A train moving 50 miles per hour meets and passes a train moving 50 miles per hour in the opposite direction. A passenger in the first train sees the second train pass in 5 seconds. How long is the second train?

The trigonometric expression 1/sin(2x) - cos(2x)/sin(2x) = tanx

A trigonometric expression is an equation that contains trigonometric ratios.

Given the expression 1/sin(2x) - cos(2x)/sin(2x), we need to find the expression that is equivalent to it.

So, we proceed as follows.

1/sin(2x) - cos(2x)/sin(2x) = [1 - cos(2x)]/sin(2x),

Using the trigonometric identity cos2x = cos²x - sin²x and sin2x = 2sinxcosx, we have that

[1 - cos(2x)]/sin(2x) = [1 - (cos²x - sin²x)]/2sinxcosx

=  [1 - cos²x + sin²x)]/2sinxcosx

Now, 1 - cos²x = sin²x.

So, substituting this into the equation, we have that

[1 - cos²x + sin²x)]/2sinxcosx = [sin²x + sin²x)]/2sinxcosx

=  [sin²x + sin²x)]/2sinxcosx

=  2sin²x/2sinxcosx

=  sinx/cosx

= tanx

So, 1/sin(2x) - cos(2x)/sin(2x),= tanx

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Answer:

Step-by-step explanation:

Select the smaller fraction. 1/10 or 1/2

1/10 = 1 : 10 = 0.1

1/2 = 1 : 2 = 0.5

so your answer is 1/10

Answer:

m/2 -6= m/4+2 can be solved as follows:

Multiply both sides of the equation by the least common multiple of the denominators, which is 4:

4(m/2 - 6) = 4(m/4 + 2)

2m - 24 = m + 8

Subtract m from both sides:

m - 24 = 8

Add 24 to both sides:

m = 32

Therefore, the value of m is C) 32.

k/12 = 25/100 can be solved as follows:

Multiply both sides of the equation by 12:

k = 12 * (25/100)

k = 3

Therefore, the value of k is A) 3.

9/5 = 3x/100 can be solved as follows:

Multiply both sides of the equation by 100:

100 * (9/5) = 3x

Simplify:

180/5 = 3x

36 = 3x

Divide both sides by 3:

x = 12

Therefore, the value of x is not one of the options provided.

Step-by-step explanation:

Answer:

[tex] \sf \longrightarrow \: \frac{m}{2} - 6 = \frac{m}{4} + 2 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{m - 12}{2} = \frac{m + 8}{4}\\ [/tex]

[tex] \sf \longrightarrow \: 4(m - 12) =2(m + 8)\\ [/tex]

[tex] \sf \longrightarrow \: 4m \: - 48 =2m + 16\\ [/tex]

[tex] \sf \longrightarrow \: 4m \: - 2m = 16 + 48\\ [/tex]

[tex] \sf \longrightarrow \:2m = 64\\ [/tex]

[tex] \sf \longrightarrow \:m = \frac{64}{2} \: \\ [/tex]

[tex] \sf \longrightarrow \:m = 32 \: \\ [/tex]

[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: C) \: \: \: 32 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

[tex] \sf \leadsto \: \frac{k}{12} = \frac{25}{100} \\ [/tex]

[tex] \sf \leadsto \: 100(k)= 12(25) \\ [/tex]

[tex] \sf \leadsto \: 100 \times k= 12 \times 25 \\ [/tex]

[tex] \sf \leadsto \: 100 k= 300 \\ [/tex]

[tex] \sf \leadsto \: k= \frac{300}{100} \\ [/tex]

[tex] \sf \leadsto \: k= 3 \\ [/tex]

[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: a) \: \: \: 3 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

[tex] \sf \longrightarrow \: \frac{9}{5} = \frac{3x}{100} \\ [/tex]

[tex] \sf \longrightarrow \: 100(9)= 5(3x) \\ [/tex]

[tex] \sf \longrightarrow \: 100 \times 9= 5 \times 3x \\ [/tex]

[tex] \sf \longrightarrow \: 900= 15x \\ [/tex]

[tex] \sf \longrightarrow \: x= \frac{900}{15} \\ [/tex]

[tex] \sf \longrightarrow \: k= 60 \\ [/tex]

[tex]\qquad{\underline{\overline {\boxed{ \sf{ \: \: a) \: \: \: 60 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

Answer:

The given pattern does not form an arithmetic sequence as there is no common difference between each term. An arithmetic sequence is a sequence in which there is a fixed difference between each consecutive term. For example, 1, 3, 5, 7 is an arithmetic sequence with a common difference of 2 (adding 2 to each term gives the next term). However, the given pattern of 1/2, 1, 2/3, 2 does not follow this pattern as the difference between each term varies. Therefore, this pattern does not fit the definition of an arithmetic sequence.

Step-by-step explanation:

The answers are 1) 360,000, 2) 217,060, 3) 37,140 and 4) 180,080.

1) To calculate the amount of premium paid by the employee and the employer =

Consider employee medical insurance payable, and employee life insurance payable.

The journal entries for accrual payroll, including employee deductions, consider sales salaries expense office salaries expense, social sec taxes payable Medicare tax payable, employee income taxes, life insurance payable, union dues, salaries payable.

2) Journal entry for cash payment of net payroll for month of July consider salaries payable and cash.

3) Calculate the unemployment tax amount, consider state unemployment taxes and federal unemployment taxes,

Journey Entries for accrued employer payroll taxes,

Payroll taxes expenses, social taxes, Medicare taxes, state unemployment taxes, federal unemployment taxes, employee medical and life insurance.

4) Journal entries for cash payment of all libraries, consider, social medical taxes, employee fed, medical, life and state income taxes payable.  

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s√3 is the distance from point A to point B. Therefore, the correct option is option D among all the given options.

While distance and displacement appear to have the same meaning, they actually have very different definitions and meanings. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "the amount of ground the object has travelled over during its motion."

Distance² = s² + s² + s²

Distance² = 3 s²

Distance = s√3

Therefore, the correct option is option D among all the given options.

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The ordered pair that is a solution to the equation 3y = -2x - 4 is given as follows:

(1, -2).

The equation for this problem is defined as follows:

3y = -2x - 4

To verify whether an ordered pair is a solution to the equation, it must make the equation true.

When x = 1 and y = -2, we have that:

Hence the ordered pair (1,-2) is a solution to the equation for this problem.

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Answer:

Step-by-step explanation:

Because we're told the amount doubles on each successive day, we know we're dealing with an exponential function.

The general form for an exponential function is

[tex]f(x)=ab^x[/tex], where a is the initial value, b is the base, and x is the exponent.

We know that Julia saved $0.01 on the first day so our a value is 0.01.

Because the amount doubles each time, our base is 2.

Furthermore, since we're want to find when Julia's savings exceed $1.00, we can turn the general exponential formula into an inequality where the formula is greater than 1 and solve for x (time in days):

[tex]1.00 < 0.01(2)^x\\100 < 2^x\\log(100) < log(2)^x\\log(100) < x*log(2)\\log(100)/log(2) < x\\6.64 < x\\7 < x[/tex]

We had to round the 6 to the nearest whole number (7) to get the answer.

We can check our work by plugging in both 6.64 for x and 7 for x to see how at 7 days, Julia's savings exceed 1.00

Plugging in 6.64 for x:

[tex]f(6.64)=0.01(2)^6^.^6^4\\f(6.64)=0.01*99.7\\f(6.64)=0.997\\f(6.64)=1.00[/tex]

Using 6.64 for x makes Julia's savings equal 1, but they don't exceed 1

Plugging in 7 for x:

[tex]f(7)=0.01(2)^7\\f(7)=0.01*128\\f(7)=1.28[/tex]

We can see here that the measure of variability using the range will be: 1.

A statistical metric known as a measure of variability tells us how widely spaced or dispersed a group of data points are. Measures of variability are used to quantify how significantly different a dataset's individual data points are from one another.

The measure of variability using range will:

Mean (Peak season) - Mean (Off Peak Season) = 6 - 5 = 1.

We see here that the mean of the peak season population is increased compared to that of the off-peak season. The mean of the off-peak season is seen to be lower.

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The length of the straw is 4.26 inches.

We have,

On the bottom face,

Applying the Pythagorean theorem,

x² = 1² + 3²

x² = 1 + 9

x² = 10

Now,

Applying the Pythagorean theorem with the diagonal side.

d² = x² + 3²

d² = 10 + 9

d² = 19

d = √19

d = 4.36 in

Thus,

The length of the straw is 4.26 inches.

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Answer:

The equation that describes a vertical translation of the square root parent function is A. y = x − 4−−√ + k where k is the vertical shift.

The square root parent function is f(x) = √x. To perform a vertical translation of this function, we add or subtract a constant value to the function. In this case, the function y = x − 4−−√ represents a vertical translation of the square root parent function by 4 units downwards.

Option B, y = x−−√−6 represents a vertical translation of the square root parent function by 6 units downwards. Option C, y = x−−√, represents the square root parent function without any vertical shift. Option D, y = −x−−√, represents a reflection of the square root parent function about the y-axis.

Answer:

4(x-1)=2(6-2x)

4x-4=12-4x

4x+4xd=12+4

8x=16

x=2

Answer:

x=2

Step-by-step explanation:

Step 1: Distribute

To solve this problem, the first step is distributing the four and the 2.

[tex]4(x-1)=2(6-2x)\\\\4x-4=12-4x[/tex]

So this is our simplified problem.

Step 2: Solve for x

Step 2a: Add 4x to both sides:

(This is because we do not have two variables in the equation, making it easier to solve.

