3. Plumbers deal with measurements in inches and common fractions of an inch, while surveyors use feet and decimal
fractions of a foot. Often one trade needs to interpret the measurements of the other.
(a) A drain has a run of 52 ft at a grade of 1/8 in./in. The high end of the drain has an elevation of 126.30 ft. What is the elevation at the low end?
(b) The elevation at one end of a lot is 84.12 ft, and the elevation at the other end is 94.67 ft. Express the difference in elevation in feet and inches and rounded to the nearest 1/8 in

The exponential model for the lily pad colony is L(t) = A[tex](1+r)^{kt}[/tex] and the values of A=5 and k=1.2.

Over time, anything grows in quantity through an exponential growth process. When a quantity's rate of change over time (or derivative) is proportional to the quantity itself, this phenomenon takes place. A number that is increasing exponentially is referred to as a function, and the exponent, which stands for time, is the variable that represents time (in contrast to other types of growth, such as quadratic growth).

When a quantity decrements with time, it is considered to be experiencing exponential decay rather than a positive constant of proportionality. It is also known as geometric growth or geometric decay when the definition's discrete domain has equal intervals since the values of the function form a geometric progression.

Given, there are 5 lily pads that are found in a pond

And after 30 days, there are 16 lily pads in that pond

Here, a=5

r=(11-5)/5=1.2

f(x)=a(1+r)ˣ

f(x)=5(1+1.2)³⁰

From the above equation, A=5, and k=1.2

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The total number of hours that Jerry would work during a week to make at least $700.00 is 11 hours

information given in the query

The amount of Jerry's pay every week before taxes, J,

a function of the number of overtime hours that he works (the number of hours over 40), h

J = $493.60 + $18.51h

The given equation is an equation of linear function

considering the equation J = $493.60 + $18.51h, the number of hours that Jerry would work is gotten by substituting the value of $700.00 and solving for number of hours

J = $493.60 + $18.51h

700 = 493.60 + 18.5h

18.5h = 700 - 493.60

18.5h = 206.4

h = 11.16

h = 11 hours

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The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

sin 18° = √(3 - √5) / 2√2

cos 18° = √ (5 + √5) / 2√2

Now,

Find the value of sin 3° as;

⇒ sin 3° = sin (18 - 15)°

   = sin 18° cos 15° - cos 18° sin 15°

   = √(3 - √5) / 2√2 × (√3 + 1) / 2√2  - √(5 + √5) / 2√2 × (√3-1)/2√2

   = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

Thus, The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

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The theorem that proves that the triangles are congruent is the Hypotenuse-leg (HL) Congruence Theorem. The correct option is the first option - HL Congruence Theorem

From the question, we are to determine by what theorem of postulate the triangles can be proven congruent.

From the Hypotenuse-leg theorem which states that "if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent".

From the given diagram, we can observe that the hypotenuse of the first triangle is congruent to the hypotenuse of the second triangle. Likewise, we can observe that one of the legs of the first triangle is congruent to the one of the legs of the other triangle.

Hence, the triangles are congruent by the Hypotenuse-leg theorem.

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Using the geometric mean theorem,

[tex]\frac{y}{14.4}=\frac{14.4}{19.2} \\ \\ y=10.8[/tex]

Using Pythagoras on triangle [tex]ABD[/tex],

[tex]x=\sqrt{14.4^2+10.8^2}=18[/tex]

Triangles [tex]ABD[/tex] and [ted]CBD[/tex] are similar because corresponding angles are congruent and pairs of corresponding sides have proportional lengths.

To determine this, use the complementary angles.

The pitcher that has the lowest number of runs allowed per inning is Randy.

In order to determine the pitcher with the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.

Division is the process of determining the quotient of two or more numbers. It is the process of putting a number into equal groups using another number.

Number of runs per innings = number of runs / number of innings

Number of runs per innings for Randy : 2 / 3 = 0.667

Number of runs per innings for Felix : 4 / 5 = 0.80

Number of runs per innings for Johan: 5 / 7= 0.714

Here is the complete question:

A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.

Which pitcher has the lowest number of runs allowed per inning?

