A machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long. What is the total length needed in inches?

The process of logarithmic functions in real-worlds problems is given below.

And an example of an application of logarithmic function is given.

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

We know,

logarithmic function and exponential function are inverse of each other.

So, whenever we solve the exponential function,

we use the help of logarithmic functions.

To compute the number with bigger exponents,

we use the logarithms.

Because it reduces the size of the numbers.

Let the bacteria is growing exponentially,

b = 2ⁿ.

We know that the bacteria grows every hour.

We want to find time.

Here, we will use the inverse function to the exponential function.

How long will it take them to get 1000 bacteria?

1000 = 2ⁿ

Taking log on both sides,

log(1000) = n log2

n = log(1000)/log(2)

n = 9.96

n ≈ 10 hours.

Therefore, an application of logarithmic function is given above.

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The graph of a piecewise function f(x) = 3x if x ≤ 3 and f(x) = 2x if x > 3 is shown in the picture.

The graph of a piecewise function contains numerous curve components. It signifies that it has a plethora of definitions based on the value of the input. In other words, a piecewise function behaves differently depending on the input.

We have:

f(x) = 3x if x ≤ 3

f(x) = 2x if x > 3

We can draw the piecewise function as shown in the attached picture.

At x = 3

f(3) = 3(3) = 9 because f(x) = 3x if x ≤ 3

Thus, the graph of a piecewise function f(x) = 3x if x ≤ 3 and f(x) = 2x if x > 3 is shown in the picture.

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The value of x is -4 and the value of y is 1.

In order to use the elimination method, rearrange the given linear equations.

y - 3x = 13 equation 1

y - 2x = 9 equation 2

Subtract equation 2 from equation 1:

-x = 4

x = -4

Substitute for x in equation 2

y - 2(-4) = 9

y  + 8 = 9

y = 9 - 8

y = 1

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Answer:

It would take Samantha 6 hours to drive 105 miles.

Step-by-step explanation:

This question can be solved by proportions.

After 4 hours she had traveled 70 miles.

This means that she travels 70/4 = 17.5 miles per hour.

How many hours would it take Samantha to drive 105 miles?

17.5 miles per hour, so for 105 miles:

105/17.5 = 6

It would take Samantha 6 hours to drive 105 miles.

The newly rewritten function expression of V(x) is V(x) = (x)(x + 1)(x – 2)/1000

From the question, we have the following parameters that can be used in our computation:

A function expression

The function expression is given as

V(x) = (x)(x + 1)(x – 2)

Where if x is in centimeters and V(x) is in cubic centimeters

The new function for the volume of the refrigerator is stated to be in cubic millimeters

Using the above as a guide, we have the following:

1 cubic centimeters = 1000 cubic millimeters

So, we have

V(x) = (x)(x + 1)(x – 2)

1 cubic centimeters = 1000 cubic millimeters

Cross multiply

V(x) * 1000 = 1* (x)(x + 1)(x – 2)

Divide both sides by 1000

V(x) = (x)(x + 1)(x – 2)/1000

Hence, the function is V(x) = (x)(x + 1)(x – 2)/1000

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Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.

Here,

are the definitions of each equation:

1. x^2 + y^2 - 4x + 6y - 5 = 0

 The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.

2. x^2 - 6y = 0

 The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.

3. 4x^2 + 9y^2 = 1

This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.

4. 7x^2 - 9y^2 = 343

 A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.

Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

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Answer:

Side A = 11

Side B = 16

Side C = 25

I added an image that shows what I did in case you need it.

Answer:

I don't know if this is right but I think it is 32m

Answer:

Hello! answer:

question 30: 128 m2

question 31: 1188 in2

Step-by-step explanation:

Hello just in advance I dont know if you need unuts or not but i believe those are correct if not Im sorry but the answers are 100% correct.

For the first one I found the area of a singular triangle then just multiplued by 4 cause all of those triangles are the same so... triangle area is... base × height ÷ 2 or base × height × 1/2

8 × 8 = 64 64 ÷ 2 = 32 32 × 4 = 128 therefore the area is 128 for the second I just did base × height therefore 36 × 33 = 1188 therefore thats the area hope that helps!

The sale price of the item is given by the equation A = $ 26.40

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the sale price of the item be represented as A

Now , the equation will be

The original price of the item = $ 33

An item on sale costs 80% of the original price

So , the sale price of the item A = 80 % x original price of the item

Substituting the values in the equation , we get

The sale price of the item A = ( 80 / 100 ) x 33

The sale price of the item A = 0.80 x 33

The sale price of the item A = $ 26.40

Therefore , the value of A is $ 26.40

Hence , the sale price is $ 26.40

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Step-by-step explanation:

Answer: 2/4, 4,8, etc.

Step-by-step explanation:

Hello!

So basically, what I think this question is asking is for an equivalent fraction to 1/2. There are countless fractions that are the same as this and I listed a couple above!

Hope this helps! :D

Answer:

y=4

Step-by-step explanation:

Answer:

y=2.5

Step-by-step explanation:

first you add -3x to both sides so you get 5-3x and then divide that by 2 to get Y by itself so now you have 5/2 - 3/2x and when you put in the equation y=5/2 - 3/2x in DESMOS, the answer is 2.5

===================================================

Explanation:

Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).

Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:

20*cos(x)+25

20*(-1) + 25

-20 + 25

5

The height of the fan tip is 5 cm when it is the closest to the table.

Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is [tex]5 \le y \le 45[/tex]

Answer:

N = 2

Step-by-step explanation:

We must solve for N.

Solve inside the parenthesis if needed, otherwise open them

7n + 21 = (14) + (21)

Now solve, then simplify

7n + 21 = 35

7n = 35 - 21

7n = 14

N = 2

Answer: 22

Step-by-step explanation:

(1 × 3) + [2 × 3 [tex]\frac{1}{2}[/tex]] + [1 × 3 [tex]\frac{3}{4}[/tex] [1 × 4 [tex]\frac{1}{4}[/tex]] + [3 × [tex]\frac{3}{4}[/tex]] + [3 × 5 [tex]\frac{1}{4}[/tex]]

= 3 + [2 × [tex]\frac{3}{2}[/tex]] + [1 × [tex]\frac{9}{4}[/tex]] + [1 × [tex]\frac{4}{4}[/tex]] + [3 × [tex]\frac{12}{4}[/tex]] + [3 × [tex]\frac{5}{4}[/tex]]

= 3 + [tex]\frac{6}{2}[/tex] +  [tex]\frac{9}{4}[/tex] +  [tex]\frac{4}{4}[/tex] (equal to 1) + [tex]\frac{36}{4}[/tex] + [tex]\frac{15}{4}[/tex]

= 3 + 3 + [tex]\frac{9}{4}[/tex] + 1 + 9 + [tex]\frac{15}{4}[/tex]

= 16 + [tex]\frac{9+15}{4}[/tex]

= 16 + [tex]\frac{24}{4}[/tex]

= 16 + 6

= 22

Answer:

Mizuki is here to help! The answer is D!

Step-by-step explanation:

Ok... So there are 24 students in the class and no other students in the class has the same name right? So the fraction should be [tex]\frac{3}{24}[/tex] since there are three madisons, which will be 0.125!

Since three people have the same name, everyone else gets less probability of getting called so the answer would be D.

Answer:

Option D

Step-by-step explanation:

Total Students in a class: 24

Total Madisons in the class: 3

Denominator is always the total number of something so; [tex]\frac{3}{24}[/tex]

3/24 = 0.125

Any other student would have a probability of [tex]\frac{1}{24}[/tex] of being chosen which is less than [tex]\frac{3}{24}[/tex], therefore, Option D is the most sensible one.

Hope this helps!

Answer:

x = 25

Step-by-step explanation:

This is a similar triangle problem

Therefor two sides of triangle A are in the same proportion as two sides of triangle B

----------------------------

Triangle A

Short leg = x

Long leg = 60

proportion = x/60

Triangle B

Short Leg = 60

Long leg = 144

proportion = 60/144

Therefor

x/60 = 60/144

multiply both sidees by 60

x = 60*60/144

x = 25

Answer:

x=1 if that's 15 x

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

Answer:

95

please don't

The fractional form of the expression [tex]\sqrt[3]a[/tex] is [tex]a^{\frac{1}{3}[/tex]

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, A radical expression [tex]\sqrt[3]a[/tex].

