A group of students noticed the shadow of the flagpole was 47 feet long at the same time a person 6 feet tall cast a shadow 7 feet long. What is the height of the flagpole to the nearest foot?

when h=130, the f-value is approximately 28.79 centimeters.

This means that if a person in this population has a femur length of 28.79 cm, their expected height would be around 130 cm.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Using the given formula

h=2.49f+58.3,

we can substitute h=130 to solve for f:

130 = 2.49f + 58.3

Subtracting 58.3 from both sides, we get:

71.7 = 2.49f

Dividing both sides by 2.49, we get:

f ≈ 28.79

Therefore, when h=130, the f-value is approximately 28.79 centimeters.

This means that if a person in this population has a femur length of 28.79 cm, their expected height would be around 130 cm.

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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The domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2

We have the following endpoints on the graph of the function;

(x, y) = Closed (-5, 2)

(x, y) = Open (3, 2)

Minimum y = 0

Remove the y values to determine the domain

x = Closed -5

x = Open 3

The closed statement represents the inequality ≤, while the closed statement represents the inequality < or >

So, we have

Domain = -5 ≤ x < 3

Also, we have:

(x, y) = Closed (-5, 2)

(x, y) = Open (3, 2)

Minimum y = 0

Remove the x values to determine the range

x = Closed 2

x = Open 2

Minimum y = 0

The above means that the y value does not include a negative value

So, we have

Range = 0 ≤ y ≤ 2

Hence, the domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2

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Answer:

48

Step-by-step explanation:

Answer:

\( \bf \large 60 \: m\)

Step-by-step explanation:

π = 22/7

r = 10 m

⟼ c = 2πr

⟼ c = 2 × 22/7 × 10 m

⟼ c = 2 × 3•14 × 10m

⟼ c = 6•28 × 10 m

⟼ c = 62•8 m

⟼ c = 62•8 m

⟼ c = 60 m

∴ circle circumference is 60 m.

Answer:

t = 6

Step-by-step explanation:

28 - 3t = 10

-3t = 10 - 28

-3t = -18

t = -18/-3

t = 6

Note: (-)/(-) = +

Answer:

t=6

Step-by-step explanation:

—3t=—18

t=6

The estimated cost for constructing the house in New Orleans, Louisiana of the given square feet is option A. $113,750.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that, construction rate per square feet is $65.

We have to find the estimated cost for a two-story home of 950 ft2 on the first floor and 800 ft² on the second floor.

Total area of the plot = 950 ft² + 800 ft²

                                   = 1750 ft²

Estimated cost can be calculated by multiplying total area with the construction rate per square feet.

Estimated cost = 1750 ft² × $65

                         = $113,750

Hence the estimated cost is $113,750.

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Answer: 90% confidence interval is; ( - 0.0516, 0.3752 )

Step-by-step explanation:

Given the data in the question;  

n1 = 72, n2 = 17

P1 = 54 / 72 = 0.75

P2 = 10 / 17 = 0.5882

so

P_good = 0.75

P_bad = 0.5882

standard ERRROR will be;

SE = √[(0.75×(1-0.75)/72) + (0.5882×(1-0.5882)/17)]

SE = √( 0.002604 + 0.01424)

SE = 0.12978

given confidence interval = 90%

significance level a = (1 - 90/100) = 0.1, |Z( 0.1/2=0.05)| = 1.645   { from standard normal table}

so

93% CI is;

(0.75 - 0.5882) - 1.645×0.12978 <P_good - P_bad<  (0.75 - 0.5882) + 1.645×0.12978

⇒0.1618 - 0.2134 <P_good - P_bad<  0.1618 + 0.2134

⇒ - 0.0516  <P_good - P_bad< 0.3752

Therefore 90% confidence interval is; ( - 0.0516, 0.3752 )

The value of z is 8633/137 or 63.01, approximately.

\(\frac{x}{y} =\frac{z}{100}\)

\(\frac{x}{y}*100 =\frac{z}{100}*100\\ \\100\frac{x}{y} =z\\ \\z=100\frac{x}{y}\)

\(z=100\frac{(86.33)}{(137)}\\ \\z=\frac{8633}{137}=63.01\)

If the calculated value of "z" is correct, then the original equation should return the same value on both sides of the equal symbol (=) when substiting all the variables by their respective value.

\(\frac{86.33}{137} =\frac{\frac{8633}{137}}{100}\\ \\0.63=0.63\)

That's correct!

Hence, the value of z is 8633/137 or 63.01.

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Answer: -2

Step-by-step explanation:

Subtract 13 on both sides

-7x = 14

Divide by -7 on both sides

x = -2

We have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

What is the Leibniz's theorem?

Leibniz's theorem, also known as the product rule for derivatives, is a rule for finding the nth derivative of a product of two functions. It states that if u(x) and v(x) are functions of x, then the nth derivative of their product

To apply Leibniz's theorem, we need to express the function in terms of a product of two functions: u and v.

Let u = xⁿ and v = ln(x)

Then, du/dx = n*xⁿ⁻¹ and dv/dx = 1/x

Using the formula,

d/dx(xⁿ ln(x)) = u(dv/dx) + v(du/dx)

= xⁿ * (1/x) + ln(x) * n * xⁿ⁻¹

= xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

To find the nth derivative, we differentiate n times using the product rule.

First, we need to find the first few derivatives:

f(x) = xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

\(f'(x) = nx^{(n-2)} + (n-1)*x^{(n-2)} ln(x)\)

\(f''(x) = n(n-2)x^{(n-3)} + 2(n-1)x^{(n-3)} ln(x) - (n-1)x^{(n-3)}/(x^2)\)

\(f'''(x) = n(n-2)(n-3)x^{(n-4)} + 3(n-1)(n-2)x^{(n-4)} ln(x) - 3(n-1)x^{(n-4)}/(x^2) - 2(n-1)x^{(n-4)} ln(x)/(x^2)\)

and so on...

The pattern becomes apparent and the nth derivative can be expressed as:

\(f^{(n)}(x) = n!/(x^{(n+1)})\)

So,

dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = \(f^{(n)}(x) = n!/(x^{(n+1)})\)

Hence, we have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

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The value of the variable 'x' in logarithmic expression is: 2

What is logarithm?

In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.

According to the question, the given logarithmic expression are as follows:

\(log_{1/2}x = -1\)

Using standard logarithmic property, we get

x = (1/2)^-1

⇒x = 2

Hence, the logarithmic value of the variable 'x' is: 2

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Answer:20 m/s

Step-by-step explanation:

Answer:

20 m/s

Step-by-step explanation:

700 ÷ 35 = 20 m/s

Answer:

Step-by-step explanation:

Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.

2p - 3q = 4 ...................... 1 * 3

3p + 2q = 9 ..................... 2 * 2

Multiplying equation 1 by 3 and 3 by 2:

6p - 9q = 12

6p + 4q = 18

Subtracting both equation

-9q-4q = 12-18

-13q = -6

q = -6/-13

q = 6/13

Substituting q = 6/13 into equation 2

2p - 3(6/13) = 4

2p - 18/13 = 4

2p = 4+18/13

2p = (52+18)/13

2p = 70/13

p = 70/26

p = 35/13

Hence p = 35/13 and q = 6/13

b) If if 223ₓ = 87 find x

Using the number base system and converting 223ₓ  to base 2 will give us;

223ₓ = 2*x² + 2*x¹ + 3*x⁰

223ₓ  = 2x²+2x+3

​

Substituting back into the equation, 2x²+2x+3 = 87

2x²+2x+3-87 = 0

2x²+2x-84 = 0

x²+x-42 = 0

On factorizing:

(x²+6x)-(7x-42) = 0

x(x+6)-7(x+6) = 0

(x+6)(x-7) = 0

x+6 = 0 and x-7 = 0

x = -6 and 7

Hence the value of x is 7 (neglecting the negative value)

Answer:

I can explain how to complete each of the steps you have provided.

1. Draw a point at (1, -2)

This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).

2.

Draw an 8-unit long radius

Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.

3. Using a compass

Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.

4. Using a protractor draw a 70 degree arc

Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.

5. Draw a central angle which intercepts your arc

Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.

6. Draw an inscribed angle which intercepts a 40 degree arc

Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.

7. Draw a tangent line

Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.

8. Draw a secant line

Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.

9. Equation of your circle

The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.

Answer:

36

Step-by-step explanation:

Ken = 6 yo

6 *3 = 18

Richard = 18 yo

8 * 2 = 36

Micah = 36

The age of Micah is 36 years.

A subfield of mathematics known as arithmetic operations deals with the study and application of numbers to all other subfields of mathematics. Operations like addition, subtraction, multiplication, and division make up the bulk of it.

These fundamental mathematical operations  (+, -, ×, and ÷) that we use every day.

Given age of Ken = 6 years

let age of Micah be m and age of Richard be r

acc. to condition

Micah is twice as old as Richard

m = 2r

Richard is three times as old as Ken

r = 3 ken

r = 3 x 6

r = 18

Richard age is 18 years.

m =2r

m = 2 x 18

m = 36 years

Hence age of Micah is 36 years.

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Answer:

The answer is 24

Step-by-step explanation:

Each quart contains 4 cups of soup. So, one gallon of soup contains 16 cups of soup. Therefore, 1 1/2 gallons of soup contains 16+8 = 24 cups. Therefore, the chef can serve 1 1/2 gallons of soup as 24 one-cup servings.

Answer:

Step-by-step explanation:

The standard deviation of the sampling distribution of sample means is given by the formula:

standard deviation = population standard deviation / sqrt(sample size)

Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:

standard deviation = 0.8 / sqrt(38)

standard deviation ≈ 0.13

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.

Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

You multiply (*) the pounds cost by the \(10\) pounds when you get that amount you divide it by the cost of granola per pound that will give you \(4\) dollars per pound.

Hope it helped!

\(\huge\boxed{Thanks,\;Plip.}\)

We want to find and solve an equation that tells us the number of pounds of raisins that we need to add to a mixture to get to a desired price.

We will see that we need to add 3 pounds of raisins.

We know that:

If we mix M pounds of raisins with 10 pounds of granola, the total mass will be:

M + 10

The price of this will be:

M*$6.50 + (10)*$3.25

And we want the price of this mixture to e $4.00 per pound, then we have:

M*$6.50 + (10)*$3.25 = (M + 10)*$4.00

Now we need to solve the above equation for M.

M*$6.50 + $32.50 = M*$4.00 + $40.00

M*$6.50 - M*$4.00 = $40.00 - $32.50

M*($6.50 - $4.00) = $7.50

M*$2.50 = $7.50

M = ($7.50)/($2.50) = 3

M = 3

This means that we need to add 3 pounds of raisins.

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The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Answer:

5 times as many

BRAINLIEST, please!

Step-by-step explanation:

I'd need more information about how many students there are at one of the schools. For example, if there are 200 students at Park Elementary, then there are 1000 at Lane High School since 200 x 5 = 1000. 1000 - 200 is 800, so there would be 800 more students at Lane High.

Answer:

X=33

Step-by-step explanation:

Hope this helps!!!

Answer:

90%

Step-by-step explanation:

Answer:

$11.69

Step-by-step explanation:

63.23 / 5.41 = 11.6876155

Answer:

C

Step-by-step explanation:

The area of cylinder is the area of the base (pi r^2) and the height (5)

Answer:

C

Step-by-step explanation:

Well if you think about it the normal formula is V=πr^2h

A cylinders base is a circle and the area for a circle is πr^2

If you cancel πr^2 you are left with height

So therefore it would be V=area of the base*height

Answer:

25

Step-by-step explanation:

Answer:

(90 km/h)(3 hours) = 270 km

9514 1404 393

Answer:

  b. $28.37

Step-by-step explanation:

In the cost function, x is the number of units. The derivative of the cost function with respect to x will tell the incremental cost of producing one more unit. That derivative is a constant, $28.37 per unit, so the cost of producing one more unit is $28.37 at any production level.

Answer:

thermal conductors conduct/ transfer heart

thermal insulators contain/prevent the transfer of heat