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3 years ago

An equilateral triangle has perimeter P. The length of one side is P/3. Which expression is equivalent to the length on one side

Mathematics

1 answer:

irina1246 [14]3 years ago

3 0

Answer: $3\times \dfrac{P}{3}=P$

Step-by-step explanation:

Given

The perimeter of one equilateral triangle is P

The lengths of the equilateral triangle are equal

Suppose x is the length of each side

$\therefore 3\times x=P\\\\\Rightarrow x=\dfrac{P}{3}$

i.e.

$\Rightarrow 3\times \dfrac{P}{3}=P$

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An office room is 12 ft by 10 ft with a door that is 30 inches wide. How many feet of baseboard are needed to go around the room

Lina20 [59]

Draw a diagram to illustrate the problem as shown below.
The length of baseboard needed is AB + BC + CD + DE + FE.
Note that 30 in = 30/12 ft = 2.5 ft.

Because of the door opening,
AB + EF = 12 - 2.5 = 9.5 ft
Also,
BC = DE = 10 ft
CD = 12 ft.

The amount of baseboard needed is
AB + BC + CD + DE + FE
= (AB + EF) + BC + CD + DE
= 9.5 + 10 + 12 + 10
= 41.5 ft

Answer:
41.5 feet of baseboard.

7 0

3 years ago

1. Make sure your answers and work is SHOWN please and steps are in order.

JulijaS [17]

Been a while since I've done synthetic division.

1a. Let's assume that's supposed to be an equals sign

p(x) = 2x⁴ - 3x³ - 6x² + 5x + 6

possible rational roots have factors of 6 in the numerator and of 2 in the denominator. We'll only worry about negative numerators.

Factors of six: 1,2,3,6, and we don't forget -1,-2,-3,-6

Factors of 2: 1,2

Possible rational roots:

(dividing by 1:) 1,-1,2,-2,3,-3,6,-6

(dividing by 2:) 1/2, -1/2 (2/2=1 is a duplicate, don't have to repeat it), 3/2, -3/2

Possible rational roots: 1,-1,2,-2,3,-3,6,-6, 1/2, -1/2, 3/2, -3/2

Synthetic division, trying x=1,

1 | 2 -3 -6 5 6

2 -1 -7 -2

2 -1 -7 -2 4

Got a remainder of 4, so 1 isn't a root;

Trying x=-1

-1 | 2 -3 -6 5 6

-2 5 1 -6

2 -5 -1 6 0

Zero remainder, found a root, x=-1. This division says

(2x⁴ - 3x³ - 6x² + 5x + 6) / (x + 1) = 2x³ - 5x² - x + 6

Same set of rational roots on the cubic, we continue with x=2

2 | 2 -5 -1 6

4 -2 -6

2 -1 -3 0

Another zero remainder, x=2 is a root. We're left with 2x² - x - 3 = 0, which factors as

(2x - 3)(x + 1) = 0

That's a second factor of x+1. Our final factorization is

2x⁴ - 3x³ - 6x² + 5x + 6 = (x + 1)²(x-2)(2x - 3)

Fourth degree with a positive leading coefficient so goes to +infinity at both ends. Double zero at x=-1, so it's tangent there, just touching the x axis, then down through x=3/2 and up through x=2.

I'll leave the actually sketching and the other two polynomials to you -- that took some time.

4 0

3 years ago

How do we find 4and1/4 hours after 11:20pm?

tigry1 [53]

there are 60 minutes in 1 hour, so 1/4 of an hour is 60(1/4), namely 15 minutes.

11:20pm + 4 hours, is 11+4:20, namely 15:20, of course the time system only uses up to 12, so that has to be 3:20, and then we add the 15 minutes.

11+4: 20 + 15.........3:35am.

5 0

3 years ago

A researcher claims that the average body mass index (BMI) of adult Canadians is more than 25.0. He takes a SRS of 250 Canadians

Serjik [45]

Answer:

The probability of obtaining a result equivalent to or greater than what was the truly observed value of the test statistic is 0.001.

Step-by-step explanation:

The researcher can use a one sample z test to determine whether his claim is correct or not.

The hypothesis to test whether the mean BMI is more than 25.0, is defined as:

H₀: The mean BMI is not more than 25.0, i.e. μ ≤ 25.0.

Hₐ: The mean BMI is more than 25.0, i.e. μ > 25.0.

The test statistic is defined as:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}$

The p-value of the test is,

p = 0.001.

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

A small p-value (typically ≤ 0.05) specifies sufficient proof against the null hypothesis (H₀), so you discard H₀. A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The p-value of 0.001 indicates that the probability of obtaining a result equivalent to or greater than what was the truly observed value of the test statistic is 0.001.

As the p-value is very small, the null hypothesis will be rejected at any level of significance.

Thus, concluding that the mean BMI of adult Canadians is more than 25.0.

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3 years ago

A bike tire has a diameter of 16 inches What is the radius of the bike What is the circumference of the bike

poizon [28]

The answer i got was 31.4.... if that’s wrong i’m so sorry.

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2 years ago