Triangle JKL was dilated using the rule D Subscript M, one-third. The image, triangle J'K'L', is the result of the dilation. Point M is the center of dilation. Triangle J K L is dilated to form smaller triangle J prime K prime L prime. The length of M L prime is 2.5. What is L'L? 5 units 7.5 units 10 units 12.5 units

Answer:

9.8

Step-by-step explanation:

updated

9^2=x^2+4^2

9*9=x*x+4*4

81=x*x-16

+16. +16

97=x*x

√97=√x*x

√97=x

So the answer is √97, but the question wants it rounded so it's actually 9.8

Answer:

[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]  

Now we can claculate the p value with this formula:

[tex]p_v =P(z<-1.42)=0.0778[/tex]  

If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.

Step-by-step explanation:

Information to given

n=735 represent the random sample taken

X=203 represent the number of people who have their prostate regularly examined

[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined  

[tex]p_o=0.3[/tex] is the value to verify

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.3[/tex]  

Alternative hypothesis:[tex]p < 0.3[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]  

Now we can claculate the p value with this formula:

[tex]p_v =P(z<-1.42)=0.0778[/tex]  

If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.

Answer:

x(2x+3)

Step-by-step explanation:

Im guessing 2x2 is 2x^2

2x^2 + 3x = 0

x(2x+3)

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

Here, we have,

From the provided 95% confidence interval, we can make the following conclusions:

The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.

The standard error of the difference between the means is 368.41116 dollars.

The degrees of freedom (DF) associated with the confidence interval is 907.34739.

The lower limit of the confidence interval is -206.29374 dollars.

The upper limit of the confidence interval is 1239.7804 dollars.

The confidence interval does not contain zero.

Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

Learn more about confidence interval here:

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The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:

The sample difference in means is 516.74334.

The standard error of the difference is 368.41116.

The degrees of freedom (DF) for the analysis is 907.34739.

The lower limit of the confidence interval is -206.29374.

The upper limit of the confidence interval is 1239.7804.

Therefore, we can conclude the following:

The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.

For more such questions on difference in the mean

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Answer:

Answer:B. $100,000

Step-by-step explanation:

x is the number of years since the purchase of the land.

That means that when 0 years have passed by, it is when the land was purchased.

At x = 0, the price of the land was $100,000.

That means that the purchase price of the land is $100,000.

Answer:3

Step-by-step explanation:

Answer:

C.3

Step-by-step explanation:

Simplifying

23 + 11a + -2c = 12 + -2c

Add '2c' to each side of the equation.

23 + 11a + -2c + 2c = 12 + -2c + 2c

Combine like terms: -2c + 2c = 0

23 + 11a + 0 = 12 + -2c + 2c

23 + 11a = 12 + -2c + 2c

Combine like terms: -2c + 2c = 0

23 + 11a = 12 + 0

23 + 11a = 12

Solving

23 + 11a = 12

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-23' to each side of the equation.

23 + -23 + 11a = 12 + -23

Combine like terms: 23 + -23 = 0

0 + 11a = 12 + -23

11a = 12 + -23

Combine like terms: 12 + -23 = -11

11a = -11

Divide each side by '11'.

a = -1

Simplifying

a = -1

Answer:

The probability that the next mattress sold is either king or queen-size is P=0.8.

Step-by-step explanation:

We have 3 types of matress: queen size (Q), king size (K) and twin size (T).

We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.

We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:

[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]

We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:

[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]

Finally, we know that the sum of probablities has to be 1, or 100%.

[tex]P_Q+P_K+P_T=1[/tex]

We can solve this by sustitution:

[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]

Now we know the probabilities of each of the matress types.

The probability that the next matress sold is either king or queen-size is:

[tex]P_K+P_Q=0.6+0.2=0.8[/tex]

Answer:

Quantitative variable

Step-by-step explanation:

The objective in this study is to find the of variable used to conduct the study. The type of variable used to conduct this study is Qualitative variable.

There are majorly two types of variable. These are:

Categorical variables are types of variables that are grouped based on some similar characteristics. The nominal scale and the ordinal scale falls under this group of variable.

The nominal scale is an act of giving name to a particular object or concept in order to identify or classify that particular thing.

On the other hand, The ordinal scale possess all the characteristics of nominal scale but here the variables can be ordered. It can be used to determine whether the item is greater or less. It express the indication of order and magnitude.

In Qualitative variables; variables are measured on a numeric scale. From the given question , This type of variable is used to measure the high levels of vitamin C (measured in mg) which were associated with a 30 percent lower risk of allergies in the infants.

The levels of vitamin C could range from 0 mg to certain mg therefore we can measure vitamin C in numerical values of measurement (Quantitative variable).

Answer:

The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Step-by-step explanation:

The complete question is:

There are 103 students in a physics class. The instructor must choose two students at random.

Students in a Physics Class

Academic Year          Physics majors           Non-Physics majors

Freshmen                              17                                     15

Sophomores                         20                                    14

Juniors                                   11                                      17

Seniors                                   5                                       4

What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution:

There are a total of N = 103 students present in a Physics class.

Some of the students are Physics Major and some are not.

The instructor has to select two students at random.

The instructor first selects a senior Physics major and then a sophomore Physics major.

Compute the probability of selecting a senior Physics major student as follows:

[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]

                                        [tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]

Now he two students are selected without replacement.

So, after selecting a senior Physics major student there are 102 students remaining in the class.

Compute the probability of selecting a sophomore Physics major student as follows:

[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]

                                        [tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]

Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:

[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]

                                     [tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]

Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Answer:

24000

Step-by-step explanation:

because 24000 * 10 =240000

Answer:

stretch of 200 shift up 10 units

Step-by-step explanation:

f(x)=1/x to 200/x+10

Multiply by 200 means a stretch of 200

f(x) = 200/x

Now shift up 10 units

f(x) = 200/x + 10

Answer:

It moves up 10 units

Step-by-step explanation:

f(x) =1/x to 200/x + 10

= 200/x

If we shift up 10 units, we get:

f(x) = 200/x + 10

Hope this helps!

Answer:

There is no correlation between age and purchase price

Step-by-step explanation:

In the survey, the researcher found out that a younger customer will not necessarily purchase a lower or higher priced computer thing it is likely true that there might be no correlation between purchase price and age.

It assumes that a younger customer can buy either buy a lower priced computer or can also buy a higher priced if he or she has the money for it.

Answer:

[tex]x = \frac{-41}{17} , y = \frac{-1}{17}[/tex]

Step-by-step explanation:

Step(i):-

Given equations are  2 x+3 y=-5  ...(i)

                                   5 x-y=-12 ...(ii)

Multiply equation (ii) by '3'

                                    2 x + 3 y  = -5  

                                   15 x - 3 y  = - 36

                                  17 x  = - 41

                                   [tex]x = \frac{-41}{17}[/tex]

Step(ii):-

Substitute [tex]x = \frac{-41}{17}[/tex]  in equation (i)

                             2 ([tex]\frac{-41}{17}[/tex]+3 y=-5

                                 3 y = - 5 + [tex]\frac{82}{17}[/tex]

                               [tex]3 y = \frac{-85 + 82}{17} = \frac{-3}{17}[/tex]

                               [tex]y = \frac{-1}{17}[/tex]

The solution of the two equations

 ( x, y ) = [tex](\frac{-41}{17} , \frac{-1}{17})[/tex]

Answer:

[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]

[tex]Area\ of\ the\ garden\ =l1*b1[/tex]

Step-by-step explanation:

Let assume the l1 is the length of the garden and b1 is the breadth of garden then

[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]

Now,

[tex]Area\ of\ Garden\ = Length * Breadth[/tex]

[tex]Area\ of\ the\ garden\ =l1*b1[/tex]

Answer:

For k = 1:

=NEGBINOMDIST(0, 1, 0.666) = 0.6660

For k = 2:

=NEGBINOMDIST(1, 1, 0.666) = 0.2224

For k = 3:

=NEGBINOMDIST(2, 1, 0.666) = 0.0743

For k = 4:

=NEGBINOMDIST(3, 1, 0.666) = 0.0248

For k = 5:

=NEGBINOMDIST(4, 1, 0.666) = 0.0083

For k = 6:

=NEGBINOMDIST(5, 1, 0.666) = 0.0028

Step-by-step explanation:

The probability of obtaining a defective 10-year old widget is 66.6%

p = 66.6% = 0.666

The probability of obtaining a non-defective 10-year old widget is

q = 1 - 0.666 = 0.334

The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.

The geometric distribution is given by

[tex]$P(X = k) = p \times q^{k - 1}$[/tex]

Solving manually:

For k = 1:

[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]

For k = 2:

[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]

For k = 3:

[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]

For k = 4:

[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]

For k = 5:

[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]

For k = 6:

[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]

Using Excel function:

NEGBINOMDIST(number_f, number_s, probability_s)

Where

number_f = k - 1 failures

number_s = no. of successes

probability_s = the probability of success

For the geometric distribution, let number_s = 1

For k = 1:

=NEGBINOMDIST(0, 1, 0.666) = 0.6660

For k = 2:

=NEGBINOMDIST(1, 1, 0.666) = 0.2224

For k = 3:

=NEGBINOMDIST(2, 1, 0.666) = 0.0743

For k = 4:

=NEGBINOMDIST(3, 1, 0.666) = 0.0248

For k = 5:

=NEGBINOMDIST(4, 1, 0.666) = 0.0083

For k = 6:

=NEGBINOMDIST(5, 1, 0.666) = 0.0028

As you can notice solving manually and using Excel yields the same results.

Answer:

17.8 in x 21.8 in

Step-by-step explanation:

Given w=width and l=length

w*l=390

l=w+4, therefore w*(w+4)=390

w^2+4w=390

w^2+4w-390=0

Quadratic equation, solve as such

w=-21.8 or 17.8

Solution can't be negative so w=17.8 in

l=w+4 so l=21.8

Answer:

12

Step-by-step explanation:

f(-4) = -8-5(-4) = -8+20 = 12

Answer:

f(-4) = 12

Step-by-step explanation:

f(-4) = -8 - 5(-4)

= -8 + 20

= 12

Answer:

c) 5√2 cm

Step-by-step explanation:

A square with side length l has a perimeter given by the following equation:

P = 4l.

In this question:

P = 20

So the side length is:

4l = 20

l = 20/4

l = 5

Diagonal

The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.

[tex]d^{2} = l^{2} + l^{2}[/tex]

[tex]d^{2} = 5^{2} + 5^{2}[/tex]

[tex]d^{2} = 50[/tex]

[tex]d = \pm \sqrt{50}[/tex]

Lenght is a positive meausre, so

[tex]d = \sqrt{50}[/tex]

[tex]d = \sqrt{2 \times 25}[/tex]

[tex]d = \sqrt{2} \times \sqrt{25}[/tex]

[tex]d = 5\sqrt{2}[/tex]

So the correct answer is:

c) 5√2 cm

The correct question is:

A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes

Answer:

The probability of getting someone who is age 23-30 or smokes = 0.575

Step-by-step explanation:

We are given;

Number consumers of age 18 - 22 = 167

Number of consumers of ages 22 - 30 = 148

Number of consumers of ages 31 - 40 = 85

Thus,total number of consumers in the survey = 167 + 148 + 85 = 400

We are also given;

Number consumers of age 18 - 22 who smoke = 59

Number of consumers of ages 22 - 30 who smoke = 31

Number of consumers of ages 31 - 40 who smoke = 23

Total number of people who smoke = 59 + 31 + 23 = 113

Let event A = someone of age 23-30 and event B = someone who smokes. Thus;

P(A) = 148/400

P(B) = 113/400

P(A & B) = 31/400

Now, from addition rule in sets which is given by;

P(A or B) = P (A) + P (B) – P (A and B)

We can now solve the question.

Thus;

P(A or B) = (148/400) + (113/400) - (31/400)

P(A or B) = 230/400 = 0.575

Answer:

448I think

Step-by-step explanation:

Answer:21

Step-by-step explanation:

Answer:

X^6

Step-by-step explanation:

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:

C.

Step-by-step explanation:

First finding height using Pythagoras theorem

(H)²=(B)²+(P)²

8.2²=5.4²+P²

P² = 67.24 - 29.16

P² = 38.08

P = 6.2

Now

Volume of cone = (1/3)πr²h

= (1/3)(3.14)(5.4)²(6.2)

= (1/3)(567.9)

= 189.2 cm³

Answer:

Step-by-step explanation:

REcall that given a set A, * is a equivalence relation over A if

- for a in A, then a*a.

- for a,b in A. If a*b, then b*a.

- for a,b,c in A. If a*b and b*c then a*c.

Consider A the set of all ordered pairs of positive integers.

- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).

- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).

- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then

a+d = b+c, c+f = d+e.  We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).

So R is an equivalence relation.

[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).

Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.

Answer:

15.86%

Step-by-step explanation:

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.

Percent of area between the mean and 0.20 standard deviations from the mean:

pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2

Z = 0.2 has a pvalue of 0.5793

Z = -0.2 has a pvalue of 0.4207

0.5793 - 0.4207 = 0.1586

So this percentage is 15.86%

Answer:

a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

b) We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]  

d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Step-by-step explanation:

Information provided

[tex]\bar X=23400[/tex] represent the sample mean

[tex]s=1412[/tex] represent the sample standard deviation

[tex]n=18[/tex] sample size  

[tex]\mu_o =22100[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

Part b

We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

Part c

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]    

Part d

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

The right answers are:

Hope it helps.

please see the attached picture for full solution

Good luck on your assignment

Answer:

Protista

Step-by-step explanation:

Archaebacteria.

Eubacteria.

Protista.

Fungi.

Plantae.

Animalia.

These are the 6 kingdoms

Answer:

1 ton = 2,000 pounds

Step-by-step explanation:

With that said, 22,000 pounds is 11 tons because 2,000 x 11 = 22,000.

So 22,000 pounds is 11 tons.

Hope it helps and pls mark me brainliest if it did! :)