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Neko [114]
3 years ago
11

Rectangle L has a perimeter of 108 centimetres. Opposite sites of the rectangle have lengths of 27 cm each. what is its missing

side lenghts?
Mathematics
1 answer:
Ahat [919]3 years ago
4 0
The perimeter P of a rectangle of length L and width l is
P = 2L + 2l
Here you know P =108 and l=27. Thus you have the equation
108 = 2L + 2 \times 27 = 2L + 54
You simplify a bit by moving the 54 on the left side
54 = 2L
and you find L=27 cm.

Oh my, this is a square!
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PLZ HELP 20 POINTS!!! I will give Brainliest!!!
natka813 [3]

Answer:

A

Step-by-step explanation:

since both equations express y in terms of x we can equate the right sides

x + 7 = - 2x + 19 ( add 2x to both sides )

3x + 7 = 19 ( subtract 7 from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

substitute x = 4 into either of the 2 equations for y

y = x + 7 ⇒ y = 4 + 7 = 11

solution is (4, 11 )


5 0
3 years ago
Read 2 more answers
The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The
Mademuasel [1]

Answer:

(a) The 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b) The confidence level is 68%.

(c) The necessary assumption is that the population is normally distributed.

(d) The 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

Step-by-step explanation:

Let <em>X</em> = temperature of a certain solution.

The estimated mean temperature is, \bar x=37^{o}C.

The estimated standard deviation is, s=0.1^{o}C.

(a)

The general form of a (1 - <em>α</em>)% confidence interval is:

CI=SS\pm CV\times SD

Here,

SS = sample statistic

CV = critical value

SD = standard deviation

It is provided that a large number of independent measurements are taken to estimate the mean and standard deviation.

Since the sample size is large use a <em>z</em>-confidence interval.

The critical value of <em>z</em> for 95% confidence interval is:

z_{0.025}=1.96

Compute the confidence interval as follows:

CI=SS\pm CV\times SD\\=37\pm 1.96\times 0.1\\=37\pm0.196\\=(36.804, 37.196)\\\approx (36.80^{o}C, 37.20^{o}C)

Thus, the 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b)

The confidence interval is, 37 ± 0.1°C.

Comparing the confidence interval with the general form:

37\pm 0.1=SS\pm CV\times SD

The critical value is,

CV = 1

Compute the value of P (-1 < Z < 1) as follows:

P(-1

The percentage of <em>z</em>-distribution between -1 and 1 is, 68%.

Thus, the confidence level is 68%.

(c)

The confidence interval for population mean can be constructed using either the <em>z</em>-interval or <em>t</em>-interval.

If the sample selected is small and the standard deviation is estimated from the sample, then a <em>t</em>-interval will be used to construct the confidence interval.

But this will be possible only if we assume that the population from which the sample is selected is Normally distributed.

Thus, the necessary assumption is that the population is normally distributed.

(d)

For <em>n</em> = 10 compute a 95% confidence interval for the temperature as follows:

The (1 - <em>α</em>)% <em>t</em>-confidence interval is:

CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}

The critical value of <em>t</em> is:

t_{\alpha/2, (n-1)}=t_{0.025, 9}=2.262

*Use a <em>t</em>-table for the critical value.

The 95% confidence interval is:

CI=37\pm 2.262\times \frac{0.1}{\sqrt{10}}\\=37\pm 0.072\\=(36.928, 37.072)\\\approx (36.93^{o}C, 37.07^{o}C)

Thus, the 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

3 0
3 years ago
If a 100.8g cement bag has 20.35 kg removed from it. what is the new weight of the bag
kykrilka [37]

100.80 kg - 20.35 kg = 80.45 kg . . . . the new weight of the bag

It's a pretty straightforward subtraction problem. As with any decimal addition or subtraction, you line up the decimal points and extend any numbers with zeros to make the number of decimal places match.

5 0
3 years ago
If the height of water in the tank is 10cm what is the volume of the water​
Kay [80]

Answer:

4500cm^3

Step-by-step explanation:

We use the normal formula for volume V= L•W•H just changing the H value from 20 to 10 because the water isn't at the full hight

10•30•15=4500

hope this helps <3

7 0
2 years ago
Read 2 more answers
the product of 2 consecutive odd integers is equal to 27 plus six times the sum of the integers. what is the larger integer
olganol [36]
2 consecutive odd integers : x and x + 2

x(x + 2) = 27 + 6(x + x + 2)
x^2 + 2x = 27 + 6(2x + 2)
x^2 + 2x = 27 + 12x + 12
x^2 + 2x - 12x - 12 - 27 = 0
x^2 -10x - 39 = 0
(x + 3)(x - 13) = 0

x + 3 = 0
x = -3 (extraneous solution)

x - 13 = 0
x = 13

x + 2 = 15 

so ur 2 integers are 13 and 15, with 15 being the largest
8 0
3 years ago
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