Yesterday, Jon drank 5 cans of Mountain Dew and 5 cans of Coke and consumed

Mathematics

1 answer:

Delicious77 [7]2 years ago

3 0

Blinks because so easy so the question is 168-0

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How long will it take a seal swimming at a speed of 8 miles per hour to travel 52 miles

Olin [163]

$8\ miles\ per\ 1\ hour\\
52\ miles\ per\ x\ hour\\\\
proportion:\\
8-1\\52-x\\\\cross\ multiplication\\\\
8x=52\ \ \ | divide\ by\ 8\\\\
x=6.5\\\\
It\ will\ take\ 6.5\ hours.$

7 0

3 years ago

What happens to the width of a confidence interval for a population mean if the level of confidence is increased without changin

natulia [17]

Answer: If the level of confidence is increased without changing the sample size then The margin of error will decrease because the critical value will decrease. The decreased margin of error will cause the confidence interval to be narrower.

where;

Margin of error = Critical value × Standard deviation

Here, it can be duly noted that Margin of error has a positive relation with critical value, i.e The margin of error will decrease because the critical value will decrease.

whereas;

The confidence interval is the value ± the margin of error.

Therefore, the decreased margin of error will cause the confidence interval to be narrower.

7 0

3 years ago

The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all p

Juliette [100K]

Check the picture below.

based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).

and that will give us two x-intercepts, at x = 3 and x = k.

since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.

now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.

let's find the y-intercept by setting x = 0 now,

$\bf y=0.5(x-3)(x+k)\implies y=\cfrac{1}{2}(x-3)(x+k)\implies \stackrel{\textit{setting x = 0}}{y=\cfrac{1}{2}(0-3)(0+k)} \\\\\\ y=\cfrac{1}{2}(-3)(k)\implies \boxed{y=-\cfrac{3k}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=3+k\\ h=y\\ \quad -\frac{3k}{2}\\ A=1.5\\ \qquad \frac{3}{2} \end{cases}\implies \cfrac{3}{2}=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)$

$\bf \cfrac{3}{2}=\cfrac{3+k}{2}\left( -\cfrac{3k}{2} \right)\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{2}}{3=\cfrac{(3+k)(-3k)}{2}}\implies 6=-9k-3k^2 \\\\\\ 6=-3(3k+k^2)\implies \cfrac{6}{-3}=3k+k^2\implies -2=3k+k^2 \\\\\\ 0=k^2+3k+2\implies 0=(k+2)(k+1)\implies k= \begin{cases} -2\\ -1 \end{cases}$

now, we can plug those values on A = (1/2)bh,

$\bf \stackrel{\textit{using k = -2}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-2)\left(-\cfrac{3(-2)}{2} \right)\implies A=\cfrac{1}{2}(1)(3) \\\\\\ A=\cfrac{3}{2}\implies A=1.5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{using k = -1}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-1)\left(-\cfrac{3(-1)}{2} \right) \\\\\\ A=\cfrac{1}{2}(2)\left( \cfrac{3}{2} \right)\implies A=\cfrac{3}{2}\implies A=1.5$

7 0

3 years ago

he following data set shows the number of dogs counted in a local park each Saturday for 4 months. 33, 36, 31, 37, 37, 38, 31, 3

lana66690 [7]

General Idea:

To create a dot plot for a set of data we should list the data from lowest to greatest number. Then create a number line which covers all the numbers given in the data. We need to plot number of circles one above as many times based on the frequency of the data.

Applying the concept:

33, 36, 31, 37, 37, 38, 31, 37, 35, 31, 38, 32, 36, 33, 38

Listing the data in ascending order we get

31, 31, 31, 32, 33, 33, 35, 36, 36, 37, 37, 37, 38, 38, 38

We need to plot three circles above 31, one circle above 32, two circles above 33, one above 35, two above 36, three above 37, and three above 38.

Conclusion:

Out of the four options, the correct option is B because that is the only dot plot representing the given set of data.