We know this describes the cube root of a or one-third root of a.

This can be written as a fractional exponent as [tex]a^{\frac{1}{3}[/tex].

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

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Answer: k^3=1

Step-by-step explanation:

Answer:k^3=1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

122

Step-by-step explanation:

<HEB=180-(42+32)

=180-74

=106

<DEA=180-106 (straight line)

=74

<NAD=48+74(exterior angle = sum of 2 interior opposite angles)

<NAD=122

Answer:

4th option

Step-by-step explanation:

open circle means more than or less than

n is more than -3 but less than 1

Answer:

1

Step-by-step explanation:

A coin only has two outcomes. Meaning that she has a 50/50 chance of landing on each side. So, 50% of 20 is 10. According to the theoretical  probabilty, the coin would have landed on heads 10 times and tails 10 times. So, for that to be true Maria would have had to land on tails one more time.  

Answer:

C) 25

Step-by-step explanation:

First, solve for the height (red dotted line) using the Pythagorean theorem 9²+b²=15²

81+b²=225

b²=225-81

b²=12

Then set up a ratio.

x/12=9/15

simplify

x/12=3/5

cross-multiply

3x=60

x=20

This gives us the base.  Now we can solve for x using the Pythagorean theorem again.

20²+15²=x²

400+225=x²

625=x²

√x²=√625

x=25

Answer:

d. 1/4

Step-by-step explanation:

comment if u need explanation

Answer:

it's D. 1/4

Step-by-step explanation: hope that helps

Answers:

The values are approximate. Round them however you need to.

====================================================

Explanation:

The diagram you have drawn is correct if you're only considering one current. Specifically current #1 which has the bearing of 290 degrees moving at 25 knots.

The red angle is 290 degrees. The remaining portion that is needed to get a full 360 degrees is 360-290 = 70. This adds to the blue portion in quadrant 1, which is 90, and we get 70+90 = 160. So the blue angle is 160 degrees.

The vector for current #1 is <25*cos(160), 25*sin(160)>

This approximates to <-23.4923155, 8.5505036>

All of this is for current #1.

------------

Vector #2 is much more simple in terms that there aren't messy decimal approximations here. The direction is due north, which means that the vector is pointing straight up toward 90 degrees.

We can then say: <12*cos(90), 12*sin(90)> = <12*0, 12*1> = <0, 12>

Vector #2 is <0,12>

When you wrote <12,0>, you were on the right track, but you had the coordinates swapped in the wrong order.

----------

Then we have to account for a wind going 4 knots in the southwest direction. This is at the angle 225 degrees (we rotate 180 degrees plus another 45 to get 225). So,

vector #3 = <4*cos(225), 4*sin(225)> = <-2.8284271, -2.8284271>

This vector's coordinates are approximate

---------

To recap everything so far, vectors 1 through 3 are the following

I'm using variables to represent the vectors at this point, so we can then add them up to get...

s = p+q+r

s = <-23.4923155, 8.5505036> + <0,12> + <-2.8284271, -2.8284271>

s = <-23.4923155+0+(-2.8284271), 8.5505036+0+(-2.8284271)>

s = <-26.3207426, 5.7220765>

Vector s represents the sum of the three vectors p, q, and r. The two currents and the wind ultimately combine together to push the boat in the direction and along the length of vector s.

----------------------

Now that we know the coordinates of vector s, we use them to find the true speed and true bearing of the boat.

speed = sqrt(a^2 + b^2)

speed = sqrt( (-26.3207426)^2 + (5.7220765)^2 )

speed = 26.935546 knots, which is approximate

angle = arctan(b/a)

angle = arctan(5.7220765/(-26.3207426))

angle = -12.265139

Add 360 to this angle to find that we get to the coterminal angle of -12.265139+360 = 347.734861 degrees

This angle is in quadrant 4, which is the southeast quadrant. If we rotate another 360-347.734861 = 12.265139 degrees, going counterclockwise, then we'll face directly east. Then another 90 degree counterclockwise rotation has us face directly north.

In total, the true bearing is approximately 90+12.265139 = 102.265139 degrees

So we'll start aiming north, and then rotate roughly 102.265139 degrees toward the east to get to the true bearing.