Answer:
27/40
Step-by-step explanation:
The percentage 67.5% as a fraction in simplest form is 16.875/25.
To convert 67.5% to a fraction in simplest form, we divide the percentage by 100 and simplify if possible.
67.5% can be expressed as 67.5/100.
To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
67.5/100 = (67.5 ÷ 2) / (100 ÷ 2)
= 33.75/50
We can simplify this fraction further by dividing both the numerator and denominator by their GCD, which is 2:
33.75/50 = (33.75 ÷ 2) / (50 ÷ 2)
= 16.875/25
Since there is no common factor other than 1 between the numerator and denominator, the fraction 16.875/25 is already in its simplest form.
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7. The University of Texas at Austin has three times as many students enrolled as the University of
Miami. The University of California, Berkley has 3,000 more than twice the number of students as
the University of Miami. If the three schools have a total enrollment of 96,000 students, what is the
enrollment at each school?
a. Describe what the variables represent:
===xyz
b. Write the system of linear equations:
c. Write the Augmented Matrix for the system of linear equations then solve using the Gauss-Jordan
Elimination Method. Show all row operations and at least 5 of the resulting matrices. Use proper
notation. Write the solution as an ordered triple, if appropriate.
d. Now, answer the question in a complete sentence with proper grammar and correct spelling:
What is the enrollment at each school?
The variables x, y, and z represent the number of students enrolled at the University of Texas at Austin, the University of Miami, and the University of California, Berkley, respectively.
x = 3y ,z = 2y + 3000 and x + y + z = 96000 are the linear equations.
On solving the matrix , we get that x = 9000 y = 3000 and z = 31500.
The enrollment at each school is 9,000 for the University of Texas at Austin, 3,000 for the University of Miami, and 31,500 for the University of California, Berkeley.
b. Let's write the system of linear equations based on the given information:
x = 3y (Equation 1)
z = 2y + 3000 (Equation 2)
x + y + z = 96000 (Equation 3)
c. To solve this system of equations using the Gauss-Jordan Elimination Method, we need to write the augmented matrix and perform row operations. The augmented matrix is:
[1 -3 0 | 0]
[0 1 2 | 3000]
[1 1 1 | 96000]
Now, let's perform row operations to get the reduced row-echelon form:
1. R3 = R3 - R1 (subtracting row 1 from row 3)
2. R3 = R3 - R2 (subtracting row 2 from row 3)
3. R3 = R3/2 (dividing row 3 by 2)
4. R2 = R2 - 2R1 (subtracting 2 times row 1 from row 2)
5. R1 = R1 + 3R2 (adding 3 times row 2 to row 1)
After performing these row operations, we get the following resulting matrices:
[1 0 3 | 9000]
[0 1 2 | 3000]
[0 0 1/2 | 31500]
From the last matrix, we can determine the values of x, y, and z:
x = 9000
y = 3000
z = 31500
Therefore, the enrollment at each school is as follows:
The University of Texas at Austin has 9,000 students enrolled.
The University of Miami has 3,000 students enrolled.
The University of California, Berkley has 31,500 students enrolled.
d. The enrollment at each school is 9,000 for the University of Texas at Austin, 3,000 for the University of Miami, and 31,500 for the University of California, Berkeley.
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Un caracol avanza a una velocidad de 3 metros por hora y cada dos horas se detiene por 6 minutos. ¿En cuánto tiempo recorrerá 21 metros?
The time needed to advance a distance of 21 meters is given as follows:
7 hours and 18 minutes.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
Considering the pattern in this problem, we have that:
2 hours -> 6 meters.4 hours and 6 minutes -> 12 meters.6 hours and 12 minutes -> 18 meters.7 hours and 18 minutes -> 21 meters.More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
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Eddie is reading a novel gor englidh class he has read 24 out of 60 pages about what percent of the book has he read
Answer: 40%
Step-by-step explanation: We can also work this out in a simpler way by first converting the fraction 24/60 to a decimal. To do that, we simply divide the numerator by the denominator:
24/60 = 0.4
Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:
0.4 x 100 = 40%
Hi, I need help with this question, please
The interquartile range for this distribution is 23.
How to calculate the interquartile range of a grouped data set?In Mathematics, the first quartile and third quartile of a grouped data set with class interval can be calculated by using this formula;
First quartile (Q₁) = [tex]L+(\frac{\frac{N}{4} -F_c}{F_q} )C[/tex]
Third quartile (Q₃) = [tex]L+(\frac{\frac{3N}{4} -F_c}{F_q} )C[/tex]
Where:
L is the lower class boundary (LCB) of the quartile class.N represents the total frequency of the data set.C is the class width.Fc is the cumulative frequency before the quartile class.Fq is the frequency of the quartile class.For the first quartile (Q₁), we have:
First quartile (Q₁) = 1/4 × 100 = 25th observation.
[tex]20+(\frac{\frac{100}{4} -19}{30} ) \times 10\\\\20+(\frac{25-19}{30} ) \times 10[/tex]
First quartile (Q₁) = 20 + 2 = 22.
For the third quartile (Q₃), we have:
Third quartile (Q₃) = 3/4 × 100 = 75th observation.
[tex]40+(\frac{\frac{300}{4} -70}{10} ) \times 10\\\\40+(\frac{75-70}{10} ) \times 10[/tex]
Third quartile (Q₃) = 40 + 5 = 45.
Mathematically, the interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 45 - 22
Interquartile range (IQR) of data set = 23.
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Which statements below are true about the graph of the function f(x) = 1/x+2?
I. The graph represents a rational function
II. The graph has a vertical asymptote at x = -2
III. The graph has a y-intercept at ( 0, 12 )
IV. The graph is continuous
A. All statements are true
B. I, II and III only
c. IV only
d. I and II only
Answer:
The correct answer is D. I and II only
Step-by-step explanation:
I. The graph represents a rational function.
This is true because the function is a ratio of two polynomials.
II. The graph has a vertical asymptote at x = -2.
This is true because the denominator of the function is equal to 0 at x = -2.
III. The graph has a y-intercept at ( 0, 12 ).
This is false because the function is undefined at x = 0.
IV. The graph is continuous.
This is false because the function has a vertical asymptote at x = -2.
What is the distance between A and C in this picture
Answer: 8
Step-by-step explanation:
I think it's 8 but im not so sure
The point (5, -2) is translated by (x,y)→
(x - 4, y + 5), then rotated 90°
clockwise. What are the coordinates of the final image?
Answer:
(1,3)
Step-by-step explanation:
hope it's help ful
I need help asap!!!!!!!!!!!!! I will give brainiest!!
Answer: 11 weeks
Step-by-step explanation:
The answer is 11 weeks when simplified.
what is wrong in this question???
You failed to start the end points of the frequency polygon from a x-value of 0.
How to draw a frequency polygon?First of all, we would determine the midpoint of the data set as follows:
0 < t ≤ 5 = (0 + 5)/2 = 2.5.
5 < t ≤ 10 = (10 + 5)/2 = 7.5.
10 < t ≤ 15 = (10 + 15)/2 = 12.5.
15 < t ≤ 20 = (15 + 20)/2 = 17.5.
In order to draw a frequency polygon for the given data set, we would construct the frequency table as follows:
Time, t minutes Frequency_
0 < t ≤ 5 7
5 < t ≤ 10 8
10 < t ≤ 15 6
15 < t ≤ 20 4
Finally, we would connect the end points of the data set on the frequency polygon by starting from a x-value of 0 as shown in the image attached below.
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The conventional algorithm for evaluating a polynomial anxn + an-1xn-1 + … + a1x + a0 at x = c can be expressed in pseudocode by
Procedure polynomial (c, a0, a1, …, an : real numbers)
power :=1
y :=a0
for i := 1 to n
begin
power := power * c
y := y + ai * power
end {y = ancn + an-1cn-1 +…+ a1c +a0}
where the final value of y is the value of the polynomial at x = c.
a. Evaluate 3x2 + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.
b. Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)
Answer:
a.) value of polynomial at x=2 is 15
b,) exactly 2 multiplications and 1 addition are used to evaluate the polynomial
Step-by-step explanation:
a.)
at x = 2,
3x²+x+1
with n = 2, a₀=1, a₁=1, a₂=3 with c=2,
firstly we set power =1
y=1
for the first time through the loop;
we have i = 1
the power increases to 2
y = 1+1*2
= 3
i =2
then going through the loop for the last time
power = 2x2 = 4
y = 3+(3*4)
= 15
we stop here because polynomial is of degree 2
b.
while passing through the loop, each pass requires that we do 2 multiplications and 1 addition. so for the for loop we have n iterations with total being 2n multiplications and n additions.
PLEASe I’m BEGGING YOU IF YOU KNOW THIS 100% percent and get it correct I will Iove u forever even tho idk you but PLEASE
Answer:
The goal here is to simplify your answer, and so in order to do that, you must combine like terms.
Step-by-step explanation:
-x+ -9x= -10x
-7+6= -1
-10x-1 is the answer, hope this helps
John is 4 years younger than Mary, write an equation using x=John's age, M=Mary's age, and the number 4
What number should be added to both sides of the following equation to solve for x? x - 7 = 4 3 4 7 11
Answer:
The answer is 4
Step-by-step explanation:
This is because if u add 4 to seven it equals eleven so that is ur answer.
If the hypothenuse of a right
triangle measures 17 meters,
and one leg measures 15 meters,
what is the length of the other
leg?
15
PLS FAST ITS DUE IN 5 MINS
Answer:
b = 8
Step-by-step explanation:
a² + b² = c²
15² + b² = 17²
225 + b² = 289
b² = 64
√b² = 64
b = 8
On a long hike, Yousif drank 5 pints of water. How much did he drink in quarts?
Answer:2.5 quarts
Step-by-step explanation:
Answer: 2.5 quarts
Divide the the volume by 2 :)
How will the volume of a cube change if its edge becomes twice as long; 3 times as long; 10 times as long; n times as long?
Let, initial side is a.
When side is n times long, new side na.
Initial volume, [tex]V_i=a^3[/tex]
Final volume, [tex]V_f=(na)^3=n^3a^3[/tex]
Change in volume, [tex]V_f-V_i=\Delta V =a^3(n^3-1)[/tex]
For, n = 2 :
[tex]\Delta V = 7a^3[/tex]
n = 3 :
[tex]\Delta V = 26a^3[/tex]
n = 10 :
[tex]\Delta V = 999a^3[/tex]
Hence, this is the required solution.
Open Ended Write a statement using ratio language
that could describe a part-to-part ratio of 4:7.
Answer:
the ratio is 4:7 which would mean that there are well lets just say like 4 boy and 7 girls
Step-by-step explanation:
For every 4 cups of sugar, he uses 7 cups of flour is the statement which is an example to describe the ratio 4:7
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The given ratio is 4:7.
This can also be written as in the form of fraction 4/7
John is baking cookies. For every 4 cups of sugar, he uses 7 cups of flour is the statement which is an example to describe the ratio 4:7.
In a dance competition, for every 4 boys there are 7 girls.
Hence, For every 4 cups of sugar, he uses 7 cups of flour is the statement which is an example to describe the ratio 4:7.
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What is the area of parallelogram #1:
15 square units
24 square units
20 square units
16 square units
22 square units
What is the area of parallelogram #2:
14 square units
16 square units
18 square units
20 square units
32 square units
The area for each parallelogram in this problem is given as follows:
Parallelogram #1: 20 square units.Parallelogram #2: 18 square units.How to obtain the area of a parallelogram?The area of a parallelogram is given by the multiplication of the base of the parallelogram by the height of the parallelogram, that is:
A = bh.
The dimensions for parallelogram 1 are given as follows:
[tex]\sqrt{(2 - 0)^2 + (6 - 2)^2} = \sqrt{20} = 2\sqrt{5}[/tex][tex]\sqrt{(4 - 0)^2 + (0 - 2)^2} = \sqrt{20} = 2\sqrt{5}[/tex]Hence the area is given as follows:
[tex]A = (2\sqrt{5})^2 = 4 \times 5 = 20[/tex]
The dimensions for parallelogram 2 are given as follows:
[tex]\sqrt{(2 - 0)^2 + (-2 - 0)^2} = \sqrt{8} = 2\sqrt{2}[/tex][tex]\sqrt{(2 - 0)^2 + (-8 - (-2))^2} = \sqrt{40} = 2\sqrt{10}[/tex]Hence the area is given as follows:
[tex]2\sqrt{2} \times 2\sqrt{10} = 4\sqrt{20} = 18[/tex]
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What is the equation of the line that passes through the point (4, -8) and has a
slope of 1/2
Answer:
y=1/2x-10
Step-by-step explanation:
y=1/2x+b
-8=1/2(4)+b
-8=2+b
-10=b
y=1/2x-10
What is the answer to this equation? 12m-4=4m+12
Answer:
m=2
Step-by-step explanation:
12m-4=4m+12
12m-4m=12+4=16
8m=16
m=16/8=2
A train travels at 75 miles per hour. What equation that compares the time (t) with the distance (d)?
Answer: d = 75t
Step-by-step explanation: The rate of change is 75.
What is the answer for
9.85÷1.25
Answer:
7.88
Step-by-step explanation:
if m angle TOK = 49° what is the measure of the angle supplement of TOK?
Answer:
67
Step-by-step explanation:
The measure of the angle supplement of TOK is 131°.
What is a supplementary angle?Supplementary angles refer to the pair of angles that always sum up to 180°. These two angles are called supplements of each other.
Now the given angle is,
m TOK = 49°
Let the supplement of 49° be x.
Now, 49° + x = 180°
Taking alike terms together we get,
⇒ x = 180° - 49°
Solving we get,
⇒ x = 131°
which is the required supplement of TOK.
Thus, the measure of the angle supplement of TOK is 131°.
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A pizza parlor charges $0.75 for each vegetable topping and $1.50 for each meat topping. You want at least five toppings on your pizza.
You have $10 to spend on toppings. Which system of inequalities models this situation where v represents the number of vegetable
toppings and m represents the meat toppings.
Answer attached hope it helps you
If 3b – (6 – b) = –22, find the value of 7b.
Answer:
Step-by-step explanation:
first solve for b:
distribute the negative sign over the parentheses so:
3b-6+b=-22
combine like terms:
3b+b=-22+6
4b=-16
b=-4
2. Plug in the value of b
7b (replace b with -4)
7(-4)
=-28
if a car can travel 45 miles in 30min, how far will the car tavel in 2.5 hours?
Answer:
180 miles in 2.5 hours
Step-by-step explanation:
45 times 4 makes 180.
Answer:
Step-by-step explanation:
225
An executive for a large national restaurant chain with multiple locations in each of 513 counties wants to personally sample the cleanliness of the chain's restaurants throughout the country by visiting restaurants. The executive wants a good-quality sample but wants to minimize travel time and expenses. Which of the following sampling methods would b most appropriate? Select the correct answer below:
A. Obtain a convenience sample by visiting the 100 restaurants that are closest to the executive's office.
B. Obtain a systematic sample by selecting every 20th restaurant from a list that orders all restaurants by date of opening
C. Obtain a stratified sample by visiting I randomly selected restaurant ik every county.
D. Obtain a cluster sample by randomly selecting 20 counties and visiting every restaurant within those counties.
Answer:
D. Obtain a cluster sample by randomly selecting 20 counties and visiting every restaurant within those counties.
Step-by-step explanation:
Since this executive wants to minimize cost and expenses he should use a cluster sample of 20 counties and using the selected counties as a representative of the whole. Cluster sampling is a good and useful way of doing market research. It is more economical than other sampling methods and as the executive cannot get information on the whole population, he would be able to get information from the clusters.
Based on this activity, what is the minimum amount of information you need to define the shape and size of the triangle? How does this information establish congruency between two or more triangles
Answer:Typically 2 sides and 1 angle need to be given in order to determine a unique triangle. Alternatively 1 side and 2 angles, or the Cartesian coordinates of three vertices, or the area, base, and height. In any case 3 pieces of information.
Step-by-step explanation:
Answer:
You can establish the size and shape of a triangle if you know two angle measurements and the length of the side between the angles (ASA). Two or more triangles are congruent if their corresponding parts coincide through the ASA criterion.
Mr. Sanchez is reading a biography. On Day 1 he had 225 pages left to
read. He plans to read 15 pages each day until he finishes the book. Write
an explicit function to represent the number of pages he has left to read.
Use the function to find the number of pages he will have left on Day 6.
(Only put numerical value as your answer) *
Write the whole number that correctly completes the word problem:
During a 24-hour day, most people spend 2/3 the time awake. This amounts to how many
hours awake.
Answer:
2/3(two thirds) of the 24 hour day awake, amounts to 24 x 2 / 3 hours awake which is equal to 16 hours awake
Step-by-step explanation:
24 x 2/3
there are many ways to evaluate this mentally, if you know 8x3=24, for instance you can multiply top and bottom of 2/3 by 8 yo gey 24 x 16/24 which is 16 hours
