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3 years ago

14

An observational study determined that there is a strong correlation between getting less than 8 hours of sleep a day and lower

test scores. Can it be determined that the low test scores are caused by sleep deprivation? Explain.

1 answer:

s2008m [1.1K]3 years ago

6 0

Answer:

No

Step-by-step explanation:

We can not determine that the low test scores are caused by sleep deprivation. Because there are many factors that can affect on a student's test score such as:

not carefully review all the lesson before the test
the feeling of nervous in the exam room
poor academic ability
....so on

So, getting less than 8 hours of sleep is just one of the independent variables determining the test score, it is not a strong correlation.

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A town has a population of 4000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will

Romashka [77]

18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.

Step-by-step explanation:

The given is,

Population of 4000

Rate of grow 3.5% every year

Population after few years 7500

Step:1

Formula to calculate the population with the grow rate every year,

$F=P(1+r)^{t}$ ..........................(1)

Where,

F - Population after t years

P - Initial population

r - Rate of grow

t - No.of years

From given,

F = 7500

P = 4000

r = 3.5%

Equation becomes (1),

$7500=4000(1+0.035)^{t}$

$\frac{7500}{4000} = (1+0.035)^{t}$

1.875 = $(1+0.035)^{t}$

$1.875 = (1.035)^{t}$

Take log on both sides,

$log 1.875 = (t)log 1.035$

Substitute log values,

$0.2730= (t) 0.014940349$

$t = \frac{0.273}{0.014940349}$

= 18.273

t = 18.273 year

or

t = 18 years 3 months 2 weeks

Result:

18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.

7 0

3 years ago

The area of the kite is 60in^2. Find the value of x.

Mashcka [7]

Answer:

8 in

Step-by-step explanation:

Area = (d1 × d2)/2

d1 = 15 in

d2 = x in

60 = ( 15 * x)/2

120 = 15x

x = 120/15

= 8 in

6 0

2 years ago

Select the locations on the number line to plot the points −6 , −12 , and −16 .

ANTONII [103]

Count backwards so -6 would be infront of -5 cause 5,6 then count 6 ahead from where -6 is then count 4 ahead from where -12 is
i’m not good at explaining sorry!

7 0

2 years ago

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

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2 years ago

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Ivanshal [37]

Answer:

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Step-by-step explanation:

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