Angelique throws a different six-sided dice 120 times.
The table shows her results.
Score 1 2 3 4 5 6
Frequency 15 26 21 14 20 24
Work out the experimental probability of throwing a multiple of 3

The Confidence interval for 95% who believes that the local businesses overcharge = (0.7026, 0.7574)

The range of values we see in our sample and hope to identify the value that most closely represents the population are referred to as a confidence interval.

Sample size n = 1000

73% of town residents believed that local businesses overcharged for their products over 1000 resident.

= (1000/100) x 73

= 730

Sample proportion p = 730/1000

                                    = .73

q = 1-p = 0.23

Std error of proportion = √(pq/n)

                                      = √((.73*0.27)/1000)

                                      = 0.0140

95% Z critical value = 1.96

Margin of error = 1.96*0.0140

                          = 0.0274

Confidence interval = sample proportion ±margin of error

(0.7026, 0.7574)

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DDDDDDDDDDDDDDDDDDDDD

Answer:

64 people

Step-by-step explanation:

Let the number of people that attended the movie last month be represented by x.

Number of people who attended the movie this month = 50

\(\frac{3}{4}\) of x + 2 = 50

\(\frac{3x}{4}\) + 2 = 50

\(\frac{3x}{4}\) = 50 - 2

\(\frac{3x}{4}\) = 48

3x =  48 x 4

3x = 192

x = 64

The number of people that attended the movie last month was 64.

The correct exponent law is  \(a^xa^y=a^(x+y)\).

What is exponent law?

 Different exponent laws exist in mathematics. Numerous mathematical issues involving repeated multiplication are solved using all of the exponentiation rules. The multiplication and division processes are made simpler by the principles of exponents, which also make problem solving simple. The process of simplifying exponent-based equations is facilitated by exponent rules, commonly referred to as the "laws of exponents" or the "properties of exponents." These guidelines can be used to help simplify expressions that contain exponents that are decimals, fractions, irrational numbers, or negative integers.

Here the given ,

=> \(a^na^m=a^(n.m)\)

We know that if base of two exponents equal , we can add their exponent.

=> \(a^xa^y=a^(x+y)\)

According to the given exponents value ,

=> \(x^3.x^6\)

=> \((x^1.x^1.x^1)(x^1.x^1.x^1.x^1.x^1.x^1)\)

=> \(x^(3+6)\)

=>\(x^9\)

Hence the correct exponent value is \(x^9\).

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Answer:

F. 230 = 7.5x - 100

Step-by-step explanation:

this equation illustrates how to determine the number of bracelets melaine sold, while the others do not

y = 0.25x + 50 and y = 0.3x + 40 will be the equation to find the cost to rent a car.

A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

Costs are the dollar amount spent on materials, labor, services, goods, equipment, and other items for use by a company or other accounting organization.

y = 0.25x + 50

y = 0.3x + 40

The equations will be written as y = mx + b, or slope-intercept form. You must determine what you have in order to determine what belongs where.

They receive $50 per day plus $0.25 per mile from Rent-A-Wreck. This indicates that the $0.25 per mile is the number that changes daily. Thus, y = 0.25x + 50 will be the equation.

They receive $40 per day with $0.30 per mile from Drive-A-Lemon. This indicates that the $0.30 per mile is the number that changes daily. y = 0.3x + 40 will be the formula.

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If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

Answer:

B

Step-by-step explanation:

Answer: 6.2x10^10

Step-by-step explanation:

There must be a number less than 10 on the left side

Answer:

Option 3

Step-by-step explanation:

Because 6.2 x 10^7 using the caret symbol

Answer:

x = - 8 and (- 8, 0 )

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

y = x² + 16x + 64 ← is in standard form, with

a = 1 and b = 16, then

x = - \(\frac{16}{2}\) = - 8

Equation of axis of symmetry is x = - 8

Substitute x = - 8 into the quadratic and evaluate for y

y = (- 8)² + 16(- 8) + 64 = 64 - 128 + 64 = 0

vertex = (- 8, 0 )

The module of x is equal to 9, this means that x has two possible values "9" or "-9"

Answer:

5/9

Step-by-step explanation:

Here, we want to write the fraction of the counters that are green

We start by calculating by the total ratio

That would be 4 + 5 = 9

The part that is green here is 5

So, the fraction of counters that are green is 5/9

The explicit formula for this sequence 6, 12, 24, 48, 96, .. is equal to aₙ = 6 * 2ⁿ⁻¹.

