Caleb performed an experiment in which he rolled a number cube 100 times. He recorded the results in a table.

What was the experimental probability of rolling a 4?

Number Rolled - Frequency - Experimental Probability
1                          15                    0.15
2                          17                    0.17
3                          17                    0.17
4                          14                      ?
5                          21                    0.21
6                          16                    0.16

Answer: [tex]\dfrac{-5}{2}[/tex]

Step-by-step explanation:

We know that equation in intercept form is given by :-

[tex]y=mx+c[/tex] , where m is the slope of the line {Coefficient of x}

The given equation of a line : [tex]5x+2y=6[/tex]

First rewrite the given equation in intercept form , we get

[tex]2y=6-5x\\\\\Rightarrow\ y=\dfrac{1}{2}(6-5x)\\\\\Rightarrow\ y=\dfrac{-5}{2}x+\dfrac{6}{2}\\\\\Rightarrow\ y=\dfrac{-5}{2}x+3[/tex]

Comparing to the general intercept form , we have , the slope of the line = [tex]\dfrac{-5}{2}[/tex]

Since the slopes of two parallel lines is equal.

Therefore, the  slope of a parallel line to [tex]5x+2y=6[/tex] : [tex]\dfrac{-5}{2}[/tex]

The total cost producing 1 camera case is:

                            $ 11

Let the quadratic function be:

[tex]c(x)=ax^2+bx+c[/tex]

Now, c(3)=45

This means:

[tex]9a+3b+c=45------------(1)[/tex]

c(7)=257

This means that:

[tex]49a+7b+c=257----------------(2)[/tex]

and c(12)=792

This imply:

[tex]144a+12b+c=792-------------------(3)[/tex]

On subtracting first equation from second we get:

[tex]40a+4b=212------------(4)[/tex]

and on subtracting second equation from third we get:

[tex]95a+5b=535-----------(5)[/tex]

Now on multiplying equation (4) by 5 and equation (5) by 4 and subtracting both equation we get:

a=6

Putting value of a in equation (4) we get:

b= -7

and putting the value of a and b in equation (1) we get:

c=12

Hence, the cost function is:

[tex]c(x)=6x^2-7x+12[/tex]

Now, the cost of producing 1 camera will be the value of c(x) when x=1

i.e.

[tex]c(1)=6-7+12\\\\\\c(1)=11[/tex]

                 Hence, the answer is:

                        $ 11

Answer:

u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye

Step-by-step explanation:

Answer:

C.Yes, because this definition fits all acute triangles and does not fit triangles that are not acute.

Step-by-step explanation:

The smaller of the two possible angles used is;

θ = 15.92°.

We are given;

Range of pass; R = 7.75 m

Speed; u = 12 m/s

Formula for range is;

R = [u²sin (2θ)]/g

Where; θ is the angle at which the ball was thrown.

Thus;

7.75 = 12² × (sin(2θ))/9.8

(sin(2θ)) = (7.75 × 9.8)/12²

(sin(2θ)) = 0.5274

2θ = sin^(0.5274)

2θ = 31.83

θ = 31.83/2

θ = 15.92°

Now, if we assume that this angle is to the vertical, it means the angle to the horizontal is;

90 - 15.92 = 74.08°

In conclusion, the two possible angles are 15.92° and 74.08°.

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The missing value to the nearest hundredth using inverse trigonometric function is 67.11°

Let us say

Cos x = 7/18

x will be the inverse of cosine of (7/18)

The inverse trigonometric functions are the inverse functions of the trigonometric functions and are used to obtain an angle from any of the angle's trigonometric ratios.

x = cos⁻¹ (7/18)

x = 67.11°

Hence, the missing value to the nearest hundredth is 67.11°.

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The number of rows in the auditorium is 45, and each row has 59 seats.

This problem can actually be solved using Algebra. If we let 'x' represent the number of rows in the auditorium, then the number of seats in each row would be x + 14 (since the number of seats in each row exceeds the number of rows by 14). Since the total number of seats is 1320, we can now set up and solve an equation: x(x + 14) = 1320.

Solving the equation, we get [tex]x^2[/tex] + 14x - 1320 = 0. This can be factored to (x - 45)(x + 29) = 0. The positive solution is x = 45. Therefore, there are 45 rows in the auditorium.

Substituting x = 45 back to our original equation x + 14, we find out that there are 45 + 14 = 59 seats in each row.

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Answer:

[tex]a_n = a_{n-1}-13.8[/tex]

Step-by-step explanation:

The recursive rule for the arithmetic sequence is given by:

[tex]a_n = a_{n-1}+d[/tex]          .....[1]

where, d is the common difference of two consecutive terms.

Given the sequence:

−7.4, −21.2, −35, −48.8, −62.6

This is an arithmetic sequence

Here, first term[tex](a_1)[/tex] = -7.4 and d = -13.8

Since,

-21.2+7.4 = -13.8,

-35+21.2 = -13.8 ans so on...

Substitute the given value in [1] we have;

[tex]a_n = a_{n-1}+(-13.8)[/tex]

⇒[tex]a_n = a_{n-1}-13.8[/tex]

Therefore, the recursive rule for the sequence is, [tex]a_n = a_{n-1}-13.8[/tex] and [tex]a_1[/tex]= -7.4

The recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex]  and [tex]\rm a_{1}[/tex] = -7.4.

The recursive rule refers to the first term of the sequence and describe  

the relation to the preceding term with the recursive equation.

The recursive formula for the arithmetic sequence is as follows

[tex]\rm a_{n} = a_{n-1} + d[/tex]

where [tex]\rm a_{n}[/tex] is the nth term and d is a common difference

The arithmetic sequence is given as

−7.4, −21.2, −35, −48.8, −62.6

[tex]\rm a_{1}[/tex] = -7.4 (first term)

d = -21.2+7.4 = -13.8,

d = -35+21.2 = -13.8

Substitute the given value, we get

[tex]\rm a_{n} = a_{n-1} + d[/tex]

[tex]\rm a_{n} = a_{n-1} -13.8[/tex]

Hence, the recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex]  and [tex]\rm a_{1}[/tex] = -7.4.

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Answer:

"  A DMP allows you to deposit a set amount of money with a credit counseling organization each month, which is then strategically dispersed to your various creditors "

" DMPs are designed to help consumers work off their debt as quickly as possible by leaving these decisions largely to credit counseling professionals "

Before sending monthly payments to the organization handling your DMP, confirm with your creditors that they have in fact accepted the plan.

Before you make any payments to the organization handling your DMP (debt management plan) you should confirm with your creditors that they have accepted the plan.

A Debt Management Plan is a laid-out framework for settling debts that is coordinated by a credit counseling organization. A certain amount of money is deposited with these organizations that help the debtor to offset his bills in a strategic manner.

So, before making any payments to the organization handling your DMP (debt management plan) you should confirm with your creditors that the plan for repayment is acceptable by them.

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After calculating Peter's earnings from working on 6 houses, the remaining amount from his total paycheck indicates that he worked for 25 hours at his hourly wage of $6.

To determine how many hours Peter worked when he received a paycheck for $210, we need to consider his earnings per house and his hourly wage. Peter makes $6 per hour for doing yard work plus $10 for every house he does work on.

First, we calculate the total earnings from the houses he worked on. Since he did yard work for 6 houses, we multiply 6 houses by $10 per house:

6 houses times $10 per house = $60

Now, subtract the total earnings from houses from his total paycheck to find out how much he earned from hourly wages:

$210 (total paycheck) - $60 (earnings from houses) = $150 (earnings from hourly wage)

$150 / $6 per hour = 25 hours

So, Peter worked 25 hours doing yard work.

Answer: with the problem you can see that

Smallest is 4.1 inches

Expression is 12 multiply by (7/10) to the power of 3

Answer:

Smallest is 4.1 inches

Expression is 12 multiply by (7/10) to the power of

Answer:

5x²-√x

Step-by-step explanation:

1)6 +p

2) x-1

3) 8x-z3

4) 5x²-√x   --> has a root so it is not a polynomial

Answer:

Hence, the length of the chord joining two perpendicular radii is:

6√2 inches.

Step-by-step explanation:

Let r denote the radius of circle.

i.e. r=6 inches.

Let AB be the chord that connects two perpendicular radii i.e. OA and OB whose lengths are given to be 6 inches.

We can apply pythagorean theorem to find the length of the chord.

[tex]AB^2=OA^2+OB^2\\\\AB^2=6^2+6^2\\\\AB^2=36+36\\\\AB^2=72\\\\AB=\sqrt{72}\\\\AB=6\sqrt{2}[/tex].

Hence, the length of a chord connecting two perpendicular radii is:

6√2 inches.

Answer:

B) Corresponding

Step-by-step explanation:

Hello! The answer to this question is that <2 and <3 are corresponding angles.  If you know the definition of corresponding angles and how they appear on a figure such as this, you should have no problem answering these problems in the future. Hope this comes to your help!