Mathematics College

find the total number of terms.32,256,2048,16384,......,2⁵⁰

Answers

Answer 1

Answer:

16 terms

Step-by-step explanation:

32,256,2048,16384,......,2⁵⁰

32=2⁵

256=2⁸

2048=2¹¹

16384=2¹⁴

2⁵, 2⁸, 2¹¹,2¹⁴, ….,2⁵⁰

[tex]t_{1}[/tex]=2⁵; [tex]t_{2}[/tex]=2⁸

r=2⁸:2⁵=2³

[tex]t_{n}[/tex]=[tex]t_{1}[/tex]*[tex]r^{n-1}[/tex]

2⁵*[tex]2^{3(n-1)}[/tex] =2⁵⁰

5+3(n-1)=50

3n-3=45

3n=48

n=48:3

n=16

So, 16 terms

Related Questions

A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph . The man can run at a constant rate in either direction to get off the bridge just in time before the train hits him. How fast can the man run?

Answers

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph. When the man

runs toward point A, the relative speed of the train with respect

to the man is the train's speed plus the man's speed (45 + M).

When he runs toward point B, the relative speed of the train is the

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.

When he runs in the direction of the train the distance he covers

is 3 units. We can now write that the ratio of the relative speed

of the train when he is running toward point A to the relative speed

of the train when he is running toward point B, is equal to the

inverse ratio of the two distance units or

(45 + M) 3

----------- = ---

(45 - M) 2

90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

Answer: 9 mph

Step-by-step explanation:

Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .

If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5

The remaining distance = 1 - 4/5 = 1/5

If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be

Speed = distance/time

Time = 1/5d ÷ speed

The time it will take the train to cover the entire distance d will be

Time = d ÷ 45

Equate the two time

1/5d ÷ speed = d ÷ 45

Speed = d/5 × 45/d

Speed = 9 mph

Show that between any two terminating decimals ,there is another terminating decimal

Answers

Answer:

1.5+1.7/2=1.6

Step-by-step explanation:

3 = 1/2x + 1/2x + 1/2x.

Answers

Answer:

x =2

Step-by-step explanation:

3 = 1/2x + 1/2x + 1/2x

Combine like terms

3 = 3/2 x

Multiply each side by 2/3 to isolate x

3 * 2/3 = 2/3 * 3/2 x

2 =x

Brainliest for the correct awnser!!! The function is not an example of a rational function. True or false?

Answers

Answer:

true

Step-by-step explanation:

g There are 60 mountain climbers in a club. 10 of these have climbed Mt. Everest. 15 have climbed Mt. Rainier. 8 have climbed both. How many have not climbed either mountain?

Answers

Answer:

43 mountain climbers have not climbed either mountain.

Step-by-step explanation:

Total number of mountain climbers, i.e. n(U) = 60

Number of mountain climbers who have climbed Mt. Everest, n(E) = 10

Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15

Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15

Using the formula to find number of climbers who have climbed either of the mountains:

[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]

[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]

To find, who have not climbed either mountain:

[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]

So, the answer is:

43 mountain climbers have not climbed either mountain.

Suppose you invest $15,000 at the age of 35, and agree to start receiving

payments at the age of 45. At age 41, you decide you want to withdraw $5000

from your account. What is the IRS fee you will have to pay? Remember, the

IRS charges 10% if you withdraw before you are 59.5.

A. $500.00

B. $750.00

C. $50.00

D. $250.00

Answers

Answer:

A. $500.00

Step-by-step explanation:

IRS popularly known as Internal revenue service charges an IRS fee under the authority of the Federal Law and policy agencies. This implementation of IRS fee is to recuperate the cost of rendering a service to the masses.

From the given information in the question:

Suppose you invest $15,000 at the age of 35 and agree to start receiving payments at the age of 45.

At age 41, you decide you want to withdraw $5000 from your account.

Since the investor is still 41 years of age ; IRS will charge 10% of the withdrawal amount.

IRS fee = 10% of $5000

IRS fee = 0.1 × $5000

IRS fee = $500

WHY IS THERE ANY HELP? PLEASE Solve the system of equations by using the substitution method. [tex]\left \{ {{x+y=6} \atop {x=2y}} \right.[/tex] Is there a solution, no solution, or infinite number? If there's a solution, what's the ordered pair?

Answers

Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a
mean of 100 and a standard deviation of 15.
n
f0 and
102
130
are
The area of the shaded region is (Round to four decimal places as needed.)
sions
Kented in
V3 and
andomly
d by in-
on affect
otes
ents
le
Enter your answer in the answer box and then click Check Answer.
section
different
version
Clear All
Check Answer
All parts showing

Answers

Answer: 0.4255

Step-by-step explanation:

Given: IQ scores of adults, and those scores are normally distributed

Mean: [tex]\mu=100[/tex]

Standard deviation: [tex]\sigma= 15[/tex]

Let X denotes the IQ of a random adults.

The area between 102 and 130 = [tex]P(102<X<130)=P(\dfrac{102-100}{15}<\dfrac{X-\mu}{\sigma}<\dfrac{130-100}{15})[/tex]

[tex]=P(0.13<Z<2)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<2)-P(Z<0.13)\\\\=0.9772- 0.5517\ [\text{By z-table}]\\\\=0.4255[/tex]

Hence, area between 102 and 130 = 0.4255

Four friends are on a basketball team. During a game, each friend kept track of how many shots they attempted and how many of those attempts they made. Henry made 0.45 of his shots. Allison made Arthur made of her shots. of his shots. Trevor missed 58% of his shots. Which friend had the best record for the number of shots made?

Answers

Answer:

Henry had the best record for the number of shots made

Step-by-step explanation:

From the given information.

Four friends are on a basketball team.

Henry

Allison

Arthur

Trevor

We are being told that Henry made 0.45 of his shots out of all his attempts

Allison made Arthur made of her shots of his shots.

i,e Arthur did the work for Allison , so out of Arthur's shot , we have to figured out Allison shots,

Trevor missed 58% of his shots.

i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot

Then the attempts Trevor made is :

= 1 - 0.58

= 0.42

SO , Trevor made 0.42 shots out of all his attempt

N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.

Therefore; we will focus on only Henry and Trevor shots

So ;

Henry made 0.45 of his shots

Trevor made 0.42 out of his shots

We can thereby conclude that :

Henry had the best record for the number of shots made

An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. it is an unbiased estimator. the variance of the estimator is zero. the difference between the estimator and the population parameter stays the same as the sample size grows larger.

Answers

Answer:

the difference between the estimator and the population parameter grows smaller as the sample size grows larger.

Step-by-step explanation:

In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.

Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.

An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.

Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.

Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.

The measure of position called the midquartile of a data set is found using the formula StartFraction Upper Q 1 plus Upper Q 3 Over 2 EndFraction . Find the midquartile of the given data set. 23 37 49 34 35 41 40 26 32 22 38 42

Answers

Answer:

35.25

Step-by-step explanation:

Give the data set:

23 37 49 34 35 41 40 26 32 22 38 42

We are expected to calculate the midquartile of the given data set.

22 23 26 32 34 35 37 38 40 41 42 49

First step is to find the lower quartile which comprises of

22 23 26 32 34 35

Here the Q1 is (26+32)/2 = 58/2= 29

Second step to find the upper quartile which comprises of

37 38 40 41 42 49

Here the Q3 is (40+41) /2 = 81/2 = 41.5

Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5

= (29+41.5)/2

= (70.5) /2 = 35.25

a variable with an exponent is a perfect square if the exponent is divisible by____

Answers

Answer: 3

Step-by-step explanation:

Which of the following triangles can be proven similar through AA?
A)
B)
C)
D)

Answers

Answer:

The options that have two angles, which are A and D prove both triangles to be similar.

Step-by-step explanation:

The postulate AA is exactly what it sounds like, and you can find the two angles, which will prove the similarity of two triangles sharing those two angles.

