select the smallest sample size (in nm) that a microscope with na = 0.6 can resolve (abbe criterion) at 480nm.

Answer:

Slope-intercept form is y=mx+b. You find the slope of the line and you plug that in for m. Then you find the y-intercept, which is where the line crosses the y-axis, and plug that in for b.

Step-by-step explanation:

The sequence that shows a pattern where each term is 1.5 times the previous term is option D

Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.

Let us test each option one by one.

Option A

1.5 x -4 = -6

But the next number in the series is 6

Option B

1.5 x 10 = 15

1.5 x 15 = 22.5

But the next number in the series is 25

Option C

1.5 x 98 = 147

But the next number in the series is 99.5

Option D

1.5 x -200 = -300

1.5 x -300 = -450

1.5 x -450 = -675

Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D

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Answer: D (-200,-300,-450,-675,...)

Step-by-step explanation:

Recognizing the pattern in a sequence is used to write the function that represents it.

Answer:

51,51,78

Step-by-step explanation:

First of all equate the two angles since it is isoceles.

3x+9= 4x-5 , therefore x= 14

sub that in and find the rest of the angles.

angle G---> 4*14 -5 = 51

angle I--->3*14+9= 51

last angle 180 - 2*51 = 78

Answer:

y=2x+4

Step-by-step explanation:

2 is the slope, you can see that with rise over run. 4 is the y intercept

Answer:

y=2x+4

Step-by-step explanation:

Look at the y-axis if the point that touches the y-axis is 4

Then the slope is 2

you go down 2 which is -2 (Since down is negative)

and you go left 1 which is -1 (Since left is negative)

now the equation looks like this:

y=-2/-1x+4

Simplify: (negative and negative cancel each other out making it positive)

y=2x+5

The exact length of  curve y = (x^4/16) + (1/2)x^2 is obtained by integrating the arc length formula.

How we find the exact length of the curve defined by the equation y = (x\(^4\)/16) + (1/2)x\(^2\).

To find the exact length of the curve defined by the equation y = (x\(^4\)/16) + (1/2)x\(^2\), we can use the arc length formula. This formula calculates the length of a curve over a given interval by integrating the square root of the sum of the squares of the derivatives of x and y with respect to a parameter.

In this case, we need to find the derivative of y with respect to x, which is given by (4x\(^3\)/16) + x.

Using this derivative, we substitute it into the arc length formula, which becomes an integral of √(1 + ((4x\(^3/16\)) + x)\(^2\)) dx over the desired interval.

By evaluating this integral, we can obtain the exact length of the curve. The result will be a numerical value that represents the length of the curve in the given interval.

It is important to note that the specific interval over which we calculate the length will affect the final result.

The arc length formula allows us to find the precise length of the curve, taking into account its shape and path.

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Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The 50th term is 290.

It is a sequence where there is a common difference between each consecutive term.

Example:

12, 14, 16, 18, 20 is an arithmetic sequence.

We have,

-4, 2, 8, 14,

This is an arithmetic sequence.

First term = a = - 4

Common difference.

d = 2 - (-4) = 6

d = 8 - 2 = 6

Now,

The nth term = a + (n -1)d

So,

n = 50

a = -4

d = 6

50th term.

= -4 + (50 - 1) 6

= - 4 + 49 x 6

= - 4 + 294

= 290

Thus,

The 50th term is 290.

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The complete question:

What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?

The answer would be A. 7 Nickels

Answer:

11 remainder 26

Step-by-step explanation:

When you enter data into SPSS (Statistical Package for the Social Sciences), each person's data or score is typically entered in its own case or row within the SPSS data file.

SPSS organizes data in a tabular format, where each row represents an individual case or participant, and each column represents a variable or a specific data point associated with that case.

In this format, each case's data is placed in a separate row, ensuring that the information remains distinct and easily identifiable.

For example, if you are collecting data from a survey or an experiment involving multiple participants, each participant's responses or scores would be entered into its respective row in the SPSS data file. This arrangement allows for convenient analysis and manipulation of data using SPSS.

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The athlete covers a distance total of 3.375 miles in two days.

To calculate this, we first need to determine how far she runs during the sprints.

Since she sprints 1/8 mile 3 times, her total distance covered during sprints is:
\(\frac{1}{8}\) mile x 3 = \(\frac{3}{8}\) mile
Adding this distance to the distance covered during her warm-up and cool-down jogs, we get:
1 mile (warm-up) + \(\frac{3}{8}\) mile (sprints) + 1 mile (cool-down)

= 2 \(\frac{3}{8}\) miles
This is the distance covered by the athlete in one day.

To find the total distance covered in two days, we simply multiply this by 2:
2 \(\frac{3}{8}\) miles x 2 = 4 6/8 miles
Simplifying this fraction, we get:
4 \(\frac{6}{8}\) miles = 4 \(\frac{3}{4}\) miles
Therefore, the athlete covers a total of 4 3/4 miles (or 3.375 miles) in two days.
The miles covered in one day.
1 mile jogged for warm-up
\(\frac{1}{8}\) mile sprinted, repeated 3 times (\(\frac{1}{8}\) x 3

= \(\frac{3}{8}\) miles)
1 mile jogged for cool down
Add up the distances for one day.
1 mile (warm-up) + \(\frac{3}{8}\) miles (sprints) + 1 mile (cool down)

= 2 \(\frac{3}{8}\) miles
The total miles covered in two days.
2 \(\frac{3}{8}\) miles (per day) x 2 days = 4 6/8 miles
The fraction.
4 \(\frac{6}{8}\) miles = 4 \(\frac{3}{4}\) miles
The athlete covers a total of 4 \(\frac{3}{4}\) miles in two days during her workout routine

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Answer:

Let's define all the possible forms:

slope-intercept: y = a*x + b

point-slope: y - y1 = a*(x - x1)   (where (x1, y1) is a point in the line)

standard form: a*x + b*y = c

then:

a) 7x + 5y = 8

This is in standard form.

b) y − 5 = 3*(x − 9)

This is in point slope form.

c) y = 7x + 9

This is in slope-intercept form.

d) 8x − 9y = −2

This is in standard form.

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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The product of (4 x 10⁶) ×  (2 x 10⁶) is 8 × 10⁶.

Scientific notation is similar to shorthand for writing extremely large or extremely small numbers. Rather than writing a number in decimal form, it is reduced to a number multiplied by ten.

Now, as per the given question;

The product of the given two number are-

= (4 x 10⁶) ×  (2 x 10⁶)

= 8 × 10⁶

Therefore, the scientific notation of the product of the give two numbers is 8 × 10⁶.

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The correct question is-

Find the product of (4 x 10⁶) and (2 x 10⁶). write the final answer in scientific notation. write the final answer in scientific notation.

Number 16 fill expressions B and C to make equations correct.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

For equation B. 8(2+9)=___ + 72

8*11=x+72

x=16

For equation C. 4(7+4)=28+___

4*11=28+x

x=44-28

x=16

Hence,

         Number 16 fill expressions B and C to make equations correct.

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Answer:

\(\huge \boxed{14}\)

Step-by-step explanation:

Q is a point on the line segment PR.

PQ = 3

QR = 11

PR = PQ + QR

PR = 3 + 11 = 14

Answer:

\(\huge\boxed{PR = 14}\)

Step-by-step explanation:

QR = 11

PQ = 3

Given that Q is on line segmant PR

So,

PR = PQ + QR

PR = 3 + 11

PR = 14

P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Answer:

-7x-4y+4y=-44+4y

-7x=4y-44

-7x/-7= 4y-44/-7

x=-4/7y+44/7

x=-4/7y+44/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total number of days

The number of days she bought a banana or orange

The probability of buying a banana or an orange is

Answer:

\(\sf \dfrac{7}{10}=0.7=70\%\)

Step-by-step explanation:

Given information:

Total number of days = 30

Probability Formula

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

Probability of buying a banana:

\(\implies \sf P(Banana)=\dfrac{12}{30}\)

Probability of buying an orange:

\(\implies \sf P(Orange)=\dfrac{9}{30}\)

Therefore,

\(\implies \sf P(Banana) \: or \: P(Orange)=\sf \dfrac{12}{30}+\dfrac{9}{30}=\dfrac{21}{30}=\dfrac{7}{10}\)

So the probability of buying either a banana or an orange is:

  \(\sf \dfrac{7}{10}=0.7=70\%\)

36

Step-by-step explanation:

4 5/8*3 is 13.875

500 decided by 13.875 is a little over 36, so you can make 36 full ribbons

Answer:36

Step-by-step explanation:

4 5/8*3 is 13.875

Answer:

7

Step-by-step explanation:

He has a 1/6 chance of rolling a 6

1/6 of 42 = 7

Answer:

Rs. 28,571.4

Step-by-step explanation:

Let

Cost price = x

Profit = 5% of x

= 0.05x

Selling price = Rs.30, 000

Profit = Selling price - cost price

0.05x = 30,000 - x

Collect like terms

0.05x + x = 30,000

1.05x = 30,000

x = 30,000/1.05

x = Rs. 28,571.428571428

Approximately,

Cost price = x = Rs. 28,571.4

Answer:

Step-by-step explanation:

25x-16y-25x+16y

-16y and 16y cancels out

25x-25x

25x and -25x cancels out too

This means the answer is 0

Answer:

tax is 52.98 and total is 102.97

Step-by-step explanation:

Answer:

inbox I think maybe I can help

Answer:

Correct answer is option D

Answer:

they got -21 when they were supposted to get +21

and they also got +6x when they were supposted to get -6x

Step-by-step explanation:

that's because -3 and 2x are multiplied together and when you are multiplying negative and positive number you need to get negative result.

when you are multiplying negative with negative number, you will get positive number.

Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)