A cruise ship traveled to Madagascar and
back. On the trip there it traveled 12 km/h
and on the return trip it went 18 km/h.
How long did the trip there take if the
return trip took six hours?
A) 12 hours
C) 9 hours
B) 10 hours
D) 7 hours

The binary number (100\()_2\) in decimal system is written as \(4_{10}\).

Given:

Binary number = \((100)_2\)

Converting Binary to decimal system:

Binary:

In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one).

Decimal:

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

\(100_2 = 1*2^2 + 0*2^1+0*2^0\)

we know that,

\(2^0 = 1\)

\(2^1 = 2\\2^2 =4\)

substitute these values

\(100_2 = 1*4 + 0*2 + 0*1\)

= 4 + 0 + 0

= 4 + 0

= \(4_{10}\)

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Answer:

The correct option is A. Parallel line.

Answer:

-5, -2/3, 7, 3/4

Step-by-step explanation:

The solutions of S(x) = 0 satisfy one of the equations:

3x^2 + 17x + 10 = 0, x - 7 = 0, 4x - 3 = 0

The latter two are straightforward to solve:

x = 7 and x = 3/4

We now factor 3x^2 + 17x + 10 = 0

Note 10 = 5 * 2, 3 = 3 * 1 and 3 * 5 + 2 - 17.

So, we can factor it as (3x + 2) (x + 5) = 0

Thus, we also have solutions -2/3, -5.

Given the parameterization

\(\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k\)

take the normal vector to be

\(\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k\)

(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)

Compute the magnitude of the normal vector.

\(\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}\)

so that the area element reduces to

\(dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du\)

Evaluate the integrand at \(\vec r\) to get

\(\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}\)

The surface integral reduces to

\(\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}\)

Two solids with the same surface and different volumes are a cube of side length of 1 unit, and a sphere of radius of 0.69 units.

First, let's define a cube of a side length of 1 unit. The surface of this cube is equal to 6 times the area of one of the faces, or:

S  = 6*(1 unit square) = 6 units square.

And the volume is equal to the side length cubed, so we have:

V = (1 unit)^3 = 1 unit cubed.

Now, let's find a sphere with the same surface than our cube. For a sphere of radius R, the surface is:

S = 4*3.14*R^2

Then we must have:

4*3.14*R^2 = 6 units square

R = √(6/(4*3.14)) units = 0.69 units.

And the volume of this sphere is:

V = (4/3)*3.14*R^3 = (4/3)*3.14*(0.69 units)^3 = 1.38 cubic units.

So the sphere has the same surface and more volume.

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Answer:

50 mm

Step-by-step explanation: i did the test and i got it right

Answer:

50 millimeters are in 5 centimeters. You have to multiply the value by 10 to get your answer when converting centimeters to millimeters.

__________________________________________________________

Questions related to this topic? Ask me in the comments box.

Answer: 6 + 18j

Step-by-step explanation: you distribute the 3

Answer:

It would be 3/2 as 1/2 is 50%, 2/2 or 1 is 100% and 3/2 is 150%

Step-by-step explanation:

The unit rate for Option A is $4.4 per pound of gummy bears.

The unit rate for each option is a mathematical expression that compares two quantities of different measures by dividing one quantity by the other.

The unit rate is used to determine how much an item costs per unit of measure.

To find the unit rate for each option, we can use the following formula: Unit rate = price ÷ weight Option A: $15.40 for 3.5 lbs of gummy bears Unit rate = 15.40 ÷ 3.5Unit rate = $4.4 per pound of gummy bears.

Therefore, the unit rate for Option A is $4.4 per pound of gummy bears.

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Here is the complete question given below:

The unit rate for each option. 9. Option A: $15.40 for 3.5 lbs of gummy bears. $7.65 for 1.8 Ibs of gummy bears.

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

7x2−4x/5

Step-by-step explanation:

7x2−4x over 5

Answer:

slope = \(\frac{5}{9}\) , y- intercept = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

5x - 9y = 45 ( subtract 5x from both sides )

- 9y = - 5x + 45 ( divide through by - 9 )

y = \(\frac{-5}{-9}\) x + \(\frac{45}{-9}\) , that is

y = \(\frac{5}{9}\) x - 5 ← in slope- intercept form

with slope m = \(\frac{5}{9}\) and y- intercept c = - 5

Answer:

It looks like you are trying to solve some math problems and are looking for help filling in some information on a geometry reference sheet. Here are the answers to the questions you provided:

A Median:

Originates at the vertex of the triangle.

Connects the vertex to the midpoint of the opposite side.

Divides the side into two equal parts.

To solve for x in the equation 2x + 1 = 0, you can subtract 1 from both sides to get 2x = -1. Then divide both sides by 2 to get x = -1/2.

To solve for x in the equation 3x - 31 = 0, you can add 31 to both sides to get 3x = 31. Then divide both sides by 3 to get x = 31/3 = 10 1/3.

An Altitude:

Originates at the vertex of the triangle.

Connects the vertex to the line containing the opposite side.

Divides the opposite side into two equal parts.

To solve for x in the equation 10x + 9 = 6x + 21, you can subtract 6x from both sides to get 4x + 9 = 21. Then subtract 9 from both sides to get 4x = 12. Finally, divide both sides by 4 to get x = 3.

Without more context, it is not possible to solve for x in the equation (pa + 53)*(5x + 2) = 0. Please provide more information about the problem you are trying to solve.

Step-by-step explanation:

Problem 1

Answers:

It costs 1.72 dollars to send a letter that is 1.5 ounces

It costs 1.72 dollars   to send a letter that is 2 ounces

In short, both answers are  1.72 dollars

--------------------------------

Explanation:

The piecewise function may seem really ugly and complicated, and I can understand why many don't like them, but they aren't too bad once you get used to it.

A piecewise function is simply a collection of many functions glued together. Instead of listing four different functions, your teacher has combined them all into one super function of sorts.

Here are the rules for this function

As you can see, the definition of F(w) will change depending on what w is.

If the weight is w = 1.5 ounces, then we're on the interval \(1 < w \le 2\) since 1.5 is between 1 and 2. So we go for the second definition shown above and we conclude that it will cost $1.72 to send this 1.5 ounce letter.

If you wanted, you could rewrite those four bulleted points into this equivalent form

which is a less mathematical way of stating it. It might also help to make it into a chart, which would help customers better who may not want to deal with math.

A letter that's 2 ounces will cost $1.72 as well since w = 2 makes \(1 < w \le 2\) true.

In short, both the 1.5 ounce and 2 ounce letters cost $1.72 each.

===========================================================

Problem 2

Answer: The graph is shown below (attached image)

--------------------------------

Explanation:

We have what is called a step function, or a staircase function. Either name will work. The graph consists of the horizontal portion of the stairs, but the vertical parts of the stairs are not drawn (or else we wouldn't have a function due to the vertical line test).

Note the placement of the open and closed endpoints. An open endpoint excludes the value in question, while a closed endpoint includes the value.

For instance, we have an open endpoint at (1, 1.72) while there's a closed endpoint at (1, 1.15). Each closed endpoint is directly connected to the "or equal to" portion of the inequality sign, and each open endpoint does not have the "or equal to" portion.

As the graph shows, we basically have the a certain flat cost for the four different regions. This corresponds to the costs given in the piecewise function. Each height is drawn from the list {1.15, 1.72, 2.29, 2.86}

The point labels of A,B,C,D,E,F,G,H are optional. I only put them in there to help identify which endpoints are open or closed. Points on the left side of each segment, or horizontal stair component, are open endpoints. Points on the right side are closed endpoints.

