100.00 decreased by 20%
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Answer:  [tex]\boldsymbol{37.5} < \mu < \boldsymbol{44.5}[/tex]

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Explanation:

At a 90% confidence level, the z critical value is roughly z = 1.645. Use a reference table or a calculator to determine this. Despite not knowing what sigma is, we can use a z interval here because n > 30. If the sample size n was smaller than 30, then we'd have to use a T distribution instead.

We'll plug that z value, along with the other given values, into the formula for the lower boundary L of the confidence interval.

[tex]L = \text{lower boundary}\\\\L = \overline{x} - z*\frac{s}{\sqrt{n}}\\\\L = 41 - 1.645*\frac{12}{\sqrt{31}}\\\\L = 41 - 3.545\\\\L = 37.455\\\\L = 37.5\\\\[/tex]

This value is approximate.

Do the same for the upper boundary as well

[tex]U = \text{upper boundary}\\\\U = \overline{x} + z*\frac{s}{\sqrt{n}}\\\\U = 41 + 1.645*\frac{12}{\sqrt{31}}\\\\U = 41 + 3.545\\\\U = 44.545\\\\U = 44.5\\\\[/tex]

This value is also approximate.

We have 90% confidence that the population mean [tex]\mu[/tex] (greek letter mu) is somewhere between L = 37.5 and U = 44.5

Therefore, we would write the 90% confidence interval as [tex]\boldsymbol{37.5} < \mu < \boldsymbol{44.5}[/tex]

This is the same as writing the confidence interval in the form [tex](\boldsymbol{37.5} , \boldsymbol{44.5})[/tex]. Both forms are two different ways to say the same thing. The first form being [tex]L < \mu < U[/tex] while the second form is [tex](L,U)[/tex].

Side note: The value 3.545 calculated earlier is the approximate margin of error.

9514 1404 393

Answer:

  B = 5

Step-by-step explanation:

The given equation has mismatched parentheses. We assume the intent is ...

  2(b +3.5) -b = -3(6 -2b)

Eliminating parentheses, we have ...

  2b +7 -b = -18 +6b

  25 = 5b . . . . . . . . . . . add 18-b to both sides and collect terms

  b = 5 . . . . . . . . . . . . divide both sides by 5

The length of the longest pipe that can be carried horizontally is given by the minimum value of the function of the length of the pipe.

The longest length that the pipe can be is approximately 16.648 feet.

Reasons:

The length of the pipe, L

Width of the first hallway = 8 ft.

The width of the second hallway = 4 ft.

We have;

(L - a)·sin(θ) = 8

a·cos(θ) = 4

Therefore;

L - a = 8·csc(θ)

a = 4·sec(θ)

L(θ) = 8·csc(θ) + 4·sec(θ)

At the minimum length, we have;

L'(θ) = 4·sec(θ)·tan(θ) - 8·csc(θ)·cot(θ) = 0

4·sec(θ)·tan(θ) = 8·csc(θ)·cot(θ)

Therefore;

[tex]\displaystyle \frac{sec(\theta) \cdot tan(\theta)}{csc(\theta) \cdot cot(\theta)} = \frac{sin(\theta) \cdot tan(\theta) \cdot tan(\theta) }{cos(\theta) } =tan^3(\theta) = \frac{8}{4}[/tex]

[tex]\displaystyle tan(\theta) =\sqrt[3]{\frac{8}{4} } ={\sqrt[3]{2} }[/tex]

θ = arctan([tex]\sqrt[3]{2}[/tex]) ≈ 51.56°

a = 4×sec(arctan([tex]\sqrt[3]{2}[/tex]))

a ≈ 6.434

L = 8·csc(θ) + a = 8 × csc(arctan([tex]\sqrt[3]{2}[/tex])) + 4×sec(arctan([tex]\sqrt[3]{2}[/tex])) ≈ 16.648

The longest length that the pipe can be, L ≈ 16.648 ft.

