PLEASE find the equation for this graph

The old microscope contained 2.5 square inches more of the sample's area than the new microscope.

Given that the apparent diameter of both the old microscope and the new microscope is 5 inches and the magnification rate of the old microscope is 12, and that of the new microscope is 15. Now, we need to find the actual diameter of the region of the microscope which is given by the equation: Apparent diameter = Magnification rate × Actual diameter.

Rearranging the above formula to solve for the actual diameter, we get Actual diameter = Apparent diameter / Magnification rate. Now, let's calculate the actual diameter for both the old microscope and the new microscope as follows: Actual diameter of the old microscope = \(5 / 12 = 0.42 inches\). Actual diameter of the new microscope =\(5 / 15 = 0.33 inches\).

Now, to find the area of the circular view of the old microscope, we use the formula for the area of a circle given as Area of a circle =\(\pi r^2\) Where r is the radius of the circle. Area of the old microscope = \(\pi (0.21)^2\)= \(0.139\)square inches.

Similarly, the area of the circular view of the new microscope = \(\pi (0.165)^2\)= 0.086 square inches. Therefore, the old microscope contained\(0.139 - 0.086 = 0.053\) square inches more than the new microscope. The old microscope contained 2.5 square inches more of the sample's area than the new microscope.

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Answer:

B. 80, -160

Step-by-step explanation:

The common ratio between these three numbers is -2.

-10 * -2 = 20

20 * - 2 = -40

-40 * -2 = 80

80 * -2 =  -160

Area = πr²

= π × 8²

= 64π cm²

The coordinates of point L are (14, 17).

What is midpoint of two points?

A point B that is situated halfway between two other points, such as A and C, is said to be the midpoint. Because of this, finding the midpoint only requires measuring the length of the line segment and dividing it by 2.

Given:

KL has a midpoint at M(13.5, 15).

Point K is at (13, 13).

We have to find the coordinates of point L.

Since the midpoint of two points is calculated as,

\((\frac{x_1+x_1}{2}, \frac{y_1+y_2}{2} )= M\)

Here,

\((x_1, y_1) = (13, 13) M = (13.5, 15)\)

⇒ \((\frac{13 + x_2}{2}, \frac{13+y_2}{2} ) = (13.5, 15)\)

⇒ \(\frac{13 + x_2}{2}= 13.5, \frac{13 + y_2}{2} = 15\)

\(13 + x_2 = 27, 13 + y_2 = 30\\x_2 = 27 - 13, y_2 = 30 - 13\\x_2 = 14, y_2 = 17\)

Hence, the coordinates of L are (14, 17).

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Answer:

The factorization of the expressions are

1. a. 9y-12 = 3 ( 3y -4)

b. 6-4x = 2( 3-2x)

c. 25y-35z = 5( 5y -7z)

d. 42y+28x-56c = 14( 3y+ 2x -4c)

2. a. x²-3x = x( x-3)

b. 4w²+10w = 2w( 2w+5)

c. x³+2x² = x²( x+2)

d. xy+xz = x( y+z)

Factoring or factorization an expression can be defined as writing an algebraic expression as a product of its factors.

For example 6x +2 can be factored by finding the expression highest common factor which is 2 and bring it out from each term

therefore ;

6x+2 = 2( 3x+1) .

Also 9y -12 , the highest common factor = 3

= 3( 3y -4)

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a) We would expect approximately 0.2325 × 200 = 46.5 vehicles

to fail in their first 2 years. Since we cannot have a fraction of a vehicle

failing, we would expect around 46 or 47 vehicles to fail in their first 2

years.

b) The approximate probability that 50 or more vehicles fail in

the first 2 years is 0.0004.

c) The approximate probability that no more than 10 of the remaining

vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.

a) The average lifespan of the vehicle is 8 years, and it follows an

exponential distribution, which has a probability density function of

\(f(x) = (1/θ) \times e^(-x/θ)\),

where θ is the mean of the distribution. Thus, θ = 8.

The probability that a vehicle fails in the first 2 years can be found by

integrating the exponential probability density function from 0 to 2:

P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx

Using a calculator or a table of integrals, we can find this probability to

be approximately 0.2325.

b) The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.

The probability that 50 or more vehicles fail in the first 2 years can be

found using the Poisson distribution with parameter λ = 46.5:

P(X ≥ 50) = 1 - P(X < 50)

Using a Poisson distribution table or a calculator, we can find that P(X <

50) is approximately 0.9996.

Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).

c) Given that 30 vehicles have already failed in under 2 years, we need

to find the probability that no more than 10 of the remaining 170 vehicles

fail in their first 2 years.

The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525

(rounded to 40).

Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable

with parameter λ = 40.

Using a Poisson distribution table or a calculator, we can find that P(Y ≤

10) is approximately 0.0002.

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Yes, the probability assignments given to the four outcomes of an experiment are valid. Probabilities are calculated subjectively, and the decision maker assigned probabilities to the four outcomes of the experiment, which is perfectly acceptable.

Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 to 1.

An event that is certain to happen has a probability of 1, while an event that is impossible has a probability of 0. The probability of any other event lies somewhere between 0 and 1.

Probability assignments, which are subjectively determined probabilities, are valid as long as they meet the following criteria:

In this case, the probability assignments are valid because they meet both of the above criteria. The probabilities assigned are between 0 and 1, and when the probabilities are added together, the sum is 1.

Therefore, the given probability assignments are valid.

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Answer:

- \(\frac{59}{2}\) simplified

Alternative form:

- 29\(\frac{1}{2}\)  or  -29.5

Answer:

2 I think i might be wrong

Answer: hers the answer

g(r)= - 3r

The number of different values that x (the number of successes) can assume in a binomial experiment consisting of five trials is 6.

This is because x can take on values from 0 to 5 (inclusive), and there are 6 possible values in that range. Therefore, the answer is d. In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume ranges from 0 to 5 successes. Therefore, x can have 6 different values: 0, 1, 2, 3, 4, or 5. Your answer is d. 6.

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Correct question:

a sequence U1, U2,U3...... is defined by the relation \(U_{n +1} = 2U_n +5\). if U1 =2, find U2​ and U3

Answer:

U2 = 9

U3 = 23

Step-by-step explanation:

Given sequence;

\(U_{n +1} = 2U_n +5\)

U1 = 2

U2 = ?

\(U_{n +1} = 2U_n +5\\\\U_2 = 2(U_1) + 5\\\\U_2 = 2(2) + 5\\\\U_2 = 4 + 5\\\\U_2 = 9\)

Solving for U3;

\(U_3 = 2(U_2) + 5\\\\U_3 = 2(9) + 5\\\\U_3 = 18 + 5\\\\U_3 = 23\)

Answer:other number is 11,4

Step-by-step explanation:

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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The composition of functions (f ∘ g)(x) can be found by substituting g(x) into f(x). In this case, (f ∘ g)(x) is equal to [(1 − 6x) − 1]^3, which simplifies to (-6x)^3 = -216x^3.

To find (f ∘ g)(x), we need to substitute g(x) into f(x) and simplify the expression. First, we substitute g(x) = 1 − 6x into f(x):

f(g(x)) = [(1 − 6x) − 1]^3.

Next, we simplify the expression inside the parentheses:

[(1 − 6x) − 1] = -6x.

Now, we substitute -6x back into the expression for f(g(x)):

f(g(x)) = (-6x)^3.

Simplifying further, we raise -6x to the power of 3:

(-6x)^3 = -216x^3.

Therefore, the composition of functions (f ∘ g)(x) is equal to -216x^3.

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Answer:

\(-2x^2+11\)

Step-by-step explanation:

\(-2x^2+11\)

Since there aren't any like terms, the answer would be:

\(-2x^2+11\)

Hope this helps!

Answer:

y=-x-1

Step-by-step explanation:

if points are (-1,-2) and (3,-4)

Answer:

slope intercept form:  y = -1/2x - 5/2  or  y = -0.5x - 2.5

Answer:

850

Step-by-step explanation:

500 times 0.7 plus 500

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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answer=To find the constant of proportionality, we need to determine the rate at which the total cost changes with respect to the number of tickets purchased.

We can use the information given in the table to find the slope of the line that represents this relationship.

Using the points (8, 2.00) and (12, 3.00), we can calculate the slope as:

slope = (3.00 - 2.00) / (12 - 8) = 0.25

Using the points (12, 3.00) and (20, 5.00), we get the same result:

slope = (5.00 - 3.00) / (20 - 12) = 0.25

Using the points (20, 5.00) and (30, 7.50), we get:

slope = (7.50 - 5.00) / (30 - 20) = 0.25

Using the points (30, 7.50) and (50, 12.50), we get:

slope = (12.50 - 7.50) / (50 - 30) = 0.25

Since the slope is the same for all pairs of points in the table, we can conclude that the relationship between total cost and number of tickets purchased is a linear relationship, and the constant of proportionality (the rate of change of y with respect to x) is:

0.25 dollars/ticket then the answer is B

Answer:3.00

Step-by-step explanation:

Answer:

I cant see it

Step-by-step explanation:

Answer:

I think they both did reason correctly! Since they got different answers, we can conclude the initial plan was incorrect.

Step-by-step explanation:

      Both of their work looks to be correct. Since they both have correct solutions, we can conclude that the initial plan was incorrect and that an angle was recorded wrong.

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

m=y8+2x

Step-by-step explanation:

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Answer:

11 weeks

Step-by-step explanation:

Kiaya has $376 but can only withdraw $276 before being charged by the bank.

First I subtracted the $100 she can't spend from $376.

-She has a total of $276 she can spend without being charged.

Next, I divided $276 by $25 (the amount she withdraws every week)

- The total is 11.04

This means she has 11 Weeks before she will have to pay the fee.

Hope I helped you out!! :)

He will pay remaining amount with interest from the beginning in 4 years.

We must calculate the interest that Ramesh would have to pay at the end of 3 years on Rs 50,000 at 10% p.a. The simple interest will be:

= (Principal x Rate x Time)/100

= (50,000 x 10 x 3)/100

= Rs 15,000

Total amount to pay at the end of 3 years would be:

= Rs 50,000 (principal) + Rs 15,000 (interest)

= Rs 65,000.

Ramesh paid half of principal (Rs 25,000) with interest of Rs 15,000. So, remaining amount to pay is:

= Rs 25,000 (principal) + Rs 20,000 (interest)

= Rs 45,000.

The time period to pay the remaining amount of Rs 45,000 with the total interest of Rs 20,000 will be derive using S.I. formula:

20,000 = (45,000 x 10 x Time)/100

Time = (20,000 x 100)/(45,000 x 10)

Time = 4.44444444444

Time = 4 years.

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Answer:

\(\text{D. 36.64}\)

Step-by-step explanation:

The Law of Sines is given by \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\) and works for any triangle.

Therefore, we have the proportion:

\(\frac{c}{\sin 41.5^{\circ}}=\frac{37}{\sin 42^{\circ}},\\\\c=\frac{37\sin 41.5^{\circ}}{\sin 42^{\circ}}=36.6399945706\approx \boxed{36.64}\)