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Answer:

The 95% confidence interval for the proportion of residences that reduced their water consumption is (0.665, 0.835).

Step-by-step explanation:

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].

Sampled 100 residential water bills and found that 75 of the residences had reduced their water consumption over that of the previous year.

This means that [tex]n = 100, \pi = \frac{75}{100} = 0.75[/tex]

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].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{100}} = 0.665[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{100}} = 0.835[/tex]

The 95% confidence interval for the proportion of residences that reduced their water consumption is (0.665, 0.835).

Answer:

m<E=120°

m<T=60°

Step-by-step explanation:

10m+4m+12=180

14m=168

m=12

m<E=10m=10(12)=120

m<T=4m+12=4(12)+12=48+12=60

Answer:

Solution given:

10m+4m+12=180°[sum of opposite angle of cyclic quadrilateral is supplementary]

14m=180-12

m=168/14=12

m<E=10×12=120°

m<T=4×12+12=60°

Answer:

46/117

Step-by-step explanation:

Answer:

46/117

Step-by-step explanation:

this is a type of fraction which can not be simplified

Answer:

Step-by-step explanation:

c=a2+b2−−−−−−√

a=182+152−−−−−−−−√

c=324+225−−−−−−−−√

c=549−−−√

c=23.4307

Answer:

x = 17

Step-by-step explanation:

Formula:

a² + b² = c²

8² + 15² = c²

64 + 225 = c²

c² = 289

[tex]\sqrt{c^2} =\sqrt{289}[/tex]

c = 17

Answer:

-6

Step-by-step explanation:

if they were both positive numbers, it would be 6. But when you multiply a negative by a positive, the answer is negative.

Answer:

-6

Step-by-step explanation:

When you multiply a positive number by another positive number, you will always get a positive number as your answer. Same thing for negative. If you multiply a negative by a negative, you will always get a positive. However, when you multiply a negative by a positive, you will always get a negative number.

Since you know this, you can multiply 2 by 3, which is 6. Because 2 is negative and 3 is positive, you know that the answer must be negative. Therefore, you add the negative symbol to 6, giving you -6.

I hope this isn't too confusing. Please let me know if you have any more questions. Good luck!

Step-by-step explanation:

subtract-13 from -13 get zero

then, subtract 13 from 77 =64

then do divide 15 from 15

then divide 15 from 64 = 4.26 repeat

Answer:

What is the equation that models this scenario?

✔ A + 5/4 = 19/4

and

How many pounds of apples did Angelica buy?

✔ 14/4 = 7/2

Step-by-step explanation:

Hope this helps!! :)

The equation A + 5/4 = 19/4 represents the number of pounds of apples Angelica bought, and the number of apples Angelica bought is 7/2 pounds.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let A = the number of pounds of apples Angelica bought.

Then the model that represents the number of pounds of apples Angelica bought:

A + 5/4 = 19/4

A = 19/4 - 5/4

A = 14/4 = 7/2 pounds

Thus, the equation A + 5/4 = 19/4 represents the number of pounds of apples Angelica bought and the number of apples Angelica bought is 7/2 pounds.

Learn more about the linear equation here:

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Answer:

70%

Step-by-step explanation:

14/20

Divide the top and bottom by 2

7/10

Multiply the top and bottom by 10

7*10

-----------

10*10

70/100

Percent means out of 100

70%

Answer:

70%

Step-by-step explanation:

14/20 and for a percentage it's out of 100 so 20*5 is 100. So, you would have to do 14*5 which is 70. So, it's 70%.

Answer:

1:8

Step-by-step explanation:

1 hour for every 8 ounces gives a 1:8 ratio

Answer:

8:3 would be the ratio

Answer:

B, -25

Step-by-step explanation:

3-4 = -1

-1(3 + 3^2 + 13) = -1(25), the answer is -25

Answer:

-25

Step-by-step explanation:

-25 is the answer...........

Answer:

Step-by-step explanation:

It really is just a matter of substituting the given values into the given equations.

f(x)=-3x

f(2)=-3(2)

f(2)=-6

h(a)=4a

h(4)=4(4)

h(4)=16

g(x)=x^2-1

g(8)=8^2-1

g(8)=64-1

g(8)=63

Answer:

like terms are terms that contains same variable

The required equivalent expression with the least number of terms has 2 terms.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
If three of the terms are like terms, then we can combine them into a single term. Let's say that the expression with 4 terms is:

a + b + c + d

where a, b, and c are like terms. Then we can combine them to get:

(a + b + c) + d

which is an expression with only 2 terms.

So the equivalent expression with the least number of terms has 2 terms. We can do this by combining the like terms to simplify the expression.

Learn more about the number system here:

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Answer:

x=8

Step-by-step explanation:

Hope this helps!!

Answer:

Swimming can improve your health.

Step-by-step explanation:

Gerunds are nouns which derive from verbs and take the -ing form. In the sentence, the noun swimming functions as the subject of the verb can.

Gerunds are usually used as subjects of sentences, after certain verbs (such as enjoy and look forward to) and after prepositions.

Step-by-step explanation:

hmph................

Answer:

800 × ( 3.87÷ 100 ) × 1

= 30.96

Answer:

x = 11

Step-by-step explanation:

5x - 8 + 43 = 90

5x = 55

x = 11

Step-by-step explanation:

5x - 8° + 43° = 90° (right Angle)

5x + 35° = 90°

5x = 90° - 35°

5x = 55°

x = 55°/5

x = 11°

5x - 8 = 5 × 11 - 8 = 47°

The first angle is 47° and second one is 43°.

Answer:

C

Step-by-step explanation:

A P E X

Answer:

1/12

Step-by-step explanation:

Fraction is the representation of the parts of a whole number. The amount of cake ate by Norma in the lunch is 9/32 parts.

Total cake left over by the Norma after the party is 3/8.

Total cake she ate for the lunch is 3/4.

The value of the whole cake is given in the fraction parts. To solve this the fraction should be understood.

Fraction is the representation of the parts of a whole number.

As the one whole of cake was there earlier. The 3/8 part of the cake is,

[tex]=\dfrac{3}{8}[/tex]

As she ate the 3/4 part of the left over cake in the lunch. Suppose the part of cake she ate is x. Therefore the part of cake she ate at lunch is,

[tex]x=\dfrac{3}{8} \times\dfrac{3}{4}[/tex]

[tex]x=\dfrac{9}{32}[/tex]

Hence, the amount of cake ate by Norma in the lunch is 9/32 parts.

Learn more about the fraction here;

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Step-by-step explanation:

5/6 was 0.833333333333333

Answer:

where are the numbers?

Step-by-step explanation:

Answer:

Ur in collage??

Step-by-step explanation:

Im in middle school learning this!! and what r the numbers?

Answer:

Step-by-step explanation:

3³ × 4³ = (3×4)³ = 12³

:::::

3⁴ × 3³ = 3⁴⁺³ = 3⁷

:::::

3⁴ × 4³ = 3 × 3³ × 4³ = 3 × (3³ × 4³) = 3 × 12³ < 12¹²

Answer:

(c).

Step-by-step explanation:

h(t) = - 16 t² + 80 t

Coordinates of the vertex are:

t = - [tex]\frac{80}{2(-16)}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 sec.

h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.

Answer:

x = -4

Step-by-step explanation:

x= 3 is a parallel to y axis. So a parallel line to x = 3 must be parallel to y axis.

A line parallel to y axis has a generic equation: x = h. We know that the line passes to the point with has x coordinate = -4

So the equation is x= -4

9514 1404 393

Answer:

  6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)

  7. (a, b, C) ≈ (180.5, 238.5, 145°)

Step-by-step explanation:

My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.

__

We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.

6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...

  A = arccos((b² +c² -a²)/(2bc))

  A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°

The other angles can be found by permuting the variables appropriately.

  B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°

The third angle can be found as the supplement to the other two.

  C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°

The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).

__

7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.

  C = 180° -A -B = 145°

  a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49

  b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52

The measures (a, b, C) are about (180.5, 238.5, 145°).

Answer:

5/7

Step-by-step explanation:

take the basic fact 5 - 3

Answer:

5/7

Step-by-step explanation:

3/7+2/7=5/7

5/7-3/7=2/7