Patricia's garden is surrounded by a fence. What is the perimeter of the
fence?

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By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.

In this triangle we know the length of a side (b = 13) and the measure of two adjacent angles (A = 57°, C = 73°). First, we determine the measure of the missing angle by using triangles properties:

B = 180° - 57° - 73°

B = 50°

Lastly, we determine the missing lengths by the law of the sines:

[tex]a = 13 \times \frac{\sin 57^{\circ}}{\sin 50^{\circ}}[/tex]

a ≈ 14.232

[tex]c = 13 \times \frac{\sin 73^{\circ}}{\sin 50^{\circ}}[/tex]

c ≈ 16.229

By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.

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Answer + Step-by-step explanation:

-2|x| = -6

⇔ 2|x| = 6

⇔ |x| = 3

⇔ x = 3  or  x = -3

[tex]\large\blue\implies \tt \large \: \sqrt{10 \: \times \: 15 \: \times \: 24} [/tex]

[tex]\large\blue\implies \tt \large \: \sqrt{150 \: \times \: 24} [/tex]

[tex]\large\blue\implies \tt \large \: \sqrt{3600} [/tex]

[tex]\large\blue\implies \tt \large \: \sqrt{3600} \: = \: 60[/tex]

[tex]\large\blue\implies \tt \large \:60[/tex]

Answer: A and D

Step-by-step explanation:

- Career A's spread is more concentrated while Career B's spread is more dispersed or spread out

- Career A's median is 25 and Career B's median is 30

- Therefore A and D are the correct answers

hope this helps :)

Answer:

a) 57

b) 19.476

c) 1.106 (rounded)

Step-by-step explanation:

a) note: the very first step here is to find the number of people of age 21 which is found through subtraction. We have a total of 250 people, and we currently have data on 193 (64 + 60 + 69) people.  This means there are (250 - 193 = 57)  57 remaining people of age 21.

The first thing we're trying to find here is the mean, which we sometimes refer to as the average, of this data set.

To find the mean, we add all values together and then divide by the number of values we've combined.

We could write out 18 + 18 + 18... sixty-four times, and then to the same thing for 19's, but that would take a while. So, we can find this value through multiplication (remember, multiplication is the same thing as repeated addition).

18 × 64 = 1152

19 × 60 = 1140

20 × 69 = 1380

21 × 57  = 1197         *see above

Now, we find the sum of our values added together:

Now, we know we have 250 values, so we will divide 4869 by 250:

4869 / 250 = 19.476

So, the mean of this sample is 19.476

Now, we are finding the standard deviation, which is found through the formula:

    ∑ (x - x^(line over x) ) ²

√ _______

       n - 1

(this is hard to write on this website sorry)

find difference between each value and mean  (that's what "x - x^(line over x)" is)

18 - 19.476 = -1.476

19 - 19.476 = -0.476

20 - 19.476 = 0.524

21 - 19.476 = 1.524

square each difference:   (that's what " (x - x^(line over x))² " is)

now, we need to add up our squared values. But first, we must account for how many of each value there are

now, let's add up our squared values:  (that's what "∑" is )  

we now need to divide this number by n - 1 (we have 250 samples, so we need to divide by 250 - 1 (249) to find our variance)

now, we find our standard deviation by taking the square root of the variance that's what the "√" is )

we can round this number to:

1.106 (or any other rounded decimal place, I did it this way to match our previous answer)

So, the standard deviation of this set is 1.106 (rounded)

hope this helps! have a lovely day :)

The value of x is 10 centimeters

The complete question is in the image

The value of x is calculated using the following Pythagoras theorem

x^2 = 6^2 + 8^2

Evaluate the sum of exponents

x^2 = 100

Take the square roots

x = 10

Hence, the value of x is 10 centimeters

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Answer:

D

Step-by-step explanation:

Let's start by crossing everything out!

12/3 can be crossed out to 4.

a^3/a^2 can be crossed out to a.

b^6/b^4 can be crossed out into b^2.

c^5/c^5 is just 1.

So which the results we got, we can multiply them, so that it is 4ab^2.

4ab^2 is our final answer!

The number of people that studied only one subject is 108.

A set is a collection of well-defined objects.

Objects in a set are called elements or members of a set.

Set notation or the use of Venn diagrams are the methods used to solve set problems.

Analysis:

let P = physics

C = chemistry

M = mathematics

n(P) = 70

n(C) = 46

n(M) = 100

n(M n P n C) = 18

n(M n P) = 30

n(M n P n C') = 30 - 18 = 12

n(M n C) = 28

n(M n C n P') = 28 - 18 = 10

n(P n C ) = 23

n(P n C n M') = 23 - 18 = 5

n(P n C' n M') = 70-(12+18+5) = 70 - 35 = 35

n(P' n C n M') = 46-(18+5+10) = 46-23 = 13

n(P' n C' n M) = 100 - (10+18+12) = 100 - 40 = 60

people that studied only one subject are = 35 + 13 + 60 = 108

In conclusion 108 students studied only one type of subject.

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The solution to the system of equations (−3, −5)

We have given that,

Two lines, A and B, are represented by the equations given below:

Line A: y = x − 6

Line B: y = 3x + 4

Line A

y = x - 2

Line B

y = 3x + 4

If we equate those 2 equations

x - 2 = 3x + 4

2x = -6

x = -3

y = -5

So the answer is

(−3, −5), because the point satisfies both equations.

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The total volume of the given figure is:

[tex]V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3[/tex]

Here we have two simple shapes.

Half a sphere, and a cone.

The volume of half a sphere of radius R is:

[tex]V = \frac{2}{3}*3.14*R^3[/tex]

And here we know that R = 5.3cm, replacing that we get:

[tex]V = \frac{2}{3}*3.14*(5.3cm)^3 = 311.65cm^3[/tex]

For a cone of radius R and height H, the volume is:

[tex]V = \frac{3.14*R^2*H}{3}[/tex]

In this case, R = 5.3cm and H = 8.4cm

The volume of the cone is:

[tex]V = \frac{3.14*(5.4cm)^2*8.4cm}{3} = 246.97cm^3[/tex]

Then the total volume is:

[tex]V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3[/tex]

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Answer:

y-x-1 < 0

Step-by-step explanation:

according to the graph (0,1) and (-1,0) lies on the doted line,

equation of the dotted line is y-x-1=0

shaded region = y-x-1 < 0

Answer:

Step-by-step explanation:

can you show part a nd b for a better understanding of the question

Step-by-step explanation:

So when a question asks what is x% of the y number. It's asking you to convert the x into decimal form by dividing by 100 and then multiply it by y. This gives you the equation: [tex]y * \frac{x}{100}[/tex] which gives you x% of y. so 15% of 43 is [tex]43 * \frac{15}{100} = 6.45[/tex]. 43% of 300 is [tex]300 * \frac{43}{100} = 129[/tex].

the 12% of what number is 43 is a bit more tricky. It's asking you to instead find a number in which 12% of it is equal to 43. So instead of plugging solving for the percentage (which is already given) you solve for y. This gives you the following equation: [tex]y * \frac{12}{100} = 43[/tex]. Now all you do is calculate 12/100 which gives you [tex]y * 0.12 = 43[/tex]. now divide both sides by 0.12 to solve for y. This gives you [tex]y = 358.\overline{33}[/tex]

43 is what percent of 106? This question is also a bit tricky, but instead of solving for y, you're solving for x. So plug in the known values, which gives you the equation: [tex]106 * \frac{x}{100} = 43[/tex]. Divide both sides by 106 to get [tex]\frac{x}{100} \approx 0.406[/tex] and now multiply both sides by 100. this gives you [tex]x \approx 40.57[/tex] which is the answer 40.57%

What percent of 43 is 6. This is asking the same thing just in a different way. So percentage = unknown, entire number = 43, entire number * percentage = 6. With these values we get the equation: [tex]43 * \frac{x}{100} = 6[/tex]. Divide both sides by 43 to get [tex]\frac{x}{100} \approx 0.140[/tex] now multiply by 100 to get [tex]x \approx 13.95[/tex] which is the answer 13.95%

The mean is 87 and median is 86.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest.

Given:

79, 91, 93, 85, 86, and 88

So,

79+85+86+88+91+93/6 = 87

and, the median

79, 85, 86, 88, 91, 93

median = 86

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By solving a system of equations we will see that the two-digit number is 84.

"The tens digit of a number is twice the ones digit"

"The sum of the digits is 12".

A two-digit number can be written as:

a*10 + b

Where a is the tens digit and b is the ones digit.

The word problem can then be written as:

a = 2*b

a + b = 12

So we have a system of equations.

To find the number we need to solve these, if we replace the first equation into the second one:

a + b = 12

(2b) + b = 12

3b = 12

b = 12/3 = 4

Then:

a = 2b = 2*4 = 8

So the two-digit number is 84.

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The probability that all 4 are teachers is  0.0000135.

The total number is =

4 + 30 + 4

= 38

The committee of 4 from 38 =

38C4 = 73815

The committee of 4 from 4 teachers =

4C4 = 1 way

The total favorable cases = 1 way

Probability = favorability/ total cases

= 1/73815

= 0.0000135

Hence the probability that all 4 are teachers is 0.0000135.

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Answer:

x^2+4x+2

Step-by-step explanation:

Answer: e

Step-by-step explanation:

The vertex is at (-3, 1).

This leaves e.

Answer

(C) y +5 =3(x+4)

We will use the point-slope formula to solve this problem.

We will use the point-slope formula to solve this problem.(y+5)=3(x+4)

)Explanation:

)Explanation:We can use the point slope formula to solve this problem.

)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)

)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.

)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:

)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:(y−(−5))=3(x--(4))

=> (y+5)=3(x+4)

Another name for the set of all x-values for a relation is: domain.

The domain of a relation can be defined as all the x-values that corresponds to the y-values that are plotted on a graph.

They are referred to as the input or the domain of the relation. Therefore, another name for the set of all x-values plotted for a relation on a graph is: domain.

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The standard deviation for the number of times an odd number is rolled is 15.8

The given parameters are:

Die = regular six-sided die

n = 1000

The probability of rolling an odd number is:

p = 1/2 = 0.5

The standard deviation is then calculated as;

[tex]\sigma = \sqrt{np(1 - p)[/tex]

This gives

[tex]\sigma = \sqrt{1000 * 0.5 * (1 - 0.5)[/tex]

Evaluate the products

[tex]\sigma = \sqrt{250[/tex]

Evaluate the root

[tex]\sigma = 15.8[/tex]

Hence, the standard deviation is 15.8

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Answer:

30 pupils

Step-by-step explanation:

first you divide 75 and 2.5 to get 30.

Answer:

30 prefer red

Step-by-step explanation:

Multiply the fraction by the number of students:

[tex]75(\frac{2}{5})=\frac{(75)(2)}{5} =\frac{150}{5} =30[/tex]

Hope this helps

Answer: -2 < x < 1

Step-by-step explanation:

move all terms not containing x from the center section of the inequality

1 < x + 3 < 4

subtract 3 from both terms outside the center

1 - 3 = -2

4 - 3 = 1

therefore our answer is:

-2 < x < 1

Answer:

C) Experiment

Step-by-step explanation:

With a controlled experiment, a researcher can use a student batch that studied the old curriculum as a control group, and the new batch of students as the 'test' group. To measure student achievement, the researcher would need to either:

1. compare test results for the 2 groups

2. do a longitudinal study - follow the 2 groups of students across several years, and track their 'achievements' (university admissions, jobs, income, etc)

With the other 3 options, the results wouldn't necessarily be accurate or relevant.  

Answer:

1000 in base 14

Step-by-step explanation:

DDD + 1 = 1000 in base 14

Answer:

2/3 x - 5 < 11

2/3 x < 16 (add 5 to both sides)

x < 16 * 3/2 (multiply both sides by 3/2)

x < 24

Step-by-step explanation:

Answer:

[tex] \small{\boxed{ \sf{Term \: in \: both \: the \: sequence \: is \: 15}}}[/tex]

Step-by-step explanation:

To determine the common term in both the sequence let's solve for each sequence individually.

Let's solve for first sequence

[tex]f(n) = f(n-1)+4[/tex]

we are already told that f(1) = 3

let's solve for f(2),f(3),f(4)........ and so on till we get the highest digit or more than the highest digit from given option.

f(2) = f(2-1)+4 = f(1)+4

f(2) = 3+4

[tex]\small{ \fbox{f(2) = 7}}[/tex]

f(3) = f(3-1)+4 = f(2)+4

f(3) = 7+4

[tex] \small{\fbox{f(3)= 11}}[/tex]

on solving further..

The series obtained is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135.....

Let's solve for second series

[tex]f(n) = 3×5^{n -1}[/tex]

given that f(1) = 3,

f(2) = 3×5¹ = 15

f(3) = 3×5² = 75

f(4) = 3×5³ = 375

The series obtained is 3, 15, 75, 375.....

The term obtained in both the sequence is 15 hence option B is correct Answer.

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Answer:

Rs 1000.97

Step-by-step explanation:

x = original price

new price =   x (1.0909)(1.0833)(1.077) = 1274

                         x = Rs 1000.97