For what slit-width-to-wavelength ratio does the first minimum of a single-slit diffraction pattern appear at (a) 30 degrees (b) 60 degrees, and (c) 90 degrees? Hint: The small-angle approximation is not valid.

Answer: the volume of the figure is 792 ft³

Step-by-step explanation:

The volume of a shape V consists of the volume of a prism V1 and

the volume of the pyramid V2

9²+12²=15²

81+144=225

225≡225

Hence, figure base is а right triangle

So, V=V1+V2

[tex]\displaystyle\\V1=\frac{12*9}{2} *10\\\\V1=6(9)(10)\\\\V1=540\ ft^3\\[/tex]

[tex]\displaystyle\\V2=\frac{1}{3}(\frac{12*9}{2} )(24-10) \\\\V2=\frac{12(9)(14)}{6} \\\\V2=252\ ft^3[/tex]

[tex]V=540+252\\\\V=792\ ft^3[/tex]

Answer:

  $824.39

Step-by-step explanation:

You want to know the monthly deposit required for a 50-year ordinary annuity to accumulate enough value at 5% so that annual withdrawals can be made of $110,000 without affecting the principal.

In order for the annual interest to be $110,000 at 5%, you have ...

  I = Prt

  110,000 = P(0.05)(1)

  2,200,000 = P . . . . . . . multiply by 20

The value of the annuity must be $2.2M after 50 years.

In order for the annuity to have that future value, the monthly payment must be $824.39. This value can be found using a suitable financial calculator or spreadsheet. (Or the appropriate formula from your list.)

0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches

Given that

A large helium balloon is being inflated at the rate of 110 cubic inches per second

radius = 12

volume = [tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]

            = 4/3 [tex]\pi[/tex] [tex](12)^{3}[/tex]

            =7234.55

V = 4/3 πr³

dV/dt = 4/3 (3πr² dr/dt) = 4πr² dr/dt

dr/dt = dV/dt / (4πr²)

dr/dt = dV/dt / (4πr²)

= 110/(4[tex]\pi[/tex]×([tex]12^{2}[/tex]))

= 0.060819 inches per second

0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches

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Answer:

A. 0°

Step-by-step explanation:

Answer:

Option A is correct.

Solution for the given equation is,

Step-by-step explanation:

Given that :

Let

then our equation become;

A quadratic equation is of the form:

.....[2] where a, b and c are coefficient and the solution is given by;

Comparing equation [1] and [2] we get;

a = 2 b = -1 and c =-1

then;

Simplify:

Simplify:

y = 1 and

Substitute y = cos x we have;

⇒

and

⇒

The solution set:  

Therefore, the solution for the given equation   is,

Answer:

C

Step-by-step explanation:

y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.

Which equation has no solution

A 4(x+2)=4(x-3)

B -2(x+1)=3x-2-5x

C 4 (x+1)-7x=-3(x-1)+1

D -5(x-7)=2(2x+3)+x+7

Answer: The answer to this quesiton is A.

B-all real numbers.

C- all real numbers.

D- x=11/5

A= no solution.

so the answer would be A i hope this helps✅

If we roll a dice three times and we can stop in the first time only when it come 6. The expected payoff is 4.557.

According to the question:

The number of times you can get 06 are:

(i). If the third toss rolls a 6:  6

In this case her first two digits can be any of the five numbers. No. The number of cases is 5 × 5 = 25.

(ii). If you get a 6 on the second throw. The number of cases is -5 (no third throw in this case)

(iii). If the first roll rolls a 6. The number of cases is -1.

2. Number of times you can get 5 Are-

(i). If there is only one 5 in 3 rolls . The number of cases will simply be

3 × 4 × 4

(Because there are 5 possibilities in 3 places and 4 in the remaining places.)

(ii). If there are two 5s, the number of cases is 3×4. (Because there are 3 places where 5 cannot exist, and the places are filled with 4 possibilities.)

(iii). If there are three 5s, the number of possibilities is -1.

Similarly, for 4,3,2,1, the number of possibilities is (3*3*3 + 3*3 + 1), (3*2*2 + 3*2 + 1), (3 × 1×1 + 3×1 + 1), 1 each.

So the number of possibilities for 1,2,3,4,5,6 are 1,7,19,37,61,31 respectively .

You can now get the expected profit by taking the weighted average of the numbers with the possible outcome odds.

So the result is (6*31 + 5*61 + 4*37 + 3*19 + 2*7 + 1)/(31+61+37+19+7+1)

which is 711/ 156 = 4.557

Therefore, the expected payout is 4.557.

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Step-by-step explanation:

graph till you find the answer

B

greatest common factor = 4x

What is GCF?

The biggest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).

[tex]64xyz=2^{6}*x*y*z\\ 36xy=2^{2}*3^{2} *x*y\\24x=2^{3}*3*x[/tex]

greatest common factor = [tex]2^{2} *x[/tex]

greatest common factor = 4x

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Answer:

In an exponential equation, both sides can be written as power of the same base when the base is the same on both sides of the equation. For example, the equation "2^x = 8" can be rewritten as "2^x = 2^3" because the base, 2, is the same on both sides of the equation.

To solve an exponential equation where both sides can be written as powers of the same base, you can set the exponents equal to each other and solve for the variable. In the example above, setting the exponents equal to each other would give us "x = 3", so the solution is x = 3.

On the other hand, in an exponential equation where both sides can not be written as powers of the same base, you cannot simply set the exponents equal to each other. Instead, you need to use a different method to solve the equation. One way to do this is to use the property of exponents that states that "a^x * a^y = a^(x+y)" to rewrite the equation so that both sides have the same base. For example, the equation "2^x * 3^y = 6" can be rewritten as "2^x * 2^(log3(6)) = 2^(x + log3(6))", where "log3" represents the logarithm with base 3. This allows us to set the exponents equal to each other, giving us "x + log3(6) = 1", and we can solve for x to find the solution.

The fraction of people that preferred lunch is of:

30%.

The three options are given as follows:

The sum of the fractions of each of these options is of:

100%.

10 of the respondents preferred breakfast, and there were 50 people, hence the fraction that preferred breakfast is of:

10/50 x 100% = 20%.

Then the fractions in this problem are given as follows:

Thus the missing fraction, which is the fraction of people that prefer lunch, is obtained as follows:

50 + 20 + x = 100

70 + x = 100

x = 30%.

(as the sum of the three fractions is of 100%, as they represent all the possible outcomes).

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By using the concept of division, it can be calculated that-

29 [tex]\div[/tex] 5123 = 0.00566

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

Here,

29 divided 5123 means

29 [tex]\div[/tex] 5123

Now,

29 [tex]\div[/tex] 5123 = 0.00566

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Draw a drawing in the scale factor of 5 / 1 then drawn drawing is said to be in ratio and get enlarge 5 times to the scale drawing.

As given in the question,

Given scale ratio is equal to 5 / 1.

Let us consider scale drawing is in the scale ratio of 1cm  : 3m

It means we have

Therefore, scale factor of 5 / 1 used to draw a drawing is said to be in ratio to  enlarge or small the given picture.

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Answer:

(-7, -5)

Step-by-step explanation:

y = x + 2

2x - 3y = 1

2x - 3(x + 2) = 1

2x - 3x - 6 = 1

-x - 6 = 1

    +6  +6

---------------

-x = 7

÷-1  ÷-1

-------------

x = -7

y = x + 2

y = -7 + 2

y = -5

I hope this helps!

Answer:Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

Step-by-step explanation:

Parallel slope intercept form is a form of linear equation that describes a line parallel to a given line with slope m.

The equation for a line parallel to the line with equation y = mx + b is y = mx + b + c, where c is any constant.

1. Start with the equation of the original line in slope-intercept form, y = mx + b

2. To make a parallel line, add a constant c to the y-intercept, so the equation is y = mx + b + c

3. That's it! You now have an equation for a parallel line in slope-intercept form.

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Answer:

There are 400 Students.

The equation of the line that passes through the point (1,2) is y = 2x – 1with slope 1.

Using the point-slope form of the equation of a line, we can write the equation of a line that passes through the point (1,2) as:

y - 2 = m(x - 1)

Since the slope of the line is m, we can set m = 1 and solve for y:

y - 2 = 1(x - 1)

y - 2 = x - 1

y = x - 1 + 2

y = 2x – 1

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After a comparison of females and males on the number of hours of a day that the subject watched the TV.

The hypotheses of a significance test to analyze whether the population means differ for females and males would be as follows:

(a) H0: μ1 = μ2 (the population means are equal for females and males)

Ha: μ1 ≠ μ2 (the population means are not equal for females and males)

(b) In order to conduct the significance test, we would need to calculate the t-statistic and the P-value. However, the question does not provide the necessary information to do so (e.g. sample means, standard deviations, sample sizes). Without this information, we cannot conduct the significance test and interpret the P-value.

(c) Without conducting the significance test, we cannot conclude anything about whether there is a gender difference in TV watching.

(d) Similarly, without conducting the significance test and calculating the confidence interval, we cannot determine whether the confidence interval would contain 0 or not.

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Best-fit values

Slope

Y-intercept

X-intercept

1/Slope

0.6000 ± 0.1155

4.000 ± 0.6633

-6.667

1.667

95% Confidence Intervals

Slope

Y-intercept

X-intercept

0.2326 to 0.9674

1.889 to 6.111

-25.31 to -2.028

Goodness of Fit

R square

Sy.x

0.9000

0.7303

Is slope significantly non-zero?

F

DFn,DFd

P Value

Deviation from horizontal?

27.00

1,3

0.0138

Significant

Data

Number of XY pairs

Equation

5

Y = 0.6000*X + 4.000

Answer:

It is a

Step-by-step explanation:

You are welcome.

ok so its just 1/125 I posted a comment about it by accident can you pick me as brainiest :>

Edit bro it took out my one it said 1/25

Ok so like i just saw it doesnt have 1/125 its 1/5^3

Letter a

:D

Pick me please! :>

The integer representing the entrance of the cave is 14.

An integer is a whole number from the set of negative, non-negative, and positive numbers. An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes: Positive Numbers: A number is positive if it is greater than zero. or we can say an integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z o

Given that, The entrance of a cave is at an elevation of 14 meters. the lowest part of the cave is at an elevation of -86 meters.

We know that, the integer numbers or simply integers are sets of numerical signs that contain the natural numbers (positive numbers), the zero number "0" and the opposite numbers corresponding to the negative numbers of the natural numbers. The integer numbers have no decimal part, are not fractional, nor have imaginary part.

The entrance is at 14 meter, that means the entrance is represented by the integer 14.

Hence, The integer representing the entrance of the cave is 14.

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The equation that has no solutions are:

x + 6 =  5 + x

5 - 3x = -3x + 4

Options A and E are the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

x + 6 =  5 + x

6 = 5

Which is not equal.

So,

It has no solutions.

-2(x - 3) = -2x + 6

-2x + 6 = -2x + 6

This has many solutions.

4 - 4x = 3x + 2

4 - 2 = 3x + 4x

2 = 7x

x = 2/7

This has one solution.

4(x + 1) = 3(x + 2)

4x + 4 = 3x + 6

4x - 3x = 6 - 4

x =  2

This has one solution.

5 - 3x = -3x + 4

5 - 4 = -3x + 3x
1 = 0

This has no solutions.

Thus,

x + 6 =  5 + x and 5 - 3x = -3x + 4 are the equations that have no solutions.

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Option A and C have a proportional relationship.

What is proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

(a) Total cost of buying x avocados be p

 So, p = 4x

(b) Let the total amount a taxi driver earns be y

So, y = 3 + m

(c) Let the total number of toys be x

So, x = 2w

(d) Let the total amount a Gardner earns be c

So, c = 10 + 15r

Hence, option A and C have a proportional relationship.

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Answer: The area is 12

Step-by-step explanation:

P=2l+2w

We are given, 

P=40in

l=2w-4

Plug these into the first formula and solve for the dimensions,

length and width, of the rectangle:

 40=2(2w-4)+2w       Simplify

40=4w-8+2w

40=6w-8

48=6w

8=w OR the width is 8 in, therefore, 

the length is

l=2(8)-4

l=12 sq in

l= area

The polar equation for the curve is x = √3cosФ and y = √3 sinФ.

Here we have to find the polar equation of the curve.

Data given:

The equation is:

x² + y² = 3

This is an equation of a circle.

Its radius is √3 and its √center is (0,0)

To find the polar equation of a circle we use the following formula:

x = h + rcosФ

y = k + r sinФ

where (h,k) is the center of the circle which in this case is (0,0) and by substituting we get:

x = √3 cosФ

y = √3 sinФ

Therefore the polar equation is x =√3cosФ and y = √3sinФ.

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The solution of the given inequality -3/2(y/6 + 4) < -2x will be 8x - y < 24.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

-3/2(y/6 + 4) < -2x

-3y/12 - 6 < -2x

2x - 3y/12 < 6

24x - 3y < 72

8x - y < 24

Hence "The given inequality -3/2(y/6 + 4) -2x has an answer of 8x - y 24.".

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The rationale underlying the use of projective personality tests, such as the Rorschach test and the thematic apperception test, is that they reveal the subjects' personalities by eliciting responses to vague, ambiguous stimuli.

The rationale underlying the use of projective personality tests, such as the Rorschach test and the Thematic Apperception Test, is that they can reveal a person's unconscious thoughts, feelings, and motivations. These tests use vague and ambiguous stimuli, such as inkblots or pictures, and ask the person to describe what they see or make up a story about the stimuli. The person's responses are believed to reflect their underlying personality traits and psychological conflicts.

The theory is that when faced with ambiguous stimuli, people project their own thoughts, feelings, and motivations onto the stimuli, revealing their unconscious processes.

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If we want to be 90% confident that the sample mean is within 17 kernels of the true population mean then the minimum sample size that should be taken is 83.

Given:

the population standard deviation for the number of corn kernels on an ear of corn is 94 kernels.

if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean

what is the minimum sample size that should be taken = ?

population standard deviation (σ) = 94

margin of error (E) = 17

for 90% confidence interval Zα/2 = 1.645

formula:

sample size (n) = [ zα/2 × σ/E]²

sample size (n) = [1.645×94/17]²

sample size (n) = 82.7

sample size (n) ≈ 83

Hence we get the required answer.

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Answer: 11

Step-by-step explanation:

I think sorry

Answer:

9

Step-by-step explanation: