Write an equation of a line in slope-intercept form with the given slope and y-intercept.
slope: -2.5, y-intercept: 3.5

Answer:

9/29

Step-by-step explanation:

3 2/9 is in improper fraction form 29/9, the recipricol just switches the numerator and denominator. So it would be 9/29

Given that the volume of a cube is decreasing at a constant rate of 94 cubic meters per minute.

Let's consider that the side length of the cube is "x".The volume of a cube is given as:

\($$V = x^3$$\)

As the volume of the cube is decreasing at a constant rate of 94 cubic meters per minute,

we can differentiate both sides of the equation with respect to time, "t" to find the rate of change of volume with respect to time.

Thus, we have:

\($$\frac{dV}{dt} = \frac{d}{dt}(x^3) = 3x^2\frac{dx}{dt}$$\)

Hence, the rate of change of volume with respect to time is:

\(\frac{dV}{dt} = 3x^2\frac{dx}{dt} = -94 \ m^3/min\)

We are asked to find the rate of change of the surface area of the cube, so we need to find:

\($$\frac{dA}{dt}$$\)

where A is the surface area of the cube.

The formula for the surface area of a cube is given as:

\($$A = 6x^2$$\)

Differentiating with respect to time "t" on both sides of the equation, we have:

\(\frac{dA}{dt} = \frac{d}{dt}(6x^2) = 12x\frac{dx}{dt}\)

Substitute the value of x and the given value of

\(\frac{dV}{dt}\) in the equation.

Therefore, we have:

\(\frac{dV}{dt} = 3x^2\frac{dx}{dt} = -94 \ m^3/min$$$$\Rightarrow \ 3(55^2)\frac{dx}{dt} = -94$$$$\Rightarrow \ \frac{dx}{dt} = -\frac{94}{3(55^2)}$$\)

Hence, the rate of change of the surface area of the cube is:

\(\frac{dA}{dt} = 12x\frac{dx}{dt}$$$$\Rightarrow \ \frac{dA}{dt} = 12(55)\left(-\frac{94}{3(55^2)}\right)$$$$\Rightarrow \ \frac{dA}{dt} = \boxed{-\frac{376}{55}} \ m^2/min$$\)

Therefore, the rate of change of the surface area of the cube at the instant when the side length of the cube is 55 meters is -376/55 m²/min.

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Answer:

Nick will get £16; Peter will get 60 sweets

Step-by-step explanation:

Angad and Nick win some money and share it in the ratio 2:1. The total ratio is:

2 + 1 = 3

Let the total amount shared be x.

Angad gets £32. This implies that:

2/3 * x = 32

=> 2x = 32 * 3 = 96

x = 96 / 2 = £48

Therefore, Nick will get:

1/3 * 48 = £16

Sushil, Alex and Peter share some sweets in the ratio 1:1:4. The total ratio is:

1 + 1 + 4 = 6

Let the total sweets shared be x.

Sushil gets 15 sweets. This means that:

1/6 * x = 15

x = 15 * 6 = 90 sweets

Therefore, Peter will get:

4/6 * 90 = 60 sweets

Answer:

90,502,084.19

Step-by-step explanation:

Just add them together

The simple interest accumulated on the principal at 12% rate for 4 years is $3,840.

Simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

First, convert the interest rate from percent to decimal.

Interest rate r = 12%

Interest rate r = 12/100

Interest rate r = 0.12

Plug the given values into the above formula and solve for interest I.

I = P × r × t

I = $8000 × 0.12 × 4

I = $3,840

Therefore, the interest earned is $3,840.

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Answer:

$15 1/10

Step-by-step explanation:

Given that :

Total amount to spend = $30

Amount spent on Gift A = $9 1/4

Amount spent on Gift B = $5 4/5

Amount left to spend on gift C ;

$30 - (9 1/4 + 5 4/5)

$30 - (37/4 + 29/5)

$30 - (185 + 116)/20

$30 - 298/20

30/1 - 298/20

$(600 - 298) / 20

$302/20

$15 2/20

= $15 1/10

Answer:

3.8

Step-by-step explanation:

----------

Answer:

solution,

\(0.18(5x - 4) = 0.5x + 0.8 \\ or \: 0.9x - 0.72 = 0.5x + 0.8 \\ or \: 0 .9x - 0.5x = 0.8 + 0.72 \\ or \: 0.4x = 1.52 \\ or \: x = \frac{1.52}{0.4} \\ x = 3.8\)

hope this helps..

Good luck on your assignment..

a) If the first 2 cards are both spades, the probability of the next 3 cards also being spades can be calculated by using the following formula:P(5 spades) = P(3 spades AND 4 spades AND 5 spades) = P(3 spades) x P(4 spades | 3 spades) x P(5 spades | 3 spades and 4 spades)The probability of picking 3 spades out of 50 cards is:P(3 spades) = (13/52) x (12/51) x (11/50)To calculate the probability of drawing the fourth spade, we know there are 11 spades left in the deck and only 49 cards remaining. Hence,P(4 spades | 3 spades) = (11/49)To calculate the probability of drawing the fifth spade, we know there are 10 spades left in the deck and only 48 cards remaining. Hence,P(5 spades | 3 spades and 4 spades) = (10/48)Therefore, P(5 spades) = (13/52) x (12/51) x (11/50) x (11/49) x (10/48) which is approximately equal to 0.0026. Hence, the probability of the next 3 cards being spades is 0.0026. The answer is rounded to four decimal places.

b) If the first 3 cards are all spades, then the probability of the next 2 cards being spades can be calculated as follows:To calculate the probability of the fourth spade, we know there are 11 spades left in the deck and only 49 cards remaining. Hence, P(4 spades | 3 spades) = (11/49)To calculate the probability of the fifth spade, we know there are 10 spades left in the deck and only 48 cards remaining. Hence, P(5 spades | 3 spades and 4 spades) = (10/48)Therefore, P(2 spades | 3 spades) = P(4 spades | 3 spades) x P(5 spades | 3 spades and 4 spades) = (11/49) x (10/48) which is approximately equal to 0.0045. Hence, the probability of the next 2 cards being spades is 0.0045. The answer is rounded to four decimal places.

We can write the probability of picking 5 spades as the probability of picking 4 spades AND 5 spades. This can be represented as:P(5 spades) = P(4 spades AND 5 spades) = P(4 spades) x P(5 spades | 4 spades).The probability of picking 4 spades out of 49 cards is: P(4 spades) = (10/48) x (9/47). This means that there are 10 spades out of the 48 cards in the deck for the first pick, and 9 spades out of the remaining 47 cards for the second pick.

Hence, the probability of drawing a spade given that the first four cards are spades is:P(5 spades | 4 spades) = (9/47). This is because there are 9 spades left in the deck and only 47 cards remaining.

Therefore, the probability of the next 2 cards being spades is calculated as follows:P(5 spades) = P(4 spades) x P(5 spades | 4 spades) = (10/48) x (9/47) x (9/47) ≈ 0.0030. This means that the probability of the next 2 cards being spades is 0.0030, rounded to four decimal places.

If the first 4 cards are all spades, then the probability of the next card being a spade is given by:P(5 spades) = P(5 spades) / P(4 spades). The probability of picking 5 spades out of 48 cards is:P(5 spades) = (9/46).

Thus, the probability of the next card being a spade is:P(5 spades) / P(4 spades) = (9/46) / (9/47) ≈ 0.9672. This means that the probability of the next card being a spade is 0.9672, rounded to four decimal places.

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Answer: \(x<\frac{2}{5}\)

Step-by-step explanation:

\((2x+3)(4x-1)<8x^2+1\)

Begin by multiplying parentheses.

\((2x*4x)+(2x*-1)+(3*4x)+(3*-1)<8x^2+1\)

\((8x^2)+(-2x)+(12x)+(-3)<8x^2+1\)

\(8x^2-2x+12x-3<8x^2+1\)

Subtract \(8x^2\)

\(8x^2-2x+12x-3+(-8x^2)<8x^2+1+ (-8x^2)\)

\(-2x+12x-3<1\)

Add 3

\(-2x+12x-3+3<1+3\)

\(-2x+12x<4\)

Combine like terms;

\(10x<4\)

Divide by 10

\(x<\frac{4}{10}\)

Simplify;

\(x<\frac{2}{5}\)

Answer:

457

Step-by-step explanation:

57;;/*_&445

Answer:

5.3+3.5=8.8

Step-by-step explanation:

x+y=8.8

x-y=1.8

add both equations togeather which cancel out y because there is a +y and a -y

2x=8.8+1.8

2x=10.6

2      2

x=5.3

8.8-5.3=3.5

5.3-3.5=1.8

5.3+3.5=8.8

Answer:

2.5

Step-by-step explanation:

2.5

Answer:

2.5s

Step-by-step explanation:

Time = \(\frac{Distance}{Speed} =\frac{5 meters}{2m/s} =2.5s\)

Answer: 8 22 7 13 from top to bottom

Step-by-step explanation:

On the first row, the number of 2-player games is 1 meaning 2 players are playing meaning 48 are left to play the 6-player games so 8 is the number

On the second, the number of 6-player games is 1 meaning 6 players are playing meaning 44 are left to play the 2-player games so 22 is the number

On the third, the number of 2-player games is 4 meaning 8 players are playing meaning 42 are left to play the 6-player games so 7 is the number

On the fourth, the number of 6-player games is 4 meaning 24 players are playing meaning 26 are left to play the 2-player games so 13 is the number

Answer:

Below

Step-by-step explanation:

Let m be the average rate of change.

● m = (f(3)-f(2)) / 3-2

● m = ( log3 - log2) / 1

● m = 0.176

Round it to the nearest tenth

● m = 0.18

y=4x , 2y + 2.5x = 105

Substituting y=4x in 2y + 2.5x = 105, we get;

=) 2(4x) + 2.5x = 105

=) 8x + 2.5x = 105

=) 10.5x = 105

=) x = 105 × 10/105

=) x = 10

Substituting x = 10 in y=4x, we get;

=) y = 4(10)

=) y = 40

Therefore, the value of x is 10 and y is 40

the area of triangle $AMN$ is 8 square cm.

To find the area of triangle $AMN$, we need to determine the lengths of its base and height.

In square $ABCD$ with side length 4 cm, $N$ is the midpoint of side $BC$, so $BN = NC = \frac{1}{2} \cdot 4 = 2$ cm.

Similarly, $M$ is the midpoint of side $CD$, so $CM = MD = \frac{1}{2} \cdot 4 = 2$ cm.

Now, we can see that $AM$ is the height of triangle $AMN$ and has a length of 4 cm, as it is parallel to side $AD$ of the square.

$AN$ is the base of triangle $AMN$ and has a length of $BN + CM = 2 + 2 = 4$ cm.

Therefore, the area of triangle $AMN$ is given by:

$A_{AMN} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8$ square cm.

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Answer:

A: Complementary

Step-by-step explanation

Trust me I'm correct

Answer:

I think the answer is C

Step-by-step explanation:

If you have a normal ginger bread cookie, its full size would be 100%. So, if you add the first 25%, 1.25%

The expression best describes the new length of the cookie will be 1.25y.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The initial length of the cookie is y after baking the length is increased by 25%

=   y  +  25%y

=   y   +  ( 25 / 100 ) y

=   y  +  0.25 y

=  1.25 y

Therefore the expression best describes the new length of the cookie will be 1.25y.

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The value written as 2/7 is a rational number and the other options are irrational numbers.

A rational number is a number that does not end in a non terminating decimal. Surd forms as well as the value pi are all irrational numbers. We must note that the option that has no surd form or pi as a denominator is a rational number.

Hence; the value written as 2/7 is a rational number and the other options are irrational numbers.

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Answer:

c

Step-by-step explanation:

A basis for the eigenspace corresponding to lambda = 5 is {}.

To find the basis for the eigenspace corresponding to the eigenvalue lambda = 5, we need to solve the equation (A - 5I)x = 0, where A is the given matrix and I is the identity matrix.

In this case, A = [6 1 2 4; 0 1 -3 -1; -1 -9 -3 -6; 0 0 0 5]. Subtracting 5 times the identity matrix from A gives us [1 1 2 4; 0 -4 -3 -1; -1 -9 -8 -6; 0 0 0 0].

To find the basis, we solve the system of homogeneous linear equations represented by the augmented matrix [1 1 2 4; 0 -4 -3 -1; -1 -9 -8 -6; 0 0 0 0].

Row-reducing this matrix leads to the row-echelon form [1 1 2 4; 0 -4 -3 -1; 0 0 0 0; 0 0 0 0].

The variables corresponding to the columns with leading 1's (in this case, the first three columns) are the basis vectors for the eigenspace. Since the last column is a dependent variable column, we can choose any three linearly independent vectors from the first three columns as the basis.

Therefore, a basis for the eigenspace corresponding to lambda = 5 is {}. This indicates that the eigenspace is the zero vector space, meaning there are no linearly independent vectors corresponding to the eigenvalue lambda = 5.

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The triangle congruence postulate which justifies why ∆ABC is congruent to ∆DEF is; SAS.

It follows from the task content that the triangle congruence postulate which justifies the congruence of ∆ABC and ∆DEF be determined.

Since it follows from the Side-Angle-Side (SAS) postulate that; if two sides of one triangle and the included angle between them are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Since it is given in the task content that AB = DE and CB = FE and evidently, the measures of angles DEF and ABC are equal (right angles);

The correct justification is the; Side-Angle-Side (SAS) triangle congruence postulate.

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The minimum hot-holding temperature for fried shrimp is d. 135 ° F 57 ° C. It is important to maintain this temperature to ensure that the food remains safe for consumption and to prevent the growth of harmful bacteria.

The minimum hot-holding temperature for fried shrimp is 135 °F (57 °C). When food is hot-held, it means it is kept at a specific temperature after cooking to maintain its quality and safety until it is served or consumed. This temperature is important because it helps prevent the growth of harmful bacteria, such as Salmonella and E. coli, that can cause food borne illnesses.

At a hot-holding temperature of 135 °F (57 °C) or higher, the heat inhibits the growth of bacteria, ensuring that the fried shrimp remains safe for consumption. This temperature range is considered a critical control point in food safety practices.

It's worth noting that the temperature of 135 °F (57 °C) is the minimum requirement for hot-holding fried shrimp. However, in practice, it's generally recommended to hold the shrimp at a slightly higher temperature to account for any temperature loss that may occur over time.

Some food establishments may set their hot-holding equipment to maintain a temperature of 140 °F (60 °C) or higher to ensure the safety and quality of the food.

By adhering to proper temperature control guidelines, including maintaining the minimum hot-holding temperature of 135 °F (57 °C), you can help prevent the risk of food borne illnesses and ensure that the fried shrimp remains safe and enjoyable to consume.

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The stem-and-leaf plot is a data visualization tool that provides a quick way to see the distribution of a set of data.

The given data represents the number of letters in the mailboxes of 10 houses. To construct a stem-and-leaf plot, we group the data by their tens digit and display them as stems on the left side of the plot, and the ones digit is shown as leaves on the right side of the plot. For the given data, the stem-and-leaf plot is:

 2 | 2

 4 | 4 5

 5 | 7 8

 7 | 0 1

 8 |

10 | 0 2

11 |

12 | 3

13 |

16 |

The plot shows that the majority of houses have between 4 and 13 letters in their mailboxes, with the most common numbers of letters being 7, 8, and 10. The plot also shows that there are two outliers: one house with only 2 letters and another with 16 letters in its mailbox.

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We can use the concept of similar triangles. Since the building and the statue are casting shadows simultaneously, the angle of elevation of the sun is the same for both. Therefore, the triangles formed by the building, its shadow, and the ground and the statue, its shadow, and the ground are similar triangles.

Let's use the given information:
- Building height = 51 feet
- Building shadow length = 48 feet
- Statue shadow length = 16 feet
- Statue height = x (this is what we need to find)

Now, set up a proportion using the ratios of the corresponding sides of the similar triangles:

(Building height / Building shadow length) = (Statue height / Statue shadow length)

(51 / 48) = (x / 16)

To find the statue height (x), cross-multiply and solve for x:

51 * 16 = 48 * x

816 = 48x

Now, divide by 48 to find the value of x:

x = 816 / 48
x = 17

So, the statue is 17 feet tall.

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Answer:

87.407

Step-by-step explanation:

circumference = 2*pie*r

= 2*pie*17

=106.8/2

=53.4

53.4+(17*2)

=87.4

Answer:

Step-by-step explanation:

it 87.38

TRUST ME

Based on the analysis of the frequency responses, none of the given filters (H1, H2, H3, H4) can be classified as GLP filters since they do not have the required structure of R(ω)e^(j(α−mω)).

To determine whether a filter is a GLP (Generalized Linear Phase) filter, we need to examine its frequency response and verify if it can be expressed in the form:

Hd(ω) = R(ω)e^(j(α−mω))

where R(ω) is a real function, α is a constant phase shift, and m is a constant slope.

Let's consider the following filters:

H1(ω) = 2e^(jω)

H2(ω) = e^(jω) + e^(-jω)

H3(ω) = 3e^(jω) + 4e^(-jω)

H4(ω) = 5e^(jω) - 5e^(-jω)

For each filter, we need to determine if its frequency response can be written in the form mentioned above.

H1(ω) = 2e^(jω):

This filter does not satisfy the GLP form because the frequency response does not have the required structure of R(ω)e^(j(α−mω)). It lacks the term for a constant slope.

H2(ω) = e^(jω) + e^(-jω):

Similarly, this filter does not satisfy the GLP form because it lacks the term for a constant slope.

H3(ω) = 3e^(jω) + 4e^(-jω):

This filter also does not satisfy the GLP form as it lacks the term for a constant slope.

H4(ω) = 5e^(jω) - 5e^(-jω):

Again, this filter does not satisfy the GLP form due to the absence of the term for a constant slope.

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The required answer is set the reorder point at approximately 304.68 units.

Explanation:-

1) To calculate the safety stock for a 95% service level, we need to find the appropriate z-value for the normal distribution. A 95% service level corresponds to a z-value of 1.645.

Safety Stock = z-value * Standard Deviation of Demand during Lead Time
Safety Stock = 1.645 * 15
Safety Stock ≈ 24.68 units

So, Thomas needs to maintain approximately 24.68 units of safety stock to provide a 95% service level.

2) To calculate the reorder point, we need to consider the average demand during lead time and the safety stock.

Reorder Point = (Average Daily Demand * Lead Time) + Safety Stock
Reorder Point = (70 units/day * 4 days) + 24.68 units
Reorder Point ≈ 280 + 24.68
Reorder Point ≈ 304.68 units

Thomas should set the reorder point at approximately 304.68 units.

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Answer:

189.571428571 miles or km

Step-by-step explanation:

Just deduct the last odometer reading with the first one and divide by the number of days,

(11,477-10,150)/7 = 189.571428571

Metonymy is a figure of speech that replaces the name of something with a word or phrase that is closely associated with it.

In each of the examples given, the italicized words can be considered metonymies because they are being used to refer to something closely associated with the thing being described, rather than using the thing's actual name.

In the first example, "The bookshop holds over 1 million titles," the word "bookshop" is a metonymy for the actual store where the books are being sold. The word "bookshop" is being used to refer to the collection of books that are available for purchase at the store.

In the second example, "Upstairs for hotel and backpackers," the word "upstairs" is a metonymy for the actual hotel or hostel that is located on the upper floor. The word "upstairs" is being used to refer to the place where guests can stay.

In the third example, "[Sign] Since Beijing, the Olympics have got even more popular," the word "Beijing" is a metonymy for the 2008 Summer Olympics that were held in Beijing. The word "Beijing" is being used to refer to the event that took place in the city.

Other metonymies with similar conceptual bases could include using "Hollywood" to refer to the American film industry, "Wall Street" to refer to the American financial industry, or "the Crown" to refer to the British monarchy. Each of these examples uses a word or phrase that is closely associated with the thing being described to stand in for the thing itself.

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