Answer:
See definitions and relation below
Step-by-step explanation:
Given points x and y of a certain set S in a metric space, a path from x to y is a continuous map f:[a,b]-->S of some closed interval [a,b] in the real line into S, such that
f(a)=x and f(b)=y
In this case, we can also say that the points x and y are joined by a path or arc.
A set S in metric space is said to be path connected or arcwise connected if every pair of points x, y of S can be joined by a path.
The relation between arcwise connectedness and connectedness of a set is that every arcwise connected set is also connected, but the converse does not hold; not every connected space is also path connected.
As an example, consider the unit square [0,1]X[0,1] with the dictionary order topology.
It can be proved that this space is connected but not path connected.
Arcwise connectedness is defined as the presence of a continuous path between any two points in a set in a metric space. There is a relation between arcwise connectedness and connectedness, where any path connected set is also connected, but the converse is not necessarily true.
Explanation:A set in a metric space is said to be arcwise connected or path connected if there exists a continuous curve or path that connects any two points in the set.
The relation between arcwise connectedness and connectedness of a set is that any arcwise connected set is also connected, but the converse is not necessarily true. In other words, every path connected set is connected, but not every connected set is path connected.
For example, consider a set consisting of two separate points in a metric space. This set is connected because we cannot find two disjoint open sets that cover the set, but it is not arcwise connected because there is no continuous path connecting the two points.
Add 0.5 kg, 50 mg, and 2.5 dg. Reduce the result to grams.
Answer:
0.25g + 0.05g + 500g = 500.30g
Step-by-step explanation:
The first step is converting everything to grams, by rules of three. Then we add.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
First step: 0.5kg to g
Each kg has 1000g. So
1kg - 1000g
0.5kg - xg
x = 1000*0.5
x = 500g
0.5kg = 500g
Second step: 50mg to g
Each g has 1000mg. So:
1g - 1000mg
xg - 50mg
1000x = 50
[tex]x = \frac{50}{1000}[/tex]
x = 0.05g
50mg = 0.05g
Third step: 2.5dg to g
Each g has 10dg. So:
1g - 10dg
xg - 2.5dg
2.5x = 10
[tex]x = \frac{2.5}{10}[/tex]
x = 0.25g
2.5 dg = 0.25g
Final step: Add
0.25g + 0.05g + 500g = 500.30g
Adding 0.5 kg, 50 mg, and 2.5 dg gives a total of 500.30 grams once all the units are converted to grams.
Explanation:First, let's convert everything to grams as it's the unit we're asked to report the result in.
0.5 kg is equal to 500 grams (1 kilogram = 1000 grams)50 mg is equal to 0.05 grams (1 gram = 1000 milligrams)2.5 dg is equal to 0.25 grams (1 gram = 10 decigrams)To find the total, we just need to add these numbers together: 500 grams + 0.05 grams + 0.25 grams = 500.30 grams. So, when you add 0.5 kg, 50 mg, and 2.5 dg together and convert it to grams, your answer is 500.30 grams.
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Choose the correct elements in the set for the following:
{y | y is an integer and y > -2}
{3,4,5,6,...}
{ 2,3,4,5,6,...}
{−2,−1,0,1,2,3,...}
{0,1,2,3,..}
This is the set of all integers greater than -2, excluded. So, the elements of the set are
[tex]\{-1,0,1,2,3,4,5,\ldots\}[/tex]
Given:
Set defining the rule → {y | y is an integer and y > -2}
To find:
The set following the given property
Solution:
Set defined by {y | y is an integer and y > -2} where y is the set of integers greater than -2.
Option (1)
{3,4,5,6........}
All the integers are greater than -2, therefore, this set will the answer.
Option (2)
{2, 3, 4, 5, 6.....}
All integers are greater than -2, therefore, this set will be the answer.
Option (3)
{-2, -1, 0, 1, 2, 3....}
There is an element which is equal to -2.
Therefore, given set will not be the answer.
Option (4)
{0, 1, 2, 3.....}
All elements are greater than -2.
Therefore, given set will be the answer.
Options (1), (2), (4) will be the answer.
