The current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water?​

Answer:

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Use the compound interest formula:

Where:

Plugging in the values, we get:

The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to  7x³.

To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.

To find the factors, we can break each term down into its prime factors:

21x⁴ = 3 * 7 * x * x * x * x

49x³ = 7 * 7 * x * x * x

The common factors are 7 and x³. To find the GCF, we multiply these common factors together:

GCF = 7  * x³

GCF = 7x³

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The ratios for the rectangles and the ovals is 4 : 3

From the question, we have the following parameters that can be used in our computation:

Rectangle = 4

Oval = 3

The ratio can be represented as

Ratio = Rectangle : Oval

When the given values are substituted in the above equation, we have the following equation

Rectangle : Oval = 4 : 3

The above ratio cannot be further simplified

This means that the ratio expression would remain as 4 : 3

Hence, the solution is 4 : 3

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The kite string is 331.77 feet long.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for labeling. Where l represents the length of kite string.

h = 225 - 3 = 222 ft

Using trig. ratio:

sin 42° = 222/l

l = 222 / sin 42°

l = 331.77 feet

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Segment BF is 36 will be the accurate statement.

A triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.

From the given triangle, the following expression is true:

EC/FC = AC/BF+FC

Substitute the given parameters into the formula to have:

20/30 = 24+20/BF+30

20/30 = 44/BF+30

2/3 = 44/BF + 30

2(BF+30) = 132

2BF + 60 = 132

2BF = 132 - 60

2BF = 72

BF = 36

Hence the correct statement will be that segment BF is 36

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The total distance she cover after running is 9600 meters

From the question, we have the following parameters that can be used in our computation:

Number of times = 12 times

Dimensions of the playground = 240 m by 160 m

The perimeter of the playground is calculated as

Perimeter = 2 * sum of dimensions

substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (240 + 160)

The total distance she cover is calculated as

total distance = 12 * 2 * (240 + 160)

Evaluate

total distance = 9600 meters

Hence, the total distance she cover is 9600 meters

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Answer:

d = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )

d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]

   = [tex]\sqrt{(-7)^2+3^2}[/tex]

   = [tex]\sqrt{49+9}[/tex]

   = [tex]\sqrt{58}[/tex]

The constant term of the polynomial 2x³-5x²+8x+3 is 3.

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.

The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.

The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.

Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.

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The given information is,$37.60 interest earned on a $460 investment at 8%.

Part:The amount of interest earned is called the part. Here, the amount of interest earned is $37.60. Hence the part is $37.60.

Percent:The rate per 100 units of the base is called the percent. Here, the percent rate is 8%.

Base:The original amount invested or borrowed is called the base. Here, the original investment amount is $460. Hence the base is $460.

Thus,

Part: $37.60

Percent: 8%

Base: $460.

Part: The part is the interest earned, which is $37.60.

Percent: The percent is 8%, which represents the annual interest rate.

Base: The base is the amount of the investment, which is $460.

The z- score of a person who scored 280 on the exam can be found to be - 0. 5.

A z-score indicates how many standard deviations an element is from the mean.

The formula is:

Z = ( X - μ ) / σ

The details here are:

X = 280, μ = 300, and σ = 40

The z - score is therefore :

Z = (280 - 300) / 40

= -20 / 40

= -0.5

In conclusion, the z - score of a person who scored 280 on the exam is -0.5. This means that their score is half a standard deviation below the mean.

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The results of increasing a gross by 10% is 158.4.

Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.

In mathematics, gross is written in figures as 144

increase a gross by 10%

= 144 + (10% × 144)

= 144 + (0.1 × 144)

= 144 + 14.4

= 158.4

Hence, 158.4 is the 10% increase in gross.

Complete question:

Calculate the increase in a gross by 10%.

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If f(x) = 1/343, then x = -3. The point on the graph of f when f(x) = 1/343 is (-3, 1/343).

A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph. Each point is identified by both an x and a y coordinate.

If f(x) = 1/343, then x = -3. This is because 343 = 7³, therefore the inverses is 1/343. The point on the graph of f when f(x) = 1/343 is (-3, 1/343

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Answer:

The ratio is 3:7

Step-by-step explanation:

You add 104+78

The un-simplified ratio is 78:182

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The surface area of the regular hexagonal pyramid is equal to 529.8 in² to the nearest tenth.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of nonagon × (n)number of side

apothem = s/[2tan(180/n)]

apothem = 10in[2tan(180/6)]

apothem = 5√3in

perimeter = 6 sides × 10in = 60 in²

Area of the bottom hexagon = 1/2 × 5√3 × 60 in²

Area of the bottom hexagon = 259.8075 in²

Area of one triangle side face = 1/2 × 10in × 9in = 45 in²

Area of 6 triangle side faces = 6 × 45 in² = 270 in²

Surface area of the regular pyramid = 259.8075 in² + 270 in²

Surface area of the regular pyramid = 529.8 in²

Therefore, the surface area of the regular hexagonal pyramid is equal to 529.8 in²

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Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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The estimated error in the calculated area is approximately 3.2ft²

To estimate the error in the calculated area of a square, use linear approximation or differentials.

The area of a square is given by the formula A = s², where s represents the length of a side.

Calculate the area of the square using the given side length of 16 ft:

A = (16 ft)²

A = 256 ft²

Now, let's consider the possible error in the side length, which is ±0.1 ft. Treat this error as a change in the side length (Δs) and use linear approximation or differentials to estimate the corresponding change in the area (ΔA).

Using linear approximation, express the change in the area as:

ΔA ≈ 2s Δs

Substituting the values:

ΔA ≈ 2(16 ft)(0.1 ft)

ΔA ≈ 3.2 ft²

Therefore, the estimated error in the calculated area is approximately 3.2ft².

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The probability p that the perdimos is also a female is 17/120

Conditional Probability is the possibility or likelihood of an event or outcome happening, based on the existence of a previous event or outcome.

How to determine this

When there were 17 females in class

And 20 male in class

When randomly selected, the female are 52

And males are 68

To calculate the selected volunteer is a student of the class.

= 20 + 17/52 + 68

= 37/120

To calculate the probability that the selected student is female.

= 17/52 + 68

= 17/120

= 0.14

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Answer:

Domain:  {-24, -12, -8, 9, 14, 50}

Range:  {23, 69, 83, 92, 97, 32}

Step-by-step explanation:

For a function like f(x), each coordinate is in the form (x, f(x)) aka (x, y)

Since our x-coordinates are -24, -12, -8, 9, 14, and 50, the domain of f(x) is {-24, -12, -8, 9, 14, 50}

Since our f(x) or y-coordinates are 23, 69, 83, 92, 97, and 32, the range is {23, 69, 83, 92, 97, 32}

Answer: where is the answer choices

Step-by-step explanation:

The probability of drawing the 2, 4, 6, and 8 of spades in that specific order is 0.0002.

The probability of drawing a specific card without replacement from a well-shuffled deck is 1/52 for the first card, 1/51 for the second card, 1/50 for the third card, and 1/49 for the fourth card.

We wish to draw the specific cards (2, 4, 6, and 8 of spades) in that specific order.

The probability will be:

Probability = (1/52) * (1/51) * (1/50) * (1/49)

probability = 0.0002.

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The volume of water that the pool can hold is  150.72 cubic centimeters.

Remember that the volume of a cylinder of radius R and height H is:

V = pi*R²*H

Where pi = 3.14

For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft

Replacing that in the volume formula we will get:

V = 3.14*(4cm)²*3cm

V = 150.72 cubic centimeters.

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The  quotient of 302 ÷ (9.1 x [tex]10^4)[/tex] in scientific notation is approximately 3.31868131868 x [tex]10^1[/tex]

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x[tex]10^1[/tex]

Therefore, the quotient of 302 ÷ (9.1 x [tex]10^4[/tex]) in scientific notation is approximately 3.31868131868 x[tex]10^1[/tex]

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Answer:

(1) 2x - 2y = 2(x - y)

(2) 5x^3 + 15xy = 5x(x^2 - 3y)

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The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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The proof of ΔRUV ≅ ΔSUT is shown below.

Given that:

RSTV is a rectangle and U is the midpoint of VT.

Here, We have to Prove:

⇒ ΔRUV ≅ ΔSUT

Now, We can prove as;

Statement                               Reason

1) RSTV is a rectangle               Given

2) Angle V and T are                Because every angle in a rectangle is 90

right triangle.

3) ∠V ≅ ∠T                               Because both are right angle.

4) U is the midpoint of VT.        Given

5) VU = UT                                By midpoint theorem.

6) VR ≅ TS                                Opposite sides of rectangle.

7) ΔRUV ≅ ΔSUT                       By SAS congruency theorem.

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The equation y = 3x - 2. can be placed in table as shown below. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.

In this table, each row represents a pair of values (x, y) that satisfy the equation y = 3x - 2. For example, when x is -2, y is calculated as 3(-2) - 2 = -8. Similarly, for the other values of x, the corresponding values of y are calculated accordingly.

Here's a table showing the values of x and the corresponding values of y for the equation y = 3x - 2:

x y

-2 -8

-1 -5

0 -2

1 1

To fill in the table, substitute each value of x into the equation and calculate the corresponding value of y. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.

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The difference between the record high and low temperatures is 149 degrees.

A negative number is a number that is less than zero. A negative number usually has a minus sign in front of it. An example of a negative number is -35. A positive number is a number that is greater than zero. An example of a positive number is 10.

In order to find the difference between two or more numbers, subtract the numbers from each other.

Difference between the temperature = record high temperature - record low temperature

114 - -35

114 + 35 = 149 degrees

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By ASA congruency triangle KBH is congruent to triangle NWH.

Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.

From the given figure,

Consider ΔKBH and ΔNWH,

∠KHB=∠NHW (Vertically opposite angles)

∠HKB=∠HWN (Interior alternate angles parallelogram)

KH=HW (Diagonals bisect each other)

By ASA congruency ΔKBH ≅ ΔNWH

Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.

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