Answer:
Step-by-step explanation:
6 X 7 = 42
This is simply the sum of 6 in seven places or 7 in six places.
x4+x3+7x2-6x+8 / x2+2x+8
Answer:
The Final answer will be [tex]x^2-x+1[/tex] with remainder 0.
Step-by-step explanation:
We have attached the division for your reference.
Given:
Dividend = [tex]x^4+x^3+7x^2-6x+8[/tex]
Divisor = [tex]x^2+2x+8[/tex]
Explaining the division we get;
Step 1: First when we divide the Dividend [tex]x^4+x^3+7x^2-6x+8[/tex] with divisor [tex]x^2+2x+8[/tex] we will first multiply [tex]x^2[/tex] with the divisor then we get the Quotient as [tex]x^2[/tex] and Remainder as [tex]-x^3-x^2-6x+8[/tex]
Step 2: Now the Dividend is [tex]-x^3-x^2-6x+8[/tex] and Divisor [tex]x^2+2x+8[/tex] is we will now multiply [tex]-x[/tex] with the divisor then we get the Quotient as [tex]x^2-x[/tex] and Remainder as [tex]x^2+2x+8[/tex]
Step 3: Now the Dividend is [tex]x^2+2x+8[/tex] and Divisor is [tex]x^2+2x+8[/tex] we will now multiply 1 with the divisor then we get the Quotient as [tex]x^2-x+1[/tex] and Remainder as 0.
Hence The Final answer will be [tex]x^2-x+1[/tex] with remainder 0.
Omar begins training for a 5 km race by running 0.75 km the first day, 0.85 km the second day, and 0.95 km the third day. If he keeps increasing his distance each day according to the pace of his first three days, what is the first day in his training program that Omar will run greater than 5 km?
Final answer:
Omar will run greater than 5 km on the 44th day of his training program, as this is when the distance he runs each day according to the pattern in his training exceeds 5 km.
Explanation:
Omar increases his running distance each day by 0.10 km (from 0.75 km on the first day to 0.85 km on the second, then to 0.95 km on the third, and so on). To find the first day he will run greater than 5 km, we can create a sequence to represent the distances he runs each day. Since the difference between consecutive days is constant (0.10 km), this is an arithmetic sequence.
The first term (a1) of the sequence is 0.75 km, and the common difference (d) is 0.10 km. The nth term of an arithmetic sequence is given by an = a1 + (n - 1)d. We need to find the smallest n such that an > 5 km.
Setting up the inequality, we get:
0.75 + (n - 1)0.10 > 5
(n - 1)0.10 > 5 - 0.75
(n - 1)0.10 > 4.25
n - 1 > 42.5
n > 43.5
Since n must be a whole number, Omar will run greater than 5 km on day 44 of his training program.
A submarine dives 270 feet below the ocean's surface. It then rises 90 feet, rises another 40 feet, and finally dives 55 feet. What action is required by the submarine to get back to the surface?
Answer:
The action required by the submarine to get back to the surface is to rise 195 feet
Step-by-step explanation:
we know that
The ocean's surface or sea level is at an elevation of 0 feet.
we have
1) A submarine dives 270 feet below the ocean's surface
In this moment the position of the submarine is
-270 ft ---> is negative because is below the sea level
2) It then rises 90 feet
In this moment the position of the submarine is
-270+90=-180 feet
3) rises another 40 feet,
In this moment the position of the submarine is
-180+40=-140 feet
4) Finally dives 55 feet
In this moment the position of the submarine is
-140-55=-195 feet
therefore
The action required by the submarine to get back to the surface is to rise 195 feet
Final answer:
The submarine initially dives to 270 feet below the surface and undergoes a series of rises and dives. After all movements, it is at a depth of 195 feet. To return to the surface, it needs to rise 195 feet.
Explanation:
A student asked: A submarine dives 270 feet below the ocean's surface. It then rises 90 feet, rises another 40 feet, and finally dives 55 feet. What action is required by the submarine to get back to the surface?
To solve this problem, we will sum up the changes in the submarine's depth and find out how much more it needs to rise to reach the surface.
Initial dive: -270 feet (diving increases the depth, so it's represented as a negative number)First rise: +90 feetSecond rise: +40 feetFinal dive: -55 feetSumming up these changes: -270 + 90 + 40 - 55 = -195 feet.
The submarine is currently 195 feet below the surface. Therefore, to get back to the surface, the submarine needs to rise 195 feet.
Scientific notation is ________.a. used to keep track of very small and very large numbers during mathematical calculations b. used to accurately measure volumes used to measure length with precision c. used to communicate the level of precision
Answer:
A. Used to keep track of very large and very small numbers during mathematical calculations.
Step-by-step explanation:
Some very large and small numbers are not easily represented in mathematical calculations. Using scientific notations help us to represent very large and small numbers to the power of 10.
What is the rate of increase for the function f(x) = One-third (RootIndex 3 StartRoot 24 EndRoot) Superscript 2 x? One-third 2RootIndex 3 StartRoot 3 EndRoot 4 4RootIndex 3 StartRoot 9 EndRoot
Answer:
D, [tex]4^{3} \sqrt{9}[/tex]
Answer:
d
Step-by-step explanation:
Humberto evaluates the expression 4t2 for t=3. He correctly substitutes 3 for t in the expression, but then says that the value is 144. However, he is incorrect!
Answer:
36
Step-by-step explanation:
He multiplied the four and the three first when he multiplied the equation together. However, according to the order of the operations, he was supposed to square three first. 3^2 = 9. Then multiplied 9*4 = 36.
ten people are in a room wearing badges marked 1 through 10. three persons are selected at random and their badge numbers are recorded. what is the probability that the smallest of these badge number is 6?
Answer:
P=1/12
Step-by-step explanation:
From Exercise we have ten people are in a room wearing badges marked 1 through 10.
For first man we conlude that the probability that is 5/10, that his number at least 6.
For second man we conlude that the probability that is 4/9, that his number at least 6.
For third man we conlude that the probability that is 3/8, that his number at least 6.
Therefore, the probability is
P=5/10 · 4/9 · 3/8 = 1/12
P=1/12
Can someone please answer this I don’t understand!
Point P is located at (2, 2) and point T is located at (7, 17). What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Use the section formula and show values for: m: n, Point 1, Point 2, and ALL work to find coordinates of partitioning point.
The coordinates of X are (5, 11).
Solution:
Given points of the line segment are P(2, 2) and T(7, 17)
Let X be the point that partitions the directed line segment PT in the ratio 3 : 2
Using section formula, we can find the coordinate of the point that partitions the line segment.
Section formula:
[tex]$X(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)[/tex]
Here, [tex]x_{1}=2, y_{1}=2, x_{2}=7, y_{2}=17[/tex] and m = 3, n =2
Substitute these in the section formula,
[tex]$X(x, y)=\left(\frac{3 \times 7+2 \times 2}{3+2}, \frac{3 \times 17+2 \times 2}{3+2}\right)[/tex]
[tex]$=\left(\frac{21+4}{5}, \frac{51+4}{5}\right)[/tex]
[tex]$=\left(\frac{25}{5}, \frac{55}{5}\right)[/tex]
[tex]=(5, 11)[/tex]
X(x, y) = (5, 11)
The coordinates of X are (5, 11).
A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. Based on the set of 356 surveys that were completed and returned, the researcher finds that these students spend an average of 3.1 hours each day watching television. For this study, the set of 356 students who returned the surveys is an example of a _______.a. parameter b. statistic c. population d. sample
Answer:
Option b) Sample
Step-by-step explanation:
We are given the following in the question:
Survey:
356 surveys on television-viewing habits of American adolescents.
Result:
Average of 3.1 hours per day.
Population and sample:
Population is a collection of all the possible observation of individuals or variable of interest.A sample is always a part of the population.It is a subset of population.For the given survey, those who responded to the survey forms a a sample as it is a part of 356 surveys that is a subset of population.
The correct answer is
Option b) Sample
Murphy family has 4 members and they went to 7 games. Chen family has 5 members and they went to 4 games. In total, the two families spent $1200. If the seats cost the same for each person, how much did the Murphy family spend?
The Murphy family spend $ 700
Solution:
Given that,
Murphy family has 4 members and they went to 7 games
Let "x" be the cost of each game
Murphy family cost: [tex]4 \times 7 \times x = 28x[/tex]
Chen family has 5 members and they went to 4 games
Chen family cost: [tex]5 \times 4 \times x = 20x[/tex]
In total, the two families spent $1200
Therefore,
28x + 20x = 1200
48x = 1200
Divide both sides by 48
x = 25
How much did the Murphy family spend?
Murphy family cost = 28x = 28(25) = 700
Thus murphy family spend $ 700
Let f(x) = -2x + 4 and g(x) = -6.0 – 7. Find f(x) – g(x).
Please show your work and explain steps! GIVING BRAINLIEST!!
Answer:
-2x + 3
Step-by-step explanation:
f(x) - g(x)
(-2x + 4) - (-6.0 - 7)
-2x + 4 - (-6.0) - 7
-2x + 4 + 6.0 - 7
-2x + 10 - 7
-2x + 3
Suppose that a basketball player different from the
ones in Example 2.5-2 and in Exercise 2.5-1 can make a
free throw 60% of the time. Let X equal the minimum
number of free throws that this player must attempt to
make a total of 10 shots.
(a) Give the mean, variance, and standard deviation of X.
(b) Find P(X = 16).
Answer:
a. Mean = 6
Variance = 2.4
Standard Deviation = 1.55
b. P(X=16) = 0.124
Step-by-step explanation:
Given
n = Total shots = 10
p = Probability of success = 60%
p = 60/100
p= 0.6
q = Probability of failure
q = 1-p
q = 1 - 0.6
q = 0.4
a.
Mean = np
Mean = 10 * 0.6
Mean = 6
Variance = npq
Variance = 10 * 0.6 * 0.4
Variance = 2.4
Standard Deviation = √Variance
Standard Deviation = √2.4
Standard Deviation = 1.549193338482966
Standard Deviation = 1.55 --------- approximated
b.
We have X = 16
x = 10
Assume that the events "success" on the various throws are independent.
The 10th success came on the 16th attempt
So, the player had exactly 10 successes and 6 failures on 16th trial
So Probability = nCr 0.6^10 * 0.4^6
Where n = 15 and r = 9 (number of attempts and success before the 16th trial)
15C9 * 0.6^10 * 0.4^6
= 5005 * 0.0060466176 * 0.004096
= 0.123958563176448
= 0.124 ------ Approximated
A. The mean, variance, and standard deviation of x are: Mean: 16.67, Variance: 11.11 and Standard deviation: 3.33. B. The probability that the player will need exactly 16 attempts to make 10 successful shots is approximately 0.123
Given that a basketball player can make a free throw 60% of the time, we are to determine the minimum number of free throws that this player must attempt to make a total of 10 shots.
Since each shot is independent and has a 60% chance of being successful, this scenario follows a negative binomial distribution.
(a) Calculating the mean, variance, and standard deviation:
Mean:
[tex]\[ \mathbb{E}[X] = \frac{r}{p} = \frac{10}{0.60} = \frac{10}{0.6} = 16.67 \][/tex]
Variance:
[tex]\[ \text{Var}(X) = \frac{r(1-p)}{p^2} = \frac{10(1-0.60)}{0.60^2} = \frac{10 \cdot 0.40}{0.36} = \frac{4}{0.36} = 11.11 \][/tex]
Standard deviation:
[tex]\[ \sigma = \sqrt{\text{Var}(X)} = \sqrt{11.11} \approx 3.33 \][/tex]
So, the mean, variance, and standard deviation of x are: Mean: 16.67, Variance: 11.11 and Standard deviation: 3.33
(b) Finding P(X = 16)
The probability mass function of a negative binomial random variable \is given by:
[tex]\[ P(X = k) = \binom{k-1}{r-1} p^r (1-p)^{k-r} \][/tex]
[tex]\[ P(X = 16) = \binom{15}{9} (0.60)^{10} (0.40)^{6} \][/tex]
Calculating the binomial coefficient:
[tex]\[ \binom{15}{9} = \frac{15!}{9!(15-9)!} = \frac{15!}{9!6!} \][/tex]
This can be computed as follows:
[tex]\[ \binom{15}{9} = \frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 5005 \][/tex]
Combining these:
[tex]\[ P(X = 16) = 5005 \cdot 0.0060466 \cdot 0.004096 \approx 0.123 \][/tex]
Therefore:
[tex]\[ P(X = 16) \approx 0.123 \][/tex]
So, the probability that the player will need exactly 16 attempts to make 10 successful shots is approximately 0.123
Lailah earns $9 per week working at the aquarium. Write and solve an inequality that can be used to find how many hours she must work in a week to earn at least $135.
Answer:
$9 per hour (not week)
9x > or = 135
x > or = 45 hours she must work
Step-by-step explanation:
Answer: she must work for at least 15 hours in a week to earn at least $135
Step-by-step explanation:
Let x represent the number of hours that Lailah must work in a week to earn at least $135.
