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A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?

[tex]\textit{volume of a rectangular prism}\\\\ V=Lwh ~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ h=1.8\\ L=4.2\\ V=26.46 \end{cases}\implies \begin{array}{llll} 26.46=(4.2)w(1.8)\implies 26.46=7.56w \\\\\\ \cfrac{26.46}{7.56}=w\implies 3.5=w \end{array}[/tex]

Answer:

320

Step-by-step explanation:

20*2 = 40

360 - 40 = 320

Answer:

C

Step-by-step explanation:

The radius of circle 2 is bigger than circle one, so the diameter will be bigger too.

The circumference of the circle 1 is less than the circumference of the circle 2.

Circumference is "a distance around the circle".

According to the question,

The area of the circle 1 is 6π and the area of the circle 2 is 7π.

Area of the circle = π.r²

Radius of the circle 1 is less than the radius of the circle 2 this implies diameter of the circle 2 is greater than diameter of the circle 1.

Hence, the circumference of the circle 1 is less than the circumference of the circle 2.

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Answer:

2xa(5x^2 + 3a).

Step-by-step explanation:

We are factorising:-

Divide the left side by 2xa and place the result in the parentheses:

10x^3a+6xa^2 = 2xa(5x^2 + 3a )

Answer:

2xa(5x² +3a-1)

Step-by-step explanation:

10x³a+ 6xa²-2xa=2xa-2xa

10x³a+ 6xa²-2xa=0

Factor 10x³a+ 6xa²-2xa:

2ax(5x² + 3a -1)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x- 5) (x - 5) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x- 5) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x- 5) [/tex]

value x lies between :

[tex]\qquad \sf  \dashrightarrow \: - 5 \leqslant x \leqslant 5[/tex]

if the value of x is taken -5

[tex]\qquad \sf  \dashrightarrow \: - 5 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 10[/tex]

if value of x is taken as 5

[tex]\qquad \sf  \dashrightarrow \:5 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:0[/tex]

So, the possible values of the required expression lies between ~

[tex]\qquad \sf  \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0[/tex]

I hope you understood the whole procedure. let me know if you have any doubts in given steps ~

The cylinder is a three-dimensional shape and it has a radius, diameter and a height

Assume the square has the following dimensions:

Base dimensions = x

Height = h

Assume the cylinder has the following dimensions:

Radius  = r

Height = h

When the square is drilled out, the lateral surface area would be:

Lateral Area = Cylinder - Square

This gives

[tex]Lateral = 2\pi rh - 4xh[/tex]

Factor out 2h

[tex]Lateral = 2h( \pi h - 2x)[/tex]

Using the same dimensions in (a), we have:

Total surface Area = Cylinder - Square

This gives

[tex]Area = 2\pi r(r +h) - 2(2x^2 - xh)[/tex]

Factor out 2

[tex]Area = 2[\pi r(r +h) - (2x^2 - xh)][/tex]

Using the same dimensions in (a), we have:

Base area = Cylinder - Square

So, we have:

[tex]Base = \pi r^2 - x^2[/tex]

Using the same dimensions in (a), we have:

Volume = Cylinder - Square

So, we have:

[tex]Volume = \pi r^2h - x^2h[/tex]

Factor out h

[tex]Volume = h(\pi r^2 - x^2)[/tex]

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Answer:

Option C

Step-by-step explanation:

See here the net seems like a equilateral triangle

Hence option C

Answer:

[tex]\sqrt{241}[/tex]

Step-by-step explanation:

3+1=4

7+8=15

4^2=16

15^2=225

16+225=241

[tex]\sqrt{241}[/tex]

Answer:

  walk area = 125.6 m²

Step-by-step explanation:

You are asked for the area of a sidewalk of given width that is around a circle of given radius. The pattern you're asked to fill in would have you compute the area of the inner circle, and of the outer circle, then find the difference between the areas.

__

The formula for the area of a circle is ...

  A = πr²

The radius is shown as 11 m, so its area is ...

  A = π(11 m)² = 121π m² = 379.94 m²

The radius is shown as 9 m, so its area is ...

  A = π(9 m)² = 81π m² = 254.34 m²

The difference between the two areas is ...

  walk area = big circle area - small circle area

  walk area = 379.94 m² -254.34 m² = 125.6 m²

_____

Additional comment

The area can also be computed by multiplying the centerline length of the sidewalk by its width. The center of the walk is (9+11)/2 = 10 m from the centers of the circles, so the circumference (centerline length) is

  C = 2πr = 2(3.14)(10 m) = 62.8 m

The width of the sidewalk is 11 -9 = 2 meters, so its area is ...

  (2 m)(62.8 m) = 125.6 m² . . . . sidewalk area

Answer:

(b)the marble is odd-numbered.P(odd)=

Answer:

x = 48

Step-by-step explanation:

5x + 12 = 6x - 36 ( subtract 6x from both sides )

- x + 12 = - 36 ( subtract 12 from both sides )

- x = - 48 ( multiply both sides by - 1 )

x = 48

Step-by-step explanation:

5x + 12 = 6x - 36

5x + 12 - 6x = - 36

- x = - 36 - 12

- x = - 48

Now change the sign of both side of the equation...

x = - ( - 48)

x = 48...

Answer

Step-by-step explanation:

easy

Answer:

B

Step-by-step explanation:

1,2  2,3  1,6  1,9  3,10  2,11  1,13  3,15  3,16  2,17

x,y

x= how many goals they made were the same

y= the actual number of soccer goals

(This is just how I organized how to make the chart)

The area of the rhombus is 24 square units.

