15 POINTS

Determine the perimeter of the right triangle shown.

right triangle with vertices at negative 4 comma 4, 4 comma 4, and 4 comma negative 2

10 units
24 units
36 units
64 units

Answer:

18.27

Step-by-step explanation:

70.50-52.01- 0.22

18.49-0.22

18.27

Using the information provided in the table, The total holding cost is  $547.50, the total setup cost is $600 and the total cost is  $1,147.50.

To develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.

The missing values can be found on the attached table.

From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.

Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.

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The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.

When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.

In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.

Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

1

explanation in head

There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria. Hence, in total after 3 hours, we have 27 bacteria.

Bacteria are ubiquitous, largely free-living creatures that frequently only have one biological cell. They make up a significant portion of the prokaryotic microbial kingdom. Bacteria, which tend to be a few micrometres long and were among the initial organisms that appeared on Earth, are found in the majority of its habitats.

n = the number of bacteria at a given hour

at zero hour=1 bacteria.

1 bacteria after an hour is split in to 3 bacteria.

n(1)  = 3

n(2)  = 3 x 3  = 9 bacteria

n(3)  = 9 x 3  = 27 bacteria

Hence, in total after 3 hours, we have 27 bacteria

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Answer:

2.83

Step-by-step explanation:

The correct order of steps is 1, 2, 3, 4. And the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, is 1/16.

To find the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, we need to follow these steps in order:
1. Identify the total number of possible outcomes when a fair coin is flipped five times, which is 2^5 = 32.
2. Determine the number of outcomes in which the first flip is tails, which is also 16.
3. Out of the 16 outcomes where the first flip is tails, identify the number of outcomes in which exactly four heads appear. There is only one such outcome: THHHH.
4. Calculate the conditional probability by dividing the number of favourable outcomes (i.e. THHHH) by the number of total outcomes given the condition (i.e. the first flip is tails), which is 1/16.
Therefore, the correct order of steps is 1, 2, 3, 4. And the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, is 1/16.

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Answer:

0.80

Step-by-step explanation:

I did the math 5 times

The value of 150 is calculated using three numbers and the subtraction and division operators using algebra as, \(x = 200, y = 50, z = 1.\)

Given that we need to calculate 150 using three numbers and the subtraction and division operators using algebra.

So let us consider the three numbers x, y, z.

According to the given conditions, we can form the equation for the above statement.

So, \(150 = x - y/z  ----------(1)\)

Now we can substitute any 2 values in equation (1) and solve for the third value.

Let us take \(x = 200, y = 50.\)

Substituting these values in the above equation, we get \(150 = 200 - 50/z\)

Multiplying z on both sides we get,\(150z = 200z - 50\)

Multiplying (-1) on both sides we get,\(50 = 200z - 150zSo,50 = 50z\)

Dividing by 50 into both sides we get,\(z = 1\)

Now we got the value of z = 1, let us substitute the values of \(x = 200, y = 50 and z = 1\) in equation (1) and verify.

\(150 = 200 - 50/1150 \\= 200 - 50 \\= 150.\)

So the value of 150 is calculated using three numbers and the subtraction and division operators using algebra as, \(x = 200, y = 50, z = 1.\)

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Let be x the amount the owner withdrew. Then, we can write and solve the following equation:

Answer

The owner withdraws $2,000.

There will be 17 students voted for the famous athlete.

You can calculate this by multiplying the number of students in the grade (85) by the percentage who voted for the athlete (20% or 0.20).

85 x 0.20 = 17

The method used here is called "Percentage calculation." The method of percentage calculation is generally applicable to many situations where you want to find the proportion of a number relative to another number. It can be used to solve problems in various fields such as mathematics, finance, statistics, and more.

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Answer:

5/7

Step-by-step explanation:

5x-7y=14

-7y=14-5x

y=-2+5/7x

y=5/7x-2

This slope is 5/7. This is because in the standard form of a line (y=mx + b), m represents the slope. In the equation above, 5/7 is the slope.

The length of one side of the new square-shaped garage is 4√3 meters.

A square is a two dimensional figure that has 4 equal sides. The area of a square can be solved by multiplying the length of its side by itself.

A = s^2

where s = side length

If the initial square-shaped garage has an area of 32 square meters and will be increased by 50%, then the new area should be 50% more than the initial area.

new floor area = 50% initial area + initial area

new floor area = 50%(32) + 32

new floor area = 16 + 32

new floor area = 48 square meters

If the new garage has a floor area of 48 square meters, using the formula for the area of a square, solve for the length of its side.

