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New plants and bushes are to be planted along a path that goes around a park. The shape of the park is shown below. What is the distance around the park?

Answer:

Equation 1 would be: 3a+2C

Equation 2 would be: 5a+3C

Step-by-step explanation:

Step-by-step explanation:

1. 51-x-5

= 46-x Answer

2. 21-24

= -3 Answer

Answer:

(-4,-4)

Step-by-step explanation:

Anytime you reflect a coordinate point across the x-axis, the y-coordinate becomes its opposite and the x-coordinate stays the same.

In this coordinate: (-4,4)

Reflecting (-4,4) across the x-axis means the x-coordinate (-4) would stay the same and the y-coordinate (4) would become its opposite (-4).

The new coordinates after being reflected across the x-axis are (-4,-4).

Answer:

a) A sample of 385 must be taken.

b) The 95% confidence interval for the proportion of workers who have changed jobs within the past year is (0.1216, 0.2784).

c) A sample of 246 is needed.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Absence of preliminary data:

This means that we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample must be taken to ensure that a 95% confidence interval will specify the proportion to within ±0.05?

A sample of n must be taken.

n is found when [tex]M = 0.05[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

Dividing both sides by 0.05

[tex]\sqrt{n} = 1.96*10[/tex]

[tex](\sqrt{n})^2 = (19.6)^2[/tex]

[tex]n = 384.16[/tex]

Rounding up,

A sample of 385 must be taken.

Question b:

In a sample of 100 workers, 20 of them had changed jobs within the past year.

This means that [tex]n = 100, \pi = \frac{20}{100} = 0.2[/tex]

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 1.96\sqrt{\frac{0.2*0.8}{100}} = 0.1216[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 1.96\sqrt{\frac{0.2*0.8}{100}} = 0.2784[/tex]

The 95% confidence interval for the proportion of workers who have changed jobs within the past year is (0.1216, 0.2784).

Question c:

Same procedure as question a, just with [tex]\pi = 0.2[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.2*0.8}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96\sqrt{0.2*0.8}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.2*0.8}}{0.05}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.2*0.8}}{0.05})^2[/tex]

[tex]n = 245.8[/tex]

Rounding up

A sample of 246 is needed.

Answer: x = 3

First, you can multiply the 4 with the x and the 1:

4x + 4 + 8 = 24

Now, you just add the 4 and the 8 together:

4x + 12 = 24

Subtract 12 from both sides:

4x = 12

Now you divide by 4 from both sides

x = 3

^ and that's your final answer!

Answer:

x=3

Step-by-step explanation:

4x+4+8=24

4x+12=24

4x=12

4x/4=12/4

(x=3)

Answer:

x = 21

Step-by-step explanation:

Based on the inscribed angle theorem, we would have:

120° = 2(3x - 3)°

Solve for x

120 = 2*3x - 2*3

120 = 6x - 6

Add 6 to both sides

120 + 6 = 6x

126 = 6x

Divide both sides by 6

126/6 = x

21 = x

x = 21

Answer:

Step-by-step explanation:

0: -2

1: -4

2: -6

Answer:

D. 11

Step-by-step explanation:

Midsegment theorem:

The length of the midsegment of a triangle is half the length of it's third side.

In this question:

Third side: 3x - 5

Midsegment: 14m

So

[tex]\frac{3x - 5}{2} = 14[/tex]

[tex]3x - 5 = 28[/tex]

[tex]3x = 33[/tex]

[tex]x = \frac{33}{3}[/tex]

[tex]x = 11[/tex]

The correct answer is given by option D.

Answer:

obtuse

Step-by-step explanation:

When c, the hypotenuse, is greater than the legs (a and b), it's an obtuse triangle

Answer:

because cfd eaquls a+b lllllllllll

Answer:

Step-by-step explanation:

IT is either the same as 7x+4 because it is infront of each other or you add 8x+6 and 6x+2 then you substract that from 180 to find out the remaining angle. Of course you have to subtitute the amount of x first.

Answer:

18,375

Step-by-step explanation:

Answer:

VUS, UST

Step-by-step explanation:

Answer

899

Step-by-step explanation:

99

Answer:

12.50

Step-by-step explanation:

Answer:

4/10, 6/15, 8/20, 10/25

Step-by-step explanation:

Answer:

$135

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

x= -6 ,1

Step-by-step explanation:

B is the answer

x= -6 ,1

Answer:

71 is 10% of 710

52 is 97% of 5200/97

Step-by-step explanation:

Let’s start with 71 is 10% of what number.

basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.

so, 71=0.1x

divide on both sides,

710=x

now the second one.

repeat the same process.

52=0.97x

divide

5200/97 =x

Answer:

Least is 7

Most is 12

Step-by-step explanation:

So 2 shirts for 12.

So 24

Take 24 off of both

Left with 21 to 36

21÷3 is 7

36÷3 is 12

Hope this helps

Answer:

least - $7

most - $12

Explanation:

if the price of a shirt is $12, she must have spent at least $24 on the shirts in total.

the least amount melissa could have spent on a skirt is:

($45 - $24) ÷ 3 = $7

and the most she could have spent is:

($60 - $24) ÷ 3 = $12

i hope this helps! :D

Answer:The mean, or average, has the property that distances from the mean to the individual ... The measure of center where half the values of the data set lie above this ... The maximum value of a data set is 200 and the minimum value is 80. ... 25 b. 24 c. 100 d. 5 e. 120. e. 120. A factorial is the product of all number from 1 to n.

Step-by-step explanation:

Answer:

B. Half the data values are greater than 100.

Step-by-step explanation:

The median is just another way to say the number in the middle.  So if in the whole group of numbers 100 is in the middle, that means that half of the numbers will be bigger than 100, and half of the numbers will be smaller than 100.

Answer:

she will see 108 humming birds

Step-by-step explanation:

30x6= 180

so mutiply how many times she sees one in a month by 6

Answer:

3240

Step-by-step explanation:

Answer:

It is already explained in simplest form

Step-by-step explanation:

It can be written as 0.925 in decimal form (rounded to 6 decimal places).

Answer:

The said friend's grade in Professor Ivy's class is 85.7.

Step-by-step explanation:

Assuming the question asks for your friend's grade in Professor Ivy's class.

0.05(95) + 0.25(89) + 0.25(80) + 0.45(86) = 85.7

tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)

… = sin²(x) (1/cos²(x) - 1)

… = sin²(x) (sec²(x) - 1)

… = sin²(x) tan²(x)

Answer:

∠4 = 22

Step-by-step explanation:

Hello There!

The angles shown are consecutive interior angles

If you didn't know consecutive interior angles are supplementary angles meaning that the sum of the two angles is 180

So we can find the missing angle by subtracting the given angle (158 in this case) from 180

180 - 158 = 22

so we can conclude that ∠4 = 22

180.timr3fzgncvdfccfxdfdxxfhk

180-158=22

the measure is 44

9514 1404 393

Answer:

  $12 for each shirt

Step-by-step explanation:

If we let 's' and 't' represent the costs of a shirt and tie, respectively, then we can write the general form equations ...

  6s +3t -79.50 = 0

  3s +2t -41.00 = 0

The solution for s can be found using the "cross multiplication" technique.

Differences of products can be formed:

  d1 = (6)(2) -(3)(3) = 3

  d2 = (3)(-41) -(2)(-79.50) = 36

Then we have ...

  1/d1 = s/d2   ⇒   s = d2/d1 = 36/3 = 12

The cost of each shirt is $12.00.

___

2 ties cost 41-36 = 5, so each one is $2.50.

_____

Additional comment

The use of simple elimination on this set of equations would eliminate the s-variable, so would mean additional work to find s after finding t. The t-variable could be eliminated by multiplying one equation by one coefficient, and the other by a different coefficient. As long as we're doing that amount of work, we may as well do just enough cross-multiplication to get the one answer we need. This is where the "cross-multiplication" method of solution comes in handy.

This method solves the general-form equations ...

by considering the two rows of coefficients:

Then differences of cross-products are formed in adjacent columns:

  d1 = ae -db

  d2 = bg -ec

  d3 = cd -ga

The solutions are ...

  1/d1 = x/d2 = y/d3   ⇒   x = d2/d1, y = d3/d1

Answer:

25

Step-by-step explanation: