(80 POINTS) What rule describes a dilation with a scale factor of ½ and the center of dilation at the origin?

Answer:87

Step-by-step explanation:

866

Answer:

c) Permutations: 40320

Step-by-step explanation:

We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.

In this case, then the batting order, therefore the order does matter, therefore, it would be a permutation, where n = 8 and r = 7

nPr = n! / (n-r)!

Replacing:

8P7 = 8! / (8-7)! = 40320

Which means that the answer is c) Permutations: 40320

Answer:

(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.

(b) Two samples are described in the above situation, that is;

(c) The average age of 37 years is a statistic.

(d) The above information represents a quantitative variable.

(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.

Step-by-step explanation:

We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.

When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.

(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.

(b) Two samples are described in the above situation, that is;

(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e. [tex]\bar X_1[/tex] = 37 years.

(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.

(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.

But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.

Answer:

m∠3 = 115°

Step-by-step explanation:

Since measure of angle 6 = (2x - 5)°

And measure of angle 8 = (x + 5)°

Since ∠6 and ∠8 are the supplementary angles,

m∠6 + m∠8 = 180°

(2x - 5)° + (x + 5)° = 180°

3x = 180°

x = 60°

Therefore, m∠6 = (2x - 5) = (120 - 5) = 115°

and m∠8 = (x + 5) = 65°

Since angle 6 and angle 3 are interior alternate angles,

Therefore, m∠6 = m∠3 = 115° will be the answer.

Answer:

[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]

And we can find this probability with this difference and using the normal standard distribution

[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]

Step-by-step explanation:

Let X the random variable that represent the amount of Jen monthly phone of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(55,12)[/tex]  

Where [tex]\mu=55[/tex] and [tex]\sigma=12[/tex]

We are interested on this probability

[tex]P(19<X<91)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Replacing the info we got:

[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]

And we can find this probability with this difference and using the normal standard distribution

[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]

Answer:

  aₙ = 7 +3(n -1)

Step-by-step explanation:

The numbers in the given sequence have a common difference, so this is an arithmetic sequence. The formula for the n-th term applies.

  aₙ = a₁ +d(n -1)

The first term is 7. The common difference is 10-7 = 3. Using the above formula for the n-th term, we find it to be ...

  aₙ = 7 +3(n -1)

__

Additional comment

This can be simplified to ...

  aₙ = 3n +4

Answer:

286 degrees and 143 degrees

Step-by-step explanation:

When line intersect the two vertical angle adds up to 180 degrees

To find the other vertical angle:

180 -37=143 degrees

So for two vertical angles

we take (180*2)-(37*2)=286 degrees

Answer:

y= 3/2x -2

Step-by-step explanation:

make y be on one side by itself ( -2y = -3x + 4 )

divide by negative 2 in order to get y by itself ( -2y/-2 = -3/-2 + 4/-2 )

two negatives make a positive ( y = 3/2 + -2 )

Answer:

72.1

Step-by-step explanation:

G(x) =19.60 + 1.75x

Let x = 30

G(30) =19.60 + 1.75*30

          =19.60 +52.5

            72.1

Answer:

Step-by-step explanation:

Hello!

The variable of interest is "the time a fight lasts" measured in seconds

The five number summary for her first 12 UFC fights are:

Minimum: Min= 14

First Quartile: Q₁= 25

Second Quartile/Median: Me= 44

Third Quartile: Q₃= 64

Maximum: Max= 289

a)

Three of her fights lasted more than one minute: 289, 267, 66. Out of these three fights, you have to determine if they are outliers using the IQR method.

The IQR is the distance between the third quartile and the first quartile

IQR= Q₃ - Q₁= 64 - 25= 39

Remember, an outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.  

Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:

X < Q₁ - 1.5 IQR

X > Q₃ + 1.5 IQR

Or extreme outliers if:

X < Q₁ - 3 IQR

X > Q₃ + 3 IQR

The limits that define if a value is an outlier or not are:

X < 25 - 1.5*39 = -33.5

X > 64 + 1.5*39= 122.5

And for extreme outliers:

X < 25 - 3*39 = -92

X > 64 + 3*39= 181

So fights that lasted less than -33.5 or more than 122.5 seconds are to be considered outliers, and those who lasted less than -92 or more than 181 seconds are extreme outliers.

Out of the three fights, the ones that lasted 289 and 267 seconds can be considered extreme values.

b) The minimum observed value for this data set is 14 seconds, values are considered to be outliers if they are less to -33.5, so there is no low outliers on the sample.

As you can see, both values that allow you to determine if the observation is an outlier or not are negative, since the variable is "the time a fight lasts" it is impossible for it to have negative values. The lowest value of time a fight can last is "zero seconds". Although mathematically correct, these values make no sense.

c)

See attachment.

d)

The average or mean is a measurement of central tendency that shows you the value around which most of the distribution will be. It is very affected by the presence of outliers, especially extreme ones. Outliers make the mean "move" towards them, this means, that if there are small outliers, then the mean will move to the lower side of the distribution. But if the outliers are big, then the mean will move to the higher side of the distribution.

For example, let's say 5 of the fight times were:

10, 37, 49, 51, 68

For these values the mean would be:

X[bar]₀= ∑X/n= (10+37+49+51+68)/5= 215/5= 43

Now let's change one of these values for an extreme one:

Small value:

0, 37, 49, 51, 68

X[bar]₁= ∑X/n= (0+37+49+51+68)/5= 205/5= 41

⇒ As you can see, one change for a smaller value reduces the mean value X[bar]₁ < X[bar]₀

Big value:

10, 37, 49, 51, 268

X[bar]₂= ∑X/n= (10+37+49+51+268)/5= 415/5= 83

⇒ In this case, changing one of the 5 values to a bigger one moved the mean to the right: X[bar]₀ < X[bar]₂

So for the given distribution, since there are at least two high outliers, you'd expect the mean to be greater than the median.

I hope this helps!

Answer:

(9x - 1)²

Step-by-step explanation:

If you can tell, the square root of 81 is 9. This should be a clue that the polynomial could be one binomial squared. If you tried factoring starting out with 9x in both parenthesis, you could see that you would get (9x - 1)² as your answer.

Answer:

(9x-1)²

Step-by-step explanation:

81x² - 18x + 1= (9x)²- 2*9x+1²= (9x-1)²

Answer:

Step-by-step explanation:

5x - c = k

Add c  to each side

5x - c+c = k+c

5x = (k+c)

Divide each side by 5

5x/5 = (k+c)/5

x = (k+c)/5

Answer:

x=(k+c)/5

Step-by-step explanation:

5x-c=k (Original Equation)

5x-c+c=k+c (Addition Property of Equality)

5x=k+c (Simplify)

x=(k+c)/5 (Division Property of Equality)

Answer:

D. 3.6

Step-by-step explanation:

=> Taking proportionality of the similar sides to find BC

[tex]\frac{AB}{AD}=\frac{BC}{DE}[/tex]

[tex]\frac{3}{5} = \frac{BC}{6}[/tex]

Multiplying 6 to both sides

[tex]BC = 0.6 * 6[/tex]

BC = 3.6

Answer:

Step-by-step explanation:

Hello!

The objective is to test the claim that less than 41% of the publisher's readers own a laptop.

To do so, a sample of 320 readers was taken and the proportion of readers that own a laptop resulted in 36%

Be X: number of readers that own a laptop.

X~Bi(n;p)

n=320

Sample proportion p'= 0.36

The hypotheses are:

H₀: p ≥ 0.41

H₁: p < 0.41

α: 0.05

[tex]Z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)

[tex]Z_{H_0}=\frac{0.36-0.41}{\sqrt{\frac{0.41(1-0.41)}{320} } }= -1.82[/tex]

This test is one-tailed to the left, meaning, that you'll reject the null hypothesis to small values of Z, there is only one critical value that defined the rejection region:

[tex]Z_{\alpha }= Z_{0.05}= -1.645[/tex]

The decision rule is:

If [tex]Z_{H_0}[/tex] ≤ -1.645, reject the null hypothesis.

If [tex]Z_{H_0}[/tex] > -1.645, do not reject the null hypothesis.

The calculated value is less than the critical value, then the decision is to reject the null hypothesis.

So at a 5% significance level, the test is significant. You can conclude that the population proportion of the publisher's readers that own a laptop is less than 41%.

I hope this helps!

Answer:

Step-by-step explanation:

A. x² = –100

This equation has no solution because x² is always positive.

B. 5x² = 1

then x² = 1/5

then x = 1/(√5) or x = -1/(√5)

C. 6x² + 17 = 11

then 6x² = 11 - 17 = -6

then x² = -6/6 = -1  

This equation has no solution because x² is always positive.

D. 7(x + 6) = 42

then x + 6 = 42/7 = 6

then x = 6 - 6 = 0

_____________________

:)

Answer:

The Supreme Court.

Step-by-step explanation:

After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.

Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.

This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.

Answer:

  7290

Step-by-step explanation:

Put 5 in the formula and evaluate.

  a(5) = 90·3^(5-1) = 90·81 = 7290

There will be 7290 bacteria at the beginning of hour 5.

Answer:

  A'(4, 3)

Step-by-step explanation:

When a point is reflected across the line y = x, the transformation is ...

  (x, y) ⇒ (y, x)

  A(3, 4) ⇒ A'(4, 3)

The reflected point is (4, 3).

[tex]the \: answer \: is \: 22.4 \: cm \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps[/tex]

The length of AE is 22.4cm rounded to one decimal place.

Answer:

The answer would be 50%

Step-by-step explanation:

You Would get this by dviding 36/72 which would give you .5 and then you convert that to a percentage

Answer:

50%

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

5x-10=15

5x=25

x=5

Answer:

Step-by-step explanation:

Confidence interval for the difference between two population means is written in the form,

difference in sample means ± margin of error

The difference in sample means is the point estimate for the difference in population means. In the given scenario, the point estimate is the difference in mean amount spent by the sampled customers on a trip to Target or​ Walmart.

Since the interval was (- $15.05​,$2.95), it means that the lower limit is - $15.05 and the upper limit us $2.95.

Therefore, the 95% confidence interval is providing a range that we are 95% confident that the true difference in mean amount spent by Target customers and Walmart customers falls between - $15.05​ and $2.95

Answer:

80

Step-by-step explanation:

46+15+19 which should give you a total answer of 80

Answer:

20

Step-by-step explanation:

Answer:

$61.20

Step-by-step explanation:

15% sale:

40% sale:

Answer:

Quadrilateral ABCD is a Quadrilateral with four equal sides so either a rhombus or square

But

Quadrilateral ABC'D is a quadrilateral with two adjacent sides equal so it's a kite shape

Step-by-step explanation:

(11, -7), B(9, -4), C(11, -1), and D(13, -4).

Let's take out the values of x and y coordinate with the way they are arranged

X = 11,9,11,13

Y = -7,-4,-1,-4

So we observe that distance of the coordinates on either x is 2 units and y is 3 units.

But when the the value was changed to

C′(11, 1), (11, -7), B(9, -4), C′(11, 1), and D(13, -4).

There was difference of 2 unit and 4 unit making the new shape a kite.

The diagram attached explain better

Answer:

1. rhombus with non-perpendicular adjacent sides

2. kite

Step-by-step explanation:

i just got it right on edmentum.

Please mark as brainliest.

Answer:

Red apples to all apples =2/11

Red apples to green apples =2/9

Step-by-step explanation:

There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples

The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11

The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9

Answer:

Red apples to all apples =2/11

Red apples to green apples =2/9

Step-by-step explanation:

There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples

The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11

The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9

Step-by-step explanation:

Answer:

[tex]x\in(-2,1)[/tex]

Step-by-step explanation:

We are given that a function

[tex]f(x)=(x+2)(x-4)[/tex]

[tex]f(x)=x^2-2x-8[/tex]

Differentiate w.r.t x

[tex]f'(x)=2x-2[/tex]

[tex]f'(x)=0[/tex]

[tex]2x-2=0[/tex]

[tex]2x=2\implies x=\frac{2}{2}=1[/tex]

Therefore, intervals

[tex](-\infty,1),(1,\infty)[/tex]

Interval :[tex](-\infty,1)[/tex]

x=0

[tex]f'(0)=-2<0[/tex]

Decreasing  function.

Interval:[tex](1,\infty)[/tex]

Substitute x=2

[tex]f'(2)=2(2)-2=2>0[/tex]

Function increasing.

From given graph we can see that function is negative for the values of x

-2<x<4

Hence, the graph is negative and decreasing for the values of x

[tex]x\in(-2,1)[/tex]

Answer:the answer is c/ all real values of x where 1<x<4

Step-by-step explanation:

edge 2020

Answer:

(1/2, 1)

2

Step-by-step explanation:

x² + y² − x − 2y − 11/4 = 0

x² − x + y² − 2y = 11/4

Complete the squares.

x² − x + 1/4 + y² − 2y + 1 = 11/4 + 1/4 + 1

(x − 1/2)² + (y − 1)² = 4

The center of the circle is (1/2, 1) and the radius of the circle is 2.

Answer:

Option  A

Step-by-step explanation:

[tex](\frac{1}2} ,1)[/tex], 2 units

Answer:

SA = 1,176 ft².

Step-by-step explanation:

To find the surface area of the triangular prism, we can solve for the rectangular base, both triangular faces, and lateral sides separately.

For the rectangular base: (Use formula l×w)

20 × 18 = 360 ft²

For the triangular faces: (Use formula 1/2(b·h)

1/2(18 × 12) = 108 ft²

Since there are two faces, we need to double the amount.

108 × 2 = 216 ft².

Finally, solve for the lateral sides:

20 × 15 = 300 ft².

There are two sides, so:

300 × 2 = 600 ft².

Add up all of these areas:

600 + 216 + 360 = 1,176 ft²