Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel?

Answer:

The answer is divergent ⇒ answer (b)

Step-by-step explanation:

* The series is -5 + 25 + -125 + ........

- It is a geometric series with:

- first term a = -5 and common ratio r = 25/-5 = -5

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = -5

∴ IrI = 5

∴ IrI > 1

∴ The series is divergent

Answer:

101 or 36 degrees

Step-by-step explanation:

If you add up the measures of the arcs it is 158. That means BC is 202 degrees. Divide it by 2 to find the angle. For the second answer, remember the question did not specify if the arcs were major or minor so you can flip them around.

Answer:

m∠BAC is 101° or 36°.

Step-by-step explanation:

Given,

[tex]m(\widehat{AB})=115^{\circ}[/tex]

[tex]m(\widehat{AC})=43^{\circ}[/tex]

To find : The measurement of angle BAC,

Let O be the center of the circle.

Since, here we have to cases ( shown in diagram ),

In Case 1 :

[tex]m\angle BOC = 360^{\circ}-[m(\widehat{AB})+m(\widehat{AC})][/tex]

[tex]=360^{\circ}-(115^{\circ}+43^{\circ})[/tex]

[tex]=360^{\circ}-158^{\circ}[/tex]

[tex]=202^{\circ}[/tex]

By the central angle theorem,

[tex]m\angle BAC = \frac{m\angle BOC}{2}[/tex]

[tex]=\frac{202^{\circ}}{2}=101^{\circ}[/tex]

In Case 2 :

[tex]m\angle BOC = m(\widehat{AB})-m(\widehat{AC})[/tex]

[tex]=115^{\circ}-43^{\circ}[/tex]

[tex]=72^{\circ}[/tex]

Again by the central angle theorem,

[tex]m\angle BAC = \frac{m\angle BOC}{2}[/tex]

[tex]=\frac{72^{\circ}}{2}=36^{\circ}[/tex]

Answer:

[tex]y=\frac{1}{4}x+2[/tex]

Step-by-step explanation:

The point-slope form of the equation of a line that passes that through points (8, 4) and (0, 2) is given as;

[tex]y-4=\frac{1}{4}(x-8)[/tex]

To find the slope-intercept form of this line, we need to expand the point-slope form.

[tex]y-4=\frac{1}{4}x-2[/tex]

We now solve for y to obtain;

[tex]y=\frac{1}{4}x-2+4[/tex]

We simplify to obtain:

[tex]y=\frac{1}{4}x+2[/tex]

This equation is now in the form;

[tex]y=mx+c[/tex]

This is what we refer to as the slope-intercept form.

There are 64 pieces that each child receive.

It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here, Joelle's parents have combined all the candy = 256 candy

          Total number of Children = 4

         Equal division of candy in 4 children = Total Candy/No. of children

                                                                        = 256 / 4

                                                                       = 64

Thus, there are 64 pieces that each child receive.

Learn more about Division from:

https://brainly.com/question/21416852

#SPJ2

Final answer:

Each of the four children, including Joelle, will receive 64 pieces of candy after dividing the total of 256 pieces evenly among them.

Explanation:

To find out how many pieces of candy each child receives, we need to divide the total number of pieces by the number of children. Joelle and her three siblings make a group of four children in total. They have accumulated 256 pieces of candy. To divide this evenly, we do the following calculation:

Divide the total number of candies (256) by the number of children (4).

The division gives us the result 64 pieces of candy for each child.

Therefore, each child, including Joelle, will receive 64 pieces of candy.

Answer: first option.

Step-by-step explanation:

Find the common difference d of the arithmetic sequence:

[tex]d=a_n-a_{(n-1)}\\d=989-997\\d=-8[/tex]

Then the formula for the 101st term is the shown below:

[tex]a_n=a_1+(n-1)d[/tex]

Where:

[tex]a_1=997\\d=-8\\n=101[/tex]

Substitute values into the formula. Therefore, you obtain:

[tex]a_n=997+(101-1)(-8)=197[/tex]

Answer:

[tex]a_{101}=197[/tex]

Step-by-step explanation:

The first term of the sequence is

[tex]a_1=997[/tex]

The given sequence  is 997, 989, 981, ...

The common difference is

[tex]d=989-997=-8[/tex]

The nth ter of the sequence is

[tex]a_n=a_1+d(n-1)[/tex]

We plug in the first term and the common ratio to obtain;

[tex]a_n=997-8(n-1)[/tex]

[tex]a_n=997-8n+8[/tex]

[tex]a_n=1005-8n[/tex]

We substitute n=101 to get;

[tex]a_{101}=1005-8(101)[/tex]

[tex]a_{101}=197[/tex]

You need to rewrite the first equation to solve for y to get y >1+3x

Then graphing the two equations, the bottom right becomes the correct answer.

Answer:

The answer would be 15.23$

Step-by-step explanation:

If you take the over all growth, 45.69, and divide that by the 3 days, you get your average of 15.23 per day

Answer:

B

Step-by-step explanation:

The correct answer is to go 4 units right (the direction is opposite to the sign) and 3 units up. The up and down direction is the same number as after the function.

Red: Parent Function y = ln(x)

Blue: 4 units right. 3 units up.

Answer: B

Answer:

b

Step-by-step explanation:

Answer:

54 square meters

Step-by-step explanation:

Similar figures have corresponding lengths as equal ratios.

Smaller trapezoid's base is given 12 and larger trapezoids base is given 18, so the scale factor is [tex]12k=18\\k=\frac{18}{12}\\k=1.5[/tex]

this means the lengths of larger is 1.5 times lengths of smaller.

In terms of area, the scale factor is squared. Hence the scale factor for area is  [tex]k^2=(1.5)^2=2.25[/tex]

this means the area of larger is 2.25 times the area of smaller.

Now, Let area of smaller trapezoid be x so we can say:  [tex]x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78[/tex]

to nearest square meter, x = 54 meters squared

In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether [tex]x=10, \ y=-3, \ z=14[/tex] is the solution to this system, that is, the ordered triple [tex]P(x,y,z)[/tex] where three planes intersect.

The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:

[tex]First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \neq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation[/tex]

STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the [tex]x=10, \ y=-3, \ z=14[/tex] is not the solution to the system of equations.

a^2+b^2=c^2 <----- the equation to find out sides for a right triangle

Every right triangle follows the pythagorean theorem: given the legs [tex]a[/tex] and [tex]b[/tex] and the hypothenuse [tex]c[/tex] we have

[tex]a^2+b^2=c^2 \implies c=\sqrt{a^2+b^2}[/tex]

In your case, a=3 and b=5, so we have

[tex]c=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}[/tex]

Answer:

Approximately after 66.15 years, there will be 100 coyotes left

Step-by-step explanation:

We can use the formula  [tex]F=P(1+r)^t[/tex] to solve this.

Where

F is the future amount (F=100 coyotes)

P is the initial amount (P=750 coyotes)

r is the rate of decrease per year (which is -3% per year or -0.03)

t is the time in years (which we need to find)

Putting all the information into the formula we solve.

Note: The logarithm formula we  will use over here is  [tex]ln(a^b)=bln(a)[/tex]

So, we have:

[tex]F=P(1+r)^t\\100=750(1-0.03)^t\\100=750(0.97)^t\\\frac{100}{750}=0.97^t\\\frac{2}{15}=0.97^t\\ln(\frac{2}{15})=ln(0.97^t)\\ln(\frac{2}{15})=tln(0.97)\\t=\frac{ln(\frac{2}{15})}{ln(0.97)}\\t=66.15[/tex]

Hence, after approximately 66.15 years, there will be 100 coyotes left.

Rounding, we will have 66 years

Answer:

112.76 feet

Step-by-step explanation:

This is a right triangle trig problem.  We have the length of the string which serves as the hypotenuse of the triangle, and we also have the reference angle (the angle the string makes with the ground) and we are looking for the height of the height, which is also the height of the triangle, which is also the side opposite the reference angle.  So it's our job now to figure out which trig ratio relates the side opposite the reference angle to the hypotenuse.  That's the sin ratio (opposite/hypotenuse).  Set it up like this:

[tex]sin(70)=\frac{x}{120}[/tex]

Multiply both sides by 120 and then do the math in degree mode on your calculator.  That gives you that x = 112.7631145

Don't know how many decimal places you need, but there you go!

