Swimming pool on a certain hot summer day, 606 people used the public swimming pool the daily prices are $1.75 for children and $2.50 for adults the receipts for admission totaled $1357.50. How many children and how many adults swam at the public pool that day

The value of the angle m∠WUV will be equal to 36°.

Triangle may be defined as a closed figure having three sides and three interior angles. The above question can be solved by using the exterior angle theorem of triangle. The exterior angle of a triangle theorem states that the measure of the angle formed, when one side of a triangle is extended, is equal to the sum of the opposite interior angles of that triangle. Applying the exterior angle of a triangle theorem:

m∠WUV + m∠UVW = m∠VWX

Substitute the values of angles.

(2x + 8) + (3x + 16) = (8x - 18)

5x + 24 = 8x - 18

5x - 8x = -24 - 18

-3x = -42

=> x = -42/-3

=> x = 14

So, the angle m∠WUV = 2x + 8

Putting in the value of x

m∠WUV = 2(14) + 8

m∠WUV = 28 + 8

m∠WUV = 36° which is required value.

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Answer: Sara is 51 and madison 19

Step-by-step explanation: Yes

Answer:0.01612759851

Step-by-step explanation:

hope this helps

Answer:

0.016127598511689 or just 0.02

Step-by-step explanation:

well, let's move like the crab, backwards, and start off with

3)

Check the picture below.

[tex]tan(A )=\cfrac{\stackrel{opposite}{BC}}{\underset{adjacent}{AC}}\implies tan(A)=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\qquad \textit{now let's find the \underline{hypotenuse}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ AB=\sqrt{(AC)^2 + (BC)^2}\implies AB=\sqrt{4^2 + 3^2}\implies \underline{AB=5} \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\hspace{5em} cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}[/tex]

2)

well, Graciella said they couldn't just using the tangent they were given, well, she needs stop playing Angry Birds too much.

1)

well, from what I read, Angelica thought it was possible, so she was correct all along, I don't see any mistakes in her statements, all we did in 3) was what Angelica suggested.

Answer:

A

Step-by-step explanation:

Proportions can be any number so other statements can't be always true

Answer:

A. Class X has a greater proportion of boys than Class Y

Step-by-step explanation:

- Before choosing any objective, first relate the two proportions.

Multiply class Y by 2:

[tex]{ \rm{y = 2(4 : 5)}} \\ { \rm{y= 8:10}}[/tex]

- So it can be related with class X as the ratios have a common proportion of girls; 10

[tex]{ \rm{x= 9:{ \green{10}}}} \\ { \rm{y = 8:{ \green{10}}}}[/tex]

- By observation, we see that class X has a greater number of boys than in class Y

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: ...creed}}}[/tex]

Answer:

R = 42

Step-by-step explanation:

given R is directly proportional to T , then the equation relating them is

R = kT ← k is the constant of proportion

to find k use the condition R = 60 when T = 10

60 = 10k ( divide both sides by 10 )

6 = k

R = 6T ← equation of proportion

when T = 7 , then

R = 6 × 7 = 42

Answer:

40 feet

Step-by-step explanation:

-10 -30

Answer: It's 35

Step-by-step explanation:5 and 7 both go into 35

Answer:

Step-by-step explanation:

Can you please send a pic of the leason

Answer:

x- intercept = - 3

Step-by-step explanation:

to find the x- intercept , where the line crosses the x- axis, let y = 0 in the equation and solve for x

2x - 0 + 6 = 0

2x + 6 = 0 ( subtract 6 from both sides )

2x = - 6 ( divide both sides by 2 )

x = - 3 ← x- intercept

To find the midpoint of the given line segment, we need to find the mean of the x coordinates and the y coordinates of the given points:

It means that the midpoint is M = (-1,0).

Step-by-step explanation:

D is directly proportional to x. D=36 when x=5. Work out the value of D when x=8.

Because they are directly proportional:

x/D = x/D

5/36 = 8/D

multiply both sides by D:
D(5/36) = D(8/D)

5D/36 = 8

multiply both sides by 36:

36(5D/36) = 8 * 36

5D = 288

divide both sides by 5:

5D/5 = 288/5

D = 288/5

or D = 57.6

Proportionately, based on Marvin's initial deposit, Victor invested Php 40,000 in the partnership.

Proportion is like a ratio that shows a numerical relationship between two variables.

Proportions equate one ratio to a value.

For instance, we can equate Marvin's investment ratio to his investment.

This equation helps us to calculate the total investment made by the four partners in the small business.

                               Jamie   Ralph   Marvin          Victor   Sum of Ratio

Investment ratio         8:         3:           12:                2           25

Investment amount    ?           ?     Php 240,000    ?            ?

Marvin investment = Php 240,000 = 12/25

Total investment by the partners = Php 500,000 (Php 240,000/12 x 25)

Victor's investment = Php 40,000 (Php 500,000 x 2/25)

Profit for the year = Php 150,000

Thus, based on proportional contributions of Marvin, Victor's investment is Php 40,000.

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Thus {u, v} is linearly independent if and only if {u v, u − v} is linearly independent

It is given that {u,v} be a linearly independent set of a set S.

This means that there exist constant a,b such that if:

                               au+bv=0

                            then a=b=0

Now we are asked to prove that:

{u+v,u-v} is a linearly independent set.

Let us consider there exists constant c,d such that:

                           c(u+v)+d(u-v)=0

To show:   c=d=0

The expression could also be written as:

cu+cv+du-dv=0

( Since, using the distributive property)

Now on combining the like terms that is the terms with same vectors.

cu+du+cv-dv=0

i.e.

(c+d)u+(c-d)v=0

Since, we are given that u and v are linearly independent vectors this means that:

c+d=0------------(1)

and c-d=0 i.e c=d-----------(2)

and from equation (1) using equation (2) we have:

2c=0

i.e. c=0

and similarly by equation (2) we have:

        d=0

Hence, we are proved with the result.

We get that the vectors {u+v,u-v} is linearly independent.

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Answer: a13=310.7

Step-by-step explanation:

Formula= an=a1r^n-1

a13=1100(0.9)13-1

a13=310.7

The number of positive Integer Pairs (x,y) that satisfy 4x+12y=640 is 160

To determine whether the function is above or below the x-axis, we must examine the graph of the function relative to the x-axis as shown below:

When a function is above the x-axis, it is positive. When a function is below the x-axis, it is considered negative. The function is described in the context of this issue as follows:

Given that both x and y have exponents of 1, this function is linear. The values above the line on the function are the ordered pairings. The values of x for which the function is positive are provided by: For integer integers, that is, numbers without decimal places, from the graph of the function given at the conclusion of the answer 0 ≤ x ≤ 160.

The number is 160.

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A compound interest that pays 5% interest compounded daily is preferable. This is so even though the interest rates on the two accounts are equal, the 5% interest compounded daily account is used more frequently.

 Interest is the cost of borrowing money, such as the sum added to a loan debt. It is also possible to classify the rate paid for holding money on deposit, such as in the case of a certificate of deposit. The two ways to calculate interest are simple interest and compound interest.

On the principal, or original loan amount, of a loan, simple interest is calculated.

Since compound interest is calculated using both the principal and the accrued interest from previous periods, it is frequently referred to as "interest on interest".

If interest is computed on a compound basis rather than a simple basis, the amount of interest that must be paid on a loan can vary significantly. Positively speaking, the magic of compounding may be a powerful tool for wealth growth and can work in your favor when it comes to your assets.

Simple interest and compound interest are fundamental financial concepts, but understanding them thoroughly may enable you to make better choices when applying for a loan or making investments.

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Let the yellow dot equal to y In the diagram I drawn. NOW I WILL USE THE REASON SUM ANGLES OF A TRIANGLE 43°+57°+ YELLOW DOT=180°

[tex]43 + 57 + y = 180 \\ 100 + y = 180 \\ y = 180 - 100 \\ y = 80[/tex]

THE YELLOW DOT FROM THE TRIANGLE ON THE RIGHT IS EQUAL TO THE DOT ON THE TRIANGLE ON THELEFT SIDE BY VERTICAL OPPOSITE

[tex]x + x + y = 180 \\ 2x + 80 = 180 \\ 2x = 180 - 80 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]

x=50°

HOPE THIS HELPS.

IF YOU HAVE ANY QUERIES ASK AS SOON AS POSSIBLE.

Answer:

The first term will be 38.375

Step-by-step explanation:

aₙ = a₁ + (n - 1) * d

a₂₀ = -40

a₂₈ = -73

-40 = a₁ + 19d

-73 = a₁ + 27d

When we have two similar equations with two unknowns, we can subtract them to get an answer.

 -40 = a₁ + 19d  --> -40 = a₁ + 19d

-(-73 = a₁ + 27d) --> 73 = -a₁ - 27d

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

33 = -8d

Solve for d by dividing by -8

d = -4.125

Now plug d into one of the original equations to solve for a₁

-40 = a₁ + 19(-4.125)

-40 = a₁ - 78.375

a₁ = 38.375

The number of minor damaged books in 73500 book collection is 8,673 books.

Given that, 661 books had no damage, 78 books had minor damage, and 26 books had major damage.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the minor damaged books be x.

Now, 78 : 661 :: x : 73,500

⇒ 661x = 73500 × 78

⇒ 661x = 57,33,000

⇒ x = 57,33,000 ÷ 661

⇒ x = 8,673.22

≈ 8,673

Therefore, the number of minor damaged books in 73500 book collection is 8,673 books.

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The angle 4 is 105°. From alternative interior angle the angle 5 is 105°.

Given that,

In the picture we can see,

The angle 4 is 105°.

We have to find the angle 5.

The parallel lines,

If a transversal divides two straight lines,

When the two alternate angles are equal, two straight lines become parallel.

The two straight lines are parallel if the pair of internal angles on the same side of traversals is supplementary.

The two straight lines are parallel if the pair of corresponding angles is equal.

The alternative interior angle are always equal.

The angle 4=angle 5

105°=angle 5

The angle 5 =105°.

Therefore, The angle 5 is 105°.

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The number of subsets of {38,76,152,304} are 32.

If every element of set A is also an element of set B, then set B is a superset of set A and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another. If every element in a set A is also an element in a set B, then the set A is a subset of the set B. The set A is therefore contained within the set B. A⊂B is used to represent the subset connection.

Given Data

Set = {38,76,152,304}

When there are "n" elements in a set, there are 2ⁿ subsets of that set, and there are 2ⁿ subsets of that subset.

Here,

n = 5

Equating in formula:

= 2⁵

= 32

The number of subsets of {38,76,152,304} are 32.

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For the given equation, the inequality is y > 14

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

x + 2×7 = y

=> y = x + 14

Here, y > x.

So, y > 14

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I WILL USE SUBSTITUTION TO SOLVE THE PROBLEM BY EQUATING -2X-6 TO 2X+10 SINCE THEY ARE BOTH EQUAL TO Y

WILL USE SUBSTITUTION TO SOLVE THE PROBLEM BY EQUATING -2X-6 TO 2X+10 SINCE THEY ARE BOTH EQUAL TO Y[tex] - 2x - 6 = 2x + 10 \\ - 2x - 2x = 10 + 6 \\ - 4x = 16 \\ \frac{ - 4x}{ - 4} = \frac{16}{ - 4} \\ x = - 4[/tex]

USE ANY OF THE EQUATIONS TO FIND THE VALUE OF Y YOU WILL GET THE SAME ANSWER

[tex]y = -2 ( - 4) - 6 \\ y = 8 - 6 \\ y = 2[/tex]

ATTACHED IS THE SOLUTION

Answer:

Simplifying

y = -2x + -6

Reorder the terms:

y = -6 + -2x

Solving

y = -6 + -2x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = -6 + -2x

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

Simplifying

y = 2x + 10

Reorder the terms:

y = 10 + 2x

Solving

y = 10 + 2x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = 10 + 2x

IN THE PLACE OF X PLUG IN 3 AND SIMPLIFY

[tex]f(3) = ({3})^{3} + 2( {3})^{2} - (3) - 1 \\ f(3) = 27 + 2(9) - 3 - 1 \\ f(3) = 27 + 18 - 4 \\ f(3) = 45 - 4 \\ f(3) = 41[/tex]

ATTACHED IS THE SOLUTION.

If the chess board is made with the height of the king the length of the square is going to be 1.75 inches

This is the term that is used to refer to the relationship that is in existence between two independent amounts.

The ratio is given as

3. 5 = 4.5 inches

? = 2.25

The unknown that we are to solve for here would be the value of the height of the king. This is to be gotten when we have to use the cross multiplication

2.25 * 3.5 = 4.5?

7.875 = 4.5?

divide through by 4.5

? = 7.875 / 4.5

= 1.75

Hence the length of the square is 1.75 inches.

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Answer:

Answer down below!

Step-by-step explanation:

If you know that he ran 2 miles in 14 minutes, you can also say he ran 1 mile in 7, because he is running in 7 minute increments

Let's go up together! (The numbers express how many miles have been run!)

So in 63 minutes, the runner will have ran 9 miles!

Answer: 5x + 15 = y

Step-by-step explanation:

mx+b = y

find rise over run

(y_2-y_1)/(x_2-x_1) = m

(-5-5)/(-4+2)

simplify

-10/-2

10/2

5 = m

plug in a point and find b

5(-2) + b = 5

-10 + b = 5

b = 15

5x + 15 = y