The bottom of a ladder must be placed 3 ft. from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? Round your answer to the nearest tenth.

Answer: the percentile is 74%

Step-by-step explanation:

The given data distribution is arranged in increasing order as:

0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6

The total number of values given in the data is 50

Percentile = number of values in the distribution lesser than the given value × 100/ total number of values in the distribution

Considering the data speed of 11.2 Mbps, the number of data speed lower than 11.2 is 37

Percentile = (37 × 100)/50 = 74%

Answer:

1, 3, 5, 6

Step-by-step explanation:

Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16

The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.

The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.

In other words, these percentages are less than 30% and can be rightly represented by the variable s.

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Answer:

Step-by-step explanation:

factor out the numerator and demoninator

(m-2)(m-1)/m(m-1)

= (m-2)/m

Answer: Options B and D.

Step-by-step explanation:

We start with the equation:

(-2 3/7)*(-6/11)

now, you need to recall the signs relations:

(+)*(+) = +

(-)*(+) = -

(-)*(-) = +

Then our initial equation has a positive sign.

a)  (3/8)*(-6/7) here we have (+)*(-), so this is negative, this option is not correct.

b) (1 2/9)*(2 16/17) here we have (+)*(+), so this is positive, this option is correct.

c)  (-9/20)*(3 4/5) here we have (-)*(+), so this is negative, this option is not correct.

d) (-1/3)*(-2/3) here we have (-)*(-), so this is positive, then this option is correct.

Answer:

The awnser is B and D

Step-by-step explanation:

Answer:

  (-3, 4) is a solution

Step-by-step explanation:

The point (-3, 4) is inside the shaded area of the graph, so is a solution.

You can check in the inequality

  y > -2x -3

  4 > -2(-3) -3 . . . . substitute for x and y

  4 > 3 . . . . . . . true; the given point is a solution

Answer:

(a) all men = 3.6351 * 10^ -7

(b) all women = 2.3483* 10^ -4

(c) 8 men and 4 women = 0.0308

(d) 6 men and 6 women= 0.2170

Step-by-step explanation:

A jury pool has 15 men and 21 women, from which 12 jurors will be selected.

Total = 36 people

Probability of

(a) all men

= 15C12/36C12

= 455/1251677700

= 3.6351 * 10^ -7

(b) all women

= 21C12/36C12

= 293930/1251677700

= 2.3483* 10^ -4

(c) 8 men and 4 women

=( 15C8 * 21C4)/36C12

= (6435*5985)/1251677700

= 38513475/1251677700

= 0.0308

(d) 6 men and 6 women

= (15C6 * 21C6)/(36C12)

= (5005*54264)/1251677700

= 271591320/1251677700

= 0.2170

Answer:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]

Step-by-step explanation:

The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.

[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]

There are two different solutions:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]

Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):

[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]

[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]

Answer:

(0,34)

Step-by-step explanation:

For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!

Answer:

The answer is (0,34)

Answer:

1)

Volume of pyramid = 1/3(Ab)(h)

Where Ab is the area of base, h is height

Volume of cone = 1/3(Ab)(h)

a) Their formula for finding volume is same. Also, their painting heads are same.

b) Pyramids have a tetragonal base while cones have a polygonal base

2) Pyramids

Volume of cone = (1/3) πr²h

Since Area of a circle = πr²

So

Volume of pyramid = (1/3)(A)(h)

So we can use the formula of a circle in cone's formula

Answer:

i dont know but i want points

Step-by-step explanation:

hehehe

Answer:

difference in area = 16 ft²

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Step-by-step explanation:

Jacks rectangular patio

width = a

length = 2a - 1

area = lw

where

l = length

w = width

area = 120 ft²

a(2a - 1)

2a² - a - 120 = 0

(a - 8) (2a + 15)

a = 8 or -15/2

Ron's rectangular patio

width = a

length = a + 5

area = lw

area = 104 ft²

a (a + 5) = 104

a² + 5a -104 = 0

(a + 8)  (a - 13)

a = -8 or 13

How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

120 - 104 = 16 ft²

The value 8 or 13 can be used for a since the width a have to be the same.

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Answer:

the Answers are : B and E

Step-by-step explanation:

From the given quadratic equation [tex]x^2 + 10x + 25 = 7[/tex] Thus, the solution is x = -1 and -9.

Suppose that the given quadratic equation is

[tex]ax^2 + bx + c = 0[/tex]

Then its roots are given as:

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

We have been given a quadratic equation

[tex]x^2 + 10x + 25 = 7[/tex]

[tex]x^2 + 10x + 25 - 7=0\\\\x^2 + 10x + 18[/tex]

The solution of the given equation;

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-10 \pm \sqrt{10^2 - 4\times 18}}{2}\\\\x = \dfrac{-10 \pm \sqrt{100- 36}}{2}\\\\x = \dfrac{-10 \pm \sqrt{64}}{2}\\\\x = \dfrac{-10 \pm 8}{2}\\[/tex]

Therefore, the solution are x = -1 and -9.

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Answer:

a. 2 groups of 2 is 4

b. 3 groups of 2 is 6

c. 4 groups of 2 is 8

d. 5 groups of 2 is 10

e. 6 groups of 2 is 12

Answer:

a - 2

b- 3

c- 4 groups of 2 is 8

d- 5 groups of 2 is 10

e- 6 groups of 2 is 12

Answer:

The 80% confidence interval for the average net change is (8.596, 12.904).

Critical value t=1.638.

Step-by-step explanation:

First, we calculate the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{4}(12+7+13+11)\\\\\\M=\dfrac{43}{4}\\\\\\M=10.75\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{3}((12-10.75)^2+(7-10.75)^2+(13-10.75)^2+(11-10.75)^2)\\\\\\s=\dfrac{20.75}{3}\\\\\\s=6.92\\\\\\[/tex]

We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=10.75.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.63}{\sqrt{4}}=\dfrac{2.63}{2}=1.315[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 80% confidence interval and 3 degrees of freedom is t=1.638.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.638 \cdot 1.315=2.154[/tex]

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

[tex]LL=M-t \cdot s_M = 10.75-2.154=8.596\\\\UL=M+t \cdot s_M = 10.75+2.154=12.904[/tex]

The 80% confidence interval for the average net change is (8.596, 12.904).

Answer:

2

Step-by-step explanation:

Given the system of equations:

[Tex]x^2+y^2=9\\9x+2y=16[/tex]

Comparing [Tex]x^2+y^2=9[/tex] with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2[/tex].

The first equation is an equation of a circle centred at (0,0) with a Radius of 3.

The second equation 9x+2y=16 is a straight line equation.

A straight line can only intersect a circle at a maximum of 2 points.

Therefore the greatest possible number of solutions to the equations in the system is 2.

Answer:

2

Step-by-step explanation:

and jj is gay of outer banks

Answer:

His pay for 4 hours of work is $106.67.

Step-by-step explanation:

2:1, full rate : reduced rate.

This means that for each 2+1 = 3 hours that he works, 2 he has full pay and 1 he has reduced pay.

4 hours

How much are full pay?

For each 3, 2 are full pay. For four?

3 hours - 2 full pay

4 hours - x full pay

[tex]3x = 8[/tex]

[tex]x = \frac{8}{3}[/tex]

So for [tex]\frac{8}{3}[/tex] hours he makes the full pay($30) and for [tex]4 - \frac{8}{3} = \frac{12}{3} - \frac{8}{3} = \frac{4}{3}[/tex] he makes reduced pay($20).

Calculate his pay for 4 hours of work

[tex]30*\frac{8}{3} + 20*\frac{4}{3} = 106.67[/tex]

His pay for 4 hours of work is $106.67.

Answer:

5

Step-by-step explanation:

We have x-2 = 5

x-2 = 5 we separate parenthesis.

x(-2) = 5(+2)

x = 7

We can check this as what the x-2 is saying is  7-2 = 5

Answer:

Since it is an equilateral triangle,

Perimeter = 3s = 3 x side

=> 15 = 3 X (x - 2)

=> 15 = 3(x - 2)

=> 15 = 3x - 6

=> 3x = 15 + 6

=> 3x = 21

=> x = 21/3

=> x = 7

When x = 7,

=> Side = 7 - 2 = 5 inches

Since, it is an equilateral triangle all sides are of 5 inches each.

Answer:

The lower limit is 72.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is more than 2 standard deviations from the mean, it is unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question, we have that:

[tex]n = 100, p = 0.8[/tex]

So

[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]

He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?

2 standard deviations below the mean is the lower limit, so X when Z = -2.

Proportion:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-2 = \frac{X - 0.8}{0.04}[/tex]

[tex]X - 0.8 = -2*0.04[/tex]

[tex]X = 0.72[/tex]

Out of 100:

0.72*100 = 72

The lower limit is 72.

Answer:

Option 2

Step-by-step explanation:

The question states "the width of the rectangle is 4 less than half the length."  Since we are looking for the value of w, w will be equal to the expression we create.  We start with half the length and than subtract 4 from it.  This is because it says 4 less than half the length, not half of 4-length or another variation.  In many of these problems the best way to solve them is by working backwards.

Answer:

Option 2

Step-by-step explanation:

Translating these words into math, we get w = 1/2l - 4 which is Option 2.

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]

Compute the probability that on a randomly selected day she will have five messages as follows:

[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]

               [tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Answer:

0.534

Step-by-step explanation:

p(0 losses) = 0.7² = 0.49

p(1 loss) = 2 x 0.3 x 0.7 = 0.42

p(2 losses) = 0.09

This is a conditional probability problem. If the number of people hospitalized is 0 or 1, then the  total loss will be less than 1. However, if two people are hospitalized, the probability that the  total loss will be less than 1 is 0.5. we need to exclude the 50% x 0.09 chance of a double loss costing more than 1. So

P(Cost < 1)

= 0.49 + 0.42 +0.045

= 0.955

P(0 losses | Cost < 1)

= P(0 losses and Cost < 1) / P(Cost < 1)

= 0.49 / 0.955 = 0.513

P(1 loss | Cost < 1)

= 0.42 / 0.955 = 0.440

P(2 losses | Cost < 1) = 0.045 / 0.955 = 0.047

Now take the expectation:

E[X] = (0)(0.513) + (1)(0.440) + (2)(0.047)

= 0.440 + 0.094

= 0.534

Answer:

4a

Step-by-step explanation:

The mean is found by adding all of the data set together and then dividing by the amount of individual pieces of data in the set.

(2+3+3+8) = 16

16/4=4

The answer is 4a.

Answer:

0.67

Step-by-step explanation:

0.668 is close to 0.67 than 0.66

Answer:

The probability is 0.2326 or 23.26%.

Step-by-step explanation:

The probability that a random customer fills their tank with premium gas is:

[tex]P( prem\ \&\ fill) = 0.2*0.5=0.10[/tex]

The probability that a random customer fills their tank is given by:

[tex]P(fill)=P( reg\ \&\ fill)+P( mid\ \&\ fill)+P( prem\ \&\ fill)\\P(fill) = 0.5*0.3+0.3*0.6+0.2*0.5\\P(fill) = 0.43[/tex]

Therefore, the probability that a customer used premium gas given that hey have filled their tank is:

[tex]P(prem| fill) = \frac{P( prem\ \&\ fill) }{P(fill)} \\P(prem| fill) =\frac{0.10}{0.43}=0.2326[/tex]

The probability is 0.2326 or 23.26%.

Answer:  [tex]\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}[/tex]

Step-by-step explanation:

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}[/tex]

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

          (2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

          (3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

                    (4, 5), (4, 4), (4, 3), (4, 2), (4, 1)

                              (5, 4), (5, 3), (5, 2), (5, 1)

                                        (6, 3), (6, 2), (6, 1)

       = 30

P(B) = (1, 2), (2, 1)                                   sum = 3

          (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)    sum = 6

          (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)  sum = 9

          (6, 6)                                           sum = 12

      = 12

P(A ∩ B) =  (1, 2), (2, 1)

                  (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

                  (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)

             = 11

Answer:

Step-by-step explanation:

The missing list of the data values for the question are as follows:

1             1.03

2             1.01

3             0.96

4             0.96

5             0.99

6             1

7             1.01

8             0.98

9             1.02

10            1.03

11             1

12             0.99

13             1

14             0.97

15             1.01

               [tex]x_i[/tex]                          [tex](x_i - \bar x)[/tex]                              [tex](x_i - \bar x)^2[/tex]

1             1.03                         0.03                                  0.0009

2             1.01                         0.01                                   0.0001

3             0.96                        -0.4                                   0.0016

4             0.96                        -0.4                                   0.0016

5             0.99                        -0.1                                   0.0001

6             1                               0.0                                   0.0

7             1.01                           0.1                                   0.0001

8             0.98                        -0.2                                   0.0004

9             1.02                          0.2                                   0.0004

10            1.03                          0.3                                   0.0009

11             1                               0.0                                   0.0

12             0.99                        -0.1                                   0.0001

13             1                               0.0                                   0.0

14             0.97                        -0.03                                   0.0009

15             1.01                           0.1                                   0.0001

The average value for x is calculated as:

[tex]\bar x = \dfrac{14.96}{15}[/tex]

[tex]\bar x = 0.997 \\ \\ \bar x \approx 1.00[/tex]

[tex]\sum (x-x_i)^2 = 0.0072[/tex]

[tex]\dfrac{\sum (x-x_i)^2 }{n-1}= \dfrac{0.0072}{15-1} \\ \\ = \dfrac{0.0072}{14} \\ \\ = 0.00051[/tex]

[tex]\sigma = \sqrt{\dfrac{\sum (x-x_i)^2 }{n-1}} = \sqrt{0.00051} \\ \\ \sigma =0.0226 \\ \mathbf { \\ \sigma =0.02 \ to \ one \ significant \ figure}[/tex]

Answer:

The probability of selecting two red balls is 0.132.

Step-by-step explanation:

In a bag there are 10 balls in a bag, 4 red balls and 6 black balls.

The conditions of selecting a ball are:

It is also provided that only one ball can be picked at a time.

Now, it is given that two balls are picked.

The number of ways to select a red ball in the first draw is: [tex]{4\choose 1}=4\ \text{ways}[/tex]

Compute the probability of selecting a red ball in the first draw as follows:

[tex]P(\text{First ball is Red})=\frac{{4\choose 1}}{{10\choose 1}}=\frac{4}{10}=0.40[/tex]

Now as a red ball is selected it will not be replaced.

So, there are 9 balls in the bag now.

The number of ways to select a red ball in the second draw is: [tex]{3\choose 1}=3\ \text{ways}[/tex]

Compute the probability of selecting a red ball in the second draw as follows:

[tex]P(\text{Second ball is Red})=\frac{{3\choose 1}}{{9\choose 1}}=\frac{3}{9}=0.33[/tex]

Compute the probability of selecting two red balls as follows:

[tex]P(\text{Two Red balls})=P(\text{First ball is Red})\times P(\text{Second ball is Red})[/tex]

                            [tex]=0.40\times 0.33\\\\=0.132[/tex]

Thus, the probability of selecting two red balls is 0.132.

Answer:

[tex]7.9584 \times 10^8[/tex]

Step-by-step explanation:

[tex]8.05 \times 10^8 - 9.16 \times 10^6[/tex]

[tex]805000000-9160000[/tex]

[tex]=795840000[/tex]

Answer:

21.b

22.c

Step-by-step explanation:

idk how to explain it lol I did mental math

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Here are some scenarios:

According to market research, a business has a 75% chance of making money in the first 3 years.

According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.

According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.

1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.

Answer:

The correct order in terms of likelihood from least to greatest would be

P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83

Car needs major repairs -> Business makes money -> Light bulb still works

Step-by-step explanation:

We are given probabilities of three different events.

According to market research, a business has a 75% chance of making money in the first 3 years.

P(Business) = 75% = 0.75

According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.

P(Light bulb) = 5/6 = 0.83

According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.

P(Car repair) = 0.70

We are asked to write these scenarios in order of likelihood from least to greatest after three years.

Which means that the events with least probability is less likely to occur.

The least probability is of car repair, then business and then light bulb.

So the correct order in terms of likelihood from least to greatest would be

P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83

Car needs major repairs -> Business makes money -> Light bulb still works

Answer:

R=9

Step-by-step explanation:

the formula for area of a circle is pi r squared

where r denotes the radius of the circle

equating the formula for area with the area of the circle provided

p\i r squared = 81 p\i

r squared = 81

r = radical 81

r =9 inches