I need help solving this problem. It tells me that I could use any method provided above but I don't really get it. Could someone help?

The Problem:
You have to be careful when using a ladder. If you place the ladder too close to the wall, it could tip over. If you place the ladder too far from the wall, it could slide down. To prevent this, safety experts recommend the 4-to-1 Rule: for every 4 feet you want to go up the wall, place the base of the ladder one foot away from the wall.

The longest ladder available at many hardware stores is 40 feet. What is the highest you could reach with this ladder?

The problem gives me three methods to pick from to solve the problem. Each method had a clue underneath.

Hints:
Method 1: Know that the height must be 4x the base. Also know that hypotenuse is the longest side, so height must be shorter than 40 (and base must be shorter than 10 feet).

Method 2: Base^2+Height^2=40^2
Height= 4 • base

Method 3:
Base^2+Height^2=40^2
Base= 0.25 • height

The answers this problem asks for is:
The base, height and length.
​

Answer:

The last option is the correct choice 33.5

Step-by-step explanation:

[tex]V=\pi r^2\frac{h}{3} \\=\pi 2^2\frac{8}{3} \\=33.51\\=33.5[/tex]

Answer:

D

Step-by-step explanation:

In the attached file

Answer:

0-4: Make it 2 units tall

5-9: Make it 5 units tall

10-14: Make it 1 unit tall

15-19: Make it 4 units tall

20-24: Make it 4 units tall

Step-by-step explanation:

0-4: 2, 2 (2 numbers)

5-9: 6, 7, 7, 8, 9 (5 numbers)

10-14: 14 (1 number)

15-19: 15, 16, 16, 18 (4 numbers)

20-24: 21, 23, 23, 24 (4 numbers)

Answer:

14m

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

153.86 = 3.14 r^2

Divide each side by  3.14

153.86 /3.14 = r^2

49 = r^2

Take the square root of each side

sqrt(49) = sqrt(r^2)

7 = r

We want the diameter which is twice the radius

d = 2r

d =2*7

d =14

Answer:

I just wanted to add on it is 14 i tried it on savaas and it worked

Step-by-step explanation:

Answer:

The proportion of the variability seen in math achievement that can be predicted by math attitude is 0.78, the same value as the correlation coefficient.

Step-by-step explanation:

The correlation coefficient r between this two variables is found to be 0.78.

This coefficient can be calculated as:

[tex]r=\dfrac{SSY'}{SSY}[/tex]

where SSY' is the sum of the squares deviation from the mean for the predicted value and SSY is the sum of the squares deviation from the mean for the criterion variable.

Then, the value of the coefficient r is giving the proportion of the variability seen in the criterion value Y that can be explained by the predictor variable X.

Answer:

r=SSY'/SSY

Step-by-step explanation:

Answer:

a) The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

c)

Step-by-step explanation:

a) Let p be  the probability of winning each ticket be = 0.1

Then q which is the probability of failing each ticket  = 1 - p = 1  - 0.1 = 0.9

Assume X represents the  number of failure preceding the 5th success in x + 5 trials.

The last trial must be success whose probability is p = 0.1 and in the remaining (x + r- 1) ( x+ 4 ) trials we must have have (4) successes whose probability is given by:

[tex]\binom{x+r-1}{r-1}*p^{r-1}*q^{x} = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

Then, the probability distribution of random variable X is

[tex]P(X=x) = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

where;

X represents the  negative binomial random variable.

K= X + 5 = number of ticket buy up to and including fifth winning ticket.

Since K =X+5 this signifies that  X = K-5

as X takes value 0, 1 ,2,...

K takes value 5, 6 ,...

Therefore:

The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

Let p represent the probability of getting a tail on a flip of the coin

Thus p = 0.5 since it is a fair coin

where L = number of flips of the coin including 33rd occurrence of  tails

Thus; the negative binomial distribution of L can be illustrated as:

[tex]P(X=x) = \binom{x-1}{r-1}(1-p)^{x-r}p^r[/tex]

where

X= L

r = 33  &

p = 0.5

Since we are looking at the 33rd success; L is likely to be : L = 33,34,35...

Thus; the PMF of L = [tex]P(L=l) = \binom{l-1}{33-1}(1-0.5)^{l}(0.5)^{33} \\ \\ \\ \mathbf{P(L=l) = \binom{l-1}{33-1}(0.5)^{l} }[/tex]

c)  

Given that:

Let  M be the random variable which represents  the number of tickets need to be bought to get the first success,

also success probability is 0.01.

Therefore, M ~ Geo(0.01).

Thus, the PMF of M is given by:

[tex]P(M = m) = (1-0.01)^{m-1} * 0.01 , \ \ \ since \ \ \ (m = 1,2,3,4,....)[/tex]

[tex]P(M=m) = (0.99)^{m-1} * 0.01 , m = 1,2,3,4,....[/tex]

Answer:

807,205

Step-by-step explanation:

Take the eight hundred and seven thousand and express that has 807,000. Then, add the two hundred and five at the end to get 807,205

The given statement is written in figures 807,205.

The given statement is eight hundred and seven thousand, two hundred and five in figures.

We need to write the given statement as the number.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

Now, eight hundred and seven thousand, two hundred and five=807,205.

Therefore, the given statement is written in figures 807,205.

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Answer:

5

Step-by-step explanation:

first you need to simplify this equation and put it in slope intercept form which is y = mx + b

after simplifying you will get y = 5x + 10

since the slope is m , the answer will be 5

Answer:

The slope of two parallel lines will always be the same. If the slope was slightly different, then the lines would intersect at some point, which breaks the definition of parallel lines.

The y-intercepts of two parallel lines have to be different, or else the two lines would be the same line. If the y-intercept and the slope are the same, then the lines will essentially equal each other.

Answer:

Sample Response: Two parallel lines will have the same slope. The slopes of parallel lines have to be equal. The y-intercepts of those two lines have to be different, otherwise they would be the same line. The x-intercepts of the parallel lines would also be different.

Step-by-step explanation:

edge 2020

Answer:

Continuously

Step-by-step explanation:

Compounded continuously:

A = Pe^(rt)

A = 11,000 e^(0.0625 × 10)

A = 20,550.71

Compounded semiannually (twice per year):

A = P(1 + r)^t

A = 11,000 (1 + 0.063/2)^(2×10)

A = 11,000 (1 + 0.0315)^20

A = 20,453.96

Answer:

The real number 'a' = 32

The real number 'b' = 0

Step-by-step explanation:

Product of a number of a number and its conjugate = a + bi

The number is = -4 + 4i

Conjugate of this number is = -4 - 4i

Product of the number and it's conjugate

= (-4 + 4i)(-4 - 4i)

= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]

= 16 + 16i - 16i - 16i²

= 16 - 16(-1)

= 16 + 16

= 32

a + bi = 32 + (0)i

By comparing both the sides,

a = 32

b = 0

Answer:

after three years

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

If X + 21 = 64

then subtract 64 by 21 and you get 43

Answer:

D

Step-by-step explanation:

An arithmetic sequence is a series of numbers that increases or decreases by a certain quantity every step. A is not an arithmetic sequence, since it alternates between 2 and -2. B is not an arithmetic sequence, since it does not grow constantly in one direction. C is not an arithmetic sequence, but rather a geometric one. D is an arithmetic sequence, decreasing by 3 with each step. Hope this helps!

Step-by-step explanation:

[tex]y = {x}^{2} - 18 \\ y + 18 = {x}^{2} \\ square \: root \: both \: sides \: \\ \sqrt{y + 18} = \sqrt{ {x}^{2} } [/tex]

[tex]x = \sqrt{y + 18} [/tex]

Answer:

√y + 18 = x

Step-by-step explanation:

Let us solve it now.

y = x² - 18

Take -18 to the left side

y + 18 = x²

Now remove the square of x

√y + 18 = x

Answer:

56

Step-by-step explanation:

Answer:

  C.  y ≤ 1

Step-by-step explanation:

The maximum value of the function is 1. So, the range is all values of y less than or equal to that.

  y ≤ 1

Answer:

Descriptive statistics

Step-by-step explanation:

Descriptive statistics describes and summarizes the basic features of a given dataset. It explains features from a collection of information, it is also said to be a form of summary statistics. Here data is characterized using its properties.

In this case, I was asked to describe my approach to the initial analysis. When describing the analysis plan for the request, I would tell the interviewer to start analysis using descriptive statistics.

Answer:

5,610 Miles

Step-by-step explanation:

To solve this you would need to multiply the average miles by how many tanks of gas she will use.

374 * 15 = 5,610

So, Eleanor can drive 5,610 miles with 15 tanks of gas.

Answer:

A.

Step-by-step explanation:

So first you need to find the slope:

[tex]\frac{-2-6}{3+2} =-\frac{8}{5}[/tex]

Since it's point slope, you have to use a point:

It's either:

[tex](y - 6)=-\frac{8}{5}(x+2)[/tex]

or

[tex](y+2)=-\frac{8}{5}(x-3)[/tex]

Check which answer has those:

A.

The solution is Option A.

The equation of line is y - 6 = ( -8/5 ) ( x + 2 ) where the slope is -8/5

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -2 , 6 )

Let the second point be Q ( 3 , -2 )

The slope of the line between the point is given by m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 6 - ( - 2 ) ) / ( -2 - 3 )

On simplifying the equation , we get

Slope m = ( 8 / -5 ) = -8/5

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = ( -8/5 ) ( x - ( -2 ) )

On simplifying the equation , we get

y - 6 = ( -8/5 ) ( x + 2 )

Hence , the equation of line is y - 6 = ( -8/5 ) ( x + 2 )

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Answer:

88/57

Step-by-step explanation:

Answer: 88:57

Step-by-step explanation:

Length is 88 and width is 57

So the ratio is 88:57

Answer:

Step-by-step explanation:

a) The number of students sampled in both populations are large. We can assume that the populations are normally distributed. The populations are also independent.

b) This is a test of 2 independent groups. Let μ1 be the mean responses of students buying lecture notes and μ2 be the mean responses of students not buying lecture notes.

The random variable is μ1 - μ2 = difference in the mean responses of students buying lecture notes and the mean responses of students not buying lecture notes.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 8.48

x2 = 7.8

s1 = 0.94

s2 = 2.99

n1 = 86

n2 = 35

t = (8.48 - 7.8)/√(0.94²/86 + 2.99²/35)

t = 1.32

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.94²/86 + 2.99²/35]²/[(1/86 - 1)(0.94²/86)² + (1/35 - 1)(2.99²/35)²] = 0.0706/0.00192021883

df = 37

We would determine the probability value from the t test calculator. It becomes

p value = 0.195

c) Since alpha, 0.01 < than the p value, 0.195, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, the samples do not provide sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students.

d) The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 99% confidence interval, the z score is 1.2.58. This is determined from the normal distribution table.

x1 - x2 = 8.48 - 7.8 = 0.68

z√(s1²/n1 + s2²/n2) = 2.58√(0.94²/86 + 2.99²/35) = 1.33

The confidence interval is

0.68 ± 1.33

The upper boundary for the confidence interval is

0.68 + 1.01 = 2.01

The lower boundary for the confidence interval is

0.68 - 1.33 = - 0.65

We are confident that the difference in population means responses between the students buying lecture notes and the students not buying lecture notes is between - 0.65 and 2.01

d) For a 95% confidence interval, the z score is 1.96.

z√(s1²/n1 + s2²/n2) = 1.96√(0.94²/86 + 2.99²/35) = 1.01

The confidence interval is

0.68 ± 1.01

The upper boundary for the confidence interval is

0.68 + 1.01 = 1.69

The lower boundary for the confidence interval is

0.68 - 1.01 = - 0.33

Therefore, a 95% confidence interval for (μ1-μ2) would be narrower. This is seen in the values in both scenarios.

Answer:

B:

Step-by-step explanation:

According to theorem, "the angle in a semi-circle is a right angle" So,

<O = 90°

<M = 54

<K = 180-90-54

<OKM = 36°

Answer:

x = 12

Step-by-step explanation:

g(x)= 2x-4

g(x)= 20

Therefore,

2x-4 = 20

Bringing -4 to the other side it becomes positive,so..

2x= 20+4

= 24

x =24/2

= 12

Answer:

(a)24

(b)8

(c)4

Step-by-step explanation:

Number of STudents in the Class = 36

Angle representing Students with Red Hair =40 degrees

Angle representing Students with Blonde Hair =240 degrees

Therefore:

(a)Number of Students with Blonde Hair

[tex]=\dfrac{240^\circ}{360^\circ} \times 36\\\\ =24$ students[/tex]

(b)Number of Students with Dark Hair

Angle representing students with dark hair = 360-(240+40)=80 degrees

Therefore:

Number of Students with Dark Hair

[tex]=\dfrac{80^\circ}{360^\circ} \times 36\\\\ =8$ students[/tex]

(c)Number of Students with Blonde Hair

[tex]=\dfrac{40^\circ}{360^\circ} \times 36\\\\ =4$ students[/tex]

There are 8 students that have blond hair

There are 24 students that have dark hair

There are 4 students that have red hair

Please find attached the pie chart used in answering this question

A pie chart is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees

To determine the number of students with a type of hair, use this formula :

(degree of the slice that represents the hair type / 360) x total number of students in the class

Degree of the slice that represents blond hair = 360 - (240 + 40) = 80

Students that have blonde hair = [tex]\frac{80}{360}[/tex]  x 36 = 8

Students that have dark hair = [tex]\frac{240}{360}[/tex] x 36 = 24

Students that have red hair = [tex]\frac{40}{360}[/tex] x 36 = 4

To learn more about pie charts, please check : https://brainly.com/question/11433309?referrer=searchResults

Answer:

6000 grams the formula would be multiply the mass value by 1000

Step-by-step explanation:

Answer:

6000 grams

Step-by-step explanation:

6 kilograms

To convert kg into grams, we multiply by 1000

So,

=> 6 * 1000 grams

=> 6000 grams

Answer:

-16x^5

Step-by-step explanation:

f(x)=x^3+10x^2-25x-250

f(x) = x^3-15x+x^2-250

f(x) = x^5-15x-250

f(x) = x^5 -x + 16

f(x) = -x^5+16

f(x) = -16x^5

// have a great day //

Answer:

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.

Step-by-step explanation:

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.

[tex]p_1=X_1/n_1=261/501=0.5210[/tex]

The sample 2 (older  adults), of size n2=352 has a proportion of p2=0.3494.

[tex]p_2=X_2/n_2=123/352=0.3494[/tex]

The difference between proportions is (p1-p2)=0.1715.

[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

Answer:

1250

Step-by-step explanation:

5% of $5000 is 250

250X5= 1250

Answer:

10-19 ⇒ 4

40-49 ⇒ 3

Answer:

10-19: 4 numbers

40-49: 3 numbers

Step-by-step explanation:

10-19: 11, 13, 17, 18 (4 numbers)

40-49: 41, 44, 47 (3 numbers)

Answer:

A. 90 sq. units

Step-by-step explanation:

5(18) = 90