Five of every six students interviewed favored a change in library hours. Among those interviewed, what is the ratio of those who favor a change to those who do not favor change?

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually means once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=300\left(1+\frac{0.05}{1}\right)^{1\cdot 10}\implies A=300(1.05)^{10}\implies A\approx 488.67\)

Answer:

P’(-1, 1), I’ (1, 2), G’(1,0)

Step-by-step explanation:

Answer:

8x + 28

Step-by-step explanation:

Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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9514 1404 393

Answer:

  z = 20

  m∠A = 70°

Step-by-step explanation:

Step 0: read and understand the question. Identify the given information and the information requested.

Step 1: consult your knowledge of inscribed quadrilaterals to determine that opposite angles are supplementary.

Step 2: identify angles A and C as being marked with expressions in z.

Step 3: use those expressions and the relation in Step 1 to write an equation.

  A + C = 180°

  (4z -10)° +(10 +5z)°= 180°

Step 4: solve for z.

  9z = 180 . . . . simplify, divide by °

  z = 20 . . . . . . divide by 9

Step 5: use the relation between z and the measure of angle A to answer the question.

  m∠A = (4z -10)° = (4·20 -10)°

  m∠A = 70°

Step 6: check your answer. This can be done by making sure that angle C is supplementary to angle A.

  C = (10 +5z)° = (10 +5·10)° = 110° = 180° -70° ∴ answer checks OK

Answer:

1384.7

Step-by-step explanation:

42/2     21^2x3.14=1384.74

Hope this Helps :)

Answer:

it is proportional

Step-by-step explanation:

constant of proportionality= 4

equation: b=4c

Answer:

The 1st one .

Step-by-step explanation:

Answer:

z: 19

Step-by-step explanation:

Answer:

87.434°

Explanation:

To write 87°26'3" as a decimal, we follow the steps below:

Thus:

The result is 87.434° to the nearest thousandth.

Answer:

p ∨ q

Step-by-step explanation:

I took the test and got a 100

The correct statement for the shape being a rectangle is p ∨ q

Any figure bounded by 3 sides and sum of all the internal angles is 180° is called a triangle.

Any figure bounded by four sides, where the opposite sides are equal and all the internal angles are 90° is called a rectangle

As we know a triangle cannot have four sides, so p cannot imply q and vice versa.

According to the problem,

This is a contradiction.

So for the shape being a rectangle the correct option will be p v q(p intersection q)

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Answer:

45

Step-by-step explanation:

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Answer:

90%

Step-by-step explanation:

1. We assume, that the number 5400 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 5400, so we can write it down as 100%=5400.

4. We know, that x% equals 6000 of the output value, so we can write it down as x%=6000.

5. Now we have two simple equations:

1) 100%=5400

2) x%=6000

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=5400/6000

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 6000 is what percent of 5400

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer:

Step-by-step explanation:

Top triangle:

The hash marks indicate congruence. So, x is congruent to 15 or x= 15

x+6= 21

The length of the sides of this triangle are 15,15, and 21.

Two sides are congruent so isosceles.

Bottom triangle:

The sum of the angles in a triangle is 180.

30+35+x=180

75+x=180

x=105

105> 90, so this is an obtuse triangle.

Answer:

Step-by-step explanation:

Top triangle

good luck God bless merry Christmas and happy new year and stay safe and good luck in life! God bless y’all! :)

Answer:

20200

Step-by-step explanation:

As you're in a hurry, I can give it later? xx

Answer:

Step-by-step explanation:

You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.

__

The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).

The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).

The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).

__

Additional comment

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

Inequalities

Solve the inequality:

Subtracting 2:

Answer: Let's call the number of percussionists on the sideline "x".

Since the ratio of percussionists to marching instruments is 2 to 13, for every 2 percussionists, there are 13 marching instruments.

So the total number of band members is 2x + 13x = 15x.

We know that the total number of band members is 150, so we can write an equation to solve for x:

15x = 150

Dividing both sides by 15:

x = 10

So there are 10 percussionists on the sideline.

Step-by-step explanation:

Answer:P(BBR) = 1/2 × 25/51 × 26/50 = 13/102 if cards are not replaced.