A = s^2

48 = s^2

s = 4√3 meters

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The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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The absolute maximum value is 2 and this occurs at x = 0. The absolute minimum value is -43 and this occurs at x = -3. To find the absolute maximum and minimum values of the function f(x) = 2 – 5x^2, we need to first find its critical points. Taking the derivative of f(x) with respect to x, we get:

f'(x) = -10x

Setting f'(x) = 0, we get x = 0 as the only critical point. We also need to check the endpoints of the given interval, x = -3 and x = 2.

Now we evaluate the function at these three points:

f(-3) = 2 – 5(-3)^2 = -43

f(0) = 2 – 5(0)^2 = 2

f(2) = 2 – 5(2)^2 = -18

Therefore, the absolute maximum value of f(x) on the interval [-3, 2] is 2, and this occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -43, and this occurs at x = -3.
To find the absolute maximum and minimum values of the function f(x) = 2 - 5x^2 on the interval [-3, 2], we need to evaluate the function at its critical points and endpoints.

First, find the critical points by taking the derivative of the function:

f'(x) = d(2 - 5x^2)/dx = -10x

Set the derivative equal to zero and solve for x:

-10x = 0
x = 0

Now, evaluate the function at the critical point and the endpoints of the interval:

f(-3) = 2 - 5(-3)^2 = -43
f(0) = 2 - 5(0)^2 = 2
f(2) = 2 - 5(2)^2 = -18

The absolute maximum value is 2 and this occurs at x = 0. The absolute minimum value is -43 and this occurs at x = -3.

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Step-by-step explanation:

Given: {x+(1/x)}³ = 3

Asked: x³ + (1/x³) = ?

Solution:

Method 1:

We have, {x+(1/x)}³ = 3

Comparing the expression with (a+b)³, we get

a = x

b = (1/x)

Using identity (a+b)³ = a³+b³+3ab(a+b), we get

⇛{x+(1/x)}³ = 3

⇛(x)³ + (1/x)³ + 3(x)(1/x){x + (1/x)} = 3

⇛(x*x*x) + (1*1*1/3*3*3) + 3(x)(1/x){x + (1/x)} = 3

⇛x³ + (1/x³) + 3(x)(1/x){x + (1/x)} = 3

⇛x³ + (1/x³) + 3{x + (1/x)} = 3

⇛x³ + (1/x³) + 3(x) + 3(1/x) = 3

⇛x³ + (1/x³) + 3x + (3/x) = 3

Our answer came incorrect.

Let's try..

Method 2:

We have,

[x+(1/x)]³ = 3

On taking cube root both sides then

⇛³√[{ x+(1/x)}³ ] = ³√3

⇛x+(1/x) = ³√3 -----(1)

We know that

a³+b³ = (a+b)³-3ab(a+b)

⇛x³+(1/x)³ = [x+(1/x)]³ - 3(x)(1/x)[x+(1/x)]

⇛x³+(1/x³) = (3)-3(1)(³√3)

[since, {x + (1/x)} = ³√3 from equation (1)]

⇛x³+(1/x)³ = 3-3 ׳√3

⇛x³ + (1/x³) = 3- ³√81 (or )

⇛x³ + (1/x³) = 3(1-³√3)

Therefore, x³ + (1/x³) = 3(1 - cube root of 3)

It is impossible to get zero

Based on the calculations, the expression \(x^3 +(\frac{1}{x})^3\) is equal to \(3(1-\sqrt[3]{3})\)

Given the following data:

First of all, we would take the cube root of both sides as follows:

\(\sqrt[3]{(x + \frac{1}{x} )^3} =\sqrt[3]{3} \\\\x + \frac{1}{x} =\sqrt[3]{3}\)....equation 1.

From trinomial, we have:

\(a^3+b^3=(a+b)^3-3ab(a+b)\)

Applying the trinomial eqn. & substituting eqn. 1, we have:

\(x^3 +(\frac{1}{x})^3 = [x+\frac{1}{x}]^3 - 3(x)(\frac{1}{x})[x+\frac{1}{x}]\\\\x^3 +(\frac{1}{x})^3 = (\sqrt[3]{3})^3 - 3[x+\frac{1}{x}]\\\\x^3 +(\frac{1}{x})^3 =3-3\sqrt[3]{3} \\\\x^3 +(\frac{1}{x})^3 =3(1-\sqrt[3]{3})\)

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The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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Relative humidity tends to be highest during the early morning hours, shortly before sunrise.

To determine the Wet-Bulb Temperature (WBT) and Wet-Bulb Depression (WBD), we need the dry-bulb temperature (DBT) and relative humidity (RH) values.

The Wet-Bulb Temperature (WBT) is the lowest temperature that can be achieved by evaporating water into the air at constant pressure, while the Wet-Bulb Depression (WBD) is the difference between the dry-bulb temperature (DBT) and the wet-bulb temperature (WBT). These values are useful in determining the potential for evaporative cooling and assessing heat stress conditions.

Day 1: Air Temperature= 86°F and RH= 60%

To calculate the WBT and WBD for Day 1, we would need additional information such as the barometric pressure or the dew point temperature. Without these values, we cannot determine the specific WBT or WBD for this day.

Day 2: Air Temperature= 41°F and RH= 90%

Similarly, without the necessary additional information, we cannot calculate the WBT or WBD for Day 2.

Regarding your question about the point during the day with the lowest and highest outside relative humidity values, it is generally observed that the relative humidity tends to be highest during the early morning hours, shortly before sunrise. This is because the air temperature often reaches its lowest point overnight, and as the air cools, its capacity to hold moisture decreases, leading to higher relative humidity values.

Conversely, the outside relative humidity tends to be lowest during the late afternoon, typically around the hottest time of the day. As the air temperature rises, its capacity to hold moisture increases, resulting in lower relative humidity values.

It's important to note that these patterns can vary depending on the local climate, weather conditions, and geographical location. Other factors such as wind patterns and nearby bodies of water can also influence relative humidity throughout the day.

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Answer:

r = -9

Step-by-step explanation:

Subtract 8 from both sides to get 2r = -18. Divide by 2 on both sides to get r = -9.

Answer:

r=-9

Step-by-step explanation:

Step 1:- Simplify both sides of the equation.

2r+8 = -10

Step 2:- For isolating the variable, subtract 8 from both sides.

2r+8-8 = -10-8

2r = -18

Step 3:- For isolating the variable, divide by 2 from both sides.

2r/2 =-18/2

r= -9

Hope this helps :)

Answer:

x = 415

Step-by-step explanation:

(0.3x - 25) + (0.1x - 51) = 90°

0.3x - 25 + 0.1x - 51 = 90

0.4x - 76 = 90

        + 76   + 76

0.4x = 166

÷0.4    ÷0.4

x = 415

The equation is a right angle so it's equal to 90°

I hope this helps!

Answer:

mabe try $24.10

Step-by-step explanation:

Answer:

48

Hope this helps!

Answer:

Donald earnings = 3(s + k)

Step-by-step explanation:

Susan earnings = s

Kurt earnings = k

Combined salary = s + k

Donald earns earns three times as much as the combined salary of his two vice presidents,

Donald earnings = 3(s + k)

= 3s + 3k

Answer:

\({ \sf{7h - (3h - 5) = 2(h - 7)}} \\ \\ { \sf{7h - 3h + 5 = 2h - 14}}\)

[distributive property open brackets ]

\({ \sf{4h + 5 = 2h - 14}}\)

[simplification of either sides]

\({ \sf{4h - 2h = - 14 - 5}}\)

[operating similar terms]

\({ \sf{2h = - 19}} \\ \)

[simplification]

\({ \sf{h = \frac{ - 19}{2} }}\)

The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

Step-by-step explanation:

x = 3y + 18

5x+4y = -5

X =

y = 0

010

X

5

The values of "x" are 1 and 9.

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Answer:

It's B and C You're welcome!

Step-by-step explanation:

Edge 2022

Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.

To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.

At that point, we know that:

2L + 2W = 10

Rearranging this condition, we get:

L + W = 5

Presently, we need to discover the most extreme range encased by the rectangle, which is given by:

Area = L x W

Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:

L = 5 - W

Substituting this expression for L into the condition for the zone, we get:

Zone = (5 - W) x W

Extending and disentangling this expression, we get:

Area = 5W - W²

To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:

dArea/dW = 5 - 2W =

Tackling for W, we get:

W = 2.5

Substituting this esteem back into the condition for the edge, we get:

L = 2.5

Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:

Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

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