5th grade math. correct answer will be marked brainliest.

The speed of current is [tex]\rm 2 \:km/h[/tex].

The relationship between distance, time and speed can be presented as:

[tex]\begin{aligned} \rm Distance &= Speed \times Time\\\\Speed &= \dfrac{\rm Distance}{Time} \\\\\rm Time &= \dfrac{\rm Distance}{\rm Speed} \end[/tex]

Calculations:

Given:

[tex]\begin{aligned} \rm Distance\: traveled\: on\: motorboat &= 25\:km\\\rm Speed\:of\:motorboat\:in\:still\:water &= 12\:km/h \end[/tex]  

Let the speed of the current be [tex]\rm x[/tex]

The speed of the boat traveling against the current is [tex]{(12 -\rm x) km/h}[/tex]

Time spent on motorboat is 10 hours less than time spent on raft.

Therefore:

[tex]\rm \dfrac{25km}{x\:km/h} - \dfrac{25km}{(12 - x)km/h} = 10[/tex]

The equation obtained will be:

[tex]\dfrac{25}{\rm x} - \dfrac{25}{(12-\rm x)} - = 10[/tex]

Multiplying both sides of the equation by [tex]\rm x(12 - x )[/tex]

[tex]\begin{aligned} \rm 25(12 - x) - 25x &= 10\times \rm x(12 - x)\\\\300 - 25x - 25x &= 120x - 10x^2\\\\300 - 50x &= 120x - 10x^2\\\\10x^2 - 120x - 50x + 300 &= 0\\\\10x^2 - 170x +300 &= 0\end[/tex]

Dividing the equation by 10

[tex]\rm x^2 - 17x + 30 = 0[/tex]

On factoring the equation,

[tex]\rm =x^2 - 2x -15x + 30 = 0\\\\=x(x - 2) -15(x - 2)\\\\=(x - 2)(x - 15)[/tex]

The values of x is 2 and 15.

Since speed of current i.e  [tex](12 -\rm x)km/h[/tex] cannot be negative, [tex]\rm x = 2[/tex] is the only acceptable value.

 Therefore the speed of current is 2 km/h.

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9514 1404 393

Answer:

  4. b =-√(3)/3

  5. 1/2

Step-by-step explanation:

4. The tangent is negative in the second quadrant. The sine value tells you the reference angle is 30°, so the actual angle is 150°. The corresponding tangent is ...

  tan(150°) = -(√3)/3

__

5. The cotangent is the inverse of the tangent, and vice versa.

  tan = 1/cot

  tan(θ) = 1/2

Answer:

x=8 x=16

Step-by-step explanation:

Given function:

Thinks:

Rewrite as:

Thereform, x=8 and x=16.

Answer:

55/4

Step-by-step explanation:

Answer:

a. -2

b. 48, -96, 192

Step-by-step explanation:

Answer:

[tex]C =\frac{5}{9}(F - 32)[/tex]

Step-by-step explanation:

Given

[tex]F = 1.8C + 32[/tex]

Required

Solve for C

[tex]F = 1.8C + 32[/tex]

Subtract 32 from both sides

[tex]F-32 = 1.8C + 32-32[/tex]

[tex]F-32 = 1.8C[/tex]

Divide both sides by 1.8

[tex]\frac{1}{1.8}(F - 32) = C[/tex]

Express the decimal as fraction

[tex]\frac{1}{18/10}(F - 32) = C[/tex]

[tex]\frac{10}{18}(F - 32) = C[/tex]

Simplify

[tex]\frac{5}{9}(F - 32) = C[/tex]

[tex]C =\frac{5}{9}(F - 32)[/tex]

Answer:

7

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

The height of the rock after t seconds is given by the following equation:

[tex]H(t) = -16t^2 + 96t + 112[/tex]

How long will it take in seconds for the rock to hit the ocean?

This is t for which:

[tex]H(t) = 0[/tex]

So

[tex]-16t^2 + 96t + 112 = 0[/tex]

Simplifying by -16

[tex]t^2 - 6t - 7 = 0[/tex]

So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]

[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]

[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]

[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]

Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.

Answer:

$20

Step-by-step explanation:

John=$12

Tony=$24

Eric=$20

multiply 12 by 2 to get Tony's money then subtract 4 for eric's money

Answer:

20

Step-by-step

Tony : 24

Eric : 24 - 4

Answer : 20

Answer:

34/15

Step-by-step explanation:

15/9 + 9/15 = 34/15

Answer:

2 4/15 or 2.27 (rounded up)

Step-by-step explanation:

15/9 + 9/15

75/45 + 27/45

102/45

2 12/45

2 4/15

Answer:

5 Probability

5.1 Probabilities

Probabilities are used to describe how likely or unlikely it is that something will happen.

Weather forecasters often talk about how likely it is to rain, or perhaps snow, in particular

parts of the country.

Worked Example 1

(a) When you roll a dice, which number are you most likely to get?

(b) If you rolled a dice 600 times how my sixes would you expect to get?

(c) Would you expect to get the same number of ones?

Solution

(a) You are equally likely to get any of the six numbers.

(b) You would expect to get a six in about 1

6

of the throws, so 100 sixes.

(c) Yes, in fact you would expect to get about 100 of each number.

Worked Example 2

Use one of the following to describe each one of the statements (a) to (d).

Certain

Very likely

Likely

Unlikely

Very unlikely

Impossible

(a) It will snow tomorrow.

(b) It will rain tomorrow.

(c) You win a car in a competition tomorrow.

(d) You are late for school tomorrow.

Solution

(a) Very unlikely for most places in Britain, especially in summer.

(b) Likely or Very likely in Britain in winter.

(c) Very unlikely if you have entered the competition. Impossible if you have not

entered the competition.

(d) Very unlikely, unless the school bus breaks down.

Answer:

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Step-by-step explanation:

Answer:

41,096

Hope it helps

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Thank you

Answer:

The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W. Ex: V = 5 in. The answer is 33 i believe

Step-by-step explanation:

100 hundred times larger

Answer:

Step-by-step explanation:

vdvfdvfdvfvfb fd

Answer:

255

Step-by-step explanation:

(15x2 - 16x - 15) = 270

(3- 5) = -15

 270

-  -15

= 255

The breadth of the rectangle is (-5x-3).

The area of a rectangle is given as the product of its length to its breadth.

[tex]\rm{Area\ of\ Rectangle = Length \times breadth\\[/tex]

area of a rectangle = (15x2 - 16x - 15)

length = (3x - 5)

[tex]Area\ of\ Rectangle = Length \times breadth\\(15x^2-16x-15)=(3x-5)\times breadth\\\\(3x-5)\times breadth=(15x^2-16x-15)\\\\breadth = \dfrac{(15x^2-16x-15)}{(3x-5)}\\\\breadth = (-5x-3)[/tex]

Hence, the breadth of the rectangle is (-5x-3).

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Answer:

42

Step-by-step explanation:

If y equals 3, then substitute y for 3, getting 45 - 3.  

45 - 3 is 42, so that's your answer.  

Hope this helped!  

Answer:

A' = (1, 2)

B' = (2, 3)

C' = (2, 4)

Step-by-step explanation:

Ok so you are given the scale factor of 1/3. You will basically multiply 1/3 to all of the values of point A, B, and C in order to find the values of point A', B', and C'.

A = (3, 6) ---> 3 × 1/3 = 1 and 6 × 1/3 = 2

A' = (1, 2)

B = (6, 9) ---> 6 × 1/3 = 2 and 9 × 1/3 = 3

B' = (2, 3)

C = (6, 12) ---> 6 × 1/3 = 2 and 12 × 1/3 = 4

C' = (2, 4)

Hope this helps and stay safe, happy, and healthy, thank you :) !!

Answer:

It is a 25 percent discount

I say this because 90/67.5 equals 75 and 25 + 75 equals what... 100

Answer:

75% off

Step-by-step explanation:

90*.75=67.50

Answer:

3/3 (1)

Step-by-step explanation:

1/3 plus 2/3 is 3/3.

Since the denominators are the same, you just keep the number the same and add the numerators (top numbers)

Answer: 159

Step-by-step explanation: 53x3

Answer:

Step-by-step explanation:

m < 1 = 53°

then

m< 3 = m<1 + 90° ( exterior angle of a triangle is equal to the sum of two opposite interior angles )

m<3 = 53° + 90°

       = 143°

hope it will help :)

Hi!!!

B. the point lies directly on the regression line.

Hope this helped!

Have a good day:)

The point lies directly on the regression line.

Option B is the correct answer.

A regression line is a straight line that represents the relationship between two variables in a scatter plot.

In other words, it is a line that best fits the data points in a scatter plot by minimizing the difference between the actual data points and the predicted values on the line.

We have,

When we talk about the residual of a data point in the context of regression analysis, we are referring to the difference between the actual value of the response variable (dependent variable) for that data point and the predicted value of the response variable based on the regression equation.

If a data point has a residual of 0, it means that the predicted value for that data point is exactly equal to the actual value of the response variable.

This can occur when the data point falls directly on the regression line, as in option B.

Thus,

The point lies directly on the regression line.

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