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The longest length of the pipe is an illustration of trigonometry functions

The longest length of the pipe is 16.64 ft

The widths of the hallways are given as:

[tex]\mathbf{w_1 = 8}[/tex]

[tex]\mathbf{w_2 = 4}[/tex]

See attachment for the diagram that represents the scenario

From the diagram, we have:

[tex]\mathbf{sin(\theta) = \frac 4x}[/tex]

[tex]\mathbf{cos(\theta) = \frac 8y}[/tex]

Make x and y the subject

[tex]\mathbf{x = \frac 4{sin(\theta)}}[/tex]

[tex]\mathbf{y = \frac 8{cos(\theta)}}[/tex]

Where, the total length (L) of the pipe is:

[tex]\mathbf{L = x + y}[/tex]

So, we have:

[tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]

Differentiate

[tex]\mathbf{L' = -\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]

Set to 0

[tex]\mathbf{-\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)} = 0}[/tex]

Rewrite as:

[tex]\mathbf{\frac{4cos(\theta)}{sin^2(\theta)} = \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]

Divide through by 4

[tex]\mathbf{\frac{cos(\theta)}{sin^2(\theta)} = \frac{2sin(\theta)}{cos^2(\theta)}}[/tex]

Cross multiply

[tex]\mathbf{2sin^3(\theta) = cos^3(\theta)}[/tex]

Divide both sides by [tex]\mathbf{2cos^3(\theta)}[/tex]

[tex]\mathbf{tan^3(\theta) = \frac 12}[/tex]

Take cube roots of both sides

[tex]\mathbf{tan(\theta) = \sqrt[3]{\frac 12}}[/tex]

[tex]\mathbf{tan(\theta) = 0.7937}[/tex]

Take arc tan of both sides

[tex]\mathbf{\theta = tan^{-1}(0.7937)}[/tex]

[tex]\mathbf{\theta = 38.4}[/tex]

Substitute [tex]\mathbf{\theta = 38.4}[/tex] in [tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]

[tex]\mathbf{L = \frac 4{sin(38.4)} + \frac 8{cos(38.4)}}[/tex]

Evaluate

[tex]\mathbf{L = 6.43+ 10.21}}[/tex]

[tex]\mathbf{L = 16.64}}[/tex]

Hence, the longest length of the pipe is 16.64 ft

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Step-by-step explanation:

earbuds

we have a 1in : 0.2in scale of drawing to reality.

0.2 = 2/10 = 1/5

so, 1in in the drawing is actually 1/5in in reality.

how long are the 4in in the drawing ?

well, 4 times the 1in thing.

4×1/5 = 4/5 = 0.8in long

again the similar triangles

similar triangles means that each pair of corresponding lines (sides, heights, ...) in the triangles follows the same scaling factor for the length.

so, what do I need to multiply the side of the large triangle with to get the corresponding side length of the small triangle ?

27 × x = 9

x = 9/27 = 1/3

and that is the scale factor.

Answer:

Richard is twenty-six and Teo is ten.

Step-by-step explanation:

Let x = Richard's age and y = Teo's age

x = 2y + 6

(2y + 6) + y = 36

3y + 6 = 36

-6            -6

3y = 30

y = 10

x = 2(10) + 6

x = 20 + 6

x = 26

Richard is 26

Teo is 10

Answer:

The answer is 7.48 or 7.5

Step-by-step explanation:

If the circumference is C which is equal to 47 feet, what you have to do is divide it by pi, or 3.14 for an estimate. After that, you'll get the diameter and then divide it by 2. Now you have your radius.

Answer:

y = — 9/2x + 6

Step-by-step explanation:

m= —9/2

y — y1 = m (x — x1)

y + 3 = —9/2 (x — 2)

y = — 9/2x + 6

Answer:

400/π

Step-by-step explanation:

Well, we know that the formula for circumference is πd. (d is the diameter) Then, we set up the equation 'πd = 400'. Now, simplifying for d, we get d = 200/π.

Answer:

400/π

Step-by-step explanation:

Answer:

AC=14

X=10

Y=1

Hoped this helped!

Step-by-step explanation:

DE is half of BC, therefore x=10. AE and EC have to be the same length, which is 7. SO, y=1 and x is 10.

Answer:

The answer would be 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.

Hope it help and if it its correct please give brainliest  

Stay Safe And Healthy

Thank You

Answer:

Step-by-step explanation:

1 3/10 x 18

(1 x 10 +3)/10 = 13/10

13/10 x 18 = (13 x 18) / 10 = 234/10 = (234/2) / (10/2) = 117/5 = 23 2/5 (a fraction is a division)

The answer to the expression showing the product of 1 3/10 x 18 is 23 2/5.

Given is an expression showing the product of 1 3/10 x 18, we need to solve it,

To multiply a mixed number by a whole number, you can convert the mixed number to an improper fraction and then multiply the fractions.

