Alejandro buys 4 bottles of pineapple juice at the corner store for a total cost of
$2.64. If each bottle costs the same amount, how much is 15 bottles of juice?

The results of the operations between the sets are given as follows:

1. U = {a, d, e, i, l, o, n, p, y}

2. E ∪ I = {d, o, l, e, p, i, n, a, y}.

3. E ∩ I = ∅.

4. J' = {d, a, l, e}

5. I ∪ J = {p, i, n, a, y, o}

6. (J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}

7. E = {p, i, n, a, y}

8. I' ∪ J = {p, i, n, y, d, o, l, e}

9. (E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}

10. (J ∪ I)' = {d, l, e}

The universal set is the set that contains all elements that belong to at least one of the sets E, I and J, hence:

U = {a, d, e, i, l, o, n, p, y}

The union operation between two sets is the set of elements that belong to at least one of the sets.

Hence, in item 2, we have that:

E ∪ I = {d, o, l, e, p, i, n, a, y}

In item 5, we have that:

I ∪ J = {p, i, n, a, y, o}

The negation operation of a set X is the set that contains all elements that belong to the universe U but do not belong to X.

Hence, for item 4, we have that:

J' = {d, a, l, e}

For item 7, we have that:

E = {p, i, n, a, y}

Item 8 involves a negation then a union, hence:

I' = {d,o,l,e}

I' ∪ J = {p, i, n, y, d, o, l, e}

Item 10 involves an union then a negation, just different precedence of 8, hence:

I ∪ J = J ∪ I = {p, i, n, a, y, o}

(J ∪ I)' = {d, l, e}

The union operation between two sets is the set of elements that belong to both of the sets.

Hence, in item 3, we have that:

E ∩ I = ∅ (no element belongs to both sets).

For item 6, we have an intersection then an union, hence:

J ∩ I = {p,i,n,y}

(J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}

For item 9, we have the intersection of two unions, hence:

E ∪ I = {d, o, l, e, p, i, n, a, y}

I ∪ J = {p, i, n, a, y, o}

(E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}

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Answer:

  d: {-5, 0, 8}

  r: {-6, -3, 1, 8}

Step-by-step explanation:

You want the domain and range of the relation T= {(-5, -3), (8, -6), (-5, 1), (0,8)}.

The domain is the set of first values. We usually like to see duplicates eliminated and the values written in increasing order:

  {-5, 0, 8}

The range is the set of second values. Again, we like them in order:

  {-6, -3, 1, 8}

__

Additional comment

If there are duplicates among the domain values (as here), the relation is not a function.

Answer: 28 miles per hour

Step-by-step explanation:

224 miles / 8 hours=

224/8= 28 miles per hour

If they have the same slope and different intercepts then they are parallel and there is no solution to the system.

If the two lines have different slopes, the system has exactly one solution (whether the lines have the same intercept or different intercepts).

If they have the same slope and the same intercept they are the same line, so there are infinitely many solutions to the system.

If they have the same slope and different intercepts then they are parallel and there is no solution to the system.

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Answer:

Yes

Step-by-step explanation:

We can check using pythagoras theorem, setting a and b equal to the shorter sides.

[tex]51^2+68^2=85^2\\2601+4624=7225\\7225[/tex]

The expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)

The expression in the question s given as

(128 + 32)

Express the numbers 128 and 32 as the product of their factors

i.e. we factor out 4 from the expression

So, we have

(128 + 32) = (4 * 32 + 4 * 8)

Next, we factor out the common factor (i.e. 4) from the expression

So, we have

(128 + 32) = 4 * (32 + 8)

Rewrite the above expression as follows

(128 + 32) = 4(32 + 8)

Hence, the expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)

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 The given function

f(x) = y = 4x(7 - 2x) , is a Quadratic function

 where its quadratic term is -8x².

 Its linear term is 28x

 Constant 0

 A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.

   A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:

f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.

4x (7 - 2x)  we apply the distributive property

28x - 8x²   is a quadratic function

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Corresponding angles of congruent must be equal .

What exactly do you mean by congruent?

Given , L is mid point of JL .

               JL = LN    Mid point

L is mid point of KM .

KL = LM            Mid point

JM = NK               Given

Δle JLM  ≅  Δ le KLN    ( SSS)

∠MJL ≅  ∠ KNL

Corresponding angles of congruent must be equal .

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Answer:

The equation for new function is

Step-by-step explanation:

We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.

If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.

We have below conditions for vertical stretch and compression.

a > 1 => vertically stretch

0 < a < 1 => vertically compression

Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3

Therefore, the equation for new function is

Step-by-step explanation:

g(x) = 1/3 |x| !

the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).

The reflection transformation can be with respect to x-axis and y-axis. When a point is reflected about the x-axis, the x-coordinates stay the same and y-coordinates are transformed and written with their opposite signs.

For example, the reflection of the point with coordinates (x, y) across x-axis is (x, -y).

When a point is reflected about the y-axis, the y-coordinates stay the same and the x-coordinates are transformed and written with their opposite signs.

For example, the reflection of the point (x, y) across y-axis is (-x, y).

As we can see that the point with coordinates ( -6, -3 ) lies in the third quadrant and thus the reflection of this point on y-axis lies in fourth quadrant. We know that in fourth quadrant  the x coordinate is positive and y coordinate is negative.  

By changing the signs according to the above rules, we get

from ( -6, -3 ) to  ( 6, -3 ).

Therefore, we can conclude that the reflection of coordinates ( -6, -3 )  on y-axis has coordinates ( 6, -3 ).

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A slope-intercept equation for each line (-5,-3) and (10,-6)

y =  (3/5)x + 3.

The slope-intercept form of the line's equation is y = MX + b, where the material has deposited the slope and b symbolizes the y-intercept. We can see from our equation, y = 7 x + 4, that the y-intercept of the line is 4.

To begin, are using the slope formula to figure out the average slope between two points here.

Let:

x1 = -5

y1 = -3

x2 = 10

y2 = -6

m = (y2-y1)/(x2-x1)

= (-6 - (-3))/ (-10-(-5))

= -3/(-5)

= 3/5

So the slope is 3/5.

We must now find the y-intercept. This will be performed by translating one of the points and the slope into to the point-slope form of a linear equation. y2-y1 = m(x2-x1).

Let’s plug in the point (10,-5).

So we get y-(-3) = (3/5)(x-(-5)) ⇒  y+3

= (3/5)x + 3  ⇒  y

=  (3/5)x + 3.  

So y =  (3/5)x + 3.

a slope-intercept equation for each line (-5,-3) and (10,-6)

y =  (3/5)x + 3.

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Answer: sinW≈0.75

Step-by-step explanation:

[tex]m\angle X=90^0\ \ \ \ XV=48\ \ \ \ \ WV=73\ \ \ \ \ VX=55\ \ \ \ sinW=?[/tex]

The sine theorem: The sides of a triangle are proportional to the sines of the opposing angles

Hence,

[tex]\displaystyle\\\frac{WV}{sinX} =\frac{VX}{sinW} \\\\\frac{73}{sin90^0} =\frac{55}{sinW} \\\\\frac{73}{1} =\frac{55}{sinW} \\\\sinW=\frac{55}{73} \\\\sinW\approx0.75[/tex]

Answer: mean = 34

median = 33

mode = 33

Step-by-step explanation:

To figure out the mean you add every number and divide them by the number of values you added together so 27 + 31 + 33 + 33 + 35 + 45 = 204 then we would divide that by 6 = 34

To find the median you put all the numbers into order so which it already is meaning now you find the number in the middle which is 33 and 33 if there were two more values you would have to find the mean of them, but in this case its 33

The mode is the number which appears the most which is 33 as it appeared more than 2 times.

Answer:

42 miles per gallon

Step-by-step explanation:

First, Convert it into a decimal to make it easier, 26.25 miles on .625 gallon. Now we Divide the two numbers 26.25 ÷ .625 = 42.

Hope this helps :D

The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

The formula so used: A = [tex]\frac{-dN}{dt}[/tex]

=> N = A ([tex]e^{-kt}[/tex]), where:

Now,

AS shown in the table (refer to the image attached), for k:

=> 322 = 1284[tex]e^{-2k}[/tex]

=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]

=> 0.25 = [tex]e^{-2k}[/tex]

Taking natural logarithm on both sides.

=> ln(0.25) = ln([tex]e^{-2k}[/tex])

=> ln(0.25) = (-2k) ln(e)

As ln (e) = 1,

=> ln (0.25) = -2k

=> -1.386 = -2k

=> k = 0.693

Now, for t = 1 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(1)}[/tex])

=> N =  1284 (0.5)

=> N = 642

For t = 3 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(3)}[/tex])

=> N =  1284 (0.125)

=> N = 160.6g

For t = 4 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(4)}[/tex])

=> N = 1284(0.0625)

=> N  = 80.3g

Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

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The expanded form of 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

To express decimal numbers in their expanded form simply means writing each number according to its place value. It can be done by multiplying each digit of the decimal by its place value and adding it all together.

Given the decimal 0.68 or sixty eight hundredths in words, first, multiply the digit 0 by its place value, which is 1.

0 x 1

Multiply the digit 6 by its place value, which is 0.1.

6 x 0.1

Multiply the digit 8 by its place value, which is 0.01.

8 x 0.01

Add it all together.

