Gary is looking over his receipts from his trip to Europe. When he was in Germany, he exchanged US dollars for euros at a rate of 1:0.7716, and when he was in Poland, he exchanged euros for Polish zloty at a rate of 1:4.0518. To four decimal places, what was the exchange rate of US dollars to Polish zloty?

Answer:

milliliters

Step-by-step explanation:

By acknowledging the linear relationship between X and Y, we set up a proportion based on the given values and solve for Y when X = 32, finding Y approximately equals 40.

This problem relates to the concept of

linear relationships

in mathematics. By understanding the relationship between two variables x and y, you can find the value of one by knowing the value of the other. Here, if y = 15 when X = 12, we can say that the ratio of y to x is constant. Therefore to find the value of Y when X = 32, we will maintain the same ratio. Now, set up a proportion 15/12 = Y/32 and solve for Y. Cross-multiplication gives us: Y = 15 * 32 / 12. After calculating this, Y equals approximately 40. Therefore, the value of Y when X is 32 will be around 40, keeping the relationship linear.

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The percent of 67.5 is equal to 7.02 is for the number 10.4.

To find what percent of 67.5 is 7.02, we can use proportions.

Let's represent the unknown percentage as 'x'. The proportion can be set up as follows:

(7.02 / 67.5) = (x / 100)

Now, solve for 'x':

7.02 × 100 = 67.5 × x

702 = 67.5x

x = 702 / 67.5

x ≈ 10.4

Therefore, 7.02 is approximately 10.4 percent of 67.5.

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Answer:

x [tex]\geq[/tex] 18

Step-by-step explanation:

Final answer:

To find the width of a rectangle with a perimeter of 54 cm and a length of 6 cm, use the formula P = 2l + 2w. After plugging in the given values and simplifying, the width is calculated to be 21 cm.

Explanation:

Finding the Width of a Rectangle

To solve this problem, we remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 54 centimeters and the length is 6 centimeters, we can set up the equation as follows: 54 = 2(6) + 2w. Simplifying this, we get 54 = 12 + 2w, and then subtracting 12 from both sides gives us 42 = 2w. Dividing both sides by 2, we find the width w to be 21 centimeters.

Step-by-Step Calculation

Therefore, the width of the rectangle is 21 centimeters.

Answer:Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.

Step-by-step explanation:

Factorizing the polynomial expression x² - 18x + 81 = (x - 9)²

Factorization is the simplification of an expression into a smaller expression using its factors.

To factor this polynomial expression. x² - 18x + 81, we proceed as follows

Since we have the polynomial expression x² - 18x + 81, we multiply x² by 81 to get x² × 81 = 81x².

Now, we look for the factors of 81x² such that the sum of those factors equal - 18x

So, we have that 81x² = -9x × (-9x)

So, -18x = -9x - 9x

So, replacing this with -18x, we have that

x² - 18x + 81 = x² - 9x - 9x + 81

Now, factorizing, we have that

x² - 9x - 9x + 81 =  x(x - 9) - 9(x - 9)

= (x - 9)(x - 9)

= (x - 9)²

So, factorizing x² - 18x + 81 = (x - 9)².

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Answer: The measure of angle PCD is 42 degree.

Explanation:

It is given that in ∆ABC,

AB = CB  

BD − altitude to AC

P ∈ BD, PB = PC

∠ABC = 48°

Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.

According to the angle sum property the the sum of interior angles of a triangle is 180.

[tex]\angle ABC+\angle BAC+\angle BCA=180^{\circ}[/tex]

[tex]48^{\circ}+2\angle BAC=180^{\circ}[/tex]

[tex]\angle BAC=66^{\circ}[/tex]

The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.

[tex]\angle PBC=\frac{48}{2}=24^{\circ}[/tex]

Since PB=PC , so triangle BPC is an isosceles triangle.

[tex]\angle PBC=\angle PCB=24^{\circ}[/tex]

From the figure it is noticed that,

[tex]\angle PCD+\angle PCB=\angle BCA[/tex]

[tex]\angle PCD+24^{\circ}=66^{\circ}[/tex]

[tex]\angle PCD=66^{\circ}-24^{\circ}[/tex]

[tex]\angle PCD=42^{\circ}[/tex]

Therefore, the measure of angle PCD is 42 degree.

The result of dividing 36 by 8 is 4.5. This means that there is no whole number that when multiplied by 8 equals 36; the closest is 4, giving us 32, with a remainder that results in 4.5 as the exact quotient.

The question the student is asking relates to basic arithmetic multiplication. Specifically, they're looking for a number that, when multiplied by 8, results in 36. To solve for this, we would generally divide 36 by 8.

However, because 36 is not a multiple of 8, we cannot get a whole number as the result. Instead, the closest we can get without going over is 4, because 4 multiplied by 8 equals 32. If we divide 36 by 8, the result is 4 with a remainder, or 4.5 (which can be expressed as 41/2).

The correct approach to find the quotient is to perform the division 36 / 8, which equals 4.5. To understand this better, you can think of it as having 36 objects that you want to divide into groups of 8 and trying to see how many full groups you can make. You would be able to make 4 full groups with 4 objects left over, or you could see it as making 4 and a half groups.

rotate the triangles so r and c line up

 when you do that Q=B, a=p, C=R, b=q, A=P

 so answer would be B. p:a

we know that

If triangle ABC is similar to triangle PQR

then

the corresponding sides are proportional

so

[tex]\frac{RQ}{CB} =\frac{RP}{AC}= \frac{PQ}{AB}[/tex]

substitute the values

[tex]\frac{p}{a} =\frac{q}{b}= \frac{r}{c}[/tex]

therefore

[tex]\frac{r}{c}[/tex]

is equal to

[tex]\frac{q}{b}[/tex] and [tex]\frac{p}{a}[/tex]

the answer is the option B

[tex]\frac{p}{a}[/tex]

You can travel a distance of 468 miles on 12 gallons of gasoline and a distance of 234 miles on 6 gallons of gasoline.

Proportion is the setting of two or more ratios to be equal.

That is, if there is a ratio between a and b and another ratio between c and d, then we can say that,

a : b = c : d ⇒ a/b = c/d ⇒ a d = b c

We have,

Distance travelled is 156 miles on 4 gallons of gasoline.

We have to find the distance travelled on 12 gallons and 6 gallons of gasoline.

Let x be the distance travelled on 12 gallons of gasoline and y be the distance travelled on 6 gallons of  gasoline.

We have a proportional relation here,

156 : 4 = x : 12 = y : 6

First taking the relation,

156 : 4 = x : 12

⇒ 156/4 = x/12

⇒ 39 = x/12

⇒ x = 39 × 12

⇒ x = 468

Taking the second relation,

156 : 4 = y : 6

⇒ 156/4 = y/6

⇒ 39 = y/6

⇒ y = 39 × 6

⇒ y = 234

Hence you can travel 468 miles on 12 gallons and 234 miles on 6 gallons.

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Answer:

(−6, 0) , (−1, −2)  and (−5, −1)

Step-by-step explanation:

The given inequality is  x+3y ≥ −8

Substitute all the given points in this inequality and check which points satisfy.

For (−6, 0)

-6+3(0) ≥ −8

- 6 + 0  ≥ −8

- 6 ≥ −8   => True.

Hence, (−6, 0) is a solution.

For (−1, −2)

-1 + 3(-2) ≥ −8

-1 - 6 ≥ −8

- 7 ≥ −8 => True.

Hence, (−1, −2) is a solution.

For (−5, −1)

-5 + 3 (-1) ≥ −8

- 5 -3  ≥ −8

-8 ≥ −8=> True.

Hence, (−5, −1) is a solution.

For (−16, 2)

-16 +3 (2) ≥ −8

-16 + 6 ≥ −8

-10≥ −8 => False.

Hence,(−16, 2) is not a solution.

For (0, -3)

0 + 3(-3) ≥ −8

-9  ≥ −8=> False.

Hence, (0, -3) is not a solution.

Therefore, below ordered pairs are solutions of the given inequality

(−6, 0) , (−1, −2)  and (−5, −1)

Answer:

Factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .

Step-by-step explanation:

As the expression is given in the question be .

= 9y² - 12y + 4

Simplify the above

= 9y² -6y -6y + 4

= 3y (3y -2) -2 (3y - 2)

= (3y-2)(3y-2)

Therefore factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .