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3 years ago

When subtracting, change the subtraction you addition and _____ the sign of the number being taken away

Mathematics

1 answer:

BabaBlast [244]3 years ago

8 0

Subtract. it from when you do good school

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Plz help me with this question

Contact [7]

Answer: KJ becuase it is the first two like on but put backwards.

7 0

3 years ago

Read 2 more answers

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

A test consists of 100 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean a

TEA [102]

Answer: Mean = 20 and standard deviation = 4

Step-by-step explanation:

Let x represents the success of getting the correct answer.

Here, the total number of trials(n) = 100

The probability of getting the correct answer, p = 1/5

Thus, the mean of the number of correct answer,

$\mu_x= np$

$\mu_x= 100\times 1/5$

$\mu_x= 20$

Now, the standard deviation, $\sigma_x= \sqrt{n\times p\times (1-p)}$

$\sigma_x= \sqrt{100\times 1/5\times 4/5}$

$\sigma_x= \sqrt{16}$

$\sigma_x= 4$

Thus, First option is correct.

6 0

3 years ago

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing

PSYCHO15rus [73]

Answer:

-1.53 , 1.53

Step-by-step explanation:

It is basically asking you to find the percentiles. so for the bottom 6.3% you would type into your calculator 2nd, VARS, invNorm, area: .063, mean: 0, and Standard Deviation: 1 which gives you -1.53.

for the upper 6.3% you have to take 1-.063=.937 to get the upper percentile. now type into your calculator 2nd, VARS, invNorm, area: .937, mean: 0, and Standard Deviation: 1 which gives you 1.53.

I hope I helped :D

6 0

2 years ago

Zena used a probability simulator to roll a 12-sided number cube 100 times. Her results are shown in the table below:

viktelen [127]

100 over 82 or 18 over 100

3 0

3 years ago

Read 2 more answers