two dice are rolled sequentially. what is the probability that the first die shows six and the other die shows an odd number?

To solve this equation, we need to distribute the 5/8 to the terms inside the parentheses. The solution to the equation is d = -5.

5/8(16d+24) = (5/8)(16d) + (5/8)(24)

Simplifying this expression, we get:

10d + 15 = 6d - 5

Now we can solve for d by isolating the variable on one side of the equation. First, we'll subtract 6d from both sides:

4d + 15 = -5

Next, we'll subtract 15 from both sides:

4d = -20

Finally, we'll divide both sides by 4:

d = -5

Therefore, the solution to the equation 5/8(16d+24)=6(d-1)+1 is d = -5.

5/8(16d+24)=6(d-1)+1. Here's a step-by-step explanation:

1. First, distribute 5/8 to both terms inside the parentheses on the left side:
  (5/8 * 16d) + (5/8 * 24) = 6(d - 1) + 1

2. Simplify the terms on the left side:
  (10d) + (15) = 6(d - 1) + 1

3. Next, distribute 6 to both terms inside the parentheses on the right side:
  10d + 15 = 6d - 6 + 1

4. Simplify the terms on the right side:
  10d + 15 = 6d - 5

5. Now, move all terms with 'd' to the left side and constants to the right side by subtracting 6d from both sides and subtracting 15 from both sides:
  10d - 6d = -5 - 15

6. Simplify both sides of the equation:
  4d = -20

7. Finally, solve for 'd' by dividing both sides by 4:
  d = -5

So, the solution to the equation is d = -5.

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Answer: Graph A

Step-by-step explanation:

When b= -3, it means the line will pass through y (vertical) at -3. Therefore, it cannot be graph b.

Why it is graph A:

Think rise-over-run. The line will increase in height by 3, and in width by 4 every intersection.  If you pick 2 spots, you can count up 3 and across 4.

(y2-y1)/(x2-x1)

(-3-0)/(0-4)

(-3)/(-4)  --> when dividing by 2 negatives, they become positve.

3/4

y = 3/4-3

Answer:

\(to \: know \: the \: answer\)

\(refer \: to \: the \: above \: attatchment\)

The rate of change between F and G is 5, while the rate of change between G and H is 3, so we conclude that the rate of change between F and G is larger.

For a given function f(x), the rate of change on an interval (a, b), where a < b, is given by the simple formula:

R = (f(b) - f(a))/(b - a)

Now, on the graph of the parabola we can see that the important points are:

Then, the rate of change between points F and G is:

R = (0 - (-5))/(-2 - (-3)) = 5/1 = 5

the rate of change between points H and G is:

R = (3 - 0)(-1 - (-2)) = 3/1 = 3

We can see that the rate of change is larger between F and G than between G and H.

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Answer:

true

Step-by-step explanation:

A correlation is symmetrical;x is as correlated with y as y is with x. The Pearson product-moment correlation can be understood within a regression context,however.

Answer:

This is a function because each x value has a different y value. If one of x values would of had two different y values then it would of not have been  a function

Step-by-step explanation:

you can rent the boat 55.92 hour if It costs $$3535 per hour to rent a boat at the lake. You also need to pay a $$2525 fee for safety equipment.

What is an example of an equation?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

It costs $$3535 per hour to rent a boat at the lake.

You also need to pay a $$2525 fee for safety equipment.

You have $$200200.

safety fee only once

so 200200-2525 = 197675

if one hour fees is 3535

then 197675/3535

= 55.92

hence he rent boat at the lake 55.92 hour

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The value of the postfix expression 32 * 2 | 53 - 84/ * is 15.

Here's how to solve it:

1. Start from the left and work towards the right.
2. Multiply 32 and 2 to get 64.
3. Use the bitwise OR operator (|) on 64 and 53. This means that the binary digits of each number are compared and if either of them is a 1, the result will have a 1 in that position. In this case, 64 is 1000000 in binary and 53 is 110101 in binary. When we use the bitwise OR operator, we get 1001101, which is 77 in decimal.
4. Subtract 77 from 53 to get -24.
5. Divide 84 by -24 to get -3.5.
6. Finally, multiply -3.5 by 15 (which is the result of the bitwise OR operation from step 3) to get -52.5.

So, the value of the postfix expression is -52.5, which rounds up to -53, or 15 when the absolute value is taken. Therefore, the correct answer is d. 15.

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Answer:

The family's average rate of travel for the day was 59.0 MPH.