This has to do with the quadrilateral that each side are of the same length.

Given the data:

Length WY is 3 - (-5) = 8 units.

Length XZ is 4 - (-2) = 6 units.

Hence, the area of the rhombus WXYZ is 1/2 of the diagonal length:

1/2 * 8 * 6

= 24 square units.

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Answer:

A

Step-by-step explanation:

Answer:

c=9.5 centimeters

Step-by-step explanation:

a^2+b^2=c^2

9^2+3^2=c^2

90=c^2

c=[tex]\sqrt{90}[/tex]

c=9.487

c=9.5

Data set T has strong linear relationship as it is a perfect positive correlation

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

In other words, it reflects how similar the measurements of two or more variables are across a dataset.

When one variable changes, the other variables change in the same direction or opposite direction.

Perfect positive correlation :When one variable changes, the other variables change in the same direction.

Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.

Part A &B  : Data set T has strong linear relationship as it is a perfect positive correlation

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Answer:

AB : XY = 2 : 3

Step-by-step explanation:

We know that :

So, if the areas ΔABC and ΔXYZ are in the ratio 4 : 9, then :

Answer:

x= 96

Step-by-step explanation:

I know this is might not be the best reasoning, but if 56+40=96, then the other consecutive angle should be 96 degrees by the Consecutive Interior Angles theorem.

Answer:

A

Step-by-step explanation:

You have to simplify the brackets in turn.

3 times x^3- 7x+1 = 3x^3- 21x+ 3

then do 3 times x + 4= 3x + 12

you then add them all together, if they have a power add them, if they just have an x add them, and if they are just a number add them.

So it goes to 3x^3- 24x - 9,

this is because 3x^3 cant be added/ subtracted by anything, -24x is made from -21x- 3x, and -9 is made from 3 - + 12, so this means 3 - 12 = -9.

I hope this helps, have a lovely day.

Using the given box and whisker plot, it is found that the mean most likely exceeds the median for Elaine, hence option B is correct.

A box and whisker plot shows three things:

In this problem:

The mean most likely exceeds the median for Elaine, hence option B is correct.

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Step-by-step explanation:

100% = $8.00

1% = 100%/100 = 8/100 = $0.08

the price went up by $8.48 - $8.00 = $0.48.

how many % is this ?

as many % as 1% fits into this difference :

0.48 / 0.08 = 6%

the price increase was 6%.

Answer:

-6.4

Step-by-step explanation:

√2(√3×2 - √1×8) = -6.41472901342

Round to the nearest tenth = -6.4

Answer:

2/3 or .66 repeated

Step-by-step explanation:

1 1/3= 1.33

1.33 + .66..7 is 2

Answer:

[tex]\huge\boxed{\sf x = \frac{2}{3}}[/tex]

Step-by-step explanation:

Let the number be x

Given condition:

[tex]\displaystyle 1 \frac{1}{3} +x=2\\\\Subtract\ 1\frac{1}{3} \ to \ both \ sides\\\\x = 2-1\frac{1}{3} \\\\x = \frac{2 \times 3}{1 \times 3} - \frac{4}{3} \\\\x = \frac{6}{3} - \frac{4}{3} \\\\x=\frac{6-4}{3} \\\\\boxed{x = \frac{2}{3}} \\\\\rule[225]{225}{2}[/tex]

Answer:

Width = 9ft.

Length=22ft.

Step-by-step explanation:

The value of two plums and a peanut, divided by a grape and a peanut is 11

The given parameters are:

Substitute Grape = 2  in Acorn + 3 grapes = 14

Acorn + 3 *2  = 14

Acorn + 6  = 14

Subtract 6 from both sides

Acorn  = 8

Substitute Acorn  = 8 in Acorn = 1/2 Plum

8 = 1/2 Plum

Multiply both sides by 2

Plum = 16

So, we have:

Peanut = 1

Grape = 2

Acorn  = 8

Plum = 16

The value of two plums and a peanut, divided by a grape and a peanut is:

(2 plums + peanut)/(grape + peanut)

This gives

(2 * 16 + 1)/(2+ 1)

Evaluate

11

Hence, the value of two plums and a peanut, divided by a grape and a peanut is 11

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Answer:

Answer is 2^2x+6=2^6 since it is equivalent to 4^x+3=64

The equivalent equation of  [tex]4^x^+^3=64[/tex] is [tex]2^6^x^+^6=2^6[/tex], option B is correct.

The given equation is [tex]4^x^+^3=64[/tex]

Four to the power of x plus three equal to sixty four

x is the variable in the equation

We have to find the equivalent equation

We know that 2×2×2× 2×2×2 , 2⁶=64

[tex]4^x^+^3=2^6[/tex]

Now [tex](2^2)^x^+^3=2^6[/tex]

[tex]2^6^x^+^6=2^6[/tex]

Hence, the equivalent equation of  [tex]4^x^+^3=64[/tex] is [tex]2^6^x^+^6=2^6[/tex], option B is correct.

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Answer:

The approximate value of x in the square that the diagonals meets to form four right angles is 5.7 units

Using Pythagoras theorem the value of x can be found as follows:

c² = a² + b²

where

Therefore,

8² = x² + x²

64 = 2x²

x² = 64 / 2

x = √32

x = 5.65685424949

x = 5.7 units

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Answer: 5.7 units

Step-by-step explanation: