Corin measures the apparent height of a tower 800 feet away by holding a ruler in front
of her eye and observing that the tower appears to be 9 inches tall. The apparent height h
(in inches) varies inversely with Corin's distance d (in feet) from the tower. Write an
equation that gives d as a function of h. How tall would the apparent height of the tower
be if she was standing 2000 feet away from the tower? Show your work.

The constant of proportionality is 10 for the proportional relationship shown in the graph.

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

The proportional relationship is shown in the given graph.

As per the given graph, we take two points (1, 10) and (2, 20)

So, the constant of proportionality will be as:

⇒ (20 - 10)/(2-1)

⇒ 10/1

⇒ 10

Hence, the correct answer would be option (A).

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When one rectangular tile is 4 cm shorter and 2 cm broader than another rectangular tile, the difference in their perimeters is 2.

4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other. A rectangle would be referred to as a square if all of its sides were the same size.

given

Allowing for a rectangular card that is x cm long and y cm broad

The perimeter of another rectangular tile is 2 cm broader and 4 cm shorter.

L+B = L+B -2 = 2(L + B)

= 2(L-4 + B+2) = 2(L + B)

= L+B = L+B -2

Therefore, when one rectangular tile is 4 cm shorter and 2 cm broader than another rectangular tile, the difference in their perimeters is 2.

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Answer:

D

Step-by-step explanation:

8x+12y-2y+3x=11x+10y

Answer:

answer D

Step-by-step explanation:

8x+12y-2y+3x

11x+ 10y

Carmen and her dog, Duke walked at a slower rate at 0.625 blocks/min

Carmen and her dog, Duke would take 19.2 minutes to work 12 blocks.

In math, a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.

Carmen/Duke walks 5/8 = 0.625

Terell/Lady walks 8/12 = 0.677

Therefore, from the average time, Carmen and Duke walk slower.

Carmen and Duke will walk 12 blocks in;

= 12/0.625

= 19.2 minutes

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Answer:

2000 workers

Step-by-step explanation:
All the workers: 100%
Women: 60%
Others: 40% = 800 workers
=> 1% of the workers: 800/40 = 20 workers
=> 100% = 20 x 100 = 2000 workers
(I can't think of another one)

Answer:

13

Step-by-step explanation:

Cuz the factor of y is angle to the 115° is to the Y value

Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:

5(y + 9) = 3

Next, we can distribute the 5 to obtain:

5y + 45 = 3

Finally, we can subtract 45 from both sides to solve for y:

5y = -42

y = -42/5

y = -8.4

Therefore, the equation that represents the given sentence is y = -8.4.

Step-by-step explanation:

Therefore the predicted full rear repair cost would be $1211.576 if y=2060-0.186x is the line of regression of a table of values comparing for front crash repair cost.

When modeling the connection between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable, while multiple linear regression is used when there are numerous variables.

Physical values known as scalars are unaffected by modifications to the vector space basis. Scalars frequently include units of measurement, such as "10 cm." Scalar quantities include things like mass, space, charge, volume, time, speed, and the overall size of physical vectors.

To predict the full rear repair cost from a full front repair cost of $4594, you would substitute 4594 for x in the equation y = 2060 - 0.186x and solve for y.

y = 2060 - 0.186(4594)

y = 2060 - 848.424

y = 1211.576

So the predicted full rear repair cost would be $1211.576

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Answer:

$1,206

Step-by-step explanation:

The heart pumps around 17280 pints of blood in a day.

To find out how many pints of blood your heart pumps in a day, we need to determine the total volume of blood that your heart pumps in one day.

We know that your heart pumps 1.5 gallons of blood per minute. To find out how much blood your heart pumps in one day, we need to multiply that amount by the number of minutes in a day.

1 day = 24 hours

1 hour = 60 minutes

So, the number of minutes in one day is 24 hours x 60 minutes = 1440 minutes

Now, we can use this information to find out how many gallons of blood your heart pumps in a day.

Gallons of blood pumped per day = 1.5 gallons/minute x 1440 minutes/day

= 2160 gallons

1 gallon = 8 pints

So the number of pints of blood that your heart pumps in a day = 2160 gallons × 8 pints/gallon = 17280 pints.

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your heart pumps 2000 gallons of blood around your body each day.

if your body pumps around 1.5 gallons of blood each minute then a day is 24 hours so yu do that x together which is 20 but as its hours you do it for 2000 and just incase yu need some more info

(1.5 imperial gallons) x 24 hours = 589.173508 m3 s

SORRY IF THIS DONT ALL MAKE SO MUCH SENSE

Answer: 1250

Step-by-step explanation: 50 x 50 = 2,500

                 2,500 divided by 2 is 1250

To simplify this expression, you can first simplify the logarithms by using the properties of logarithms and the simplified expression is -0.00195

A logarithm is a mathematical function that is used to determine the power to which a number must be raised in order to produce a certain value. The logarithm of a number "b" to base "a" is represented as loga(b) or logb. The logarithm of b to base a is equal to the exponent to which we must raise a to get b.

[tex]1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]

To simplify this expression, you can first simplify the logarithms by using the properties of logarithms.

[tex]1/2 log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]

=[tex]1/2( log10 25 - log10 4) - 2 (log10 4 - log10 5) + (log10 320 - log10 125)[/tex]

= 1/2(1.397940008672037 - 0.6020599913279624) - 2*(-0.6020599913279624 - 0.6989700043360187) + (2.505149978319906 - 2.0969100130080566)

= 0.397940008672037 - 1.204120018655925 - 1.397940008672037 + 0.40825006983185

= -0.2 - 0.2062 + 0.40825

= -0.00195

So the simplified expression is -0.00195

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Complete question is: simplify the given equation:  1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125

Answer:

Question is not clear

Step-by-step explanation:

The width and the length that gives the largest possible areas are 75 meters by 37.5 meters

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

Number of warehouses = 4

Perimeter of fence = 300 meters

Represent the width with x and the length with y

So, we have the following equations

Area = 4xy

Perimeter = 2(4x + y)

Substitute the known values in the above equation, so, we have the following representation

2(4x + y) = 300

Divide both sides by 2

2x + y = 150

Make y the subject

y = 150 - 2x

Substitute y = 150 - 2x in Area = 4xy

A = 4x(150 - 2x)

This gives

A = 600x - 8x²

Differentiate and set to 0

600 - 16x = 0

So, we have

16x = 600

Divide by 16

x = 37.5

Recall that

y = 150 - 2x

So, we have

y = 150 - 2 x 37.5

Evaluate

y = 75

Hence, the dimensions are 75 meters by 37.5 meters

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Answer:

3.4 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]

where

The ball will strike the ground when its height is zero.

Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute these values into the quadratic formula:

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]

[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]

As time cannot be negative, t = 3.4 s only.

Therefore, the ball strikes the ground 3.4 seconds after it is launched.

Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.

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Using the given function and the ordered pairs, we observed that Mr. Poppen pays more initially, to join the club

From the question, we are to determine who pays more initially to join the club between Mr. Poppen and Mrs. Zagorski  

From the given information,

"Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70"

The initial amount paid by Mr. Poppen is the value of y when x is 0

y = 10x + 70

y = 10(0) + 70

y = 0 + 70

y = 70

From the given ordered pairs

(0, 50)

(1, 60)

(2, 70)

(3, 80)

We can conclude that the initial amount paid by Mrs. Zagorski is 50

Hence, Mr. Poppen pays more initially

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Answer:

Corresponding Parts of Congruent Triangles are Congruent.

ASA

Step-by-step explanation:

We know that <YPC and angle <YPX are congruent angles.  They are both 90°.

Side YP is congruent to YP, so these sides are congruent in both triangles.

<XYP and <YPZ are congruent, because the perpendicular bisector cuts <XYZ in two equal parts.

ASA (Angle, Side, Angle)

Answer: To find the factor pairs for -240, we can use the following steps:

Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)

For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).

The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).

Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

9+2+4+6+123=

11+10+123
21+123
144

Jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80.

The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

In baseball, each time a player attempts to hit the ball, it is recorded.

The ratio of hits compared to total attempts is their batting average.

Each player on the team wants to have the highest batting average to help their team the most.

For the season so far,

Jana has hit the ball 7 times out of 10 attempts.

Tasha has hit the ball 10 times out of 16 attempts.

To find the ratio of batting average:

We must find the same number of attempts.

So,

Jana has ratio 7/10.

So, 56 /80 = 0.7

Tasha has ratio 10/16.

So, 50 / 80 = 0.625

Therefore, Jana has the highest batting average.

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Answer:

Step-by-step explanation:

-1 +2=1

2+2=4

5+1=6

Answer:

  57

Step-by-step explanation:

You want a positive number that gives a product of 1995 when it is multiplied by each of its digits.

The prime factors of 1995 are 3, 5, 7, 19. The product of 3 and 19 gives 57, so multiplying 57 by 5 and 7 will result in the product 1995.

The original number is 57.

<95141404393>

Answer: 109 it says 109 in the corner of b and d

We calculated length of model bird in the picture = 2 ¹⁵₁₆ inch and scale factor =1/2

It is expressed as the ratio of the dimension of a model object and dimension of an actual object.

A scale factor is a number which is multiplied by an object in order to form a proportional enlarged or reduced object.

Given, the length of an actual bird = 5⁷₈ inch = 47/8 inch

also given, 1 inch = 0.5 inch

   1 inch = 1/2 inch

we need to determine the length of model bird by multiplying the above factor.

now, length of model bird = 47/8 × 0.5 inch = 47/16 inch = 2¹⁵₁₆ inch

scale factor = length of model bird/ length of actual bird = 47/16 /47/8

scale factor = 1/2

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Answer:

yes

Step-by-step explanation:

51 to nearest ten is 50

37 to nearest ten is 40

50 * 40 = 2000

and it's an estimate so yes

Answer:

m=10

Step-by-step explanation:

m/5+9=11 subtract 9

m/5 = 2 multiply 5 by both sides

m = 10