[tex]4x+4x-4=12-4x+4x\\\\8x-4=12+0\\\\8x-4=12[/tex]
Step 2b: Add 4 to both sides:

(We do this to leave the variable on one side and the constant on the other. )

[tex]8x-4+4=12+4\\\\8x+0=16\\\\8x=16[/tex]

Step 2c: Divide both sides by 8:

(The reason why we do this is to isolate the variable without any coefficient in front.)

[tex]\frac{8x}{8} =\frac{16}{8} \\\\x=2[/tex]

Two ten thousandths are 0.0002.

The number 2 will be in ten thousand place

TENS   ONES    .       TENTHS       HUNDREDTHS        THOUSANDTHS    

                          .               0                       0                                 0              

TEN THOUSANDTHS

            2

Answer: x = -5

Step-by-step explanation:

Answer:

x=-5

7 - 4 * (-5)

Negative times a negative equals a positive

-4*-5=20

7+20=27

Answer:

Dividing both sides by 4, we get:

4m/4 = 28/4

Simplifying, we get:

m = 7

Therefore, the answer is D. 7.

The amount she invested at each rate of interest for the simple interest are $39,100 and $78,200.

Given that,

Jolene invests her savings in two bank accounts.

Rate of interest for one account = 6% per year

Rate of interest for the other account = 10% per year

Let x be the principal amount invested in the account yielding 10% interest.

Interest amount = 0.1x

Principal amount in the account of 6% interest = 2x

Interest amount = 0.06 × 2x = 0.12x

Annual interest = $8602

0.1x + 0.12x = 8602

0.22x = 8602

x = $39,100

Amount invested for 10% interest account = $39,100

Amount invested for 6% interest account = 2 × $39,100 = $78,200

Hence the amount invested are $39,100 and $78,200.

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The expected values are 60 blues, 30 reds and 30 greens

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

6 blue cubes, 3 red cubes, and 3 green cubes

This means that we have the following proportions

Blue = 6/(6 + 3 + 3) = 1/2

Red = 3/(6 + 3 + 3) = 1/4

Green = 3/(6 + 3 + 3) = 1/4

If you draw a cube and replace it in the bag 120 times, we have

Blue = 1/2 * 120 = 60

Red = 1/4 * 120 = 30

Green = 1/4 * 120 = 30

Hence, the expected values are 60 blues, 30 reds and 30 greens

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Answer:

p

Step-by-step explanation:

ok so first u take away the underlined letter and give and carry sorry the first one

The given equation in exponential form will be [tex]20 = x^e[/tex]

Given is an equation, x = ㏑ 20,

So, we know that,

㏑(x) = [tex]log_e(x)[/tex]

And,

logₐ (x) = b

x = bᵃ

Therefore,

x = ㏑ 20

will be converted into,

[tex]20 = x^e[/tex]

Hence, the given equation in exponential form will be [tex]20 = x^e[/tex]

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Answer:

Suppose X ~ N(12,2) represents a normal distribution with mean 12 and standard deviation 2. According to the empirical rule, about 68% of the x values lie within one standard deviation of the mean .

We can calculate the endpoints of the interval that represents one standard deviation from the mean as follows:

Lower endpoint: 12 - 2 = 10

Upper endpoint: 12 + 2 = 14

Therefore, about 68% of the x values lie between 10 and 14 1.

Step-by-step explanation:

A statement which is correct include the following: A. Roses cost $2.75 more than daisies.

In order to write a system of linear equations to describe this situation, we would assign variables to the cost of roses and cost of daisies, and then translate the word problem into a linear equation as follows:

Based on the information provided about the flowers purchased by Marla and Kelly. we have the following system of linear equations;

7x + 10y = 40.5

3x + 15y = 30.75

By solving the system of linear equations simultaneously, we have:

x = 4 and y = 1.25

Difference = 4 - 1.25

Difference = $2.75

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The acceleration of the collar at point A is 5 ft/s^2.

A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:

N - 5 = 0

where N is the normal force. Solving for N, we get:

N = 5 lb

B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:

x = L - y = 3 - 0 = 3 ft

where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:

F = kx = 10 lb/ft × 3 ft = 30 lb

The weight of the collar is:

W = mg = 5 lb

where g is the acceleration due to gravity. The net force on the collar is therefore:

Fnet = F - W = 30 - 5 = 25 lb

Using Newton's second law, we can write:

Fnet = ma

where a is the acceleration of the collar. Solving for a, we get:

a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2

Therefore, the acceleration of the collar at point A is 5 ft/s^2.

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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The polynomial equation of the smallest degree is f(u) = (u + 2)³(u - 1)²(u - 3)

Given that we have the graph of a polynomial

The degree of the graph is the number of times the graph intersect and/or crosses the x-axis

In this case, we have the following points at which the graph intersect and/or crosses the x-axis

When the multiplicities are added, we have

Degree = 3 + 1 + 2

Degree = 6

So, the degree is 6

In (a), we have

This means that

The zero at u = 1 has a multiplicity of 1

The equation is represented as

f(u) = (u - zero)^multiplicity

So, we have

f(u) = (u + 2)³(u - 1)²(u - 3)

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