A bicyclist pedals 40 miles in 3 hours. Write the bicyclist's speed as a rate (but not a unit rate yet). Then use the dropdown menus to report the bicyclist's rate. Numerator (top of the fraction): [ Select ] [ Select ] Denominator (bottom of the fraction): [ Select ] [ Select ]

Answer:

? = x = 12

Step-by-step explanation:

Remark

This is a proportion question. A proportion is 2 equal ratios. The two triangles are similar, which means that a proportion can be set up.

Givens

? = x

x + 8

9

9 + 6

Equation

x/(x + 8) = 9 / (9 + 6)       Combine

Solution

x/(x + 8) = 9/15                Cross multiply

15x = 9(x + 8)                  Remove the brackets

15x = 9x + 72                  Subtract 9x from both sides

15x - 9x = 72                   Combine

6x = 72                            Divide both sides by 6

6x/6 = 72/6

x = 12

Answer x = 12

From the calculation below, the actual difference, if Robert had read the numbers correctly, is 168.

Let X represents the number from which subtrahend is subtracted.

Therefore, we can calculate X as follows:

X – 17 = 222

X = 222 + 17 = 239

If the subtrahend is read correctly as 71 and then subtracted from 239, we have:

Actual difference = 239 – 71

Actual difference = 168

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Answer:

Volume

For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3

For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, [tex]\pi[/tex] = 3.14
V = radius^2 x height x [tex]\pi[/tex]
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)

Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3

Surface Area

Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2

A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)

Semi-circular prism:
A = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2

Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2

Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.

Answer:

[tex]\dfrac{1}{64}[/tex]

Step-by-step explanation:

Hemi-, demi- and semi- are prefixes which mean half.

When applied to musical notation, each time a prefix is added it means the note's value is halved.

Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.

[tex]\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}[/tex]

Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.

Based on the difference in the observed means given, we can infer that energy drink does indeed have an effect on performance.

First find the observed mean difference:

= 11.6 - 10.8

= 0.8 seconds

When the exercise is done only once, we see that on average, those who took the energy drink were faster and so finished earlier than those who didn't.

We can therefore infer that the energy drink has an effect on performance.

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Answer:

the third option

Step-by-step explanation:

because the numbers down there are the coefficients of the top equations

Answer:

10

Step-by-step explanation:

no. of students in each group=164/18=9.111111...=10 (nearest 10)

Answer:

8

Step-by-step explanation:

When rounding to the nearest 10:

Therefore:

164 rounded to the nearest 10 = 160

18 rounded to the nearest 10 = 20

To approximate the number of students in each year group, divide the rounded number of students by the rounded number of groups:

⇒ 160 ÷ 20 = 8

The expression which represents Sherly's total income is 7e + 13n.

The cost price represents the specific value that represents unit price purchased.

Here,

total pair of earrings = e

total pair of necklaces = n

Cost of 1 pair of earring = $ 7

Cost of 1 necklace = $ 13

earning from earring = 7e

earning from necklace = 13n

Total earning = earning from earring + earning from necklace

Total earning = 7e + 13n

Thus, the expression which represents Sherly's total income is 7e + 13n.

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Step-by-step explanation:

mean value is always the sum of all data divided by the number of data points.

we can see just by looking at the numbers that team B is way below team A.

mean team A : 1529/8 = 191.125

mean team B : 1141/8 = 142.625

so, clearly, team B had to make dinner.

the median is the value of all the data points, where half of the others are smaller, and the other half are bigger.

in case of an even number of data points (like here with 8), we find the 2 middle values and calculate the mean value of these 2 :

median team A : (180+189)/2 = 184.5

median team B : (143+134)/2 = 138.5

the mode is the number in the set of data that occurred must often. if they are all unique, then they ALL are the mode. it is NOT 0 or empty. it is then really all the data points.

mode team A : 212

mode team B : 99, 102, 105, 134, 143, 145, 202, 211

if we take 30 to be the 100%, what is 27 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90[/tex]

Using the slope concept, it is found that the distance from point A to point B is of 465 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

To find the horizontal position at point A, we have that:

tan(10º) = 107/dA

dA = 107/tan(10º)

dA = 607.

For the horizontal position at point B, we have that:

tan(37º) = 107/dB

dB = 107/tan(37º)

dB = 142.

Hence the distance is given by:

D = dA - dB = 607 - 142 = 465.

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The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.

Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;

Adjacent supplementary are angles with a common vertex and arm.

Non- adjacent supplementary angles are angles without a common vertex or arm.

∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.

They add up to 180°.

∠ BAC = 110° and ∠CAD = 70°

Hence, the angles could be 110° and 70°.

Note, this is an overview as the question is not complete.

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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.

Step-by-step explanation: Edmentum Answer

Answer:

True

Step-by-step explanation:

Using the combination formula, it is found that the number of candidates that can get a unique number sequence is given by:

b. 45.

