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3 years ago

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Stan's heart rate, in beats per minute, was measured 20 times at random. The results are 82, 84, 98, 112, 97, 93, 91, 87, 112, 8

7, 79, 80, 72, 82, 94, 89, 89, 74, 80, and 72 beats per minute. Construct a 99% confidence interval for Stan's mean heart rate. (82.5659, 92.8341) (80.4942, 92.8341) (82.5659, 94.9052) (82.4288, 92.9712) (80.4942, 94.9052)

1 answer:

Licemer1 [7]3 years ago

6 0

Answer:

(80.4942, 94.9052)

Step-by-step explanation:

The sample mean is x = 87.7.

The sample standard deviation is s = 11.26.

At 99% confidence and 19 degrees of freedom, the critical value is t = 2.861.

The confidence interval is:

x ± t (s/√n)

87.7 ± 2.861 (11.26 / √20)

87.7 ± 7.2053

(80.4947, 94.9053)

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Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard. The length is 5 feet le

frutty [35]

Answer:

Width = 17.5 feet,

Length = 82.5 feet.

Step-by-step explanation:

We have been given that Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard. This means that perimeter of rectangular front yard is 200 feet.

We know that perimeter of rectangle is two times the sum of length and width of rectangle. We can represent this information in an equation as:

$2(l+w)=200...(1)$

We are also told that the length is 5 feet less than 5 times the width. We can represent this information in an equation as:

$l=5w-5...(2)$

Upon substituting equation (2) in equation (1), we will get:

$2(5w-5+w)=200$

$2(6w-5)=200$

$12w-10=200$

$12w-10+10=200+10$

$12w=210$

$\frac{12w}{12}=\frac{210}{12}$

$w=17.5$

Therefore, the width of rectangular front is 17.5 feet.

Upon substituting $w=17.5$ in equation (2), we will get:

$l=5(17.5)-5$

$l=87.5-5$

$l=82.5$

Therefore, the length of rectangular front is 82.5 feet.

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2 years ago

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According to the scatterplot below, which statement is correct?

FinnZ [79.3K]

Answer:

Hey there

Step-by-step explanation:

The input, or independent variable, is years in operation.

Step-by-step explanation:

In an ordered pair (x, y), the independent variable or input is x and y is the dependent variable or the output.

Therefore, the values on x-axis determine the results or output on y-axis.

The ordered pairs (x, y) are:

(1, 11) ⇒ there are 11 enrollees on Year 1

(2, 33) ⇒ there are 33 enrollees on Year 2

(3, 39) ⇒ there are 39 enrollees on Year 3

(4, 58) ⇒ there are 58 enrollees on Year 4

(5, 85) ⇒ there are 85 enrollees on Year 5

Where:

x are values on the x-axis that refers to number of years in operation

y are values on the y-axis that refers to the corresponding numbers of enrollees for each year.

Even without the graph, the correct statements i:

The input, or independent variable, is years in operation.

- brainly user

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2 years ago

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Write an equation of the line that passes through point P and is parallelto the line with the given equation.P(-2, 1), 10x + 4y

Klio2033 [76]

$\begin{gathered} 10x+4y=-8 \\ 4y=-10x-8 \\ y=-\frac{10}{4}x-2 \\ \text{The slope is m=-}\frac{10}{4} \\ \text{The new equation is-} \\ y-1=-\frac{10}{4}(x+2) \\ 4y-4=-10x-20 \\ 4y=-10x-16 \\ y=-\frac{10}{4}x-4\text{ (equation)} \\ \\ m=-\frac{10}{4} \\ b=-16 \end{gathered}$

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1 year ago

Solve 5x(x-6)(4x+9)=0

xxTIMURxx [149]

Greetings and Happy Holidays!

Solve for x.
$5x(x-6)(4x+9)=0$ <span>

Distribute the parenthesis:
</span> $5x(x-6)(4x+9)=0$

$(5x^2-30x)(4x+9)=0$

$(20x^3-120x^2)+(45x^2-270x)=0$

Combine like terms:
$20x^3-75x^2-270x=0$

Factor out GCF (5x):
$5x(4x^2-15x-54)=0$

Factor the Complex Trinomial:
$5x(4x^2+9x-24x-54)=0$

$5x(x(4x+9)-6(4x-9))=0$

$5x((4x+9)(x-6))=0$

Set Factors to Equal 0:
$5x=0$

$x=0$

or

$4x+9=0$

$4x=-9$

$x=\frac{-9}{4}$

or

$x-6=0$

$x=6$

The Answers Are:
$\boxed{x=0} \\ \boxed{x= \frac{-9}{4}} \\ \boxed{x=6}$

I hope this helped!
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2 years ago

If one factor of x2 + 2x - 24 is (x+6), what is the other factor?

steposvetlana [31]

Answer:

( x - 4)

Step-by-step explanation:

x² + 2x - 24

From here, you must find the two factors of -24 (the first and third terms' coefficients multiplied together) that add up to 2 (the middle terms coefficient)

( x - 4) ( x + 6)

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2 years ago

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