20)/(140P20)
P(N) = (120!/(120-20)!)/(140!/(140-20)!)
P(N) = (120!/100!)/(140!/120!) = 0.035618370821
P(N) = 0.0356
The probability that at least one defective card appears in the sample is;
P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644
P(D) = 0.9644 or 96.44%
Note: xPr = x permutation r
Consider the polynomial 9x2 – 16.
Answer: 2
Step-by-step explanation:
9 × 2 - 16
18 - 16
2
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Step-by-step explanation:
The complete question is:
There are 103 students in a physics class. The instructor must choose two students at random.
Students in a Physics Class
Academic Year Physics majors Non-Physics majors
Freshmen 17 15
Sophomores 20 14
Juniors 11 17
Seniors 5 4
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Solution:
There are a total of N = 103 students present in a Physics class.
Some of the students are Physics Major and some are not.
The instructor has to select two students at random.
The instructor first selects a senior Physics major and then a sophomore Physics major.
Compute the probability of selecting a senior Physics major student as follows:
[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]
[tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]
Now he two students are selected without replacement.
So, after selecting a senior Physics major student there are 102 students remaining in the class.
Compute the probability of selecting a sophomore Physics major student as follows:
[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]
[tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]
Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:
[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]
[tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]
Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1/2
Step-by-step explanation:
Find two points on the line
(2,0) and (4,1)
The slope is given by
m= (y2-y1)/(x2-x1)
=(1-0)/(4-2)
= 1/2
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
60
25
Answer:
65
Step-by-step explanation:
C^2= A^2 + B^2
C^2 = (60)^2 + (25)^2
C^2 = 4225
Take the square root of C
C = 65
Answer:
65
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.
[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]
The hypotenuse should measure 65 units.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. -6 ≤ y ≤ 9
Step-by-step explanation:
→Looking at the graphed function, you can see that the line starts at when y = -6. Then the function slowly increases, until it finally stops when y = 9.
→This means that the range (y-values) of the function can be from -6 through 9.
The correct answer should be "A. -6 ≤ y ≤ 9."