The sequence shown above is a geometric sequence because each term is obtained by multiplying the previous term by 2. To find the explicit formula for this sequence, we can use the formula:

aₙ = a₁ * rⁿ⁻¹

where:

aₙ = the nth term of the sequence

a₁ = the first term of the sequence

r = the common ratio between terms

n = the position of the term in the sequence

In this case, a₁ = 6 and r = 2, so the formula becomes:

aₙ = 6 * 2ⁿ⁻¹

Using this formula, we can find any term in the sequence by plugging in the value of n. For example, to find the 7th term, we would plug in n = 7:

a₇ = 6 * 2⁷⁻¹ = 6 * 2⁶ = 384

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Answer:

x = 5

Step-by-step explanation:

Solve for x:

-1 - 5 (-x - 1) + 4 x = 49

-5 (-x - 1) = 5 x + 5:

(5 x + 5) + 4 x - 1 = 49

Grouping like terms, 5 x + 4 x - 1 + 5 = (5 x + 4 x) + (-1 + 5):

((5 x + 4 x) + (-1 + 5)) = 49

5 x + 4 x = 9 x:

9 x + (-1 + 5) = 49

5 - 1 = 4:

9 x + 4 = 49

Subtract 4 from both sides:

9 x + (4 - 4) = 49 - 4

4 - 4 = 0:

9 x = 49 - 4

49 - 4 = 45:

9 x = 45

Divide both sides of 9 x = 45 by 9:

(9 x)/9 = 45/9

9/9 = 1:

x = 45/9

The gcd of 45 and 9 is 9, so 45/9 = (9×5)/(9×1) = 9/9×5 = 5:

Answer:  x = 5

Answer:

EVALUATE

=9x+4

St−5(−x−1)+4x−1

Use the distributive property to multiply −5 by −x−1.

−5(−x)+5+4x−1

Multiply −5 and −1 to get 5.

5x+5+4x−1

Combine 5x and 4x to get 9x.

9x+5−1

Subtract 1 from 5 to get 4.

9x+4

EXPAND

=9x+4

−5(−x−1)+4x−1

Use the distributive property to multiply −5 by −x−1.

−5(−x)+5+4x−1

Multiply −5 and −1 to get 5.

5x+5+4x−1

Combine 5x and 4x to get 9x.

9x+5−1

Subtract 1 from 5 to get 4.

9x+4

Please find attached the graph of the linear equation for the total cost of transportation of sugar created with MS Excel is attached.

A graph is a pictorial representation of the relationship between the variables in an equation.

The amount it costs to rent the truck =  $5000

The amount it cost to transport a ton  of sugar = $200

The amount of sugar transported in tons = S

The equation for the total cost C is; C = 5000 + 200·s

The graph of the equation for the cost of transportation  can be created with a spreadsheet application such as MS Excel, by entering the formula, = 5000 + 200*RefCell, in a cell and the value of S in an adjacent cell, the values for S are then populated and the values of C are generated using the formula in the cell

The two columns are then selected

Then the insert, Chart menu is then used to create the graph.

Please find attached the required graph created with MS Excel

The  graph for the total cost for the transportation is therefore a straight line graph with a slope of 200 and a y-intercept of 5,000,

The

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Answer:

-5

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Answer:

There 6.

Step-by-step explanation:

9/2 divided 3/4

9/2 divided 4/3

9/1  x 2/3 = 18/3 = 6

There are 364 different committees of 3 people. There are 436 different committees of 4 people.

There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:

To calculate the number of different committees of 3 people, we can use the combination formula, which is:

\(${n \choose k} = \frac{n!}{k!(n-k)!}$\)

where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:

\(${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$\)

Therefore, there are 364 different committees of 3 people that can be formed from this group.

To solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:

\(${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$\)

Next, we calculate the number of committees that do not include a freshman, which is:

\(${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$\)

Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:

\(${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$\)

\(${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$\)

\(${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$\)

Now we can apply the principle of inclusion-exclusion, which is:

Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.

Plugging in the values, we get:

$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$

Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.

Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.

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The lines are parallel, thus, the system of equations is inconsistent.

Here we have the graph of a system of equations (because we have two graphs on the same coordinate axis). We can see that the two equations are linear equations, and we can see that the lines are parallel (the distance between the lines remains constant).

Thus, the lines will never intercept, which means that the system of equations has no solutions.

Then we define this system (with no solutions) as an inconsistent system of equations.

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The equation of the parabola is y = ( 4/3 ) ( x + 1 )² + 4

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation of parabola be represented as A

Now , the value of A is

Let the vertex of the parabola be V

Now , the coordinates of P is V ( -1 , 4 )

and , equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

On simplifying , we get

y = a ( x - ( - 1 ) ) + 4

y = a ( x + 1 )² + 4

Now , the point on the parabola is given by P ( 2 , 16 )

On simplifying , we get

when x = 2 and y = 16

16 = a ( 2 + 1 )² + 4

16 = 9a + 4

12 = 9a

a = 4/3

So , the the value of a is 4/3

And , the equation is g ( x ) = ( 4/3 ) ( x + 1 )² + 4

Therefore , the value of g ( x ) is ( 4/3 ) ( x + 1 )² + 4

Hence , the equation of parabola is g ( x ) = ( 4/3 ) ( x + 1 )² + 4

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The best sample frame when studying the nature of product defects generated by two types of stamping machines is a D) list of all stamping machines in the factory, divided into two groups by type of machine.

When studying the nature of product defects generated by two types of stamping machines, the best sample frame is the list of all stamping machines in the factory divided into two groups by the type of machine. A sample frame refers to a list of items or individuals from which a sample is drawn.

The sample frame is an important element of a research study as it forms the basis for choosing the sample. It should be inclusive, accurate, and up-to-date. It is also critical to define the sampling unit and the population so that the correct sample frame can be selected.

The list of all machines in your factory would not be an appropriate sample frame because not all machines would be involved in the production of the stamped products.

A list of all serial numbers of stamping machine output during one month would not be suitable as the sample frame as it would be biased towards a specific time period and may not represent the entire population of the stamping machines in the factory.

None of the options listed above provide the best sample frame.

Therefore, the best sample frame when studying the nature of product defects generated by two types of stamping machines is a list of all stamping machines in the factory divided into two groups by the type of machine.

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Answer:

highlighted answer is correct

Step-by-step explanation:

Answer:

4.85/ 4.90 rounded to nearest tenth

Step-by-step explanation:

1+1+4+8+9+3+8 = = 34

34/7 = 4.85

Answer:

4.9

Step-by-step explanation:

1+1+4+8+9+3+8 = 34

34 ÷ 7 = 4.857142857

Rounded = 4.9

Answer:

52°

Step-by-step explanation:

360 - 33 - 165 - 20 - 90 = x

x = 52

Answer:

Step-by-step explanation:

Let's find the size of angle x

The angle in a complete turn add up to 360°

\( \mathsf{x + 20 + 165 + 33 + 90 = 360}\)

Add the numbers

\( \mathsf{x + 308 = 360}\)

Move constant to R.H.S and change it's sign

\( \mathsf{x = 360 - 308}\)

Calculate the difference

\( \mathsf{x = 52}\) °

Hope I helped!

Best regards!

Answer:y = 4x-5.

Step-by-step explanation:

Answer:

after 8years

Step-by-step explanation:

Complete question;

In what time will Rs 10000 will yield a compound interest of Rs 2769​ at 3% per annum

Using the compound interest formula;

A =P(1+r)^n

Given

P = Rs10000

A = 10000+2769

A = 12769

rate = 3% = 0.03

Substitute and get the time t

12769 = 10000(1+0.03)^n

12769/10000 = 1.03^n

1.2769 = 1.03^n

log 1.2769 = nlog1.03

n =  log 1.2769/log 1.03

n = 0.1062/0.01283

n = 8.27

Hence the time is approximately after 8years

The number of centimeters in an inch is approximately 2.54, while the number of inches in a centimeter is approximately 0.39.

Using the customary ruler, the length of the side of the wooden block is measured as 1 3/32 inches.

This means the length is slightly over 1 inch but less than 1 1/8 inches.

To estimate one place value beyond the ruler's gradations, we can round the measurement to 1.1 inches.

Using the metric ruler, the length is measured as 2.78 centimeters. This measurement provides a more precise value in the metric system.

To calculate the ratio between centimeters and inches, we find that there are approximately 2.54 centimeters in an inch.

This means that for every 1 inch, there are approximately 2.54 centimeters.

Conversely, there are approximately 0.39 inches in a centimeter.

This means that for every 1 centimeter, there are approximately 0.39 inches.

In conclusion, the length of the wooden block's side is measured as 1.1 inches using the customary ruler and 2.78 centimeters using the metric ruler.

The conversion ratios between centimeters and inches are approximately 2.54 cm/inch and 0.39 inch/cm, respectively.

These ratios can be used to convert measurements between customary and metric systems.

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Answer:

Step-by-step explanation: