HELP been stuck for 1 hour please​

the inverse Laplace transform of 2s / (s^2 - 1) is 2cosh(t).

We want to find the inverse Laplace transform of:

2s / (s^2 - 1)

Using partial fraction decomposition, we can write:

2s / (s^2 - 1) = A/(s - 1) + B/(s + 1)

Multiplying both sides by the denominator, we get:

2s = A(s + 1) + B(s - 1)

Setting s = 1, we get:

2 = 2A

A = 1

Setting s = -1, we get:

-2 = -2B

B = 1

So we have:

2s / (s^2 - 1) = 1/(s - 1) + 1/(s + 1)

Taking the inverse Laplace transform of both sides, we get:

2 cosh t

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Answer:

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As Convex polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The

Convex Polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.

Lets simplify the given problem,

If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180, where n = number of sides

\(1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180\)

n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.

Hence the number of sides is 8

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

Explanation:

h = number of hours past 7 pm

20h = the number of glasses sold after h hours

20h+180 = adding on the 180 glasses already sold

20h+180 > 240 is the inequality to set up

Let's solve for h

------------------

20h+180 > 240

20h > 240-180

20h > 60

h > 60/20

h > 3

They must remain open more than 3 hours past 7 pm in order to sell more than 240 glasses of juice.

The earliest that they can close is 11 pm (since 4+7 = 11).

--------------------

If h = 3, then

20h+180 = 20*3 + 180 = 240

meaning that they haven't reached their goal of getting over 240

So they have to stay open that extra hour to get past 240.

Answer:

  at least 5

Step-by-step explanation:

You want to know the number of cups needed to contain 7/8 pitcher of water when each cup holds 3/16 pitcher.

The number of cups can be found by dividing the water quantity by the amount each cup holds:

  (7/8 pitcher)/(3/16 pitcher/cup) = 14/3 cups = 4 2/3 cups

Eve needs at least 5 cups to hold the amount of water in the bottle.

__

Additional comment

If every cup is filled to capacity, then the 5th cup will be 2/3 full. The number of cups can be any number greater than or equal to 5.

If you want, you can write an inequality relating the capacity of the cups to the amount of water:

  n(3/16) ≥ 7/8

  n ≥ 4 2/3 . . . . . . . . . where n is a counting number

  n ∈ {5, 6, 7, ...}

This more clearly shows that the number is not restricted to 5.

Answer:

2x^2 +11

Step-by-step explanation:

2x^2 +11

Step-by-step explanation:

(x) = 3 x^2 + 2

g(x) = x^2 - 9

(f - g)(x) =3 x^2 + 2 - (x^2 - 9)

Distribute the minus sign

            = 3x^2 +2 - x^2 +9

Combine like terms

            = 2x^2 +11

The given expression is

(2a^3c^5)^3

Recall the law of exponents which is expressed as

(a^b)^c = a^bc

By applying this rule, we have

2^3a^3*3c^5*3

= 8a^9c^15

The last option is correct

The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.

Then the expected value of the number of heads can be evaluated by multiplying each probability with its  corresponding number of heads and suming them.
For the given case, we possess five coins with different probabilities of getting heads when flipped.
Therefore, getting heads for each coin in context of probability are 0.1, 0.2, 0.3, 0.4 and 0.5

Now, the expected value of the number of heads is
Expected value = \((0.1 * 1) + (0.2 * 1) + (0.3 * 1) + (0.4 * 1) + (0.5 * 1)\)
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5
=1.5
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.

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The data value that corresponds to the 46th percentile is 10.

To find the data value that corresponds to the 46th percentile, we need to arrange the given data in ascending order and then identify the value at the desired percentile.

Arranging the data in ascending order:

7, 12, 14, 16, 19, 19, 19, 25, 25, 27, 28, 28, 34, 37, 38, 40, 53, 69, 92, 115, 200

Since we have 21 data values, the 46th percentile corresponds to the (46/100) * 21 = 9.66th value.

To find the corresponding data value, we round up the decimal value to the nearest whole number, which is 10.