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Kyle, a single taxpayer, worked as a free-lance software engineer for the first three months of 2018. During that time, he earned $94,000 of self-employment income. On April 1, 2018, Kyle took a job as a full-time software engineer with one of his former clients, Hoogle Inc. From April through the end of the year, Kyle earned $188,000 in salary.
What amount of FICA taxes (self-employment and employment related) does Kyle owe for the year?
Total amount owed by Kyle = $21573
Step-by-step explanation:In the question,
Amount of money earned by Kyle in first three months = $94,000
Amount of money earned by Kyle in Remaining months working as a Full Time = $188, 000
Total Money earned by Kyle = $282,000
Now,
We know that the Percent of FICA(Federal Insurance Contributions Act) taxes are,
Social Security tax = 6.2 %
Medicare tax = 1.45 %
So,
Total percent of tax paid = 7.65 %
So,
Total amount paid in taxes = 7.65 % of Total Money earned by Kyle
Therefore,
Total amount paid in tax = 0.0765 x 282000 = $21573
Are the irrational numbers closed under multiplication?
Answer:
No, irrational numbers are not closed under multiplication.
Step-by-step explanation:
Irrational numbers are the numbers that cannot be demonstrated in the form of a fraction [tex]\frac{x}{y}[/tex]. We can define rational numbers in other ways as well. Irrational numbers are the numbers which when written in decimal form, the decimal expansion does not end. For example √2, √3, etc.
The closed property of multiplication of irrational numbers state that if two irrational numbers are multiplied, then their product is also an irrational number.
Let a and b be two irrational numbers, then a×b = c(c is product of a and b), c should also be an irrational number.
Irrational numbers are not closed under multiplication and this can be illustrated with the help of an example:
√2 × √2 = 2
It is clear that 2 is not an irrational number.
Hence, irrational numbers are not closed under multiplication.
Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading greater than -1.05 in degrees Celsius. (up to four decimal place, please)
Answer: 0.8531
Step-by-step explanation:
Let x be the random variable that represents the readings on scientific thermometers .
Given : The readings on scientific thermometers are normally distributed,
Population mean : [tex]\mu=0^{\circ}\ C[/tex]
Standard deviation : [tex]\sigma=1^{\circ}\ C[/tex]
Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Now, the z-value corresponding to -1.05 : [tex]z=\dfrac{-1.05.-0}{1}=-1.05[/tex]
P-value = [tex]P(x>-1.05)=P(z>-1.05)=1-P(z\leq-1.05)[/tex]
[tex]=1-0.1468591=0.8531409\approx0.8531\text{ (Rounded to four decimal places)}[/tex]
Hence, the probability of the reading greater than -1.05 in degrees Celsius.= 0.8531
A board 18 feet long is cut into two pieces. Express the length of the shorter piece in terns of the length of the longer piece,L?
Answer:
l = 18 - L
Step-by-step explanation:
Since 18 feet board is cut into two pieces L and l.
L + l = 18
Subtracting both sides by L
l = 18 - L
Which difference is about 10?
A. 33.2-28.4
B. 70.9-58.7
C. 42.5-16.8
D. 65.7-65.6
Answer:
D. 65.7-65.6
(the exact difference is 10.1, which is "about" 10)
The difference that is about 10 is 70.9-58.7. The correct option is B. 70.9-58.7
To determine the difference that is about 10, we will evaluate the given expressions one after the other.
The result that is closest to 10 gives the difference that is about 10
For A - 33.2-28.4Evaluating this, we get
33.2-28.4 = 4.8
For B - 70.9-58.7
Evaluating this, we get
70.9-58.7 = 12.2
For C - 42.5-16.8Evaluating this, we get
42.5-16.8 = 25.7
For D - 65.7-65.6
Evaluating this, we get
65.7-65.6 = 0.1
From above, we can observe that from A to D, the answer that is closest to 10 is 12.2
Hence, the difference that is about 10 is 70.9-58.7. The correct option is B. 70.9-58.7
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The hospital pharmacy receives an order for morphine sulfate ¼ gr IM stat. The concentration on hand is 10mg per mL How many mL is needed for the dose?
Answer:
1.5 ml
Step-by-step explanation:
We have been given that the concentration on hand is 10 mg per ml.
We know that gr stands for grains.
We know that 1 gr equals 60 mg.
First of all, we will convert 1/4 gr to mg as:
[tex]\frac{1}{4}\text{ gr}\times \frac{60\text{ mg}}{\text{ gr}}[/tex]
[tex]\frac{1}{4}\times 60\text{ mg}[/tex]
[tex]15\text{ mg}[/tex]
1 ml equals 10 mg. We can set an a proportion as:
[tex]\frac{x}{15\text{ mg}}=\frac{\text{1 ml}}{10\text{ mg}}[/tex]
[tex]\frac{x}{15\text{ mg}}*15\text{ mg}=\frac{\text{1 ml}}{10\text{ mg}}*15\text{ mg}[/tex]
[tex]x=\text{1 ml}*1.5[/tex]
[tex]x=\text{1.5 ml}[/tex]
Therefore, 1.5 ml is needed for the dose.
Is the set \mathbb{Z} a group under the following operations:
a.) a*b = a + b - 1
b.) a*b = a - b + ab
Answer:
a) yes
b) no
Step-by-step explanation:
[tex](\mathbb{Z}, *)[/tex] is a gruop if satisfies the following conditions:
1. If a and b are two elements in [tex]\mathbb{Z}[/tex], then the product a*b is also in [tex]\mathbb{Z}[/tex].
2. The defined multiplication is associative, i.e., for all a,b,c in [tex]\mathbb{Z}[/tex], (a*b)*c=a*(b*c).
3. There is an identity element e such that e*a=a*e=a for every element a in [tex]\mathbb{Z}[/tex].
4. There must be an inverse of each element. Therefore, for each element a of [tex]\mathbb{Z}[/tex], the set contains an element b=a^(-1) such that a*a^(-1)=a^(-1)*a=e.
Let's see if the conditions are satisfied:
a)
1. if x and y are integers then x+y-1=a*y is an integer
2. If x,y and z are integers then
(x*y)*z= (x+y-1)*z= (x+y-1) + z - 1= x +y+z-2,
x*(y*z)= x*(y+z-1)= x + (y+z-1) -1 = x+ y + z -2
Then (x*y)*z=x*(y*z), i.e, * is associative.
3. Let e=1 and b an integer. Observe that
1*b=1+b-1=b and b*1= b + 1 -1= b.
Then e is an identity element.
4. a and integer and b= 2- a. Observe that
b*a= 2-a+a-1= 1 and a*b= a+2-a-1=1,
the b= a^(-1) is the inverse of a.
We conclude that [tex](\mathbb{Z}, *)[/tex] is a group.
b)
1. If x,y and z are integers then
(x*y)*z= (x-y+xy)*z= (x-y+xy) - z + (x-y+xy)z= x -y-z+xy+xz-yz+xyz
x*(y*z)= x*(y-z+yz)= x - (y-z+yz) +x(y-z+yz) = x-y +z + xy -xz -yz+xyz
Then (x*y)*z≠x*(y*z), i.e, * isn't associative.
We conclude that [tex](\mathbb{Z}, *)[/tex] isn't a group.
If a person receive a heritage and plans to invert one part at 9% and $2,000 more that the amount before in an invert less secured that gave 10%. How much the person need toinvert in each interest to win $1150 at year, by interest concept?
Answer:
The person has to invest $5000 at 9% and $7000 at 10%.
Step-by-step explanation:
As stated in the problem, we have an ammount C that the person invest at 9% and an ammount (C+2000) that it is invested at 10%.
To gain $1150 a year, the ammount C needs to satisfy this equation:
[tex]C*0.09+(C+2000)*0.10=1150[/tex]
Applying distributive property,
[tex]0.09C+0.10C+200=1150\\0.19C=1150-200[/tex]
[tex]C=950/0.19\\C=5000[/tex]
So the person has to invest C=$5000 at 9% and (C+2000)=$7000 at 10% to gain $1150 of interest yearly.
graph the function f (x)=x4 -7x2 on the interval x=-3 to x=3 which of the following best describes the graph from left to right
Answer:
when graphing f(x) between x=-3 & x=3, the result is a function that comes from x=-infinite and positive y, crosses the x-axis at (-2.646,0), continues to decrease until (-1.871,-12.25) and then increases until (0,0).
This function is symetrical by the y axis, therefore, after reaching (0,0), f(x) decreases until (1.871,-12.25), starts to increase until it crosses the x axis at (2-646,0) and continues to increase until x=+infinite
Step-by-step explanation:
This funcion appears as a large W, with it's points on (-1.871,-12.25) , (0,0) & (1.871,-12.25)
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 3/4 for the flowers to last the longest. Her cylinder vase has a radius of 4 inches and a height of 10 inches. How much water should Mary pour into the vase ?
Answer: 376.98192 mL
Step-by-step explanation:
We are going to use this equation.
V = π * r² * h
according to the question we have the value for r and h, if you replace the values into the equation we will get following product:
note: also keep in mind that value of π is 3.141516
V = π * r² * h
V = π * (4in)² * (10in)
V = 502.64256 in³
after we can divide this value in 4 equals parts
then we get the following equation:
502.64256 in³ / 4 = 125.66064 in³
after that that you can multiply this value by 3 to get the 3 parts of the cylinder vase for example:
125.66064 in³ * 3 = 376.98192 in³
and this result is the volume of water that we have to pour into the vase
What is the area of the triangle?
A)
60 in2
B)
100 in2
C)
200 in2
D)
400 in2
Answer:
B.) 100 in2
Explanation:
20 x 10 = 200
200 ÷ 2 = 100
B.) 100 in2
Answer: It's b
Step-by-step explanation:
a group of school children consist of 25 boys and 18 girls. how many ways are there:
1. to arrange the children in a row
2. To arrange the children in a row with all the boys next to each other
3. To arrange the children in a row with all the boys next to each other and all the girls next to each other.
4. To choose a chess team of 6 from the group if 1. Anyone can be chosen?
2. Exactly 2 girls must be chosen?
3. At least 2 boys must be chosen?
Answer:
Step-by-step explanation:
1. Number of boys in the group = 25
Number of girls in the group = 18
Total children = 25 + 18 = 43
Number of ways to arrange the children in a way = 43!
2. If we consider all the boys as an individual then number of ways children can be arranged = 19!
Number of ways boys can sit next to each other = 25!
So the number of ways can be arranged = 19!×25!
3. Number of ways boys can sit next to each other = 25!
Number of ways girls can sit next to each other = 19!
Then number of ways to arrange the children in a row with all boys next to each other and all the girls next to each other will be = 2 × 18! × 25!
4. 1. To choose a chess team if anyone can be chosen
= [tex]^{43}C_{6}[/tex]
= 6096454
4. 2. Exactly 2 girls must be chosen then number of ways
= [tex]^{18}C_{2}\times ^{25}C_{4}=1935450[/tex]
4. 3. At least two boys must be chosen
= [tex]^{25}C_{2}\times ^{18}C_{4}+^{25}C_{3}\times ^{18}C_{3}+^{25}C_{4}\times ^{18}C_{2}+^{25}C_{5}\times ^{18}C_{1}+^{25}C_{6}[/tex]
= 5863690
A shuttle launch depends on three key devices that may fail independently of each other with probabilities 0.01, 0.02, and 0.02, respectively. If any of the key devices fails, the launch will be postponed. Compute the probability for the shuttle to be launched on time, according to its schedule.
Answer:
[tex]0.950796[/tex]
Step-by-step explanation:
Given that a shuttle launch depends on three key devices that may fail independently of each other with probabilities 0.01, 0.02, and 0.02, respectively.
Required probability = the probability for the shuttle to be launched on time
= Probability that all three do not fail
Since each key device is independent of the other
we have
prob that all three do not fail = [tex](1-0.01)(1-0.02)(1-0.02)\\=0.99*0.98*0.98\\=0.950796[/tex]
Early in the semester, only 5 grades have been entered. Given the following grades, what is this students current weighted average?
Q1: 100
Q2: 93
IW1: 82
IW2: 83
H1: 80
Answer:
Hence the current weighted average of student = 87.60
Step-by-step explanation:
Grades obtained by student are
Q1= 100
Q2= 93
IW1= 82
IW2= 83
H1= 80
the weighted average = sum of all the grades/ number of subjects
[tex]= \frac{100+93+82+83+80}{5}[/tex]= 87.60
Hence the current weighted average of student = 87.60
Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.) 7.7% compounded weekly.
"rule of 72" yr
exact answer yr
Answer:
Using the rule of 72, the doubling time is 9.35 years.
The exact answer is that the doubling time is 8.89 years.
Step-by-step explanation:
By the rule of 72, we have that the doubling time D is given by:
[tex]D = \frac{72}{Interest Rate}[/tex]
The interest rate is in %.
In our exercise, the interest rate is 7.7%. So, by the rule of 72:
[tex]D = \frac{72}{7.7} = 9.35[/tex].
Exact answer:
The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
So, for this exercise, we have:
We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.
[tex]A = 2P[/tex]
[tex]r = 0.077[/tex]
There are 52 weeks in a year, so [tex]n = 52[/tex]
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]2P = P(1 + \frac{0.077}{52})^{52t}[/tex]
[tex]2 = (1.0015)^{52t}[/tex]
Now, we apply the following log propriety:
[tex]\log_{a} a^{n} = n[/tex]
So:
[tex]\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2[/tex]
[tex]52t = 462.44[/tex]
[tex]t = \frac{462.44}{52}[/tex]
[tex]t = 8.89[/tex]
The exact answer is that the doubling time is 8.89 years.
When considering the normal power demand as reported by a utility company, the power demand at midnight is 1040 MW. During the first five hours, the power demand rises to 1600 MW, and at the eight-hour mark, the power demand rises to 1960 MW. What is the average rate of change of the power demand with respect to time for the period from 5 hours to 8 hours after midnight? 360 MW 282.5 MW/hour 120 MW/hour 1780 MW/hour None of these
Answer:
120 MW/hour
Step-by-step explanation:
The formula of the average rate of change between two points in a function is:
Average rate of change (ARC) = f(x2) -f(x1)/(x2-x1)
Let's think the power demad as a function d(x) depending of the hour of the day, so the variable x= hour of the day.
Now we have:
d(5)= 1600
d(8)= 1960
If we apply the mentioned ARC formula = [d(8)-d(5)] MW/(8-5)hour= (1960-1600)MW/3hour= 360/3=120 MW/Hour
You deposit $27,580.00 in an interest-bearing account. After one year, your accrued interest is $1,442.43.
What is the interest rate of this account?
Principal:
$
27
,
580.00
time:
1
year
Interest:
$
1
,
442.43
r
=
I
P
t
Round your answer to the nearest hundredth of a percent, if necessary.
Answer:
[tex]r=5.23\%[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ years\\ P=\$27,580\\I=\$1,442.43\\r=?[/tex]
substitute in the formula above
[tex]1,442.43=27,580(r*1)[/tex]
Solve for r
[tex]r=1,442.43/27,580[/tex]
[tex]r=0.0523[/tex]
convert to percent
[tex]r=0.0523*100=5.23\%[/tex]
In one country during one year, 804665 women gave birth. Of these women, 3738 gave birth to identical twins. Use these data to estimate how many women, out of a group of 1000 pregnant women, you might expect to give birth to identical twins. Choose the two correct options below. Select one or more: 0 The expected number of women is 5. o The expected number of women is 46. The expected number of women is 465. The calculation is 3738 x 1000 800927 3738 x 1000 804665 The calculation is
Answer:
The expected number of women expected to give birth to identical twins is 5.
The calculation is:
[tex]x = \frac{3738*1,000}{804,665}[/tex]
Step-by-step explanation:
This is a proportionality problem, that can be solved by a rule of three. Here, the measures(the number of women that gave birth to identical twins and the nuber of women that gave birth) are directly related. It means that we have a direct rule of three(cross multiplication).
The problem states that of the 804,665 women that gave birth, 3,738 gave birth to identical twins. It asks of 1,000 women, how many are expected to give birth to identical twins? So, 3,738 of 804665 is how much of 1,000?
3,738 - 804,665
x - 1,000
[tex]804,665x = 3738*1,000[/tex]
[tex]x = \frac{3738*1,000}{804,665}[/tex]
[tex]x = 4.64[/tex]
Rounding up, the expected number of women expected to give birth to identical twins is 5.
whats the sum of two rational numbers
Answer:
The sum of two rational numbers is always a rational number.
Step-by-step explanation:
Rational Number is the number of the form [tex]\frac{p}{q}[/tex], q≠0 and p and q are integers.
Further, when we add or subtract two rational number it is always a rational number. Example:
[tex]\dfrac{4}{64} +\dfrac{25}{4} = \dfrac{4+25\times 16}{64} \\= \dfrac{4+400}{64} = \dfrac{404}{64} =\dfrac{101}{16}[/tex]
which is also a rational number.
Thus, the sum of two rational numbers is always a rational number.
To complete your spring schedule, you must add Calculus and Physics. At 9:30, there are three Calculus sections and two Physics sections; while at 11:30, there are two Calculus sections and three Physics sections. How many ways can you complete your schedule if your only open periods are 9:30 and 11:30?
Answer:
You can complete your schedule in 13 different ways.
Step-by-step explanation:
You initially have two general options:
1) You can take Calculus at 9.30 and Physics at 11.30 OR
2) You can take Physics at 9.30 and Calculus at 11.30.
Let's examine each option:
1) If you take Calculus at 9.30 you'd have 3 options (since there are 3 Calculus sections), and then you'd have 3 options at 11.30 to take Physics. This makes 3 x 3 = 9 options.
2) If you choose to take Physics at 9.30, you'd have 2 options and then you'd have 2 Calculus options at 11.30. This makes 2x2 = 4 options.
Since you can take either option one OR two, we will sum up both results, and therefore you have 9 +4 = 13 different ways to complete your schedule.
Which inequality statement best describes the probability of event (P) ?
0≤P≤1
1≤P≤2
.1≤P≤.9
0≤P≤.99
Answer:
[tex]0\le P\le 1[/tex]
Step-by-step explanation:
The probability of an event is a number describing the chance that the event will happen.
Definition: The probability of an evant is
[tex]P=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]
1. An event that is certain to happen (Number of favorable outcomes = Number of all possible outcomes) has a probability of 1.
2. An event that cannot possibly happen (Number of favorable outcomes = 0) has a probability of 0.
3. If there is a chance that an event will happen, then its probability is between 0 and 1.
Thus,
[tex]0\le P\le 1[/tex]
The probability of an event occurring is always between 0 and 1, inclusive. Therefore, the correct inequality is 0≤P≤1.
Explanation:The probability of an event (P) in a standard probability model is always defined between 0 and 1. Here, 0 represents the impossibility of the event, whereas 1 represents the certainty of the event. Therefore, the inequality that best describes the probability P is 0≤P≤1. Any other range for probability does not fit into the standard probability model used in mathematics.
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A student has a GPA of 2.25 after accumulating 20 credit hours. If she is enrolled in 17 additional credit hours and desires a 2.9 GPA after those additional courses, what minimum GPA in those additional hours would she need to earn? It's OK if you end up with a crazy number like something greater than a 4.0. That just means this student can't quite get there in that number of hours. You can come back to this question and correct your answer at any time before you submit the entire CW/IW module.
Answer:
3.66
Step-by-step explanation:
Having a 2.9 GPA means there was a certain quantity of points divided by a quantity of credit hours.