Step-by-step explanation:

From 10:15AM to 4:45PM, they travelled a distance of 383.5 miles and a total of 6 hours and 30 minutes.

There are 60 minutes in an hour. 30 minutes translates into 1/2 an hour or .5

So, 6.5 hours and a total distance of 383.5 miles.

Velocity (MPH) = Distance (in miles) / Time (in hours)

MPH means Miles Per Hour

Variables:

Velocity (MPH) = x

Distance (in miles) = 383.5

Time (in hours) = 6.5

Plug in the variables into the formula

x = 383.5 / 6.5

Divide

x = 59.0 MPH

Answer:

59 miles/hr

Step-by-step explanation:

To solve this, lets make the time in 24 hours format:

10:15 am = 10 hours and 15 minutes

4:45 pm = 16 hours and 45 minutes

so time taken = ( 16 hours and 45 minutes ) - ( 10 hours and 15 minutes )

                       = 6 hours 30 minutes

                       = [6 + (30/60)] hours

                       = 6.5 hours taken for the journey to complete

Average rate of travel = Total distance / time taken

                                     = 383.5 / 6.5

                                     = 59 miles/hr

Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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Answer:

Step-by-step explanation:

(a + b)(a - b) = a² - b²

\((7 + 4\sqrt{3}) (7 - 4\sqrt{3}) = 7^{2}-(4\sqrt{3} )^{2}\\\\ = 49 - 4^{2}*(\sqrt{3})^{2}\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1\)

\(\boxed{1}\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((7 + 4 \sqrt{3} ) \: (7 - 4 \sqrt{3} ) \\ \\ = 7 \: (7 - 4 \sqrt{3} ) + 4 \sqrt{3} (7 - 4 \sqrt{3} ) \\ \\ = 49 - 28 \sqrt{3} + 28 \sqrt{3} - 48 \: (since \: \sqrt{3} \times \sqrt{3} = 3)\\ \\ = 49 - 48 \\ \\ = 1\)

You can also use the identity:

( a + b ) ( a - b ) = \( {a}^{2} - {b}^{2}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

The researcher draws a random sample using a Multistage cluster sample

At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.

In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.

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Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2

sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2

Given:  sin Ф = k sin β      -->   (sin Ф)/(sin β) = k

Proof RHS → LHS

\(\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}\)

\(\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}\)

\(\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}\)

 \(\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark\)

The answer to this question is:

Size of a square's side = 11 cm

A Square is a flat geometric shape with four right angles and equal sides. The square's four sides are equal to one another or congruent. The square's opposing sides run parallel to one another. The square's diagonals form a 90° angle with one another. The two diagonals of the square are equivalent to one another. The square is made up of four vertices and four sides.

Area of square = ( Side )²

Given that:

Area of square = ( Side )² = 121 cm²

Dimensions of a square's side = √ Area

so, the length of the square's side = √ 121

                                          = √ 11*11

                                          = √ ( 11 )²  

                                          = 11

Thus, side of the square = 11 cm

Therefore, side length of square = 11cm

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To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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Answer:

no

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

Hawa can walk 1 mile every 16 minutes so 60/16=3.75 :) hope this helped

The -1 part is not inside the natural log.

==============================================

Work Shown:

1 + 2*e^(x+1) = 9

2*e^(x+1) = 9-1

2*e^(x+1) = 8

e^(x+1) = 8/2

e^(x+1) = 4

x+1 = Ln(4)

x = Ln(4) - 1

Answer:

6x + 6    

Step-by-step explanation:  

\((g-f)(x)\) is equal to \(g(x)-f(x)\). So, the question is asking for you to subtract the given functions in that order. We know that \(g(x) = 11x-1\) and \(f(x) = 5x-7\). Thus, take the values of those functions and subtract them:

\(g(x) - f(x)\\= (11x-1)-(5x-7)\\= 11x-1-5x+7\\=6x+6\)

Thus, the answer is 6x + 6.

Answer: 15/7 2 1/7

Step-by-step explanation: First divide 8x-3=x+12 Then add 3 to both sides.

8x=x+15 Subtract x from both sides. 7x=15 Then divide again so 7/7 and 15/7. If you simplify it become 2 1/7

Answer:

x = 15/7

Step-by-step explanation:

Reduce the fraction with 2

8x - 3 = x + 12

Move variable to the left-hand side and change its sign

8x - x - 3 = 12

Move constant to the right-hand side and change its sign

8x - x = 12 + 3

collect like terms

7x = 12 + 3

Add the numbers

7x = 15

Divide both sides of the equation by 7

Solution: x = 15/7

Alternate form

x = 2 1/7, x = 2.142857

The plane EFG  in the rectangular prism is parallel to plane ABC.

