Answer:B
Step-by-step explanation:
17, 300+ 1.25% You can take the decimal and move it to the other side then start doing the math
Answer:
C; 21625
Step-by-step explanation:
Ten slips of paper labeled from 1 to 5 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper.
What is the probability of selecting a number less than 3 then a number greater than 4?
3/50
1/15
3/100
1/10
Answer:
The probability of given event = [tex]\frac{1}{15}[/tex]
Step-by-step explanation:
Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper.
We have to find the probability of selecting a number less than 3 and then a number greater than 4.
Probability of an event = [tex]\frac{number of favourable events}{total number of events}[/tex]
The probability of selecting number less than 3 = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
The probability of selecting number greater than 4 = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]
Total probability = [tex]\frac{1}{5}\times \frac{1}{3}[/tex] = [tex]\frac{1}{15}[/tex]
A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fractin in terms of Pie.
Answer:
Step-by-step explanation:
it is given that Square contains a chord of of the circle equal to the radius thus from diagram
[tex]QR=chord =radius =R[/tex]
If Chord is equal to radius then triangle PQR is an equilateral Triangle
Thus [tex]QO=\frac{R}{2}=RO[/tex]
In triangle PQO applying Pythagoras theorem
[tex](PQ)^2=(PO)^2+(QO)^2[/tex]
[tex]PO=\sqrt{(PQ)^2-(QO)^2}[/tex]
[tex]PO=\sqrt{R^2-\frac{R^2}{4}}[/tex]
[tex]PO=\frac{\sqrt{3}}{2}R[/tex]
Thus length of Side of square [tex]=2PO=\sqrt{3}R[/tex]
Area of square[tex]=(\sqrt{3}R)^2=3R^2[/tex]
Area of Circle[tex]=\pi R^2[/tex]
Ratio of square to the circle[tex]=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }[/tex]
any help appreciated <333
Answer:
A. 67°
Step-by-step explanation:
Since AC is tangent to the circle, ∠C must be 90°.
You know all angles of a triangle should add up to 180°, so with A given as 23°, that leaves 180-90-23 = 67° for O.
Explain how probability can be used to help a sales person forecast future sales.
Answer with explanation:
A salesperson can use probability to get an idea of his business as using probability he can estimate his sale of the next month as well, based on the present and previous months sales.
It can help him sort issues or errors he is facing in his business as he will get a complete idea of his business using probability.
Moreover, he can forecast future sales by using a technique which involves assigning percentages or weighting benchmarks in sales cycle, so that he can estimate the expected revenue generated.
For example:
A supermarket sales person can assign probabilities to benchmarks in sale cycle as providing needs analysis (25 % probability), adding new product (50%Probability) , Remove a product ( 75 % probability), closing sale (100% Probability) . If these probabilities are large, then forecast model can be objective.
_____________________________________________________
So just like that by assigning probabilities to benchmarks, a sales person can forecast future sales
Answer:
Probability can be used to help a sales person forecast future sales best my showing the likelihood of a certain event occurring. The sales person can then plan around the events that are deemed to be the most likely to occur.
Explanation:
100%Attempt 1 Complete
Describe the Distributive Property and give an example of how it works.
There is a bag filled with marbles: 5 red, 8 blue, 4 yellow, and 3 green.
You want to draw a red then a blue marble. Do you have a better chance of drawing a red then a blue marble with or without replacing the first marble? Explain your answer.
please give an explanation. i seriously don't understand this question. have a wonderful day and happy holidays!
Answer:
Step-by-step explanation:
total marbles=5+8+4+3=20
when he is drawing without replacing means red marble is drawn from 20 marbles.
Blue marble is drawn from 19 marbles.
when he is drawing with replacing means he draws one red marble from 20 marbles.Then he replaces it and draws blue marble from 20 marbles also.
We have a better chance of drawing a red and then a blue marble without replacing the first marble.
What is probability?It is the ratio that shows the likelihood of a particular event happening from when many other events could also happen.
The total number of marbles = 5 + 8 + 4 +3
= 20 marbles.
P( Drawing a red marble ) = 5/20
Now draw a blue marble:
With replacement:Total marbles = 20
P( Drawing a blue marble ) = 8/20
Joint probability = 5/20 * 8/20
= 0.1
Without replacement:Total marbles = 19
P( Drawing a blue marble ) = 8/19
Joint probability = 5/20 * 8/19
= 0.105
This means that there is a higher probability of drawing a blue marble after a red marble without replacement.
Thus we have found that we have a better chance of drawing a red and then a blue marble without replacing the first marble.
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If an individual earns an annual salary of $100,000 and invests $10,000 in a 401k, what will be the employee's taxable income?
$110,000
$10,000
$100,000
$90,000
Answer:
90k
Step-by-step explanation:
Taxable income is calculated by subtracting certain eligible deductions from gross income. In this scenario, a $10,000 investment in a 401k reduces the individual's taxable income from a $100,000 salary to $90,000.
Explanation:When determining taxable income, it's important to subtract certain eligible deductions from the gross income. In this case, the individual earns a salary of $100,000 and invests $10,000 in a 401k plan. This investment is a pre-tax contribution, which means it lowers the amount of income that is subject to tax. Therefore, by investing $10,000 into a 401k, the individual's taxable income would be reduced to $90,000. So the correct answer is $90,000.
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Explain how to find n, the number of copies the machine can print in one minute. I need an algebraic expression for the answer.
Once the first part is done, I need help with this question.
Working at the same rate, how long will it take the machine to print 5,200 copies? Explain how you found your answer.
Answer:
It will take 80 minutes!
Step-by-step explanation:
From the table we see that in 5 minutes we get 325 copies.
This means in one minute we get [tex]$ \frac{325}{5} $[/tex] = 65 copies.
So, assume we get 5200 copies in 'x' minutes.
So, we form the equation.
i.e., 65x = 5200
⇒ x = 80
This means it would take 80 minutes to get 5200 copies.
Only the top! The first three questions! Help pleAseee!!
Answer:
Step-by-step explanation:
1.
3a+7=4a
a=7
2b=b+11
b=11
2.
y=101°
101+x=180
x=180-101=79°
3.
x+6=11
x=11-6=5
y-7=10
y=10+7=17
what is the maximum number of sections into which a circle may be divided into by drawing four straight lines?
Answer:
11 sections
Step-by-step explanation:
This problem is called the circle cutting or pancake cutting problem.
Let the number of cuts or divisions by straight line = n
With this information it is possible to calculate any number of pieces or section a circle will be divided into what straight lines are drawn (cut) across the circle.
When a straight line is drawn across the circle, it divides the circle into 2 sections or regions. The nth straight lines will divide the circle into n new sections or regions, so the progression is;
f(1) = 2
f(2) = 2 + f(1)
f(3) = 3 + f(2)
.
.
.
f(n) = n + f(n-1)
Therefore,
f(n) = n + [(n-1) + f(n-2)}
= n + n-1 + ... + 2 + f(1)
= f(1) + ∑[tex]_{i = 2}^{n}[/tex]i
= [tex]2 + \frac{1}{2} (n + 2) (n - 1)[/tex]
= [tex]\frac{1}{2}(n^{2} + n + 2)[/tex]
When n = 4
= [tex]\frac{1}{2}(4^{2} + 4 + 2)[/tex]
= 22/2
= 11 sections
A group of 100 students took a quiz Their average score was 76 points If the average score of the boys is 80 and the average score of the girls is 70, how many girls participated in the quiz?
Answer:
40
Step-by-step explanation:
Let the number of boys participating in the quiz be b and the number of girls be g. Since the total number is 100, we have our first equation.
b + g = 100
The average score was 76 points. This means the total score was 76 * 100 = 7600
The average score for the boys was 80 meaning total scores for the boys was 80b while that of the girls was 70g
Hence, we have our second equation:
80b + 70g = 7600
Now let’s put the equations together and solve simultaneously to get g which is the number of girls:
b + g = 100
80b + 70g = 7,600
Let’s simply make a substitution. We can say b = 100 - g. Substituting this will yield:
80(100 - g) + 70g = 7,600
8000 - 80g + 70g = 7600
10g = 400
g = 400/10 = 40
Final answer:
By creating and solving two equations that represent the average scores and total number of students, it was determined that 40 girls participated in the quiz.
Explanation:
To solve this problem, we can create two equations using the information about the average scores of the boys and girls, and the overall average. Let's denote the number of girls as G and the number of boys as B. We are told that there are a total of 100 students, which means:
Equation 1: G + B = 100
We're also told the average scores for boys and girls separately, and the overall average score for the group. We can express this with the following equation:
Equation 2: (80B + 70G) / 100 = 76
Now we can solve these equations simultaneously. We already have the total number of students from Equation 1, so we can use that to express B in terms of G: B = 100 - G. Then we can substitute this into Equation 2:
(80(100 - G) + 70G) / 100 = 76
Expanding this, we get:
8000 - 80G + 70G = 7600
Combining like terms, we have:
-10G = -400
Dividing both sides by -10 gives us G = 40.
So 40 girls participated in the quiz.
Lauren is ordering a taxi from an online taxi service. The taxi charges $2 just for the pickup and then an additional $1.50 per mile driven. How much would a taxi ride code if Lauren is riding for 8 miles? How much would a taxi ride cost that is m?
Answer:
It costs Lauren 14 dollars to ride 8 miles
Step-by-step explanation:
The equation for the price of the taxi ride is
y= 1.5x+2
where y is the price, and x is the number of miles driven. Lauren needs to ride 8 miles, so the price of her taxi ride is
y= 1.5*8 +2 =12+2=14
Nitrites are often added to meat products as preservatives. In a study of the effect of these chemicals on bacteria, the rate of uptake of a radio-labeled amino acid was measured for a number of cultures of bacteria, some growing in a medium to which nitrites had been added. Here are the summary statistics from this study. Group n x s Nitrite 30 7880 1115 Control 30 8112 1250.
Carry out a test of the research hypothesis that nitrites decrease amino acid uptake at the 2% significance level.
Answer:
H0:[tex]\mu_{N}\geq \mu_{C}[/tex]
H1:[tex]\mu_{N} < \mu_{C}[/tex]
[tex]t=\frac{7880-8112}{\sqrt{\frac{1115^2}{30}+\frac{1250^2}{30}}}}=-0.759[/tex]
[tex]p_v =P(t_{(58)}<-0.759)=0.225[/tex]
So the p value is a very High value and using any significance level given [tex]\alpha=0.02[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the mean for the nitrite group is significantly lower than the mean for th control group .
Step-by-step explanation:
1) Data given and notation
[tex]\bar X_{N}=7880[/tex] represent the mean for the sample Nitrite
[tex]\bar X_{C}=8112[/tex] represent the mean for the sample control
[tex]s_{N}=115[/tex] represent the sample standard deviation for the sample Nitrite
[tex]s_{C}=1250[/tex] represent the sample standard deviation for the sample control
[tex]n_{N}=30[/tex] sample size for the group nitrite
[tex]n_{C}=30[/tex] sample size for the group control
t would represent the statistic (variable of interest)
[tex]\alpha=0.02[/tex] represent the significance level
Confidence =1-0.02=0.98 or 98%
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the nitrites decrease amino acid uptake , the system of hypothesis would be:
H0:[tex]\mu_{N}\geq \mu_{C}[/tex]
H1:[tex]\mu_{N} < \mu_{C}[/tex]
If we analyze the size for the samples both are equal to 30, but we don't know the population deviations, so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{N}-\bar X_{C}}{\sqrt{\frac{s^2_{N}}{n_{N}}+\frac{s^2_{C}}{n_{C}}}}[/tex] (1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
3) Calculate the statistic
We can replace in formula (1) like this:
[tex]t=\frac{7880-8112}{\sqrt{\frac{1115^2}{30}+\frac{1250^2}{30}}}=-0.759[/tex]
4) Statistical decision
The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{N}+n_{C}-2=30+30-2=58[/tex]
Since is a left tailed test the p value would be:
[tex]p_v =P(t_{(58)}<-0.759)=0.225[/tex]
So the p value is a very High value and using any significance level given [tex]\alpha=0.02[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the mean for the nitrite group is significantly lower than the mean for th control group .
Maria drove from Los Angeles (elevation 330 feet) to Death Valley (elevation –282 feet). What is the difference in elevation between Los Angeles and Death Valley?
Answer:
612 feet
Step-by-step explanation:
LA is located at 330 feet ABOVE SEA LEVEL
Death Valley is located 282 feet BELOW SEA LEVEL
We let the sea level be at 0 (consider a number line).
So,
LA would be at +330 feet
and
Death Valley would be at -282 feet
The elevation change between the two would be the difference:
330 - (-282) = 330 + 282 = 612 feet
The difference in elevation = 612 feet
Answer:
D
Step-by-step explanation:
rectangular yard measuring 24ft by 29ft is bordered (and surrounded) by a fence. Inside, a walk that is 2ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
Answer:
Area of the walk = 110 square feet
Step-by-step explanation:
The rectangular yard measuring 24ft by 29ft
Area of the rectangle = length times width
Area of the rectangular yard = 24 times 29=696 square feet
Length of side walk is 2 feet wide
Length of the rectangular yard with walk = 24+2= 26 ft
Width of the rectangular yard with walk = 29+2=31 ft
Area of the rectangular yard with walk = 26 times 31=806 square feet
Area of the walk = [tex]806-696=110 squarefeet[/tex]
The entry fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5000 is collected. The number of children attended the fair is___________.
Answer:
The number of children attended the fair is 1520.
Step-by-step explanation:
We are given the following in the question:
Entry fee foe children = $1.50
Entry fee foe adult = $4.00
Total number of people in fair = 2200
Total money collected = $5000
Let x be the number of children and y be the number of adults in the fair.
Then, we can write the following equations:
[tex]x + y = 2200\\1.5x + 4y = 5000[/tex]
Solving the two equations, we have:
[tex]1.5x + 1.5y = 3300\\1.5x + 4y = 5000\\\Rightarrow 2.5y = 1700\\y = 680\\x = 2200-680 = 1520[/tex]
Thus, there were 1520 children and 680 adults in the fair.
The crude association between occupational exposure and lung cancer (outcome) among the study sample was 8.4. When data were stratified by alcohol intake, the associations were 2.2 (for non-drinkers) and 14.5 (for drinkers). Assume that all (crude, and stratified) measures of association were statistically significant. Alcohol use was (use 15% difference rule):
a. An effect modifier
b. A potential confounder
c. A random error
d. A confounder
Answer:
Option D
Step-by-step explanation:
This are variables that have relationship with the outcome and exposure that is the confounding effect of alcohol on cancer is the fact that an alcohol consumers are more likely to smoke and smokers are likely to have cancer.
The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume that s = 14 minutes based on previous studies. Show all your work.
Answer: 11
Step-by-step explanation:
Formula to find the sample size using sample standard deviation (s) :
[tex]n= (\dfrac{z^*\cdot s}{E})^2[/tex] , where z* = critical z-value and E = Margin of error.
As per given , we have
E= 7
s= 14 minutes
We know that the critical value for 90% confidence interval = z*=1.645
Then, the required sample size = [tex]n= (\dfrac{(1.645)\cdot (14)}{7})^2[/tex]
[tex]n= (1.645\cdot 2)^2=(3.29)^2=10.8241\approx11[/tex]
Hence, the required sample size = 11
To estimate the mean length of time it takes for buses to arrive and unload students, a sample size of 29 is needed to assert with 90% confidence that the sample mean is off by, at most, 7 minutes.
Explanation:To determine the sample size needed to estimate the mean length of time it takes for buses to arrive and unload students, we can use the formula:
n = (Z * σ / E)^2
Where n is the required sample size, Z is the z-score corresponding to the desired confidence level (1.645 for 90% confidence), σ is the standard deviation (14 minutes), and E is the maximum error allowed (7 minutes).
Substituting the values into the formula:
n = (1.645 * 14 / 7)^2 = 5.3229^2 = 28.27.
Rounding up to the nearest whole number, the sample size needed is 29.
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There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB, how many color patterns are possible?A. 10B. 12C. 24D. 60E. 100
Answer:
Option A - 10
Step-by-step explanation:
Given : There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB.
To find : How many color patterns are possible?
Solution :
Total number of chips = 5
So, 5 chips can be arranged in 5! ways.
There are 3 red chips and 2 blue chips.
So, choosing 3 red chips in 3! ways
and choosing 2 blue chips in 2! ways.
As changing the places of similar chip will not create new pattern.
The total pattern is given by,
[tex]T=\frac{5!}{3!\times 2!}[/tex]
[tex]T=\frac{5\times 4\times 3!}{3!\times 2}[/tex]
[tex]T=10[/tex]
Therefore, color patterns are possible are 10.
Option A is correct.
On Monday morning, Susan bought 2.5 pounds of grapes at the supermarket. That day, Susan ate some grapes and had 1.75 pounds of grapes left. What is the percent decrease of pounds of grapes on Monday?
Answer:
Step-by-step explanation:
On Monday morning, Susan bought 2.5 pounds of grapes at the supermarket. That day, Susan ate some grapes and had 1.75 pounds of grapes left. This means that the amount of grapes that she ate would be 2.5 - 1.75 = 0.75
The percentage decrease of pounds of grapes on Monday would be the amount that she ate on Monday divided by the initial amount times 100. It becomes
0.75/2.5 × 100 = 30℅
Willis tower in Chicago is 1450 feet tall. The John Hancock Center in Chicago is 1127 feet tall. Suppose you are asked to build a small-scale replica of each. If you make the Willis Tower 3 meters tall, what would be the approximate height of the John Hancock replica? Round you answer to the nearest hundredth.
The approximate height of the John Hancock replica is 2.33 meters.
Given that;
Willis Tower in Chicago is 1450 feet tall.
And, The John Hancock Center in Chicago is 1127 feet tall.
Let us assume that,
The approximate height of the John Hancock replica = x
Hence by using the definition of proportion, we get;
1450/3 = 1127/x
Cross multiplication,
1450x = 1127 × 3
x = 2.331
Round to the nearest hundredth;
x = 2.33
Thus, The approximate height of the John Hancock replica is 2.33 meters.
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A researcher reports that there is no consistent relationship between grade point average and the number of hours spent studying for college students. The correlation between grade point average and the number of hours studying is an example of __________.(A) a positive correlation(B) a negative correlation(C) a correlation near 0(D) a correlation near 1
Answer:
C
Step-by-step explanation:
Since there is no relationship between the two , there exists no correlation between them.
This is simply because the effect of one is not felt on the other
Given the two vertices and the centroids of a triangle, how many possible locations are there for the third vertex?
Answer:
1
Step-by-step explanation:
The centroid is the average of the coordinates of the three vertices. If you know two vertices (A and B) and the centroid (Q), then the third vertex (C) is ...
C = 3Q -A -B
It has only one possible location.
Given the coordinates of two vertices and the centroid, the third vertex can be located by solving a system of linear equations derived from the centroid's coordinates. This results in only one possible location for the third vertex.
To find the number of possible locations for the third vertex of a triangle given two vertices and the centroid, we need to use the properties of the centroid. The centroid of a triangle is the point where the three medians intersect and it is located 1/3 of the way from each side towards the opposite vertex.
If we denote the vertices of the triangle as (x1, y1), (x2, y2), and (x3, y3), and the centroid as (Gx, Gy), the coordinates of the centroid can be calculated as:
Gx = (x1 + x2 + x3) / 3
Gy = (y1 + y2 + y3) / 3
Since we know the coordinates of the centroid (Gx, Gy) and two vertices (x1, y1), (x2, y2), we can set up the following system of equations:
(x1 + x2 + x3) / 3 = Gx (y1 + y2 + y3) / 3 = Gy
Solving these equations for x3 and y3 gives:
x3 = 3Gx - x1 - x2
y3 = 3Gy - y1 - y2
Therefore, there is only one possible location for the third vertex given the two vertices and the centroid.
A total of 300 trees will be planted in a park, for every two pine trees there will be 3 maple trees what is the number of pine and maple trees that were planted in the park?
Step-by-step explanation:
Total number of trees = 300
Given that for every two pine trees there will be 3 maple trees.
Let 2t be the total number of pine trees.
Then total number of maple trees is 3t.
Total number of trees = 2 t + 3 t = 5 t
That is
5t = 300
t = 60
Total number of pine trees = 2t = 2 x 60 = 120
Total number of maple trees = 3t = 3 x 60 = 180
There are 120 pine trees and 180 maple trees.
The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50. What is the cost of a pizza with 5 toppings? Round to the nearest penny. a. $19.00 b. $22.75 c. $43.75 d. $70.00
Answer: b. $22.75
Step-by-step explanation:
Given : A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.
Let x denotes the number of toppings and y be the cost of that pizza.
Then, [tex]y=mx+c[/tex] , m= cost per topping and c= cost of pizza without any topping.
From the given information.
c= $14
Function of cost becomes = [tex]y=mx+14[/tex]
For x= 2 and y= 17.50, we have
[tex]17.50=m(2)+14[/tex]
tex]3.50=m(2)[/tex] [Subtract 14 from both sides]
[tex]m=\$ 1.75[/tex] [Divide both sides by 2]
For c= 14 and m =1.75 , our function becomes.
[tex]y=1.75x+14[/tex]
Now, for x= 5
[tex]y=1.75(5)+14=8.75+14=22.75[/tex]
Hence, the cost of a pizza with 5 toppings = $22.75
A diver dives from a 10m springboard. the equation f(t) = -4.9t² + 4t + 10 models her height above the pool at time t. When will she be at her highest?
Answer:
At time t = 0.408 sec diver will be at maximum height
Step-by-step explanation:
We have given equation of the height [tex]f(t)=-4.9t^2+4t+9[/tex]
We know that velocity is the rate of change of distance with respect to time
So [tex]v=\frac{df(t)}{dt}=\frac{df(-4.9t^2+4t+10)}{dt}=-9.8t+4+0=-9.8t+4[/tex]
At maximum height velocity will be zero
So [tex]-9.8t+4=0[/tex]
t = 0.408 sec
So at time t = 0.408 sec diver will be at maximum height
Last month,Margo bought a tree that grows 2.5cm each day.It was 5cm tall when she bought it and now it 65cm tall. Write a equation to determine the number of days Margo has owned the plant
Answer:
The equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].
Step-by-step explanation:
Given:
Actual length of the tree = 5 cm
Current length of the tree = 65 cm
Per day growth Rate of plant = 2.5 cm
Let number of days she owned the plant be 'x'
Now We can say that,
Current length of the tree is equal to sum of Actual length of the tree and Per day growth Rate of plant multiplied by number of days she owned the plant.
Farming the above sentence in equation form we get;
[tex]5+2.5x=65[/tex]
Hence the equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].
Represent each of these relations on {1, 2, 3, 4} with a matrix (with the elements of this set listed in increasing order). a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)} b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)} c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)} d) {(2, 4), (3, 1), (3, 2), (3, 4)}
The concept in the question is about representing relations as matrices. In the matrices, the rows and columns correspond to the numbers in the set {1, 2, 3, 4}. The positions in the matrices that are filled with 1s correspond to the numbers in the given relationships.
Explanation:The relations can be represented on the set {1, 2, 3, 4} with a matrix as follows:
a) For this relationship, a 4x4 matrix can be created. The rows and columns correspond to the numbers in the set {1, 2, 3, 4}. The elements of the set [tex]{(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}[/tex] correspond to positions in the matrix that will be filled with 1s, while the rest will be filled with 0s.
b) A matrix for this relationship would look similar to the above matrix but with different elements in the set [tex]{(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}[/tex]. In this case, the position of 1s and 0s in the matrix changes.
c) The matrix corresponding to this relationship would have 1s in positions corresponding to the elements of the set [tex]{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}.[/tex]
d) The last matrix would have 1s only at the positions corresponding to the relationship {(2, 4), (3, 1), (3, 2), (3, 4)}.
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A positive integer with exactly two different divisors greater than 1 must be(A) a prime(B) an even integer(C) a multiple of 3(D) the square of a prime(E) the square of an odd integer
Answer:
(D) the square of a prime
Step-by-step explanation:
You want to know the kind of number that will have exactly two distinct positive divisors other than 1.
DivisorsThe number of divisors a number will have can be found from its prime factorization. If that is described by ...
[tex]\displaystyle N=p_1^{e_1}\times p_2^{e_2}\times\dots=\prod\limits_n(p_i)^{e_i}\\ \\\text{\# of divisors of N}=\prod\limits_n (e_i+1)[/tex]
This count of divisors includes 1 and the number N. If there are 2 divisors other than 1, then we must have the product of all "bumped" exponents be 3. Since 3 is prime, its only factors are 1 and 3. That means there must be only one exponent, and its value must be 3-1 = 2.
That is, N = p², where p is a prime, has 2+1 = 3 divisors, including 1.
An integer with exactly 2 distinct divisors greater than 1 is the square of a prime, choice D.
the empire state building is 1250 feet tall. IF an object is thrown upward from the top of the building at an initial velocity of 38 feet per second, its height s seconds after it is thrown is given by the function h(s) = -16s^2 + 38s + 1250. round to the nearest hundreth
Answer:
Time for the object to get h(max) s = 1.1875 sec
h (max) = 1272.57 feet
Down time for the object to hit the ground = 4.25 sec
Step-by-step explanation:
The relation
h(s) = - 16*s² + 38* s + 1250 (1)
Is equivalent to the equation for vertical shot
Δh = V(i)*t - 1/2g*t² (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.
The description of the movement is:
V(s) = V(i) - g*s ⇒ V(s) = 38 - 32*s
At h(max) V(s) = 0 38/32 = s
So the maximum height is at s = t = 1.1875 sec
The time for the object to pass for starting point is the same
t = 1.1875 sec
h(max) is
h(max) = - 16* (1.1875)² + 38 (1.1875) + 1250
h(max) = - 22,56 + 45.13 + 1250
h(max) = 1272.57 feet
Time for the object to hit the ground is
h(s) = - 1250 feet
-1250 = - 16 s² + 38*s + 1250
-16s² + 38s = 0
s ( -16s + 38 ) = 0
First solution for that second degree equation is x = 0 which we dismiss
then
( -16s + 38 ) = 0 ⇒ 16s = 38 s = 38/16
s = 2.375 sec and we have to add time between h (max) and to get to starting point ( 1. 1875 sec)
total time is = 2.375 + 1.875
Total time = 4.25 sec