The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).

Temp. 174 176 177 178 178 179 180 181
Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74
Temp. 184 184 184 184 184 185 185 186
Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94
Temp. 186 186 186 188 188 189 190 192
Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16
(a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.)
y =

(b) Calculate a point estimate for true average efficiency ratio when tank temperature is 186. (Round your answer to four decimal places.)


(c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 186. (Round your answers to four decimal places.)

(186, 0.94)
(186, 1.85)
(186, 2.02)
(186, 2.64)
(d) What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables? (Round your answer to four decimal places.)

Answers

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Temp. 174 176 177 178 178 179 180 181

Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74

Temp. 184 184 184 184 184 185 185 186

Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94

Temp. 186 186 186 188 188 189 190 192

Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16

A)

Using the online linear regression calculator, the lie of best fit which models the data above is :

ŷ = 0.09386X - 15.55523

Where ;

X = independent variable

ŷ = predicted or dependent variable

- 15.55523 = intercept

0.09386 = gradient / slope

B)

Point estimate when tank temperature is 186

ŷ = 0.09386(186) - 15.55523

ŷ = 17.45796 - 15.55523

ŷ = 1.90273

C)

Residual error (y - ŷ), ŷ = 1.90273 when x = 186

(0.94 - 1.90273) = −0.96273

(1.85 - 1.90273) = −0.05273

(2.02 - 1.90273) = 0.11727

(2.64 - 1.90273) = 0.73727

D)

To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.


Related Questions

Hakim is making a mosaic
from square tiles. The area he
needs to fill measures 150 mm
by 180 mm. The tiles have side
lengths of 4, 6 or 8 mm and are
too small to cut. Which tiles
should Hakim use?​

Answers

Answer:

6×6 tile

Step-by-step explanation:

First let's calculate the total area Hakim should fill.

Let A be that area.

The area is a rectangle so its area is the product of the length and the width.

● A = 180*150

● A = 27000 mm^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

The tiles Hakim has are all squares with different sides(4,6,8).

Let calculate the area of each tile.

Let A' , A" and A"' be the areas respectively of the 4,6 and 8 squares.

Since all tiles are squares, the area is the side times itself.

■■■■■■■■■■■■■■■■■■■■■■■■■■

● A' = 4^2 = 16 mm^2

● A" = 6^2 = 36 mm^2

● A"' = 8^2 = 64 mm^2

Divide the total area by each area and see wich one will give you a whole number.

●A÷A' = 27000÷16 = 1687.5

This isn't a whole number

● A÷A" = 27000÷36 = 750

This is a whole number, so it is the right tile.

● A+A"' = 27000÷64 = 421.875

This isn't the right tile.

Hakil should use the 6×6 tile

Hakim should use a tile of 6×6 side.

What is area?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Given that, Hakim is making a mosaic from square tiles. The area he needs to fill measures 150 mm by 180 mm. The tiles have side lengths of 4, 6 or 8 mm and are too small to cut.

To know that which tile fits best, we will divide the area of mosaic to the area of the tile, and see if we get a whole number if not a whole number then it should be cut, but we are restricted to do so, therefore we will look for the whole number,

Area of the mosaic = 150×180 = 27000 mm²

Area of the tile with side 4 mm = 4² = 16 mm²

Number of tile = 27000/16 = 1687.5 tiles. (not a whole number)

Area of the tile with side 6 mm = 6² = 36 mm

Number of tile = 27000/36 = 750 tile. (a whole number)

Hence, Hakim should use a tile of 6×6 side.

For more references on area, click;

https://brainly.com/question/27683633

#SPJ2

In one city, 35% of all aluminum cans distributed will be recycled each year. A juice company distributes 110,000 cans. The number still in use after time t, in years, is given by

Answers

Answer: [tex]n(t) = 110000(0.35)^t[/tex]

Step-by-step explanation:

Given: Rate of of all aluminum cans distributed will be recycled each year. = 35%

= 0.35

Total cans distributed =  110,000

Now , the number of cans recycled in 1 year = 110,000 ×0.35

The number of cans recycled in 2 years   = 110,000 ×0.35 ×0.35  = 110,000 ×(0.35)²

..so on

The number of cans recycled in t years   = [tex]110000(0.35)^t[/tex]

Let n(t) be the number still in use after time t, in years:

Then, [tex]n(t) = 110000(0.35)^t[/tex]

A projectile is fired vertically upward from a height of 300
300
feet above the ground, with an initial velocity of 900
900
ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0
h
(
t
)
=

16
t
2
+
v
0
t
+
y
0
. Write a quadratic equation to model the projectile's height h(t)
h
(
t
)
in feet above the ground after t seconds.

Answers

Step-by-step explanation:

It is given that, a projectile is fired vertically upward from a height of 300  feet above the ground, with an initial velocity of 900 ft/s.

The general equation with which a projectile are modled by the function is given by :

[tex]h(t)=-16t^2+v_ot+y_o[/tex]

y₀ is the initial height above the ground

v₀ = initial velocity

So,

[tex]h(t)=-16t^2+900t+300[/tex]

This is the quadratic equation that models the projectile height in feet above the ground after t seconds.

plz help i'm having a really hard time with this

Answers

Answer:

Domain all reals

Range  all reals

Step-by-step explanation:

The domain is the values that x can take, or the values of the input

x can be any real number

The range is the values that y can take, or the values of the output

y can be any real number

Answer:

C)

Step-by-step explanation:

it's fully continous, linear function thus all values are possible for both, x and y

1. Approximate the given quantity using a Taylor polynomial with n3.
2. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Fourth underroot(94)
a. p3(94)
b. absolute error

Answers

Answer:

See the explanation for the answer.

Step-by-step explanation:

Given function:

[tex]f(x) = x^{1/4}[/tex]

The n-th order Taylor polynomial for function f with its center at a is:

[tex]p_{n}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(n)}a}{n!} (x-a)^{n}[/tex]

As n = 3  So,

[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{3!} (x-a)^{3}[/tex]

[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{6} (x-a)^{3}[/tex]

[tex]p_{3}(x) = a^{1/4} + \frac{1}{4a^{ 3/4} } (x-a)+ (\frac{1}{2})(-\frac{3}{16a^{7/4} } ) (x-a)^{2} + (\frac{1}{6})(\frac{21}{64a^{11/4} } ) (x-a)^{3}[/tex]

[tex]p_{3}(x) = 81^{1/4} + \frac{1}{4(81)^{ 3/4} } (x-81)+ (\frac{1}{2})(-\frac{3}{16(81)^{7/4} } ) (x-81)^{2} + (\frac{1}{6})(\frac{21}{64(81)^{11/4} } ) (x-81)^{3}[/tex]

[tex]p_{3} (x)[/tex] = 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6  

                                                                                  (0.0000018522752) (x-81)³

[tex]p_{3} (x)[/tex]  =  0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254

                                                                                                       (x-81)³ + 2.25

Hence approximation at given quantity i.e.

x = 94

Putting x = 94

[tex]p_{3} (94)[/tex]  =  0.0092592593 (94) - 0.000042866941 (94 - 81)² +          

                                                                 0.00000030871254 (94-81)³ + 2.25

         = 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +    

                                                                                                                       2.25

         = 0.87037 03742 - 0.000042866941 (169) +  

                                                                      0.00000030871254(2197) + 2.25

         = 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25

[tex]p_{3} (94)[/tex]  = 3.113804102621

Compute the absolute error in the approximation assuming the exact value is given by a calculator.

Compute [tex]\sqrt[4]{94}[/tex] as [tex]94^{1/4}[/tex] using calculator

Exact value:

[tex]E_{a}[/tex](94) = 3.113737258478

Compute absolute error:

Err = | 3.113804102621 - 3.113737258478 |

Err (94)  = 0.000066844143

If you round off the values then you get error as:

|3.11380 - 3.113737| = 0.000063

Err (94)  = 0.000063

If you round off the values up to 4 decimal places then you get error as:

|3.1138 - 3.1137| = 0.0001

Err (94)  = 0.0001

During two years in college, a student earned $9,500. The second year she earned $500 more than twice the amount she earned the first year. How much did she earn the first year?

Answers

The answer would be $3000

If you rent a car for one day and drive it for 100 miles the cost is 40 dollars if you drive it 220 miles the cost is 46 dollars what is the linear equation for this

Answers

Answer:

[tex] y = \dfrac{1}{20}x + 35 [/tex]

Step-by-step explanation:

Let y = cost.

Let x = number of miles.

We have two (x, y) points: (100, 40) and (220, 46).

Now we find the equation of the line that passes through those two points using the two-point form of the equation of a line.

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

[tex] y - 40 = \dfrac{46 - 40}{220 - 100}(x - 100) [/tex]

[tex] y - 40 = \dfrac{6}{120}(x - 100) [/tex]

[tex] y - 40 = \dfrac{1}{20}(x - 100) [/tex]

[tex] y - 40 = \dfrac{1}{20}x - 5 [/tex]

[tex] y = \dfrac{1}{20}x + 35 [/tex]

6. Classify the traianle as scalene, isosceles or equilateral. Explain. Leave answers in square root form.
TAL

Answers

Answer:

  isosceles

Step-by-step explanation:

The point B is located on the perpendicular bisector of AC. No calculation is necessary. AC has a slope of 1, so it is easy to count grid squares to see where the perpendicular bisector goes.

When the altitude of the triangle bisects the side opposite the vertex, it is an isosceles triangle.

_____

Apparently, you're to use the distance formula to determine the lengths of the sides of the triangle. Doing that, you would find ...

  AB² = (6-4)² +(1 -6)² = 4 + 25

  CB² = (6-1)² +(1-3)² = 25 + 4

At this point, it doesn't require much thought to realize these sides are the same length: √29.

Write 41/12 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats. Write as a decimal.

Answers

Answer:

3.416, bar above 6

Step-by-step explanation:

41/12 = 3.4166666666666

41/12 = 3 & 5/12

Answer:

66

Step-by-step explanation:

41/12 = 3.4166

The fastest fish in the world is the sailfish. If a
sailfish could maintain its speed, as shown in the
table, how many miles could the sailfish travel in 6
hours?
p.s the top is hour traveled and the bottom is miles traveled

Answers

Answer:

(C) 408 miles

Step-by-step explanation:

Looking at this table, we can see that the beginning point is (0,0) so this is a linear slope, meaning we won’t have to add anything.

This means that for every time we rise in x, y will rise by the same amount.

When x is 1, y is 68 - so the constant of proportionality here is 68.

So, to find how much 6 hours would be we just multiply.

[tex]6\cdot68=408[/tex]

Hope this helped!

The minute hand of a watch has a length of 1.4 cm. Find the; (a) distance moved by the tip of the minute hand from 8.13 am to 8.49 am. (b) angle swept by the minute hand if the tip moves 8.8 mm (c)time it will bee when the minute hand sweeps the angle calculated in (b), if the minute hand started moving at 8.39 am

Answers

Answer:

A). The distance covered= 5.2752 cm

B). Angle swept = 36°

C). The time = 8:45 am

Step-by-step explanation:

The watch is assumed to be a circle while the minute hand is assumed to be the radius

Radius = 1.4cm

A). From 8:13 to 8:49= 36 minutes

Recall, there is 60 minutes in a round watch.

The distance covered= 2πr*36/60

The distance covered= 2*3.14*1.4*0.6

The distance covered= 5.2752 cm

B). If distance covered is 8.8 mm

8.8 mm = 0.88cm

0.88= 2*3.14*1.4*(x/360)

0.88/(8.792)=x/360

0.1= x/360

0.1= x/360

36°= x

Angle swept = 36°

C). The time it will be if the watch started from 8:39 am and moved 36°

36/360= y/60

0.1= y/60

0.1*60= y

6 minutes= y

The time with be 8:39+6 minutes

The time = 8:45 am

NEED IT ASAP
Tony is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 10% sales tax plus a state-mandated $45 fee for disposing of his old tires. If Tony has determined that he will spend less than $559.80 total, then what is the price range he can spend on the tire set?
Select one:
a. Less than $468
b. At least 472
c. $468 or more
d. Less than 473

Answers

Answer:

A

Step-by-step explanation:

Let:

Total price be T

And price of tire set be x

T<559.80 ---(1)

T=x +(10% of x)+ 45. ——(2)

T=x+(1/10)x+45

T=(11/10)x+45

Substitute T into equ. 1

T<559.80

(11/10)x +45<559.80

(11/10)x < 514.80

11x < 5148

x < 468

How many ways are there to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants

Answers

Answer:

There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.

Step-by-step explanation:

Given:

There are 5 types of croissants:

plain croissants

cherry croissants

chocolate croissants

almond croissant

apple croissants

broccoli croissants

To find:

to choose 22 croissants with:

at least one plain croissant

at least two cherry croissants

at least three chocolate croissants

at least one almond croissant

at least two apple croissants

no more than three broccoli croissants

Solution:

First we select

At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants

So

1 + 2 + 3 + 1 + 2  = 9

Total croissants = 22  

So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.

n = 5

r = 13

C(n + r - 1, r)

= C(5 + 13 - 1, 13)

= C(17,13)

[tex]=\frac{17! }{13!(17-13)!}[/tex]

= 355687428096000 / 6227020800 ( 24 )

= 355687428096000 / 149448499200

= 2380

C(17,13) = 2380

C(n + r - 1, r)

= C(5 + 12 - 1, 12)

= C(16,12)

[tex]=\frac{16! }{12!(16-12)!}[/tex]

= 20922789888000 / 479001600 ( 24 )

