1. When analyzing population density in Canada it was found the density was 14 people/km2. Given this, how many people do expect would be found within an area of 1400 m by 1.3 km? (Please show work).
2. A cubed object has a density of. 25 g/m3. Given this would what be the mass of the cube for the object that has the side lengths of 56 cm. (Please show work).

The difference in elevation for A and B is the difference in elevation for line AB minus the slope correction: D = 330.422m

The slope correction formula is:
C = L * (D^2 / (2 * R)), Where:
- C is the slope correction
- L is the horizontal length of the line
- D is the difference in elevation
- R is the Earth's radius

For line BC, we can plug in the given values to find the slope correction:
C = 660.97m * (10.85m^2 / (2 * 6371000m))
C = 0.059m

For line AB, we need to find the difference in elevation first. We can do this by subtracting the slope correction from the slope distance:
D = 330.49m - 0.059m
D = 330.431m

Now we can plug in the values for line AB into the slope correction formula: C = 330.431m * (330.431m^2 / (2 * 6371000m))  C = 0.009m

The difference in elevation for A and B is the difference in elevation for line AB minus the slope correction:
D = 330.431m - 0.009m
D = 330.422m

Therefore, the difference in elevation for A and B is 330.422m.

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-12.87 ≈ -12.87

The given expression is:
(x-50)/(s/√n)

To evaluate it using the given values, we substitute the given values in the formula:
(45.3-50)/(4.7/√48) = -4.7/0.366 = -12.87

Rounding the result to two decimal places, we get:
-12.87 ≈ -12.87

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The cafeteria earned $945 from all of the lunches sold on Friday.

percentage, a relative value indicating hundredth parts of any quantity.

Let us calculate the number of students who bought each pizza.

Number of students who bought cheese pizza = 50% of 270 = 0.5 x 270 = 135

Number of students who bought pepperoni pizza = 40% of 270 = 0.4 x 270 = 108

Total lunches sold = Number of cheese pizzas sold + Number of pepperoni pizzas sold + Number of fried chicken sold

= 135 + 108 + 27

= 270

Therefore, a total of 270 lunches were sold on Friday.

To calculate how much money the cafeteria earned from all of the lunches, we can multiply the total number of lunches sold by the cost of each lunch:

Total earnings = Total lunches sold x Cost per lunch

= 270 x $3.50

= $945

Therefore, the cafeteria earned $945 from all of the lunches sold on Friday.

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The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].

To locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2] using the Bisection Method with 17 iterations, we will follow the steps below:

1. Define the function f(x) = x/3 + In(x) - 1
2. Set the initial values for the interval: a = 1 and b = 2
3. Start the iteration process by finding the midpoint of the interval: c = (a+b)/2
4. Evaluate the function at the midpoint: f(c) = f((a+b)/2)
5. Determine if the root lies in the left or right half of the interval by checking the sign of f(c)
6. If f(c) is positive, then the root lies in the left half of the interval, so we set b = c and repeat the process from step 3.
7. If f(c) is negative, then the root lies in the right half of the interval, so we set a = c and repeat the process from step 3.
8. Continue the iteration process until we have completed 17 iterations.

After 17 iterations, we will have narrowed down the interval to a very small range and the midpoint of this interval will be an approximation of the root of the function.

The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].

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Answer: C and D

Step-by-step explanation:

∠AFD measures 150°, not 130° and ∠AFB & ∠CFD are complementary, not supplementary.

The total cost for the dinner date including sales tax and tip is $88.44.

Let's calculate the cost of each item first:

Now, let's calculate the subtotal by adding up the costs of all the items:

Next, let's calculate the sales tax by multiplying the subtotal by the tax rate:

Sales Tax = 8% x $68.00

Sales Tax = $5.44

Now, let's calculate the total cost by adding the subtotal and the sales tax:

Total Cost = Subtotal + Sales Tax

Total Cost = $68.00 + $5.44

Total Cost = $73.44

Finally, let's add the tip to get the final cost:

Final Cost = Total Cost + Tip

Final Cost = $73.44 + $15.00

Final Cost = $88.44

Therefore, the total cost for the dinner date including sales tax and tip is $88.44.

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If Anna has 95 deliveries to make and has delivered 57, she has completed 60% of the total deliveries.

To find the percentage of deliveries that Amna has completed, we can use the formula:

percentage = (part/whole) × 100

So in this case, the part is the number of deliveries Amna has completed, which is 57, and the whole is the total number of deliveries she needs to make, which is 95. Plugging these values into the formula, we get:

percentage = (57/95) × 100 %

percentage = 0.6 × 100 %

percentage = 60 %

Therefore, Amna has completed 60% of her total deliveries.

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The factored form of the given polynomial is 5(x-9)(x-2).

To factor the given polynomial, 5x^(2)-55x+90, we first need to factor out the greatest common factor (GCF) which is 5. Factoring out the GCF will make the polynomial easier to factor completely.

5x^(2)-55x+90 = 5(x^(2)-11x+18)

Now, we need to factor the polynomial inside the parentheses completely. We can do this by finding two numbers that multiply to give us the constant term (18) and add to give us the coefficient of the x term (-11).

The two numbers that fit these criteria are -9 and -2. So, we can factor the polynomial inside the parentheses as follows:

x^(2)-11x+18 = (x-9)(x-2)

Putting it all together, we get the completely factored form of the given polynomial:

5x^(2)-55x+90 = 5(x-9)(x-2)

Therefore, the factored form of the given polynomial is 5(x-9)(x-2).

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Answer:

36.9

Step-by-step explanation:

sinJ=[tex]\frac{21}{35}[/tex]

    J= [tex]sin^{-1}[/tex][tex]\frac{21}{35}[/tex]

    J= 36.9

Answer:

[tex]2 \sqrt{5} [/tex]

Is the simplified form

Step-by-step explanation:

Greetings!!!

Given expression

[tex] \frac{10}{ \sqrt{5} } [/tex]

factor the number 10:5.2

[tex] = \frac{5.2}{ \sqrt{5} } [/tex]

Apply radical rule

[tex]a = \sqrt{a} \sqrt{a} [/tex]

[tex]5 = \sqrt{5} \sqrt{5} \\ = \frac{ \sqrt{5} \sqrt{5}.2 }{ \sqrt{5} } [/tex]

Cancel the common factor :✓5

[tex] = \sqrt{5} .2 \\ = 2 \sqrt{5} [/tex]

If you have any questions tag me on comments

Hope it helps!!!

Answer:

2 * [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\frac{10}{\sqrt{5} }[/tex]

Using the basis formula, you simplify it to:

2×[tex]\sqrt{5}[/tex]

In A parallelogram MNPQ with MN=12cm, MQ = 10 cm

a) The length of side PQ is equals to the 12 cm.

b) The measure of angle Q is equals to the 155°.

In a geometry, a parallelogram is a simple quadrilateral with

We have a parallelogram MNPQ, with

Side length, MN = 12cm

Other side length, MQ = 10 cm

Measure of angle M is = 25°

Also, MN|| PQ and MQ||NP

a) From the definition of parallelogram, the length of side MN is parallel to PQ and are of equal length. So, PQ = MN

= 12 cm

b) By the definition of parallelogram, opposite angles of a parallelogram are of equal measure. So, the measure of angle P = measure of angle M = 25°

Also, measure of angle N = measure of angle Q = x

Sum of all interior angles of quadrilateral

= 360°

=> m∠P + m∠N + m∠M + m∠Q = 360°

=> 25° + x + 25° + x = 360°

=> 2x + 50° = 360°

=> 2x = 310°

=> x = (310/2)° = 155°

Hence, required value of measure of angle Q is 155°.

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Complete question:

In A parallelogram MNPQ if MN=12cm , MQ = 10 cm and mZM = 25°. What is a)PQ

b) measure of angle Q

D. No, not similar

ΔFNY: 8<10<12 ⇔ FN<NY<FY

ΔWRY: 14 <18<21 ⇔ WR<YW<YR

[tex]\dfrac{FN}{WR} = \dfrac{8}{14} = \dfrac{4}{7}[/tex]

[tex]\dfrac{NY}{YW} = \dfrac{10}{18} = \dfrac{5}{9}[/tex]

[tex]\dfrac{FY}{YR} = \dfrac{12}{21} = \dfrac{4}{7}[/tex]

[tex]\dfrac{FN}{WR} = \dfrac{FY}{YR} \bf \neq \dfrac{NY}{YW}[/tex]

The solution to the system of equations using the substitution method is (7,2).

No, the substitution approach cannot be used to solve every system of equations. It can be challenging to replace one equation with another in some systems because they feature equations that are challenging or impossible to solve for one variable in terms of the other. Other approaches, such graphing or elimination, could be more useful in such circumstances.

Given that, the two equations are:

x= 4y - 1

3x + 2y = 25

Substitute x = 4y - 1 into the second equation:

3(4y - 1) + 2y = 25

12y - 3 + 2y = 25

14y - 3 = 25

14y = 28

y = 2

Substitute the value of y in equation:

x = 4y - 1

x = 4(2) - 1

x = 7

Hence, the solution to the system of equations using the substitution method is (7,2)

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A $450 principal and a simple interest rate of 0.35% each quarter for 212 years would result in a savings account balance of $3768.

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal x Rate x Time

where Rate is the interest rate as a decimal, and Time is the time in years.

The quarterly interest rate is 0.35% / 4 = 0.00875, and the time is 212 years, or 848 quarters.

Plugging in these values, we get:

Simple Interest = $450 x 0.00875 x 848 = $3318

Therefore, the balance of the savings account after 212 years would be:

Balance = Principal + Simple Interest = $450 + $3318 = $3768

Therefore, the balance of the savings account after 212 years with a simple interest rate of 0.35% each quarter and a principal of $450 would be $3768.

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Answer: -14.9 and 2.1

Step-by-step explanation:

If you take -6.4 - 8.5 in one direction you get -14.9 .

And if you add them together (-6.4 + 8.5) you get 2.1,

those are two possible values depending on if you add or subtract the 8.5 .

The measure of the arc of the ferris wheel in which the lines of sight intersect is approximately 320.1 degrees.

An arc is a segment of a curved line or curve that forms part of a circle or other curved shape. In geometry, an arc is defined as a part of a curve that is contained between two endpoints, known as the arc's endpoints.

Let's draw a diagram to help us visualize the problem:

                      B

                      / \

                     /    \

               18 /        \

                  /            \

               /                  \

             /    O                \

           /                           \

        /  40°                         \

     /                                      \

    A----------------------------------C

Here, the ride operator is standing at point A, and the ferris wheel is centered at point O. Points B and C represent the top and bottom of the ferris wheel, respectively.

We want to find the measure of the arc BC that is intercepted by the lines of sight of the ride operator.

First, we can use trigonometry to find the height of the ferris wheel. We know that angle AOB (the complement of angle AOC) is 50° (since the angles in a triangle add up to 180°). Using trigonometry, we have:

tan(50°) = height / 18

height = 18 * tan(50°) ≈ 22.6

So the height of the ferris wheel is approximately 22.6 meters.

Next, we can use the height to find the distance between points B and C. Since the ferris wheel is a circle, we know that the distance between B and C is twice the height:

BC = 2 * height ≈ 45.2

So the distance between points B and C is approximately 45.2 meters.

Finally, we can use the distance between points A and O (which is 18 meters) and the distance between points B and O to find the angle that the lines of sight make with each other. Let's call this angle x. Using trigonometry again, we have:

tan(x) = height / (18 - r)

where r is the radius of the ferris wheel. Since we know that the distance between A and O is 18 meters and the height is approximately 22.6 meters, we can solve for r:

tan(x) = 22.6 / (18 - r)

(18 - r) * tan(x) = 22.6

18 - r = 22.6 / tan(x)

r = 18 - 22.6 / tan(x)

We also know that the distance between B and O is equal to the radius, so we have:

r = BC / 2 ≈ 22.6

Now we can solve for x:

18 - 22.6 / tan(x) ≈ 22.6

tan(x) ≈ 22.6 / (18 - 22.6)

tan(x) ≈ -5.65

x ≈ -79.9° (using arctan on a calculator)

Note that we get a negative angle because the lines of sight are intersecting below the horizontal line passing through the ferris wheel.

