Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 14 based on earlier studies.

Full Question:

The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 113. use a significance level of 0.05.

Systolic| 150 129 142 112 134 122 126 120

Diastolic| 88 96 106 80 98 63 95 64

a. What is the regression equation?

^y = __ + __x (Round to two decimal places as needed.)

b. What is the best predicted value?

^y is about __ (Round to one decimal place as needed.)

Answer:

A. yhat = a + bx = -10.64 + 0.75x

B. 74.0

Step-by-step explanation:

A. To find the regression equation here, we apply the formulas and then apply it to find the value of y given value of x:

calculate xbar and ybar which is the average of the variables:

Where n(number of values in x or y)=8

xbar = sum of x/n = 129.375

ybar = sum of y/n = 86.25

to calculate b

b= [Sum x^2 * Sum y - Sum x * Sum x*y] / [N*Sum x^2 - (Sum x)^2]

b = 0.74891

To calculate a

a = ybar - b * xbar = -10.64023

Regression equation:

y=mx+b= -10.64 + 0.75x

B. given x = 113,

y = -10.64023 + 0.74891 * 113

y= 74.0

Answer:

[tex]-|9|[/tex]   and [tex]-|-9|[/tex]

Step-by-step explanation:

Given

Expression = -9

Required

Select all equivalent expressions

To do that, we examine each of the options.

First Option

[tex]-|9|[/tex]

This can be rewritten as

[tex]-|9| = -1 * |9|[/tex]

[tex]|9| = 9[/tex]

So, the expression becomes

[tex]-|9| = -1 * 9[/tex]

[tex]-|9| = -9[/tex]

Hence, |-9| is equivalent to -9

Second Option

[tex]|-9|[/tex]

[tex]|-9| = 9[/tex]

So, the expression is not equivalent to -9

Third Option

[tex]-|-9|[/tex]

This can be rewritten as

[tex]-|-9| = -1 * |-9|[/tex]

[tex]|-9| = 9[/tex]

So, the expression becomes

[tex]-|-9| = -1 * 9[/tex]

[tex]-|-9| = 9[/tex]

Hence, -|-9| is equivalent to -9

Fourth Option

[tex]-(-9)[/tex]

This can be rewritten as

[tex]-(-9) = -1 *(-9)[/tex]

[tex]-(-9) = -1 *-9[/tex]

[tex]-(-9) = 9[/tex]

Hence, -(-9) is not equivalent to -9

Fifth Option

The distance from 0 to 9

This is calculated as thus;

[tex]Difference = 9 - 0[/tex]

[tex]Difference = 9[/tex]

Hence, the difference from 0 to 9 is not equivalent to -9

Answer:

Approximately 36.5885

Approximately 4.2426

Step-by-step explanation:

Please reference the drawing I've provided (sorry it's kind of awful. Drawing on a computer is hard :(

Problem 1)

So, the trapezoid can be split into a right triangle and a rectangle. To find the perimeter, we just need to find all the side lengths and add them.

We already know the dimensions of the rectangle. So, we need to find the dimensions of the right triangle.

We know that the height is 9 since it's opposite to the rectangle. Importantly, we know that the angle opposite to 9 is 60°.

This means that the other angle is 30°. So, the right triangle is a "special right triangle." In the 30-60-90 triangle, the hypotenuse is 2x, the side opposite to 60° is x√3, and the side opposite to 30° is x.

So, we know that 9 is the side opposite to 60°. Substitute and solve for x:

[tex]9=x\sqrt{3}\\ x=\frac{9}{\sqrt{3} } \\ x=\frac{9\sqrt3}{3}=3\sqrt3[/tex]

So, x is 3√3. This means that the side opposite of angle 30 or d is 3√3.

And since x is 3√3, this means that the hypotenuse is 2(3√3) or 6√3.

Therefore, the perimeter of the figure would be:

[tex]9+6+6+3\sqrt3+6\sqrt3\\=21+9\sqrt3\\\approx36.5885[/tex]

Problem 2:

For the bookcase, we simply need to find the value of c.

The braces that will be built is simply the hypotenuse of the right triangles. Therefore:

[tex]a^2+b^2=c^2\\[/tex]

Plug in 3 for a and b:

[tex]3^2+3^2=c^2\\c^2=9+9=18\\c=\sqrt{18}=\sqrt{9\cdot 2}=3\sqrt2\approx4.2426[/tex]

Therefore, each of the braces will be approximately 4.2426 feet long.

Edit: Grammar

Let's take as x and y the age of the man and of his son

We will do a system, so we can satisfy all the request:

1. sum of ages = 2 (difference)

2. product = 675

[tex]\left \{ {x + y = 2 (x-y)} \atop {x*y=675}} \right.[/tex]

semplify the first equation

x + y = 2x -2y

now let's choose one of the incognite (x) and we solve for it

x - 2x = - 2y - y

- x = - 3y

x = 3y

Let's substitute this solution in the second equation

[tex]\left \{ {x=3y} \atop {(3y)*y=675}} \right.[/tex]

note: x = 3y, so in the second equation x * y = 3y * y

Now let's solve the second equation

3y * y = 675

3y² = 675

y² = 675 / 3 =

y² = 225

y = 15

Son's age is 15

Man's age is 15 * 3 = 45 (See the first equation [x = 3y])

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{3 {i}^{2} + 6i}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(2 + i)(i + 2i)}[/tex]

Use the distribute property to multiply each term of the first binomial by each term of the second binomial.

⇒[tex] \sf{2(i + 2i) + i(i + 2i)}[/tex]

⇒[tex] \sf{2i + 4i + {i}^{2} + 2 {i}^{2} }[/tex]

Collect like terms

⇒[tex] \sf{3 {i}^{2} + 6i}[/tex]

Hope I helped!

Best regards!

Answer:

Lol hi emelio

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use tan

tan∅ = opposite/ adjacent

From the question

x is the opposite

10 is the adjacent

Substitute the values into the above formula and solve for x

That's

[tex] \tan(20) = \frac{x}{10} [/tex]

x = 10 tan 20

x = 3.63970

We have the final answer as

Hope this helps you

Answer:

10 times.

Step-by-step explanation:

We need to find that the value of 3 in 546300 is how many times more than 3456.

The place value of 3 in 546300 is 300 and the place value of 3 in 3456 is 3000.

Now dividing 3000 by 300 as follows :

[tex]\dfrac{3000}{300}=10[/tex]

It means that the value of 3 in 546300 is 10 times more than the value of 3 in 3456.

Answer: $428.00

Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.

Answer: 93 and 4/5

Step-by-step explanation:

6 7/10 divided by 1/14

= 67/10 divided by 1/14

= 67/10 x 14/1

= 67/5 x 7/1

= 469/5

Answer:

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

Step-by-step explanation:

From the table of function given, you would observe that if you subtract 2 from half of the x-variable values, you'd get the y-variable values.

For example, half of -8 = -4. If you add 2 to -4, you'd get: -4 + 2 = -2. Same applies to other x-values on the table.

Thus, an expression for the function represented by the table values can be written as,

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

Answer:

Step-by-step explanation:

[tex] \sf{ \frac{a}{9} = - 4}[/tex]

Apply cross product property

⇒[tex] \sf{a = - 4 \times 9}[/tex]

Multiply the numbers

⇒[tex] \sf{a = - 36}[/tex]

Hope I helped!

Best regards!!

Answer:

608 squared centimeters.

Step-by-step explanation:

To find the surface area of the net of the triangular prism, we can find the area of each individual shape and add them up.

For the net, we have 3 rectangles and 2 (congruent) triangles.

The left rectangle has a length of 16 and a width of 10. Thus, it's area is A=16(10)=160 squared centimeters.

The middle rectangle has a length of 16 and a width of 12. Thus, it's area is A=16(12)=192 squared centimeters.

The right rectangle has a length of 16 and a width of 10. Thus, it's area is identical to the left rectangle. It's area is 160 squared centimeters.

Now, for the two triangles, it's important to note they are the congruent since they belong to one triangular prism. Thus, we only need to figure out the area of one and then multiply by 2 to get the area of both of them.

One triangle has a base length of 12 and a height of 8. In other words, its area is (1/2)(12)(8)=48. Two of them will be 48(2) or 96.

Now, let's add all the areas together to find the surface area of the triangular prism. Thus, the area is:

96+160+160+192=608 squared centimeters.

Answer:

608 cm^2

Step-by-step explanation:

Find the area of the large rectangle

length is 10+12+10 = 32 and width is 16

A = 32*16 =512 cm^2

Then we have 2 triangle

The area of 1 is

A = 1/2 bh where b = 12 and h = 8

A = 1/2 ( 12 *8)

 = 1/2 (96)

But we have 2 triangles

2 * 1/2 (96)

96 cm^2

Add the area of the large rectangle and the two triangles

512+96 =608 cm^2

Answer:

Step-by-step explanation:

If a mass of 2.5 grams costs a penny, we want to know the amount of mass that will cost $75.  Before we get the mass, we need to convert 75 dollars to penny. Using the conversion:

$1 = 100pennies

$75 = (75*100)pennies

$75 = 7,500 pennies

Using the law of equivalence

1 penny = 2.5 grams

7,500pennies = x grams

Cross multiply

1 * x = 2.5 * 7500

x = 18,750 grams

Hence 18,759 grams will cost $75

Converting grams to kilograms

If 1000 grams = 1kg

18,750grams -= y

cross multiply

1000*y = 18750

Divide both sides by 1000

1000y = 18750/1000

y = 18.750kg

Hence the amount in kilogram of $75 coin in pennies is 18.750kg

Answer:

So how many days do we need to solve for?

Step-by-step explanation:

Answer:

The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4

Step-by-step explanation:

Let x represent the number of  1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. Each of 1 point free throw is 1 point, each of 2 point free throw is 2 points and each of the 3 point free throw is 3 points. This is represented by the equation:

x + 2y + 3z = 33             (1)

Also, The player scored 17 times, therefore it is represented by:

x + y + z = 17                   (2)

The player scored  3 more 2-point field goals than 1-point free throws, it is represented by:

y = x + 3                      

-x + y = 3                         (3)

Solving equation 1, eqn 2 and eqn 3 simultaneously:

x = 5, y = 8, z = 4.

The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4

Answer:

No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4

Step-by-step explanation:

Equations : x + y + z = 17 [ Total times taken to score ]

1x + 2y + 3z = 33 [ Total Score ]

Also, y = x + 3

Putting the value of 'y' in both equations :

x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14  (i)

1x + 2 (x + 3) + 3z = 33 →  x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)

Solving these equations :

From (i), z = 14 - 2x

Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27

42 - 3x = 27 → 3x = 15 → x = 5

y = x + 3 = 5 + 3 → y = 8

z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4

Answer:

wire for square to maximize total area = 23 m

Wire to minimize total area = 2.019 m

Step-by-step explanation:

For the square, let's say the total length of the square is "y" m.

Thus, length of one side is = y/4

And area of the square = (y/4) = y²/16

Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.

Thus, length of one side of equilateral triangle = (23 - y)/3

Using trigonometric ratio, we can find the height of the triangle and thus area.

Area of triangle = (√3)/4) × ((23 - y)/3)²

Area of triangle = (√3)/36)(23 - y)²

So, total area of square and triangle is;

A_total = (y²/16) + (√3)/36)(23 - y)²

Now, extremizing this function by derivatives, we have;

dA/dy = (y/8) - (√3)/18)(23 - y)

d²A/dy² = ⅛ + (√3)/18)

So, d²A/dy² > 0

Now,let's find the maximum or minimum of the function.

So, we equate dA/dy to zero.

Thus;

(y/8) - (√3)/18)(23 - y) = 0

y/8 = (√3)/18)(23 - y)

(y/8) + (√3)/18)y = 23((√3)/18)

Multiply through by 8 to give;

y + 0.0962y = 2.2132

1.0962y = 2.2132

y = 2.2132/1.0962

y = 2.019 m

2.019 will be a minimum because d²A/dy² > 0

The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.

Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.

Answer: Hi!

121 ÷ 3 = 40.3

987 ÷ 9 = 109.7

675 ÷ 5 = 135

432 ÷ 7 = 61.7

Hope this helps you!

Answer:

40 1/3

109 2/3

135

61.7

Step-by-step explanation:

Hey there!

