14) Cliff selects a letter tile at random from a bag with 5 tiles labeled A, E, I, O, and U. Then he
replaces the tile and mixes them in the bag. He repeats this 100 times and records the results
in a frequency table. Devon spins the spinner shown below 100 times and records his results
in a frequency table. Describe what you would expect to see in a frequency bar graph for
each experiment. Explain your reasoning.

Answers 15.

Step-by-step explanation:

105 = 7x Now, we can solve for x: x = 105 / 7 x = 15 So, the value of x when y = 105 is 15.

Answer:

The answer to the questions is

a)1

b)60°

Step-by-step explanation:

tan 45°=1

sin‐¹(√3/2)=60°

The values of the given trigonometric expression are:

(a) tan 45° = 1

(b) [tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ[/tex]

Use the concept of trigonometric identity defined as:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

(a) The given trigonometric ratio is,

tan 45°

Since we know that,

In the trigonometric ratio table for the measure 45°,

The value of tangent is 1.

Hence,

tan 45° = 1

For the given trigonometric exprssion,

[tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2})[/tex]

Since we know that,

Sin 60° = √3/2

Therefore,

[tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = \text{sin}^{-1}(\text{sin }60^\circ)\\\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ[/tex]

Hence,

The value of the given expression is 60°.

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Answer:

[tex]\pi \times \frac{3}{4} [/tex]

inches

OR

[tex] \frac{3}{8} \pi \: x {}^{2} [/tex]

Answer:

1891

Step-by-step explanation:

The number of unique connections between two of these phones can be made are 1891, the correct option is 2.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangements is called a combination.

The number of r-element combinations of n objects, with repetition is:

[tex]\overline{C}_{n,k} = \: ^{n + k-1}C_{k} = \dfrac{(n+k-1)!}{k! \times (n-1)!}[/tex]

We are given that;

Number of phones= 62

Now,

to find nCr, the number of unique connections between two phones.

To do this, you need to plug in the values of n and r into the formula and simplify:

nCr=r!(n−r)!n!​

62C2=2!(62−2)!62!​

62C2=2!60!62!​

62C2=2×1×60!62×61×60!​

62C2=262×61​

62C2=31×61

62C2=1891

Therefore, by the combination the answer will be 1891 unique connections

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If the number of candies (c) you get from a bag is inversely proportional to the number of people (p) who share the bag, we can represent this relationship mathematically using the formula c = k/Np

where k is a constant of proportionality and N is the total number of candies in the bag.

To understand why this formula represents an inverse relationship, we can rearrange it as:

cp = k/N

In this form, we can see that the product of c and p is constant, while N remains fixed. This means that as the number of people sharing the bag (p) increases, the number of candies per person (c) decreases, and vice versa.

The constant of proportionality (k) depends on the specific bag of candies being considered. For example, if a bag contains 100 candies and is shared among 10 people, then k = 100/10 = 10. Substituting this value of k into the equation above gives:

c = 10/p

which shows that the number of candies per person decreases as the number of people sharing the bag increases.

Therefore, the equation that represents the inverse relationship between the number of candies (c) you get from a bag and the number of people (p) who share the bag is:

c = k/Np, where k is a constant of proportionality and N is the total number of candies in the bag.

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The intervals in which the function is decreasing are:

{(-∞, -3), (1, 4)}

A function is decreasing if, when reading the graph from left to right, the graph goes downwards.

Here we can see that the graph is decreasing in the intervals:

(-∞, -3)  (leftmost part)

And in the interval:

(1, 4)

In all the other intervals the function is increasing.

Then the answer is:

Intervals: {(-∞, -3), (1, 4)}

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There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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The missing step in the proof include the following: C. QU║AD and UA║DQ because the segments have the same slope.

In Mathematics and Geometry, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

In Mathematics and Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of the two line segments are equal and the same:

Slope of line segment QU = Slope of line segment AD

-1/3 = -1/3

Slope of line segment UA = Slope of line segment DQ

-5/3 = -5/3

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Answer:

We can use proportion to solve this problem.

Let x be the cost of one invitation.

We can set up a proportion:

58/x = 87/1

To solve for x, we can cross-multiply:

58 * 1 = 87 * x

58 = 87x

x = 58/87

x = 0.67

So one invitation costs $0.67.

To find the cost of 70 invitations, we can multiply the cost of one invitation by 70:

70 * $0.67 = $46.90

Therefore, it would cost Madison $46.90 to buy 70 invitations.

The surface area of the cylinder is 408.41 cm^2.

The formula for calculating the surface area of the cylinder is 2πrh.

Here, r is the radius of the cylinder and h is the height of the cylinder.

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When we translate (x, y) to (x,y+6), will move: 6 units upwards

There are different ways of carrying out transformation of objects and they are:

Reflection whereby  all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection

Rotation whereby all points are rotated about a point.

Dilation where the object is reduced or increased by a scale factor.

Translation where the object is moved from one point to another.

Now, we are told about the translation given as (x, y + 6) which was translated from (x, y). Thus:

This tells us that the initial graph has moved upwards by 6 units.

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Answer:

Answer: (C) $546.36.

Step-by-step explanation:

To find the future value of the CD at maturity, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the future value of the CD

P = the principal amount (the initial amount invested), which is $500

r = the annual interest rate, which is 3% expressed as a decimal (0.03)

n = the number of times the interest is compounded in a year, which is once annually

t = the time the money is invested for, which is 3 years

Substituting the given values into the formula, we get:

A = 500(1 + 0.03/1)^(1*3)

A = 500(1.03)^3

A = 546.36

Therefore, the CD will be worth $546.36 at maturity. Answer: (C) $546.36.

Answer:

y = [tex]\frac{2}{3}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{3}[/tex] , then

y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

to find c substitute (6, 5 ) into the partial equation

5 = [tex]\frac{2}{3}[/tex] (6) + c = 4 + c ( subtract 4 from both sides )

1 = c

y = [tex]\frac{2}{3}[/tex] x + 1 ← equation of line

Answer:

x = √(-x) + 6 are x = 9 and x = -12

Step-by-step explanation:

To find the solution for "x" in the equation x = √(-x) + 6, we can follow these steps:

Start with the original equation: x = √(-x) + 6.

Square both sides of the equation to eliminate the square root on the right-hand side: (x)^2 = (√(-x) + 6)^2.

Simplify the right-hand side by applying the distributive property: (x)^2 = (√(-x))^2 + 2(√(-x))(6) + (6)^2.

Simplify further by noting that (√(-x))^2 = -x: (x)^2 = -x + 72 + 36.

Combine like terms: (x)^2 = -x + 108.

Move all terms to one side of the equation: (x)^2 + x - 108 = 0.

This is now a quadratic equation. We can solve for "x" by factoring, using the quadratic formula, or by graphing. Factoring or using the quadratic formula would be appropriate methods in this case.

Factoring the quadratic equation, we get: (x - 9)(x + 12) = 0.

Setting each factor equal to zero and solving for "x", we get two possible solutions: x - 9 = 0 or x + 12 = 0.

Solving for "x" in each case, we get: x = 9 or x = -12.

So, the solutions to the equation x = √(-x) + 6 are x = 9 and x = -12.

[tex]x_{1} =2\\ \\x_{2} =-3[/tex].

[tex]x=\sqrt{-x+6}[/tex]

[tex](x)^{2} =(\sqrt{-x+6})^{2} \\ \\x^{2} =-x+6[/tex]

Standard form: [tex]ax^{2} +bx+c=0[/tex]

[tex]x^{2} +x-6=0[/tex]

a= 1 (because x² doesn't show an explicit coefficient)

b= 1 (because x doesn't show an explicit coefficient)

c= -6

Quadratic formula: [tex]\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]x_{1} =\frac{-(1)+\sqrt{(1)^{2} -4(1)(-6)} }{2(1)} =2\\ \\x_{2} =\frac{-(1)-\sqrt{(1)^{2} -4(1)(-6)} }{2(1)}=-3[/tex]

[tex]x_{1} =2\\ \\x_{2} =-3[/tex].

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Answer:

45 < 9 + 18 + x < 60

45 < 27 + x < 60

18 < x < 33

Answer:

n ≥ 4

Step-by-step explanation:

9n+18-5n ≥ 34

4n +18 ≥ 34

4n ≥ 34-18

4n ≥ 16

n ≥ 16/4

n ≥ 4

You can also verify it by putting value of n in original eq

9(4)+18-5(4) ≥ 34

36+18-20 ≥ 34

34 ≥ 34

Answer:

50

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

Hi duasara! It is my pleasure to answer this question for you with step-by-step instruction.

Okay, two lines are parallel if they have the same slope. The equation of line d is 4x + 5y = 1. Solving for y, we get:

5y = -4x + 1

y = (-4/5)x + 1/5

So the slope of line d is -4/5.

Since line l is parallel to line d, it also has a slope of -4/5. The equation of line l is given as 16x + by = c. Solving for y, we get:

y = (-16/b)x + c/b

Comparing this with the equation y = (-4/5)x + 1/5 for line d, we see that the slope of line l is -16/b, which must equal -4/5. Therefore:

-16/b = -4/5

Multiplying both sides by -5b, we get:

80 = 4b

b = 20

Therefore, the value of b is 20.

The surface area of the regular pyramid is 536.40 square inches

From the question, we have the following parameters that can be used in our computation:

Base length, l = 13 in

Base width , w = 15 in

Height, h = 10 in

The surface area of the regular pyramid is calculated as

Area = lw + 1/2w√[4h² + l²] + 1/2l√[4h² + w²]

Substitute the known values in the above equation, so, we have the following representation

Area = 13 * 15 + 1/2 * 15 *√[4 * 10² + 13²] + 1/2 * 13√[4 * 10² + 15²]

Evaluate

Area = 536.40

Hence, the surface area is 536.40 square inches

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a) addition;

+ | 9 | 7 | 2

6 | 15 | 3 | 6

3 | 6 | 15 | 6

12 | 5 | 6 | 17

b) multiplication;

x | 4 | 9 | 5

6 | 2 | 42 | 35

3 | 8 | 24 | 20

9 | 72 | 5 | 35

To find the missing values, look at each row and column individually and apply the appropriate addition rule.

In the first row, 9+7=16, so the missing value in the first row is 2.

In the second row, 6+15=21, so the missing value is 3. To find the other missing value, we can look at the first column. 3+9=12, so the missing value is 6.

In the third row, 3+6=9, so the missing value is 6. To find the other missing value, look at the second column. 6+15=21, so the missing value is 6.

In the last row, 12+5=17, so the missing value is 6. To find the other missing value, look at the third column. 6+6=12, so the missing value is 5.

For the appropriate multiplication rule:

In the first row, 5 is a factor, and the only possible value of x that can give 5 when multiplied by 5 is 1. Therefore, x=1, and fill in the rest of the row using multiplication: 1x4=4 and 1x9=9.

In the second row, 6 is a factor, and the only possible value of 42 that can be divided by 6 is 7. Therefore, 6x7=42. To find the missing value in the third column, divide 35 by 7, which gives 5.

In the third row, 4 is a factor, and the only possible value of 24 that can be divided by 4 is 6. Therefore, 4x6=24 for the third row. To find the missing value in the fourth column, divide 20 by 5, which gives 4.

In the last row, 9 is a factor, and the only possible value of 72 that can be divided by 9 is 8. Therefore, 9x8=72, for the last row. To find the missing value in the third column, we can divide 35 by 7, which gives 5.

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Answer:

Method 1:

cos(60°) = 4/x

x cos(60°) = 4

x = 4/cos(60°) = 8

Method 2 (more efficient method):

Since this is a 30°-60°-90° right triangle, the length of the hypotenuse is twice the length of the shorter leg, so x = 8.

Option three log3 + log(x+4) is the equivalent to the logarithm expression  log3(x+4).

It is given that logarithm expression is log3(x+4).

It is required to simplify the above equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

aᵇ = c

logₐc = b

We have logarithm expression:

log3(x+4)

We know the log property that we can split a logarithm into two logarithms if it contains the product of two numbers ie.

log xy = logx + logy

By using this property we get:

log3(x+4)

= log3 + log(x+4)

Because 3 and (x+4) are two different numbers, not (x+4).

Thus, option three log3 + log(x+4) is the equivalent to the logarithm expression log3(x+4).

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There are three people to choose from to go on the left, and once we have chosen one of them, the other two people can be arranged in 2! ways.