In this case 37 hours because of the 20 given to obtain 2.25 and 17 additional hours to get 2.9
So to know the points to get 2.9, we multiply 2.9 by the hours (37)
gpa=[tex]\frac{points}{hours}[/tex]
gpa*hours= points
[tex]2.9*37= 107.3 points[/tex]
Now we need to find out how many points were given in 20 credit hours to get 2.25;
we do a similar calculation by multiplying 2.25 by the credit hours given to obtain that gpa.
gpa*hours=points
[tex]2.25*20=45[/tex]
Then from 45 points to get 107.3 we need to know the difference
[tex]107.3-45=62.3[/tex]
and because those points are needed in 17 additional credit hours, we make a division and we get
[tex]gpa=\frac{points}{hours}[/tex]
[tex]gpa=\frac{62.3}{17}=3.66[/tex]
So the student needs to make a 3.66 gpa minimum in order to improve her current 2.25 gpa to 2.9
The student needs to achieve a minimum GPA of 3.65 over the 17 additional credit hours to reach their goal of a 2.9 overall GPA, showing the importance of planning and effort.
Explanation:To calculate the minimum GPA needed in the additional 17 hours for the student to achieve an overall GPA of 2.9 after already earning a 2.25 GPA over 20 credit hours, we will use a weighted average formula. Currently, the student has accumulated (2.25 * 20) = 45 quality points from the 20 credit hours. To reach a 2.9 GPA after adding 17 more credit hours, the student will need a total of (20 + 17) * 2.9 = 107.1 quality points.
Subtracting the quality points already earned from the total needed gives us 107.1 - 45 = 62.1 quality points needed over the 17 additional hours. Therefore, the minimum GPA required across these hours is 62.1 / 17 ≈ 3.65. This calculation indicates that, even though the target seems high, clearly understanding the effort needed can help in planning the study strategy accordingly.
Two exterior angles of a triangle equal 100° and 150°. Find all the interior angles.
Answer:
The interior angles for this triangle are 80º, 30º and 70º.
Step-by-step explanation:
The sum of a interior angle with it's respective exterior angle is also always 180º.
So, for the exterior angle that is 100º, we can find the first interior angle of the triangle
100º + A1 = 180º
A1 = 180º - 100º
A1 = 80º
The first interior angle of this triangle is A1 = 80º;
For the exterior angle that is 150º, we can find the second interior angle of the triangle.
150º + A2 = 180º
A2 = 180º - 150º
A2 = 30º
The second interior angle of this triangle is A2 = 30º.
From here, to find the third interior angle, we apply the following definition
The sum of the three interior angles of a triangle is always 180º.
So:
A1 + A2 + A3 = 180º
80º + 30º + A3 = 180º
110º + A3 = 180º
A3 = 180º - 110º
A3 = 70º
The third interior angle of this triangle is A3 = 70º.
The interior angles for this triangle are 80º, 30º and 70º.
A can of soft drink at room temperature is put into the refrigerator so that it will cool. Would you model the can of soft drink as a closed system or as an open system? Explain.
Answer:
Open system
Step-by-step explanation:
We are putting can of soft drink in the refrigerator so that it will cool down. As we can see the can of soft drink cool down when it releases its heat to the refrigerator. As it can exchange its temperature with it's surrounding so it will be an open system. If it would be a closed system then it won't be able to release its heat to the surrounding so it won't be able to cool down.
A recipe calls for 2 tsp of salt, 1 tsp of pepper, and 4 tsp of garlic powder. How much pepper and garlic powder would you need for a larger batch if you are using 15 tsp of salt?
Answer:
amount of pepper required= 7.5 tsp
amount of garlic powder required = 30 tsp
Step-by-step explanation:
Given,
amount of salt used for small batch of the recipe = 2 tsp
amount of pepper used for small batch of the recipe = 1 tsp
amount of garlic powder used for small batch of the recipe = 4 tsp
amount of salt used for the larger batch = 15 tsp
= 2 x 7.5 tsp
= amount of salt used for small batch the recipe x 7.5
So,
the amount of pepper needed for the larger batch= 7.5 x amount of pepper used for the small batch of recipe
= 7.5 x 1 tsp
= 7.5 tsp
the amount of garlic powder needed for the larger batch= 7.5 x amount of garlic powder used for the small batch of recipe
= 7.5 x 4 tsp
= 30 tsp
Final answer:
To adjust the recipe for 15 tsp of salt, you will need 7.5 tsp of pepper and 30 tsp of garlic powder, by applying a scaling factor based on the original recipe proportions.
Explanation:
The question asks how much pepper and garlic powder are needed if a recipe is scaled up to use 15 tsp of salt, from an original recipe that calls for 2 tsp of salt, 1 tsp of pepper, and 4 tsp of garlic powder. To solve this, we first determine the scaling factor for the recipe by dividing the new quantity of salt by the original quantity of salt, which is 15 tsp ÷ 2 tsp = 7.5. Next, we apply this scaling factor to the measurements for pepper and garlic powder.
Pepper needed = 1 tsp (original amount) x 7.5 (scaling factor) = 7.5 tsp of pepper.
Garlic Powder needed = 4 tsp (original amount) x 7.5 (scaling factor) = 30 tsp of garlic powder.
An article reports, "attendance dropped 4% this year, to 300. What was the attendance before the drop to the nearest whole number)?
Answer:
312
Step-by-step explanation:
Let the attendance before the drop be x
Now we are given that attendance dropped 4% this year
So new attendance = [tex]x-4\% \times x[/tex]
= [tex]x-\frac{4}{100} \times x[/tex]
= [tex]\frac{96x}{100}[/tex]
We are also given that attendance dropped 4% this year, to 300
So, [tex]\frac{96x}{100}= 300[/tex]
[tex]x= 300 \times \frac{100}{96}[/tex]
[tex]x=312.5[/tex]
Hence the attendance before the drop was 312
width of rectangle is 4 inches, area 32 inches. find the length of rectangle?
Answer: 8 inches
Step-by-step explanation:
We know that the area of a rectangle is given by :-
[tex]A=l\times w[/tex], where l is length and w is width of the rectangle.
Given : The width of rectangle : w=4 inches
The area of rectangle : A =32 inches.
Then substitute these values in the above formula, we have
[tex]32=l\times4\\\\\Rightarrow\ l=\dfrac{32}{4}=8[/tex]
hence, the length of rectangle = 8 inches.
A student received the following grades last semester. Find the student's semester grade point average. An A is Algebra (3 credits), a B in History ( 3 credits), A in sociology ( 3 credits) a D in English ( 3credits) and a C in seminar ( 2credits). An A is worth 4 points, a B is worth 3 points a C is worth 2 points and a D is worth 1 point.
Answer:
If it is a simple average, the average is 2.8 points.
If it is a weigthed-by-credits average, the average is 2.86 points.
Step-by-step explanation:
To calculate the simple average of this 5 grades, we sum all the points and divide it by 5:
In Algebra: A = 4 points
In History: B = 3 points
In Sociology: A = 4 points
In English: D = 1 point
In Seminar: C = 2 points
Average = (4+3+4+1+2)/5 = 2.8 points
If the average is weighted by the credits, we must add each score multiplied by the credits and, in total, divide it by the total amount of credits.
[tex]weighted-average = \sum(points_i*credits_i)/\sum(credits_i)\\\\weighted-average = (4*3+3*3+4*3+1*3+2*2)/(3+3+3+3+2)\\weighted-average = 40 / 14 = 2.86[/tex]
Final answer:
To find the student's semester GPA, assign points to each grade based on the grading scale, multiply by the credits for each course, sum these totals, and divide by total credit hours. The student's GPA is approximately 2.86.
Explanation:
To calculate the student's semester grade point average (GPA), we first multiply each grade by its respective credit hours, then sum these numbers, and finally divide by the total number of credit hours. Here is the breakdown:
Algebra: A (4 points) × 3 credits = 12
History: B (3 points) × 3 credits = 9
Sociology: A (4 points) × 3 credits = 12
English: D (1 point) × 3 credits = 3
Seminar: C (2 points) × 2 credits = 4
Next, we add these totals: 12 + 9 + 12 + 3 + 4 = 40. The sum of the credit hours is 3 + 3 + 3 + 3 + 2 = 14. The GPA is calculated as the total points divided by the total credit hours, which is:
GPA = Total Points / Total Credit Hours = 40 / 14 ≈ 2.86
Therefore, the student's semester GPA is approximately 2.86.