P(RBB) = 1/2 × 26/51 × 25/50 (simplified 1/2) = 13/102

P(BRB) = 1/2 × 26/51 ×25/50 (simplified 1/2) = 13/102

Step-by-step explanation: P(B) at first step is 26 cards out of a possible 52 therefore 26/52 (or simplified 1/2). We then have 25 black cards left out of a possible 51 therefore 25/51. The final card then has to be red to meet the criteria, we have 26 red cards still out of a possible 50 therefore 26/50.

This would be an example of binomial probability as at each step there are only 2 options R or B.

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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The sequence is geometric, with a common ratio of 1/3, and the missing terms are 12 and 4.

To determine if the sequence is arithmetic, geometric, or neither, let's examine the given terms: 972, 324, 108, 36.

To find the missing terms of the sequence, let's look for a pattern in the numbers:

If we divide each term by 3, we get:

972/3 = 324

324/3 = 108

108/3 = 36

It seems that each term is obtained by dividing the previous term by 3.

Now, let's check if the sequence is arithmetic or geometric:

If we calculate the common difference between consecutive terms, we see that there is no constant difference. For example:

324 - 972 = -648

108 - 324 = -216

36 - 108 = -72

Since the differences are not constant, the sequence is not arithmetic.

If we calculate the common ratio between consecutive terms by dividing a term by its previous term, we find that the ratio is constant:

324/972 = 1/3

108/324 = 1/3

36/108 = 1/3

The common ratio is 1/3, which indicates that the sequence is geometric.

The missing terms in the sequence are:

(36/3) = 12

(12/3) = 4

The complete sequence is: 972, 324, 108, 36, 12, 4.

The sequence is geometric, with a common ratio of 1/3, and the missing terms are 12 and 4.

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Answer:

28.4

Step-by-step explanation:

Add 5.5 to both sides.

x - 5.5+5.5 cancels out the -5.5 to get x.

x = 22.9+5.5

x=28.4

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer: 1 slice for each person

Step-by-step explanation: It depends on how many slices you cut it into. Suppose we cut it into 6 equal pieces. Since we already know that they will save half of the pizza for dinner, there will only be 3 remaining because. This means Aaron, Michael and Johnny will all get 1 equal slice.

Answer:

{x,y} = {6/5,23/10}

Step-by-step explanation:

 [1]    7x + 2y = 13

  [2]    4x + 4y = 14  <---------- linear equations given

Graphic Representation of the Equations : PICTURE
2y + 7x = 13        4y + 4x = 14  

Solve by Substitution :

// Solve equation [2] for the variable  y

[2]    4y = -4x + 14

[2]    y = -x + 7/2

// Plug this in for variable  y  in equation [1]

  [1]    7x + 2•(-x +7/2) = 13

  [1]    5x = 6

// Solve equation [1] for the variable  x

  [1]    5x = 6

  [1]    x = 6/5

// By now we know this much :

   x = 6/5

   y = -x+7/2

// Use the  x  value to solve for  y

   y = -(6/5)+7/2 = 23/10

// Plug this in for variable  y  in equation [1]

 [1]    7x + 2•(-x +7/2) = 13

  [1]    5x = 6

// Solve equation [1] for the variable  x

 [1]    5x = 6

[1]    x = 6/5

// By now we know this much :

   x = 6/5

   y = -x+7/2

// Use the  x  value to solve for  y

  y = -(6/5)+7/2 = 23/10

Answer:

205.74 cm

Step-by-step explanation:

Explanation

To answer the question, we will make use of the formula

Where

Thus

Thus, the balance will be $5635.20

1) 3:00 to 4:00

2) 103

The required solution is 4:00 to 5:00 and  87  customers.

It is required to fill in the blanks.

The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given:

According to question , Initially, there were 75 customers.

From 1:00 to 2:00, a total of 30 more people entered, meaning there were

 75 + 30 - 12

= 93 people.

From 2:00 to 3:00, a total of 14 more people entered, meaning there were

93 + 14 - 8  

= 99 people.

From 3:00 to 4:00, a total of 18 people entered, meaning there were

 99 + 18 - 30

= 87 people.

4:00 to 5:00   :  If the store does not accept any more customers except those who are already inside then, all 87 must leave between 4:00 to 5:00 in order to left from the store by 5:00.

Therefore, the required solution is 4:00 to 5:00 and  87  customers.

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Answer:

$3040 profit made

Step-by-step explanation:

$13×95=$1235 cost to make all the shoes they sold

$45×95=$4275 money she made

$4275-$1235=$3040 profit