What is the measure of central angle COB?


What is the measure circumscribed angle A>

Answer:

hey good

Step-by-step explanation:

Therefore, the particular solution that satisfies f(0) = 2 is: \(f(x) = 4e^a x + x^3 + 2\).

To evaluate the integral ∫f f'(x) dx, we can use the fundamental theorem of calculus, which states that if F'(x) = f(x), then ∫f(x) dx = F(x) + C, where C is the constant of integration.

In this case, we have \(f'(x) = 4e^a + 3x^2\)

To find f(x), we need to integrate f'(x) with respect to x:

∫\((4e^a + 3x^2) dx\) = 4\(e^a\) ∫dx + 3 ∫\(x^2\) dx

Integrating each term:

=\(4e^a x + x^3 + C\)

where C is the constant of integration.

Now, to find the particular solution that satisfies f(0) = 2, we substitute x = 0 into the expression for f(x):

\(f(0) = 4e^a * 0 + 0^3 + C\)

Since f(0) = 2, we have:

2 = 0 +0 + C

C = 2

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Answer:

\(y = \sqrt{ 900 - x\²\)

Step-by-step explanation:

In the complete question, the area of  the roller coaster is:

\(x\² + y^2 = 900\)

Required

Solve for y

We have:

\(x\² + y^2 = 900\)

Subtract \(x\²\) from both sides

\(y^2 = 900 - x\²\)

Take positive roots of both sides

\(y = \sqrt{ 900 - x\²\)

Answer:

the interger would be 15 because you earn 15 so therfore it would be 15.

Step-by-step explanation:

Answer:

10:51

Step-by-step explanation:

Given that :

Distance from A to B = 130km

Departure time = 8 : 15

Average speed = 50 km/hr

Recall :

Speed = distance / time

Time = distance / speed

Time = (130 km) ÷ (50km/hr)

Time = 130 / 50

Time = 2.6 hours = 2 hours + (0.6 * 60) = 2 hours 36 minutes

Arrival time = (8:15) + (2 hours 36 minutes) = 10:51

Answer:

x=85/11

Step-by-step explanation:

\(\frac{x}{5}= \frac{17}{11} \\\\5*\frac{x}{5} =\frac{17}{11} \\\\x=\frac{85}{11}\)

The blue graph has been shifted to the right by 3 units

The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Answer:

Step-by-step explanation:

Answer:

a) (5×103)=5000

(9×107)=90000000

5000×90000000=450000000000

or 4.5×10 restipa 11

b)(7×105)=700000

(2×102)=200

70000÷200=3500

or 3.5×10 restipa 3

The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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In this probability experiment, the sample space is S = {2,3,4,5,6,7,8,9,10,11,12,13). The event E is defined as E = {3,4,5,6). Assuming that each outcome is equally likely, we can list all the outcomes of the experiment as follows:

1. If we roll a 2, it is not included in event E, so the outcome is not included.
2. If we roll a 3, it is included in event E, so the outcome is included.
3. If we roll a 4, it is included in event E, so the outcome is included.
4. If we roll a 5, it is included in event E, so the outcome is included.
5. If we roll a 6, it is included in event E, so the outcome is included.
6. If we roll a 7, it is not included in event E, so the outcome is not included.
7. If we roll an 8, it is not included in event E, so the outcome is not included.
8. If we roll a 9, it is not included in event E, so the outcome is not included.
9. If we roll a 10, it is not included in event E, so the outcome is not included.
10. If we roll an 11, it is not included in event E, so the outcome is not included.
11. If we roll a 12, it is not included in event E, so the outcome is not included.
12. If we roll a 13, it is not included in event E, so the outcome is not included.

Therefore, the outcomes of the experiment that are included in event E are 3, 4, 5, and 6.

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Answer:

67.5

67.5

40

Answer:

x = 22.5

top angle = 45

bottom angles = 67.5

Step-by-step explanation:

2x + 3x +3x = 180

8x = 180

x = 22.5

2x

2(22.5) = 45

3x

3(22.5) = 67.5

45 + 67.5 + 67.5 = 180

Answer:

225 = (1,3,5,9,15,25,45,75,85,225.)

Step-by-step explanation:

Factors of 225

225 = (1, 3 ,5, 9, 15, 25, 45, 75, 85, 225).

Factors of 225 are (1, 3 ,5, 9, 15, 25, 45, 75, 225).

What is a factor?

Factors are the numbers that can divide a number exactly.  Hence, after division, there is no remainder left. Factors are the numbers you multiply together to get another number. Thus, a factor is the divisor of another number.

Some of the important properties of factors of a number are listed below:

Now,

Using multiplication method

We can multiply only odd numbers for 225 because 225 is odd. So,

1*225=225

3*75=225

5*45=225

9*25=225

15*15=225

As multiplication of these numbers is equal to 225

Hence,

            Factors of 225 are (1, 3 ,5, 9, 15, 25, 45, 75, 225).

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Answer:

Mean=7.7

Median=7

Mode=10 and 6

Range=7

Answer:

Mean = 7.7

Median = 7

Mode = 6 and 10

Step-by-step explanation:

Arrange the data in ascending order :

4 , 6 , 6 , 7 , 10 , 10 , 11

Mean is the sum of the data by number of data.

\(Mean = \frac{ 4 + 6 + 6 + 7 + 10 + 10+ 11}{7} = \frac{54}{7} = 7 . 7\)

Median is the middle number.

\(Median = \ 7\)

Mode most frequent value in the data

\(Mode = \ 6 \ and \ 10\)

Answer: Hello! I'm JK!.....

Yes there is!

First, divide the large number by a small number.

If the remainder is left, then divide the first divisor by remainder.

If the remainder divides the first divisor completely, then it is the HCF or highest common factor of the given two numbers.

Step-by-step explanation:

I hope this helps you! <3 XoXoGoldenMaknae

Answer:

1) X = 10 Therefore, 10 + 2 + 10 = 22.

2) B = 2 Therefore, 15 = 8(2) - 5 + 2(2)

3) B = -0.9 Therefore, -10 + 4(3(-0.9) + 10) = 19.

Answer:

Radius = 17.

Step-by-step explanation:

If(h,k) is centre and rradius, the eqn. of circle is :(−x h)2+(y−k)2=r2

Comparing with the given eqn. of circle, we find, r2=289 Hence, radius  is 17

Answer:

  A. one along the x-axis, and one along the y-axis

Step-by-step explanation:

For any kind of a plot, one variable is displayed along each axis.

__

A scatter plot has variables displayed one along the x-axis, and one along the y-axis.

Answer:

A. one along the x-axis, and one along the y-axis

Step-by-step explanation:

Edge 2023

If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:

Selling price = Cost price + Mark-up

Mark-up = 100% x Cost price

= 100% x R200

= R200

So the mark-up is R200.

Selling price = Cost price + Mark-up

= R200 + R200

= R400

Therefore, the selling price of the goods is R400.

Answer:

Since the point (2,12) is inside the double shaded region, one possible solution to the system of inequalities would be:

Sarah could have 2 nickels and 12 dimes.

Step-by-step explanation:

Variable Definitions:

​x = the number of nickels  

y = the number of dimes

“a maximum of 18 coins" → 18 or fewer coins

Therefore the total number of coins, x + y, must be less than or equal to 18:  

                                            x + y ≤ 18

“no less than $1.20" → $1.20 or more

One nickel is worth $0.05, so x nickels are worth 0.05x. One dime is worth $0.10, so y dimes are worth 0.10y. The total 0.05x+0.10y must be greater than or equal to $1.20:

                                   0.05x + 0.10y ≥ 1.20

                              Solve each inequality for y:

                    x + y ≤ 18                       0.05x + 0.10y ≥ 1.20

                   y ≤ 18−x                         0.10y ≥ 1.20 − 0.05x

                                                          y ≥ 1.20 - 0.05x / 0.10  

                                                          y ≥ 12 − 1/2x

​Graph y ≤ 18 − x by shading down and graph y ≥ 12 − 1/2x by shading up: (png given)

Step-by-step explanation:

The number of solution for the equation  x₁ + x₂ + x₃ = 14 where x₁ , x₂ , x₃  are integers for different condition are

a. 91 solution for each variable greater than or equal to zero

b. 66 solution when each variable greater than or equal to one.

Total number of solution for the equation x₁ + x₂ + x₃ = 14.

a. Each variable x₁ , x₂, x₃ is an integer greater than or equal to zero.

When x₁ = 0 and x₂ , x₃ have different values

0 + 0 + 14 = 14

0 + 1 + 13 = 14

0 + 2 + 12 = 14

0 + 3 + 11 =14

0 + 4 + 10 =14 .......so on

0 + 13 + 1 = 14

Total outcome = 14

Two place needs to be fill one place is fixed by certain number.

Total number of possible solution is equal to

= ¹⁴C₂

= ( 14! ) / ( 14 - 2 )! 2!

= ( 14 × 13 ) / ( 2 × 1 )

= 7 × 13

= 91

b. Each integer is an integer greater than or equal to one

When x₁ = 1 and x₂ , x₃ have different values

1 + 1+ 12 = 14

1 + 2 + 11 = 14

1+ 3 + 10 =14

1 +4 + 9 =14 .......so on

1+ 12 + 1 = 14

Total outcome = 12

Total number of possible solution when each variable is greater than or equal to 1

= ¹²C₂

= ( 12! ) / (12 - 2)! 2!

= ( 12 × 11 ) / 2

= 66

Therefore , total number of solution for the equation having integer variable x₁ + x₂ + x₃ = 14 is

a. Each variable greater than or equal to zero has 91 solution.

b. Each  variable greater than or equal to one has 66 solution.

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Answer: x=11

Step-by-step explanation:

\(1.5x+3=3(1.5x-10)\\Distribute\\1.5x+3=4.5x-30\)

Subtract 3 from both sides

\(1.5x=4.5x-33\)

Now subtract 4.5x from each side

\(-3x=-33\\Divide\\x=11\)

Answer:

11

Step-by-step explanation:

1.5x+3=3(1.5x-10)

1.5x+3=4.5x-30

4.5x-1.5x-30=3

3x-30=3

3x=3+30

3x=33

x=33/3

x=11