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Solve for x to the nearest tenth.

The path difference if the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30° is 1.57 × 10⁻⁶ m.

When the maxima of two waves add up (the two waves are in phase), the amplitude of the resultant wave equals the total of the separate amplitudes, this is known as constructive interference.

We know that for constructive interference, therefore, the formation of bright fringe through a diffraction grating is given by:

d sin θ = n λ

where d is the distance between slits, θ is the angle of diffraction, n is the order of fringe, and λ is the path difference.

As it is given that the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°, therefore, the path difference can be written as,

[tex]\begin{aligned}\lambda &= \dfrac{(d sin \theta)}{ n} \\\\&=\dfrac{0.60 \times 10^{-3 }m) \times sin (0.30)}{2}\\\\ &= 1.57 \times 10^{-6}\rm\ m\end{aligned}[/tex]

Hence, the path difference is 1.57 × 10⁻⁶ m.

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The sum of all the probabilities must be one. Then the probability that the gymnast scores a 9 or 9.95 is 0.14.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

Researching on the internet, the probability of the gymnast getting each score is given by:

Considering that it is a distribution, the sum of all the probabilities must be one.

0.02 + 0.02 + 0.06 + 0.1 + 0.16 + 0.14 + 0.18 + 0.18 + x + 0.02 = 1

0.88 + x = 1

           x = 0.12

The probability that the gymnast scores a 9 or 9.95 will be

P(9 or 9.5) = (X = 9) + P(X = 9.5) = 0.12 + 0.02 = 0.14

More about the probability distribution link is given below.

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Answer: D

Step-by-step explanation:

trust me bro I got it right

Answer:

Approximate population ≈ 74.36 million.  

Step-by-step explanation:

The given problem involves modeling of an exponential growth or decay function of a population.      

We can model the exponential growth of a population using the following Exponential Growth Model:

Where:

Based from the given equation, [tex]\displaystyle\mathsf{y\:=\:58.7(1.03)^t }[/tex] , we can infer that:

⇒   [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex] or  [tex]\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }[/tex]

Where:

Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :

[tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]

⇒   [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }[/tex]

Step 2: Follow the order of operations, addition inside the parenthesis:

⇒   [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }[/tex]

Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):

⇒  [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }[/tex]  

Step 4: Follow the order of operations, multiplying  58.7 (P₀) into the parenthesis:

⇒  [tex]\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}[/tex]

Therefore, the approximate population of the country in January 2002 is 74.36 million.  

Exponential functions

Exponential growth

Exponential decay

Exponential growth model

____________________________

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Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean strength gain of all students from this school if they joined the program is (7.85, 15.37).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.

The other parameters are given as follows, with the help of a calculator.

[tex]\overline{x} = 11.61, s = 4.89, n = 9[/tex]

Hence:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 11.61 - 2.306\frac{4.89}{\sqrt{9}} = 7.85[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 11.61 + 2.306\frac{4.89}{\sqrt{9}} = 15.37[/tex]

The 95% confidence interval for the mean strength gain of all students from this school if they joined the program is (7.85, 15.37).

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Answer:

Part A = $180

Part B = $104

Step-by-step explanation:

Part A:

You do 255÷5=51

51 x 4 = 180

Part B:

You do 130÷5=26

26 x 4 = 104

Answer:

$180 for the coat, $104 for the boots

Step-by-step explanation:

first: percent = decimal (20 = 0.20)

for the coat:

225-(225x0.20)

225-40 = 180

for the boots:

130- (130x0.20)

130-26 = 104

Answer:

C. p = h + 16

Step-by-step explanation:

Answer:

y = - 2x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c

to find c substitute (4, 2 ) into the equation

2 = - 8 + c ⇒ c = 2 + 8 = 10

y = - 2x + 10 ← equation of line

Answer:

y = - 2x + 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c

To find c we must substitute (4, 2 ) into the equation

2 = - 8 + c, c = 2 + 8 = 10

y = - 2x + 10

Answer:

∠ XYZ ≈ 72.9°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan XYZ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{XY}[/tex] = [tex]\frac{13}{4}[/tex] , then

∠ XYZ = [tex]tan^{-1}[/tex] ( [tex]\frac{13}{4}[/tex] ) ≈ 72.9° ( to 1 dec. place )

The doubling time of the hourly wage of the workers is an illustration of an exponential function that has a rate of 2

The doubling time of the wage is 4 years

A doubling function is represented as:

[tex]p = w \times 2^{\frac{x}{t}}[/tex]

Where:

So, we have:

[tex]10.19 = 6.80 \times 2^{\frac{x}{7}}[/tex]

Divide both sides by 6.80

[tex]1.50 = 2^{\frac{x}{7}}[/tex]

Take the logarithm of both sides

[tex]\log(1.50) = \log(2^{\frac{x}{7}})[/tex]

Apply the law of logarithm

[tex]\log(1.50) = \frac{x}{7}}\log(2)[/tex]

Multiply both sides by 7

[tex]7 \times \log(1.50) = x\log(2)[/tex]

Divide both sides by log(2)

[tex]x = 7 \times \log(1.50) \div \log(2)[/tex]

[tex]x = 4.09[/tex]

Approximate

[tex]x \approx 4[/tex]

Hence, the doubling time is 4 years

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Answer:

8

Step-by-step explanation:

Given:

To Find:

How many footballs will be needed for 48 players?

Solve:

Since there are 2 balls for every 12 players..

Let's b = balls and P = Players

2b = 12p

4b = 24p

6b = 36p

8b = 48

Hence, we can conclude that there will be 8 footballs needed for 48 players

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Answer:

8 balls

Step-by-step explanation:

We can use ratios to solve.

2 balls             x balls

-------------    = -----------------

12 players        48 players

Using cross products

2 * 48 = 12 *x

96 = 12x

Divide each side by 12

96/12 =12x/12

8=x

They needs 8 balls

Answer:

Each of them will have 0.8 kg of the candy.

Step-by-step explanation:

Don't have one sorry!

If the two sides of the triangle are equal then these two triangles are similar. The sides EF and GF are congruent to each other. Then the correct option is D.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In ΔEDF and ΔGDF

DF = DF = radius (common side)

ED = GD = radius

If the two sides of the triangle are equal then these two triangles are similar.

Thus, EF and GF are congruent to each other.

More about the triangle link is given below.

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Answer:

the answer is D

Step-by-step explanation:

EF and GF

Answer:

[tex]-(x-y)^2[/tex]

Step-by-step explanation:

Original expression:

[tex]-x^2+2xy-y^2[/tex]

Factor out -1:

[tex]\implies -(x^2-2xy+y^2)[/tex]

Factor [tex]x^2-2xy+y^2[/tex]:

[tex]\implies -(x-y)(x-y)[/tex]

Apply exponent rule [tex]aa=a^2[/tex]:

[tex]\implies -(x-y)^2[/tex]

Using the z-distribution, as we are working with a proportion, it is found that:

A. The 98% confidence interval  is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.

B. Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.

For each sample, they are given by:

[tex]p_F = \frac{53}{150} = 0.3533, s_F = \sqrt{\frac{0.3533(0.6467)}{150}} = 0.039[/tex]

[tex]p_M = \frac{89}{275} = 0.3236, s_M = \sqrt{\frac{0.3236(0.6764)}{275}} = 0.0282[/tex]

Hence, for the distribution of differences:

[tex]p = p_F - p_M = 0.3533 - 0.3236 = 0.0297[/tex]

[tex]s = \sqrt{s_F^2 + s_M^2} = \sqrt{0.039^2 + 0.0282^2} = 0.048[/tex]

It is given by:

[tex]p \pm zs[/tex]

98% confidence interval, hence, using a z-distribution calculator, the critical value is of z = 2.327.

Then:

[tex]p - zs = 0.0297 - 2.327(0.048) = -0.082[/tex]

[tex]p + zs = 0.0297 + 2.327(0.048) = 0.141[/tex]

The 98% confidence interval  is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.

Item b:

Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.

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Answer:

Step-by-step explanation:

at the end of;                Karabo                         John

1st hour                           80km                          0km(bcause he hasn't started)

2nd hour                       160 km                         100km

3rd hour                        240 km                         200km

4th hour                        300 km                         300km

now I'm not sure whether we should consider the time period after the starting time of karabo, or that of John (they have a gap of one hour u know..)

so, from the starting time of karabo, it takes 4 hours, and from the starting time of John it's 3hours. (Because John started 1 hour later)

The equation of the circle can be written in standard form and in a general form

The center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]

The equation of the circle is given as:

[tex]x^2 + 8x + y^2 - 12y = -29[/tex]

Rewrite as:

[tex]x^2 + 8x + k - k + y^2 - 12y + k - k= -29[/tex]

Express k as the square of the half of the coefficients of x and y.

So, we have:

[tex]x^2 + 8x + (4)^2 - (4)^2 + y^2 - 12y + (6)^2 - (6)^2= -29[/tex]

Evaluate the exponents

[tex]x^2 + 8x + 16 - 16 + y^2 - 12y + 36 - 36 = -29[/tex]

Collect like terms

[tex]x^2 + 8x + 16 + y^2 - 12y + 36 = -29 + 16 + 36[/tex]

Express as perfect squares

[tex](x + 4)^2 + (y - 6)^2 = -29 + 16 + 36[/tex]

[tex](x + 4)^2 + (y - 6)^2 = 23[/tex]

The standard equation of a circle is:

[tex](x - a)^2 + (y - b)^2 + r^2[/tex]

Where:

Center = (a,b)

Radius = r

So, we have:

Center = (-4,6)

Radius = [tex]\sqrt{23[/tex]

Hence, the center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]

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Answer: 15/16

Step-by-step explanation:

5/4 * (3 * 1/4) =

Mutiply 3 * 1/4

5/4 * 3/4 =

Mutiply 5/4 * 3/4

5/4 * 3/4 = 15/16

Answer:

[tex]\frac{15}{16}[/tex]

Step-by-step explanation:

[tex]\frac{5}{4}\cdot \:3\cdot \frac{1}{4}[/tex]

[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:3=\frac{3}{1}[/tex]

[tex]=\frac{5}{4}\cdot \frac{3}{1}\cdot \frac{1}{4}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]

[tex]=\frac{5\cdot \:3\cdot \:1}{4\cdot \:1\cdot \:4}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:5\cdot \:3\cdot \:1=15[/tex]

[tex]=\frac{15}{4\cdot \:1\cdot \:4}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1\cdot \:4=16[/tex]

[tex]\frac{15}{16}[/tex]

Hence, 15/16 is the correct Answer.

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Answer:

This shirt has 8 holes :)

Please mark as brainliest

Answer:

the first

Step-by-step explanation:

it just is. Be smarter.

Answer:

ans at lower left

Step-by-step explanation:

scale up every element in the matrix in the question by 2 will get you the ans.

Answer:

a) Red = 0.2 Blue= 0.4 and White =0.4

b) 90 counters in total

Step-by-step explanation:

a)Firstly we know that the probability of mutually exclusive events is equal to 1 and the question states that the probability of blue and white counter is the same so we subtract 1-0.2 = 0.8 and we divide that by 2 as a result 0.4 .

b) P= Favourable outcomes / total number of outcomes

P(red) = 0.2

total number of red counters = 18

0.2 = 18/t cross multiplying have 0.2t= 18

Dividing throughout by 0.2 having 90

Answer:

You started at (3, 4)

The distance of the image from the lens V=22.5cm and the height of the image h=6.25cm.

It is given that

Hieght of an object H = 5cm

Distance of an object =18cm

Focal lenght of lens = 10cm

As we know that the lens formula is given by

[tex]\dfrac{1}{f} =\dfrac{1}{v} +\dfrac{1}{u}[/tex]

[tex]\dfrac{1}{v} =\dfrac{1}{10} -\dfrac{1}{18}=\dfrac{8}{180}[/tex]

so now

[tex]v= \dfrac{180}{8} =22.5\ cm[/tex]

Now to find the height of the image

[tex]\rm magnification =\dfrac{v}{u} =\dfrac{-Image\ Hieght }{object\ height}[/tex]

[tex]\rm magnification =\dfrac{22.5}{18} =\dfrac{-x}{5}[/tex]

[tex]x=-6.25\ cm[/tex]

Thus the distance of the image from the lens is V=22.5cm and the height of the image h=6.25cm.

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Answer:

424 miles

Step-by-step explanation:

53  x 8 = 424 miles