Felipe and Gregory are given the arithmetic sequence - 1, 6, 13, ..... Gregory wrote the explicit definition an = - 1 + 7(n - 1) for the sequence. Felipe wrote the definition as an = 7n -8. Which one of them is correct? Explain. Choose the correct answer below. O A. Only Felipe's definition is correct because it is simplified. Gregory's definition is not simplified, so it cannot be correct. O B. Only Gregory's definition is correct. The explicit definition of an arithmetic sequence is an = a, + d(n - 1), and only Gregory's definition is of that form. O C. Both are correct. Gregory's definition can be simplified to get Felipe's definition. O D. Both are correct. Gregory's definition uses n = 1 for the first term whereas Felipe's definition uses n = 0 for the first term, but both definitions describe the given sequence.

The probability that one head in the three tosses, at least two heads is 0.7692, and the probability that exactly one head, at least one head in the three tosses is 0.2308.

What is a toss?

Formula for Probability of a Coin Toss: (Number of Successful Outcomes) (Total occurances of possible outcomes)

It's a binomial distribution with n=3, P=2/3

(a) P(one head in the three tosses, at least two heads)

P(x≥2 | x≥1)=[P(x≥2)∩P(x≥1)]/P(x≥1)

=0.7407/0.9630

=0.7692

(b) P(exactly one head, at least one head in the three tosses)

P(x=1 | x≥1)=[P(x=1∩ (x≥1)]/P(x≥1)

=0.222/0/9630

=0.2308

The probability that one head in the three tosses, at least two heads is 0.7692, and the probability that exactly one head, at least one head in the three tosses is 0.2308.

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Answer:

43.5(Maybe)

Step-by-step explanation:

All I did was divide it by 4 but im not sure what the 2 means

Area of square (let's labelled as x) is calculated by the formula : a^2, where a is the side.

Therefore, to calculate the side, we use the formula : a = [tex]\sqrt{x}[/tex]
Applying it : a = [tex]\sqrt{174}[/tex] = approx. 13.191 in (3 d.p)

Answer: maybe 1 ‍♀️

Step-by-step explanation:

Answer:

the 2nd, 3rd, 5th

i hope this helps :)

Answer:

2

Step-by-step explanation:

To find the slope, you need to use the term y2-y1/x2-x1

To do this, first do:

-4-2:

-6

Now, do -1-2=

-3

Now, since -6/-3 has two negatives, the fraction will turn into

6/3

Now simplify

2.

The slope of the line is two.

The initial expression is:

So first we can divide by 2 so:

now we rest 10 in bout sides so:

Answer:

27,348

Step-by-step explanation:

Answer: W h y d i d y o u

Step-by-step explanation:

The rate of change of the area at the instant the radius is 10 ft is 376.99 ft² / min.

The rate of change describes how one quantity changes in relation to the change in another quantity.

If a circle has an initial radius of 50 ft and decreases at a rate of 2 ft/min, then the time it took the radius to become 10 ft is 20 min.

r = r₀ - (rate)(time)

10 ft = 50 ft - (2 ft/min)(time)

(2 ft/min)(time) = 40 ft

time = 20 min

Solve the rate of change in area by dividing the change in area after time = 20 min.

rate of change = change in area / change in time

rate of change = A(r = 50) - A(r = 10) / 20 min

rate of change = π(50² - 10²) / 20 mins

rate of change = 376.99 ft² / min

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Answer:

a = 11cm

Step-by-step explanation:

We can use the Pythagorean theorem to find the value of a.

Let us solve it now.

[tex] \sf {a}^{2} + {12}^{2} = {15}^{2} [/tex]

Now solve for a and and find the length of the side.

[tex] \sf {a}^{2} + 144 = 225 \\ \sf {a}^{2} = 225 - 144 \\ \sf{a}^{2} = 121 \\ \sf \: a = \sqrt{121} \\ \sf \: a = 11[/tex]

Answer: 27/5.

Step-by-step explanation: 5 and 2/5 is already a mixed fraction, so I think you mean a improper fraction. If not, then its 5 and 2.5. Hope this helps.

The equation to represent the number of pages is: 0.25x = 10.

What is equation?

In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.

According to the question, the given parameters to form the equation are as follows:

The cost of each print is: $10

The cost of each page printed: $0.25

Now, let us assume number of printed pages are: 'x'

Therefore, the equation which shows the relationship between the number of pages and the cost of order is: 0.25x = 10

Hence, the equation to represent the number of pages is: 0.25x = 10

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Answer:

3/4

Step-by-step explanation:

up 3 right 4

The given statement is not true because the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.

We are given the scale of the map as;

1 inch : 100 miles

What this means is that 1 inch on the map represents an actual distance of 100 miles.

Now, from conversion values, we know that;

1 mile = 63360 inches

Now, the question is trying to suggest that the actual distance between two towns 100 times the map distance between the two towns

The given statement is not true because as seen from the conversion above, the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.

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3) The measures of the numbers are ∠1 =∠3 = ∠4 = ∠6 = 139° and ∠2 = ∠5 = ∠7 = 41°

4) The measures of the numbers are ∠1 =∠3 = ∠5 = 117° and ∠2 = ∠4 = ∠6 =∠7 = 63°

3.) ∠2 = 41° ( By Vertical Angles Theorem, vertically opposite angles are congruent and equal.)

41° + ∠4 = 180°(Same Side Interior Angles Theorem, when a transversal connects two parallel lines, the interior angles on the same side are supplementary.)

∠4 = 180° - 41° = 139°

∠3 =∠4  = 139°(By the Alternate angle theorem, alternate interior angles are congruent.)

Similarly, ∠5 = 41°

∠1 =∠4  = 139°(By Corresponding Angles Postulate, corresponding angles are congruent in parallel lines are cut by a transversal.

∠4 =∠6  = 139° and ∠7 =∠5 = 41°(By Vertical Angles Theorem, as they both are pairs of vertically opposite angles)

4) ∠5 = 117°  (By Vertical Angles Theorem, vertically opposite angles are congruent and equal.)

117° + ∠4 = 180° (By Same Side Interior Angles Theorem)

∠4 = 180°- 117° = 63°

∠2 = ∠4 = 63°  (By Vertical Angles Theorem)

∠2 = ∠6 = 63°  (By Corresponding Angles Postulate)

∠3 = 117°   (By Corresponding Angles Postulate)

∠1 = ∠3 = 117°  (By Vertical Angles Theorem)

∠6 = ∠7 = 63°  (By Vertical Angles Theorem)

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Solution

I think the interest is compounded yearly, if so

First, convert R as a percent to r as a decimal

r = R/100

r = 6.25/100

r = 0.0625 per year

A = 10000

P = 5000

Use logarithms or a scientific calculator

t = 11.5

In 11.5 years $5000 investment be worth of $10000

>>>>>>>>>>>>>

In case the interest is simple interest

Interest = Amount - Principal = $10000-$5000 = $5000

Time = 100*Interest / (Principal*Rate

= 100*5000 / (5000*6.25)

t = 16 years

In 16 years $5000 investment be worth of $10000

The pizzas sold were (n + 5).

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If I throw a ball with an Initial velocity Vi=10 m/s with an angle Theta of 60 degrees above the Horizontal axis x, then the velocity Vx and Vy are; C. Vx= 5 m/s Vy=8.66 m/s

The formula to find the velocity of an object thrown at an angle is;

Horizontal velocity component; Vx = v_i*cosθ

Vertical velocity component; Vy = v_i*sinθ

where;

v_i is initial velocity

θ is angle at which object is thrown.

Now, we are given that;

Initial velocity; v_i = 10 m/s

Angle of throw; θ = 60°

Thus;

V_x = 10 * cos 60

V_x = 10 * 0.5

V_x = 5 m/s

V_y = 10 * sin 60

V_y = 10 * 0.8660

V_y = 8.66 m/s

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The width of a confidence interval decreases as the sample size increases and increases as the confidence level increases.

So, we know that smaller samples result in narrower intervals.

Therefore, a confidence interval narrows as the sample size grows and widens as the level of confidence rises.

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The average velocity of the entire trip is 42.5 mph east

An object's average velocity is calculated by dividing its total displacement by its total travel time.

It measures how quickly an object shifts from one location to another.

It is a Vector magnitude

For one hour, an automobile travels 25.0 miles due east.

Then it continues for an extra hour and travels another 60.0 miles east.

We must determine his overall journey average speed.

He does the entire journey going straight east.

He travels a total distance of 25 + 60 = 85 miles east.

He takes an hour to get there from here and another hour to get there from there.

The total travel time is 1 + 1 = 2 hours.

Total displacement times total time equals the average velocity.

His average speed = 85 ÷ 2 = 42.5 miles/hour east

The average velocity of the entire trip is 42.5 mph east

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I would think this would be 100 apples

Marvin had 100 apples since he had 10 apples in each basket.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

The following elements can be used to identify algebraic expressions: a variable or a group of variables. For example, the algebraic expression 4x contains the variable x, while 3xy+4 contains the variables x and y.

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The number 1.9 represent in the equation means C. How much the taxi cost per mile

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, the equation to represent her total cost is y = 1.9x+3. In this case, the x represents the number of miles. Therefore, 1.9 represent the cost for each miles that travelled.

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It is the average amount by which the function changed per unit throughout that time period. The average rate of change of a linear function exists 9/3.

It exists the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

The average rate at which one quantity changes in relation to another's change exists directed to as the average rate of change function. A method that defines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

The average rate of change of a linear function (the slope) exists constant. The rate of change of the linear relationship = change in y / change in x

The rate of change from x = 1 to x = 4

= (5 - -4) / (4 - 1) = 9 / 3

Therefore, the average rate of change of a linear function exists 9/3.

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The ball takes 6.3 seconds to reach the ground when thrown upwards.

The height of the baseball thrown is 5 feet.

The function or equation for the height of the ball at a certain time t is given as:

h( t ) = - 16t² + 100t + 5

When the ball will reach the ground the height of the ball will be h = 0.

Therefore,

- 16t² + 100t + 5 = 0

Comparing the equation with general quadratic equation ax² + bx + c =0

We have, a = - 16, b = 100, and c = 5

Using the quadratic formula,

[tex]t=\frac{-b\pm \sqrt{b^{2} - 4ac } }{2a}[/tex]

[tex]t = \frac{-100\pm \sqrt{(100)^{2} - 4(-16)(5) } }{2(-16)}[/tex]

[tex]t=\frac{-100 \pm \sqrt{10000+320} }{-32}[/tex]

[tex]t = \frac{-100\pm \sqrt{10320} }{32} \\[/tex]

t = [ 25 ± √(645) ] / 8

When,

t = [ 25 + √(645) ] / 8 = 6.299 = 6.3 seconds

t = [ 25 - √(645) ] / 8 is false as the time cannot be negative.

The correct option is (b) 6.3 seconds.

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Answer:

5

Step-by-step explanation:

G.C.F means greatest common factor

this means the highest number that will go into both 25 and 40

5 is the highest number that will divide into both

Answer: Point P is a midpoint

Step-by-step explanation:

A rectangle has a length of 4.3 cm and a perimeter of 14.8 cm. The width of the rectangle is 3.1 cm.

A rectangle is a shape that has four right angles and whose adjacent lengths are not the same.

Given, the length L is 4.3 cm

The perimeter of the rectangle is 14.8 cm.

To calculate the perimeter = 2(l + w)

Putting the values:

14. 8 = 2(4.3) + 2w

Expand the bracket

14. 8 = 8. 6 + 2w

Collect like terms

2w = 14. 8 - 8.6

2w = 6. 2

Divide through by the coefficient of w

w = 6.2/2

w = 3.1 cm

Therefore, the width of the rectangle is 3.1 cm.

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A. y = 1x +4

B. y = -2x +4

C. y = -6

D. x = 1

Consider the following matrix equation:

Applying the additive property, this is equation is equivalent to:

This is equivalent to the following linear system of equations:

Equation 1:

Equation 2:

Equation 3:

Equation 4:

From equation 1, we get:

From equation 2, we get:

From equation 3, we get:

From equation 4, we get:

we can conclude that the correct answer is:

and