The front of a storage bunker can be modeled by y=-5/216(x-72)(x+72), where x and y are measured in inches. The x axis represents the ground. Find the width of the bunker at ground level.
The width of the bunker at ground level is 14.58 inches.
Explanation:The x-axis is the ground level, so the y-axis must be the scale for the length. Using the provided model, the x-intercepts, namely where the x-axis gets touched, we can just get the distance between them and that's the ground-level width.
The width of the bunker at ground level can be found by substituting x = 0 into the equation y = -5/216(x-72)(x+72).
This equation represents a quadratic function, which means it is a parabola.
By substituting x = 0, we get y = -5/216(-72)(72)
= 14.58 inches.
It is very common for television series to draw a large audience for special events of for cliff-hanging story lines. suppose that on one of these occasions, the special show drew viewers from 38.2% of all us tv households. suppose that three tv households are randomly selected. what is the probability that all three households viewed this special show?
To find the probability that all three randomly selected households watched a special TV show when 38.2% of all households watched it, you multiply the probability for one household by itself three times, resulting in approximately 0.055 or 5.5%.
The question asks about calculating the probability that all three randomly selected US TV households watched a special television show, given that 38.2% of all US TV households viewed it. To find this probability, we use the rule of independent events since the viewing status of one household is assumed to not affect another. The probability that all three households viewed this show can be calculated by multiplying the probability of one household viewing the show three times.
The calculation would look like this:
0.382 (the probability one household watched the show) x 0.382 x 0.382 = 0.055 (approximately).
This is the probability that all three households viewed the special show.
select the locations on the number line to plot the points _2 _11 and _17
A trail is 7/12 mile long, which trail is shorter, than 7/12
3/8,5/6,3/4,2/3
Among the given options, the trail which is shorter than 7/12 is 3/8
Determining the magnitude of a fractionFrom the question, we are to determine which trail is shorter than 7/12
To determine which of the given fractions is shorter than 7/12, we will express all the fractions in a common denominator
The given fraction are
3/8, 5/6, 3/4, 2/3
Using a common denominator of 48,
7/12 = 28/48
For the given options,
3/8 = 18/48
5/6 = 40/48
3/4 = 36/48
2/3 = 32/ 48
Now, we will compare their numerators. The fraction which has a numerator that is smaller than the numerator in 28/48 is the fraction smaller than 7/12.
Among the fraction, 18 is the smallest of the numerators and it is lesser than 28.
18/48 corresponds to 3/8
Hence, the trail which is shorter than 7/12 is 3/8
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Another term for dual enrollment is:
Answer:
Another term for dual enrollment is: Concurrent enrollment.
Step-by-step explanation:
Concurrent enrollment or dual enrollment are those programs where students gets enrolled in two schools simultaneously.
There are many types of dual enrollment programs available for students like studying in high school students along with taking college classes etc.
A book is opened, and the PRODUCT of the two visible page numbers is found to be 306. The equation which correctly represents this situation is A) x2 = 306 B) 2x2 = 306 C) x2 + x = 306 D) 2x2 + x = 306
Answer:
Option C is correct
[tex]x^2+x = 306[/tex]
Step-by-step explanation:
Let the consecutive page number be x and x+1
As per the statement:
A book is opened, and the PRODUCT of the two visible page numbers is found to be 306.
" PRODUCT of the two visible page numbers" translated to x(x+1)
then;
[tex]x(x+1) = 306[/tex]
Using distributive property, [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]x^2+x = 306[/tex]
Therefore, the equation which correctly represents this situation is [tex]x^2+x = 306[/tex]
Item 9 A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use xx to represent the number of one-person tubes rented and yy to represent the number of cooler tubes rented. How many of each type of tube does the group rent?
The group rents 11 one-person tubes and 4 cooler tubes and the two system of equations are:
x + y = 15
20x + 12.5y = 270
And the solution: x = 11, y = 4.
Define Variables:
x = number of one-person tubes rented
y = number of cooler tubes rented
Translate information into equations:
Total tubes: The group rents a total of 15 tubes. Translate this into an equation:
x + y = 15
Cost: Each one-person tube costs $20 and each cooler tube costs $12.50. Use these known costs to represent the total cost:
20x + 12.5y = 270
System of Equations:
x + y = 15
20x + 12.5y = 270
Solving for x and y:
Elimination
Multiply the first equation by -12.5:
-12.5x - 12.5y = -187.5
Add the top and bottom equations:
7.5x = 82.5
Divide both sides by 7.5:
x = 11
Substitute the value of x back into the first equation to solve for y:
11 + y = 15
y = 4
The group rents 11 one-person tubes and 4 cooler tubes.
Therefore, the two system of equations are:
x + y = 15
20x + 12.5y = 270
And the solution: x = 11, y = 4.
Complete question:
A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use x to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. a one person tube costs $20 and a cooler tube costs $12.50 How many of each type of tube does the group rent? what are the two system of equations?
The system of equations representing the situation is x + y = 15 and 20x + 12.50y = 270. The group rents 11 one-person tubes and 4 cooler tubes.
Let's denote:
x as the number of one-person tubes rented
y as the number of cooler tubes rented
Given:
The cost of renting one-person tube is $20
The cost of renting a cooler tube is $12.50
The total amount spent by the group is $270
We can set up the following system of linear equations to represent the situation:
The total number of tubes rented:
x (number of one-person tubes) + y (number of cooler tubes) = 15 (total tubes)
The total cost spent:
20x (cost of one-person tube) + 12.50y (cost of cooler tube) = 270
So, the system of equations is:
x + y = 15
20x + 12.50y = 270
To find the number of each type of tube rented, we can solve this system of equations.
Now, let's solve this system of equations:
From equation 1, we can express x in terms of y:
x = 15 - y
Substitute this expression for x into equation 2:
20(15 - y) + 12.50y = 270
Now, solve for y:
300 - 20y + 12.50y = 270
-7.50y = -30
y = 4
Now that we have found y, let's substitute it back into equation 1 to find x:
x = 15 - 4
x = 11
So, the group rents 11 one-person tubes and 4 cooler tubes.
Complete Question:
A company that offers tubing trips down a river rents tubes for a person to use and "cooler' tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Usex to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. How many of each type of tube does the group rent?
1 Person Tube = $20, Cooler Tube = $12.50.
The system of equations is ___ and ___.
The group rents ___ one-person tubes and _____ cooler tubes.
5 -2 (4a + 1) + 3a = 13 what is (a) equal to a) - 6/5 b) - 2 c) 2 d) 6/5
The solution of the equation 5 -2 (4a + 1) + 3a = 13 is 2/3.
What is an equation?An equation is an expression that indicates the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given the equation as follows;
5 -2 (4a + 1) + 3a = 13
Therefore, solving the equation
3(4a+1)+3a=13
12a+3+3a=13
15a+3=13
15a=10
a=2/3
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Describe the image of D first reflected across line l, then across line m.
Answer:
Let's approach this step by step.
First, reflect D across line l.
From there, reflect that image across line m.
Your final image should be the letter D.
Check out the image provided.
Hope this helped someone!
Step-by-step explanation:
................
what is the cosine ratio for ∠F? p.s. show how you got your answer!
Answer:
cosF = [tex]\frac{3}{5}[/tex] is the answer.
Step-by-step explanation:
In a right angle triangle cosine of any angle = [tex]\frac{Base}{Hypotenuse}[/tex]
In the given triangle base or adjacent side of the angle is = 6
Hypotenuse given as 10
So by putting the values of hypotenuse and base in the formula
∠F = [tex]\frac{6}{10}=\frac{3}{5}[/tex]
Therefore cosine of angle [tex]cosF=\frac{3}{5}[/tex] is the answer.
Which of the following is the correct way to name the entire figure shown? A line has 4 points. From left to right, the points are M, unlabeled point, unlabeled point, N. (1 point) Modifying Above Upper M Upper N with two-way-arrow The image shows a ray MN. Modifying Above Upper M Upper N with bar
The general form of the equation of a circle is x2+y2−4x−8y−5=0.
What are the coordinates of the center of the circle?
Enter your answer in the boxes.
( , )
Answer:
(2,4)
Step-by-step explanation:
The students at a school assembly were divided into 4 equal groups. There were 63 students in each group. Write and solve an equation to determine the number of students that were at the assembly. use x as the variable.
equation _______
_______students
A bakery made 10 birthday cakes and 3 wedding cakes in one week. Enter the values that form the ratio of the number of birthday cakes the bakery made to the number of wedding cakes the bakery made.
J read 147 pages in a book. He has completed 70% of the book. How many more pages does he need to read to finish the book.
HELP HELP HELP !!!!!!!!
A jar contained 6 red marbles, 10 green marbles, and 8 blue marbles. A marble was selected at random, the color was recorded, and the marble was placed back in the jar. The table shows the results after 60 trials.
What was the relative frequency of selecting a red marble?
Enter your answer in the box to the nearest percent.
%
Outcome Number of times outcome occurred
Red : 13
Green: 30
Blue: 17
Calculate the average rate of change of the function f(x) over the interval -[4,-1] using the formula. A_____ The value of f(-1) is.B._____The value of f(-4) is. C.________ the average rate of change of f(x) over the interval [-4,-1] is D.________
GRAPH WITH QUESTION: Y intercept:5 X intercept: -2.5 slope: 2
A: [f(-4)-f(-1)]/[-5]
[f(-1)-f(-4)]/[-5]
[f(-1)-f(-4)]/[3]
[f(-4)-f(-1)]/[3]
B. 3
2
-1
C. -4
-3
4
D. -2
-1.5
2
4
he temperature equivalent to 77°F is °C.
Use the formula to convert the temperature.
Trig question -- please help if you can!
I have to write y = r cos(θ + R) and z = r sin(θ + R) in terms of y, z, and R. I'm not really sure how to do this, so would you mind showing work so I can learn the steps properly? (teacher hasn't taught this super well, haha) Thank you!!
what is the ratio of 12 percent
PLEASE ANSWER FAST I NEED ANSWER QUICK!!!
To estimate 103% of 63, Rich rounded 103% down to 100%, 63 down to 60, and multiplied 60 by 1 to get 60. Which of these statements is correct?
A) Rich’s estimate is reasonable because it should be less than 63.
B) Rich’s estimate is reasonable because it should be greater than 63.
C) Rich’s estimate is unreasonable because it should be less than 63.
D) Rich’s estimate is unreasonable because it should be greater than 63.
If h(x) = 3 + 2f(x) , where f(1) = 3 and f '(1) = 4, find h'(1).
Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answer:
The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
What is the difference between the absolute value of –8 and the absolute value of 6?
2
8
14
16
Answer:
It will be A. (2)
Step-by-step explanation:
Because its the only answer that makes sense plus i got it right :3
Last week, maria drove 231 miles. This week, she drove k miles. Using k, write an expression for the total mumber of miles she drove in two weeks?
The expression for the total number of miles Maria drove in two weeks is 231 + k miles.
Explanation:In order to find the total number of miles Maria drove in two weeks, we first need to find the sum of the miles she drove last week and the miles she drove this week.
Last week, Maria drove 231 miles.
This week, she drove k miles.
Therefore, the expression for the total number of miles she drove in two weeks is 231 + k miles.
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13/40 as a decimal and percent
Answer:
Step-by-step explanation:
13/40 as a decimal = 0.325
0.325
40√ _ 130
120
_100
80
_200
200
13/40 as percent
13/40 x 100% = 0.325 x 100% = 32.5%
Trigonometric Identities Help!?
solve and express the solution set in simplest form. 8x-2/9 = 2/1
Final answer:
The solution to the equation 8x-2/9 = 2/1 is obtained by multiplying both sides by 9, adding 2 to both sides, dividing by 72, and simplifying the fraction to get x = 5/18.
Explanation:
To solve the equation 8x-2/9 = 2/1, we first want to isolate the variable x. Here are the steps to do this:
Multiply both sides of the equation by 9 to eliminate the denominator on the left side, which gives us 72x - 2 = 18.
Add 2 to both sides to get 72x = 20.
Divide both sides by 72 to solve for x, resulting in x = 20/72.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. The solution in simplest form is x = 5/18.
The lengths of the legs of a right angle triangle 12 cm and 35 cm. What is the length of the hypotenuse?
∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.
Answer:
1= 45
2= 135
Step-by-step explanation:
(did it on usatp)