Sam needs to find the circumference of a circle with a diameter of 24 inches. He uses a calculator to find the circumference. Which answer is reasonable?

72.013678 in
75.398223 in
85.335372 in
80.332161 in

Answer:

x = 2 2/3

Step-by-step explanation:

6(x - 2) = 4

Distribute

6x - 12 = 4

Add 12 to each side

6x-12+12 = 4+12

6x = 16

Divide by 6

6x/6 = 16/6

x = 8/3

x = 2 2/3

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x = 2 \frac{2}{3}}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]6 \: ( \: x - 2 \: ) = 4[/tex]

➼[tex] \: 6x - 12 = 4[/tex]

➼[tex] \: 6x = 4 + 12[/tex]

➼[tex] \: 6x = 16[/tex]

➼[tex] \: x = \frac{16}{6} [/tex]

➼[tex] \: x = \frac{8}{3} [/tex]

➼[tex]\:x = 2 \frac{2}{3} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]6 \: ( \: x - 2 \: ) = 4[/tex]

➺[tex]\:6 \: ( \: 2 \frac{2}{3} - 2 \: ) = 4[/tex]

➺[tex] \: 6( \: \frac{8}{3} - 2 \: ) = 4[/tex]

➺[tex] \: 6 \: ( \: \frac{8 - 6}{3} \: ) = 4[/tex]

➺[tex] \: 6 \: ( \: \frac{2}{3} \: ) = 4[/tex]

➺[tex] \: 6 \times 0.667 = 4[/tex]

➺[tex] \: 4.002 = 4[/tex]

➺[tex] \: 4 = 4[/tex]

➺[tex] \: L.H.S.=R. H. S[/tex]

[tex]\boxed{Hence\:verified.}[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

Step-by-step explanation:

28 kg + 750 g = 28*1000 + 750

                          28000 + 750

                       = 28750 g

Number of sack = Total quantity of sugar ÷ quantity of sugar in a sack

                           = 28750 ÷ 500

                           =  57 sacks

Answer:

57 sacks

Step-by-step explanation:

28750 ÷ 500 =

57 sacks

Glad to help! :)

Answer:

x = 4

Step-by-step explanation:

Given that DE is parallel to AC then DE divides the sides proportionally, so

[tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex] , substitute values

[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3x = 2(x + 2) ← distribute

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Step-by-step explanation:

[tex]1) \\ - 2 \leqslant x \leqslant 1 \\ 2) \\ - 3 > x \geqslant 2 \\ 3) \\ x> 0[/tex]

[tex]4) \\ x \leqslant - 3 \\ 5) \\ - 4 \leqslant x \geqslant 1[/tex]

[tex]6) \\ - 2< x \leqslant 0[/tex]

Step-by-step explanation:

Objective: Circle Theorems

The arcs add up to 360 and they are in proportion so

[tex]3x + 3x + 4x + 5x = 360[/tex]

[tex]15x = 360[/tex]

[tex]x = 24[/tex]

So this means that Arc AB and BC measure is 72 each. Arc CD measure is 96 and Arc DA measures is 120.

Angle 1 measure is a inscribed angle of Arc CD.

So it measures

[tex] \frac{96}{2} = 48[/tex]

Angle 2 is a inscribed angle of Arc AB so it measures

[tex] \frac{72}{2} = 36[/tex]

Angle 3 is a inscribed angle of Arc DA.

[tex] \frac{120}{2} = 60[/tex]

Angle 4 is a inscribed angle of Arc BC so it measures

[tex] \frac{72}{2} = 36[/tex]

Angle 5 is formed by tangent line ED. Since D lies on the circumference, it also is tangent to point e so it also measures 90 degrees.

Angle 4 measures 32 so Angle 5 is it complement to Angle 4.

[tex]32 + x = 90[/tex]

[tex]x = 58[/tex]

Angle 6 is formed by two intersecting chrods

so it measures

[tex] \frac{1}{2} (120+ 72) = 96[/tex]

Answer:

84 cm^2

Step-by-step explanation:

8 * 21/2=84

Answer:

S55°E is the compass bearing

Step-by-step explanation:

145° - 90° = 55°

The bearing will be in between South and East because from North to South is 180° and 145° is bigger than 90°

Answer:

option A

Step-by-step explanation:

since the two sides of the triangle are equal the given triangle is an isosceles triangle.

Base angles of an isosceles triangle are equal.

angle P = angle R

32 degree = angle R

The measure of <QRP = 32 degree.

An isosceles triangle is one with two sides that are the same size and a third side that is a different size.

According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.

We have,

A triangle whose two sides are 8 unit each and an angle 32.

As, we know a triangle whose two sides are equal is said to be isosceles triangle.

So, the given triangle is isosceles.

Now, angle opposite to equal sides are also equal.

so, <QPR = <QRP = 32 degree

Learn more about isosceles triangle here:

https://brainly.com/question/2456591

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Complete question:

4x³ - 4x + 3 is divided by (2x - 1). Find the quotient and the remainder

Answer:

The quotient =  2x² +  x  - ³/₂  and the remainder = ³/₂

Step-by-step explanation:

Given function;

4x³ - 4x + 3 divided by (2x-1)

Use long division method to obtain the remainder and the quotient.

                               2x² +  x  - ³/₂

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

                 2x - 1 √4x³ - 4x + 3

                           - (4x³ - 2x²)

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

                                    2x²  - 4x + 3

                                 - ( 2x² - x)

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

                                        -3x + 3

                                      -(-3x + ³/₂)

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

                                            ³/₂

Therefore, the quotient =  2x² +  x  - ³/₂  and the remainder = ³/₂

Answer:

57

Step-by-step explanation:

the whole angle is 90

So 90 minus 33 is 57

Answer:

C) 119.75 + 2.25p <= 500; p <= 169

Step-by-step explanation:

My friend, for this problem you must realize that there is a fixed cost of 119.75 that we add always. Then $2.25 per pastry manufactured is also part of the total costs. Thus, we add both of them where p represents pastry to get 119.75 + 2.25p.

But, the question says the shopkeeper would like to stay under or be exactly at $500 for total costs. Thus, for this inequality, we set this equation as being less than equal to 500.

Solve for p by adding 119.75 on both side and dividing both sides by 2.25 afterwards and you get 169.

Answer:

B. y= -2x +2

Step-by-step explanation:

the slope is negative 2 and the point where the line crosses the y-int is 2

Answer:

22 sides total

Step-by-step explanation:

a hexagon has 6 sides, while a pentagon has 5 sides. In order to find out how many there are total, we would multiply each by two, and add them together.

[tex]2(6)+2(5)=\\12+10=22[/tex]

Answer:

Hsbsbbsysbwisuqiqiqjqjqjqjqjjqjqjqj1 1b1bh2jo

Answer:

-2 + 6i

Parallelogram

Step-by-step explanation:

( 5 - 2i ) + ( - 7 + 8i )

remove parenthesis

5 - 2i + ( -7 ) + 8i

combine like terms

5 + (-7) = -2

-2i + 8i = 6i

-2 + 6i

The arrows on the opposite sides indicate that the sides are parallel

A shape with two sets of parallel sides is known as a parallelogram

Answer:

rtyujn

Step-by-step explanation:

er456y7ujm

Answer:

(10) Person B

(11) Person B

(12) [tex]P(5\ or\ 6) = 60\%[/tex]

(13) Person B

Step-by-step explanation:

Given

Person A [tex]\to[/tex] 5 coins (records the outcome of Heads)

Person [tex]\to[/tex] Rolls 2 dice (recorded the larger number)

Person A

First, we list out the sample space of roll of 5 coins (It is too long, so I added it as an attachment)

Next, we list out all number of heads in each roll (sorted)

[tex]Head = \{5,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,0\}[/tex]

[tex]n(Head) = 32[/tex]

Person B

First, we list out the sample space of toss of 2 coins (It is too long, so I added it as an attachment)

Next, we list out the highest in each toss (sorted)

[tex]Dice = \{2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6\}[/tex]

[tex]n(Dice) = 30[/tex]

Question 10: Who is likely to get number 5

From person A list of outcomes, the proportion of 5 is:

[tex]Pr(5) = \frac{n(5)}{n(Head)}[/tex]

[tex]Pr(5) = \frac{1}{32}[/tex]

[tex]Pr(5) = 0.03125[/tex]

From person B list of outcomes, the proportion of 5 is:

[tex]Pr(5) = \frac{n(5)}{n(Dice)}[/tex]

[tex]Pr(5) = \frac{8}{30}[/tex]

[tex]Pr(5) = 0.267[/tex]

From the above calculations: [tex]0.267 > 0.03125[/tex] Hence, person B is more likely to get 5

Question 11: Person with Higher median

For person A

[tex]Median = \frac{n(Head) + 1}{2}th[/tex]

[tex]Median = \frac{32 + 1}{2}th[/tex]

[tex]Median = \frac{33}{2}th[/tex]

[tex]Median = 16.5th[/tex]

This means that the median is the mean of the 16th and the 17th item

So,

[tex]Median = \frac{3+2}{2}[/tex]

[tex]Median = \frac{5}{2}[/tex]

[tex]Median = 2.5[/tex]

For person B

[tex]Median = \frac{n(Dice) + 1}{2}th[/tex]

[tex]Median = \frac{30 + 1}{2}th[/tex]

[tex]Median = \frac{31}{2}th[/tex]

[tex]Median = 15.5th[/tex]

This means that the median is the mean of the 15th and the 16th item. So,

[tex]Median = \frac{5+5}{2}[/tex]

[tex]Median = \frac{10}{2}[/tex]

[tex]Median = 5[/tex]

Person B has a greater median of 5

Question 12: Probability that B gets 5 or 6

This is calculated as:

[tex]P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}[/tex]

From the sample space of person B, we have:

[tex]n(5\ or\ 6) =n(5) + n(6)[/tex]

[tex]n(5\ or\ 6) =8+10[/tex]

[tex]n(5\ or\ 6) = 18[/tex]

So, we have:

[tex]P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}[/tex]

[tex]P(5\ or\ 6) = \frac{18}{30}[/tex]

[tex]P(5\ or\ 6) = 0.60[/tex]

[tex]P(5\ or\ 6) = 60\%[/tex]

Question 13: Person with higher probability of 3 or more

Person A

[tex]n(3\ or\ more) = 16[/tex]

So:

[tex]P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Head)}[/tex]

[tex]P(3\ or\ more) = \frac{16}{32}[/tex]

[tex]P(3\ or\ more) = 0.50[/tex]

[tex]P(3\ or\ more) = 50\%[/tex]

Person B

[tex]n(3\ or\ more) = 28[/tex]

So:

[tex]P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Dice)}[/tex]

[tex]P(3\ or\ more) = \frac{28}{30}[/tex]

[tex]P(3\ or\ more) = 0.933[/tex]

[tex]P(3\ or\ more) = 93.3\%[/tex]

By comparison:

[tex]93.3\% > 50\%[/tex]

Hence, person B has a higher probability of 3 or more

Using it's concept, the probability that a student liking music given they already like art is of 10/17 = 0.5882 = 58.82%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, from the Venn Diagram, there are 17 students who like art, and of those, 10 like music, hence the probability is given by:

10/17 = 0.5882 = 58.82%.

More can be learned about probabilities at https://brainly.com/question/14398287

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Answer:

-9 1/4

Hope that this help!

Answer:

-k

Step-by-step explanation:

Cos(140)=cos(180-40)=-cos(40)=-k

Answer:

Step-by-step explanation:

Sin (90 - A)  = Cos A

Cos (90 + A) =   -Sin A

Sin 50 = Sin (90 - 40)

          = Cos 40

         = k

Cos 140 = Cos (90 + 50)

             = - Sin 50

            = (- k)

Answer:

[tex]y = - \frac{1}{2} x + 4[/tex]

Step-by-step explanation:

Let us consider two points through which the line passes through

[tex](x_1 , y _ 1 ) = ( 0 , 4 ) \ and \ (x_ 2 , y _ 2 ) = ( 4, 2 )[/tex]

Step 1 : Find slope of the line

[tex]Slope, m_1 = \frac{rise}{run} \\\\That \ is \ m_1 \ = \frac{y_2 - y _ 1}{x_2 - x_1}[/tex]

                  [tex]= \frac{2 - 4}{4-0} \\\\=-\frac{2}{4}\\\\= - \frac{1}{2}[/tex]

Step 2 : Find equation of the line.

[tex](y - y _ 1) = m_ 1 (x - x_1)\\\\( y - 4) = - \frac{1}{2}(x - 0)\\\\y = -\frac{1}{2}x + 4[/tex]

Answer:

[tex]\frac{31}{(5x+2)^2}[/tex]

Step-by-step explanation:

See image for quotient rule

f(x)= numerator = 3x-5

g(x)= denominator = 5x+2

so we have

[tex]\frac{(5x+2)(3x-5)'-(3x-5)(5x+2)'}{(5x+2)^2}\\(3x-5)'=3\\(5x+2)'=5\\\frac{(5x+2)(3)-(3x-5)(5)}{(5x+2)^2}\\\frac{15x+6-(15x-25)}{(5x+2)^2}\\\frac{31}{(5x+2)^2}[/tex]

Answer:

6/9 and 4/6

Step-by-step explanation:

Double and Triple the number

Answer:

find X in X with x if you find X with x in with x you got a formula

Answer:

if you add 14 to 1750 you will get 1764 which equals 42²

Step-by-step explanation:

Answer:

c.12

Step-by-step explanation:

you do 33-9 which gets you 24. You then divide that by 2 so you get 12.

Answer:

Step-by-step explanation:

C

Answer:

y= 5x

Step-by-step explanation:

since each x number is 1/5 of the y, it's 5 times x = y

Answer:

35/87

Step-by-step explanation:

To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.

The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87