A water truck is filling a swimming pool. The equation that represents this relationship is y = 18.25x where y is the number of gallons of water in the pool and x is the number of minutes the truck has been filling the pool. Select True or False for each statement.the unit rate for this relationship is 1 gallon per 18.25 minutesO TrueO Falsethis is a proportional relationship because the graph of the equation is a straight line through the orginO TrueO Falsethe water in the swimming pool increases about 33 gallons every 10 minutesO TrueO Falsea table of related x- and y- values for this relationship would show equivalent ratiosO TrueO Falsethe point (12, 219) could be a point on this graphO TrueO False

Answer: I don’t know much but I still know some! If you ever need help reply to this comment please

Step-by-step explanation:

Answer:

5(2 + y)

Step-by-step explanation:

The sum of 2 and y is 2 + y and 5 times this sum is

5(2 + y)

Answer:

Step-by-step explanation:

The hourly output per worker, O = W/U

Given

U=W/O

Here,

U=factory's unit labor cost

O=hourly output per worker

W=hourly compensation per worker

Now take O to left hand side.

U * O = W (where O is the hourly output per worker and WW is the hourly compensation per worker)

Now take U to right hand side

To rearrange the formula to solve for hourly compensation per worker (W), We multiply both sides by W and divide both sides by U we getO = W/U

Hence, the hourly output per worker, O = W/U

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Answer:

B

Step-by-step explanation:

JK = LM (equidistant from centre)

3x+19=6x+7

19-7=6x-3x

12 = 3x

Dividing both sides by 3

x = 4

JK = 3(4)+19

JK = 12+19

JK = 31

Answer:

31

Step-by-step explanation:

JK = LM (since they are equidistant from centre)

3x + 19 = 6x + 7

- 3x = - 12

x = 4

JK = 3 * (4) + 19

= 12 + 19

= 31

Hope this helps!

Answer:

(\(\sqrt[5]{x}\))^7

Step-by-step explanation:

to cancel out the radical you do the exponent inside and divide it by the out side one so it will be 7/5 so make it x to the expontent of 7/5 and to do rational exponets it will be (^5radicalx)^7

Answer:

11.4

Step-by-step explanation:

57/5 as a mixed number is 11 2/5.

2/5 of a number is also known as 4/10 or 0.4, so add that to 11 to get 11.4.

Answer:

11.4

Step-by-step explanation:

57/5 = 11.4

Answer:

  48 inches

Step-by-step explanation:

The greatest common factor of 144 and 240 is 48. If Hector orders 48" square tiles, he can use 3 of them in the direction of the short dimension, and 5 of them in the direction of the long dimension.

The tiles can be 48 inches square.

__

Using Euclid's algorithm to find the GCF, we have ...

  240/144 = 1 r 96

  144/96 = 1 r 48

  96/48 = 2 r 0 . . . . . 48 is the GCF

At each step, if the remainder from the division is not zero, we replace the larger number with the remainder and do the division again. The divisor that gives a zero remainder is the GCF.

bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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\( \quad\rule{300pt}{1.5pt}\)

Using the property of alternate angles , let's first make the pair of equal angles :

‎ㅤ‎ㅤ‎ㅤ➙ m∠1 = m∠ 5

‎ㅤ‎ㅤ‎ㅤ➙ m∠2 = m∠ 6

‎ㅤ‎ㅤ‎ㅤ➙ m∠4 = m∠3 + m∠ 5

‎ㅤ‎ㅤ‎ㅤ➙ Since , m∠ 5 = m∠1

‎ㅤ‎ㅤ‎ㅤ➙ m∠ 4 = m∠ 3 + m∠1

Alternate Angles :

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

\( \rule{350pt}{2pt}\)

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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The proof of ΔRUV ≅ ΔSUT is shown below.

Given that:

RSTV is a rectangle and U is the midpoint of VT.

Here, We have to Prove:

⇒ ΔRUV ≅ ΔSUT

Now, We can prove as;

Statement                               Reason

1) RSTV is a rectangle               Given

2) Angle V and T are                Because every angle in a rectangle is 90

right triangle.

3) ∠V ≅ ∠T                               Because both are right angle.

4) U is the midpoint of VT.        Given

5) VU = UT                                By midpoint theorem.

6) VR ≅ TS                                Opposite sides of rectangle.

7) ΔRUV ≅ ΔSUT                       By SAS congruency theorem.

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Answer:

55 x 224 yards

Step-by-step explanation:

w + w  +  2 * ( 4 + 4w)  = 558     (given)

10 w + 8 =558

w = 55      then L = 4 + 4w = 224 yards

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

3x +216

when we solve by the factor theorem

3(x+72)

Answer:

the answer is (x+6)³

Step-by-step explanation:

x³+216

(x+6)³

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

3 x's at 1

4 x's at 1 1/4

3 x's at 1 1/2

1 x at 1 3/4

No x's at 2.

Now, let's combine all the recipes with 1 1/4

5/4 * 4 = 20 / 4 = 5 teaspoons

He will be eating pizza

S + will + be + V_ing

the length of the diagonal is approximately 10.8 cm.

The  find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem, which states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).

In this case, the diagonal is the hypotenuse of a right triangle whose legs are the length and width of the rectangular prism. So we can calculate it as

diagonal = sqrt(\(lenght^{2}\) +\(width^{2}\) + \(height^{2}\))

= sqrt(\(10^{2}\) + \(4^{2}\)+ \(10^{2}\))

= sqrt(116)

≈ 10.8 cm

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The two properties newton used to rewrite the expression are;

- Associative Property; Because it involves change of grouping of numbers in the expression.

- Distributive Property; Because it involves distribution of a number outside a bracket to numbers inside that same bracket.

- Associative Property

- Commutative Property

- Distributive Property

Let us define each of them;

1) Associative Property; This property in algebra is one that means that no

matter how we group the numbers, we will still get the same result. e.g.

x + (y + z) = (x + y) + z.

2) Commutative Property; This property means that we can change the

order of operation and still get the same answer. For example;

p × q × r = p × r × q

3) Distributive Property; This property means that multiplying the sum of

two or more which are in a bracket by a number outside the will be equal to

the answer gotten when we multiply each number in the bracket

individually by the number outside and then adding their respective

products together. For example; p(q + r) = (p * q) + (p * r)

Newton has the expression; (4 × 23) × 25

Since it is multiplication, he can use any of the three properties above but let us use the associative and distributive properties as they are most suited to this expression.

(4 × 23) × 25 = 4 × (23 × 25)

(4 × 23) × 25 = (25 × 4) + (25 × 23)

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Answer:

1 sunflower

Step-by-step explanation:

Start at 15 then go to the left of the line graph. After count how many X there are which there is one.

Answer:

The height of the tree is 35 meters.

Step-by-step explanation:

Let the height of the tree be x meters, then the length  of the wire is

x+2 meters.

The distance from the tree to the anchor is  x-23 meters.

So using the pythagoras theorem:

(x + 2)^2 = x^2 +(x -23) ^2

x^2 + 4x + 4 = x^2 + x^2 - 46x + 529

x^2 - 50x + 525 = 0

( x - 15)(x - 35) = 0

x = 15, 35

x cannot be 15   as this would make the distance 15-23 which is negative so x mustr be 35 meters,

Answer:

2a+15b+11

Step-by-step explanation:

Simplify

Answer:

60, 80, 100

Step-by-step explanation:

All 3 of these numbers are between 55 and 101, and can be divided by all 3 numbers provided.

Answer:

Lower quartile = 6

Median = 8

Upper quartile = 9

Step-by-step explanation:

If you take away a number from each end of the number set one by one, you will end up with 7 and 9 in the middle. To find the median between two numbers, add them together then divide them by 2.

7 + 9 = 16

16 ÷ 2 = 8

_________________

To find the lower and upper quartiles, split the number set into two where the median is, then, find the median of those two sections.

Lower quartile: 4, 5, 6, 6, 7

Median = 6

-

Upper quartile: 9, 9, 9, 9, 9

Median = 9

So, the median of the whole set is 8, the lower quartile is 6, and the upper quartile is 9.

hope this helps!

Answer:

The sample statistics follows a standard normal distribution since the sample size are large enough.

Step-by-step explanation:

Given that:

First population:

Sample size \(n_1\) = 49

Population standard deviation \(\sigma_1\)  = 3

Sample mean \(\overline x _1\)= 10

Second population:

Sample size \(n_2\) = 64

Population standard deviation \(\sigma_2\)= 4

Sample mean \(\overline x_2\)= 12

The sample statistics follows a standard normal distribution since the sample size are large enough.

The null and alternative hypotheses can be computed as:

\(\mathbf{H_o:\mu_1=\mu_2}\)

\(\mathbf{H_1:\mu_1\ne\mu_2}\)

Level of significance  = 0.01

Using the  Z-test statistics;

\(Z = \dfrac{\overline x_1 - \overline x_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}}\)

\(Z = \dfrac{10- 12}{\sqrt{\dfrac{3^2}{49} + \dfrac{4^2}{64}}}\)

\(Z = \dfrac{-2}{\sqrt{\dfrac{9}{49} + \dfrac{16}{64}}}\)

\(Z = \dfrac{-2}{\sqrt{0.18367 +0.25}}\)

\(Z = \dfrac{-2}{\sqrt{0.43367}}\)

\(Z = \dfrac{-2}{0.658536}\)

Z = - 3.037

Z \(\simeq\) - 3.04

The P-value = 2P (z < -3.04)

From the z tables

= 2 × (0.00118)

= 0.00236

Thus, since P-value is less than the level of significance, we fail to reject the null hypotheses \(H_o\)