Let the number of students who take the bus home be x.
Determine the value of x as ratio of number of students who take the bus home to total number of student is equal.
[tex]\begin{gathered} \frac{86}{100}=\frac{x}{1200} \\ x=\frac{86\cdot1200}{100} \\ =1032 \end{gathered}[/tex]Answer: 1032 students.
Order the angles of the triangle from smallest to biggest T R 12 addre S
It's important to know that each side is related to its angle in front. In other words, the greatest side has the greatest angle in front, and so on.
Having said that, the order of the angles from least to greatest is
[tex]\begin{gathered} 6<11<12 \\ \angle S<\angle R<\angle T \end{gathered}[/tex]Therefore, the order is S, R, and T.what is the absolute value of -435 and 72
The absolute value of 72 is the distance between 72 and 0 on a number line.
There will be 72 point on the number line if we count. So,
Campbells wants to try and sell their soup in boxes rather than cans. The originalcans have a height of 6 inches and a diameter of 4 inches. If the boxes can only be 2inches deep, 4 inches wide and the keep the volume the same, what is the height ofthe new rectangplar box?
Given
Original cans
Height of 6 inches
Diameter of 4 inches
New boxes
2 inches deep
4 inches wide
Same volume
Procedure
Now let's calculate the volume of the soup cans.
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(2)^2(6) \\ V=75.36\text{ cubic inches} \end{gathered}[/tex]Now let's calculate the volume of the boxes
[tex]\begin{gathered} V=2\cdot4\cdot h \\ V=8h \end{gathered}[/tex]Now we must equal the volume of the cans and then calculate the height.
[tex]\begin{gathered} 75.36=8h \\ h=\frac{75.36}{8} \\ h=9.42\text{ inches} \end{gathered}[/tex]The height of the boxes must be equal to 9.42 inches.
A. Substitute the x-values shown to the right into y = xand y = |x| to find several points on their graphs. Usethe probe to check your work.
For the function y=x we just have to replace the values in the table for the x so:
[tex]\begin{gathered} -3\to x=-3 \\ -2\to x=-2 \\ -1\to x=-1 \\ 0\to x=0 \\ 1\to x=1 \\ 2\to x=2 \\ 3\to x=3 \end{gathered}[/tex]and for y = |x| we have to change all the negative values for positive:
[tex]\begin{gathered} -3\to\mleft|x\mright|=3 \\ -2\to|x|=2 \\ -1\to|x|=1 \\ 0\to|x|=0 \\ 1\to|x|=1 \\ 2\to|x|=2 \\ 3\to|x|=3 \end{gathered}[/tex]Two systems of equations are given below.For each system, choose the best description of its solution.If applicable, give the solution.System AThe system has no solution.The system has a unique solution:3x + 5y = 112x + 5y=4(x, y) = (1,5The system has infinitely many solutions.System BThe system has no solution.The system has a unique solution:y = 3x + 7y = 3x + 4(x, y) = (2, 2)The system has infinitely many solutions.
We are given the following system of equations:
[tex]\begin{gathered} 3x+5y=11,(1) \\ 2x+5y=4,(2) \end{gathered}[/tex]We can solve this system of equations using the method of elimination. To do that we will multiply equation (2) by -1:
[tex]-2x-5y=-4,(3)[/tex]Now we add equations (1) and (3):
[tex]3x+5y-2x-5y=11-4[/tex]Adding like terms:
[tex]x=7[/tex]Now we replace the value of "x" is equation (1):
[tex]\begin{gathered} 3(7)+5y=11 \\ 21+5y=11 \end{gathered}[/tex]Now we subtract 21 to both sides:
[tex]\begin{gathered} 5y=11-21 \\ 5y=-10 \end{gathered}[/tex]Dividing both sides by 5:
[tex]\begin{gathered} y=-\frac{10}{5} \\ y=-2 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex](x,y)=(7,-2)[/tex]For the second system of equations:
[tex]\begin{gathered} y=3x+7,(1) \\ y=3x+4,(2) \end{gathered}[/tex]These equations represent two lines with the same slope, and therefore, parallel lines. Since they are parallel lines this means that the system has no solutions.
you have the numbers 1-24 written on slips of paper. If you choose one slip at random, what is the probability that you will not select a number which divisible by 3?a. 1/3b. 2/3c. 5/8d. 3/8
24 is divisible by 3
21 is divisible by 3
18 is divisible by 3
15 is divisible by 3
12 is divisible by 3
9 is divisible by 3
6 is divisible by 3
3 is divisible by 3
8 numbers are divisible by 3
Total numbers: 24
24-8 = 16 numbers are not divisible by 3
Divide the number that are not divisible by 3 , by the total numbers:
16 /24 = 2/3
A family is driving home from Georgia. The graph shows the distance away 1 point from home, in miles, as a function of time, in hours. Use the graph to estimate the average rate of change from t=0 to t=7.2. **Round answer to 1 decimal place. ***
Basically we need to find the slope:
[tex]\begin{gathered} avg=\frac{f(b)-f(a)}{b-a} \\ \text{Where:} \\ a=0 \\ b=7.2 \\ f(a)=420 \\ f(b)=0 \\ avg=\frac{0-420}{7.2-0}=\frac{-420}{7.2}=-\frac{175}{3}\approx-58.33 \end{gathered}[/tex]Mrs. Roberts bought 4 student movietickets and one adult ticket that cost $12.Write an expression to represent the totacost of the tickets. Let s represent eachstudent ticket
Total cost = 4s+12
student's ticket price = s
Number of students tickets= 4
Adult's tickets price = $12
Number of Adult's tickets = 1
Total cost = (number of students tickets x price of each student's ticket) + ( number of adult tickets x price of each adult ticket)
Total cost of the tickets (y)= 4s + 1(12)
y = 4s+12
Tell which choice, 100, 500, or 1,000, is the best estimate of the solution.39.4x = 37,627a. 1,000b.500c.100Please select the best answer from the choices providedΑВС
39.4 x = 37627
Divide both sides by 39.4
[tex]\begin{gathered} \frac{39.4x}{39.4}=\frac{37627}{39.4} \\ x=955 \end{gathered}[/tex]955 is nearest to 1000 than 500 or 100
Then the best estimate is 1000
The answer is A
The lenath of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of .7 minutes. What is the probability that a conversation lasts longer than 6 minutes?
To solve this problem we can use a z-table. First, we convert our score to a z-score using the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where mu represents the mean and sigma represents the standard deviation.
Using this formula in our problem, we have:
[tex]z=\frac{6-5}{0.7}=\frac{10}{7}\approx1.429[/tex]This z-score represents the position where the phone call is equal to 6 minutes. On a z-table, we're going to find the area between the mean and this z-score, since we want the probability that a conversation lasts longer than 6 minutes, we want the area above it. To calculate this area, we're going to subtract the value given on the z-table from 0.5.
The value on the z-table is:
Then, our probability is:
[tex]P(x>6)=0.5-0.4236\approx0.077[/tex]The answer is 0.077.
You poured 1/4 of the juice from a 2-liter bottle while serving guests at a party. How much juice, in liters, is still left in the bottle?
How much juice was used?
How much is left?
Answer:
1.5 litters is left and 0.5 litters was used
Step-by-step explanation:
2 litters divided by 4 = 0.5 litters and you can do the rest of the math if needed
I need help solving theses 3 problems I don't understand and need help.
.
From the image;
The two points are (-5, 3) and (-2,-3)
The distance between two points is given by:
[tex]D=\sqrt{(x_2-x_2)^2+(x_2-x_2)^2}[/tex]On substitution
[tex]\begin{gathered} D=\sqrt{(-2--5)^2+(-3-3)^2} \\ \\ D=\sqrt{(3)^2+(-6)^2} \\ \\ D=\sqrt{45} \\ D=6.71units \end{gathered}[/tex]Therefore the distance between two points on the graph is 6.71units
I need to know the answer to this question please
Answer:
Explanation:
Given:
[tex]3)\text{ }(32\div16)\div4\text{ = 32 }\div\text{ \lparen16}\div4)[/tex]To find:
the property demonstrated in the equation
Associative property is in the form:
(a + b) + c = a + (b + c)
The left side = right side
[tex]\begin{gathered} (32\div16)\div4\text{ = 32 }\div\text{ \lparen16}\div4) \\ Associative\text{ property was applied but the left side is not equal to the right side} \end{gathered}[/tex]That is why associative priperty is used for addition and multiplication
Find the perimeter (or circumference) and area of the figure. (Where necessary, use 7= 3.14.)
This is a Triangle. The perimeter of a triangle is given by the sum of all sides:
[tex]\begin{gathered} P=a+b+c \\ a,b,c=\text{the sides of the triangle} \\ a=5,b=5,c=6 \\ P=5+5+6=16 \\ P=16units \end{gathered}[/tex]Area of triangle is given by 1/2 * bh
[tex]\begin{gathered} A=\frac{1}{2}bh+\frac{1}{2}bh(For2\text{Triangles)} \\ \Rightarrow A=bh \\ b=6,h=4 \\ A=6\cdot4=24 \\ A=24units^2 \end{gathered}[/tex]the boiling point at atmospheric pressure of Ammonia is -28 1/10 °F and of propylene is -5÷ 9/10 °F. what is the difference In their boiling points?