Lailah earns $9 per week working at the aquarium. This means that in a week in which she worked for x hours, the total amount of money that she would earn is 9x
Therefore, the inequality that can be used to find how many hours she must work in a week to earn at least $135 would be
9x ≥ 135
x ≥ 135/9
x ≥ 15
for box A find the constant proportionality
Answer:
Are there like any images or opinions for your question
Can someone please help me with this? will give you brainiest if correct
Thank you so much <3
Answer: The solution is [2, 1]
Step-by-step explanation:
The given system of simultaneous equations is expressed as
7x - 6y = - 20 - - - - - - - - - - 1
3x + 5y = - 1 - - - - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 3 and equation 2 by 7. It becomes
21x - 18y = - 60 - - - - - - - - - - 3
21x + 35y = - 7 - - - - - - - - - - 4
Subtracting equation 4 from equation 3, it becomes
- 53y = - 53
Dividing the left hand side and the right hand side of the equation by - 53, it becomes
- 53y/ - 53 = - 53/ - 53
y = 1
Substituting y = 1 into equation 2, it becomes
3x + 5 × 1 = - 1
3x + 5 = - 1
Subtracting 5 from the left hand side and the right hand side of the equation, it becomes
3x + 5 - 5 = - 1 - 5
3x = - 6
Dividing the left hand side and the right hand side of the equation by 3, it becomes
3x/3 = - 6/3
x = 2
Claudia scores 275 points on a video game. Hannah scores 268 points on the same video game. The high score for the same game is 306. How many points did the girls score in all?
Answer:
543
Step-by-step explanation:
Given: Claudia score= 275 points
Hannah score= 268 points
Now, finding the how many points girls scored in the game.
Total score by girls= [tex]Score\ of\ Claudia + score\ of\ Hannah[/tex]
⇒ Total score by girls= [tex]275+268[/tex]
Total score by girls= 543.
Hence, Total score by girls is 543.
A homes value increases at a average rate of 5.5% each yea. The current value is $120,000. What function can be used to find the value of the home after X years?
Answer: the function is
A = 120000(1.055)^x
Step-by-step explanation:
A homes value increases at an average rate of 5.5% each year. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r/n)^ nt
Where
A represents the value of the home after t years.
n represents the period of growth
t represents the number of years.
P represents the initial value of the home.
r represents rate of increase in value.
From the information given,
P = 120000
r = 5.5% = 5.5/100 = 0.055
n = 1
Therefore
A = 120000(1 + 0.055/1)^ x × 1
A = 120000(1.055)^x
Julia has 2 children who are 4 years apart in age. Julia is four times older than her youngest child. The sum of the ages of Julia and her 2 kids is 76 years
Answer: Julia is 48 years
The oldest child is 16 years
The youngest child is 12 years
Step-by-step explanation:
Let x represent the age of the youngest child.
Let y represent the age of the oldest child.
Let x represent Julia's age.
The sum of the ages of Julia and her 2 kids is 76 years. This means that
x + y + z = 76- - - - - - - - - - -1
Julia has 2 children who are 4 years apart in age. This means that
y = x + 4
Julia is four times older than her youngest child. This means that
z = 4x
Substituting z = 4x and y = x + 4 into equation 1, it becomes
x + x + 4 + 4x = 76
6x = 76 - 4 = 72
x = 72/6 = 12
y = x + 4 = 12 + 4
y = 16
z = 4x = 4 × 12
z = 48
Answer:
what?
Step-by-step explanation:
Jason drew a scale drawing of a city. He used the scale 1 inch : 4 yards. A neighborhood park is 68 yards wide in real life. How wide is the park in the drawing?
Answer:
17 inches
Step-by-step explanation:
The scale is the same at every distance, so ...
[tex]\dfrac{\text{1 in}}{\text{4 yd}}=\dfrac{w}{\text{68 yd}}\\\\\text{(1 in)}\dfrac{\text{68 yd}}{\text{4 yd}}=w \qquad\text{multiply by 68 yd}\\\\\text{17 in}=w[/tex]
The park is 17 inches wide on the drawing.
Answer:
17 in
Step-by-step explanation:
68 yds divided by 4 equals 17 in
In how many ways can 3 apple trees, 4 peach trees, and 2 plum trees be arranged along a fence line if one does not distinguish between trees of the same kind?\
Answer:
24 ways
Step-by-step explanation:
4x3x2
12x2
24
Which set of ordered pairs has point symmetry with respect to the origin (0, 0)?
(-8, 3), (8, -3)
(-8, 3), (-3, 8)
(-8, 3), (-8, -3)
(-8, 3), (8, 3)
Answer:
(-8, 3), (8, -3)
Step-by-step explanation:
Point symmetry about origin means reflection of the given point about the origin.
The reflection of a point about the origin will cause the 'x' and 'y' value of the point to change its sign.
Therefore, the coordinate rule for point symmetry about the origin is given as:
[tex](x,y)\to (-x,-y)[/tex]
Now, let us check each of the given options.
Option 1:
(-8, 3), (8, -3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3)
So, option 1 is correct.
Option 2:
(-8, 3), (-3, 8)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-3, 8)
So, option 2 is not correct.
Option 3:
(-8, 3), (-8, -3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-8, -3)
So, option 3 is not correct.
Option 4:
(-8, 3), (8, 3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (8, 3)
So, option 4 is not correct.
Hence, only option 1 is correct.
Why is the answer A?
Step-by-step explanation:
F(x) is the antiderivative (or integral) of f(x).
F(x) = ∫ f(x) dx
F(x) = sin(1/(x² + 1))
∫₁² f(x) dx
= F(2) − F(1)
= sin(1/(2² + 1)) − sin(1/(1² + 1))
= sin(⅕) − sin(½)
= -0.281
Two trained professionals observe the behavior of children in a classroom. They each rate observed behaviors using the same form and the number of items that were rated the same is calculated. This is an example of which type of reliability?
a. inter-rater reliability
b. test-retest reliability
c. none of the above
d. parallel reliability
Answer: a) inter rater
Step-by-step explanation:
Inter rater is a type of relativity that measures the degree of agreement between rates and judges.
It is used to ensure that the score gotten among rates are in consensus with one another.
Inter rater relativity reduces inconsistency in the application of data collected.
The scenario where two trained professionals rate observed children's behaviors using the same form and comparing their ratings exemplifies inter-rater reliability (option a), focusing on the consistency of measurements between different observers.
The type of reliability being described in the scenario is inter-rater reliability. This type of reliability is concerned with the level of agreement between two or more independent observers or raters when they assess the same behaviors using a standardized method or form. To ensure that a study's measures are consistently capturing the concepts of interest, researchers often assess inter-rater reliability.
Inter-rater reliability can involve qualitative categories (like behavioral observations in a classroom) where the agreement percentage reflects the reliability. Alternatively, for measurements on interval or ratio scales, the correlation between the raters' scores can be used. When two professionals observe children and rate their behavior on the same form, looking for agreement in items rated, they establish inter-rater reliability.
Consider two population distributions labeled X and Y. Distribution X is highly skewed while the distribution Y is slightly skewed. In order for the sampling distributions of X and Y to achieve the same degree of normality
A. Population Y will require a larger sample size
B. Population X will require a larger sample size
C. Population X and Y will require the same sample size
D. None of the above
Answer: B. Population X will require a larger sample size
Step-by-step explanation:
If a random variable say p has skewed distribution (whether right or left ) in a population then a bigger sample size is needed to make sure that the sampling distribution follows normal distribution.Given : Two population distributions labeled X and Y.
Distribution X → highly skewed
Distribution Y → slightly skewed.
Since Distribution X more skewed so , we will need a larger sample size of population X as compared to Y.
Hence, the correct answer is B. Population X will require a larger sample size
The correct option is B. Population X will require a larger sample size.
According to the Central Limit Theorem, the sampling distribution of the sample mean will tend to be normally distributed as the sample size becomes larger, regardless of the shape of the population distribution. However, the rate at which the sampling distribution approaches normality depends on the degree of skewness in the population distribution.
For a population distribution that is highly skewed (like Distribution X), a larger sample size is needed for the sampling distribution to approximate a normal distribution compared to a population distribution that is only slightly skewed (like Distribution Y). This is because the effects of skewness are more pronounced and take longer to "average out" in larger samples.
Therefore, to achieve the same degree of normality in their respective sampling distributions, Population X, with its high skewness, will require a larger sample size than Population Y, which is only slightly skewed.
Please help i need answer
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle,
BC represents the hypotenuse of the right angle triangle.
With m∠C as the reference angle,
AC represents the adjacent side of the right angle triangle.
AB represents the opposite side of the right angle triangle. if Sin C = 15/17, it means that
Opposite side = 15
Hypotenuse = 17
We would find the adjacent side by applying Pythagorean theorem. Therefore,
Adjacent side² = 17² - 15² = 64
Adjacent side √ 64 = 8
To determine the ratio of Cos C, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos C = 8/17
The conference method estimates cost functions: A. Using quantitative methods that can be very time consuming and costly B. Based on analysis and opinions gathered from various departments C. Using time-and-motion studies D. By analyzing the relationship between inputs and outputs in physical terms
Answer:
B. Based on analysis and opinions gathered from various departments
Step-by-step explanation:
Conference method of cost estimation envisages a widespread process in which head of different unit of organisation is consulted and their skill in their area of operation is tapped to make estimation of cost of the operation of different department.
If Felicia lives 1 1/5 miles from the school and 9/10mile from the doctor field how much closer would she live if she lived 7/10 like from the doctor field
Suppose that the probability density function for the length x in feet of some type of fish caught by sport fishermen is given by p(x)=14 if 0≤x≤4, and is zero otherwise. What is the probability that a fish caught by a fisherman is between 0.25 and 2 feet long? 1/4 is less than 0.25 feet long?
For the described uniform distribution, the probability that a fish is between 0.25 and 2 feet long can be found by calculating the area under the probability density function graph, which gives a result of 43.75%.
Explanation:The given situation implies a uniform distribution as the probability density function is constant (equal to 1/4) for fish lengths between 0 and 4 feet, and zero otherwise. For such a distribution, the probability that the length x is in an interval can be found by calculating the area under the probability density function graph for that interval. As the graph is a rectangle, this is as simple as length times width.
Here, the interval is from 0.25 to 2 feet. The length of this interval is (2 - 0.25)= 1.75 feet. The width of the rectangle is the constant probability density function value of 1/4. Hence, the probability that a fish caught by the sports fishermen is between 0.25 and 2 feet long is 1.75 * 1/4 = 0.4375 or 43.75%.
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Alice has seven times the amount of pens that Maurice has. Paul has two-thirds of the amount of pens as Alice and Suzy have combined. Dawn has a dozen more pens than Paul. Suzy has half the pens that Maurice has. If Suzy has 2 pens, how many does Dawn have?
Answer:
Dawn has 32 pens.
Step-by-step explanation:
Let No. of pens Alice has = ALet No. of pens Maurice has = M Let no of pens Paul has = P Let no. of pens Suzy has = S Let no of pens Dawn has = DGiven :
A = 7M P = 2/3 (A + S) D = P + 12 S = 1/2 MIf S = 2 {Given} M = 4 [∵ S = 1/2 M → M = 2S = 2X(2) ] A = 28 [ ∵ A = 7M → A = 7 x 4 ] P = 20 [∵ P = 2/3 (A+S) → P = 2/3 (28 + 2) = 2/3 (30) ] D = 32 [ ∵ D = P + 12 → D = 20 + 12 ]By following the relationships between the number of pens each person has, it is calculated that Dawn has 32 pens.
Explanation:This is a multi-step problem involving proportions and addition. First, we determine Maurice's number of pens based on Suzy's: because Suzy has half the pens Maurice does, and Suzy has 2 pens, Maurice therefore has 4 pens. Then, to find out how many pens Alice has, we multiply Maurice's number of pens by 7 (Alice having 7 times Maurice's number of pens), hence Alice has 28 pens. As Paul has two-thirds the number of all the pens that Alice and Suzy have (28 + 2 = 30 pens), Paul has 20 pens. Finally, as Dawn has a dozen more pens than Paul, Dawn has 32 pens (20 + 12).
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What is the momentum of each hockey player? Hockey player 1 has a mass of 65 kg and a velocity of 3.8 m/s
Hockey player 2 has a mass of 58 kg and a velocity of 4.3 m/s
Answer:
Momentum of hocking player [tex]1:[/tex] [tex]247\ kg\ m/s[/tex]
Hockey player [tex]2:[/tex] [tex]=249.4\ kg\ m/s[/tex]
Step-by-step explanation:
For first hockey player :
Given that
mass (m) [tex]=65\ kg[/tex]
Velocity (v) [tex]=3.8\ m/s[/tex]
[tex]p=mv\................(1)[/tex]
where [tex]p[/tex] is momentum
put the value in equation (1)
[tex]p=65\times3.8\\\\p=247kg\times m/s[/tex]
For second hockey player :
Given that
mass (m) [tex]=58\ kg[/tex]
velocity (v) [tex]=4.3\ m/s[/tex]
[tex]p=mv\ ...............(2)[/tex]
Where [tex]p[/tex] is momentum
put the value in equation (2)
[tex]p=58\times4.3\\p=249.4\ kg\times m/s[/tex]