0 x 1 + 6 x 0.1 + 8 x 0.01

Hence, the expanded for of the decimal 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

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As shown in the above figure:

AB = 4m, AD = 8m, AC = 3m, DE = 12m

Ratio of the length AB to the length AD

[tex] →\frac{AB}{AD} = \frac{4}{8} = \frac{1}{2} [/tex]

Ratio = 1:2

The length AE

[tex] \frac{AB}{AD} = \frac{AC}{AE} → \frac{4}{8} = \frac{3}{AE} [/tex]

Cross multiply the above.

[tex]4AE = 24[/tex]

Divide both sides by 4

[tex]AE = 6m[/tex]

The length BC

[tex] \frac{AB}{AD} = \frac{BC}{DE} → \frac{4}{8} = \frac{BC} {12} [/tex]

Cross multiply the above

[tex]8BC = 48[/tex]

Divide both sides by 8

[tex]BC = 6m[/tex]

Please mark my answer brainliest

Answer:

x ≈ 25.73

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )

x × tan25° = 12 ( divide both sides by tan25° )

x = [tex]\frac{12}{tan25}[/tex] ≈ 25.73 ( to 2 dec. places )

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The measure of the length 'x' is calculated by the tangent of angle 25°. The tangent of an angle is the ratio of the perpendicular to the base of the right-angle triangle. Then we have

tan 25° = 12 / x

x = 12 / tan 25°

x = 12 / 0.466

x = 25.75 units

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

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Answer:

55

Step-by-step explanation:

[tex]\sqrt{3025} =55^2\\\sqrt{55^2}\\\sqrt{55^2}=55\\=55[/tex]

Hope this helps.

Answer:

5.5 = 5 5/10 = 5 1/2 (simplified)

Hope this helps in any way :)

The equation of the line in point-slope form, which passes through the pair of points located at (7 , 11) and (13 , 17), is y - 11 = (x - 7).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (7 , 11) and (13 , 17).

m = (y2 - y1)/(x2 - x1)

m = (17 - 11)/(13 - 7)

m = 6/6

m = 1

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = 1 and (x1 , y1) = (7 , 11)

(y - 11) = 1(x - 7)

y - 11 = (x - 7)

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The six rational number between 7 and 8 are 7.5 ,7.75, 7.875 , 7. 9375 ,7.9675 and 7.98375

The distance between the given 2 points using the distance formula is 4√2.

So, the Distance formula: [tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Substitute values in the distance formula as follows:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\d=\sqrt{\left(0-(-4)\right)^2+\left((-2)-2\right)^2}\\d=\sqrt{\left(4\right)^2+\left(-4\right)^2}\\\\d=\sqrt{16+16}\\d=\sqrt{32}\\\\d=\sqrt2*2*2*2*2\\d=2*2\sqrt2\\\\d=4\sqrt2[/tex]

Therefore, the distance between the 2 points is 4√2.

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The equivalent expression of -6(b + 2) + 8 is -6b - 4

The expression is given as

-6(b + 2) + 8

Expand

-6b - 12 + 8

Evaluate the like terms

-6b - 4

Hence, the equivalent expression of -6(b + 2) + 8 is -6b - 4

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Answer:

x = 10

Step-by-step explanation:

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

[tex]\frac{TS}{TB}[/tex] = [tex]\frac{TR}{TC}[/tex] ( substitute values )

[tex]\frac{10x+17}{65}[/tex] = [tex]\frac{90}{50}[/tex] ( cross- multiply )

50(10x + 17) = 90 × 65 = 5850 ( divide both sides by 50 )

10x + 17 = 117 ( subtract 17 from both sides )

10x = 100 ( divide both sides by 10 )

x = 10

A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.

The percent of the given number 92% of 90 is 82.8.

A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.

Let the equation be 92% of 90

Percentage = (value/total value) × 100 %.

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

92% of 90 = 92/100 of 90

92/100 × 90 = 82.8

Therefore, the percent of the given number 92% of 90 is 82.8.

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Step-by-step explanation:

Philipp Heinrich Scheidemann was a German politician of the Social Democratic Party of Germany. In the first quarter of the 20th century he played a leading role in both his party and in the young Weimar Republic. Wikipedia

Born: July 26, 1865, Kassel, Germany

Died: November 29, 1939, Copenhagen, Denmark

Party: Social Democratic Party of Germany

Spouse: Johanna Dibbern (m. 1889–1926)

Previous offices: Mayor of Kassel (1919–1925), Chancellor of the German Reich (1919–1919), More

Books: The Making of New Germany: The Memoirs of Philipp Scheidemann

Nationality: German, Weimar

The profit of the concession is $350.

So, c - e:

Substitute the values in the expression:

Therefore, the profit of the concession is $350.

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