The reason being is if two angles are the same between the two triangles, the third can't be different.

ALGEBRA HELP PLEASE THANKS Evaluate the expression using exponential rules. Write the result in standard notation. [tex]\frac{4 x 10^{-4} }{20 x 10^{2} }[/tex]

Answers

Answer:

[tex]2 \times 10 {}^{ - 7} [/tex]

Step-by-step explanation:

[tex] \frac{4 \times 10 {}^{ - 4} }{20 \times 10 {}^{2} } = \frac{0.0004}{2000} = 2 \times 10 {}^{ - 7} [/tex]

Hope this helps ;) ❤❤❤

of the 1248 students enrolled 24% did not like the new mascot design. what is the mean of this binomial distribution
A. 299.5
B. 948.5
C. 17.3
D. 300.3

Answers

Answer: A. 299.5

Step-by-step explanation:

1248 · 24%

1248 · 0.24=299.50

State the degrees of freedom error in each of the following tests. (a) A consultant measures job satisfaction in a sample of 14 supervisors, 14 managers, and 14 executives at a local firm. (b) A researcher tests how nervous public speakers get in front of a small, medium, or large audience. Ten participants are randomly assigned to each group. (c) A high school counselor has 8 students in each of five classes rate how much they like their teacher.

Answers

Answer:

Step-by-step explanation:

Section 8
Find the mean of these numbers:
24 18
37
82 17
26

Answers

Answer:

[tex]\boxed{Mean = 34.33}[/tex]

Step-by-step explanation:

Mean = Sum of Observations / No. Of Observations

Mean = (24+18+37+82+17+26)/6

Mean = 206 / 6

Mean = 34.33

11. Caroline wraps packages at a store. She wraps
9 packages each hour. Which statement is true
about the number of packages she wraps?
A. In 2 hours, Caroline wraps an odd number of
packages.
B. In 3 hours, Caroline wraps an even number of
packages.
C. In 5 hours, Caroline wraps an odd number of
packages.
D. In 7 hours, Caroline wraps an even number of
packages.

Answers

Answer:

C. in five hours Caroline wraps an odd number of packages

Step-by-step explanation:

for A until hours you would multiply 2 by 9 and 2 by 9 is 18 and that's an even number so it's not A.

A eliminated.

for B in 3 hours 3 by 9 is 27 and that's an odd number so B is automatically eliminated.

for C in 5 hours all you would do is multiply the 9 by 5 and 9 by 5 is 45 and 45 is indeed an odd number so C is your answer.

for D 7 by 9 is 63 and 63 is an odd number so we already know that C is the answer but still we got to check and D is wrong because 63 is not an even number.

The average student loan debt for college graduates is $25,800. Suppose that that distribution is normal and that the standard deviation is $14,150. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar The middle 20% of college graduates' loan debt lies between what two numbers?

Answers

The answer would have to be 10

CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.

Answers

Answer:

The adult ticket costs $18 and the children ticket costs $13.

Step-by-step explanation:

Let the price of the adult ticket be a.

Let the price of the children ticket be c.

Three adults and four children must pay $106. This implies that:

3a + 4c = 106 _______(1)

Two adults and three children must pay $75. This implies that:

2a + 3c = 75 ________(2)

We have two simultaneous equations:

3a + 4c = 106 _____(1)

2a + 3c = 75 ______(2)

Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):

6a + 9c = 225

- (6a + 8c = 212)

c = $13

Put this value of c in (2):

2a + 3*13 = 75

2a + 39 = 75

=> 2a = 75 - 39

2a = 36

a = 36/2 = $18

Therefore, the adult ticket costs $18 and the children ticket costs $13.

PLEASE PLEASE PLEASE HELP PLEAS :( THE SECOND ONE JEJEJEJDD PLEASEEEEEE

Answers

Answer:

Step-by-step explanation:

Count the line endings in each letter as you write it down.

Answer:

I agree with tonb .Ace,he's/she's right

Which of the following is represented by MN ?

