The equation y =7400x represents the number of miles, y, that the satellite Space Explorer flies in x hours. Find the rate of change. ​

To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.

To calculate the volume of water contained in the system, you would use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the pipe (half the diameter), h is the length of the pipe, and π is approximately 3.14.

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Answer:

$460

Step-by-step explanation:

Therefore the regular price of the sofa is $460

As per the concept of compounding interest, the amount he deposited on each year is $471.55

Compounding interest in math is the term defined as the interest on a deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Here we know that the final amount is 12,400.00 and the time period is 13 years and interest rate is 6.05%.

Here we have identified that the compounding frequency is monthly basis.

Then the amount is calculated by using the compound interest formula

A = P(1 + r/n)ⁿˣ

Here we have to convert R as a percent to r as a decimal

r = R/100

r = 6.05/100

r = 0.0605 per year,

Now we have to solve the equation for P

P = A / (1 + r/n)ⁿˣ

P = 12,400.00 / (1 + 0.0605/12)⁽¹²ˣ¹³⁾

P = 12,400.00 / (1 + 0.0050416666666667)¹⁵⁶

P = $5,658.58

Here we know that the principal amount for one year for each month the amount is calculated as,

=> 5,658.58/12 = 471.55

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This data will be considered as Qualitative sample.

Qualitative data is the data that is not represented by numbers, On the other hand, the quantitative data is represented by numbers and it is classified as discrete and continuous.

Qualitative sample

In qualitative research, only a sample  of a population is selected for any given study. The study's research objectives and the characteristics of the study population determine which and how many people to select.

Quantitative sample

The quantitative research sampling method is the process of selecting representable units from a large population. Quantitative research refers to the analysis wherein mathematical, statistical, or computational method is used for studying the measurable or quantifiable dataset.

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The All the expressions that are equivalent to "3.5 - (4.7)" are (b) -4.7 + 3.5 and (e) 3.5+ (-4.7)  .

to find the equivalent expressions , we solve the expressions :

the main expression is 3.5 - (4.7) = -1.2 ;

Simplifying the expressions :

(a) 4.7 - (3.5) = 1.2    False

(b) -4.7 + 3.5 = -1.2   True

(c) 3.5 + 4.7 =  8.2  False

(d) 3.5 - (-4.7) = 3.5 + 4.7 = 8.2   False

(e) 3.5 +(-4.7) = 3.5 - 4.7  = -1.2   True

So , the only value of the expressions that matches with the main expressions are (b) -4.7 + 3.5 and (e) 3.5+ (-4.7)  .

The given question is incomplete , the complete question is

Select ALL of the expressions that are equivalent to "3. 5 - (4. 7)"

(Select all that apply. )

(a) 4.7 - (3.5)

(b) -4.7 + 3.5

(c) 3.5 +4.7

(d) 3.5 - (-4.7)

(e) 3.5 + (-4.7)

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Answer: its -81

hope this helps

The minimum weight of the middle 95% of the players are 151 pounds.

The question is asking for the lower bound of the 95% two tailed Confidence interval of the normally distributed population.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

95% of C.I. is given by 220 + or - 1.96(15)

       = 200 + or - 29 = (191)

Two standard deviations is =2×15=30 pounds

Minimum Weight =220−29 =  191 pounds

Therefore, the minimum weight of the middle 95% of players is 191 pounds.

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We can write the expression as →

{z} = n{x + y}

Given is that Bryce, Alejandro and Dominic went for hiking.

Assume that Bryce and Alejandro travelled {x} and {y} miles respectively.

Assume that Dominic hiked {z} miles and {n} times as far as Bryce and

Alejandro hiked.

We can write the expression as -

z = n{x + y}

Therefore, we can write the expression as →

{z} = n{x + y}

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The solution to the first system of equations is given as follows:

(0, -0.6).

The solution to the second system of equations is given as follows:

(0.64, 1.18).

The first system of equations is given as follows:

Multiplying the first equation by -2, the system is given as follows:

Adding the two equations, the solution for y is given as follows:

15y = -9

y = -9/15

y = -0.6.

Hence the solution for x is of:

7x - 10(-0.6) = 6

7x + 6 = 6

x = 0.

The second system of equations is given as follows:

Multiplying the first equation by 3 and the second by 2, we have that:

Adding them, the solution for y is obtained as follows:

22y = 26

y = 26/22

y = 1.18.

The solution for x is of:

6x + 12(1.18) = 18

x = (18 - 12 x 1.18)/6

x = 0.64.

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The time when h(t) = 169 is 4.13am.

For (a), one possible formula for h(t) is the sinusoidal function, h(t) = Asin(Bt + C) + D, where A is the amplitude (maximum height - minimum height), B is the angular frequency (2 pi/period), C is the phase (starting point), and D is the minimum height. In this case, A = 3, B = 2pi/24, C = 0, and D = 170. Therefore, the formula for h(t) is h(t) = 3sin(2pit/24) + 170.

For (b), we need to solve for t when h(t) = 169. We can rearrange the equation to 3sin(2pit/24) = -1 and solve for t. Using a calculator, we can find that t = 8.21 hours. As 8.21 hours after midnight is 4.13am, the time when h(t) = 169 is 4.13am.

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Answer:

The answer is

[tex]48[/tex]

Step-by-step explanation:

Greetings!!

N.B

Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Thus,

[tex]50 + 82 + x = 180 \\ 132 + z= 180 \\x = 180 - 13 \\ x = 48[/tex]

Hope it helps!!!

The solution of the given inequalities is given below:

a. x < 5 or x < -3

b. x ≥ 4

The solution of an inequality is the value that will make the inequality true.

The solution of the given inequalities is determined as follows:

a. x² - 2x - 15 < 0

x² - 5x + 3x - 15 < 0

x(x - 5) + 3(x - 5) < 0

x - 5 < 0

x < 5

or

x + 3 < 0

x < -3

b. |3x-2| ≥ 10

3x - 2 ≥ 10

3x ≥ 10 + 2

3x ≥ 12

x ≥ 4

The solutions are shown in the number lines attached.

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The symbolic representation is pUq

Symbolic representation is defined as the representation of a principal, a nation for example, through a symbol, such as a flag, that evokes particular meanings and emotions about the nation

Papa Smurf is green or the Snorks use clams as money

let's suppose p = Papa Smurf is green

or q = Snorks use clams as money

here and logic is used in between Papa Smurf being green or the Snorks using clams as money

Or logic is represented by "U".

pUq will be the correct answer.

NOTE- a symbolic representation of Or is  U.

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The x-coordinates of the endpoints are the same.

What are the coordinates?

Coordinates are a set of numbers that are used to specify the position of a point on a graph or a coordinate plane. The most common type of coordinate system is the Cartesian coordinate system, which uses two perpendicular number lines called the x-axis and the y-axis to define the position of a point.

When talking about coordinates, there are two types of coordinates: x-coordinates and y-coordinates. The x-coordinate refers to the horizontal position of a point on a graph or a coordinate plane, while the y-coordinate refers to the vertical position of the point.

In the statement "The x-coordinates of the endpoints are the same," it means that the horizontal position of the two endpoints is the same. These endpoints could be the two points that define a line segment, a geometric figure, or a graph. The x-coordinates of both of these points are the same, while the y-coordinates could be different.

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Answer: The number of elk that are likely to be infected can be estimated using the sample proportion of infected elk. The sample proportion is the ratio of the number of infected elk in the sample to the total number of elk in the sample.

In this case, the sample proportion is:

7/50 = 0.14

This proportion can be used to estimate the proportion of the entire population of elk that is infected. To do this, we can multiply the sample proportion by the total population of elk and round to the nearest whole number.

0.14 * 6,000 = 840

So, it's likely that 840 elk are infected.

Please note that this is an estimate and the actual number of infected elk could be different. Additionally, this estimation is based on a random sample, so it can have a margin of error.

Step-by-step explanation:

(a) The Total Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height + Base area

(b) The Lateral Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height

A pyramid's surface area is a measurement of the entire area occupied by all of its faces. Check out the pyramid shown below to view all of its faces as well as its peak, altitude, slant height, and base.

The whole area of a pyramid's faces makes up its surface area. There are two different types of surface areas in a pyramid: the total surface area(TSA) and the lateral surface area (LSA).

(a) The total surface area of the pyramid is measured as:

The Total Surface Area of a pyramid = lateral surface area of pyramid + Base area

The Total Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height + Base area

(b) The lateral surface area of the pyramid is measured as:

The Lateral Surface Area of a pyramid = The total area of the pyramid's side faces (triangles)

The Lateral Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height

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The cruise ship will be 70 units (could be nautical miles, kilometers or any other unit) away from the iceberg.

What is the slope intercept?

The slope-intercept form of a linear equation is y = mx + b, where x and y are the coordinates of a point on the line, m is the slope of the line (the steepness of the line), and b is the y-intercept (the point where the line crosses the y-axis).

To determine how close the cruise ship will get to the iceberg, we need to find the point of intersection between the ship's path (y = x + 40) and the location of the iceberg (x = 40, y = 10).

Substituting x = 40 into y = x + 40, we get:

y = 40 + 40

y = 80

So the point of intersection is at (40, 80).

We can then use the distance formula to find the distance between the point of intersection and the location of the iceberg:

d = √((40 - 40)^2 + (80 - 10)^2)

d = √((0)^2 + (70)^2)

d = 70

So the cruise ship will be 70 units (could be nautical miles, kilometers or any other unit) away from the iceberg.

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Answer:

The house's value decreased by $46580

The current value of the house is $227420

Step-by-step explanation:

How much did the house's value decrease in dollars?

17% = 0.17

$274,000 x 0.17 = $46580

So, the house's value decreased by $46580

What is the current value of the house?

$274,000 - $46580 = $227420

So, the current value of the house is $227420

Answer: Image attached below

Simply draw a dashed line at 6 and shade below the line

Inequalities are relationships between numbers or expressions that show whether a value is greater, less, or equal to another value.

Graph of y = 6

The first step of graphing any inequality is to graph it as though it were an equation. So, first graph the line y = 6. This line is a horizontal line at the y-value 6.

Then, go back to the inequality. The inequality states that y is less than 6. Since there is no "or equal to" sign, the line should be dotted. If there were an "or equal to" sign, then the line should have been solid. This is because the solutions to the inequality do not include 6.

Shading

Whenever you graph an inequality, the portion of the graph that satisfies the inequality should be shaded. In this case, the inequality is looking for all y-values less than 6. So, the portion of the graph under the line should be shaded in.

Answer:

graphing on a graph

Step-by-step explanation:

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.

From the problem, we know:

L = 2H (the length is twice the height)

W = L - 10 (the width is 10 meters less than the length)

2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)

We can substitute the first and second equations into the third one to obtain:

2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)

Solving this equation we get H = 10m

With this value we can solve for the other dimensions:

L = 2H = 2 * 10 = 20m

W = L - 10 = 20 - 10 = 10m

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

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So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.

From the problem, we know:

L = 2H (the length is twice the height)

W = L - 10 (the width is 10 meters less than the length)

2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)

We can substitute the first and second equations into the third one to obtain:

2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)

Solving this equation we get H = 10m

With this value we can solve for the other dimensions:

L = 2H = 2 * 10 = 20m

W = L - 10 = 20 - 10 = 10m

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

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The mechanic that would charge less for a 50-hour repair is Mechanic A.

Mathematically, the point-slope form of any straight line can be modeled by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

For the table for Mechanic B, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 300 = (600 - 300)/(20 - 10)(x - 10)

y - 300 = 300/10(x - 10)

y = 30x - 300 + 300

y = 30x.

When x = 50 hours, the charges for Mechanic A is given by:

y = 25x + 100

y = 25(50) + 100

y = $1,350

When x = 50 hours, the charges for Mechanic B is given by:

y = 30x

y = 30(50)

y = $1,500

In conclusion, we can logically deduce that Mechanic B charges a higher fee than Mechanic A.

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The thieves could take approximately 1555 bars of platinum.

Pt stands for platinum, an atomic number 78 chemical element. It is a thick, malleable, ductile, very inert, silvery-white-colored transition metal. Its name comes from the Spanish diminutive platina, meaning "silver"

One 1 lb bar of platinum has a volume of approximately 0.11 cubic feet. Assuming the density of platinum to be approximately 21 g/cm^3, the weight of 1 lb bar of platinum is approximately 0.45 kg. The maximum payload capacity of the small truck is approximately 317 kg. Hence, the thieves could take approximately 700 / 0.45 = 1555 bars of platinum.

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Factor out x from the expression

answer : x×(x-2y)

Answer:

900

Step-by-step explanation:

90 x 10

i think it is 326.7 but i really not sure

In a connection that is represented by an exponential function, the independent variable's proportional change is unchanged with a constant change in the independent variable.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.

The fundamental exponential function generally has the shape,

y = nakx-------

(0,3) is the function's y intercept.

This location has to satisfy the equation (1). So let's substitute in order to get,

3 = na k(0)

⇒ 3 = n x a 0

⇒ 3 = n x 1

⇒ n = 3

Our equation 1 now changes.

y = nakx-------

Noting that the graph crosses through,(1 ,1) it must also satisfy its equation because it does so. Equation (2) can be solved by substituting this point, giving us

1 = 3ak (1)

⇒ 1/3 = ak

Now let's enter the value of ak = 1/3 into equation (3) to get,

y = 3(1/3)x

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Answer:

a) linear function

b) quadratic function

Step-by-step explanation:

a) j(n) is a linear function since 5 is added everyday.

b) t(n) would be a quadratic function because the total amount of jumping jacks wouldn't have the same number that is beiung added.

day 1 = 5

day 2 = 15

day 3 = 30

day 4 = 50

day 5 = 75

This is showing that at first 10 jumping jacks are added but then for day 2 15 are added, for day 3 20 are added and so on.

The length of the arc SU is given by 1.63978 units.

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The angle ∠STU=94 and ST=17

Thus ST forms the radius of the circle.

Now we know the angle subtended by the arc is given by

SU=2πr×94°/360

  =2×3.14×0.2611

  =1.63978 units

Hence, The length of the arc SU is given by 1.63978 units.

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Answer:

-299 ft

Step-by-step explanation:

Start: -184 ft

Climb: + 53 ft

Descent: - 168 ft

-184 ft + 53 ft - 168 ft = -299 ft

Answer: -299 ft