The difference between the boiling points is the subtraction between them. The two boiling points are given in mixed fractions, to subtract them we need to subtract the integer part and the fractional part separately. With this in mind let's solve the problem:
[tex]\begin{gathered} -28\frac{1}{10}-(-53\frac{1}{10}) \\ -28\frac{9}{10}+53\frac{1}{10} \\ 25\frac{8}{10} \\ 25\frac{4}{5} \end{gathered}[/tex]The correct answer is the option "B".
Please help will mark brain list
answer:
y = -2/3x -4/3
step-by-step explanation:
you start with 6x-9y = 12. you need to get y alone and on its own side of the equal sign.
starting easy, all coefficients (6, -9, and 12) have a GCF of 3. so, let's divide all sides by 3.
you are left with 2x-3y=4. now, we need to get -3y on its own side of the equal sign before we can get rid of its coefficient (-3). also, when identifying the coefficient of x, y, or any variable, include the + or - sign. you just don't need to write +, but you have to write -.
2x-3y=4 means we subtract 2x from both signs because it is positive. we now have
-3y = 2x + 4. let's divide by -3 to get y on it's own
y = -2/3x -4/3
Which of the following expressions can be used to rationalize the fractions below?
SOLUTION:
Case: Rationalizing fractions
Method:
[tex]\begin{gathered} \frac{16}{\sqrt{2}} \\ \Rightarrow \\ \frac{16}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\ =\frac{16\sqrt{2}}{\sqrt{4}} \\ =\frac{16\sqrt{2}}{2} \\ =8\sqrt{2} \end{gathered}[/tex]Final answer: Option (A)
[tex]\frac{\sqrt{2}}{\sqrt{2}}[/tex]Cost for assembling a smart phone is given in formula C(q) = 500 - 2q. Where C is cost, and q is cost for parts. If cost for parts equal $75, find total cost to assemble 1500 smart phones.
The total cost to assemble 1, 500 smart phones, given the cost formula, can be found to be $525,000
How to find the cost of the smart phones?The total cost of a smart phone is found by the formula, C(q) = 500 - 2q.
Here q is the cost of parts which is 75.
The assembly cost of a single phone is therefore:
= 500 - 2(75)
= 500 - 150
= $350
If there are 1, 500 smart phones, the total cost would be:
= 350 x 1, 500
= $525,000
Find out more on the total cost at https://brainly.com/question/13042567
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What type of number is 4π?whole numberintegerrational numberirrational number
Answer:
(D)Irrational number
Explanation:
The number π is Irrational because the digits after the decimal point go on indefinitely.
Therefore, a product of a number and π is also an Irrational Number.
17. A publisher marks up a textbook by 60%, and a bookstore further marks up the textbook by 25%. What percentage of the original cost do you pay?%
A publisher marks up a textbook by 60%, and a bookstore further marks up the textbook by 25%. What percentage of the original cost do you pay?
Let
x ------> original cost
so
1) publisher marks up a textbook by 60%
cost=1.60x
2) bookstore further marks up the textbook by 25%
cost=1.60x(1.25)=2x
therefore
200%Find the coordinates of the centroid.F(1,5) G(-2,7) H(-6,3)
The coordinates of the centroid is
[tex](-\frac{7}{3},5)[/tex]Explanation:The coordinates of the centroid of a triangle is given as:
[tex](\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]Using the above formula, we have:
[tex]\begin{gathered} C=(\frac{1+(-2)+(-6)}{3},\frac{5+7+3}{3}) \\ \\ =(-\frac{7}{3},\frac{15}{3}) \\ \\ =(-\frac{7}{3},5) \end{gathered}[/tex]Michael rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 85 cents for each mile driven. Michael had to pay$134.89 when he returned the truck. For how many miles did he drive the truck?
Let the number of miles Michael drove the truck be m.
Then, the cost of the drive is given by the expression,
[tex]20.99+0.85m[/tex]The actual cost is given as $134.89
Hence, we must have that
[tex]\begin{gathered} 20.99+0.85m=134.89 \\ \text{ Subtracting 20.99 from both sides we have} \\ 0.85m=113.9 \\ \text{ Dividing both sides by 0.85 we have} \\ m=\frac{113.9}{0.85}=134 \end{gathered}[/tex]Thus the number of miles is 134 miles
The distance from Becca’s house to Liz’s house is 13 kilometers. Approximately how many miles does Becca live from Liz? Use the conversion factor shown below.
Data:
13 km
Convert to miles
(1 km is equal to 0.6214 miles)
[tex]13\operatorname{km}\cdot\frac{0.6214mi}{1\operatorname{km}}=8.078mi[/tex](1 mile is equal to 1.6093km)
[tex]13\operatorname{km}\cdot\frac{1mi}{1.6093\operatorname{km}}=8.078mi[/tex]Then, Becca lives 8.078 miles (aprroximately 8.1 miles) from LizGiven the function h described by h(x) = x + 2, find each of the following.h(0)=h(-7)=h( - 13)=h(10) =h(d + 4)=
Given the function h described by h(x) = x + 2, find each of the following:
h(0) = 0 + 2 = 2
h(-7) = -7 + 2 = -5
h( -13) = -13 + 2 = -11
h (10) = 10 + 2 = 12
h (d + 4) = d + 4 + 2 = d + 2 + 6
Please explain step by step on how to solve As I am brand new to this What is the median of 19,3,7,1,11,19,2,3,17,4,14,12
Answer:
The median is 9
Explanation:
The median of a data set is the value that lies in the middle of the ordered data set.
In this case, we have:
19,3,7,1,11,19,2,3,17,4,14,12
We need to order the list in ascending order:
1, 2, 3, 3, 4, 7, 11, 12, 14, 17, 19, 19
There are 12 values, since is an even number, the median is the average of the pair in the middle.
In this case, the pair in the middle is 7 and 11. The average is:
[tex]\frac{7+11}{2}=\frac{18}{2}=9[/tex]Thus, the median is 9
1455 is 150% of blank
We have to calculate of which value x we have that 1455 is the 150%.
We have to express mathematically "150% of x is 1455". This can be written as:
[tex]\begin{gathered} \frac{150}{100}\cdot x=1455 \\ 1.5x=1455 \\ x=\frac{1455}{1.5} \\ x=970 \end{gathered}[/tex]Answer: 1455 is 150% of 970.
A line passes through (10, 3) and (13, -6). What is the equation of the line in standard form?A. 3x - y = 1B. 3x + y = 27C. 3x + y = 33D. 3x - y = 27
In general, given two points on a line, we can find its equation by using the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (10,3),(13,-6) \\ \Rightarrow y-3=\frac{-6-3}{13-10}(x-10) \\ \Rightarrow y-3=-\frac{9}{3}(x-10) \\ \Rightarrow y-3=-3(x-10) \\ \Rightarrow y-3=-3x+30 \\ \Rightarrow3x+y=33 \end{gathered}[/tex]Thus, the answer is 3x+y=33, option C.
Enter an equation for the function. Give your answer in the form a(6"). In theevent that a = 1, give your answer in the form b".A laser beam with an output of 4 milliwatts is directed into a series of mirrorsThe laser beam loses 6% of its power every time it reflects off of a mirror. Thepower p(n) is a function of the number n of reflections.The equation is p(n) = 0
From the data provided, we have the following;
Initial power output = 4 milliwatts
Power lost per reflection = 6% (OR 0.06)
We need to find a function that shows the power each time the laser beam is reflected off a mirror.
Note that the general equation for an exponential decay/loss is given as;
[tex]\begin{gathered} y=a(1-r)^x \\ OR \\ f(x)=a(1-r)^x \end{gathered}[/tex]Note also that (1 - r) is often replaced by b. Therefore, the equation can be written as;
[tex]\begin{gathered} f(x)=a(1-r)^x^{} \\ f(x)=ab^x \end{gathered}[/tex]Where the number of reflections is given by n and p(n) is a function of the number of reflections, we now have;
[tex]p(n)=ab^n[/tex]Where the variables are;
[tex]\begin{gathered} a=4\text{ milliwatts (initial value)} \\ r=0.06 \end{gathered}[/tex]We now have the function as;
[tex]\begin{gathered} p(n)=a(1-0.06)^n \\ p(n)=a(0.94)^n \end{gathered}[/tex]ANSWER:
[tex]p(n)=a(0.94)^n[/tex]Write inequalities to represent the situation below.Latoya exercises no less than 50 minutes per day.Use t to represent Latoya's amount of exercise (in minutes per day).(Thank you for the help!)
To answer this question, we have that:
1. Latoya exercises no less than 50 minutes per day.
In this case, we can say that Latoya exercises more than 50 minutes per day.
Therefore, if we have that t represents Latoya's amount of exercise - in minutes per day, we can express this using inequality as follows:
[tex]t>50[/tex]In summary, we can represent the situation as:
[tex]t>50[/tex]the sum of the measures of the angles in a triangle equal
Given:
sum of measure of the angle in a triangle
Sum of three angle is:
[tex]x+y+z=180[/tex]then the sum of the measures of the angle in a triangle is equal to 180.