A.
Radius of the circle

B.
Diameter of the circle

C.
A chord of the circle

D.
Circumference of the circle

Answers

Answer:

Step-by-step explanation:

That is the radius. Since its half of the diameter.

Answer:

A. Radius of the circle

Step-by-step explanation:

A line segment that has as endpoints the center of a circle and a point on the circle is called a radius.

Answer: A. Radius of the circle

If one termite can destroy 1.2mg of wood per day, how many kilograms of wood can 10 termites destroy in 1 week? *Can someone please explain how to do this*

Answers

Answer:

10 termites will destroy 0.000084kg of wood per week

Step-by-step explanation:

Convert milligram to kilogram

1.2mg=(1.2 / 1,000,000)kg

1.2mg=0.0000012kg

1 termite destroys=0.0000012kg per day

10 termites will destroy (per day) =0.0000012×10 termites per day

10 termites in one day will destroy=0.000012kg

There are 7 days in a week

Therefore,

10 termites will destroy=destruction per day × 7 days

=0.000012×7

=0.000084kg per week

here are the 2 questions in the 2 pics separated lol

Answers

Answer:

60 and 87

Step-by-step explanation:

Question 1: The chance of losing would be 100% - 40% = 60%.

Question 2: Again, we just have to do 100% - 13% = 87%.

Answer:

Below

Step-by-step explanation:

First question:

Jade has a 40% chance of winnig wich could be expressed as 2/5

The chance of losing is the remainning pourcentage from 100%

●100-40 =60%

60% is the chance of losing wich could be expressed as 3/5

The sum of 3/5 and 2/5 is 1 so it's true.

■■■■■■■■■■■■■■■■■■■■■■■■■

Same method for the 2nd question:

The person has a 13 % chance of winning.

The chance of losing is 87%

● 100-13 =87

Find the solution(s) of the system of equations: x2 + y2 = 8 y = x – 4 options: (–2,–6) (2,–2) and (–2,–6) (2,–2) No solutions

Answers

Answer: x=2 y=-2

(2,-2) one solution

Step-by-step explanation:

Solve by substitution

[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]

[tex]\mathrm{Subsititute\:}y=x-4[/tex]

[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]

[tex]2x^2-8x+16=8[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]

[tex]\mathrm{For\:}y=x-4[/tex]

[tex]\mathrm{Subsititute\:}x=2[/tex]

[tex]y=2-4[/tex] [tex]2-4=-2[/tex]

[tex]y=-2[/tex]

[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]

[tex]x=2,\:y=-2[/tex]

Question
Given that cot(0)= -1/2
and O is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.
Provide your answer below:

Answers

Answer:

sin(O) = 2/sqrt(5) or 2sqrt(1/5)

Step-by-step explanation:

using 1+cot^2(x) = csc^2(x)

we have, taking reciprocal on both sides,

sin(x) = 1/sqrt(1+cot^2(x)

= 1/sqrt(1+(-1/2)^2)

= 1/sqrt(5/4)

= 2/sqrt(5) or 2sqrt(1/5)

Since angle x is in the second quadrant, sin(x) is positive.

Find the area under the standard normal probability distribution between the following pairs of z-scores. a. z=0 and z=3.00 e. z=−3.00 and z=0 b. z=0 and z=1.00 f. z=−1.00 and z=0 c. z=0 and z=2.00 g. z=−1.58 and z=0 d. z=0 and z=0.79 h. z=−0.79 and z=0

Answers

Answer:

a. P(0 < z < 3.00) = 0.4987

b. P(0 < z < 1.00) = 0.3414

c. P(0 < z < 2.00) = 0.4773

d. P(0 < z < 0.79) = 0.2852

e. P(-3.00 < z < 0) = 0.4987

f. P(-1.00 < z < 0) = 0.3414

g. P(-1.58 < z < 0) = 0.4429

h. P(-0.79 < z < 0) = 0.2852

Step-by-step explanation:

Find the area under the standard normal probability distribution between the following pairs of z-scores.

a. z=0 and z=3.00