Here's how you can solve the problem:

Step 1: Convert the mixed number to an improper fraction:

1 3/10 = (1 × 10 + 3) / 10 = 13/10

Step 2: Multiply the fractions:

13/10 x 18/1 = (13 x 18) / (10 x 1) = 234 / 10

Step 3: Simplify the fraction, if possible:

234/10 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

234/10 = (234 ÷ 2) / (10 ÷ 2) = 117/5

Therefore, 1 3/10 x 18 = 117/5.

Alternatively, you can express the answer as a mixed number by dividing the numerator by the denominator:

117 ÷ 5 = 23 with a remainder of 2

So, the final answer is 23 2/5.

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Answer:

the info they gave us is to suppose that angle 6 is = 126°

step 1:

We know that angle 8 = angle 6 = 126°

Why? — when a circle (360°) is split by 2 lines that intersect, there will be 2 equal pairs of angles formed

step 2:

angle 2 = angle 8 = 126°

Why? — they’re alternate angles

step 3:

angle 4 = angle 2

Why? — when a circle (360°) is split by 2 lines that intersect, there will be 2 equal pairs of angles formed

step 4:

angle 1 = 180-126 (angle 4) = 54°

Why? — total angles in a straight line = 180°

Key Term:

Alternate angles:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Answer:

Step-by-step explanation:

2(144) = 288 cm²

Answer:

[tex]5^{\frac{5}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponent

[tex]\sqrt[3]{a}[/tex] = [tex]a^{\frac{1}{3} }[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

[tex]\frac{25}{\sqrt[3]{5} }[/tex]

= [tex]\frac{5^2}{5^{\frac{1}{3} } }[/tex]

= [tex]5^{\frac{6}{3}-\frac{1}{3} }[/tex]

= [tex]5^{\frac{5}{3} }[/tex]

Answer:

Step-by-step explanation:

2 : (-2.5) + 4.1 + 1.2 * (3+6) : (-0.1 ) =

-0.8 + 4.1 + 10.8 : (-0.1) =

-0.8 + 4.1 + (-108) =

3.3 - 108 =

-104.7

Check the picture below.

Answer:

The quotient is 10x+16

The remainder is 28x^2+10x+22

Step-by-step explanation:

(18+12+15+19)÷5

64÷5

15

Answer:

Step-by-step explanation:

If 2% × 410 = 8.2 => Divide 8.2 by 410And see if we get as a result: 2% Note: Multiply a number by the fraction 100/100, and its value doesn't change.

Answer:

m = 410

Step-by-step explanation:

Let the number be n.  Then:

 8.2

--------- = 0.02

    n

Cross-multiplying yields 0.02n = 8.2, from which we find n = 410

Recall that a percentage, such as 2%, is equivalent to a decimal fraction, such as

2%

-------- = 0.02

100%

Answer:

just look at picture's That's the answer

Answer:

1.13

Step-by-step explanation:

to turn a fraction to a decimal divide the denomitator by the numerator [tex]\frac{-25}{22}[/tex] can also be written as -25÷22 which equals 1.13 or 1.136 with a line over it

Hope this helps!

Answer:

Correct choice: B

Step-by-step explanation:

Equation Solving

The area of a trapezoid with height h and bases b1 and b2 is given by:

We must solve this formula for h.

First, multiply by 2 to eliminate denominators:

Now, divide by b1+b2:

Swapping sides:

Correct choice: B

Answer:B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

               3x = -6 --->  x = -2

Answer:

expression.

2(4x+3y)

2(4(4)+3(7))

2(16+21)

2( 37)

74

Answer:

fuctions and constants

Step-by-step explanation:

please mark as brainliest if it helped :D

Answer:

B. 0.36

Step-by-step explanation:

9/25 = x/100

9x100= 900

900 divided by 25 will be 36/100, so 0.36

Answer:

B) 26,400

An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?

13,200

26,400

39,600

79,200

158,400

26400 yards of cable is used.

the answer is B) 26,400

What is unit conversion?

Unit conversion is the process of changing a physical quantity from one unit of measurement to another. For example, converting kilometers to miles, Celsius to Fahrenheit, or liters to gallons. The process involves multiplying or dividing the original measurement by a conversion factor, which is a ratio of equivalent units

To convert miles to yards, we need to multiply by the conversion factor of 1 mile = 1760 yards.

15 miles * 1760 yards/mile = 26,400 yards

So, the electrician will use 26,400 yards of cable.

Hence, 26400 yards of cable is used.

the answer is B) 26,400

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