Finally, we can find the measure of the arc BC by using the central angle formula:

arc BC = x + 40° ≈ -39.9°

Again, we get a negative value because the arc is measured clockwise from point B. To get the positive measure of the arc, we can subtract this value from 360°:

arc BC ≈ 320.1°

So the measure of the arc of the ferris wheel in which the lines of sight intersect is approximately 320.1 degrees.

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Answer:

its 0183

Step-by-step explanation:

jfirst queal then u have to divided then zjs

Answer: It is a minimum

Step-by-step explanation:

It is a minimum because the coefficient (5) is positive.

The expense function consists of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula: P = (r(PV)) / (1 - (1+r)^(-n)) = $1,062.66 per month. The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months).

A depreciation function is a mathematical model that explains how the worth of an object decreases over time. It denotes the pace at which the worth of an asset depreciates over time.

In the given question,

a. The expense function will consist of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula:

[tex]P = (r(PV)) / (1 - (1+r)^(-n))[/tex]

where P is the monthly payment, r is the monthly interest rate (4.875%/12 = 0.40625%), PV is the present value of the loan (54,000 - 8,000 = 46,000), and n is the total number of payments (4 years x 12 months per year = 48). Plugging these values into the formula, we get:

[tex]P = (0.0040625(46000)) / (1 - (1 + 0.0040625)^(-48)) = $1,062.66 per month[/tex]

The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months), so the monthly depreciation can be calculated as:

d = (54000 - 0) / 120 = $450 per month

Therefore, the expense function E(x) and depreciation function D(x) are:

E(x) = 1062.66 + 450x

D(x) = 450x

where x is the number of months since the car was purchased.

b. The graph of the expense function and depreciation function on the same axes is attached.

c. At the intersection point (around 66 months), the monthly loan payment becomes greater than the monthly depreciation cost, meaning that Winnie is paying more each month than the car is depreciating. After 66 months, the expense function is increasing faster than the depreciation function, so the total value of the car is decreasing rapidly. By the end of 120 months, the car will have depreciated to a value of $0 and Winnie will have paid a total of $62,719.20 in loan payments.

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The table of values is added below and and the graph is attached

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

y < |4x + 1| - 3

To create a table of values for y < |4x + 1| - 3, we can choose different values of x and substitute them into the expression to find the corresponding values of y.

Let's choose some values of x: -2, -1, 0, 1, 2.

When x = -2, we have:

y < |4(-2) + 1| - 3

y < 4

When x = -1, we have:

y < |4(-1) + 1| - 3

y < 0

When x = 0, we have:

y < |4(0) + 1| - 3

y < |1| - 3

y < -2

When x = 1, we have:

y < |4(1) + 1| - 3

y < 2

When x = 2, we have:

y < |4(2) + 1| - 3

y < 6

Putting it all together, we have the following table:

x y values

-2 y < 4

-1 y < 0

0 y < -2

1 y < 2

2 y < 6

The graph is attached

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Answer:

We can solve for p by isolating it on one side of the inequality symbol. First, we'll subtract 7 from both sides:

55 - 7 < -12p

48 < -12p

Next, we'll divide both sides by -12. Since we're dividing by a negative number, we'll need to flip the direction of the inequality:

48/-12 > p

-4 > p

Therefore, p is greater than -4. Written in interval notation, this solution is p ∈ (-∞, -4).

The area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

To get the area of the shaded region, we subtract the area of the sector from the area of the triangle as follows:

The angle m∠AOB = 180° - (34 + 90) {sum of interior angles of a triangle}

m∠AOB = 56°

area of sector = 56/360 × 22/7 × 26 cm × 26 cm

area of sector =14872/45 cm²

area of sector = 330.4888 cm²

area of the triangle = 1/2 × 26 cm × 39 cm

area of the triangle = 507 cm²

area of the shaded region = 507 cm² - 330.4888 cm²

area of the shaded region = 176.5111 cm²

Therefore, the area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

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Answer:

Step-by-step explanation:

I am definitely willing to help anyone with algebra!

