Kathy stood on the middle rung of a ladder. She cimbed up 3 rungs, moved down 5 rungs, and then climbed up 9 rungs. Then she climbed up the remaining 2 rungs to the top of the ladder. How many rungs are there in the whole ladder?

Answers

Answer 1

Answer:

18 rungs

Step-by-step explanation:

Let x = number of rungs

x/2 = middle

Climbed 3

x/2 +3

Down 5  

x/2 +3 -5

Climbed 9

x/2 +3 -5+9

Then climbed 2 more

x/2 +3 -5+9 +2

Now is at the top

x/2 +3 -5+9 +2 =x

Combine like terms

x/2 +9 = x

Subtract x/2 from each side

x/2+9-x/2 = x - x/2

9 = x/2

Multiply each side by 2

18 =x


Related Questions

o perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one, two, or three steps. The second procedure requires either one or two steps. Answer the first and second questions using this information.List the experimental outcomes associated with performing the blood analysis. (Hint: The first procedure has three possible outcomes (steps needed), the second procedure has two possible outcomes (steps needed)).(1), (2), (3), (1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3)(1), (2), (3), (1,1), (2,1), (3,1), (1,2), (2,2), (3,2)(1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3)(1,1), (2,1), (3,1), (1,2), (2,2), (3,2)

Answers

Answer:

11, 12, 13, 21, 22 and 23

Step-by-step explanation:

Given

[tex]Procedures = 2[/tex]

[tex]1 \to[/tex] Step 1

[tex]2 \to[/tex] Step 2

[tex]3 \to[/tex] Step 3

Required

List all possible experimental outcomes

From the question, we understand that:

[tex]Procedure\ 1 = 3\ steps[/tex]

[tex]Procedure\ 2 = 2\ steps[/tex]

So, the total possible steps (n) are:

[tex]n=Procedure\ 1 * Procedure\ 2[/tex]

[tex]n = 3 * 2[/tex]

[tex]n = 6\ steps[/tex]

Such that the 2nd steps cannot take the value of 3.

So, the outcomes are: 11, 12, 13, 21, 22 and 23

Explain why the square root of a number is defined to be equal to that number to the 1/2 power

Answers

9514 1404 393

Answer:

  (x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x

Step-by-step explanation:

The rule of exponents is ...

  (x^a)(x^b) = x^(a+b)

From which ...

  (x^a)(x^a) = x^(a+a) = x^(2a)

So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that ...

  x^(2a) = x^1

  2a = 1

  a = 1/2

The square root is defined as one of two identical factors that have a product equal to the specified value. That is ...

  (√x)(√x) = x

Above, we have shown that ...

  (x^(1/2))(x^(1/2)) = x

so, we can conclude ...

  √x = x^(1/2)

_____

Additional comment

In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It's really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

Solve 3(5x + 7)= 9x + 39

Answers

Answer:

x=3

Step-by-step explanation:

some one plz help its algebra 1

Answers

The correct answer is B
Yea ofc fjfjfjfnfnfnfnfjfjffjfj


Find the sine and the cosine of 30^degrees

Answers

Answer:

Step-by-step explanation:

sine 30° = opposite / hypotenuse = 4/8 = 1/2

cosine 30° = adjacent / hypotenuse = 4sqrt(3) / 8 = sqrt(3) / 2

Samples of rejuvenated mitochondria are mutated (defective) in 2% of cases. Suppose 12 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
(c) is 0.00
Round your answers to two decimal places

Answers

Answer:

a) 0.7847 = 78.47% probability that no samples are mutated.

b) 0.9769 = 97.69% probability that at most one sample is mutated.

c) 0% probability that more than half the samples are mutated.

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either they are mutated, or they are not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

2% of cases.

This means that [tex]p = 0.02[/tex]

12 samples are studied

This means that [tex]n = 12[/tex].

(a) No samples are mutated.

This is [tex]P(X = 0)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]

0.7847 = 78.47% probability that no samples are mutated.

(b) At most one sample is mutated.

This is:

[tex]P(X \geq 1) = P(X = 0) + P(X = 1)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]

[tex]P(X = 1) = C_{12,1}.(0.02)^{1}.(0.98)^{11} = 0.1922[/tex]

[tex]P(X \geq 1) = P(X = 0) + P(X = 1) = 0.7847 + 0.1922 = 0.9769[/tex]

0.9769 = 97.69% probability that at most one sample is mutated.

(c) More than half the samples are mutated.

This is:

[tex]P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,7}.(0.02)^{7}.(0.98)^{5} \approx 0[/tex]

So the others(greater than 7) wil be 0 too

0% probability that more than half the samples are mutated.