Answer:

  (1, 2) and (-1, -2)

Step-by-step explanation:

Since y = 2x, the first blank tells you

  2x = 2

  x = 1

____

Since the variables are squared, a negative solution is as good as a positive solution, so x = -1 and y = -2 will also work.

Answer:

Last choice: 14 = (1/2)x(x - 12)

Step-by-step explanation:

base = x

height = x - 12

area = (1/2)bh

14 = (1/2)x(x - 12)

The answer is C. Thank Me Later ?

It's not C because

[tex](AB)_{1,1}=A_{1,c}B_{r,1}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}3\\-5\\-1\end{bmatrix}=-2[/tex]

where [tex](AB)_{1,1}[/tex] denotes the element of [tex]AB[/tex] in row 1, column 1, [tex]A_{1,c}[/tex] denotes the first row of [tex]A[/tex], and [tex]B_{r,1}[/tex] denotes the first column of [tex]B[/tex].

It's not A because

[tex](AB)_{1,2}=A_{1,c}B_{r,2}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=16[/tex]

It's not D because

[tex](AB)_{2,2}=A_{2,c}B_{r,2}=\begin{bmatrix}-5&-4&-2\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=46[/tex]

So B must be the correct answer (and it is).

Answer:

one sample t-test will be appropriate in this case

Step-by-step explanation:

We are carrying out a hypothesis test of the mean with the population standard deviation being unknown. We shall estimate the population standard deviation with the sample equivalent, s in determining the value of the test-statistic.

Answer:

A left-tailed test

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The equation [tex]x^2-y^2=a[/tex] under the translation of  T (p,q) will have the form  [tex](x-p)^2-(y-q)^2=a[/tex]

Now, using the translation T(-4,2) in the equation given, we can write:

[tex](x+4)^2-(y-2)^2-9=0\\x^2+8x+16-y^2+4y-4-9=0\\x^2-y^2+8x+4y+3=0[/tex]

Looking at the choices, B is the right answer.

Answer:

Looking at the choices, B is the right answer.

Answer:

Step-by-step explanation:

Part A

If it is compounded quarterly, the interest of 1.5 must be cut into a quarter of its present size. 1.5 //4 = 0.375 % per quarter.

In addition, the number of times that payment will be received is

4 quarters * 5 years = 20 quarters.

i = principle (1 + 0.375/100) ^20

i = principle (1 + 0.00375)^20

The principle = 4000 dollars.

i = 4000 * (1.00375)^20

i = 4000 * 1.07773

i = 4310.93

So she's tied up 4000 dollars to make 300 dollars.

Part B

I can't really give you an answer to this because I don't know if the 7% is compounded and over what period of time if it is, or if they mean 7% annually. There's a lot of variation in this question. Most people don't take money out of the market, so if it compounded, the formula would be

New Principle = starting amount (1.07)^4

New Principle = 4000 * 1.07^4

New Principle = 5243.18 so she would make about 4 times as much as the 300 she makes if she puts the money in a bond.

=============

If the interest is simple interest

Gain would be 0.07 * 4000 = 280 dollars.

Over four years = 4*280 = 1120 dollars.

You are going to have to ask your teacher what is intended by this question.

60 minutes = 1 hour

55 + 5 = 60 70 - 5 = 65 10:00

10:00 + 60 min = 11:00 65 - 60 = 5

11:00 + 5 min = 11:05

Bob finished mowing at 11:05

Answer:

b. -1

Step-by-step explanation:

When evaluating a limit at a specific value like this, just plug in the number and evaluate.

(2)³ - 3(2)² + 3

   8 - 12 + 3  

         -4 + 3

             -1

Answer:

b. [tex]-1[/tex]

Step-by-step explanation:

The given limit is

[tex]\lim_{x \to 2} (x^3-3x^2+3)[/tex]

This is the limit of a polynomial function so we plug in the value of x directly to obtain;

[tex]\lim_{x \to 2} x^3-3x^2+3=(2)^3-3(2)^2+3[/tex]

Evaluate

[tex]\lim_{x \to 2} x^3-3x^2+3=8-12+3[/tex]

This simplifies to

[tex]\lim_{x \to 2} x^3-3x^2+3=-1[/tex]

The correct choice is B.

Answer:

This is called the independent variable.

Step-by-step explanation:

We know this because it is independent of all outside factors. Additionally, the horizontal axis (also known as the x axis), is the axis known for the independent variable.

Answer:

quad

Step-by-step explanation:

Answer: the answers are a and d !!

Step-by-step explanation:

Answer:135.9

Step-by-step explanation:you just have to multiply

Answer:

The distance between Bert and Ernie's apartments from Big Bird's nest

is 21 miles

Step-by-step explanation:

* Lets change the story problem to an equation to solve the problem

- The information i the story problem is

# The Big Bird's nest is halfway from there apartments

# The distance between Bert's apartment and Big Bird's nest is (5x + 4)

# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)

* Now lets solve

∵ The Big Bird's nest is halfway from there apartments

∴ The distance between Bert's apartment and Big Bird's nest = The

   distance between Ernie's apartment and Big Bird's nest

∴ 5x + 4 = 15x - 30

- Collect the variable terms in one side and the numerical terms

 in th other side

∴ 15x - 5x = 30 + 4 ⇒ add

∴ 10x = 34

∴ x = 34 ÷ 10 = 3.4

* Now lets find the distance between Bert and Ernie's apartments

from the Big Bird's nest

- We can use any relation to find the distance

∵ The distance = 5x + 4

∵ x = 3.4

∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles

You can check the answer by using second equation

∵ The distance = 15x - 30

∵ x = 3.4

∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles

Answer:

The distance between Bert and Ernie's apartments from Big Bird's nest

is 21 miles

Step-by-step explanation:

* Lets change the story problem to an equation to solve the problem

- The information i the story problem is

# The Big Bird's nest is halfway from there apartments

# The distance between Bert's apartment and Big Bird's nest is (5x + 4)

# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)

* Now lets solve

∵ The Big Bird's nest is halfway from there apartments

∴ The distance between Bert's apartment and Big Bird's nest = The

  distance between Ernie's apartment and Big Bird's nest

∴ 5x + 4 = 15x - 30

- Collect the variable terms in one side and the numerical terms

in th other side

∴ 15x - 5x = 30 + 4 ⇒ add

∴ 10x = 34

∴ x = 34 ÷ 10 = 3.4

* Now lets find the distance between Bert and Ernie's apartments

from the Big Bird's nest

- We can use any relation to find the distance

∵ The distance = 5x + 4

∵ x = 3.4

∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles

You can check the answer by using second equation

∵ The distance = 15x - 30

∵ x = 3.4

∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles

I guess that's f(x) = -3x^2+2

Well :

-3x^2+2=0

-3x^2=-2 / : (-3)

x^2= -2/-3

x^2= 2/3 / sqrt

x= +/ - sqrt(2)/sqrt(3)

We got the zero points.

x ~ +/- 0.81

f(0)= -3(0)^2 + 2

f(0)= 2

Mark three points:

(0.81;0)

(-0.81;0)

(0;2)

Connect with parabolic line and ya got a your graph

➷ We know this:

3/7 = 27

You need to find the value of 1/7

To do this, divide by 3

27/3 = 9

1/7 = 9

Multiply this by 7 to get the total number of balls:

9 x 7 = 63

There are 63 balls.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

$ 11.36

Step-by-step explanation:

The advance cost​ him;

3.20 + 3.4% of 240

3.20 + (3.4/100)*240

3.20 + 8.16 = $ 11.36

Answer:

The measure of the line segment GE is [tex]18\ units[/tex]

Step-by-step explanation:

we know that

The Intersecting Secant-Tangent Theorem states that, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

In this problem

[tex]GE*GF=GH^{2}[/tex]

substitute the values

[tex](8+x)(8)=12^{2}[/tex]

solve for x

[tex]8x+64=144[/tex]

[tex]8x=144-64[/tex]

[tex]8x=80[/tex]

[tex]x=10[/tex]

Find the measure of the line segment GE

[tex]GE=8+10=18\ units[/tex]