Assuming that a 390 foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 39°, how far from the base of the tree am I?

The culture will have a count of 1200 after approximately 2.77 hours. Rounded to the nearest tenth, this is 2.8 hours.

What is equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

We can solve for the time "t" by substituting the given count of 1200 into the equation and solving for "t":

[tex]1200 = 3000e^{(0.5t)}[/tex]

Divide both sides by 3000 to get:

[tex]0.4 = e^{(0.5t)}[/tex]

Take the natural logarithm of both sides to isolate the exponent:

ln(0.4) = 0.5t

Solve for "t" by dividing both sides by 0.5:

[tex]t = (ln(0.4))/0.5 = 2.77 hours[/tex]

Therefore, the culture will have a count of 1200 after approximately 2.77 hours.

[tex]1200 = 3000e^{(0.5t)}[/tex]

Divide both sides by 3000 to get:

[tex]0.4 = e^{(0.5t)}[/tex]

Take the natural logarithm of both sides to isolate the exponent:

ln(0.4) = 0.5t

Solve for "t" by dividing both sides by 0.5:

[tex]t = (ln(0.4))/0.5 = 2.77 hours[/tex]

Therefore, the culture will have a count of 1200 after approximately 2.77 hours. Rounded to the nearest tenth, this is 2.8 hours.

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Answer:

3.25 hours

Step-by-step explanation:

1250 miles / (500 miles/hour) = 2.5 hours

45 minutes × (1 hour)/(60 minutes) = 0.75 hours

2.5 hours + 0.75 hours = 3.25 hours

Answer: 3.25 hours

We are given the following lengths:

We will solve it by using this formula:

[tex]\boxed{\mathfrak{\purple {Median = \frac{1}{2}(lower \: base+upper \: base)}}}[/tex]

[tex]\boxed{\mathcal{\purple { XY = \frac{1}{2}( CO+PY)}}}[/tex]

[tex] \green{ \sf4m + 3 = \frac{1}{2} (2m - 10 + 3m + 37)}[/tex]

[tex] \red \implies \green{ \sf4m + 3 = \frac{1}{2} (5m+ 27)}[/tex]

[tex] \red \implies \green{ \sf4m + 3 = \frac{5}{2} m + \frac{27}{2} }[/tex]

[tex] \red \implies \green{ \sf8m + 6 = 5m + 27 }[/tex]

[tex] \red \implies \green{ \sf8m + 6 - 5m = 27 }[/tex]

[tex] \red \implies \green{ \sf8m - 5m= 27 - 6 }[/tex]

[tex] \red \implies \green{ \sf3m = 21 }[/tex]

[tex] \boxed{ \mathfrak{ \red{m = 7}}}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =4m + 3}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =4(7) + 3}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =28 + 3}[/tex]

[tex] \boxed{ \underline{ \underline{ \blue \longmapsto \orange{ \tt \: XY =31}}}}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 2m - 10}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 2(7) - 10}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 14 - 10}[/tex]

[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:CO=4}}}}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 3m + 37}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 3(7) + 37}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 21 + 37}[/tex]

[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:PY=58}}}}[/tex]

The length of each leg of an isosceles right triangle with a hypotenuse of 12 inches is approximately 8.49 inches.

In an isosceles right triangle, the two legs are congruent, so let's call the length of each leg "x". Then, using the Pythagorean theorem, we can write:

[tex]x^2 + x^2 = 12^2[/tex]

Simplifying the left side, we get:

[tex]2x^2 = 144[/tex]

Dividing both sides by 2, we get:

[tex]x^2 = 72[/tex]

Taking the square root of both sides, we get:

x = sqrt(72)

We can simplify this by factoring 72 as 36 * 2:

x = sqrt(36 * 2)

Taking the square root of 36, we get:

x = 6 * sqrt(2)

So each leg of the isosceles right triangle is approximately 8.49 inches long (rounded to two decimal places).

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The hypotenuse of an isosceles right triangle is 12 inches. What is the length of each leg?

Using functions,

Part A: f (3) = 6(3) + 14 = 32.

g (3) = 3 + 2 = 5

Part B: (f/g) (3) will be 6.4.

The core concept of calculus in mathematics is a function. The relations are certain kinds of the functions. In mathematics, a function is a rule that produces a different result for every input x. In mathematics, a function is represented by a mapping or transformation. Letters like f, g, and h are widely used to indicate these operations. The set of all potential values that can be passed into a function while it is specified is known as the domain. The entire set of values that the function's output is capable of creating is referred to as the "range." The range of potential values for a function's outputs is known as the co-domain.