GIVEN a = (2 -3) and b = (1 -5 ) find 3a - b

Answers

Answer:

3a - b = 1

Step-by-step explanation:

a = (2-3)

b = (1-5)

Substitute the values of a and b to the 3a-b.

3(2-3) - (1-5)

6-9 - (-4)

6 - 9 + 4

-3 + 4

= 1

Therefore, 1 is the answer.

Step-by-step explanation:

Solution :

Given,

a= (2 - 3)

b= (1 - 5)

Now,

3a-b

= 3(2 - 3) -(1 - 5)

= 3×(-1) - (-4)

= -3+4

= 1

.

. .The value of 3a-b is 1

Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at Furniture Patch Inc.

$4.3 $6.1 $7.4 $10.7 $13.1 $13.6 $14.7 $16.5 $17.1 $17.4 $18.7 $22.3 $36.7 $43.2 $79.4

Required:
a. Determine the mean, median, and the standard deviation.
b. Determine the coefficient of skewness using Pearson.

Answers

Answer:

Mean = 21.413

Median = 16.5

Standard deviation = 19.182

0.768

Step-by-step explanation:

Given the data :

Ordered data, X : 4.3 6.1 7.4 10.7 13.1 13.6 14.7 16.5 17.1 17.4 18.7 22.3 36.7 43.2 79.4

The sample size, n = 15

The mean, m= ΣX / n = 321.2 / 15 = 21.413

The median, Md:

1/2(n + 1)th term

1/2 (15 +1) th term

1/2(16) = 8th term

Median = $16.5

The standard deviation, s = √[Σ(x - m)²/ n]

The standard deviation obtained using a calculator is ; 19.182

Coefficient of skewness : = 3(m - Md) / s

= 3(21.413 - 16.5) / 19.182

= 14.739 / 19.182

= 0.768

HELP!!!! NUMBER 2

2. Find the distance between these two points.
First Point
Second Point
Distance
(5, - 2)
(8,6)
(5,6)
(-3,6)
(-3,6)
(5,-2)

Answers

Answer:

1. 8

2 . 11

[tex]3 . \sqrt{128} \ or \ 8 \sqrt2[/tex]

Step-by-step explanation:

[tex]Distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2 }[/tex]

1 . ( 5 , - 2 ) and ( 5 , 6 )

  [tex]Distance = \sqrt{(5 -5)^2 + ( 6-(-2))^2} = \sqrt{ 0 + 8^2 } = \sqrt{64} = 8[/tex]

2 . ( 8 , 6 ) and ( - 3 , 6 )

  [tex]Distance = \sqrt{( -3 -8)^2 + ( 6 - 6)^2 } = \sqrt{ (-11)^2 + 0 } = \sqrt { 121 } = 11[/tex]

3. ( 5 , - 2 ) and ( -3 , 6 )

  [tex]Distance = \sqrt{(-3 - 5)^2 + ( 6 --2)^2} = \sqrt{(-8)^2 + ( 8)^2} = \sqrt{ 64 + 64 } = \sqrt{128}[/tex]

   

          [tex][ \ \sqrt{128} = \sqrt{ 2 \times 64} = \sqrt{ 2 \times 8^2 } = 8 \sqrt{2} \ ][/tex]

Solve the quadratic function by graphing.
-4x^2 + 16x - 16 = 0
0,-4)
(-4,0)
(2,0)
(0,2)

Answers

-4x²+16x-16=0

X=2

The choose (2,0)

Phân biệt chi phí sản xuất và giá thành sản phẩm?

Answers

Answer:

* Giống nhau: đều là biểu hiện bằng tiền về lao động sống và lao động hóa trong quá trình sản xuất

* Khác nhau:

+ Về thời gian: chi phí sản xuất gắn liền với từng thời kỳ, còn giá thành sản phẩm gắn với thời hạn hoàn thành sản phẩm. ...

+ Có những chi phí được tính vào giá thành nhưng không được tính vào chi phí kỳ này.

+ Mối quan hệ chi phí và tính giá thành sản phẩm: Chi phí là cơ sở để tính giá thành, giá thành là thước đo chi phí sản xuất mà doanh nghiệp bỏ ra để có được khối lượng hoàn thành.

+ Có nhiều chi phí phát sinh trong kỳ nhưng chưa có sản phẩm hoàn thành do đó chưa có giá thành.

Step-by-step explanation:

I have a mix of 12 nickels and dimes in my pocket. All together I have $1 . How many nickles and dimes do I have?