Answer:I think it Is the second

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

92.4/2.8 = 33

Answer:

[See Below]

Step-by-step explanation:

\(Hey~There!\)

_____________________

→ Divide:

_____________________

\(Hope~this~helps!\)

\(-Shane,~SpamIsTheMan :)\)

Answer:

17

Step-by-step explanation:

3(5)+2=17

Answer:

17

Step-by-step explanation:

3x+2   substitute 5 for x

3(5) +2 distribute

15+2 solve

17

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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Answer:

(4.44 + 0.55n) / n = p

(4.44 + 0.55 * 6) / 6 = p

(4.44 + 3.3) / 6 = p

(7.74) / 6 = p

1.29 = p

or

4.44 / 6 + 0.55 = p

Step-by-step explanation:

n = number of bottles

p = 1.29

Y=2+-4x

Step-by-step explanation:

Hope ot helps

Answer:

code answer :unknown 976765 answer .geometric

9514 1404 393

Answer:

  1 : 48

Step-by-step explanation:

The scale is ...

  drawing : world =

  2 in : 8 ft = 2 in : 96 in

  = 2 : 96 = 1 : 48

Answer:

The calculated value  t = 1.3788 < 2.0262 at 0.05 level of significance

the null hypothesis is accepted

There  is no significant difference between  their counterparts across the nation

Step-by-step explanation:

Step(i):-

Given that the mean of the U.S residents  = 1.65

Given that the size of the sample 'n' = 38

Mean of the sample = 1.84

Given that the standard deviation of the sample (S) = 0.85

Step(ii):-

Null hypothesis:H₀:

There  is no significant difference between  their counterparts across the nation

Alternative Hypothesis:-H₁:

There  is  a significant difference between  their counterparts across the nation

Test statistic

                \(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)

               \(t = \frac{1.84-1.65}{\frac{0.85}{\sqrt{38} } }\)

              t =  1.3788

Degrees of freedom

                ν = n-1  = 38-1 = 37

t₀.₀₅ ,₃₇ =    2.0262

The calculated value  t = 1.3788 < 2.0262 at 0.05 level of significance

Null hypothesis is accepted

Final answer:-

There  is no significant difference between  their counterparts across the nation.

The value of the product of the number as given in the task content is; Choice B; 1.

It follows from the task content that the numbers whose product are to be determined are; ¾ and 1⅓.

To effectively multiply, we must convert the mixed number to a fraction as follows;

1⅓ = 4/3.

Hence, the product is; 4/3 × 3/4 = 12/12 = 1.

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Answer:

Dr Domeur is using repeated measures t-test

Step-by-step explanation:

Dr Dormeur is using the repeated measures t test also known as within-subjects design because the design is between participants. Repeated Measures assesses the change in a continuous outcome across time or within-subject.

Dr Domeur makes measurements using only one group of subjects, and the tests on each subject can be repeated more than once after different treatments. From the question, the researcher Dr Domeur uses the same subjects with every condition of the research and the control. Repeated measures are collected in a longitudinal study that assesses change over time.

Answer:

12.56 units

Step-by-step explanation:

Hello!

The circumference of a circle given the diameter is \(C = d\pi\), where d is the diameter.

Given that π is 3.14, solve for the circumference.

The circumference is 12.56 units.

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer: Rejecting the mean weight of each cake as 500 gram when H subscript 0 equals 500

Step-by-step explanation:

Given that :

Null hypothesis : H0 =500

Alternative hypothesis : Ha < 500

Type 1 Error: Type 1 error simply occurs when we reject the Null hypothesis when the Null is true. Alternatively, type 11 error occurs when we fail to reject a false null hypothesis.

Hence, in the scenario above, a type 1 error will occur when we reject the mean weight as 500 even though the Null hypothesis is True.

Answer: A) Rejecting the mean weight of each cake as 500 grams when H₀ = 500.

Step-by-step explanation:

Type I error is when we incorrectly reject a true null hypothesis