Here in the question,

f (x) = 6x + 14

g (x) = x + 2

Now we have to find for the value of x,

f (3) = 6(3) + 14 = 32.

g (3) = 3 + 2 = 5

So, f (3) = 32 and g (3) = 5.

Now,

(f/g) (3) will be 32/5 = 6.4.

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The missing angles in the diagram are: Angle ABD = 60 degrees, Angle BDC = 120 degrees, Angle ACD = 60 degrees, and Angle ADC = 120 degrees.

To find the measure of the missing angles, we can use the fact that the sum of the angles in a triangle is 180 degrees, and the sum of the angles around a point is 360 degrees.

Let x be the measure of angle ABD.

Therefore, angle BDC has measure 180 - x degrees.

Similarly, angle ACD and angle ADC form a straight line, so their measures sum to 180 degrees. Therefore, angle ADC has measure 180 - 60 = 120 degrees.

Finally, since angle BCD and angle ADC form a straight line, their measures sum to 180 degrees. Therefore, angle BCD has measure 180 - 120 = 60 degrees.

Let y be the measure of angle CFE.

Similarly, angle DEF and angle CDF form a straight line, so their measures sum to 180 degrees. Therefore, angle DEF has measure 180 - 75 = 105 degrees.

Finally, since angle CDE and angle DEF form a straight line, their measures sum to 180 degrees. Therefore, angle CDE has measure 180 - 105 = 75 degrees.

Therefore, the missing angles have measures of 60 degrees and 75 degrees for the left and right triangles.

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find the measure of missing angles?

The answer of given Theoretical  Probability Question is  0.1379 , 0.125

Experimental probability of the name Fred being chosen = number of times Fred is chosen / total number of trials

= 17/124

= 0.1379 (rounded to four decimal places)

Theoretical probability of the name Fred being chosen = number of outcomes in which Fred is chosen / total number of possible outcomes

Since there are eight different names in the hat, the total number of possible outcomes is 8. The number of outcomes in which Fred is chosen is 1 (since there is only one Fred in the hat).

Therefore, the theoretical probability of Fred being chosen is:

1/8 = 0.125 (rounded to three decimal places)

If the number of names in the hat were different, both the experimental and theoretical probabilities would change.

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The correct value of expression at r = 7 is  [tex]$r=7, (r+6)^2 = 169$[/tex].

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Sayid's reasoning is incorrect because [tex]$(r+6)^2$[/tex]means that we need to square the entire expression [tex]$r+6$[/tex], not just r and 6 separately.

To evaluate the expression for r=7, we first substitute 7 for r in the expression and then simplify:

[tex]$$(7+6)^2 = (13)^2 = 169$$[/tex]

Therefore, when [tex]$r=7, (r+6)^2 = 169$[/tex]

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Answer:

Step-by-step explanation:

Bing chilling

Answer: The answer is 169

Step-by-step explanation:

Add 8 + 3, then subtract that from 180 to get 169 :)

The type of transformation represented in the figure is the translation transformation i.e. (c) none of these

Given the triangles ABC and A'B'C'

The transformation between the triangles is translation

The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.

This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.

In this case, the direction is horizontally and vertically

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The number of students that will receive the attendance award is 26. The correct option is a.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

We must first ascertain how many students will be recognized. We can achieve this by dividing the overall number of students (650) by the proportion of recipients (4%). 650 x 0.04 = 26 Hence, 26 kids will be recognized for their flawless attendance.

According to the given conditions, 650 students and 4 will receive a perfect attendance award.

650 x 4% = 26

Therefore, the correct option is a, 26.

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The options are:

26

25

24

23

Answer: The running club can buy 25 uniforms

Step-by-step explanation: If the running club has $1,328 to spend on new uniforms and each uniform costs $52, we can find the number of uniforms they can buy by dividing the total amount of money by the cost of each uniform:

$1,328 ÷ $52 = 25.54

Therefore, the running club can buy 25 uniforms with $1,328.

I hope this helps, and have a great day!

Answer:3/10

Step-by-step explanation:

2/5 = 4/10

1/5 = 2/10

            4/10 + 2/10 = 6/10

               6/10-3/10 = 3/10

Answer: 41

Step-by-step explanation:

-26+z =1 5

       z= 15+26

       z= 41

Answer:

z = 41

Step-by-step explanation:

-26 + z = 15.                      | + 26
-26 + z + 26 = 15 + 26
z = 41

x²=22.136

Its the last one

Step-by-step explanation:

Find slope using the two points    ( y1-y2) / ( x1-x2) =  (-1-3) / (-3-3) = 2/3

y = 2/3 x  + b     b is the y-axis intercept  = 1

y = 2/3 x + 1

Answer: 2.5 dm

Step-by-step explanation:

Divide 25.0 by 10

= 2.5

Answer: To solve the problem, we can use Bayes' theorem. Let D be the event that a device is defective, and let A be the event that the quality assurance check concludes that a device is defective.

We want to find P(A and not D) + P(not A and D), which represents the probability of an incorrect conclusion.

We know that P(D) = 1 - P(not D) = 1 - 0.84 = 0.16, and that P(A | not D) = 0.03 and P(A | D) = 0.97.

Using Bayes' theorem, we can compute:

P(not A | not D) = 1 - P(A | not D) = 1 - 0.03 = 0.97

P(not A | D) = 1 - P(A | D) = 1 - 0.97 = 0.03

Therefore,

P(A and not D) = P(not D) * P(A | not D) = 0.84 * 0.03 = 0.0252

P(not A and D) = P(D) * P(not A | D) = 0.16 * 0.03 = 0.0048

So the probability of an incorrect conclusion is:

P(A and not D) + P(not A and D) = 0.0252 + 0.0048 = 0.03

Therefore, the probability of an incorrect conclusion is 0.03, or 3% (rounded to the nearest tenth of a percent).

Why was this answer deleted prior?

The time taken by the Lamonte would be  6 hours to drive 93 miles at a speed of 15.5 miles per hour.

We can use the following formula to answer this question:

rate x time = distance

We know Lamonte drove 62 miles in four hours, so we can use that to calculate his speed:

62 miles = rate multiplied by 4 hours

When we solve for the rate, we get:

rate = 62 miles divided by 4 hours equals 15.5 miles per hour

We can now use this rate to calculate how long it would take Lamonte to drive 93 miles:

93 miles = time x rate

Substituting the recently discovered rate yields:

93 miles = 15.5 miles per hour multiplied by time

When we solve for time, we get:

time = 93 miles / 15.5 miles per hour = 6 hours

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Answer: b

Step-by-step explanation:

As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a) where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°. Plugging those values into the formula, we get d = 300 * tan(15°) = 517.4 feet. Rounding this to the nearest whole number, we get 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a). This equation is derived from the Pythagorean Theorem, where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°, so we can plug these values into the equation. When we do this, we get d = 300 * tan(15°) = 517.4 feet. As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

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Tο maximize its prοfits, the cοrpοratiοn shοuld thus sell the phοnes fοr $250 as the value οf x that οptimizes the functiοn [tex]r(x) = x[/tex].

A functiοn in mathematics is a principle οr cοnnectiοn that links οne input value tο οne οutput value. A functiοn, in mοre technical terms, is a cοllectiοn οf οrdered pairs (x, y) where there is precisely οne y fοr every x.

The argument οr independent variable is the input value x, and the value οr dependent variable is the οutput value y. Algebraic equatiοns, tables, diagrams, and verbal explanatiοns are just a few οf the nοtatiοns that can be used tο represent functiοns.

Finding the value οf x that οptimizes the functiοn r(x) = x will help us determine the price that will generate the mοst prοfit (1000 - 2x).

We can start by simplifying and expanding this functiοn:

[tex]r(x) = 1000x - 2x^2[/tex]

We can nοw take the derivative οf this functiοn with respect tο x and put it equal tο zerο in οrder tο determine the highest value οf r(x):

[tex]r'(x) = 1000 - 4x = 0[/tex]

After finding x, we οbtain:

[tex]x = 250[/tex]

Tο maximize its prοfits, the cοrpοratiοn shοuld thus sell the phοnes fοr $250.

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The expressions can be written as  :a. log5.625 ≈ 0.75.

                                                             b. log6.4 + log6.12 ≈ 1.67.

                                                             c. log3.9^{4} ≈ 2.47.

What is logarithm function?

A logarithm function is a mathematical function that determines the power to which a fixed number, called the base, must be raised to produce a given value and The logarithm function is the inverse of the exponential function. The most commonly used base for logarithmic functions is 10 (log base 10), but other bases such as 2 (log base 2) and the natural logarithm base e (ln) are also used.

a. Since there is no base specified, we assume the base to be 10 by default. Therefore, we can write:

log5.625 = log(5625/1000)

Using the property log(a/b) = log(a) - log(b), we can simplify this expression to:

log5.625 = log(5625) - log(1000)

Using the change of base formula, we can convert the logs to a common base, such as 2 or e:

log5.625 = log(5625)/log(10) - log(1000)/log(10)

Evaluating the logs using a calculator or by simplifying, we get:

log5.625 ≈ 0.75

Therefore, log5.625 ≈ 0.75.

b. Using the property log(a) + log(b) = log(ab), we can simplify the expression:

log6.4 + log6.12 = log(6.4 × 6.12)

Using the change of base formula, we can convert this to a common base:

log6.4 + log6.12 = log(6.4 × 6.12)/log(10)

Evaluating the log using a calculator or by multiplying 6.4 and 6.12 and simplifying, we get:

log6.4 + log6.12 ≈ 1.67

Therefore, log6.4 + log6.12 ≈ 1.67.

c. Using the property log(a^{n}) = n log(a), we can simplify the expression:

log3.9^{4} = 4 log3.9

Using the change of base formula, we can convert this to a common base:

log3.9^{4} = 4 log(3.9)/log(10)

Evaluating the log using a calculator or by simplifying, we get:

log3.9^{4} ≈ 2.47

Therefore, log3.9^{4} ≈ 2.47.

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Answer:

if sales tax was 6.75 dollars, then 31.75 is the total cost. If it’s in percent, the total cost is 26.69

Step-by-step explanation:

1).    12.5(2) = 25

2).    25 + 6.25 = 31.25

OR

2).    25(1.0675)=26.69

Answer:

see explanation

Step-by-step explanation:

(4)

5x³ - 10x² - 3x + 6

factor out 5x² from first 2 terms and - 3 from last 2 terms

= 5x²(x - 2) - 3(x - 2) ← factor out (x - 2) from each term

= (x - 2)(5x² - 3)

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

(5)

9a³ - 45a² - 7a + 35

factor out 9a² from first 2 terms and - 7 from last 2 terms

= 9a²(a - 5) - 7(a - 5) ← factor out (a - 5) from each term

= (a - 5)(9a² - 7)

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

(6)

5x²y - 15y - 2x² + 6

factor out 5y from the first 2 terms and - 2 from the last 2 terms

= 5y(x² - 3) - 2(x² - 3) ← factor out (x² - 3) from each term

= (x² - 3)(5y - 2)

Answer:

Starting with:

-15 > -11 + w

Add 11 to both sides:

-15 + 11 > w

Simplifying:

-4 > w

Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:

w < -4

If Jake whittles little wooden figurines and begins to sell them. If the demand function for his figurines is given by D(q) = 80 - 1.25q and the supply function is S(q) = 0.75g. The equilibrium quantity is  40 units.

Given the demand function D(q) = 80 - 1.25q and the supply function S(q) = 0.75q, we can find the equilibrium quantity by setting these two functions equal to each other and solving for q:

D(q) = S(q)

80 - 1.25q = 0.75q

Simplifying this equation, we get:

2q = 80

q = 40

Therefore, the equilibrium quantity is q = 40. At this quantity, the quantity demanded is:

D(q) = 80 - 1.25q = 80 - 1.25(40) = 30

And the quantity supplied is:

S(q) = 0.75q = 0.75(40) = 30

Thus, the equilibrium quantity of Jake's wooden figurines is 40 units.

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According to the solution we have come to find that, the length of the box is  [tex](V/2)^{1/3}[/tex].

what is volume?

Volume is the measure of the amount of space occupied by a three-dimensional object or region of space. It is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³), depending on the unit of length used to measure the dimensions of the object. The formula for calculating the volume of a geometric shape depends on the shape, but generally involves multiplying the dimensions of the shape together, such as the length, width, and height of a rectangular prism, or the radius and height of a cylinder.

Let's start by defining the variables:

Let's call the height of the box "h".

The length and width are each twice as long as the height, so we can write: length = 2h and width = 2h.

The volume of the box is given as "V".

We can use the formula for the volume of a rectangular box to write:

V = length × width × height

V = (2h) × (2h) × h

V = 4h^3

Now we can solve for h in terms of V:

4h³ = V

h³ = V/4

h = [tex](V/4)^{(1/3)[/tex]

This gives us the formula for the height of the box in terms of its volume V.

If we are given the volume V and asked to find the length of the box, we can use the formula for length in terms of height:

length = 2h

length = 2(V/4[tex])^{(1/3)[/tex]

length = (2V/4[tex])^{(1/3)[/tex]

length = (V/2[tex])^{(1/3)[/tex]

So, the length of the box is  [tex](V/2)^{1/3}[/tex].

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