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Answer:

Vanilla = 10 sundaes

Step-by-step explanation:

Total sundaes = 25

1/5 of the sundaes are mint ice cream

Mint ice cream = 1/5 of 25

= 1/5 * 25

= 25/5

= 5

Sundaes remaining = total sundaes - sundaes for mint ice cream

= 25 - 5

= 20 sundaes

Sundaes remaining = 20 sundaes

1/2 of the remaining sundaes are chocolate

= 1/2 of 20

= 1/2 * 20

= 20/2

= 10

Chocolate ice cream = 10

The rest will be vanilla

Sundaes remaining = 20 - 10

= 10 sundaes

Vanilla = 10 sundaes

The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.

In the first year, Nora's salary is $40,000.

In the second year, her salary will be increased by 3%, so it will be:

$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.

In the third year, her salary will again increase by 3%, so it will be:

$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.

We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.

To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:

Total = $40,000 + $41,200 + $42,436 + ... (21 terms)

To simplify the calculation, we can use the formula for the sum of an arithmetic series:

Total = (n/2) * (2a + (n - 1)d)

where:

n = number of terms (21 in this case)

a = first term ($40,000)

d = common difference (3% of the previous year's salary)

Plugging in the values:

Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]

Simplifying further:

Total = (21/2) * [80,000 + 20(0.03)(40,000)]

= (21/2) * [80,000 + 2,400(40,000)]

= (21/2) * [80,000 + 96,000]

= (21/2) * 176,000

= 21 * 88,000

= 1,848,000

Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

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A candy store sells 8 pound bags of mixed almonds and cashews. If c pounds of cashews are in a bag,...

c=1 was already given as described. The store sells pound bags.

The rest of the description and question seem not to match. Maybe each bag contains 8 pounds of the two nuts. Eight pounds and some of this is of cashews. Now, c is how many pounds of cashews in one bag.

-

p=2.59%2Ac%2B1.72%288-c%29

You want to know the quantity of cashews if p=18.11 dollars per bag.

2.59c%2B1.72%2A8-1.72c=p

2.59c-1.72c=p-1.72%2A8

%282.59-1.72%29c=p-1.72%2A8

0.87c=p-13.76

(x)+(x+1)+(x+2)=41

3x+3=41

3x=38

x=38/3

Answer:

Step-by-step explanation:

1.    200%A = 2A

B is 200% more than A means:

B = A + 200%A = A + 2A = 3A

2.    65%F = 0.65F

D is 65% more than F means:

D = F + 65%F = F + 0.65F = 1.65F

3.    250%T = 2.5T

Y is 250% more than T means:

Y = T + 250%T = T + 2.5T = 3.5T

Answer:

26-x

Step-by-step explanation:

we don't know how many has moved out so we use x to represent that. Obviously for example if he had 5 leave his class we would do 26-5.

Answer:

Step-by-step explanation:

27. LMN = LMO- NMO = 85-53 = 32

Answer:

3

Step-by-step explanation:

g(x)= -5x + 12

\(g^{-1}(x) = -\frac{x - 12}{5}\)

Substitute x for 3, solve

\(g^{-1} (-3) = 3\)

Since probabilities cannot be negative, we can conclude that the given probabilities are inconsistent or there might be an error in the information provided. Please verify the values and provide correct probabilities so that we can accurately calculate P(B|A), the probability of the flight being delayed when it is raining.

Let's denote the events as follows:

A: It will rain

B: The flight will be delayed

We are given the following probabilities:

P(A) = 0.11 (probability of rain)

P(B) = 0.14 (probability of flight delay)

P(A'∩B') = 0.76 (probability of no rain and on-time departure)

We can use the probability formula to calculate the probability of the flight being delayed when it is raining, P(B|A), which is the probability of B given A.

We know that:

P(B|A) = P(A∩B) / P(A)

To find P(A∩B), we can use the formula:

P(A∩B) = P(A) - P(A'∩B')

Substituting the given values:

P(A∩B) = P(A) - P(A'∩B')

P(A∩B) = 0.11 - 0.76

P(A∩B) = -0.65

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The pribability P(Freshman | Male) = 4/14 = 0.2857 = is 29%.

