How many quarts of pure antifreeze must be added to 7 quarts of a 10​% antifreeze solution to obtain a ​30% antifreeze​ solution?

The lessons from Clare B. Dunkie's The Hollow Kingdom, and the quote it matches are:

One lesson that we see is that people who care about someone, are able to make sacrifices to ensure the wellbeing of that person. We see it with the narrator saying that the person loved another so much that they sacrificed their world for that person.

Another less is that nature can often help us gain the courage we need to do something. This is shown with the subject looking to the moon and stars to back her up.

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Using the combination formula, the committee can be selected in 1,211,760 ways.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Combination formula is the number of different combinations of x objects from a set of n elements.

In this problem:

There are 10 sophomore, 8 junior, and 9 senior members in student council.

They are independent, so we can just multiply them, thus;

T = 18!/ 2! 16! x 12!/ 2! 10! x 10!/ 3! 7!

T  = 1,211,760

Hence, The committee can be selected in 1,211,760 ways.

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The definite integral that represents the area of the region under the given curves is:  [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]

Given:

The points where the two intersect will be given by:

y₁ = y₂

=> x² + 2x + 3 = 2x + 12

=> x² + 3 = 12

=> x² = 9

=> x = ± 3

For x₁ = 3, y₁ = 2(3) + 12 = 18 => (x₁, y₁) = (3, 18)

For x₂ = -3, y₂ = 2(-3) + 12 = 6 => (x₂, y₂) = (-3, 6)

Now, for the area of the region under first curve [tex]y_1=x^2+2x+3[/tex]:

A₁ =  [tex]\int\limits^3_{-3} {x^2+2x+12} \, dx[/tex]

For the area of the region under the second curve [tex]y_2=2x+12[/tex]:

A₂ = [tex]\int\limits^3_{-3} {2x+12} \, dx[/tex]

For the required area of the region bounded by the two curves will be given by:

A = A₂ - A₁ = [tex]\int\limits^3_{-3} {x^2+2x+3 - (2x +12)} \, dx[/tex]

A = [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]

Refer to the image for the area so bounded by the curves.

Hence, The definite integral that represents the area of the region under the given curves is:  [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex].

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Answer:

if the peak level is 14949 above sea level , so the difference in elevation is 14949 + 39 =14988 feet

The average interest rate does he pay on the total $32,000 he owes is 9. 5%

From the information given, we have that;

Given the total pay he owes as;

= $22, 000 +$ 10, 000

= $32, 000

The average interest rate is expressed as;

= sum of interest rate for college loan and car/ number of interest rate

Substitute the values

= 8 + 11/ 2

= 19/ 2

Find the quotient

= 9. 5%

Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%

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The given equations have in one, (1/5) is the coefficient of x, in the second equation, (1/5) is the coefficient of (x + 2), while both equations equals 6. Therefore, the value of x is different in both equations which do not represent the same situation.

The given equations are presented as follows;

[tex]\frac{1}{5} \cdot x + 2 = 6...(1)[/tex]

[tex] \frac{1}{5} \cdot (x + 2) = 6...(2)[/tex]

Solving each equation for x gives;

For equation (1), x = 5×(6 - 2) = 20

x = 20

For equation (2), we have;

x = 6 × 5 - 2 = 28

x = 28

Given that the value of x in the given equations are different, the situations are different.

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Answer:

see explanation

Step-by-step explanation:

a bit more info is needed so this may be wrong.

so first you add up the x values which is 12x+8x+x=21x

then you can see we have a problem, we dont know the x value so the answer would be 21x +3

but we can go a bit further to get an answer as 3(7x+1)

this is also known as factorisation.

so ans: 3(7x+1)

Answer:

[tex]{ \tt{change = \frac{y_{b} - y _{a} }{x _{b} - x _{a} } }} \\ \\[/tex]

[tex]{ \tt{ change = \frac{16 - 2}{4 - 1} }} \\ \\ = { \tt{ \frac{14}{3} }} \\ \\ = 4 \frac{2}{3} [/tex]

The 9th term of the geometric sequence can be determined by using the nth term of geometric sequence formula: an=arn-1

Geometric sequence is the series of number in which each term is determined by multiplying the common ratio with the preceding term.

In the formula, an=arn-1, a is the first term, n is the number of terms, and r is the common ratio.

The geometric sequence from the part b is 2,4,8,…

The first term a = 2

The common ratio r = 2

The number of term n = 9

Hence, to find the 9th term,

a9=2(2)9-1

a9=2(2)8

a9=512

The 9th term of the geometric sequence 2,4,8,… is 512

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The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Given the triangle  ΔJ K L

Base = a  and Perpendicular = 4b

By Pythagoras theorem,

Hyp² = Base² + Perp²

Hyp² = a² + (4b)²

LJ = √(16b² + a²).

Hence "The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²)".

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the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).

We are given the functions:

f ( x ) = 4ˣ

g ( x ) = x - 2

Now, we have a function y defined as:

y = f ( g ( x ) )

Now, we need to find the equation for y.

We know that:

f ( g ( x ) ) = 4⁽ ˣ⁻ ² ⁾

f ( g ( x ) ) = 4ˣ / 4²

f ( g ( x ) ) = 4ˣ / 16

Therefore, we get that, the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).

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The 20th term of the arithmetic sequence is 122.

nth term = a1 + d(n - 1) so here:

20th term = -30 + 8(20 - 1)

- 30 +  152

[tex]a_{20}[/tex] = 122.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer:

Step-by-step explanation:

y = -3x + 7

since the slope of the line AB = (4 - 2) /( 3 - (-3)) = 1/3

slope of line perpendicular to AB will be -3

Range - { 4 , 0 , -4 , -3 } is the domain and range of each relation.

What does the math term domain mean?

What is domain and range mathematics?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Domain - { 0, 4 , -3 , -4 }

Range - { 4 , 0 , -4 , -3 }

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-5/3 is the constant of variation where y varies directly with x.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

A DIRECT VARIATION is a mathematical relationship between two variables that can be stated mathematically by an equation in which one variable equals a constant times the other.  y = kx

⇒ 5 x+3 y=0

⇒ 3y= -5x

⇒ y = -5x/3

Thus, y  = -5/3 × x, here k is constant = -5/3

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A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that circumference of the circle as 124 ft. Therefore, the radius and the diameter of the circle can be written as,

Circumference of circle = 2 × π × (Radius of the circle)

124 ft = 2 × π × (Radius of the circle)

(Radius of the circle) = 124 ft/ (2 × π)

The radius of the circle = 19.73 ft

Diameter of circle = 2 × (Radius of the circle)

                              = 2 × 19.73 ft

                              = 39.46 ft

Hence, the radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.

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Answer:

Hello,

Step-by-step explanation:

[tex]x^2+6x-16\\\\=x^2+2*3x+3^2-9-16\\\\=(x+3)^2-25\\[/tex]

Answer:

5 gg

Step-by-step explanation:

Let us treat the number of gigabytes of data she can use (at max) per month as x.

We can say that [tex]54.5 + 5x = 74[/tex] will always be deducted from her and $5x per month for the extra data she uses.

    [tex]54.5 + 5x = 74[/tex]

⇒  [tex]5x = 74 - 54.5[/tex]

⇒  [tex]5x = 25.5[/tex]

⇒  [tex]x = 25.5 / 5[/tex]

⇒ [tex]x = 5.1[/tex]

As she can only buy a fixed number of data, which cannot be a decimal, let us take the number directly below 5.1 - which is 5 - as the answer.

Caroline can use up to 5gg of data

Answer: jane has 1.5 meters of ribbon

Step-by-step explanation:

Answer:

1/2 + 3/4 + 5/8

4/8 + 6/8 + 5/8 = 15/8 or 1 7/8 cups

Step-by-step explanation:

probably right dunno

This is one batch right? if so shud be right

The Slope-intercept form of the given equation is y = -3x + 18 .

An equation in Slope-intercept form is of the form

[tex]y = mx + b[/tex]

where m is the slope and b is the y intercept.

Now, the given equation is (y/9) + (x/3) = 2

Taking LCM on the left hand side of the equation, we get

⇒ [tex](3y+9x)/(2y) = 2[/tex]

⇒ 3y + 9x = 54

⇒ 3y = 54 - 9x

Dividing both side of the equation by 3, we get

⇒ y = [tex](54 - 9x)/3[/tex]

⇒ y = 18 - 3x

⇒ y = -3x + 18

∴ The equation y = -3x + 18 is in Slope-intercept form.

In the equation the slope is -3 and the y-intercept is 18.

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Answer: Two planes intersecting in a line

Explanation:

The wall and floor are two different planes. They meet up to form a line which is the crease between them.

A plane is a flat surface without any bends or curves to it. In theoretical terms, planes go on forever in all directions. Realistically there are limits of course. The wall or floor cannot go on forever.

Another example of two planes would be found in a book. Each page is a plane. Two adjacent pages meet up to form a line (i.e. the spine of the book is a line).

Answer:

2b + 9

Hope this helps :)

Step-by-step explanation:

This equation shows the statement, "Ava's sister is 9 years less than twice Ava's age b."

Answer: f(-1) = -12

Step-by-step explanation:

        To solve, we will substitute t for -1 into the function.

Given:

    h(t) = (t + 7)(t - 1)

Substitute:

    h(-1) = (-1 + 7)(-1 - 1)

Add and subtract:

    h(-1) = (6)(-2)

Multiply:

    f(-1) = -12

4)

The measures of the angles m∠1 and m∠2  are: m∠1 = 109 and m∠2 = 71

Linear pair angles are two angles which are adjacents and supplementary.

Given that: m∠2 and m∠1 form a linear pair

we know that the angles   and   are supplementary, which means that they add up to 180 degrees.

In order to solve for "x," we can write the following expression:

180 = (5x + 9) + (3x + 11)

8x = 180 - 20

x = [tex]\frac{160}{8}[/tex]

x = 20

Therefore, substituting, we get that the measures of the angles   and   are

m∠1 = 5(20) +9 = 109

m∠2 = 3(20) + 11 = 71

5)

the angle m∠2 = 86°

Given that m∠1 and m∠2 are vertical angles and m∠1 = (17x + 1) and m∠2 =  (20x - 14)

Vertical angles are always congruent

m∠1 = 17x + 1

m∠2 = 20x - 14

Since ∠1 and ∠2 are vertical:

m∠1 = m∠2

17x + 1  = 20x - 14

Collect like terms

20x - 17x = 1 + 14

3x = 15

Divide both sides by 3

3x / 3 = 15/3

x = 5

m∠2 =  20x  -  14

m∠2 =  20(5)  -  14

m∠2 =  100    -   14

m∠2 =   86°

6)

The value of each angle that is p=119 and q=61

In light of this, the measure of an angle is P, which is three less than the measure of angle q.

P + q = 180  ( By definition of supplementary)

p = 2q -3

Substitute the value

Then ,we get

2q - 3 + q =180

3q = 180 + 3

3q = 183

q= [tex]\frac{183}{3}[/tex]

= 61

then, if you substitute q's value, you get

p= 2(61) - 3 = 122 - 3 = 11.9

Hence, p= 119 and q= 61

7)

The value of x is 19°

Given that : ∠DBE =2x - 1

∠CBE =5x – 42  and BD is perpendicular to AC.

A right angle is formed when two lines are perpendicular.

∠DBE + ∠CBE = 90

90 = (2x - 1) + (5x - 42)

7x = 133

x = 19°

8)

The value of x and y are : x= 26° and y= 9°.

As a linear pair, (5x - 17)° + (3x - 11)° = 180°.

or, 8x - 28°= 180°

8x = 180° + 28°

Therefore, the value of x is 26°.

Now,

3x - 11°= 3×26°-11° = 67°

Again,

67°+90°+(2y+5)° = 180° { being linear pair}.

157°+2y+5° = 180°

or, 2y + 162° = 180°

or, 2y = 180° - 162°

y = [tex]\frac{18}{2}[/tex]

Therefore, the value of y is 9°.

The value of x is 26° and y is 9°.

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Answer:

$10

Step-by-step explanation:

Let's begin with adding all of the items Greg bought.

36.62 + 11.25 + 17.75 = 65.62

Let the money paid to the cashier be x.

Now, it's stated he paid 60 dollars to the cashier and that he also got $4.38 back from the cashier.

Then, it must be that x=65.62+4.38

x=70

The money he borrowed from friend = 70-60=10

Therefore, the money Greg borrowed from his friend to pay for all the items is $10.

Greg borrowed $1.24 from his friend.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations.

This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

Given:

Greg bought a blanket for $36.62,

a flag for $11.25,

and a glove for $17.75.

Total expense of the objects he brought

= 36.62+ 11.25 + 17.75

= $65.62

He paid $60 then

=65.62 - 60 = $5.62 remaining

Also, he got $4.38 in change from the cashier

= 5.62 - 4.38

= $1.24.

Hence, Greg borrowed $1.24 from his friend.

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Answer: $244.55

A = $250  ;  r=0.002   t= 11   [From 2007 to 2018 , t=2018-2007]

The equivalent expression by distributing the sign outside the parentheses: -(-8.2w+10) −(−8.2w+10) will be 16.4w - 20.

It should be noted that bwsed on the information given, the expression is illustrated as:

-(-8.2w+10) −(−8.2w+10)

The signs should be taken into consideration. This will be:

-(-8.2w+10) −(−8.2w+10)

= 8.2w - 10 + 8.2w - 10

= 16.4w - 20

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Answer:

1 7/8

Step-by-step explanation:

KCF method.

[tex]\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\[/tex]

                       [tex]\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}[/tex]