In this question, we have been given the rectangular prism ABCDEFGH

We need to find the plane which is parallel to plane ABC.

We can observe that in given rectangular prism,

plane ABH is parallel to the plane CDF

plane BCE is parallel to the plane AGF

plane EFG is parallel to plane ABC.

Therefore, the plane EFG  in the rectangular prism is parallel to plane ABC.

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The equation will be 5r + 1.25b = 20. This represents the beef and radishes to buy.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Radishes costs $5 per pound, and beet cost $1.25 per pound. Sasha has $20 to spend on these items to make a large salad for a potluck dinner.

Let b = number of pounds of beets Sasha buys.

Let r = number of pounds of radishes she buys when she spends all her money on this salad.

The equation will be 5r + 1.25b = 20

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Complete question

Radishes costs $5 per pound, and beet cost $1.25 per pound. Sasha has $20 to spend on these items to make a large salad for a potluck dinner. Let b be the number of pounds of beets Sasha buys and r be the number of pounds of radishes she buys when she spends all her money on this salad. Illustrate the equation

Answer-

Not quite sure what your asking but the if I understood correctly the answer is -122z+56

Answer:

−112z+56

Step-by-step explanation:

−56z+28−56z+28

Combine −56z and −56z to get −112z.

−112z+28+28

Add 28 and 28 to get 56.

−112z+56

Answer:

20a²b-8ab= 4ab(5a -2b)

a) The line is called a level curve because all points on this line have the same function value of ln(3x + y) = 0.

b) Circle is called a level curve because all points on this circle have the same function value of g(x, y).

(a) We are given the function f(x, y) = ln(3x + y).

We need to find the level curve of the function for the given c-value. Here, c = 0.

Now, the level curve of the function for c = 0 can be found by setting f(x, y) = 0.

Therefore,

ln(3x + y) = 0

We know that ln eˣ = x, where e is a constant known as Euler's number.

Therefore, ln(3x + y) = 0 ⇒ e⁰ = 3x + y, which gives 3x + y = 1 as the level curve.

(b) We are given the function g(x, y) = x/x^2 + y^2.

We need to find the level curve of the function for the given c-value. Here, c = − 1/2.

Now, the level curve of the function for c = − 1/2 can be found by setting g(x, y) = − 1/2.

Therefore, x/x² + y² = − 1/2

Multiplying both sides by x² + y², we get

x = − x²/2 − y²/2

Rearranging the terms, we get

x² + 2x/2 + y²/2 = 0

Adding 1/2 on both sides, we get

x² + 2x/2 + y²/2 + 1/2 = 1/2

Simplifying, we get

(x + 1)² + y² = 1

Now, the given equation represents a circle with a center at (-1, 0) and a radius 1. Therefore, the name of the curve is a circle.

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The critical values zα or z/2α are the boundary values for the rejection region(s) in hypothesis testing. The correct answer is D. 0.04, as it is the only value less than 0.05.

These values are determined based on the level of significance (α), which represents the probability of making a Type I error (rejecting a true null hypothesis).
In other words, if the calculated test statistic falls outside of the rejection region(s) defined by the critical values, we reject the null hypothesis at the given level of significance.
Therefore, for the second question, if we reject the null hypothesis at the 0.05 level of significance, we would also reject it for α values less than 0.05.

Thus, the correct answer is D. 0.04, as it is the only value less than 0.05.

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The values of the variable x is 3 and the variable m is not represented in the figure

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

The similar triangles

When two triangles are similar, the corresponding angles are congruent, and the corresponding sides are proportional in length

The corresponding angles of similar triangles are congruent

Using the above as a guide

so, we have the following representation

11x - 2 = 6x + 13

Collect the like terms in the equation

11x - 6x = 2 + 13

Evaluate the like terms

5x = 15

Divide both sides by 5

x = 3

The variable m is not represented in the figure

So, it cannot be solved

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Answer:

x = 5°

Step-by-step explanation:

Linear pair: a pair of adjacent angles formed when two lines intersect. The two angles are always supplementary and so their measures sum to 180°.

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.  The sum of the exterior angles of a polygon is 360°.

Sum of exterior angles:

⇒ 45° + 90° + 25° + 90° + x° + (180° - 140°) + (180° - 115°) = 360°

⇒ 355° + x° = 360°

⇒ x = 5°