It seems you need explanations on mode, median and mean. First, let's remember that these terms are related to data sets.

Example: I have a list of grades in Algebra 2, which list off as 94, 94, 95, 96, 98, 99, 99, 99, 99, 100.

I want the mode, median and mean. The mode is the number that appears the most in a data set, the median is the number in the exact middle of a data set, and the mean is the average value of the data set.

Mode: The number that appears most in this list of grades is 99. My mode is 99, and usually people use this to represent the whole of a data set, especially when the mode appears in the majority of the data set, at least 80% of the data set.

Median: My median is basically the number in the middle of the list. Since I have an even number of 10 grades, I need to find the two numbers closest to the middle, which is 98 and 99, the fifth and sixth term. I find the average of these two numbers- (98+99)/2 = 98.5. This is my median grade. This is usually used to represent data sets when describing demographics.

Mean: This is the average of the whole data set, which means we add up all the numbers and divide them by the number of items there are. Since we have ten grades in the data set, I add (94+94+95+96+98+99+99+99+99+100)/10 = 97.3

This is my mean, which represents my average grade. The mean is used a lot when teachers create our report cards! Hope this helps, but if you need anything else, feel free to comment back on this. If you want, my electronic mail account is my username and I use g mail dot com. Feel free to each out, and Happy Birthday!

The area of the rug is A = 1/2 × 7/6 and the area is 7/12

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

The area of a rectangle = l× w

The length = 7/6

The width = 1/2

Therefore the area = 7/6 × 1/2

= 7/12

therefore the area of the rug is 7/12

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The solutions to this 3x^(2)-4x=-2  are x=(2/3)+i*√(2/9) or x=(2/3)-i*√(2/9).

To solve this equation by completing the square, we need to first rearrange the equation and then complete the square for the x terms. Here are the steps:

1. Rearrange the equation:
3x^(2)-4x=-2 becomes 3x^(2)-4x+2=0

2. Divide the entire equation by the coefficient of the x^(2) term:
(3x^(2)-4x+2)/3=0/3 becomes x^(2)-(4/3)x+(2/3)=0

3. Complete the square by adding the square of half the coefficient of the x term to both sides of the equation:
x^(2)-(4/3)x+(2/3)+(4/3)^(2)/4=(4/3)^(2)/4 becomes x^(2)-(4/3)x+(4/9)=(4/3)^(2)/4-(2/3)

4. Simplify the right side of the equation:
(4/3)^(2)/4-(2/3)=(16/9)/4-(2/3)=(4/9)-(2/3)=(4/9)-(6/9)=-(2/9)

5. Factor the left side of the equation:
(x-(2/3))^(2)=-(2/9)

6. Take the square root of both sides of the equation:
x-(2/3)=+/-sqrt(-(2/9))

7. Solve for x:
x=(2/3)+/-sqrt(-(2/9)) becomes x=(2/3)+i*sqrt(2/9) or x=(2/3)-i*sqrt(2/9)

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Answer:

Let's assume that the price before adding the VAT is x.

We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.

The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:

Total price = price before VAT + VAT amount

or

2,700 = x + 0.08x

Simplifying this equation, we can combine like terms on the right-hand side to get:

2,700 = 1.08x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:

x = 2,700 / 1.08

x = 2,500

Therefore, the price before VAT was added is 2,500.

Answer: First we have to check the information they are giving in the problem. do we can see that the photocopier can copy 4 pages every 2 seconds.

so with this info we can calculate the ratio, or the number of copies that can be done in one second:

So we made a rule of 3 to solve that

So, if the photocopier can print 2 copys every second, the we can calculate the the time that takes to print 120 pages:

solving this rule of 3:

so is going to take 60 seconds to copy 120 pages.

Answer:

101.80

Step-by-step explanation:

Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.

The values of x that make the equation equals 0 are -3 and 3

The equation given from the question is represented as

(6x^2 - 54)/(5x^2 - 20) = 0

The format of the above equation is that of a radical equation

For the expression to equal to 0, the numerator must be 0

So, we have

6x^2 - 54 = 0

Evaluate the like terms

6x^2 = 54

Divide both sides by 6

x^2 = 9

take the square root of both sides

x = -3 and x = 3

Hence, the solutions are -3 and 3

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The product of the polynomials is 4x^(2)-28x+49, which is a single polynomial in standard form.

A polynomial is an expression consisting of variables, constants and coefficients, in which the exponents of the variables are either whole numbers or zero. It can be written in the form of a summation, where each term is the product of a coefficient and a variable raised to a power.

To multiply the polynomials using a special product formula, we can use the formula for squaring a binomial, which is (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=2x and b=7.

So, we can plug these values into the formula and simplify:

(2x-7)^(2) = (2x)^(2)-2(2x)(7)+(7)^(2)

= 4x^(2)-28x+49

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The answer is (1) x = 22.5; (2) x = 16.7; (3) x = 13.5; (4) x = 16.8; (5) x = 24.5; (6) x = 16.15; (7.a) height of the image on film is 11.2mm; (7.b) distance between camera and her friend is 1,875mm.

(1) We can see that in the given figure all three corresponding angles are congruent and all three corresponding sides are in equal proportion so, these are similar triangles.

As per properties of similar triangle:

Three pairs of corresponding sides are proportional i.e. Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

                        Therefore, [tex]\frac{32}{24} =\frac{30}{x}[/tex],

then by cross multiplying them, we get,

                                        32x = 720

                                            x = 720/32

                                           x = 22.5

(2) As, this is already given that these are similar triangle and by applying the properties of similar triangle we get,

                                           [tex]\frac{39}{26} =\frac{25}{x}[/tex]

                                         39x = 650

                                             x = [tex]16\frac{2}{3}[/tex]

                                            x = 16.7

(3) As these are similar triangle again we can say that,

                                        [tex]\frac{2x+1}{x+4} =\frac{40}{25}[/tex]

                                 40(x + 4) = 25(2x + 1)

                                40x + 160 = 50x + 25

                                          40x = 50x - 135

                                          -10x = -135

                 (by cancelling (-) sign from both sides we get,

                                              x = 135/10

                                             x = 13.5

(4) By applying similar triangle's property, we can get

                                           [tex]\frac{20}{30} =\frac{28-x}{x}[/tex]

                                         20x = 840 - 30x

                                         50x = 840

                                             x = 840/50

                                             x = 16.8

(5) As ΔJKL [tex]\sim[/tex] ΔNPR,

                                           [tex]\frac{KM}{PT} =\frac{KL}{PR}[/tex]

                                          [tex]\frac{18}{15.75} =\frac{28}{x}[/tex]

                                            18x = 441

                                                x = 441/18

                                               x = 24.5

(6) As ΔSTU [tex]\sim[/tex] ΔXYZ,

                                         [tex]\frac{UA}{ZB} =\frac{UT}{ZY}[/tex]

                                        [tex]\frac{6}{11.4} =\frac{8.5}{x}[/tex]

                                          6x = 96.6

                                            x = 96.6/6

                                            x = 16.15

(7.a) First we have to change 3 m and 140 cm into mm(millimeters).

So, 1m = 1000 mm

     3m = 3000mm.

And 1cm = 10 mm

   140cm = 1400 mm.

Then to find the height of the image on the film, we have to solve:

                                          [tex]\frac{24}{3000} =\frac{x}{1400}[/tex]

             by cross multiplication we get,

                                      3000x = 33,600

                                               x = 33,600/3000

                                              x = 11.2 mm

the height of the image on the film is 11.2millimeters.

(7.b) For this also, we have to find x by solving the equation:

                                            [tex]\frac{24}{3000} =\frac{15}{x}[/tex]

                                            24x = 45,000

                                                x = 45,000/24

                                              x = 1,875 mm

The distance between camera and her friend is 1,875 millimeters.

To know more about Similar Triangles:

brainly.com/question/30104125

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