(Create a system of equations and solve that system)

Answers

Answer:

Step-by-step explanation:

n + d = 12

0.05n + 0.1d = 1    ║ × ( - 10 )

n + d = 12 ..... (1)

- 0.5n - d = - 10 ..... (2)

(1) + (2)

0.5n = 2 ⇒ n = 4

d = 12 - 4 = 8

There are 4 nickels and 8 dimes in the pocket.

I need help please I dont understand

Answers

It’s like this. Mark as brainliest!! Much appreciated

Which infinite geometric series diverges?
A. S= 4.2 + 3.57 + 3.0345 +...
B. S= 262 + 301.3 + 346.5 +...
C. S= 6,651 + 729 -- 81 -- ...
D. S = 100 + 50 + 25 +...

Answers

Answer:

I thikn the answer is B

Step-by-step explanation:

For a geometric series to diverge the absolute value of the common ratio has to be 1 or greater

given f(x) = 5x + 7,g(x) = 3x-1 find f(g(x))

Answers

Answer:

f(g(x)) = 15x + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Algebra I

FunctionsFunction NotationComposite Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 5x + 7

g(x) = 3x - 1

Step 2: Find

Substitute in functions:                                                                                    f(g(x)) = 5(3x - 1) + 7[Distributive Property] Distribute 5:                                                                 f(g(x)) = 15x - 5 + 7[Addition] Combine like terms:                                                                        f(g(x)) = 15x + 2

which of the following steps were applied to ABCD to obtain A' B'C'D'

Answers

Answer:

Thus, The steps applied to ABCD to obtain A'B'C'D' is shifted x coordinate 2 units to right and y coordinate 3 units down

There are twelve empty rooms in the office of Acme Softwares, inc. Alif and Laila joins the company. How many ways can they be assigned a room each from these twelve

Answers

Answer:

132.

Step-by-step explanation:

That would be the number of permutations of 2 from 12.

12P2 = 12! / (12-2)!

= 132.

An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft = 124 + 2t, and it was developed using data from periods 1 through 10.
t units sold
11 147
12 148
13 151
14 145
15 155
16 152
17 155
18 157
19 160
20 165
Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? (Round your answers to 2 decimal places.)
MAD (Naive)=
MAD (Linear)=
MSE (Naive)=
MAD (Linear)=

Answers

Answer:

Following are the responses to the given question:

Step-by-step explanation:

Mean Absolute Deviation MAD

[tex]MAD = \sum_{i=1}^{n} \frac{\left | actual_{i}-forecast_{i} \right |}{n}[/tex]

Mean squared error  

[tex]MSE=\Sigma^{n}_{i=1} \frac{(Actual_i - Forecast_i)^2}{(n - 1)}[/tex]

linear trend equation is [tex]Ft = 124 + 2t[/tex]

[tex]MAD = \frac{23}{10} = 2.3\\\\MSE = \frac{91}{9}= 10.11\\\\[/tex]

Naive method

[tex]MAD = \frac{36}{9} = 4\\\\MSE = \frac{202}{8}=25.25\\\\MAD (Naive) = 4\\\\MAD (Linear) =2.3\\\\MSE (Naive)=25.25\\\\MSE (Linear)=10.11\\\\[/tex]

Please find the attached file.

Do 5, 5, and 5 form a right triangle?

Answers

No, this isn’t true because of the Pythagorean theorem where a^2 + b^2 = c^2 which would not apply (5)^2 + (5)^2 = 5^2
25 + 25 = 50
50 is not the square of 5

can anyone please help me with this?

Answers

Answer:

I believe that It would be b

The solution for 7x + 4 = x – 2

Answers

Answer:

x = -1

Step-by-step explanation:

Add two on both sides. This makes the equation 7x + 6 = x. Now subtract 7x on both sides. This equals 6 = -6x. Divide by -1 on both sides. x = -1.

State whether the data described below are discrete or continuous and explain why?

The distance between cities in a certain contry.

a. The data are discrete because the data can only take on specific values.
b. The data are discrete because the data can take on any value in an interval.
c. The data are continuous because the data can take on any value in an interval.
d. The data are continuous because the data can only take on specific values.

Answers

Answer:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

Discrete data are those which can take up only specific values. Discrete data values may include the number of children in a particular school, the number of visitors received per day. All this values are specific and cannot just take up any number one f values within an interval. Continous data on the other hand can take up any number of data values between an interval. Continous data types are usually height temperature, length(distance data). There can be infinite number of possible data within interval values.

A researcher investigated whether following a vegetarian diet could help to reduce blood pressure. For a sample of 85 people who followed a vegetarian diet for 4 months, the mean systolic blood pressure was 124 mmHg. For a sample of 75 people who followed a non-vegetarian diet for 4 months, the mean systolic blood pressure was 138 mmHg. Methods of statistics show that if a vegetarian diet had no effect on blood pressure, there would be less than 1 chance in 100 of getting these results. Does the result have statistical significance? Why or why not? Does the result have practical significance?

