A person standing on a moving walkway travels 90 feet in 30 seconds. What equation represents this relationship? How many feet will the person travel in 10 seconds?

A. y = 3x; 30 feet

B. y = 9x; 90 feet

C. y = 1/3x; 3 feet

D. y = 3x; 3 feet

a) Using the standard divisors according to Jefferson's apportionment method, the number of salespeople assigned to work each shift is as follows:

Shift                              Morning     Midday     Afternoon     Evening   Total

Number of

salespeople assigned  1               3                  5                 7                16

b) The modified or adjusted divisor used represents the average number of customers for each shift divided by the standard divisor.

The standard divisor shows the ratio of the total population to the number of seats.

The standard divisor gives an insight about the number of people each seat represents.

Standard divisor = Total number of customers / Total number of salespeople

The total number of customers = 1,425

The number of salespeople = 16

a) Standard divisor = 1,425 ÷ 16

= 89.0625

Shift                              Morning     Midday     Afternoon     Evening   Total

Average number of

customers                     125            280             460             560       1,425

Standard divisor      89.0625     89.0625      89.0625      89.0625

b) Modified divisor     1.4035        3.1438          5.165           6.288

Number of

salespeople assigned  1               3                  5                 7                16

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If the graph of \(f(x) = 4e^{0.1x}\) is blue, then the graph of \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is: C. red.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

For the rate of change of the blue exponential function \(f(x) = 4e^{0.1x}\), we have the following:

b = \(e^{0.1}\)

b = 1.11

For the rate of change of this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\), we have the following:

b = 1 + 0.1/0.5

b = 1.2

Therefore, this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is represented by the red line on the graph.

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The correct answer is Option D i.e;  It would depreciate to E2

Given that,

Please see Figure 13-2.  The economy was originally in equilibrium at r0 and E0

To find : What would happen to the exchange rate if import quotas were eliminated by the government ?

Economic forces must be in balance for there to be economic equilibrium. Economic variables essentially hold true to their equilibrium values in the absence of outside influences. Market equilibrium is another name for economic equilibrium.

Therefore, the correct answer is Option D i.e;  It would depreciate to E2

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Answer:

Hope this helps....

Step-by-step explanation:

A closed circle indicates "greater than or equal to" or "less than or equal to," while and open circle indicates "greater than" or "less than".

The equations that could be used to solve for the number of male runners (m) in the race are (m+75)/m = 3 / 2 and 150 + 2m = 3m. The correct options are A and B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that at a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.

The ratio is written as,

f/ m = 3 / 2

There are 75 more female runners than male runners.

f = m + 75

The equation can be written as,

f / m = 3 / 2

( m + 75 ) / m = 3 / 2

Or

150 + 2m = 3m

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Answer:

8...its 8 from the origin.

Step-by-step explanation:

Recall the following:

• If the discriminant equals zero, the function has one real zero.

• If the discriminant is positive, the function has two real zeros.

• If the discriminant is negative, the function has two imaginary zeros.

Note that since the graph of the function intersects the x-axis at two points, the function has two real zeros.

Since there are two zeros, it follows that the discriminant must be positive.

The correct option is C.

Answer:

84 sq meters

Step-by-step explanation:

First, divide the shape in 2 or more parts so that you can find it step by step

Divide this shape in three parts:

One part (blue): 2 m and 3 m rectangle

Second part (orange): 5 m and 12 m rectangle

Third part (red): 6 m and 3 m rectangle

(you can also see this below: in the pic there are three parts so you figure out that which is the correct value for the sides)

Now, find area of each shape by multiplying its values:

1st shape: 3 x 2 = 6

2nd shape: 5 x 12 = 60

3rd shape: 6 x 3 = 18

As you have the area of all the different shapes,

add all of them:

6 + 60 + 18 = 84 sq meters

I hope this helps :)

For the time period of  the projectile at least 192 feet above the ground is between 2 second and 6 second

Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:

16t2-128t+192=0 or, simplified, 8t2-64t+96=0

or t2-8t+12=0

since it is now in quadratic form, we can solve using the quadratic formula:

t = 2 and 6

So the time period from approximately 2 second and 6 second has the projectile above 192 feet.

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The perimeter of the composite figure that is given above would be = 96.6m.

To calculate the perimeter of the given shape, it has to be divided into two.

First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)

Where ;

length = 16m

width = 11m

perimeter = 2(16+11)

= 2×27

= 54m

The second shape:

Perimeter of triangle = l+w+h

where;

length = 18-11 = 7m

width = 16m

height = 19.5m

perimeter = 7+16+19.5 = 42.5m

Therefore, the perimeter of the shape = 54+42.5 = 96.6m

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Let’s say the first class is X.

Avg(X)= x/20=15

X=300

Let’s say the second class is Y.

Avg(Y)= Y/30=20

Y=600

X+Y=900

AVG(X+Y)=900/(20+30)=900/50=18

The average of both classes is 18.

Answer:

The answer is C

Step-by-step explanation:

c.  8√(2^4 )

given 2^(4/8)  can be written as 2^(4×1/8)  

eg: 2^(1/2) is √2 hence same rule we can apply here and since 2^(1/8) we can write as 8√2 and given 2^4

further knowledge: so if asked to expand more we can write it as 8√16 simplifying this further we get 2^(1/2) which is actually √2

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Answer:

SOLUTION SET={x/x>-1} and SOLUTION SET={x/x<-1}

Step-by-step explanation:

1)4x-39>-43

evaluating the inequality

adding 39 on both sides

4x-39+39>-43+39

4x>-4

dividing 4 on both sides

4x/4>-4/4

x>-1

SOLUTION SET={x/x>-1}

2)8x+31<23

evaluating the inequality

subtracting 31 on both sides

8x+31-31<23-31

8x<-8

dividing 8 on both sides

8x/8<-8/8

x<-1

SOLUTION SET={x/x<-1}

i hope this will help you :)

Answer: There are no solutions

Step-by-step explanation:Khan Academy

The period of the function f(t) = 2.3cos(0.25t) is 8π. Hence, the correct answer is d) period 8π.

To determine the period of the function f(t) = 2.3cos(0.25t), we need to consider the coefficient of t inside the cosine function.

In this case, the coefficient is 0.25, which represents the frequency of the cosine function. The period of a cosine function is given by the formula T = 2π/frequency.

Using this formula, we can calculate the period of the function f(t) as follows

T = 2π / 0.25

T = 8π

Therefore, the period of the function f(t) = 2.3cos(0.25t) is 8π.

Hence, the correct answer is d) period 8π.

The period of a function represents the length of one complete cycle or the distance between two consecutive identical points on the graph of the function. In this case, the function is a cosine function, and the period determines how long it takes for the function to repeat its values

The coefficient 0.25 in the function f(t) = 2.3cos(0.25t) affects the frequency of the cosine function. A smaller coefficient results in a slower oscillation, while a larger coefficient leads to a faster oscillation. In this case, since the coefficient is 0.25, it means that the function completes one full cycle within 8π units of time.

Understanding the period of a function is crucial for analyzing its behavior, identifying the frequency of oscillation, and studying its repetitive patterns.

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Answer:

26.0 years

Step-by-step explanation:

It will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.

To determine how long it will take for the 20 grams of the element to decay to four grams, we need to calculate the time using the given decay rate.

Given:

Initial mass (M₀) = 20 grams

Decay rate: 6% per year

Let's set up an equation to represent the decay of the element:

M(t) = M₀ * (1 - r)^t

Here, M(t) represents the mass at time t in years, M₀ is the initial mass, r is the decay rate (expressed as a decimal), and t is the time in years.

We want to find the value of t when M(t) = 4 grams:

\(4 = 20 * (1 - 0.06)^t\)

Dividing both sides by 20:

\(0.2 = (1 - 0.06)^t\)

Taking the natural logarithm of both sides:

\(ln(0.2) = ln[(1 - 0.06)^t]\)

Using logarithmic properties, we can simplify further:

\(ln(0.2) = t * ln(1 - 0.06)\)

Now, we can solve for t by dividing both sides of the equation by ln(1 - 0.06):

t =\(ln(0.2) / ln(1 - 0.06)\)

Using a calculator, we find:

t ≈ 16.79 years

Therefore, it will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.

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We should be cautious about making predictions that are far outside the range of the data used to create the line of best fit.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Based on the line of best fit shown in the scatterplot, we can see that there is a positive linear relationship between the high temperature and the number of hot cocoas sold.

The equation of the line of best fit appears to be y = 23.25x - 705.5, where y represents the number of hot cocoas sold and x represents the high temperature.

To make a prediction for a high temperature of 54, we substitute x = 54 into the equation and solve for y:

y = 23.25x - 705.5

y = 23.25(54) - 705.5

y = 694.5 - 705.5

y = -11

According to this prediction, if the high temperature is 54, Josue would sell approximately -11 hot cocoas. However, this result doesn't make sense, as we can't sell a negative number of hot cocoas.

It's possible that the line of best fit is not an accurate model for the data at very high or very low temperatures, or that there are other factors besides temperature that affect hot cocoa sales.

Therefore, we should be cautious about making predictions that are far outside the range of the data used to create the line of best fit.

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Answer:

I think you meant cm, not em. So the answer is 6 cm.

Step-by-step explanation:

18cm x 6cm = 108 cm

answer:

4d + 2w and 1/2(8d + 4w)

- read each line correctly and try to make something out of it, if that makes sense

Answer:

1008

Step-by-step explanation:

10!•4!

---------

6!•5!

Rewriting as

10 * 9*8*7*6!  * 4!

---------

6!•5*4!

Canceling like terms

10 * 9*8*7

---------

5

1008

Answer:

1,008

Step-by-step explanation:

The answer is not 4/3 or 2/3. So, it has to be 1,008.

The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The ship turned approximately 71.1° north of west when it changed direction.

The Law of Cosines, also known as the Cosine Formula or the Cosine Rule, is a mathematical theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's start by drawing a diagram of the situation:

   A

   *         x

   |       /

   |    /

94 | /     119

   / θ

  *----------B

         173

We want to find the angle θ, which represents the direction the ship turned. To do this, we need to find the length of side BC first. We can use the Law of Cosines for that:

BC² = AB² + AC² - 2 * AB * AC * cos(θ)

We know that AB is 94 miles and AC is 119 miles. We also know that BC is 173 miles. Plugging these values into the equation, we get:

173² = 94² + 119² - 2 * 94 * 119 * cos(θ)

29929 = 8836 + 14161 - 22446 * cos(θ)

Simplifying:

69932 = 22446 * cos(θ)

cos(θ) = 69932 / 22446

cos(θ) ≈ 0.3116

Now we can solve for θ:

θ = acos(0.3116)

θ ≈ 71.1°

Therefore, the ship turned approximately 71.1° north of west when it changed direction.

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The ship turned approximately 71.1° north of west when it changed direction.

What is law of cosines?

The Law of Cosines, also known as the Cosine Formula or the Cosine Rule, is a mathematical theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.

We want to find the angle θ, which represents the direction the ship turned. To do this, we need to find the length of side BC first. We can use the Law of Cosines for that:

BC² = AB² + AC² - 2 * AB * AC * cos(θ)

We know that AB is 94 miles and AC is 119 miles. We also know that BC is 173 miles. Plugging these values into the equation, we get:

173² = 94² + 119² - 2 * 94 * 119 * cos(θ)

29929 = 8836 + 14161 - 22446 * cos(θ)

Simplifying:

69932 = 22446 * cos(θ)

cos(θ) = 69932 / 22446

cos(θ) ≈ 0.3116

Now we can solve for θ:

θ = acos(0.3116)

θ ≈ 71.1°

Therefore, the ship turned approximately 71.1° north of west when it changed direction.

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Answer:

0.4 pi

Step-by-step explanation:

find the circumference by doing 2 pi r

then you multiply that by a slice of the circle which is 72 degrees divided by 360.

Answer:

B.) P(A/B) = P(A)

Step-by-step explanation:

If two events, A and B are independent:

We have that:

\(P(A \cap B) = P(A)P(B)\)

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

Since they are independent:

\(P(A \cap B) = P(A)P(B)\)

Then

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)\)

So

\(P(B|A) = P(B)\), or either:

\(P(A|B) = P(A)\), and thus, the correct answer is given by option B.

First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6. Then the value you get is 531,441.

At the point when the important parts and fundamental cycles of a mathematical technique are given qualities, the articulation's outcome is the consequence of the calculation it portrays.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

⇒ 9⁶

First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6.

The value of the exponent numerical expression 9⁶ will be 531,441.

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The correct question is given below.

What is the correct sequence of steps for calculating 9⁶ on a scientific calculator?

Answer:

3sqrt2

Step-by-step explanation:

b jhf vj fjvfd vmnd fmv ndkfv mndfvdf nkvvdf lkv nf khlfd hjvdf

Answer:

y = 1/405 x² + 25

101 feet

Step-by-step explanation:

The vertex of the parabola is (0, 25).

The equation of the parabola is:

y − 25 = a (x − 0)²

y = ax² + 25

Two points on the parabola are (-225, 150) and (225, 150).

Plugging in one of those points:

150 = a (225)² + 25

125 = 50625 a

a = 1/405

The equation is therefore:

y = 1/405 x² + 25

50 feet from a tower is 175 feet from the center.

y = 1/405 (175)² + 25

y ≈ 101

Answer:

1) \(y=\frac{1}{4}x-4\)

2) \(y=-4x+17\)

Step-by-step explanation:

We know that Line A is represented by the equation \(y=\frac{1}{4}x+5\).

Notice that the slope of Line A is 1/4.

Part 1) Parallel and Passes Through (8, -2).

Since the new line is parallel, this means that we will have the same slope.

We also know that it passes through (8, -2). So, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

So, let’s substitute 1/4 for m and (8, -2) for (x₁, y₁), respectively. This yields:

\(y-(-2)=\frac{1}{4}(x-(8))\)

Simplify and distribute the right:

\(y+2=\frac{1}{4}x-2\)

Subtract 2 from both sides. Therefore, our equation in slope-intercept form is:

\(y=\frac{1}{4}x-4\)

Part 2) Perpendicular and Passes Through (4, 1).

Since the new line is perpendicular, the slope will be the negative reciprocal of the old slope.

To find the negative reciprocal, we flip the number and then multiply it by a negative.

Our old slope is 1/4. Flipping this yields 4/1 or 4. Multiplying by a negative gives us -4.

Therefore, the slope of our new line is -4.

And we also know that it passes through (4, 1).

Again, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

This time, substitute -4 for m and (4, 1) for (x₁, y₁). This yields:

\(y-(1)=-4(x-(4))\)

Simplify and distribute:

\(y-1=-4x+16\)

Add 1 to both sides. Therefore, our equation is:

\(y=-4x+17\)

And we are done!

Texas' location and climate led to the development of the aviation industry.

What is the significance of Texas in the development of the aviation industry?

The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.

Reason what led to the development of the aviation industry :

Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.

Therefore, option (d) is correct.

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Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5