What is the written form of 7.007
2 answers:
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The total number of students that plotted the number of books they read was <u>18,</u> making the <u>4th option</u>, a correct choice, using the dot plot.
Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.
In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.
We are asked to find the total number of students that plotted the number of books they read using the dot plot.
The dot plot is attached to the solution.
The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.
Thus, the total number of students that plotted the number of books they read was <u>18,</u> making the <u>4th option</u>, a correct choice, using the dot plot.
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Answer:
Step-by-step explanation:
Assuming the given logarithmic equation is
We interchange x and y to get:
We solve for y now:
We add 4 to both sides to get;
Divide through by 4:
Answer:
a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)
b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)
Step-by-step explanation:
a:
So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation
. In this case a=1, b=-1, c=-6. So plugging those values in you get
, which simplifies to
. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of
where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be
Move c to the other side
Complete the square by adding (b/2)^2
Rewrite as square binomial
Isolate y
(h, k) = 0.50, -6.25 which is the vertex
b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation . which simplifies to
which gives the values -2 and 3. To find the vertex it's the same process as before
Factor out -1
Add 6 to both sides (on the left side add -6 since -1 was factored out).
Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)
Rewrite as square binomial
Add 6.25 to both sides
(h, k) = (0.50, 6.25)
When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.