6. What are the dimensions of the vertical cross
section shown on this right rectangular prism?

18/35 fraction of students are girls who brought their lunch today.

A fraction is a mathematical concept that denotes a component of a whole or, more generally, any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.

Let's say,

Total number of students over school = x

Number of girls = (6/7)x

Number of girls who brought their lunch = 3/5 of (6/7)x

⇒ 3/5(6/7)x

⇒ (18/35)x

Hence "18/35 fraction of students are girls who brought their lunch today".

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The Laplace transforms of the given time domain functions are:

(a) E(s) = ω/(s + a)² + ω²   

(b) E(s) = s/(s + a)² + ω²   

(c) E(s) = 6/s⁴

The Laplace transform is a mathematical tool used to convert a function from the time domain to the complex frequency domain. The Laplace transform of a function f(t) is denoted by F(s), where s is the complex frequency variable.

(a) For the function e(-at)sin(ωt), we can use the Laplace transform property for the time-shifted sine function:

L{sin(ωt)} = ω/(s² + ω²)

Applying this property and taking into account the exponential decay factor, we get:

L{e(-at)sin(ωt)} = ω/(s + a)² + ω²

(b) For the function e(-at)cos(ωt), we can use a similar approach:

L{cos(ωt)} = s/(s² + ω²)

Applying this property and taking into account the exponential decay factor, we get:

L{e(-at)cos(ωt)} = s/(s + a)² + ω²

(c) For the function t³, we can use the Laplace transform property for the power of t:

L{tⁿ} = n!/(s(n+1))

Applying this property with n = 3, we get:

L{t³} = 6/s⁴

These are the Laplace transforms of the given time domain functions.

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Answer:

-35

Step-by-step explanation:

\(-5 = \frac{1}{7}a\\-35 = a\)

I got this by multiplying the numerator by 7. This allows the denominator to be the same as the numerator, thus equalling 1.

1 * a = a

Answer: a = -35

Step-by-step explanation:

1. -5 = 1/7(a) || GIVEN

2. -5 * (7) = (7) * 1/7(a) || Isolate "a" on one side of the equation by multiplying 7 to the other side.

3. -35 = a

Answer:

Step-by-step explanation:

Verifying pairs:

(1,0)

(5, 28)

(6, 20)

(3, 19)

Answer:

Step-by-step explanation:

Answer:

The new coordinate of B' will be ( -1, 6)

The translated coordinate of the point B' will be (-1,6).

The process of changing the location of the image on the coordinate system will be known as the translation.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the coordinates of point B of the triangle are (1,6). The translated coordinates will be,

B = ( 3, 0 )

Translated 4 units down and 6 units right,

B' = ( 3 - 4 , 0 + 6 )

B' = ( -1, 6 )

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Answer:

\((-\infty ,\infty)\)

\(y\in \mathbb{R}\)

Step-by-step explanation:

\($y=3-\frac{x}{3} $\)

The domain is all Real numbers.

The range is all Real numbers.

Once it is a linear an equation and there's no restriction for x, both domain and range will be all Real numbers.

Answer:

3r^6

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

The distance of Saturn from the sun is 9.5 astronomical units.

Orbital period p of a planet and the planet’s distance from the sun, a in astronomical units are related by:

\(p = a^{3/2}\)

The orbital period is the time a given astronomical object takes to complete one orbit around the sun.

Given that Saturn's orbital period is 29.5 years.

So, \(29.5 = a^{3/2}\)

\(a = 29.5^{2/3}\)

a = 9.5 au

Therefore, the distance of Saturn from the sun is 9.5 astronomical units.

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Answer:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

The probability that the time until the first critical-part failure is 5 years or more is approximately 0.611 or 61.1%.

To find the probability that the time until the first critical-part failure is 5 years or more, we can use the cumulative distribution function (CDF) of the exponential distribution:

P(X ≥ 5) = 1 - P(X < 5)

where X is the time until the first critical-part failure.

The CDF of the exponential distribution with mean μ is given by:

\(F(X) = 1 - e^{-\frac{X}{\mu}}\)

Substituting μ = 3.4 years, we get:

\($P(X < 5) = F(5) = 1 - e^{-5/3.4} \approx 0.389$\)

Therefore,

P(X ≥ 5) = 1 - P(X < 5) ≈ 0.611

So the probability that the time until the first critical-part failure is 5 years or more is approximately 0.611 or 61.1%.

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The correct solution are,

(C) a=1, b=2, c=3.

The code segment does not work in the case where a > b, c > b, but a < c.

In this case, the value of 'low' is set to 'b' instead of 'a', which causes the code segment to print the incorrect value.

The values of a, b, and c that fall into this case are a=1, b=2, and c=3.

Let's trace through the code segment using a=1, b=2, and c=3:

Since a=1 and b=2, the first conditional statement (a > b && b > c) evaluates to false, so we skip the first 'if' block.

Since a=1 and c=3, the second conditional statement (a > b && c > b) evaluates to true, so we set 'low' to 'b'.

However, since we have an 'else' block following the second conditional statement, it will always be executed. So, 'low' is set to 'a' instead.

Finally, the code segment prints the sum of a + b + c - low, which is 1+2+3-1 = 5, which is incorrect.

The correct answer should be 1 + 3 = 4.

Therefore, the answer is (C) a=1, b=2, c=3.

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Answer:

A: -6

Step-by-step explanation:

Flip around the question

what is 12 - 18

If you count the numbers in between 12 and 18

You get 6

So now just make the answer negative

your answer is A.-6, i think its helpful

Answer:

x=19

3x+123= 180

3x =180-123

3x =57

x=57/3

x=19

The base (b) of the exponential decay model for the given scenario is 1/2.The given scenario represents an exponential decay model, not a linear model. Therefore, it does not have a linear equation or slope (m). Instead, we can calculate the base (b) of the exponential function.

In an exponential decay model, the number of owls decreases by half every decade. We start with an initial population of 20,000 owls and halve it every ten years. Mathematically, this can be represented as:

N(t) = N(0) * (1/2)^(t/10)

Where:

N(t) is the number of owls after t years,

N(0) is the initial number of owls (20,000),

t is the time in years.

We are interested in finding the base (b) of the exponential function, which is the value of (1/2) in this case.

The base (b) of the exponential decay model for the given scenario is 1/2. This means that the population of owls is halved every decade. By plugging in different values of t into the equation N(t) = 20,000 * (1/2)^(t/10), we can calculate the population of owls at different points in time.

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The same well-liked crackers are discounted at Value Grocery Mart and Market City are 5.25, 10.5,  15.75, and 21.

As the cost per pack is C=1.75b. C is the Cost in dollars.

3×1.75=5.25

6×1.75=10.5

9×1.75=15.75

12×1.75=21

An example of a chart is one that uses symbols to depict the data, such as bars in a bar chart, columns in a line chart, or slices in a pie chart.  A chart can convey various information by representing tabular numerical data, functions, or certain types of quality structures.

Users can change numerous rows and columns in a table at once using a tabular form and a single page.

A chart displays data that can be shown as a table, graph, or diagram. There are different ways to convey vast amounts of information in it.

Here, the table is.

Number of Boxes of Crackers ║   Grocery Mart  ║    Market City:

  3                                              ║       5                  ║  5.25

 6                                                ║     10                   ║ 10.5

 9                                                ║      15                   ║ 15.75

 12                                              ║      20                    ║ 21

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Answer:

x = 40 m∠Q = 105° m∠R = 40° m∠P = 35°

Step-by-step explanation:

sum of angles in a triangle equal 180°

m∠Q + m∠R + m∠P = 180°

2x + 25 + x + x - 5 = 180°

Solve for X

4x + 20 = 180

4x = 160

x = 40

Solve for each angle measure

m∠Q = 2x + 25

m∠Q = 2(40) + 25 = 80 + 25 = 105°

m∠R = x

m∠R = 40°

m∠P = x - 5

m∠P = 40 - 5 = 35°

Answer: $115,000

Step-by-step explanation:

The common stock is 9000 times 5 = $45000

To Paid-in Capital in Excess of Par = 160,000 - 45,000 = $115,000

9514 1404 393

Answer:

  y = 3x + 2

Step-by-step explanation:

Assuming your table values are (x, y) = (4, 14), (6, 20), (7, 23), the slope and intercept formulas can be used.

  m = (y2 -y1)/(x2 -x1)

  m = (20 -14)/(6 -4) = 6/2 = 3

  b = y -mx

  b = 14 -3(4) = 2 . . . . for (x, y) = (4, 14)

Then the equation of the line is ...

  y = mx + b

  y = 3x + 2

Given that an insurance policy pays 100 per day for up to three days of hospitalization. And the number of days of hospitalization, N, is a discrete random variable that satisfies the following:

Pr(N=k)=\frac{\binom{3}{k} \cdot (0.1)^k \cdot (0.9)^{3-k}}{\binom{3}{k-1} \cdot (0.1)^{k-1} \cdot (0.9)^{4-k}} for k starting at 1.

Now, we need to calculate the expected payment under this policy. Formula used: Expectation of the discrete random variable is given by, \sum_{k=1}^{\infty} x_k P(X=x_k).

Here, the amount of expected payment is $100$ and the probability of each event is given by,

P(N=k)=\frac{\binom{3}{k} \cdot (0.1)^k \cdot (0.9)^{3-k}}{\binom{3}{k-1} \cdot (0.1)^{k-1} \cdot (0.9)^{4-k}} For k starting at 1.

Therefore, we have, \begin{align*}E(X)&=100 \cdot E(N) \\ &

=100 \sum_{k=1}^{3} k \cdot P(N=k) \\ &

=100 [1(0.729)+2(0.243)+3(0.027)] \\ &=100(0.999) \\ &

=99.9 \end{align*}

Hence, the expected payment under this policy is $99.9. Therefore, the answer to the given problem is a long answer.

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It would take them a total of 882 seconds to straighten their ties 42 times.

To find the total time it takes for both Perfectionist Anchorman #1 and Perfectionist Anchorman #2 to straighten their ties 42 times, we need to calculate the time taken individually by each anchor and then add them together.

Perfectionist Anchorman #1 straightens his tie once every 5 seconds. To straighten his tie 42 times, he would take:

Time taken by Anchorman #1 = 42 times * 5 seconds per tie straightening

= 210 seconds

Perfectionist Anchorman #2 straightens his tie once every 16 seconds. To straighten his tie 42 times, he would take:

Time taken by Anchorman #2 = 42 times * 16 seconds per tie straightening

= 672 seconds

Now, to find the total time taken by both anchors, we add the individual times:

Total time taken = Time taken by Anchorman #1 + Time taken by Anchorman #2

= 210 seconds + 672 seconds

= 882 seconds

Therefore, it would take them a total of 882 seconds to straighten their ties 42 times.

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The inequality that could be used to determine the range of body temperature is; |t − 100| ≤ 1.2

An absolute value inequality is defined as an expression with absolute functions including inequality signs. For example, the expression |x + 2| ≥ 1 is an absolute value inequality containing a greater than or equal to symbol.

Now, we are told that The normal body temperature for an adult horse is 100° F, but it can vary by as much as 1.2°.

Now, since it varies by as much as 1.2 degrees, it means the maximum varied temperature is  1.2°. Thus, we can say that the absolute value inequality is; |t − 100| ≤ 1.2

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9514 1404 393

Answer:

Step-by-step explanation:

3(4) could be 3 added 4 times:

  3 + 3 + 3 + 3 = 12

or it could be 4 added 3 times:

  4 + 4 + 4 = 12

The sum is 12.

Answer:

Step-by-step explanation:

\(Sin \ 30 = \frac{opposite \ side}{hypotenuse}\\\\\frac{1}{2}=\frac{h}{6}\\\\\frac{1}{2}*6=h\\\\3 = h\)

h = 3 cm

Area of parallelogram = b * h

                                    = 6 * 3

                                     = 18 sq.cm

Answer:

estoybuscdo ad isciloa

:

Answer:

are you sure its a polynomial

Step-by-step explanation:

A polynomial is a combination of terms separated by

+

or

−

signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.

Polynomial

If p and q vary inversely and p = 14 when a = 4, then the work is  q = 8, p = 7.

What is inverse proportionality?

Inverse proportionality occurs when x increases and y decreases, and when x decreases and y increases.

If p and q vary inversely, this means that their product is constant:

p * q = k

where k is a constant. We can use this relationship to solve the problem.

We are given that when a = 4, p = 14. This means that:

p * a = k

14 * 4 = k

56 = k

So we know that the product of p and a is 56.

To find p when q = 8, we can use the fact that p and q vary inversely. This means that:

p * q = k

We know that k = 56, so we can substitute:

p * q = 56

We are given that q = 8, so we can substitute this as well:

p * 8 = 56

Solving for p, we get:

p = 56 / 8 = 7

Therefore, when q = 8, p = 7.

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Answer:

width=4.75cm

length=12.25cm

Step-by-step explanation:

let the width of the rectangle=x

the length=3x-2

Given that perimeter=34cm,

2(x)+2(3x-2)=34

2x+6x-4=34

8x-4=34

8x=38

x=38/8=4.75cm

Therefore,

width=4.75cm

length=12.25cm

Answer:

Perimeter= 12y units

3y(4) = 12y

Step-by-step explanation:

3y + 3y + 3y + 3y= 12y

Answer:

Step-by-step explanation:

To find the amount of sales in the clothing department, we need to calculate 28% of the total sales.

Total sales: 20,000,000.00 Pesos

Amount of sales in the clothing department:

Sales = 28% of total sales

Sales = 28/100 * 20,000,000.00

Sales = 0.28 * 20,000,000.00

Sales = 5,600,000.00 Pesos

Therefore, the amount of sales in the clothing department is 5,600,000.00 Pesos.