Well lets divide all given expressions,

121 ÷ 3 = 40 1/3

987 ÷ 9 = 109 2/3

675 ÷ 5 = 135

432 ÷ 7 = 61.7 rounded to the nearest tenth

Hope this helps :)

Answer:

0

Step-by-step explanation:

First, simplify for both sides

6/15 -> 2/5

2/5 -> 2/5

x+2/5 = 2/5

Subtract 2/5 from each side.

(x+2/5)-2/5-> x

2/5-2/5 -> 0

x = 0

Answer:

y = 1

Step-by-step explanation:

5·x

x=2

5·2=10

10+2y

y=1

2·1=2

10+2=12

Answer:1

Step-by-step explanation:5(x)+2(y)=12

5 x 2 =10

2 x 1=2

10 + 2=12

Answer:

331.52 ounces

Step-by-step explanation:

For this problem, we need to know the conversion from gallon to ounces.  The conversion is for every one gallon, there are 128 ounces.  Using this, we simply will perform the conversion.

2.59 Gallons * ( 128 ounces / 1 Gallon) == 331.52 ounces

So in 2.59 gallons, there are 331.52 ounces.

Cheers.

Answer:

x = 18

Step-by-step explanation:

ΔABC ≅ ΔDEC

∠ B ≅ ∠E

40 = 2x + 4

-2x = 4 - 40

-2x = -36

2x = 36

x = 36/2

x = 18

Answer:

C

Step-by-step explanation:

We know that A is not true because the angle is formed by rays, not line segments. We know this because the ends of the lines are arrowheads, which indicates that they are rays. You might be saying that A is true because BA and BC form the angle but actually, even if you removed points A and C, you would still have the angle. B is not correct because according to the diagram, the vertex is point B, not point A. The vertex of an angle is the common endpoint of the two rays that form the angle, therefore it would be point B. D is not correct because angles can have multiple names, the letters do not have to be in alphabetical order. Therefore, C is correct.

Answer:

4×(-5)=-20

Step-by-step explanation:

Answer:

[tex]\huge \boxed{-20}[/tex]

Step-by-step explanation:

[tex]4*(-5)[/tex]

[tex]\Rightarrow 4* -5[/tex]

Multiplying.

[tex]\Rightarrow -20[/tex]

Answer:

23

Step-by-step explanation:

18+5=23

The value of AD for the given line segment such that AC = 18 and CD = 5 will be 23.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

A line section that can connect two places is referred to as a segment.

As per the given line segment, AC and CD have been drawn below,

Since, AD = AC + CD

AD = 18 + 5 = 23

Hence "The value of AD for the given line segment such that AC = 18 and CD = 5 will be 23".

For more about line segments,

https://brainly.com/question/25727583

#SPJ2

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(0,5) and (8,0)

So the distance between them is

d = 9.4339811

We have the final answer as

Hope this helps you

Complete Question

Apabila a =2 b = 3 dan c =12 tentukan nilai dari bentuk :

a⁶× b⁴ × c²

(ab)² ×c³

Answer:

1) a⁶× b⁴ × c² = 746496

2) (ab)² ×c³ = 62208

Step-by-step explanation:

a =2, b = 3, c =12

a) a⁶× b⁴ × c²

2⁶× 3⁴ × 12²

= (2 × 2 × 2 × 2 × 2 × 2) × (3 × 3 × 3 × 3) × (12 × 12)

= 64 × 81 × 144

= 746496

b) (ab)² ×c³

(2 × 3)² × 12³

= 6² × 12³

= (6 × 6 )× (12 × 12 × 12)

= 36 × 1728

= 62208

Answer: c(x) = y = $0.132*x + $27.16

Step-by-step explanation:

The chargers are a fixed price plus a charge for every copy, then we have a linear relationship.

A linear relationship can be written as:

c(x) = y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, c(x) = y represents the cost in dollars,  x is the number of copies bought, and b is the fixed cost.

We know two points in this line:

(80, $37) and (209, $54)

Whit those two points we can find the slope:

a = ($54 - $37)/(209 - 80) = $17/129 = $0.132 per copy.

Then our equation is:

c(x) = y = $0.132*x + b

To find the value of b, we know that 80 copies cost $37, we can replace those values in the equation:

$37 = $0.132*80 + b

$37 = $9.84 + b

($37 - $9.84) = $27.16 = b.

Then the equation is:

c(x) = y = $0.132*x + $27.16