= 20922789888000  / 11496038400

= 1820

C(16,12) = 1820

C(n + r - 1, r)

= C(5 + 11 - 1, 11)

= C(15,11)

[tex]=\frac{15! }{11!(15-11)!}[/tex]

= 1307674368000 / 39916800 (24)

= 1307674368000 / 958003200

= 1307674368000 / 958003200

= 1365

C(15,11) = 1365

C(n + r - 1, r)

= C(5 + 10 - 1, 10)

= C(14,10)

[tex]=\frac{14! }{10!(14-10)!}[/tex]

= 87178291200 / 3628800 ( 24 )

= 87178291200 / 87091200

= 1001

C(14,10) = 1001

Adding them:

2380 + 1820 + 1365 + 1001 = 6566 ways

PLZZZZZZZZZZZZZZ HELP I WILL GIVE BRAINLIEST TO THE FIRST TO ANSWER

Answers

Answer:

B

Step-by-step explanation:

-(-a)/b = a/b

Option A is not equal to a/b

But Option B is, after cancelling out the negative sign

Answer:

[tex]\large \boxed{ \mathrm{B.} \ - \frac{a}{-b} }[/tex]

Step-by-step explanation:

[tex]\displaystyle -\frac{-a}{b} =-(- \frac{a}{b} ) = \frac{a}{b}[/tex]

The first option is not equivalent to a/b.

[tex]\displaystyle \frac{a}{-b}\neq \frac{a}{b}[/tex]

The second option is equivalent to a/b.

[tex]\displaystyle -\frac{a}{-b} =\frac{-a}{-b} = \frac{a}{b}[/tex]

Please help, thanks!!!!!

Answers

Answer:

[ 2+0+8. 0+0+12]

[-4+10+2. 0+25+3]

[10. 12]

[8. 28]

Option 3 is the solution

At the dog show, there are 4 times as many boxers as spaniels. If there are a total of 30 dogs,how many dogs are spaniels? Plz help me ​

Answers

Answer:

6 spaniels

Step-by-step explanation:

Create 2 equations to represent this, where b is the number of boxers and s is the number of spaniels:

4s = b

s + b = 30

We can plug in 4s as b into the second equation, s + b = 30:

s + b = 30

s + 4s = 30

5s = 30

s = 6

So, there are 6 spaniels.

Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)
(a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

Answers

Answer:

a

  [tex]df = 24.32[/tex]

b

 [tex]df = 30.10[/tex]

c

 [tex]df = 30.7[/tex]

d

[tex]df = 25.5[/tex]

Step-by-step explanation:

Generally degree of freedom is mathematically represented as

          [tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]

Considering a

         a) m = 12, n = 15, s1 = 4.0, s2 = 6.0

           [tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]

         [tex]df = 24.32[/tex]

Considering b

       (b) m = 12, n = 21, s1 = 4.0, s2 = 6.0

          [tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]

        [tex]df = 30.10[/tex]

Considering c

      (c) m = 12, n = 21, s1 = 3.0, s2 = 6.0

           [tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]

           [tex]df = 30.7[/tex]

Considering c

        (d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

                [tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]

               [tex]df = 25.5[/tex]

   

Rewrite the expression in part A by breaking up each of the place values. In this case, the place values are tens, ones, and tenths. 72.3 degrees f

Answers

Answer:

72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees

Step-by-step explanation:

The number, 72.3 degrees, can be rewritten by breaking up the place value of each digit in the expression as folliws,:

70 degrees + 2 degrees + 0.3 degrees

The place value of 7 is tens

The place value of 2 is ones

The place value of 3 is tenths

[tex] 72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees [/tex]

Answer:

72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)

Step-by-step explanation:

got the off the assignment

Please Help quick!!! What is the value of a missing angle?​

Answers

Answer:

69

Step-by-step explanation:

90-21=69

Answer:

69 degrees

Step-by-step explanation:

The full angle = 90 degrees.

One part of the full angle = 21 degrees

The other part of the full angle = x

Other angle = 90 - 21

=> the other angle = 69 degrees

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?

Answers

Answer:

The total number of votes= 9999

Step-by-step explanation:

The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.

There is a total of 4545 no votes.

Yes/no = 6/5

Yes= no(6/5)

Yes= 4545(6/5)

Yes= 5454

The total number of yes votes are 5454.

The total number of votes= yes votes+ no votes

The total number of votes= 5454+4545

The total number of votes= 9999

limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)​

Answers

Step-by-step explanation:

I(S) = aS / (S + c)

As S approaches infinity, S becomes much larger than c.  So S + c is approximately equal to just S.

lim(S→∞) I(S)

= lim(S→∞) aS / (S + c)

= lim(S→∞) aS / S

= lim(S→∞) a

= a

As S approaches infinity, I(S) approaches a.

PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!

The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?

1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B​

Answers

Answer:

3)  20% of the students earned a D

Step-by-step explanation:

9 students got a D.

5 students got a C.

14 students got a B.

17 students got an A.

Total number of students:

9 + 5 + 14 + 17 = 45

1)  1/5 of the students earned a C

1/5 of 45 = 9

5 students got a C

False

2) 3% more students earned an A then B

3 more students got an A than a B, but not 3%.

False

3)  20% of the students earned a D

20% of 45 = 9

9 students got a D.

True

4)  1/4 of the class earned a B​

1/4 of 45 = 11.25

There were 14 B's.

False

Answer: 3)  20% of the students earned a D

Given: AQRS where m2Q = 20° and m2S = 90°
R
1,000 meters
Q
S
What is the length of segment RS?
342 m
364 m
500 m
940 m

Answers

Answer:

342 m

Step-by-step explanation:

SIn(20) * 1000 = RS

342 = RS

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 1.99 and draw a sketch of the region.

Answers

Answer:

Step-by-step explanation:

To find this probability, we shall be using the z-score route

Mathematically ;

z-score = (x -mean)/SD

From the question, x = 1.99, mean = 0 and SD = 1

So z = (1.99-0)/1 = 1.99

So the probability we want to calculate is;

P(z<1.99)

This value can be obtained from the standard normal distribution table.

P(z < 1.99) = 0.9767

The sketch of the region is as shown as in the attachment.

Robert has $20,000, part or all of which he wants to invest into a combination of government bonds and municipal bonds. He wants to invest no more than $5,000 into municipal bonds, and at least twice as much into government bonds than into municipal bonds.

Answers

Answer:

x + y ≤ 20,000y ≤ 5,000x ≥ 2y

Step-by-step explanation:

Given:

Total amount = $20,000

Assume

Government bonds = x

Municipal bonds = y

Computation:

1. Invest total money

x + y ≤ 20,000

2. invest no more than $5,000 into municipal bonds

y ≤ 5,000

3. at least twice as much into government bonds.

x ≥ 2y

Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points. H0: μ=140; Ha: μ>140 α=0.05 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Answers

Answer:

The  test statistic is  [tex]t = 3.744[/tex]

Step-by-step explanation:

From the question we are told that

  The population mean is  [tex]\mu = 140[/tex]

  The  The  level of significance is  [tex]\alpha = 0.05[/tex]

  The  sample size is  n =  18

   The  null hypothesis is  [tex]H_o : \mu = 140[/tex]

    The  alternative hypothesis is  [tex]H_a : \mu > 140[/tex]

    The sample mean is  [tex]\= x = 155[/tex]

     The  standard deviation is  [tex]\sigma = 17[/tex]

Generally the test statistics is mathematically represented as

       [tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{ 155 - 140 }{ \frac{ 17 }{ \sqrt{18} } }[/tex]

      [tex]t = 3.744[/tex]

I help! solve 12x^2+54x=-42

Answers

Answer: Hi!

Let's solve your equation step-by-step.

12x^2 + 54x = −42

Step 1: Subtract -42 from both sides.

12x^2 + 54x − (−42) = − 42 − (−42)

12x^2 + 54x + 42 = 0

Step 2: Factor left side of equation.

6(2x + 7)(x + 1) = 0

Step 3: Set factors equal to 0.

2x + 7 = 0 or x + 1 = 0

You have two answers.

x = −7/2 or x = −1

Hope this helps!


What is an equation of the line that passes through the points (-5, 8) and (5,0)?

Answers

Answer:

y= -0.8x + 4

Midpoint is 0,4

Which expression is equal to 7 times the sum of a number and 4

Answers

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

7.619 by 10^-3



7.254 by 10^2​

Answers

Answer:

0.007619

0.07254

Step-by-step explanation:

1)7.619*10^-3

0.007619

2)7.254*10^2

0.07254

Explanation:

7.619*10^-3

The number here is 7.619 and the number written in scientific notation has minus 3 as its exponent.

.007.619

So the distance between the first decimal point and the second decimal is only three numbers.

Since it is exponent is minus three.

Another way to get the answer.

[tex]7.619 \times 10 {}^{ - 3} = \frac{7619}{1000} \times \frac{1}{1000} = \frac{7619}{1000000} = 0.007619 [/tex]

This applies to the second one too.

Hope this helps ;) ❤❤❤

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