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3 years ago

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The width of a rectangle is five less than three times the width of the rectangle. If the perimeter of the rectangle is 70 inche

s what are the dimension of the rectangle?

1 answer:

Sergeeva-Olga [200]3 years ago

8 0

Do you mean the width is five less than the LENGTH of the rectangle

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On a 6-sided die, what is the probability of rolling an even number that is not 4? 1/6 1/3 2/3 5/6

myrzilka [38]

The probability of rolling an even number on a six sided die is 1/3.

8 0

4 years ago

find the area of the isocele triangle formed by the points of intersection of parabolas y=-x^2+9 and y=2x^2-3 and the origin

leonid [27]

Answer:

$10\ \text{sq. units}$

Step-by-step explanation:

The parabola's are

$y=-x^2+9$

$y=2x^2-3$

So

$-x^2+9=2x^2-3\\\Rightarrow 12=3x^2\\\Rightarrow \\\Rightarrow x=\sqrt{\dfrac{12}{3}}\\\Rightarrow x=\pm 2$

$y=-x^2+9=-(2)^2+9\\\Rightarrow y=5$

$y=-(-2)^2+9=5$

So, the points at which the parabola's intersect each other is $(2,5)$ and $(-2,5)$

The three points of the triangle are $(2,5)$ , $(-2,5)$ and $(0,0)$

Area of a triangle is given by

$A=\dfrac{1}{2}[x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)]\\\Rightarrow A=\dfrac{1}{2}[2(5-0)+(-2)(0-5)+0(5-5)]\\\Rightarrow A=10\ \text{sq. units}$

Area of the triangle formed is $10\ \text{sq. units}$ .

3 0

3 years ago

3p + 4q = 22<br> 10p + 12 q = 68<br> What is p and what is q<br> (Similtaneous equations)

Rashid [163]

Answer:

q=4

p=2

Step-by-step explanation:

3p+2q=14

10p+6q=44

10(3p+2q=14)

3(10p+6q=44)

30p+20q=140-

30p+18q=132

2q=8

2q/2=8/2

q=4

3p+2*4=14

3p+8=14

3p=14-8

3p/3=6/3

p=2

hope this helps

7 0

3 years ago

Read 2 more answers

The angle of elevation to a nearby tree from a point on the ground is measured to be

sladkih [1.3K]

Answer:

h ≈ 66.4 ft

Step-by-step explanation:

The situation can be modelled by a right triangle with h representing the height of the tree.

Using the tangent ratio in the right triangle

tan39° = $\frac{opposite}{adjacent}$ = $\frac{h}{82}$ ( multiply both sides by 82 )

82 × tan39° = h , then

h ≈ 66.4 ft ( to the nearest tenth )

7 0

3 years ago

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

$X=1$ number of citrus trees that are infected with the citrus red mite.

$n=5$ random sample taken

$\hat p=\frac{1}{5}=0.2$ estimated proportion of citrus trees that are infected with the citrus red mite.

$p$ true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56$

And rounded up we have that n=6147

5 0

4 years ago