Answers

Answer:

Yes, the result does not have statistical significance

Yes, the result has practical significance

Step-by-step explanation:

An experiment or claim may be said to be statistically significant if it's occurence is likely not due to chance for a certain level of stated significance. From the scenario described, it is stated that if vegetarian diet has no effect on blood, then the result obtained wipukd likely occur in less Than 1 of 100 ; this is < 0.01. This means that the effect of vegetarian diet on blood could not have occurred by chance. Hence, result is statistically significant.

The result does have practical significance too, since there is a distinctive difference in blood pressure of non - vegetarians(138mmHg) and Vegetarians (124mmHg).

7(x – 3) = 5(x+3)
Solve for x

Answers

Step-by-step explanation:

7x-21 = 5x +15

7x-5x = 15 + 21

2x = 36

x = 36/2

x = 18

Answer:

x=18

Step-by-step explanation:

Distribute 7 through the parentheses

7x-21=5(x+3)

Move the variable to the left -hand side and change its sign

7x-21-5x=15

Collect like terms

2x=15+21

divide both sides of the equation by 2

x=18

If Clive was charged $3.92 for a minute 38 call, what is Clive's per minute base rate?

Answers

pretty sure it’s $0.10

at sunrise, the outside temperature was 3 below zero by lunchtime the temperature rose by 27 and fell by 10 by night what was the temperature at the end of the day?​

Answers

Answer:11 degrees at sunrisde the temp was -1 degree

Step-by-step explanation:

474 ( ) 548 42. - 8 how do I arrive at this answer.

Answers

9514 1404 393

Answer:

  (64x^28)/(5y^22)

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

__

First, eliminate the outside exponent on the left factor. Then use the above rules to combine factors with the same base.

  [tex]\displaystyle\left(\frac{4x^4}{5y^6}\right)^5\cdot\left(\frac{5^4y^8}{4^2x^{-8}}\right)=\frac{(4^5x^{20})(5^4y^8)}{(5^5y^{30})(4^2x^{-8})}=4^{5-2}5^{4-5}x^{20-(-8)}y^{8-30}\\\\=4^35^{-1}x^{28}y^{-22}=\boxed{\frac{64x^{28}}{5y^{22}}}[/tex]

A biologist is studying the migratory patterns of sandhill cranes. His study focuses only on sandhill cranes that are bred and hatched in Alaska, and eventually migrate south to warmer climates. Each year he randomly tags a sample of 50 cranes with GPS trackers to gather data about their migratory patterns.

In this scenario, the population is
.

In this scenario, the sample is

Answers

Answer:

Population = All Sandhill cranes bred and hatched in Alaska that migrate south

Sample = The 50 crane samples which are tagged yearly.

Step-by-step explanation:

The population refers to all members or subjects which belongs to a defined study. Each and every subject which meets the requirement of a study makes up the population.

The sample however, is a subset of the population, the sample is a smaller group of subject which is selected from the population randomly to for a representative sample of the population. Here, it is the 50 sampled sandhill cranes bed per year.

Answer:

These are the answers

Step-by-step explanation:

you can never divide any one angle into smaller angle. true or false​

Answers

Answer:

true.

hope it helps..

I believe the answer is true

QUESTION 1
The adult dosage of a medication is 15 mg** per day.
1. What is the pediatric dosage of that same medication for a child weighing 52 pounds? Refer to the formula below:
(Child weight divided by 150 lbs.) x Adult Dose = Pediatric Dosage
2. Explain in a well-written paragraph

Answers

Answer:

Step-by-step explanation:

Given that the adult dosage = 15 mg/day.

1. The pediatric dosage for a child weighing 52 pounds can be determined by;

Pediatric Dosage = (Child weight divided by 150 lbs.) x Adult Dose

                             = [tex]\frac{52}{150}[/tex] x 15 mg/day

                             = 5.2 mg/day

The pediatric dosage of the medication for a child weighing 52 pounds is 5.2 mg per day.

2. The medication can be consume by either an adult or a  pediatric at a measured quantity. If an adult takes 15 mg of the medication per day, then any child whose weight is 52 pounds can take a maximum quantity of 5.2 mg of the medication per day. This implies that a child of the measured weight should not take more than 5.2 mg of the medication per day, and probably not at once.

The dosage of the medication for a pediatric can be determined by;

Pediatric Dosage = (Child weight divided by 150 lbs.) x Adult Dose

That is, once the weight of a child is determined, the dosage can be calculated.

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