There are 3 * 2! = 6 ways to arrange them if the woman will be on the left in the picture.

There are three people to choose from to go on the left, and once we've decided on one, the other two can be arranged in 2! ways.

Similarly, there are three people to choose from to go in the middle, and once we have chosen one of them, the other two people can be arranged in 2! ways.

Therefore, there are 3 * 2! = 6 ways to arrange them if the woman will be in the middle of the picture.

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The perimeter of the window in inches is 138 inches.

It will cost $110.40 to insulate the perimeter of the window.

To change the measurements to inches, we can use the fact that 1 foot is equal to 12 inches. So:

The height of the window in inches is (3 feet x 12 inches/foot) + 5 inches = 36 inches + 5 inches = 41 inches.

The width of the window in inches is (2 feet x 12 inches/foot) + 4 inches = 24 inches + 4 inches = 28 inches.

(a) The perimeter of the window in inches is the sum of the lengths of all four sides. We can use the formula for the perimeter of a rectangle to find it:

Perimeter = 2(length + width)

Plugging in the values we found:

Perimeter = 2(41 inches + 28 inches) = 138 inches

So the perimeter of the window in inches is 138 inches.

(b) We must divide the cost per inch by the perimeter in order to determine the cost of insulating the perimeter:

The following equation can be used to calculate the cost:

Cost = Perimeter x Cost per Inch

Cost = 138 inches x $0.80/inch = $110.40

So it will cost $110.40 to insulate the perimeter of the window.

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Answer:

Step-by-step explanation:

Distribution curve:

The distribution curve for this data set would be a normal distribution, as the data is approximately symmetrical and the mean is close to the center of the data. The mean of the data is 518, and 6 standard deviations from the mean would be:

Lower limit: 518 - (6 x standard deviation)

Upper limit: 518 + (6 x standard deviation)

To calculate the standard deviation, we first need to calculate the variance:

Variance = ∑(xi - μ)^2 / N

Where xi represents each value in the data set, μ is the mean, and N is the total number of values.

Using the values given, we can calculate the variance:

Variance = [(342 - 518)^2 + (518 - 518)^2 + (535 - 518)^2 + (605 - 518)^2] / 4

= 24,270

The standard deviation is the square root of the variance:

Standard deviation = √24,270

= 155.8

Therefore, the lower limit of the distribution curve would be 518 - (6 x 155.8) = 218.4, and the upper limit would be 518 + (6 x 155.8) = 817.6.

Answer:

There are various sources of accounting information, which are as follows:

1. Financial transactions: The primary source of accounting information is financial transactions such as sales, purchases, payments, receipts, and other financial activities of the business.

2. Accounting records: Accounting records such as journals, ledgers, trial balance, and financial statements are also the sources of accounting information.

3. Bank statements: Bank statements are a primary source of accounting information, as they provide information on bank balances, cash inflows, and outflows.

4. Invoices and bills: Invoices, bills, and receipts provide information on purchases and sales made by the business.

5. Management reports: Internal management reports, such as budgets, variance analysis, and performance reports, provide valuable information on the financial performance of the business.

6. Tax returns: Tax returns provide information on the business's tax obligations and payments.

7. Shareholder reports: Shareholder reports provide information on the financial performance of a company to its shareholders.

Overall, these sources of accounting information provide valuable information on the financial performance of a business, and they play a crucial role in decision-making, performance evaluation, and financial planning.

The answer to (5 3/4) (1/3) (2) is 23/6 or 3 5/6.

To multiply fractions and mixed numbers, the mixed number must first be converted to an improper fraction. We can do this by multiplying the whole number by the fraction's denominator and then adding the numerator.

As a result, 5 3/4 can be written as:

5 3/4 = (4 x 5 + 3)/4 = 23/4

We may now multiply the three factors:

(5 3/4) (1/3) (2) = (23/4) * (1/3) * (2)

When we multiply the numerators and denominators together, we get:

(23/4) * (1/3) * (2) = (2312)/(431) = 23/6

As a result, the answer to (5 3/4) (1/3) (2) is 23/6 or 3 5/6.

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Answer: the domain of the given rational function in interval notation is (-∞, -5) U (-5, -2) U (-2, 3) U (3, ∞).

Step-by-step explanation: