One solution to the problem below is 7. What is the other solution?

The most appropriate measure of center is Median. As the data has a large value (290) at the end, it is the better choice to choose the median for finding the center because the mean or average is appropriate to represent the general level if there are not too large or too small values in the set. The median for the given bowling scores for 6 people is 117.5.

Since the standard deviation and range gives the variability of the given data, the mean and median are used for calculating the center.

Given data values are,

112, 114, 115, 120, 122, 290

Mean of the given data values,

Mean = Sum of all values / number of values

Sum of values = 112 + 114 + 115 + 120 + 122 + 290 = 873

Number of values = 6

∴ Mean = [tex]\frac{873}{6}[/tex]

             = 145.5

Median of the given data values,

Arranging the data values in the ascending order - 112, 114, 115, 120, 122, 290

Number of values = 6 (even)

So, the median is the average between the two centers

∴ Median = [tex]\frac{115+120}{2}[/tex]

                = 117.5

Since the last value in the set is larger than all the values (a sudden change or rise in the value), the most appropriate measure of center is the median and it is 117.5.

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#SPJ2

12,500-11,625=875

1%=125

10%=1250

5%=625

625+125=750=6%

750+125=875=7%

so the percentage is 7%

Step-by-step explanation:

All you have to do is this;

use the formula: y2-y1/x2-x1

fill it in: 12 - 18/11 - 12

solve: -6/-1 > 6

the answer is 6, the slope = 6

Answer:

The answer is hyperbola; with angle of rotation = 45° ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

- xy = -2.5

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 0 , B = 1 , C = 0

∴ cot(2Ф) = 0/1 = 0

∴ 2Ф = 90°

∴ Ф = 45°

* The answer is hyperbola; with angle of rotation = 45°

Answer: 20 pounds.

Step-by-step explanation:

We know the weight of each flower arrangement (each one weighs 6 2/3 pounds) and the total number of flower arrangaments Isabelle ordered (3 flower arrangements).

To make the calculus easier, we can rewrite the mixed number 6 2/3 as a decimal number:

Divide the numerator 2 by the denominator 3 and add the result to the whole number 6:

[tex](6+0.666)lb=6.666lb[/tex]

If 1 arrangement weighs 6.666 pounds, the total weigth of 3 arrangements can be calculated by multiplying 6.666 pounds by 3:

[tex]weight_{(total)}=(6.666lb)(3)\\weight_{(total)}=20lb[/tex]

There are no compound periods given, so use the simple interest formula:

A = P(1+rt) where P is the principal, r is the rate and t is the time.

A = 5000(1+0.0975(6))

A = 5000(1+0.585)

A = 5000(1.585)

A = $7,925

Interest = 7925 - 5000 = $2,925

Total paid back = $7,925

Answer:

The Interest is 2,925.00 and now you owe 7,925.00. I hope this helps

Step-by-step explanation:

The answer is a Hyperbola

Answer:

Hyperbola

Step-by-step explanation:

Given is an equation in x and y as

[tex]xy = -16[/tex]

We know that for ellipse both x and y will have degree 2.

For parabola one variable would be of degree 2 and other degree 1.

Circle both will have degree 2 and equal coefficients.

So this equation is not a circle, a parabola or an ellipse.

We know that rectangular hyperbola will have equation as

[tex]xy=c^2 \\xy =-c^2[/tex]

Hyperbola is the right answer.

Answer:

c)

{0,4,8,12,16,20,24,28,32,36,40}

Step-by-step explanation:

Given in the question is graph which shows height of tower depending on number of blocks use.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain, x values.

By looking at graph

domain  range

     0       0

      1        4

      2       8

      3       12

      4       16

      5       20

       .          .

       .          .

      10      40

Answer:

[tex]\large\boxed{Q1.\ A_{\triangle PQR}=90\ cm^2}\\\\\boxed{Q2.\ V\approx321\ m^3}[/tex]

Step-by-step explanation:

[tex]Q1.\\\\\text{If}\ \triangle ABC\sim\triangle PQR\ \text{then the quotient of the areas is equal}\\\text{the square of the similarity scale}\ k.\\\\\text{The sides}\ AB\ \text{and}\ QP\ \text{are corresponding}.\ \text{Calculate the scale:}\\\\k=\dfrac{4}{6}=\dfrac{4:2}{6:2}=\dfrac{2}{3}\\\\\text{The area of }\ \triangle ABC=40\ cm^2.\\\\\text{Let the area of}\ \triangle PQR=x,\ \text{then}\\\\\dfrac{40}{x}=\left(\dfrac{2}{3}\right)^2\\\\\dfrac{40}{x}=\dfrac{4}{9}\qquad\text{cross multiply}\\\\4x=(9)(40)\qquad\text{divide both sides by 4}\\\\x=(9)(10)\\\\x=90\ cm^2[/tex]

[tex]Q2.\\\\\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{We have the diameter}\ 2R=8.5\ m\to R=\dfrac{8.5}{2}\ m=4.25\ m.\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(4.25)^3=\dfrac{4}{3}\pi(76.765625)=(4)(25.588541)\pi=102.354164\pi\\\\\pi\approx3.14\\\\V=(102.354164)(3.14)\approx321\ m^3[/tex]

Answer: The answers are

(1) 90 cm²   and (2) 321 m³.

Step-by-step explanation:  The calculations are as follows:

(1) The triangles ABC and PQR are similar. And the area of ΔABC is 40 cm².

Also, AB = 4 cm  and PQ = 6 cm.

We are to find the area of triangle PQR.

Similarity ratio of two similar triangles is equal to the ratio of any two corresponding sides of the triangles.

So, the similarity ratio of ΔABC and ΔPQR is given by

[tex]\dfrac{AB}{PQ}=\dfrac{4}{6}=\dfrac{2}{3} =2:3\\\\\\\Rightarrow AB:PQ=2:3.[/tex]

Now, let the area of ΔPQR be denoted by [tex]A_{PQR}.[/tex]

We know that the ratios of the area of two similar triangles is equal to the ratios of the squares of any two corresponding sides of the triangles.

Therefore, we must have

[tex]\dfrac{\textup{area of triangle ABC}}{\textup{area of triangle PQR}}=\dfrac{AB^2}{PQ^2}\\\\\\\Rightarrow \dfrac{40}{A_{PQR}}=\left(\dfrac{AB}{PQ}\right)^2\\\\\\\Rightarrow \dfrac{40}{A_{PQR}}=\left(\dfrac{2}{3}\right)^2\\\\\\\Rightarrow \dfrac{40}{A_{PQR}}=\dfrac{4}{9}\\\\\\\Rightarrow 4\times A_{PQR}=40\times 9\\\\\\\Rightarrow A_{PQR}=90~\textup{cm}^2.[/tex]

Thus, the area of triangle PQR is 90 cm².

(2) Given that a science museum has a spherical model of the earth with a diameter of 8.5 m.

We are to find the volume of the model.

Since the model is spherical in shape, so will be using the following formula:

the volume of a sphere with radius 'r' units is given by

[tex]V=\dfrac{4}{3}\pi r^3.[/tex]

The diameter of the model is 8.5 cm, so the radius of the model will be

[tex]r=\dfrac{8.5}{2}=4.25~\textup{m}.[/tex]

Therefore, the volume of the model is given by

[tex]V\\\\\\=\dfrac{4}{3}\pi r^3\\\\\\=\dfrac{4}{3}\times3.14\times(4.25)^3\\\\\\=\dfrac{964.17625}{3}\\\\\\=321.39\sim 321~\textup{m}^3.[/tex]

Thus, the volume of the model is 321 m³.

Hence, the answers are

(1) 90 cm²   and (2) 321 m³.

Answer:

Step-by-step explanation:

c) possible because there are 3 of each  

Answer:

C) possible

Step-by-step explanation:

There are 3 red symbols and 3 green symbols. There is a 50% chance that you will pick a red or a green. So it is possible that you will pick a red with your eyes closed.

The Y intercept is the same for both -3/11

The slope is the fraction with the letter x.

For P the slope is 5/8, which is less than 1

For q the slope is 8/5 which is greater than 1

Because the slope of p is less than  the slope of q, the slope would be less steep.

The answer is the second one.

Answer:

B

Step-by-step explanation:

sides of right angle triangle follows Pythagoras theroem

which states

a^2 +b^2 = c^2

where a , b and c are sides of right angle triangle.

here none of options do not follow this.

so answer is option D

Answer:

D

Step-by-step explanation:

Which of the following are measurements of the sides of a right triangle?

Check c^2 = a^2 + b^2 where c is the largest of the 3 sides.

If c^2 = a^2+b^2 you have a right triangle. If it doesn't, you don't.

Answer:

x = -5,-1

Step-by-step explanation:

6=3(x+3)^2-6

Add 6 to each side

6+6=3(x+3)^2-6+6

12 =3(x+3)^2

Divide each side by 3

12/3 = 3/3(x+3)^2

4 = (x+3)^2

Take the square root of each side

sqrt(4) = sqrt((x+3)^2)

±2 = x+3

Separate into 2 equations

2 = x+3                     -2 = x+3

Subtract 3 from each side

2-3 =x+3-3               -2-3 = x+3-3

-1 =x                        -5 =x

I. If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

True.

II. If the slope of the regression line is negative, then the linear correlation coefficient is negative.

False.

III. The value of the linear correlation coefficient always lies between -1 and 1.

True.

IV. A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82.

False.

So, the correct statements are I and III.

Therefore, the correct answer is:

OB. I and II

Let's evaluate each statement:

I. If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

True. A correlation coefficient of zero indicates no linear relationship between the variables. However, it's important to note that there could still be a nonlinear relationship.

II. If the slope of the regression line is negative, then the linear correlation coefficient is negative.

False. The linear correlation coefficient (Pearson correlation coefficient) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1. The sign of the correlation coefficient indicates the direction of the relationship (positive or negative), not the slope of the regression line. So, this statement is not necessarily true.

III. The value of the linear correlation coefficient always lies between -1 and 1.

True. The linear correlation coefficient, also known as Pearson's correlation coefficient, ranges from -1 to 1. A correlation coefficient of -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.

IV. A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82.

False. The magnitude (absolute value) of the correlation coefficient indicates the strength of the linear relationship, regardless of the sign. Therefore, a correlation coefficient of -0.82 suggests a stronger linear relationship compared to a correlation coefficient of 0.62.

So, the correct statements are I and III.

Therefore, the correct answer is:

OB. I and IV

The complete question is here:

Which of the following statements concerning the linear correlation coefficient are true? 1: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies between - 1 and 1. IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. A. III and IV

B. I and IV

C. I and II

D. II and III

The true statements for the given information are:

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

III: The value of the linear correlation coefficient always lies betweenminus1 and 1.

The correct options are I and III.

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. This statement is true. The linear correlation coefficient, also known as Pearson's correlation coefficient (r), measures the strength and direction of the linear relationship between two variables. When r = 0, it indicates that there is no linear relationship between the variables.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. This statement is not necessarily true. The slope of the regression line indicates the direction and steepness of the relationship between the variables, while the correlation coefficient indicates the strength and direction of the linear relationship. The correlation coefficient can be negative even if the slope of the regression line is positive, and vice versa.

III: The value of the linear correlation coefficient always lies between -1 and 1. This statement is true. The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. Therefore, the correlation coefficient always falls within this range.

IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. This statement is false. The magnitude of the correlation coefficient indicates the strength of the linear relationship, regardless of whether it is positive or negative. Therefore, in this case, the correlation coefficient of -0.82 suggests a stronger linear relationship compared to 0.62 because the magnitude of -0.82 is larger than that of 0.62.

In summary, statements I and III are true, while statements II and IV are false.

Complete question

Which of the following statements concerning the linear correlation coefficient are true?

I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies betweenminus1 and 1.

IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of minus 0.82.

Answer:

The correct answers are as follows.

a. 8.624%

b. 60.84%

c. 27.75%

Step-by-step explanation:

In order to find each of these, take the likelihood of each of steps and multiply them together.

a. For this one, we need to note that the first two spins should not be blue. The likelihood of them not being blue is the chance for red and green put together (37%). Then we want the third spin to be the blue odds (63%)

.37 * .37 * .63 = .08624 = 8.624%

b. For the purpose of this, we are looking just for the first two spins to not be red (78% probability). After that, it does not matter what the third spin is since it says "at least 3 times)

.78 * .78 = .6084 = 60.84%

c. For this one, we need to combine two things. Firstly, the chance that the first spin is green (15%). Then we would add in the likelihood that the first spin is not green (85%), but the second is.

.15 + (.85 * .15) = .2775 = 27.75%

The probabilities of obtaining the required event based on the likelihood of the pointer stopping on each color are 0.086247, 0.6084 and 0.2775 respectively

Probability of Blue ; P(B) = 0.63

Probability of Red ; P(R) = 0.22

Probability of Green ; P(G) = 0.15

Probability of Blue after exactly 3 spins :

1st spin = P(not B) = P(R)+P(G) = (0.22+0.15) = 0.37

2nd spin = P(not B) = P(R)+P(G) = (0.22+0.15) = 0.37

3rd spin = P(B) = 0.63

P(R exactly after 3 spins) = (0.37 × 0.37 × 0.63) = 0.086247

2.)

Probability of spinning atleast 3 times before obtaining RED;

P(not R) on first two spins ;

P(not R) = P(B) + P(G) (0.63+0.15) = 0.78

P(not R) × P(not R) = 0.78 × 0.78 = 0.6084

3.)

Probability of obtaining Green after 2 or fewer spins :

P(Green after 2 spins) + P(Green on first spin)

P(not G) = 0.63 + 0.22 = 0.85

[P(not G) × P(G)] + P(G)

[(0.85 × 0.15) + 0.15]

(0.1275 + 0.15)

= 0.2775

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Answer:   a) 36x + 3

                b) 36x + 27

                c) 16x + 15

                d) 81x

Step-by-step explanation:

f(x) = 4x + 3         g(x) = 9x

a) f(g(x)) = 4(9x) + 3       replaced x in f(x) equation with 9x

             = 36x + 3

b) g(f(x)) = 9(4x + 3)      replaced x in g(x) with 4x + 3

             = 36x + 27

c) f(f(x)) = 4(4x + 3) + 3     replaced x in f(x) with 4x + 3

           = 16x + 12   + 3

           = 16x + 15

d) g(g(x)) = 9(9x)            replaced x in g(x) with 9x

              = 81x

Answer:

solution given:

f(x) = 4x + 3

g(x) = 9x

answer:

a.fog(x)=f(9x)=4×9x+3=36x+3

domain=real number

b.gof (x)=g(4x+3)=9(4x+3)=36x+26

domain=real number

c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3

=16x+15

domain: real number

d.

gog(x)=g(9x)=9×9x=81x

domain: real number.

Answer:

5 mi/h

Step-by-step explanation:

S = v*t

S - space (miles)

v - velocity (mi/h)

t - time (h)

stream speed = x

The distance upstream(S_1) is expressed by :

60 min -> 1 hour

S_1 = (10-x)*1

The distance downstream is expressed by :

20 min -> 0.3(3) hour

S_2 = (10+x)*0.3(3)

The distance traveled upstream for 60 min is equal to the distance traveled downstream in 20 min. -> S_1 = S_2

(10-x) * 1 = (10+x)*0.3(3)

10 - x = 3.3(3) + 0.3(3)x

6.6(6) = 1.3(3)x

x = 6.6(6) / 1.3(3)

x = 5 mi/h

The speed of the stream is equal to 5.79 mi/h

Given the following data:

To calculate the speed of the stream:

Speed can be defined as the distance covered by an object per unit time.

Mathematically, speed is given by the formula;

[tex]Speed = \frac{distance}{time}[/tex]

Note: The upstream distance of the boat must be equal to the downstream distance of the boat.

[tex]D_u = D_d\\\\(10-s) \times 1 = (10+s)0.33\\\\10-s=3.3+0.33s\\\\10-3.3=0.33s+s\\\\7.7=1.33s\\\\s=\frac{7.7}{1.33}[/tex]

Speed, s = 5.79 mi/h

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10

6/3 =n/5

times n by 2 basically

answer is 10

it’s basically ratios

I think the answer is 5

Answer:

The volume is also tripled when one length of the prism is tripled. It becomes 180 cubic inches instead of 60 cubic inches.

Step-by-step explanation:

Volume is the measurement of the amount a 3D object can hold. Each 3D object has 3 measurements: length, width, and height.. This object is a rectangular prism. Its volume is found as V = l*w*h. Substitute h = 4, l = 5, and w = 3. Then simplify for the volume.

V = l*w*h

V = 5*3*4

V = 60 cubic inches

Now repeat the process except multiply the depth by 3. So the length 5 inches becomes 15 inches. Substitute and simplify.

V = 15*3*4

V = 180 cubic inches

The volume is also tripled when one length of the prism is tripled.

Answer:

80

Step-by-step explanation:

Answer:

250

Step-by-step explanation:

Since you are looking for the amount of shirts he had you will need to divide 25 by .10 or just multiply by 10.

Set up an equal proprtion. 25/x = 10/100 because 25 is 10% of the number you're looking for, or x. 25* 100 = 10x → 2500 = 10x → 250 = x. Uncle Percy started with 250 t-shirts.

Answer:

Option b

Step-by-step explanation:

By definition we know that:

[tex]cos ^ 2(\theta) = 1- sin ^ 2(\theta)[/tex]

We know that for this case:

[tex]sin(\theta) = \frac{1}{4}[/tex]

Then:

[tex]cos ^ 2(\theta) = 1- (\frac{1}{4})^2\\\\cos ^ 2(\theta) = 1- (\frac{1}{16})\\\\cos ^ 2(\theta) = \frac{15}{16}\\\\[/tex]

Apply square root on both sides of the equation

[tex]\sqrt{cos ^ 2(\theta)} = \sqrt{\frac{15}{16}}\\\\cos(\theta) = \sqrt{\frac{15}{16}}\\\\cos(\theta) = \frac{\sqrt{15}}{4}[/tex]

Answer: a=-6; b=1

Explanation:

This is the same thing as saying -6+1i. Therefore for the general form a+bi, a equals -6 and b equals 1

Answer:

a = -6 and b = 1

Step-by-step explanation:

We have given a complex number.

i-6

We have to find the value of a and b using general form of complex numbers.

The general form of complex numbers is a+bi.

given complex number can be written as:

-6+1i

Comparing with general form , we have

a = -6 and b = 1 which is the answer.

Answer:

Solution set is

[tex]x=5\\y=7[/tex]

Step-by-step explanation:

Given that in a picture there is a parallelogram PQRS

The diagonals PR and QS intersect at T

[tex]PT=x+2, TR=yQT=2x, TS = y+3[/tex]

By properties of parallelograms we know that diagonals bisect each other

Using this we get

[tex]PT=TR\\QT=TS\\x+2=y\\2x=y+3[/tex]

Substitute for y to get

[tex]2x=x+2+3\\x=5\\y=7[/tex]

Solution set is

[tex]x=5\\y=7[/tex]

Answer:

X=5 y=7

Step-by-step explanation:

Final answer:

Jody will have a total profit of $1280.00 after all of her transactions.

Explanation:

Jody initially bought 20 shares of Amazon at $121.00 per share, which amounts to a total cost of

20 * $121.00 = $2420.00.

A year later, she bought 20 more shares at $127.00 per share, which amounts to a total cost of

20 * $127.00 = $2540.00.

Two years later, she sold all of her shares at $133.00 per share, which amounts to a total revenue of

40 * $133.00 = $5320.00.

However, she paid $40 for each transaction, so her total transaction cost is 2 * $40.00 = $80.00.

Therefore, her total profit is $5320.00 - ($2420.00 + $2540.00 + $80.00) = $1280.00.

Answer:

2 2/3 lbs

Step-by-step explanation:

Convert Alya's mixed number to an improper fraction

   3*1+1 = 4/3

multiply 4/3 times 2/1

    4*2 = 8

    3*1 = 3

8/3 - convert back to mixed number

    8/3 = 2 2/3

ANSWER

[tex]2v + u = \binom{5}{15}[/tex]

EXPLANATION

It was given that:

[tex]u = \binom{1}{3} [/tex]

and

[tex]v = \binom{2}{6} [/tex]

[tex]2v + u =2 \binom{2}{6} + \binom{1}{3} [/tex]

Perform the scalar multiplication to obtain:

[tex]2v + u = \binom{4}{12} + \binom{1}{3} [/tex]

We add the corresponding components to get;

[tex]2v + u = \binom{4 + 1}{12 + 3}[/tex]

[tex]2v + u = \binom{5}{15}[/tex]

The first choice is correct.

Answer:

A

Step-by-step explanation:

Answer:

10 ft

Step-by-step explanation:

To get their total reach, we add the two numbers.

 5⅙

+4⅚

Add integers and fractions

 5⅙

+4⅚

 9⁶/₆

Convert the fraction to an integer

⁶/₆ = 1

Add the 1 to the 9

9 + 1 = 10 ft

If Madison and Jade lay end to end, they will they reach 10 ft.

Answer:

Sorry i do not know the answer but....

Step-by-step explanation:

can u sub to Pewdiepie on YT.. Plz? Brofist

25. Step-by-step explanation:

[tex]\text{The general form of an ellipse is:}\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1\\\\\bullet \text{(h, k) is the Center}\\\bullet \text{a is the radius of x}\\\bullet \text{b is the radius of y}\\\bullet \text{the largest value between a and b is the major}\\\bullet \text{the smallest value between a and b is the minor}\\\bullet \text{the vertices are the (h, k) value plus the major (a or b) value}\\\bullet \text{the co-vertices are the (h, k) value plus the minor (a or b) value}\\\bullet \text{Length is the diameter}=2r\\[/tex]

[tex]\dfrac{x^2}{16}+\dfrac{y^2}{25}=1\quad \text{can be rewritten as}\ \dfrac{(x-0)^2}{4^2}+\dfrac{(y-0)^2}{5^2}=1\\\\\bullet (h, k)=(0,0)\\\bullet a=4\\\bullet b=5\\\bullet \text{b is the largest value so: b is the major and a is the minor}\\\bullet \text{Vertices are }(0, 0+5)\ and\ (0, 0-5)\implies (0, 5)\ and\ (0, -5)\\\bullet \text{Co-vertices are }(0+4, 0)\ and\ (0-4, 0)\implies (4,0)\ and\ (-4,0)\\\bullet \text{Length of major is }2b:2(5)=10\\\bullet \text{Length of minor is }2a:2(4)=8[/tex]

To find the foci, first we must find the length of the foci using the formula:

[tex](r_{major})^2-(r_{minor})^2=c^2[/tex]

Then add the c-value to the h (or k)-value that represents the major.

b² - a² = c²

25 - 16 = c²

        9 = c²

       ±3 = c

The center is (0, 0) and the major is the y-value so the foci is:

(0, 0+3) and (0, 0-3) ⇒ (0, 3) and (0, -3)

26. Answers

Follow the same steps as #25:

Center: (0, 0)

Vertices (7, 0) and (-7, 0)

Co-vertices: (0, 3) and (0, -3)

foci: (2√10, 0) and (-2√10, 0)

length of major: 14

length of minor: 6

Answer:

A) 0.123; B) 0.8078; C) Because the population is normally distributed.

Step-by-step explanation:

For part A,

We first calculate the z-score, which tells us how many standard deviations from the mean our score is.

Since we are finding the z-score of an individual score and not a sample, we use the formula

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

Our score, X, is 209.3; our mean, μ, is 200; and our standard deviation, σ, is σ.  This gives us

[tex]z=\frac{209.3-200}{8}=\frac{9.3}{8}=1.1625[/tex]

We look this value up in a z-table.  However, we must round it to the nearest hundredth first; this is 1.16.  From a z-table, we get that the area under the curve to the left of, or less than or equal to, this score is 0.8770.

However we want the probability that the value is greater than this; this means we subtract our found probability from 1:

1-0.8770 = 0.123

For part B,

Again we first calculate the z-score.  However this time we are finding the probability of a mean of a sample rather than an individual score; this means we use the formula

[tex]z=\frac{\bar{X}-\mu}{\sigma\div \sqrt{n}}[/tex]

Our X is 198.20; our μ is still 200, and our σ is still 8; our value of n is our sample size, 15:

[tex]z=\frac{198.20-200}{8\div \sqrt{15}}=\frac{-1.8}{2.0656}=-0.87[/tex]

Looking up this value in a z-table, we get 0.1922.

However, we want the probability that the area, or probability, is greater than this; so we subtract from 1:

1-0.1922 = 0.8078

For part C,

When a population is normally distributed, this means that a sample taken from this population will also be normal; this means we can use the normal distribution.