The order of the pieces is not important, hence the combination formula is used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 2 pieces are taken from a set of 10, hence the number of sequences is given by:

[tex]C_{10,2} = \frac{10!}{2!8!} = 45[/tex]

Which means that option b is correct.

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Answer:

35 hrs

Step-by-step explanation:

Hope this helps! Have a great day!!

Answer:

A

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{120}{360}[/tex]

     = 2π × 8 × [tex]\frac{1}{3}[/tex]

    = 16π × [tex]\frac{1}{3}[/tex] = [tex]\frac{16\pi }{3}[/tex] m

Answer:

y = (1/3)*x + 5

Step-by-step explanation:

Step 1: determine slope or m

m = change in y-coordinates ÷ change in x-coordinates

m = (4-7)/(-3-6) = -3/-9 = 1/3

Step 2: determine y-intercept or b

y = m*x + b

y = (1/3)*x + b

4 = (1/3)*(-3) + b

4 = -1 + b

b = 5

Step 3: substitute values for m and b into the slope intercept equation

y = (1/3)*x + 5

The expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]

The points are given as:

(-3, 4) and (6, -2)

The distance between two points is calculated using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

This gives

[tex]d = \sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]

Hence, the expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]

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Answer:

the sequence begins as {4, 7, ... }

Step-by-step explanation:

a(n) = 3n + 1

The first term is a(1) = 3(1) + 1 = 4, and

the second term is a(s) = 3(2) + 1 = 7

So the sequence begins as {4, 7, ... }

Answer:

C

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{RS}{FG}[/tex] = [tex]\frac{ST}{GH}[/tex] ( substitute values )

[tex]\frac{RS}{21}[/tex] = [tex]\frac{4}{12}[/tex] ( cross- multiply )

12 RS = 84 ( divide both sides by 12 )

RS = 7 cm

Based on the information shown through the bar graph, a misrepresentation of the data is that: B. the categories along the horizontal axis are missing one of the days.

A bar graph can be defined as a type of chart that is used for the graphical represent of data (information), especially through rectangular bars or vertical columns.

Based on the information shown through the bar graph in the image attached below, we can logically deduce that a misrepresentation of the data is that the categories along the horizontal axis are missing one of the days (Friday).

In conclusion, this bar graph misrepresented the data because Friday is missing from the categories along the horizontal axis.

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

Explanation:

A full circle of radius r = 14 cm has a circumference of...

C = 2pi*r

C = 2*3.14*14

C = 87.92

This is the approximate distance around the circle, aka the perimeter.

Half of this is 87.92/2 = 43.96 which is the curved distance of this semicircle.

The straight line portion is 14+14 = 28 cm long.

The total perimeter of the semicircle shown is 43.96+28 = 71.96 cm

Answer:

21 liters

Step-by-step explanation:

14 liters + 7 liters = 21 liters

Hope this helped :)

Answer:

95

Step-by-step explanation:

The smallest number that divided by 6, 15, and 18 leavses 5 in each case is 95

Answer:

A.2x^2 + 12x

Step-by-step explanation:

Here,
f(x) = 1/2 x^2 + 3x
Now,
4.f(x) = 4(1/2 x^2 + 3x) = 4/2 x^2 + 12x = 2x^2 + 12x

Answer:

  5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

__

In navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

  N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

__

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

The final position is the sum of these two changes in position:

  3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

  = 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

__

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

  a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

  a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

  a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

Additional comment

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

  (0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

  OB = √(1.434² +5.048²) ≈ 5.248

Answer:

[tex](6x-5)(x^2+2)[/tex]

Step-by-step explanation:

[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]

Answer:

-12 and 2

Step-by-step explanation:

-12 × 2 is -24

and

-12 + 2 is -10

Answer:

The airplane flies 95 miles.

Step-by-step explanation:

Question:

An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.

Answer:

The plane flew 91 miles.

Step-by-step explanation:

City 1 - City 2

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

[tex]d_{1}[/tex] = [tex]\sqrt{(33 - 0)^{2} + (56 - 0)^{2}[/tex]

[tex]d_{1}[/tex] = [tex]\sqrt{33^{2} + 56^{2}[/tex]

[tex]d_{1[/tex] = [tex]\sqrt{1089 + 3136[/tex]

[tex]d_{1}[/tex] = [tex]\sqrt{4225}[/tex]

[tex]d_1[/tex] = [tex]65[/tex]

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

City 2 - City 3

[tex]d_2[/tex] = [tex]\sqrt{(33 - 23)^2 + (56 - 32)^2[/tex]

[tex]d_2[/tex] = [tex]\sqrt {10^2 + 24^2}[/tex]

[tex]d_2[/tex] = [tex]\sqrt{676}[/tex]

[tex]d_2[/tex] = 26

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

[tex]d_1 + d_2 = 65 + 26[/tex]

[tex]d_1 + d_2 = 91[/tex]

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

Therefore, the airplane flew a total of 91 miles through every city

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<3 Lots of love!

-The Book Worm.