EXAMPLE 11 Show that the points (1,-1),(5,2) and (9,5) are collinear​

If you double the amount of fluid ounces, then the amount of cups will double as well. This is a true statement.

Consider the statement "there are 8 fluid ounces in one cup" to be written as the equation

8 fluid ounces = 1 cup

We can multiply both sides by 2 to get

16 fluid ounces = 2 cups

We must multiply both sides by the same number to keep the equation the same (keep things balanced).

Answer:

(a) The median estimate is 450.

(b) The first and third quartiles are 300 and 750 respectively.

(c) The interquartile range is 450.

(d) The particular value which is less than 150 or it is more than 1200, is considered as an outlier.

(e) Yes, there is one outlier in our data which is the value of 1,500.

(f) The distribution is positively skewed.

Step-by-step explanation:

We are given that the box plot shows the undergraduate in-state tuition per credit hour at four-year public colleges. 0, 300, 600, 900, 1,200, 1,500.

(a) As we can see in the box plot that the middlemost data lies between 300 and 600, that means;

Median is given by the average of the two numbers, i.e;

             Median =  [tex]\frac{300+600}{2}[/tex]

                           =  [tex]\frac{900}{2}[/tex]  = 450

So, the median estimate is 450.

(b) As we know that the first quartile represents 25% of the data values and the third quartile represents 75% of the data values.

So, from the box plot given; we can observe that the first quartile, [tex]Q_1[/tex] = 300 and the third quartile lies between the values of 600 and 900, i.e;

Third quartile, [tex]Q_3[/tex] = [tex]\frac{600+900}{2}[/tex]

                             =  [tex]\frac{1500}{2}[/tex]  = 750

So, the first and third quartiles are 300 and 750 respectively.

(c) The interquartile range is given by the following formula;

          Interquartile range = Third quartile - First quartile

                                          =  [tex]Q_3-Q_1[/tex]

                                          =  750 - 300 = 450

(d) From the box plot; it is clear that if the particular value is less than 150 or it is more than 1200, then it is considered as an outlier.

(e) Yes, there is one outlier in our data which is the value of 1,500.

(f) The distribution is positively skewed because the more values are on the right side of the curve and it skewed towards the right.

Answer:

Step-by-step explanation:

if m and n are irrational number then the product of mn sometimes rational and sometime irrational

ex: √5 *√2=√10 irrational

ex: √8*√2=√16=4 rational

b-y=|x|+3

explain why |x|+3≥|x+3|

absolute value of any number is always positive

x           |x|+3          ≥            |x+3|

1              4              =               4             in this case equal

2             5                                5

-2             5             ≥                 1             in this case |x|+3≥|x+3|

in case of negative value of x then |x|+3>|x+3|

Answer:

214.6

Step-by-step explanation:

214.557 -> 214.6

Two hundred fourteen and five hundred fifty-seven thousandths to the nearest tenth​ will be 214.6.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Two hundred fourteen and five hundred fifty-seven.

The expression in mathematical form thousandths to the nearest tenth​, we have

⇒ 514.557

⇒ 214.6

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Answer:

Solution : (- 9, - 3)

Step-by-step explanation:

Approach 1 : Imagine that this point (3, - 9) is rotated 90 degrees clockwise. We know that this point lies in the fourth quadrant, so if it is rotated 90 degrees, you can imagine the x - coordinate will be greater than the y - coordinate, if you take their absolute value(s). Remember that the new coordinates will also lie in the third quadrant. Based on these requirements we have the resulting point (- 9, - 3) or option c.

________________________________________

Approach 2 : There is another approach to this, a more exact approach.

Rotation of axis, θ : (x, y) --> (X, Y)

X = xcos(θ) + ysin(θ),

Y = - xsin(θ) + ycos(θ)

Here θ = 90 degrees. Substitute and solve for the exact coordinates.

X = 3cos(90) + - 9sin(90) = 3cos(90) - 9sin(90) = 3 * 0 - 9 * 1 = - 9,

Y = - 3sin(90) + - 9cos(90) = - 3sin(90) - 9cos(90) = - 3 * 1 - 9 * 0 = - 3

As you can see our solution is the same, (- 9, - 3), or option c.

10:11 A.M

11:00 A.M is 11 hours from 12 A.M (12 midnight)

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes= 2 hours 49 minutes

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes= 2 hours 49 minutes11 hours - 2 hours 49 minutes

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes= 2 hours 49 minutes11 hours - 2 hours 49 minutes= 10 hours 11 minutes = 10:11 A.M

Therefore, she can start making the cake batter from 10:11 A.M.

Hope it helps you.

9:25 am is the latest time she can start making the cake batter

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Meg is going to make a cake for her mother's birthday.

The time to bake make the cake batter is 1 hour 15 minutes.

This we can take only in minutes

1 hour = 60 minutes

So 60+15 =75 minutes to make the batter.

the cake needs to bake in the oven for 1 hour and 20 minutes

60+20=80 minutes.

Meg wants the cake to be out of the oven by 11:00 A.M.

We need to find the latest time to start the cake.

Let us find the total time to make the cake

80+75=155

155 minutes means 2 hrs 35 minutes.

Now we have to remove 2 hrs 35 minutes from 11:00 am

Which 9 hours 25 minutes.

Hence, 9:25 am is the latest time she can start making the cake batter

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Answer for the first box = -31.67

Answer for the second box = 17.22

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

Work Shown:

Plug in F = -25 and solve for C

F = (9/5)C+32

-25 = (9/5)C + 32

(9/5)C + 32 = -25

(9/5)C = -25-32 ... subtract 32 from both sides

(9/5)C = -57

C = (5/9)*(-57) ... multiply both sides by 5/9, its the reciprocal of 9/5

C = -31.667 approximately

C = -31.67 rounding to 2 decimal places

This shows that -25 degrees F converts to roughly -31.67 degrees C.

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

Repeat the same basic steps, but now use F = 63

F = (9/5)C+32

63 = (9/5)C+32

(9/5)C+32 = 63

(9/5)C = 63-32

(9/5)C = 31

C = (5/9)(31)

C = 17.222 approximate

C = 17.22

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

If the temperature ranges from -25 degrees F to 63 degrees F, then this converts to the range of roughly -31.67 degrees C to 17.22 degrees C

Answer:

64/7 years

9.143 years

Step-by-step explanation:

[tex]Simple Interest = \\ \frac{Principal \times Rate \times Time}{100} [/tex]

[tex]Time = \frac{simple \: interest \times 100}{Principal \times Rate} [/tex]

[tex]Principal = 400 \\ Rate = 14 \\ Time = \\ simple \: interest = 512[/tex]

Input the values

[tex]Time = \frac{512 \times 100}{400 \times 14} \\ Time = \frac{51200}{5600} \\ [/tex]

[tex]Time = \frac{64}{7} \\ Time = 9.142 \: years \\ best \: answer \: = \frac{64}{7} years[/tex]

Answer:

repeating decimal/number

Step-by-step explanation:

If you divide 11 by 24, you get 0.458333333...

The 3 gets repeated, so 11/24 is a repeating decimal/number

Answer:

[tex]1 \frac{1}{15}[/tex]

Step-by-step explanation:

Hey there!

Well when dividing fractions you need to use Keep, Change, Flip.

[tex]\frac{8}{6} / \frac{5}{4}[/tex]

Keep, Change, Flip

[tex]\frac{8}{6} * \frac{4}{5}[/tex]

[tex]\frac{32}{30}[/tex]

Simplified

16/15

[tex]1 \frac{1}{15}[/tex]

Hope this helps :)

Answer:

The answer is 16/15 or 1 1/15.

Step-by-step explanation:

First, you have to multiply it by converting the second fraction upside down:

[tex] \frac{8}{6} \div \frac{5}{4} [/tex]

[tex] = \frac{8}{6} \times \frac{4}{5} [/tex]

Next, you have to cut out the common terms and multiply all:

[tex] \frac{8}{6} \times \frac{4}{5} [/tex]

[tex] = \frac{8}{3} \times \frac{2}{5} [/tex]

[tex] = \frac{16}{15} \: \: or \: \: 1 \frac{1}{15} [/tex]

Answer:

[tex]\Huge \boxed{300 \° }[/tex]

Step-by-step explanation:

A revolution is 360 degrees.

5/6 of a revolution is 5/6 of 360 degrees.

5/6 × 360 = 300

Answer:

solve for b

1/3 - 3x/6 = -1/6

3y + 5 + 2 + y = 2y + 4

x'2 + 2x - 8 = 0

I think this is correct.

A relation is a function if each element of the domain is paired with exactly one element of the range. ... If given a table, or a set of ordered pairs, you can look to see if any value of the domain has more than one corresponding value in the range.

tbh google

Answer:

[tex]3\frac{1}{5}[/tex]

Step-by-step explanation:

there are 3 5s in 16, and 1 remainder.

So, you write the remainder in the numerator, and 3 as a whole number.

To check, you can do:

5✖️3=15+1=16

Answer:

               [tex]\bold{m\ =\ \dfrac5{(p-r)n}}[/tex]

Step-by-step explanation:

                                             [tex]\bold{r+\dfrac5{mn}\ =\ p}\\\\ {}\quad-r\qquad-r\\\\{}\ \ \bold{\dfrac5{mn}\ =\ p-r}\\\\{}\ ^{_\times}(mn)\quad ^{_\times}(mn)\\\\{}\quad\bold{5\ =\ (p-r)^{_\times}(mn)}\\\\\div(p-r)\quad\div(p-r)\\\\{}\ \ \bold{\dfrac5{p-r}\ =\ mn}\\\\{}\quad \ \div n\quad\ \ \div n\\\\\bold{\dfrac5{(p-r)n}\ =\ m}[/tex]

If you mean (r+5)/mn then:

[tex]\bold{\dfrac{r+5}{mn}\ =\ p}\\\\{}\ ^{_\times}(mn)\quad ^{_\times}(mn)\\\\{}\ \bold{r+5\ =\ pmn}\\\\\div(pn)\quad\div(pn)\\\\{}\ \ \bold{\dfrac{r+5}{pn}\ =\ m}[/tex]

Answer: B: 8*1 = 8

Step-by-step explanation:

The identity property of multiplication says that:

There exist a number, called the identity, such that when we multiply any real number N by this identity, the result is the same number N.

The identity is 1.

then N*1 = N.

The option that is an example of that is:

8*1 = 8.

Option B

Answer:

x = 8 units.

Step-by-step explanation:

We'll begin by calculating the length of the two squares attached to the triangle.

From the question given above, the areas of the two square are the same i.e 32 units². Therefore, the length of the two square will be the same.

Now, we shall determine the length of the square as follow:

Area of square (A) = 32 units²

Length (L) =?

Area of square (A) = Length (L) × Length (L)

A = L × L

A = L²

32 = L²

Take the square root of both side

L = √32 units

Therefore, the length of the square is √32 units. This implies that the length of both side of the triangle is √32 units

Now, we shall determine the value of x using pythagoras theory.

From the diagram above we can see that x is the Hypothenus i.e the longest side. Thus, the value of x can be obtained as follow:

x² = (√32)² + (√32)²

x² = 32 + 32

x² = 64

Take the square root of both side

x = √64

x = 8 units.

Therefore, the value of x is 8 units.

Answer:

B

Step-by-step explanation:

2 units to right and 1 up

You find the litres of petrol you want and go up until you find where the line crosses this point and then see how far you can travel on the left so

a is 15km

and b is 39km

Step-by-step explanation:

Hey, there!!