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The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:

X = N(17.5)

Where μ = 17.5 and σ = 4

Since the distribution for X is normal then, the distribution for the sample mean  is given by:

X = N(17.5, σ/√n)

X =N(17.5.4/√50) = 0.566

We select a sample of n =50 people. And we want to find the following probability

P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )

And using the normal standard table or excel we find the probability:

P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92

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Answer:

x=28

Step-by-step explanation:

angle b and angle c are the same measure because it is a iso triangle.

you know triangle sum is 180 so 3x+2(x+20)=180. simplify it to 5x=140

divide both sides by 5

x=28

Answer:

x = 28

Step-by-step explanation:

The triangle is isosceles, meaning that the two base angles (x + 20) are congruent. We can then create an equation that states: (x + 20) + (x + 20) + 3x = 180. Simplifying this, we get 5x + 40 = 180. We can then use reverse order of operations to solve it. Subtract 40 from both sides to get 5x = 140. We will then divide both sides by 5 to get x by itself, getting us the equation x = 28.

Answer: 13

Step-by-step explanation:

20(.65) = 13

Hope that helps!

1/2 is the probability of getting at least one answer correct

Given that: the exam has 4 multiple choice with 5 possible answers. This means there are 20 possible choices ( 5×4 = 20).

That means each problem has a probability of 1/20 correct answer. The probability of getting at least one answer means you either get one, two, three or four correct answers. Thus:

P (at least one correct) = P(1) + P(2) + P(3) + P(4)

                                      = 1/20 + 2/20 + 3/20 + 4/20

                                      = (1+2+3+4)/20

                                     = 10/20

                                     =   1/2

Therefore, the probability of getting at least one answer correct is 1/2

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The probability of getting at least one answer correct is equal to 7

That I guess at least one answer correctly means that I could get all four answers correct or three answers correct or two answers correct or only one answer correct. The probability of getting any one answer is 1/4 and probability of not getting an answer is 1 - 1/4=3/4. Or implies addition.

probability of getting all four answers correct = 1/4 +1/4 + 1/4 + 1/4 = 4/4 = 1

probability of getting three answers correct = 1/4 +1/4 + 1/4 + 3/4 = 6/4 = 3/2

probability of getting two answers correct = 1/4 +1/4 + 3/4 + 3/4 = 8/4 = 2

probability of getting all four answers correct = 1/4 +3/4 + 3/4 + 3/4 = 10/4 = 5/2

The probability of getting at least one answer correct = 1 + 3/2 + 2 + 5/2

The probability of getting at least one answer correct = (2 + 3 + 4 + 5)/2

The probability of getting at least one answer correct = 14/2

Thefore, the probability of getting at least one answer correctly is the whole number 7

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ 1 }{ -2 } \implies - \cfrac{1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{3}) \\\\\\ y-1=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}\implies y=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}+1\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x+\cfrac{5}{2} \end{array}}[/tex]

Answer: 3x²(5x+y)

Step-by-step explanation:

15x³ + 3x²y​

Apply exponent rule: 15x²x+3x²y

Rewrite 15 as 5*3: 5*3x²x+3x²y

Factor out common terms 3x²: 3x²(5x+y)

Hope this helps!!! :)

The amount of Tritium that bottle contains now will be 439,421.

Consider the function:

y = a (1 - r)ˣ

Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.

Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.

Then the amount of Tritium that bottle contains now will be given as,

y = 856,000 (1 - 0.05)¹³

Simplify the equation, then we have

y = 856,000 (1 - 0.05)¹³

y = 856,000 (0.95)¹³

y = 856,000 (0.51334)

y = 439,421

The amount of Tritium that bottle contains now will be 439,421.

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The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

Given,

When using re-grouping to solve 25 x 45, we have to find the problems that would be calculated to find the final answer;

Here,

25 × 45 = 1125

Now,

This is simply multiplicity;

1. 20 x 40: 20 x 5: 40 x 5

800 ; 100 ; 200

1100

This is not the problem.

2. 20 x 40; 5 x 40; 20 x 5 ; 5 x 5

800 ; 200 ; 100 ; 25

1125

This is the problem

3. 20 x 40 ; 5 x 20 ; 20 x 5 ; 5 x 5

800 ; 100 ; 100 ; 25

1025

This is not the problem

4. 20 x 20 ; 40 x 40 ; 20 x 5 ; 5 x 5

400 ; 1600 ; 100 ; 25

2125

This is not the problem

Therefore,

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

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a) The test statistic is: t = -1.11.

b) The p-value is: 0.1342.

c) The conclusion is that the null hypothesis is not rejected.

d) The final conclusion is that there is not sufficient evidence to conclude that the population mean is of 6.

The standard deviation for the population is unknown, only the sample standard deviation is known, hence the t-distribution is obtain the test statistic.

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the variables of the equation are given as follows:

For this problem, the values of these parameters are as follows:

[tex]\overline{x} = 5.83, \mu = 6, s = 2.11, n = 189[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{5.83 - 6}{\frac{2.11}{\sqrt{189}}}[/tex]

t = -1.11.

The p-value is obtained using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less a value, with 189 - 1 = 188 df and t = -1.11, hence it is of 0.1342.

Since the p-value is greater than the significance level of 0.10, it is found that:

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Step-by-step explanation:

3 consecutive even integer numbers :

x

x + 2

x + 4

their sum is the perimeter : 60 ft.

x + x + 2 + x + 4 = 60

3x + 6 = 60

3x = 54

x = 18

the shortest of the 3 sides is 18 ft.

and then we have the other 2 sides with 20 and 22 ft.

Answer:

Step-by-step explanation:

1.) -112*-7=784

784=v+4

2.)784-4=780

v=780

Answer:

v = 12

Step-by-step explanation:

-112 = -7v -28

7v = 112 - 28

7v = 84

7/7 v = 84/7

v = 12

Answer:

-2/5

Step-by-step explanation:

the slope is change in y over change in x

formula for slope is

(y2-y1)/(x2-x1), so if you input the coordinates, (10-(-2))/(-11-19) = 12/30 = 2/5

The expression that Langston have written -24 +3.

Expression:

Expression refers the finite combination of symbols that is well-formed according to rules that depend on the context and it consists of numbers, mathematical operations etc.

Given,

Langston wrote an expression with a value of -21.

Here we need to find the expression that could Langston have written.

In order to find the correct expression we have to solve each and every one in the options,

When we take the first expression

-20 - (-1)

Which is equal to

=> -20 + 1

When we simplify it then we get

=> -19

Then the second one is simplified as,

=> -25 - 4 = -29

And the third one given the value of

=> -24 + 3

=> -21

Therefore, this one is the correct expression and this one is taken by Langston.

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Answer:

θ = 64.98310506 degrees (65 degrees rounded to unit)

Step-by-step explanation:

4.2 * tanθ = 9

4.2 * tanθ/ 4.2 = 9/4.2

tanθ = 2.142857

θ = arctan 2.142857

θ = 64.98310506

Step-by-step explanation:

using the SOH CAH TOA Rule,

tan 0=opp÷adj

tan 0=9÷4.2

tan 0=2.14

0=tan inverse of 2.14

The value of cos 2A/cos A-sin A = cos A + sin A is proved

cos 2A =  2cos²A - 1

= 2cos²A - (sin²A + cos²A)

= 2cos²A - sin²A - cos²A

= cos²A - sin²A

We need to prove that

cos 2A/cos A-sin A = cos A + sin A

L.H.S

cos 2A/cos A-sin A

= cos²A - sin²A/ cos A-sin A

= (cos A + sin A)(cos A-sin A)/ cos A-sin A

= cos A + sin A

R.H.S

LHS = RHS proved

Therefore, cos 2A/cos A-sin A = cos A + sin A is proved

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Answer:

The answers are:

1. 2(x2 + 6x + 9) = 3 + 18

2. 2(x2 + 6x) = 3

Let's take a look at the first choice:

2(x² + 6x + 9) = 3 + 18

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's take a look at the second choice:

2(x² + 6x) = 3

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0 Man that was so hard MARK ME Brainilest Thanks Peace

Step-by-step explanation:

Answer:

- 18

Step-by-step explanation:

let the number be n then double the number is 2n and

2n + 32 = [tex]\frac{2}{9}[/tex] n

multiply through by 9 to clear the fraction

18n + 288 = 2n ( subtract 2n from both sides )

16n + 288 = 0 ( subtract 188 from both sides )

16n = - 288 ( divide both sides by 16 )

n = - 18

the original number is - 18

Answer:

I think the answer is 33?

Answer:

Step-by-step explanation:

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