What is the pribability ?

The probability of selecting a male freshman can be found by dividing the number of male freshmen by the total number of male students:

P(Freshman | Male) = (Number of Male Freshmen) / (Total Number of Male Students)

From the table, we see that there are 4 male freshmen out of a total of 4+6+2+2=14 male students.

P(Freshman | Male) = 4/14 = 0.2857 = 28.57%

Rounded to the nearest whole percent, the probability is 29%.

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Complete question is: If a male student is selected at random, what is the probability the student is a freshman.

P(Freshman | Male) = 29%.

The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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Answer:

20 miles in 2 hours

Step-by-step explanation:

2 is h, which is the time, and 20 is mi, which is the distance

Answer:

165 hope this helps

Step-by-step explanation:

\(--------------------------------------------\)

Answer:

159

\(--------------------------------------------\)

Step-by-step explanation:

-4 + 91=87

87 + 72=159

\(--------------------------------------------\)

SIMPLE

The average daily growth rate  of the bacteria culture is 6.96%

Growth rate is the rate or speed at which the number of organisms in a population increases.

Growth rate is expressed as ;

growth rate =\((P_{0}/P_{t})^{1/t}\) - 1

where p(t) is the present population at time t

p(o) is the initial population and t is the time

p(o) = 25000

p(t) = 35000

t = 5 days

Therefore growth rate

= (35000/25000)\(^{1/5}\) - 1

= \(1.4^{0.2}\) - 1

= 1.0696 -1

= 0.0696

= 6.96%

Therefore the growth rate of the bacterial culture is 0.0696 or 6.96%

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Step-by-step explanation:

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Answer:

1*4 = 4 in^2

Step-by-step explanation:

The area for this shape is calculated by multiplying width and length:

1*4 = 4 in^2

Answer:

Isometry: An isometry is a transformation that maintains congruency.  This means that the transformation does not change the figure's size or shape.

Make sure your child is familiar with the Cartesian coordinate system including the horizontal x-axis, the vertical y-axis, and the (x,y) convention used for locating points.

If you have not already done so, you may wish to review this congruency lesson with your child.

Translations

This section will help your child to translate congruent figures on a Cartesian plane. It will also introduce translation vectors which show the distance and direction of the translation.

Translations

Figure J is the pre-image. Figure S is translated.

A figure is a translation if it is moved without rotation.

Translation Vector

A Translation Vector is a vector that gives the length and direction of a particular translation. Vectors in the Cartesian plane can be written (x,y) which means a translation of x units horizontally and y units vertically.

figure being translated

Vectors translations can be written as shown in either of these two ways:

format example for writing vectors

This vector can be said to be ray AB or vector D.

You translate a figure according to the numbers indicated by the vector.  So if one point on a figure has coordinates of (-3,3)  and the translation vector is (-1,3), the new coordinate is (-4,6). You add or subtract according to the signs in the numbers in the vector.

Work through the two examples below with your child to see how to apply translation vectors.

square translated on cartesian grid

The red square's coordinates are:

(-4,3); (-4,8); (-9,3); (-9,8).

What are the coordinate pairs under a translation vector of (1,-1) as shown by the blue square?

The new coordinates are:

(-3,2); (-3,7); (-8,2); (-8,7).

You can see that the translation did not move the figure far because the vector translation is small.

square translated on cartesian grid

We will try a different vector translation of (3,-9) on the same red square

The new coordinates are:

(-1,-6); (-1,-1); (-6,-6); (-6,-1).

Get you child to try the next example. Do not look at the answer until he or she has tried to work it through the task.

single triangle on cartesian grid

Task: Translate ΔABC with a vector translation of (6,-2)

Steps:

Find the coordinates of Δ ABC.

Add 6 to the X coordinates and subtract 2 (or add -2) from the Y coordinates.

Plot the new coordinates on the grid.

Answer and Explanation

Coordinates of ΔABC are:

(-5,1); (-2.5,7); (0,1)

Add 6 and subtract 2

A1 = (-5 + 6, 1 - 2) = (1,-1)

B1 = (-2.5 + 6, 7 - 2) = (3.5,5)

C1 = (0 + 6, 1 - 2) = (6,-1)

Plot ΔA1B1C1

Rotations

This section will show your child how to rotate a figure about the origin on a Cartesian plane. Work through the two examples below:

Note: Make sure your child knows that the origin is the intersection of the X and Y axes; (0,0) on the Cartesian plane.

Rotation Transformation: Example 1

Look at the four triangles on the Cartesian plane below. Each one is rotated about the origin as shown in the table.

Triangle B Triangle C Triangle D

90° rotation of Triangle A about the origin 90° rotation of Triangle B about the origin 90° rotation of Triangle C about the origin

 180° rotation of Triangle A about the origin 180° rotation of Triangle B about the origin

   270° rotation of Triangle A about the origin

The coordinates are:

Triangle A (-2,2) (-10,2) (-6,8)

Triangle B (2,2) (2,10) (8,6)

Triangle C (2,-2) (10,-2) (6,-8)

Triangle D (-2,-2) (-2,-10) (-8,-6)

Note the pattern in the coordinates for corresponding vertices on the triangles.

Rotation Transformation: Example 2

The coordinates of Pentagon ABCDE are:

(0,4); (7,4); (9,2); (7,0); (0,0)

Pentagon ABCDE is rotated 180° about

the origin making the coordinates of

Pentagon A1B1C1D1E1:

(0,-4); (-7,-4); (-9,-2); (-7,0); (0,0)

Note how the coordinates of

corresponding vertices are opposite

integers (just the +/- sign is different).

This is always the case with 180°

rotations about the origin.

Reflections

This section will help your child to reflect a figure over an axis on a Cartesian plane

Work through the two reflection examples below.

Reflection Transformation: Example 1

The coordinates of LMNO are:

(-7,5); (0,5); (-2,1); (-5,1)

LMNO is reflected over the X-axis

making the coordinates of

L1M1N1O1:

(-7,-5); (0,-5); (-2,-1); (-5,-1)

Note how the x-coordinates remain the

same but the y-coordinates change to

their opposite integer (i.e. the sign changes).

This is always the case with reflections over the X-axis.

Step-by-step explanation:

The solution is, the coordinates of Z'  will be z' = (6,7),

i.e. option B is correct.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Given that,

X' are (5,11).

now, See attachment

Required that,

The image of Z i.e. z'

From the attachment:

X =(7,11)

This implies that:

X' = ( x- 2, y)

Using the same rule for z;

z=(8,7)

z' = (8-2, 7)

z' = (6,7)

Hence, The solution is, the coordinates of Z'  will be z' = (6,7),

i.e. option B is correct.

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The balance of Ana's checking account after the transaction on October 22 is $1,213.49.

To determine the balance of Ana's checking account after the transaction on October 22, we'll follow these steps:

1. Start with the initial balance on October 8: $1,093.12
2. Subtract the withdrawal for rent on October 15: $1,093.12 - $525.50 = $567.62
3. Add the deposit from the paycheck on October 22: $567.62 + $645.87 = $1,213.49

The balance of Ana's checking account after the transaction on October 22 is $1,213.49.

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Yes, the given statement is true if the variance of the population 'a' is smaller than the variance of population 'b' it represents that population 'b' is more variable than 'a'.

Therefore, the given statement is true for the variance of population 'a' and 'b'.

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The maximum possible value for 'h' = 6 for the given set of system of inequalities.

For the given set of inequalities;

y ≤ 1/2x - 5

y ≥ 3x - 20

Equation both equation;

(1/2)x - 5 = 3x - 20

x - 10 = 6x - 40

Further simplifying;

-5x = -30

x = 6

Thus, the maximum possible value for 'h' is same as the value find for the x = 6; as h also represents the point on the x-axis.

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