Let's simply work with it,

Here,

In figure ABC,

let a= 14

b= 19

and c= 8.

Using cosine rule,

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab.cosc[/tex]

putting value of all we get,

[tex] {8}^{2} = {14}^{2} + {19}^{2} - 2 \times 14 \times 19 \times cosx[/tex]

Now, simplifying them we get,

[tex]64 = 196 + 361 - 532.cosx[/tex]

[tex]532cosx = 557 - 64[/tex]

[tex]or \: 532cosx = 493[/tex]

[tex]or \: cosx = \frac{493}{532} [/tex]

cosx= 0.926691

Putting cos inverse,

[tex]x = {cos}^{ - 1} (0.926691) [/tex]

Therefore, x= 22.0752°

By rounding off we get,

x= 22° { as 0 is smaller than 5 itsvalue dont change}.

Hope it helps....

Answer:

2√5 ≈ 4.47214

Step-by-step explanation:

You can draw a triangle with corner points (-1,2); (1,2) and (-1,-2), and the distance will be the hypotenuse, use pythagoras to solve:

√(2²+4²) = √20 = 2√5

Answer:

4.472 units

Step-by-step explanation:

1-(-1)=1+1=2

2-(-2)=2+2=4

2²+4²=c²

4+16=c²

20=c²

c=√20

c=4.472 units

Answer: y =[tex]\frac{ax - 2}{9x}[/tex]

Step-by-step explanation: look for the lcm

a=[tex]\frac{9xy + 2}{x}[/tex]

cross multiply

ax =9xy + 2

ax - 2 = 9xy

divide both sides by 9x

[tex]\frac{ax - 2}{9x} = \frac{9xy}{9x}[/tex]

y=[tex]\frac{ax - 2}{9x}[/tex]

Answer

Step-by-step explanation:

domain : red

range: blue

Answer:

Alisa practiced for 240 minutes (4 hours). In total, they practiced for 288 minutes (4.8 hours).

Step-by-step explanation:

If James practiced for 48, and Alisa practiced 5 times as long, then we would multiply 48 by 5 (240 minutes).

If we want to find how many minutes in total they practiced, then we would add 240 minutes (Alisa's practice time) and 48 minutes (James' practice time) together, which would equal 288 minutes (4.8 hours).

Equation: y=48+x

Answer:

[tex]3 \frac{7}{9}[/tex]

Step-by-step explanation:

We know that the first digit of 3.7, 3, will just be a 3.

However, if we have [tex].\overline{77}[/tex], we have to know what gets this.

If we have a number over 9, it will be that number repeating (excluding 9 itself).

So if we have .77 repeating, it would have to be [tex]\frac{7}{9}[/tex], adding 3 to this gets us [tex]3 \frac{7}{9}[/tex].

Hope this helped!

Answer:

[tex]- 2x + 3[/tex]

Step-by-step explanation:

[tex] - 3(2x -1 ) + 4x \\ - 6x + 3 + 4x \\ = - 2x + 3[/tex]

Answer:

6

Step-by-step explanation:

Let thee number be x

Square of number: x²

Product of 6 and square of number = 6 *x² = 6x²

Expression: 6x² + 15

Coefficient of x² = 6

The value of the coefficient will be 6 for the expression.

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Let thee number be x

Square of number: x²

Product of 6 and square of number

[tex]= 6 \times x^2 = 6x^2[/tex]

Expression will be

[tex]6x^2 + 15[/tex]

Coefficient of x² will be = 6

hence the value of the coefficient will be 6 for the expression.

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Answer: B

Step-by-step explanation:

Let's work this problem backwards. So, if he has y dollars left after spending 25% the second time or 3/4 of the money left. So, inverse it to get  [tex]\frac{4}{3}[/tex]y. Then, do the same for 20% or 4/5, then 4/3y * 5/4 = 5/3y

Answer:

The leading coefficient is 4

Step-by-step explanation: